TTC- THERMODYNAMIC THEROY OF CREATION
description
Transcript of TTC- THERMODYNAMIC THEROY OF CREATION
Pier Maria Boria Thermodynamics amp life
TTC ndash Thermodynamic Theory of Creation (Refreshed in AD 2013)
Part 1 (of 4) Entropy
11 ENTROPY
To understand the meaning of Entropy1 the first pillar of this paper it would be useful to start
with its generalized qualitative definition it is an indicator of the state of disorder of a defined
group of bodies The greater is the disorder the greater the Entropy (ldquoEntropy synonymous
with disorderrdquo Helmholtz 1821-1894)
We will proceed backwards until its first inception a strictly thermodynamic origin
To provide clarity let us consider the following situation a room containing a table and on
the table a bottle which is sealed and filled with smoke (of unknown nature) An observer can take a
photograph as a witness of the initial state of order clearly defined are the bottle the table the
smoke which occupies a well defined volume as well as the room (which constitutes our
ldquouniverserdquo) system being observed plus environment
Figure 11 ndash From the point of view of Thermodynamics the only possible spontaneous
transformation is that of increasing entropy
Opening the bottle Figure 11 will result in diffusion of the smoke into the room After a
certain period of time (letrsquos say a day) the observer will be able to record a state of increased disorder the smoke has come out of the bottle
One could imagine that after a million days the table could have disintegrated or in any case
the interaction of this universe with others (caused for example by a cataclysm) would have
resulted in the destruction of the table and the bottle and finally of the room itself the observer will
take a different photograph
Since the observations could be thought to extend over an unlimited time the photographs in
succession will indicate an increasing state of disorder in other words entropy Adopting the
language of Prigogine the transformation towards increasing entropy ldquoproducedrdquo positive entropy
(the difference in entropy between the final and initial states ge 0) while those of decreasing entropy
produce negative entropy
In parentheses we note that the inverse transformation (the smoke re-entering into the bottle)
could not occur due to at least two reasons each sufficient in themselves first the escape of smoke
1 En = inside tropien = direction in the sense of side evolution
Pier Maria Boria Thermodynamics amp life
is an asymptotic function and its concentration tends towards perfect uniformity in volume with
infinite time second without a concentration gradient it is not possible to have any movement of
mass within the expanded smoke
Proceeding backwards in history we observe that the concept of entropy makes its first entry
in physics thanks to the work of Clausius (Germany 1822-1888) who was searching for principles
of conservation which govern thermodynamics
The principles of conservation (which answers the question ldquowhat remains the
same after a transformationrdquo) represents the pillars of any scientific discipline2
Curiously he falls upon a principle of non conservation and comes to define an index of state
which someone defined as anomalous and which he called Entropy
Therefore initially the concept of entropy was strictly thermodynamic (the state of the
system under observation depends on variables such as temperature pressure and volume) while
the observation with which we started as stated are macroscopic qualitative generalizations It is understood that entropy is not an entity of conservation (except in reversible
transformations which are entirely theoretical) in transformations which can be performed in practice in which there is an interaction between the system under observation and the
environment there is an increase in entropy after the transformation (this allows a prediction of the direction which the transformation will take)
In Figure 12 is another example a ldquocoldrdquo body at temperature T1 is placed into contact with a ldquowarmrdquo body at temperature T2 the variables at play are the quantity of heat exchanged Q and the
temperature T experience tells us that the quantity of heat Q will pass from the body of higher temperature to that of lower temperature (Clausiusrsquo postulate) until an equilibrium temperature Te is
reached somewhere between the two
Figure 12 ndash For Clausiusrsquo Postulate
Clausius identifies that the relationship for the ldquoquantity of heat transformedrdquo Q between
final and initial temperatures is
0
2 We are reminded for example amongst others of the principle of conservation of energy the principle of the
conservation of Angular Momentum etc
Pier Maria Boria Thermodynamics amp life
because
Te lt T2
Clausius called Entropy the ratio S = QT
Using current thinking we can say that the heat exchanged has performed a transformation in
that
∆S gt 0
12 A NUMERICAL APPLICATION
Now we do a simple numerical example using what we call the Clausius Calorimeter
consisting of an adiabatic calorimeter containing water and a warm body (a cube of copper)
Figure 13 ndash The Clausius Calorimeter
We postulate the following conditions
bull Starting temperature of water 300 K
bull Starting temperature of copper 400 K
bull Equilibrium temperature 310 K
bull Quantity of heat exchanged 30 J
Since as it is well known the elementary variation of entropy is
introducing the thermal capacity C (mass m multiplied by itrsquos specific heat c) of the bodies we have
13 ∙ ∙ ∙ and integrating for each of the two bodies we obtain
for the copper
Pier Maria Boria Thermodynamics amp life
4
∆
∙ 0255
for the water
∆
∙ +0033
More simply we obtain the thermal capacity of each body
∆
5090 0 5
∆
5010 5
and subsequently we can calculate the total variation in entropy of our closed system
∆ ∆ + ∆ 0142 + 0165 +0023 amp () 01
As a preview to the second law of Thermodynamics
In the equation 1) we found two addends of opposite sign each one representing a ldquolocalrdquo
variation of entropy it follows that even though the total entropy of the testing universe increases
we can have local variations of opposite sign3
In fact generally when we have a thermal transformation some mass increase in temperature
and the other decrease the heat exchanged is equal and we can say
∆ 0ℎ- lt 0∆ lt 0ℎ-
that is the cooled body decreased its own enthalpy in an opposite direction to that of overheating
(the meaning of indices is obvious)
This observation will soon be useful when talking about ldquoEntropy and Liferdquo
13 ANALOGY BETWEEN ENTROPY AND WEIGHT
The content of this paragraph is not essential for the purpose of this paper However we
consider it useful to complete the understanding of entropy
Amongst the physicists of the XIX century Zeuner (Germany 1828-1907) proposed an
interesting analogy between the gravitational potential energy of a weight P and the entropy of a
mass with a heat Q and a temperature T
With reference to Figure 14 we know that the potential energy (ie the mechanical work which can be performed) of the water mass of the reservoir is L = P ∆H
3 It seems rational to accept the popular statement according to which the entropy of the astronomical universe is
indefinitely increasing in spite of our lesser knowledge of the astronomical universe (see also the ldquoAnthropic Principlerdquo)
in any case pay attention not to confuse that with testing a closed universe
Pier Maria Boria Thermodynamics amp life
5
Figure 14 ndash System to transform gravitational potential energy into mechanical energy of a
motor shaft
Zeuner studied the work obtainable from a thermal motor capable of transforming heat into
work with a Carnot Cycle4 allowing the efficiency of the heatwork transformation to be expressed
exclusively in temperature terms (as opposed to quantity of heat) which leads us to our goal In fact as is widely known the efficiency of the Carnot Cycle is
T
T
T
TT 00 1minus=minus
=η
where T-T0 is the difference in temperature between ldquosourcerdquo and ldquocoolantrdquo
Consequently introducing the quantity of heat Q into the motor the mechanical work L obtainable will be
1 ∆ ∆2
or rather the expression that appears in Figure 4 where the entropy ∆QT is a factor of
proportionality analogous to the weight P where the change in height ∆H corresponds to the change in temperature ∆T which the motor is able to produce (from ∆rdquoT lt ∆rsquoT one has in
proportion LrdquoltLrsquo with the consequence that the residual internal energy after being depleted and not able to be transformed into work will be Urdquo gt Ursquo)
We can observe that a functional tie exists between Q and T such that by increasing Q T is
increased in direct proportion (considering as constant the specific heat of the mass which runs the
cycle with no latent heat exchange) and therefore given a particular initial entropy the work
obtainable depends exclusively on the ∆T achievable
A motor which expels heat at a lower temperature produces more mechanical work at equal
ldquoconsumptionrdquo this is the purpose of the comparison between the two thermal motors in Figure 15
4 A car run on petrol will produce an Otto Cycle one on diesel a Diesel Cycle an exothermic motor will produce a Rankin
Cycle etc
Pier Maria Boria Thermodynamics amp life
6
Figure 15 ndash Comparison between the mechanical work obtained from two identical thermal motors
functioning according to the Carnot cycle for two different exhaust temperatures
(T0rdquo in case A and T0rsquo in case B)
The point of view seen above and resumed in equation 2) seems favorable to the presence of
high values of entropy tout court to avoid erroneous generalizations it needs remember that Gibbs
says that the maximum energetic gain in thermal transformations that is to obtain the maximum
ldquofree energyrdquo G is to exploit the total energy (enthalpy) H of the active mass minimizing the
entropy at discharge In fact the Gibbs equation states that
2 3 ∙ ∆
where H represents the entalpy of the mass transformed
We stress that it is necessary to compare two cases with identical initial temperature (as in
Figure 41) and to consider that it is the factor ∆T which determines the efficiency of the transformation5
Sea water contains an enormous amount of thermal energy but at a temperature T (of the source) very near to T0 (that of the coolant) in other words rendering unusable the heat it contains
we can state that sea water contains a ldquolargerdquo amount of thermal energy but no practical possibility of making a thermal motor work (the thermal difference available is ldquopractically nilrdquo)
Exactly for this reason a boiler which burns a combustible fossil material capable of achieving ldquohighrdquo temperatures enabling it to provide water at 90 degC is to be considered the perpetrator of a
grave ldquothermodynamic crimerdquo That combustible could be used with more results for example in a
cogeneration plant where water at low temperature is a ldquowasterdquo product
5 Sources at high temperature are necessary to produce thermodynamic cycles with acceptable results Our car be it Otto
or Diesel develops a temperature of around 1500 degC in the combustion chamber and give us a mechanical efficiency at the
wheels of about 35 (approx 30 remains ldquointernal energyrdquo and is expelled to the exhaust The coolant temperature is
that of the atmosphere the remainder is transformed into heat by thermal loss and passive resistances and is dispersed
mainly by the radiator)
Pier Maria Boria Thermodynamics amp life
7
14 ENTROPY AND LIFE
Livio Gratton (Italian cosmologist from Trieste died in 1991 and considered the father of
Italian Astrophysics) observed that the phenomenon ldquoliferdquo contains something singular which does
not fit in with the mechanism described up to this point The appearance of life in an electromagnetically structured universe constitutes a singular moment which cannot be explained
technically In fact an organism is alive when within itself it produces transformations of negative
entropy (that is with ∆Slt0) which contradicts the second principle Let us observe a plant seed if it is alive in conditions expected in nature it germinates
spontaneously and grows capturing carbon from the atmosphere giving body to the plant and releasing oxygen through chlorophyll synthesis
A small wheat seedling recently sprouted amongst the snow germinates and grows warming itself up at the expense of the ground (who has not observed the molten snow round the seedling
The seedlings under a thin blanket of snow poke out and are clearly visible green seedlings on a
white blanket in the middle of a dark patch of earth free from that which surrounds them)
Naturally if we were to also consider the interaction of the plant with the quanta of solar
energy and the surrounding minerals we would find that the sum of transformations has generated
positive entropy (the affirmation that the entropy of the universe tends to increase without limits is
correct)
A living animal organism should it be injured is capable of healing itself the vis vitalis as
our ancestors called it produces such an effect while a dead animal organism remains injured and
decomposes with the passing of time (increase of disorder)
One could consider the possibility of turning to entropy to define the state of life or death
about which we periodically debate even in practical cases (Terry Schiavo Eluana Englarohellip) if the organism produces negative entropy it is alive in the opposite case it is nothellip
One could also suggest a crude experimental procedure of a slightly Hitlerian nature which would settle the matter once and for all consisting of injuring an organism that has a dubious state
of life to verify its reactions in one entropic direction or the otherhellip The vis vitalis departs even if all the mechanical organs would be perfectly functional we can
think of the so called cardiac arrest (a phrase that could be a savior for the corner of the art of medicine) One could certainly object that the arrest is the cause while the departure of the vis
vitalis is the effect who knows The only certainty is that with death an irreversible process starts with the production of positive entropy and we fall back into line with the second principle
In conclusion it can be said that the property of entropy is that of an increase in every
transformation that can be performed practically (like saying in every irreversible transformation)
except in the case of living organisms
How to produce heating of the plant at the expense of the surrounding masses and to increase
the order of the molecules to the point of ldquoforcingrdquo the carbon taken from the most formless state in
existence (that of gaseous CO2) to take on the shape of a trunk giving rise to transformations of
decreasing entropy
Also an ordinary refrigerator can produce a local decrease of entropy expending some
energy in the following figure we represent the energy transformations occurring in it at the end of
the transformation we have the temperatures marked with an asterisk after the energy Q leaves the
cool body to join the warmest body with the energy Q3 that is needed for the refrigerator to run6
6 The ratio (Q2+Q+Q3)Q3 is the widely known COP (Coefficient Of Performance) of the heat pumps
Pier Maria Boria Thermodynamics amp life
Figure 16 ndash Heat pumping in a refrigerator
In this sketch the external energy Q3 appears essential and the system is open the energy Q
increase its entropy gaining the temperature T2 entering the condensator Restarting the numerical example of the Clausius calorimeter we reconfirm Q=50 J as the
heat exchanged in this condition it is easy to verify that the water temperature decreases by 10 K while the copper increases by 90 K
Assuming COP=3 we have
final temperature of water T1 = 290 K
and for the copper T2 = 490+903 = 520 K
proceeding as above it follows that
for the copper
∆ 520400 0 5 ∙ 004 002
(
for the water
∆ 290300 5 ∙ 0034 0170
(
Therefore the quantity of transformed heat Q is subject to the variation
∆ ∆ + ∆ 002 0170 015 lt 0 ( ∶
thanks to the contribution of the external energy Q3 the exchanged heat decreases its entropy
Now we will see in what way nature does the heat pumping
Pier Maria Boria Thermodynamics amp life
9
Part 2 (of 4) Boltzmannrsquos Distribution
21 THE BOLTZMANNrsquoS DISTRIBUTION
We will reply to the question after having examined the second pillar on which we base this paper Boltzmannrsquos Distribution (Ludwig Boltzmann Austria 1844-1906)
As can also be seen in excellent web pages the disorganized vibrational velocity of the molecules of a gas (but also those of liquids and solids) at a given temperature take on values
which are continuously and randomly variable following a particular distribution represented graphically in Figure 21
Figure 21 ndash Probability distribution of the velocity of molecules of a gas as a function
of the velocity itself according to Boltzmannrsquos Statistic
It is thanks to this distribution discovered by Boltzmann that living nature vegetable and animal can perform local transformations with decreasing entropy the great masters have
thought up theoretical experiments based on devices capable of selecting molecules of colder gas having higher velocities than what is thought to be the average velocity of the molecules of the
warmer gas (Maxwell the demon Polvani the choosing porter Amerio the selecting valve) to allow them to pass from a lower temperature environment to another adjacent environment with
higher temperature in this way obtaining a transformation which locally invalidates the second
principle of thermodynamics
In Figure 22 it is possible to see that at every average velocity (considered) of the ldquowarmrdquo
molecules one can find a corresponding branch of the ldquocoldrdquo curve related to those particles that
should they pass to the warmer side could cause an increase in that average velocity and therefore
of the temperature
Pier Maria Boria Thermodynamics amp life
10
Figure 22 ndashThe Maxwell demon allows the passage from the colder to the warmer
environment only of the molecules which have a velocity higher than the
weighted average velocity of the warmer molecules
It is necessary to perform a sorting of the molecules one by one with mechanical means not
available to man while the experimental observations of the type reported above would suggest
that nature is capable of it operating at a molecular level in the realm of living organisms
In Figure 23 is represented the device which allows the ldquotheoretical experimentrdquo in the form
proposed by Prof Amerio of the Polytechnic of Milano (1955) Maxwell had proposed a ldquodemonrdquo
as selector of the molecules (1867) the selection device has been the object of particular attention
on the part of Szilard (1929) and later Bennet (1981) with the scope of correctly counting the
variation of entropy in the test universe and calculate the required energy for the selection
Figure 23 ndash The selective valve allows the passage from the colder to the warmer
environment only of the molecules which have a velocity higher than the
weighted average velocity of the warmer molecules as shown in Fig 22
Pier Maria Boria Thermodynamics amp life
These elementary applications of classic thermodynamics based on the concept of entropy
and on Bolzmannrsquos Distribution suggest to us that the phenomenon ldquoliferdquo is to be associated with a
ldquovis-vitalisrdquo external to the dissipative mechanism for which we have ample and daily experience
Obviously it is impossible for man to build a Maxwell device but in our research we have
found a very interesting observation by Jaques Monod (Nobel Prize in 1965) that confers the part of
demon to the natural enzymes7
According to this point of view we can convert the Figure 16 as follows
Figure 24 ndash The natural heat pumping performed by enzymes
and this sketch we consider as typical of the phenomenon ldquoliferdquo The role played by the vis-vitalis seems essential because the only electro-chemical energy
associated with enzymes are components easily deliverable in the biological laboratories but
nobody has been able to start life from these components8
There are those who attempt an approach to this argument with improper methods and with
arbitrary applications of the concept of probability which leads to theories that are devoid of the
required respect for a sound scientific doctrine
22 CONCLUSIONS FROM THE FIRST AND SECOND PART
Rivers of ink have been written about the origin of life to the point that it is possible to read
about the most bizarre theories that completely ignore that which is suggested by the Queen of
Physics Thermodynamics
Paleontology Biology extraterrestrials UFOs Cosmic Palingenesis and similar are all
stirred numbers equations concepts of probability principles of conservation etc are not used
7 Le hazard et la neacutecessiteacute 1970 ndash Arnoldo Mondadori Editore Spa ndash Milan ndash Pag 58
8 See the Stanley Miller experiment at the end of paragraph 54
Pier Maria Boria Thermodynamics amp life
12
correctly These are the only foundations possible for a correctly stated scientific discussion (there
is no adjective more abused than the term ldquoscientificrdquo)
The reader could (perhaps on a rainy Sunday) do some research on the ldquoprimordialrdquo soup (but
if it is not Knorr for whorsquos brand modestly in youth we made thermodynamics projects does not
taste good) on the ldquocosmic tankrdquo on the ldquotyping monkeysrdquo on the cycle of carbon and oxygen (in relation to the demonization of CO2) on the hydrological cycle (which is a substance that cannot
be ldquoconsumedrdquo as is currently heard said otherwise what cycle would it complete subjects often treated by substituting Science with ideology and making ample use of the principle of superior
authority (the ipse dixit of historical memory) upholding disjointed dogma but which are
politically correct
Sometimes one has the feeling of witnessing the squalid discourse of gossiping women by the fountain
It can be noted that in the observations made up to now we have practically not talked about energy whorsquos role in the economy of our discourse has been secondary Itrsquos the definition of the
entropy index state which changes the way to view the cosmos we would not talk of it if it were
possible to carry out reversible reactions
We would come to suspect that the irreversibility is a ldquodefectrdquo of the cosmos having the
function of forcing it to a gradual entropic enrichment (and therefore to a degeneration of energy)
such that the final form of all the energy available becomes one that is thermally and entropically
unusable therefore by virtue of what has been discussed at a certain point in the evolution of the
universe at a finite time it will not be possible to practically perform any thermodynamic cycle9
That is to say the thermal death of the universe
9 We will be further willing to suspect a decay of the cosmological properties correlated to the original sin Ah free
thought
Pier Maria Boria Thermodynamics amp life
13
Part 3 (of 4) Probability
31 PROBABILITY IN BOLTZMANNrsquoS STATISTICS
Boltzmann obtained the graph of the probability as a function of temperature postulating that
a certain number m of particles which are indistinguishable from each other (which we will call A
B C M) and a number n of possible states (a b c n) in which one or more particles (even if
m) can find themselves the presence of particles in each state could occur with different possibilities
If the identical particles are free to occupy the various states (as in the case of a gas) these could continuously exchange states between themselves (for example thanks to reciprocal impacts
as in Figure 23) whilst ldquoon averagerdquo maintaining a certain distribution subject to the conditions around them (for example temperature) a certain distribution of the possible configurations would
be typical of such conditions
Continuing with this example if by state of the particles we mean possessing a certain amount
of kinetic energy E associated with each molecule of a gas in a certain interval of values of energy
∆E there will be a stable quantity of molecules even if amongst themselves continues exchanges of
energy occur Therefore in the range of the same interval some particles enter and some leave
If for the sake of imagination in what follows particles will be considered as ldquoballsrdquo and
states as levels of energy the balls will represent the particles while the levels will represent an
interval of energy (∆E)
Let us start with a very simple case consisting of 3 particles (m=3) able to be hosted by two
levels (n=2) as illustrated in Figure 31
In the left column we see all the possible combinations In the central section we see that certain combinations repeat themselves in such a way that if the particles become indistinguishable
(column 3) they are to be considered the same amongst themselves Therefore three possibilities exist such that both the combinations 234 and 567 can occur
and only once for the combinations 1 and 8 If we ldquonormalizerdquo the possibility (expressing it in unitary or percentage terms) it assumes the
role of probability (ratio between favorable cases and possible cases) which we have done in the last column by expressing it in percentage terms as is common practice
Pier Maria Boria Thermodynamics amp life
14
Figure 31 ndash A rather simple case to demonstrate how given m=3 and n=2 it is possible to
have different probabilities for each combination
Pier Maria Boria Thermodynamics amp life
15
This allows us to draw the graph of Figure 32 where we can begin to see the
Boltzmann distribution forming
Figure 32 ndash The embryonic Boltzmann diagram increasing particles and the number of
possible states the envelope of the columns (in this particular case not yet)
acquires the characteristic asymmetric bell shape
Following in the footsteps of the great Ludwig we enter into systems which are numerically
more substantial three combinations of seven states with an arbitrary arrangement of four particles
as represented in Figure 33 the three combinations are equivalent because the particles are
indistinguishable by hypothesis
Pier Maria Boria Thermodynamics amp life
16
Figure 33 - The three configurations are equivalent if the four particles are indistinguishable
amongst themselves
Each of the n states can be associated with A B C etc (that is to each or more of the m
particles) and since a single particle can occupy each time a different state (and other particles
other states) m times the possible combinations C are ntimesntimesntimeshelliptimesn (m factors equal to n)
C = nm
We could also be convinced observing for example Figure 34 where it is assumed that n=5
(it looks like a musical stavehellip) and m=2 particles (therefore 52=25 combinations)
Pier Maria Boria Thermodynamics amp life
Figure 34 ndash Beyond the 25th beat the preceding configurations are repeated because A and B are
indistinguishable Within the range of the 25 possible configurations some are more favored
because they appear more frequently for example 6 and 22 9 and 25 etc The unoccupied
states are identified by a circle
As is fair to expect configuration 1 is least favored
Pier Maria Boria Thermodynamics amp life
18
We can arrive at the same result with a more practical method suitable also for very large
values of n and m which we will use as follows
It consists of a tabular method stolen from Combinatorial Analysis where for n and m equal to
various units it avoids the need to write hundreds or thousands of key strokes as used above
Let us take two rows and as many columns as there are states thereby obtaining a grid in
Figure 35 to verify what has been said above we have taken 2 rows and 5 columns (n=2 m=5)
Figure 35- With this grid we obtain the number of possible configurations
To further demonstrate we will build a grid for n=5 and m=4 as in Figure 36 where there are sufficient rows to progressively expose the number of particles (from 4 to 1 in the first box of
the first column of the occupancy numbers) and there are n columns
Pier Maria Boria Thermodynamics amp life
19
Figure 36 - Since 54= 625 there are 625 possible combinations the relative probabilities are
listed in the last column note the asymmetry
Pier Maria Boria Thermodynamics amp life
20
It is necessary to observe that in the figure the table of numbers of occupancy reminds
us not by chance of Tartagliarsquos Triangle while the Boltzmann type diagram that can be
associated shown in Figure 37 takes on an almost familiar shape
Figure 37 - Graphical representation of Figure 62 the bars are asymmetric
Pier Maria Boria Thermodynamics amp life
21
To provide an example and referring to Figure 36 we can see how it is possible to obtain 80
possibilities corresponding to his second line
If a box is occupied by 3 particles out of an available 4 the simple combinations of 4 objects
with 3 by 3 (as taught by the Combinatorial Analysis) are given by the binomial coefficient
6437 4
and the four possible groups of three numbers have five positions from which to choose From here 4times5=20 possibilities for the group of three numbers
The single remaining particle has the possibility of the four remaining locations and therefore has 1times4=4 possibilities
The product 20times4=80 gives us the total possibilities in the case that the particles arrange themselves in two groups one with three and one with a single particle and having five boxes
suitable It is easy to verify that we will obtain the same result considering first the single particle
having five boxes suitable (five possibilities 1x5=5) and after the three having the four remaining
(one is occupied by the single particle therefore 4x4=16 and 5x16=80)
Applying the procedure line by line it produces the results shown
Pier Maria Boria Thermodynamics amp life
22
Part 4 (of 4) Chance
41 CHANCE
A sharp-shooter shoots at a target with an excellent rifle he aims carefully chooses the
moment when his breathing will not interfere and the amount of force with which to pull the trigger so as not to move the barrel fires the shot and hits the bullrsquos-eye
Immediately afterwards he takes all the same precautions but the shot ends up being slightly off target it could have been a slight disturbance to his sight an involuntary variation in his
breathing an imperceptible abnormal movement of the finger a very slight unpredictable wind or who knows what else
The causes are many and imponderable slight if each is considered in itself but interacting differently each time ensuring that each shot has a different fate
This complex of innumerable causes of disturbance which are not controllable or predictable
and which not being able to take each into account one by one are called the Law of Probability
(Gaussrsquos Law)10
Probability for the reasons given and law thanks to Carl Friedrich Gauss (1777-1855) who
wrote an equation capable of taking into consideration in a global manner all those fleeting causes
so as to be able to predict with near accurate approximation how the shots will arrange themselves
percentage wise round the target with different distances from the bullseye The approximation will
be more accurate the greater the number of shots that are fired
Let us assume that the target is as represented in Figure 41 and is divided into two parts by
means of the section AB and that our sharpshooter fires many shots after which we count the
number of shots which hit the target in each half
Figure 41- The segmented target
If the reasons for the error are truly random (rifle without defects such that it does not tend to
deviate the shot systematically and neither does the sharpshooter have an analogous defect there is
10
The example of the sharpshooter was published by Engineer Mario Manaira in Ndeg 256 of ldquoJournal of Mechanicsrdquo
together with our first article concerning thermodynamics more than half a century ago (1961)
Pier Maria Boria Thermodynamics amp life
23
not a steady wind etc in other words there does not exist a cause which always influences with the
same bias called a systematic cause) we could note the following
1 The shots will be greater in number in the first band round the center
2 The shots will progressively decrease in number in the subsequent bands as these distance themselves further from the center until there are very few in the bands furthest away
3 The shots in the two halves right and left in any similar band will tend to have the same number and will even be identical if sufficient shots are fired
It is therefore possible to represent the phenomenon graphically as in the following figure
Figure 42 ndash The random distribution of the shots in each band and the Gaussian distribution that
would be obtained with an infinite number of shots fired
If the marksman were less capable the concentration of shots near the zero on the abscissa would reduce and the curve would flatten itself while maintaining the characteristics given and
represented in Figure 43 The first observation is that the maximum height of the curve constitutes the ldquotargetrdquo in other words the goal of the operation while the absence of systematic causes (in
antithesis of randomness) ensures the symmetry of the curve with respect to the vertical which
represents our target zero
Pier Maria Boria Thermodynamics amp life
24
Figure 43 - If the marksman is less skilled the Gaussian flattens
In the case of a systematic cause of error the curve loses its symmetry if we assume that the
test is performed with a constant wind from left to right the graph will take on the shape of Figure
44
Figure 44 ndash When the Gaussian is asymmetric it implies that the phenomenon is not ldquoentirely
randomrdquo11
Let us suppose now that our sharpshooter is blindfolded the target becomes very large and is
moved he will have to shoot blindly (randomly) left and right high and low Given that the Gauss
11
Gauss suggests that the analytical expression of the Law of Randomness is the function
2xey minus
=
where it can be seen that the curve is symmetrical with respect to the axis x=0 and decreasing both towards the left and
right of this line and has a maximum for x=0
It can be shown further that the area subtended is
π=int+infin
infinminus
minusdxe
x2
To ensure that this area is equal to unity as opposed to π appropriate steps can be taken which without
changing the general properties illustrated give the normalized Gaussrsquos Law
Pier Maria Boria Thermodynamics amp life
function still applies the probability curve will flatten itself maintaining the essential
characteristics in particular the two tails which will tend towards a tangent with the abscissa
tending towards infinity a maximum point a point of inflection and the other characteristics
illustrated in Figure 45
Figure 45 ndash Typical characteristics of a normalized Gaussian
Supposing once more that the Gauss function still applies it would be logical to expect a distribution with a curve that is so flat that it will be difficult to see a maximum point corresponding
to the center of the target it will be necessary to fire enough shots so as to occupy every position on the abscissa and to have hit with 100 certainty the bullrsquos-eye
This implies that everything is possible as long as an infinite number of shots are available
(using rhetorical language)
42 SOME PROPERTIES OF RANDOM EVENTS
The perplexities regarding the applicability of chance as referred to the blind sharpshooter
depend on the fact that the Gaussian assumes that programming has been applied to reach an
objective which implies that the operator is conscious of the objective an element which in this
case is absent
Both the existence of a program (the sharpshooter sets out to hit the bullrsquos-eye) and the
existence of an objective (the card with circles) appear to be essential to be able to talk about
chance
Another example let us imagine a machine programmed to produce a certain mechanical
piece the program is the design of the piece written in machine language and the objective is the production of the piece In mass production we will find that it is the case that despite the work
conditions being maintained the same each piece will be different to the other to the point that the pieces which exceed the tolerances (which would not allow them to be interchangeable) will be
rejected Innumerable examples could be presented identifying in every case these two characteristics
a program and an objective Statistics also operate in reverse from the measurement of a group of subjects it creates a bar
chart its envelope will be the curve of the random distribution It will give us the average of the values measured if the curve is symmetrical it will tell us that the phenomenon is not influenced by
systematic causes further it will tell us the value of the standard deviation etc
Pier Maria Boria Thermodynamics amp life
26
To fix this thought in our heads let us suppose that we want to study the average height of a
population of people who are male we make many measurements on many subjects creating bars
for every centimeter we will obtain a graph similar to Figure 46
Figure 46 ndash A practical application the Gaussian deduced from experimental measurements for
statistical purposes
In this statistical application where are the program and objective They are there they are
there they were contained in the information which the people naturally had at conception a
matter of genes and of DNA (an observation coherent with ldquoThe Kid Equationrdquo See the
ldquoIntroduction to Hyperspacerdquo12
)
These considerations lead us to think that the meaning of the word ldquochancerdquo commonly given
does not make sense that ldquochancerdquo does not exist and lead us to suspect that Anatole France had an
inspired guess when he said ldquochance is Godrsquos pseudonym when He does not want to sign his
namerdquo
This strongly agrees with what illustrious philosophers have been confirming for centuries
ldquoDeus absconditus estrdquo (Is XLV XV)
12
In our first volume ldquoCaro amico miohelliprdquo ndash Ed Pagine ndash 2010 In our second volume (ldquoVerba volant eqvuationes
manentrdquo) other considerations about a fundamental theorem of Genetics the Hardy Weinberg theorem
Pier Maria Boria Thermodynamics amp life
27
43 CHANCE amp PROBABILITY
We can now summarize some salient functions of Boltzmann and Gauss
Boltzmann
1 Deals with probability regarding the characteristics that can be assumed by many identical particles having a certain number of positions available (Dirac and Fermi deal
with particles which are distinguishable but the correct reference in our observations are the identical particles)
2 The function presents a maximum and aesthetically looks like a Gaussian but it is not symmetrical
3 It has only a single asymptote to the right of the maximum and its minimum at infinity coincides with zero the origin of the reference system
4 It is normalized so that the area subtended represents the total probability of 100
Gauss
1 Deals with chance and is applicable when an objective exists that is defined by a
program
2 The phenomenon ldquopurely by chancerdquo is represented by a curve that is symmetrical
about the axis x=0
3 The Gaussian has a maximum and no minimum at infinity
4 It possesses two asymptotes one to the right and one to the left of the maximum
5 Well defined values of probability can be associated with multiples of the standard deviation
6 It is normalized as for Boltzmannrsquos
44 THE EDDINGTONrsquoS PARADOX13
Eddingtonrsquos famous ldquoInfinite monkey theoremrdquo can be counted amongst the most discussed
paradoxes for the fact that it is often quoted by so called ldquoscientific popularizersrdquo The original assertion states ldquohellipa monkey hitting keys at random on a typewriter keyboard
for an infinite amount of times will almost surely type a given text such as the complete works of
William Shakespearerdquo
Having taken away the condition of an infinite amount of time the paradox remains acceptable
(from the moment we are able to demonstrate that a finite amount of time is sufficient) However
such a long period of time is necessary that the original statement could be seen as an hyperbolic
discussion
We have seen that random phenomena require a program in light of an objective In the case
of the typing monkeys the program could include the elimination of duplicate pages (actually the
identical pages as we will see below) and the objective could consist in the conservation of ldquogoodrdquo
pages arranged in the right sequence
Applying Boltzmannrsquos statistics let us assume that the typewriter has m=30 keys (we can think of ldquoblindrdquo keys without any writing and all identical) and that we want to write a book of
only 106
letters (a thousand typed pages) as we have observed in paragraph 31 all the possible combinations are
13
The reader can find all the details regarding these various arguments on the web
Pier Maria Boria Thermodynamics amp life
C = nm = (10
6)30
= (10)180
In other words there are 10180
possible configurations
Let us assume that the monkeys are capable of striking 10 keyssec (skilled typistshellip) the
time necessary would be
t = 10180
x 106 10 = 10
185 sec
Since we can count 1016 seconds in a billion years it is also possible to say that the time
required will be
10185
1016
= 10169
billion years (giga-years)
(let us remember that the big-bang has an age of ldquoonlyrdquo 14 billion years)
In reality the situation is even ldquoworserdquo in fact this calculation (which is generally accepted)
is wrong because we cannot talk about only thirty objects (the letters punctuation marks spaces between lines etc) to be arranged in 10
6 positions otherwise in each of 10180 configurations
obtainable we would find empty spaces up to 106-30 in each configuration
It is necessary to postulate that there are 106 letters to be arranged like conceding that the
monkeys have to insert 106 objects ie 10
6 key strokes In other words it is necessary that n = m =
106 and in this case the formula of the combinations gives us an astronomical value
6106 )10(===
mm mnC combinations
At a rhythm of 10 key strokes sec the time corresponds to
9899995005000616106 10sec101010)10(
6
equiv=sdotsdot=minust years
Figure 47 ndash Summary table of the probabilities according to Boltzmann
In realty the situation is even ldquoworserdquo still In fact in the calculation of the combinations duplicate configurations are not considered
(which necessarily must be considered as possible) in other words our monkeys could produce the same combinations several times (or two identical pages) anyway the duplications will be useless
in the compilation of our small book of only 106 letters
To this end we invoke chance (to attempt to appreciate the incidence of the repeating of
identical pages) and having constructed a Gaussian by arranging the frequency of identical pages we can reason as follows having produced all the astronomical combinations as above in the time
calculated (which we will call a cycle) the highest probability of identical pages is in pairs (which
Pier Maria Boria Thermodynamics amp life
29
we will assign the maximum position) then in threes and so on At infinity with a probability of
zero all the pages will be identical
It seems fair to presume that the standard deviation could be very large qualifying for a very
flat Gaussian and let us suppose that the pages to be rejected (one for the doubles two for the
triplets etc) are contained within the first standard deviation (as in Figure 48) then the duplicate pages to be thrown away would be about 68
Figure 48 ndash The postulated conditions (pages to be eliminated because they are duplicated equal
to the standard deviation) make 68 of the pages produced useless Iterating the cycle one could
consider the duplication of other pages however it can be demonstrated that the phenomenon
continues to imply finite times
How much does the required time increase to generalize we assume the length of a cycle to be of one unit and we identify with K the average cost of discarded pages (in the previous numerical
case K= 068) and then we observe Figure 49
Figure 49 ndash Having exhausted the first cycle identified by 1 the second of length K allows the
replacement of the duplicate pages produced in the first cycle the third of length K2 is used to
replace those produced in the second cycle and so on
The time necessary to complete the cycles required to eliminate the duplicates as they are produced will be given by the sum
suminfin
=0n
nK
which constitutes a geometric series
The Mathematical Analysis teaches us that such a series converges for 1ltK as is confirmed
in our case where it takes on the value 068
KS
minus=
1
1 and if K = 068 gives 1253
6801
1=
minus=S
Pier Maria Boria Thermodynamics amp life
30
Therefore multiplying by 3125 the time dedicated to complete a cycle (317middot105999989 billion
years) for the hypothesis made we also eliminate all the duplicate pages of our little book of 106
key strokes
Changing the value of K (always lt1) one obtains different multipliers but always of a finite
value let the reader imagine the time necessary to type all of Shakespearersquos works It must be highlighted that the monkey operation to be considered a success requires the
intervention of external intelligence capable of selecting the useful pages (like thought by Theory of
Information) and ordering them in the right sequence to obtain a final legible manuscript this
obvious necessity implies that negative entropy be introduced into the system as covered at the
beginning this is like a living being taking the trouble to ldquoput in orderrdquo otherwise the ldquopurely
randomrdquo work would be entirely useless because it will exclusively produce positive entropy
All experiments attempted by man with the goal of demonstrating the random production of
complex molecules (first building blocks of living organisms) have the defect of requiring an a
priori living system like man to arrange this production
When later chaotic physical-chemical conditions are created (temperature pressure
methane electrical arching etc) hoping to obtain that which Thermodynamics does not permit the
inventors of the moto perpetuo come to mind who never give up
The research on the ldquoprimordial souprdquo belongs to this type of experimentation a battle horse
of the followers of the ldquomaitre agrave penserrdquo of the last century and which regard in particular the laboratory experiments of Stanley Miller the goal of his research of a physical-chemical nature
was to recreate life it was an understandable but too ambitious of a project for a researcher The result was absolutely negative (Miller himself recognized it) however this last piece of information
is only whispered in scientific circles so that we still find genuine touts who speak with enthusiastic coram populo of the primordial soup and its miraculous effects14 with a self-assurance
that is truly shameful
45 CONCLUSION
On 4 July 2007 at the London Kinetics Museum a serious presentation of a perpetual motion
machine was scheduled a machine capable of supplying the user with a power greater than that
absorbed ldquoObviouslyrdquo the presentation was postponed due to ldquoa technical problemrdquo15
It would appear impossible but advocates convinced of such a motion exist and many
inventors submit patent after patent even though still in illo tempore Max Planck declared himself
to be contrary to such a possibility which violates the principles of Thermodynamics
Based on the reasoning we have developed regarding entropy probability and chance the
violation of such principles is implicit even in the attempts to obtain living organisms in a
laboratory (characterized as we have seen as being producers of negative entropy) and as such a
strong analogy can be seen between the advocates of perpetual motion and those aspiring to create
life
1 The correct application of Boltzmannrsquos statistics a phenomenon for which we call on
probability demonstrates that combinations of large numbers of particles to the point of generating complex organisms require very long periods of time in comparison the age of
the universe is but the blink of an eye
2 The probabilities take on the largest numbers in correspondence with the most disordered
configurations
14
From ldquoCorriere della Serardquo october 2008 ldquoLa vita sulla Terra Cominciograve nei vulcani con un innesco chimicordquo 15
-Source Wikipedia
Pier Maria Boria Thermodynamics amp life
3 The most ordered combinations are those which characterize organic structures and the action
of an intelligent being is necessary to select order and conserve in time the favorable
combinations
4 The phrase ldquochance phenomenonrdquo is somewhat less intuitive than what ldquocommon senserdquo
would suggest In fact the Gaussian perspective implies that such phenomena are necessarily
associated with a program this program implies the existence of an objective around which
we have an increased concentration of events
5 In every case it is necessary to postulate the existence of an intelligent design without which
the configurations and the favorable events constitute events without any functional link
between themselves
6 The existence of life as a producer of negative entropy on a continuous basis (not cyclical) is a fact visible with our own eyes
All this leads us to support the existence of a Co-ordinating Entity which possesses life ldquoa
priorirdquo and which is capable of transmitting it to animals (animalis homo included) and vegetation It can be noted that the two living systems animal and vegetable complement each other in the
sense that the design requires that emissions from the first (CO2) are the nutrients for the second and the byproducts of the second (O2) are essential for the first the carbon and oxygen cycles look
like they have been designed According to the author there is only one explanation we are in the presence of the greatest
Design Physicist of all times God the Creator
This is what we call Him as Christians while Israelites call Him Jehovah the Ishmaelites
Allah the Masons GADU (Great Architect of the Universe) etc
In other terms
the Creation is a thermodynamic necessity
Amen
Pier Maria Boria Thermodynamics amp life
is an asymptotic function and its concentration tends towards perfect uniformity in volume with
infinite time second without a concentration gradient it is not possible to have any movement of
mass within the expanded smoke
Proceeding backwards in history we observe that the concept of entropy makes its first entry
in physics thanks to the work of Clausius (Germany 1822-1888) who was searching for principles
of conservation which govern thermodynamics
The principles of conservation (which answers the question ldquowhat remains the
same after a transformationrdquo) represents the pillars of any scientific discipline2
Curiously he falls upon a principle of non conservation and comes to define an index of state
which someone defined as anomalous and which he called Entropy
Therefore initially the concept of entropy was strictly thermodynamic (the state of the
system under observation depends on variables such as temperature pressure and volume) while
the observation with which we started as stated are macroscopic qualitative generalizations It is understood that entropy is not an entity of conservation (except in reversible
transformations which are entirely theoretical) in transformations which can be performed in practice in which there is an interaction between the system under observation and the
environment there is an increase in entropy after the transformation (this allows a prediction of the direction which the transformation will take)
In Figure 12 is another example a ldquocoldrdquo body at temperature T1 is placed into contact with a ldquowarmrdquo body at temperature T2 the variables at play are the quantity of heat exchanged Q and the
temperature T experience tells us that the quantity of heat Q will pass from the body of higher temperature to that of lower temperature (Clausiusrsquo postulate) until an equilibrium temperature Te is
reached somewhere between the two
Figure 12 ndash For Clausiusrsquo Postulate
Clausius identifies that the relationship for the ldquoquantity of heat transformedrdquo Q between
final and initial temperatures is
0
2 We are reminded for example amongst others of the principle of conservation of energy the principle of the
conservation of Angular Momentum etc
Pier Maria Boria Thermodynamics amp life
because
Te lt T2
Clausius called Entropy the ratio S = QT
Using current thinking we can say that the heat exchanged has performed a transformation in
that
∆S gt 0
12 A NUMERICAL APPLICATION
Now we do a simple numerical example using what we call the Clausius Calorimeter
consisting of an adiabatic calorimeter containing water and a warm body (a cube of copper)
Figure 13 ndash The Clausius Calorimeter
We postulate the following conditions
bull Starting temperature of water 300 K
bull Starting temperature of copper 400 K
bull Equilibrium temperature 310 K
bull Quantity of heat exchanged 30 J
Since as it is well known the elementary variation of entropy is
introducing the thermal capacity C (mass m multiplied by itrsquos specific heat c) of the bodies we have
13 ∙ ∙ ∙ and integrating for each of the two bodies we obtain
for the copper
Pier Maria Boria Thermodynamics amp life
4
∆
∙ 0255
for the water
∆
∙ +0033
More simply we obtain the thermal capacity of each body
∆
5090 0 5
∆
5010 5
and subsequently we can calculate the total variation in entropy of our closed system
∆ ∆ + ∆ 0142 + 0165 +0023 amp () 01
As a preview to the second law of Thermodynamics
In the equation 1) we found two addends of opposite sign each one representing a ldquolocalrdquo
variation of entropy it follows that even though the total entropy of the testing universe increases
we can have local variations of opposite sign3
In fact generally when we have a thermal transformation some mass increase in temperature
and the other decrease the heat exchanged is equal and we can say
∆ 0ℎ- lt 0∆ lt 0ℎ-
that is the cooled body decreased its own enthalpy in an opposite direction to that of overheating
(the meaning of indices is obvious)
This observation will soon be useful when talking about ldquoEntropy and Liferdquo
13 ANALOGY BETWEEN ENTROPY AND WEIGHT
The content of this paragraph is not essential for the purpose of this paper However we
consider it useful to complete the understanding of entropy
Amongst the physicists of the XIX century Zeuner (Germany 1828-1907) proposed an
interesting analogy between the gravitational potential energy of a weight P and the entropy of a
mass with a heat Q and a temperature T
With reference to Figure 14 we know that the potential energy (ie the mechanical work which can be performed) of the water mass of the reservoir is L = P ∆H
3 It seems rational to accept the popular statement according to which the entropy of the astronomical universe is
indefinitely increasing in spite of our lesser knowledge of the astronomical universe (see also the ldquoAnthropic Principlerdquo)
in any case pay attention not to confuse that with testing a closed universe
Pier Maria Boria Thermodynamics amp life
5
Figure 14 ndash System to transform gravitational potential energy into mechanical energy of a
motor shaft
Zeuner studied the work obtainable from a thermal motor capable of transforming heat into
work with a Carnot Cycle4 allowing the efficiency of the heatwork transformation to be expressed
exclusively in temperature terms (as opposed to quantity of heat) which leads us to our goal In fact as is widely known the efficiency of the Carnot Cycle is
T
T
T
TT 00 1minus=minus
=η
where T-T0 is the difference in temperature between ldquosourcerdquo and ldquocoolantrdquo
Consequently introducing the quantity of heat Q into the motor the mechanical work L obtainable will be
1 ∆ ∆2
or rather the expression that appears in Figure 4 where the entropy ∆QT is a factor of
proportionality analogous to the weight P where the change in height ∆H corresponds to the change in temperature ∆T which the motor is able to produce (from ∆rdquoT lt ∆rsquoT one has in
proportion LrdquoltLrsquo with the consequence that the residual internal energy after being depleted and not able to be transformed into work will be Urdquo gt Ursquo)
We can observe that a functional tie exists between Q and T such that by increasing Q T is
increased in direct proportion (considering as constant the specific heat of the mass which runs the
cycle with no latent heat exchange) and therefore given a particular initial entropy the work
obtainable depends exclusively on the ∆T achievable
A motor which expels heat at a lower temperature produces more mechanical work at equal
ldquoconsumptionrdquo this is the purpose of the comparison between the two thermal motors in Figure 15
4 A car run on petrol will produce an Otto Cycle one on diesel a Diesel Cycle an exothermic motor will produce a Rankin
Cycle etc
Pier Maria Boria Thermodynamics amp life
6
Figure 15 ndash Comparison between the mechanical work obtained from two identical thermal motors
functioning according to the Carnot cycle for two different exhaust temperatures
(T0rdquo in case A and T0rsquo in case B)
The point of view seen above and resumed in equation 2) seems favorable to the presence of
high values of entropy tout court to avoid erroneous generalizations it needs remember that Gibbs
says that the maximum energetic gain in thermal transformations that is to obtain the maximum
ldquofree energyrdquo G is to exploit the total energy (enthalpy) H of the active mass minimizing the
entropy at discharge In fact the Gibbs equation states that
2 3 ∙ ∆
where H represents the entalpy of the mass transformed
We stress that it is necessary to compare two cases with identical initial temperature (as in
Figure 41) and to consider that it is the factor ∆T which determines the efficiency of the transformation5
Sea water contains an enormous amount of thermal energy but at a temperature T (of the source) very near to T0 (that of the coolant) in other words rendering unusable the heat it contains
we can state that sea water contains a ldquolargerdquo amount of thermal energy but no practical possibility of making a thermal motor work (the thermal difference available is ldquopractically nilrdquo)
Exactly for this reason a boiler which burns a combustible fossil material capable of achieving ldquohighrdquo temperatures enabling it to provide water at 90 degC is to be considered the perpetrator of a
grave ldquothermodynamic crimerdquo That combustible could be used with more results for example in a
cogeneration plant where water at low temperature is a ldquowasterdquo product
5 Sources at high temperature are necessary to produce thermodynamic cycles with acceptable results Our car be it Otto
or Diesel develops a temperature of around 1500 degC in the combustion chamber and give us a mechanical efficiency at the
wheels of about 35 (approx 30 remains ldquointernal energyrdquo and is expelled to the exhaust The coolant temperature is
that of the atmosphere the remainder is transformed into heat by thermal loss and passive resistances and is dispersed
mainly by the radiator)
Pier Maria Boria Thermodynamics amp life
7
14 ENTROPY AND LIFE
Livio Gratton (Italian cosmologist from Trieste died in 1991 and considered the father of
Italian Astrophysics) observed that the phenomenon ldquoliferdquo contains something singular which does
not fit in with the mechanism described up to this point The appearance of life in an electromagnetically structured universe constitutes a singular moment which cannot be explained
technically In fact an organism is alive when within itself it produces transformations of negative
entropy (that is with ∆Slt0) which contradicts the second principle Let us observe a plant seed if it is alive in conditions expected in nature it germinates
spontaneously and grows capturing carbon from the atmosphere giving body to the plant and releasing oxygen through chlorophyll synthesis
A small wheat seedling recently sprouted amongst the snow germinates and grows warming itself up at the expense of the ground (who has not observed the molten snow round the seedling
The seedlings under a thin blanket of snow poke out and are clearly visible green seedlings on a
white blanket in the middle of a dark patch of earth free from that which surrounds them)
Naturally if we were to also consider the interaction of the plant with the quanta of solar
energy and the surrounding minerals we would find that the sum of transformations has generated
positive entropy (the affirmation that the entropy of the universe tends to increase without limits is
correct)
A living animal organism should it be injured is capable of healing itself the vis vitalis as
our ancestors called it produces such an effect while a dead animal organism remains injured and
decomposes with the passing of time (increase of disorder)
One could consider the possibility of turning to entropy to define the state of life or death
about which we periodically debate even in practical cases (Terry Schiavo Eluana Englarohellip) if the organism produces negative entropy it is alive in the opposite case it is nothellip
One could also suggest a crude experimental procedure of a slightly Hitlerian nature which would settle the matter once and for all consisting of injuring an organism that has a dubious state
of life to verify its reactions in one entropic direction or the otherhellip The vis vitalis departs even if all the mechanical organs would be perfectly functional we can
think of the so called cardiac arrest (a phrase that could be a savior for the corner of the art of medicine) One could certainly object that the arrest is the cause while the departure of the vis
vitalis is the effect who knows The only certainty is that with death an irreversible process starts with the production of positive entropy and we fall back into line with the second principle
In conclusion it can be said that the property of entropy is that of an increase in every
transformation that can be performed practically (like saying in every irreversible transformation)
except in the case of living organisms
How to produce heating of the plant at the expense of the surrounding masses and to increase
the order of the molecules to the point of ldquoforcingrdquo the carbon taken from the most formless state in
existence (that of gaseous CO2) to take on the shape of a trunk giving rise to transformations of
decreasing entropy
Also an ordinary refrigerator can produce a local decrease of entropy expending some
energy in the following figure we represent the energy transformations occurring in it at the end of
the transformation we have the temperatures marked with an asterisk after the energy Q leaves the
cool body to join the warmest body with the energy Q3 that is needed for the refrigerator to run6
6 The ratio (Q2+Q+Q3)Q3 is the widely known COP (Coefficient Of Performance) of the heat pumps
Pier Maria Boria Thermodynamics amp life
Figure 16 ndash Heat pumping in a refrigerator
In this sketch the external energy Q3 appears essential and the system is open the energy Q
increase its entropy gaining the temperature T2 entering the condensator Restarting the numerical example of the Clausius calorimeter we reconfirm Q=50 J as the
heat exchanged in this condition it is easy to verify that the water temperature decreases by 10 K while the copper increases by 90 K
Assuming COP=3 we have
final temperature of water T1 = 290 K
and for the copper T2 = 490+903 = 520 K
proceeding as above it follows that
for the copper
∆ 520400 0 5 ∙ 004 002
(
for the water
∆ 290300 5 ∙ 0034 0170
(
Therefore the quantity of transformed heat Q is subject to the variation
∆ ∆ + ∆ 002 0170 015 lt 0 ( ∶
thanks to the contribution of the external energy Q3 the exchanged heat decreases its entropy
Now we will see in what way nature does the heat pumping
Pier Maria Boria Thermodynamics amp life
9
Part 2 (of 4) Boltzmannrsquos Distribution
21 THE BOLTZMANNrsquoS DISTRIBUTION
We will reply to the question after having examined the second pillar on which we base this paper Boltzmannrsquos Distribution (Ludwig Boltzmann Austria 1844-1906)
As can also be seen in excellent web pages the disorganized vibrational velocity of the molecules of a gas (but also those of liquids and solids) at a given temperature take on values
which are continuously and randomly variable following a particular distribution represented graphically in Figure 21
Figure 21 ndash Probability distribution of the velocity of molecules of a gas as a function
of the velocity itself according to Boltzmannrsquos Statistic
It is thanks to this distribution discovered by Boltzmann that living nature vegetable and animal can perform local transformations with decreasing entropy the great masters have
thought up theoretical experiments based on devices capable of selecting molecules of colder gas having higher velocities than what is thought to be the average velocity of the molecules of the
warmer gas (Maxwell the demon Polvani the choosing porter Amerio the selecting valve) to allow them to pass from a lower temperature environment to another adjacent environment with
higher temperature in this way obtaining a transformation which locally invalidates the second
principle of thermodynamics
In Figure 22 it is possible to see that at every average velocity (considered) of the ldquowarmrdquo
molecules one can find a corresponding branch of the ldquocoldrdquo curve related to those particles that
should they pass to the warmer side could cause an increase in that average velocity and therefore
of the temperature
Pier Maria Boria Thermodynamics amp life
10
Figure 22 ndashThe Maxwell demon allows the passage from the colder to the warmer
environment only of the molecules which have a velocity higher than the
weighted average velocity of the warmer molecules
It is necessary to perform a sorting of the molecules one by one with mechanical means not
available to man while the experimental observations of the type reported above would suggest
that nature is capable of it operating at a molecular level in the realm of living organisms
In Figure 23 is represented the device which allows the ldquotheoretical experimentrdquo in the form
proposed by Prof Amerio of the Polytechnic of Milano (1955) Maxwell had proposed a ldquodemonrdquo
as selector of the molecules (1867) the selection device has been the object of particular attention
on the part of Szilard (1929) and later Bennet (1981) with the scope of correctly counting the
variation of entropy in the test universe and calculate the required energy for the selection
Figure 23 ndash The selective valve allows the passage from the colder to the warmer
environment only of the molecules which have a velocity higher than the
weighted average velocity of the warmer molecules as shown in Fig 22
Pier Maria Boria Thermodynamics amp life
These elementary applications of classic thermodynamics based on the concept of entropy
and on Bolzmannrsquos Distribution suggest to us that the phenomenon ldquoliferdquo is to be associated with a
ldquovis-vitalisrdquo external to the dissipative mechanism for which we have ample and daily experience
Obviously it is impossible for man to build a Maxwell device but in our research we have
found a very interesting observation by Jaques Monod (Nobel Prize in 1965) that confers the part of
demon to the natural enzymes7
According to this point of view we can convert the Figure 16 as follows
Figure 24 ndash The natural heat pumping performed by enzymes
and this sketch we consider as typical of the phenomenon ldquoliferdquo The role played by the vis-vitalis seems essential because the only electro-chemical energy
associated with enzymes are components easily deliverable in the biological laboratories but
nobody has been able to start life from these components8
There are those who attempt an approach to this argument with improper methods and with
arbitrary applications of the concept of probability which leads to theories that are devoid of the
required respect for a sound scientific doctrine
22 CONCLUSIONS FROM THE FIRST AND SECOND PART
Rivers of ink have been written about the origin of life to the point that it is possible to read
about the most bizarre theories that completely ignore that which is suggested by the Queen of
Physics Thermodynamics
Paleontology Biology extraterrestrials UFOs Cosmic Palingenesis and similar are all
stirred numbers equations concepts of probability principles of conservation etc are not used
7 Le hazard et la neacutecessiteacute 1970 ndash Arnoldo Mondadori Editore Spa ndash Milan ndash Pag 58
8 See the Stanley Miller experiment at the end of paragraph 54
Pier Maria Boria Thermodynamics amp life
12
correctly These are the only foundations possible for a correctly stated scientific discussion (there
is no adjective more abused than the term ldquoscientificrdquo)
The reader could (perhaps on a rainy Sunday) do some research on the ldquoprimordialrdquo soup (but
if it is not Knorr for whorsquos brand modestly in youth we made thermodynamics projects does not
taste good) on the ldquocosmic tankrdquo on the ldquotyping monkeysrdquo on the cycle of carbon and oxygen (in relation to the demonization of CO2) on the hydrological cycle (which is a substance that cannot
be ldquoconsumedrdquo as is currently heard said otherwise what cycle would it complete subjects often treated by substituting Science with ideology and making ample use of the principle of superior
authority (the ipse dixit of historical memory) upholding disjointed dogma but which are
politically correct
Sometimes one has the feeling of witnessing the squalid discourse of gossiping women by the fountain
It can be noted that in the observations made up to now we have practically not talked about energy whorsquos role in the economy of our discourse has been secondary Itrsquos the definition of the
entropy index state which changes the way to view the cosmos we would not talk of it if it were
possible to carry out reversible reactions
We would come to suspect that the irreversibility is a ldquodefectrdquo of the cosmos having the
function of forcing it to a gradual entropic enrichment (and therefore to a degeneration of energy)
such that the final form of all the energy available becomes one that is thermally and entropically
unusable therefore by virtue of what has been discussed at a certain point in the evolution of the
universe at a finite time it will not be possible to practically perform any thermodynamic cycle9
That is to say the thermal death of the universe
9 We will be further willing to suspect a decay of the cosmological properties correlated to the original sin Ah free
thought
Pier Maria Boria Thermodynamics amp life
13
Part 3 (of 4) Probability
31 PROBABILITY IN BOLTZMANNrsquoS STATISTICS
Boltzmann obtained the graph of the probability as a function of temperature postulating that
a certain number m of particles which are indistinguishable from each other (which we will call A
B C M) and a number n of possible states (a b c n) in which one or more particles (even if
m) can find themselves the presence of particles in each state could occur with different possibilities
If the identical particles are free to occupy the various states (as in the case of a gas) these could continuously exchange states between themselves (for example thanks to reciprocal impacts
as in Figure 23) whilst ldquoon averagerdquo maintaining a certain distribution subject to the conditions around them (for example temperature) a certain distribution of the possible configurations would
be typical of such conditions
Continuing with this example if by state of the particles we mean possessing a certain amount
of kinetic energy E associated with each molecule of a gas in a certain interval of values of energy
∆E there will be a stable quantity of molecules even if amongst themselves continues exchanges of
energy occur Therefore in the range of the same interval some particles enter and some leave
If for the sake of imagination in what follows particles will be considered as ldquoballsrdquo and
states as levels of energy the balls will represent the particles while the levels will represent an
interval of energy (∆E)
Let us start with a very simple case consisting of 3 particles (m=3) able to be hosted by two
levels (n=2) as illustrated in Figure 31
In the left column we see all the possible combinations In the central section we see that certain combinations repeat themselves in such a way that if the particles become indistinguishable
(column 3) they are to be considered the same amongst themselves Therefore three possibilities exist such that both the combinations 234 and 567 can occur
and only once for the combinations 1 and 8 If we ldquonormalizerdquo the possibility (expressing it in unitary or percentage terms) it assumes the
role of probability (ratio between favorable cases and possible cases) which we have done in the last column by expressing it in percentage terms as is common practice
Pier Maria Boria Thermodynamics amp life
14
Figure 31 ndash A rather simple case to demonstrate how given m=3 and n=2 it is possible to
have different probabilities for each combination
Pier Maria Boria Thermodynamics amp life
15
This allows us to draw the graph of Figure 32 where we can begin to see the
Boltzmann distribution forming
Figure 32 ndash The embryonic Boltzmann diagram increasing particles and the number of
possible states the envelope of the columns (in this particular case not yet)
acquires the characteristic asymmetric bell shape
Following in the footsteps of the great Ludwig we enter into systems which are numerically
more substantial three combinations of seven states with an arbitrary arrangement of four particles
as represented in Figure 33 the three combinations are equivalent because the particles are
indistinguishable by hypothesis
Pier Maria Boria Thermodynamics amp life
16
Figure 33 - The three configurations are equivalent if the four particles are indistinguishable
amongst themselves
Each of the n states can be associated with A B C etc (that is to each or more of the m
particles) and since a single particle can occupy each time a different state (and other particles
other states) m times the possible combinations C are ntimesntimesntimeshelliptimesn (m factors equal to n)
C = nm
We could also be convinced observing for example Figure 34 where it is assumed that n=5
(it looks like a musical stavehellip) and m=2 particles (therefore 52=25 combinations)
Pier Maria Boria Thermodynamics amp life
Figure 34 ndash Beyond the 25th beat the preceding configurations are repeated because A and B are
indistinguishable Within the range of the 25 possible configurations some are more favored
because they appear more frequently for example 6 and 22 9 and 25 etc The unoccupied
states are identified by a circle
As is fair to expect configuration 1 is least favored
Pier Maria Boria Thermodynamics amp life
18
We can arrive at the same result with a more practical method suitable also for very large
values of n and m which we will use as follows
It consists of a tabular method stolen from Combinatorial Analysis where for n and m equal to
various units it avoids the need to write hundreds or thousands of key strokes as used above
Let us take two rows and as many columns as there are states thereby obtaining a grid in
Figure 35 to verify what has been said above we have taken 2 rows and 5 columns (n=2 m=5)
Figure 35- With this grid we obtain the number of possible configurations
To further demonstrate we will build a grid for n=5 and m=4 as in Figure 36 where there are sufficient rows to progressively expose the number of particles (from 4 to 1 in the first box of
the first column of the occupancy numbers) and there are n columns
Pier Maria Boria Thermodynamics amp life
19
Figure 36 - Since 54= 625 there are 625 possible combinations the relative probabilities are
listed in the last column note the asymmetry
Pier Maria Boria Thermodynamics amp life
20
It is necessary to observe that in the figure the table of numbers of occupancy reminds
us not by chance of Tartagliarsquos Triangle while the Boltzmann type diagram that can be
associated shown in Figure 37 takes on an almost familiar shape
Figure 37 - Graphical representation of Figure 62 the bars are asymmetric
Pier Maria Boria Thermodynamics amp life
21
To provide an example and referring to Figure 36 we can see how it is possible to obtain 80
possibilities corresponding to his second line
If a box is occupied by 3 particles out of an available 4 the simple combinations of 4 objects
with 3 by 3 (as taught by the Combinatorial Analysis) are given by the binomial coefficient
6437 4
and the four possible groups of three numbers have five positions from which to choose From here 4times5=20 possibilities for the group of three numbers
The single remaining particle has the possibility of the four remaining locations and therefore has 1times4=4 possibilities
The product 20times4=80 gives us the total possibilities in the case that the particles arrange themselves in two groups one with three and one with a single particle and having five boxes
suitable It is easy to verify that we will obtain the same result considering first the single particle
having five boxes suitable (five possibilities 1x5=5) and after the three having the four remaining
(one is occupied by the single particle therefore 4x4=16 and 5x16=80)
Applying the procedure line by line it produces the results shown
Pier Maria Boria Thermodynamics amp life
22
Part 4 (of 4) Chance
41 CHANCE
A sharp-shooter shoots at a target with an excellent rifle he aims carefully chooses the
moment when his breathing will not interfere and the amount of force with which to pull the trigger so as not to move the barrel fires the shot and hits the bullrsquos-eye
Immediately afterwards he takes all the same precautions but the shot ends up being slightly off target it could have been a slight disturbance to his sight an involuntary variation in his
breathing an imperceptible abnormal movement of the finger a very slight unpredictable wind or who knows what else
The causes are many and imponderable slight if each is considered in itself but interacting differently each time ensuring that each shot has a different fate
This complex of innumerable causes of disturbance which are not controllable or predictable
and which not being able to take each into account one by one are called the Law of Probability
(Gaussrsquos Law)10
Probability for the reasons given and law thanks to Carl Friedrich Gauss (1777-1855) who
wrote an equation capable of taking into consideration in a global manner all those fleeting causes
so as to be able to predict with near accurate approximation how the shots will arrange themselves
percentage wise round the target with different distances from the bullseye The approximation will
be more accurate the greater the number of shots that are fired
Let us assume that the target is as represented in Figure 41 and is divided into two parts by
means of the section AB and that our sharpshooter fires many shots after which we count the
number of shots which hit the target in each half
Figure 41- The segmented target
If the reasons for the error are truly random (rifle without defects such that it does not tend to
deviate the shot systematically and neither does the sharpshooter have an analogous defect there is
10
The example of the sharpshooter was published by Engineer Mario Manaira in Ndeg 256 of ldquoJournal of Mechanicsrdquo
together with our first article concerning thermodynamics more than half a century ago (1961)
Pier Maria Boria Thermodynamics amp life
23
not a steady wind etc in other words there does not exist a cause which always influences with the
same bias called a systematic cause) we could note the following
1 The shots will be greater in number in the first band round the center
2 The shots will progressively decrease in number in the subsequent bands as these distance themselves further from the center until there are very few in the bands furthest away
3 The shots in the two halves right and left in any similar band will tend to have the same number and will even be identical if sufficient shots are fired
It is therefore possible to represent the phenomenon graphically as in the following figure
Figure 42 ndash The random distribution of the shots in each band and the Gaussian distribution that
would be obtained with an infinite number of shots fired
If the marksman were less capable the concentration of shots near the zero on the abscissa would reduce and the curve would flatten itself while maintaining the characteristics given and
represented in Figure 43 The first observation is that the maximum height of the curve constitutes the ldquotargetrdquo in other words the goal of the operation while the absence of systematic causes (in
antithesis of randomness) ensures the symmetry of the curve with respect to the vertical which
represents our target zero
Pier Maria Boria Thermodynamics amp life
24
Figure 43 - If the marksman is less skilled the Gaussian flattens
In the case of a systematic cause of error the curve loses its symmetry if we assume that the
test is performed with a constant wind from left to right the graph will take on the shape of Figure
44
Figure 44 ndash When the Gaussian is asymmetric it implies that the phenomenon is not ldquoentirely
randomrdquo11
Let us suppose now that our sharpshooter is blindfolded the target becomes very large and is
moved he will have to shoot blindly (randomly) left and right high and low Given that the Gauss
11
Gauss suggests that the analytical expression of the Law of Randomness is the function
2xey minus
=
where it can be seen that the curve is symmetrical with respect to the axis x=0 and decreasing both towards the left and
right of this line and has a maximum for x=0
It can be shown further that the area subtended is
π=int+infin
infinminus
minusdxe
x2
To ensure that this area is equal to unity as opposed to π appropriate steps can be taken which without
changing the general properties illustrated give the normalized Gaussrsquos Law
Pier Maria Boria Thermodynamics amp life
function still applies the probability curve will flatten itself maintaining the essential
characteristics in particular the two tails which will tend towards a tangent with the abscissa
tending towards infinity a maximum point a point of inflection and the other characteristics
illustrated in Figure 45
Figure 45 ndash Typical characteristics of a normalized Gaussian
Supposing once more that the Gauss function still applies it would be logical to expect a distribution with a curve that is so flat that it will be difficult to see a maximum point corresponding
to the center of the target it will be necessary to fire enough shots so as to occupy every position on the abscissa and to have hit with 100 certainty the bullrsquos-eye
This implies that everything is possible as long as an infinite number of shots are available
(using rhetorical language)
42 SOME PROPERTIES OF RANDOM EVENTS
The perplexities regarding the applicability of chance as referred to the blind sharpshooter
depend on the fact that the Gaussian assumes that programming has been applied to reach an
objective which implies that the operator is conscious of the objective an element which in this
case is absent
Both the existence of a program (the sharpshooter sets out to hit the bullrsquos-eye) and the
existence of an objective (the card with circles) appear to be essential to be able to talk about
chance
Another example let us imagine a machine programmed to produce a certain mechanical
piece the program is the design of the piece written in machine language and the objective is the production of the piece In mass production we will find that it is the case that despite the work
conditions being maintained the same each piece will be different to the other to the point that the pieces which exceed the tolerances (which would not allow them to be interchangeable) will be
rejected Innumerable examples could be presented identifying in every case these two characteristics
a program and an objective Statistics also operate in reverse from the measurement of a group of subjects it creates a bar
chart its envelope will be the curve of the random distribution It will give us the average of the values measured if the curve is symmetrical it will tell us that the phenomenon is not influenced by
systematic causes further it will tell us the value of the standard deviation etc
Pier Maria Boria Thermodynamics amp life
26
To fix this thought in our heads let us suppose that we want to study the average height of a
population of people who are male we make many measurements on many subjects creating bars
for every centimeter we will obtain a graph similar to Figure 46
Figure 46 ndash A practical application the Gaussian deduced from experimental measurements for
statistical purposes
In this statistical application where are the program and objective They are there they are
there they were contained in the information which the people naturally had at conception a
matter of genes and of DNA (an observation coherent with ldquoThe Kid Equationrdquo See the
ldquoIntroduction to Hyperspacerdquo12
)
These considerations lead us to think that the meaning of the word ldquochancerdquo commonly given
does not make sense that ldquochancerdquo does not exist and lead us to suspect that Anatole France had an
inspired guess when he said ldquochance is Godrsquos pseudonym when He does not want to sign his
namerdquo
This strongly agrees with what illustrious philosophers have been confirming for centuries
ldquoDeus absconditus estrdquo (Is XLV XV)
12
In our first volume ldquoCaro amico miohelliprdquo ndash Ed Pagine ndash 2010 In our second volume (ldquoVerba volant eqvuationes
manentrdquo) other considerations about a fundamental theorem of Genetics the Hardy Weinberg theorem
Pier Maria Boria Thermodynamics amp life
27
43 CHANCE amp PROBABILITY
We can now summarize some salient functions of Boltzmann and Gauss
Boltzmann
1 Deals with probability regarding the characteristics that can be assumed by many identical particles having a certain number of positions available (Dirac and Fermi deal
with particles which are distinguishable but the correct reference in our observations are the identical particles)
2 The function presents a maximum and aesthetically looks like a Gaussian but it is not symmetrical
3 It has only a single asymptote to the right of the maximum and its minimum at infinity coincides with zero the origin of the reference system
4 It is normalized so that the area subtended represents the total probability of 100
Gauss
1 Deals with chance and is applicable when an objective exists that is defined by a
program
2 The phenomenon ldquopurely by chancerdquo is represented by a curve that is symmetrical
about the axis x=0
3 The Gaussian has a maximum and no minimum at infinity
4 It possesses two asymptotes one to the right and one to the left of the maximum
5 Well defined values of probability can be associated with multiples of the standard deviation
6 It is normalized as for Boltzmannrsquos
44 THE EDDINGTONrsquoS PARADOX13
Eddingtonrsquos famous ldquoInfinite monkey theoremrdquo can be counted amongst the most discussed
paradoxes for the fact that it is often quoted by so called ldquoscientific popularizersrdquo The original assertion states ldquohellipa monkey hitting keys at random on a typewriter keyboard
for an infinite amount of times will almost surely type a given text such as the complete works of
William Shakespearerdquo
Having taken away the condition of an infinite amount of time the paradox remains acceptable
(from the moment we are able to demonstrate that a finite amount of time is sufficient) However
such a long period of time is necessary that the original statement could be seen as an hyperbolic
discussion
We have seen that random phenomena require a program in light of an objective In the case
of the typing monkeys the program could include the elimination of duplicate pages (actually the
identical pages as we will see below) and the objective could consist in the conservation of ldquogoodrdquo
pages arranged in the right sequence
Applying Boltzmannrsquos statistics let us assume that the typewriter has m=30 keys (we can think of ldquoblindrdquo keys without any writing and all identical) and that we want to write a book of
only 106
letters (a thousand typed pages) as we have observed in paragraph 31 all the possible combinations are
13
The reader can find all the details regarding these various arguments on the web
Pier Maria Boria Thermodynamics amp life
C = nm = (10
6)30
= (10)180
In other words there are 10180
possible configurations
Let us assume that the monkeys are capable of striking 10 keyssec (skilled typistshellip) the
time necessary would be
t = 10180
x 106 10 = 10
185 sec
Since we can count 1016 seconds in a billion years it is also possible to say that the time
required will be
10185
1016
= 10169
billion years (giga-years)
(let us remember that the big-bang has an age of ldquoonlyrdquo 14 billion years)
In reality the situation is even ldquoworserdquo in fact this calculation (which is generally accepted)
is wrong because we cannot talk about only thirty objects (the letters punctuation marks spaces between lines etc) to be arranged in 10
6 positions otherwise in each of 10180 configurations
obtainable we would find empty spaces up to 106-30 in each configuration
It is necessary to postulate that there are 106 letters to be arranged like conceding that the
monkeys have to insert 106 objects ie 10
6 key strokes In other words it is necessary that n = m =
106 and in this case the formula of the combinations gives us an astronomical value
6106 )10(===
mm mnC combinations
At a rhythm of 10 key strokes sec the time corresponds to
9899995005000616106 10sec101010)10(
6
equiv=sdotsdot=minust years
Figure 47 ndash Summary table of the probabilities according to Boltzmann
In realty the situation is even ldquoworserdquo still In fact in the calculation of the combinations duplicate configurations are not considered
(which necessarily must be considered as possible) in other words our monkeys could produce the same combinations several times (or two identical pages) anyway the duplications will be useless
in the compilation of our small book of only 106 letters
To this end we invoke chance (to attempt to appreciate the incidence of the repeating of
identical pages) and having constructed a Gaussian by arranging the frequency of identical pages we can reason as follows having produced all the astronomical combinations as above in the time
calculated (which we will call a cycle) the highest probability of identical pages is in pairs (which
Pier Maria Boria Thermodynamics amp life
29
we will assign the maximum position) then in threes and so on At infinity with a probability of
zero all the pages will be identical
It seems fair to presume that the standard deviation could be very large qualifying for a very
flat Gaussian and let us suppose that the pages to be rejected (one for the doubles two for the
triplets etc) are contained within the first standard deviation (as in Figure 48) then the duplicate pages to be thrown away would be about 68
Figure 48 ndash The postulated conditions (pages to be eliminated because they are duplicated equal
to the standard deviation) make 68 of the pages produced useless Iterating the cycle one could
consider the duplication of other pages however it can be demonstrated that the phenomenon
continues to imply finite times
How much does the required time increase to generalize we assume the length of a cycle to be of one unit and we identify with K the average cost of discarded pages (in the previous numerical
case K= 068) and then we observe Figure 49
Figure 49 ndash Having exhausted the first cycle identified by 1 the second of length K allows the
replacement of the duplicate pages produced in the first cycle the third of length K2 is used to
replace those produced in the second cycle and so on
The time necessary to complete the cycles required to eliminate the duplicates as they are produced will be given by the sum
suminfin
=0n
nK
which constitutes a geometric series
The Mathematical Analysis teaches us that such a series converges for 1ltK as is confirmed
in our case where it takes on the value 068
KS
minus=
1
1 and if K = 068 gives 1253
6801
1=
minus=S
Pier Maria Boria Thermodynamics amp life
30
Therefore multiplying by 3125 the time dedicated to complete a cycle (317middot105999989 billion
years) for the hypothesis made we also eliminate all the duplicate pages of our little book of 106
key strokes
Changing the value of K (always lt1) one obtains different multipliers but always of a finite
value let the reader imagine the time necessary to type all of Shakespearersquos works It must be highlighted that the monkey operation to be considered a success requires the
intervention of external intelligence capable of selecting the useful pages (like thought by Theory of
Information) and ordering them in the right sequence to obtain a final legible manuscript this
obvious necessity implies that negative entropy be introduced into the system as covered at the
beginning this is like a living being taking the trouble to ldquoput in orderrdquo otherwise the ldquopurely
randomrdquo work would be entirely useless because it will exclusively produce positive entropy
All experiments attempted by man with the goal of demonstrating the random production of
complex molecules (first building blocks of living organisms) have the defect of requiring an a
priori living system like man to arrange this production
When later chaotic physical-chemical conditions are created (temperature pressure
methane electrical arching etc) hoping to obtain that which Thermodynamics does not permit the
inventors of the moto perpetuo come to mind who never give up
The research on the ldquoprimordial souprdquo belongs to this type of experimentation a battle horse
of the followers of the ldquomaitre agrave penserrdquo of the last century and which regard in particular the laboratory experiments of Stanley Miller the goal of his research of a physical-chemical nature
was to recreate life it was an understandable but too ambitious of a project for a researcher The result was absolutely negative (Miller himself recognized it) however this last piece of information
is only whispered in scientific circles so that we still find genuine touts who speak with enthusiastic coram populo of the primordial soup and its miraculous effects14 with a self-assurance
that is truly shameful
45 CONCLUSION
On 4 July 2007 at the London Kinetics Museum a serious presentation of a perpetual motion
machine was scheduled a machine capable of supplying the user with a power greater than that
absorbed ldquoObviouslyrdquo the presentation was postponed due to ldquoa technical problemrdquo15
It would appear impossible but advocates convinced of such a motion exist and many
inventors submit patent after patent even though still in illo tempore Max Planck declared himself
to be contrary to such a possibility which violates the principles of Thermodynamics
Based on the reasoning we have developed regarding entropy probability and chance the
violation of such principles is implicit even in the attempts to obtain living organisms in a
laboratory (characterized as we have seen as being producers of negative entropy) and as such a
strong analogy can be seen between the advocates of perpetual motion and those aspiring to create
life
1 The correct application of Boltzmannrsquos statistics a phenomenon for which we call on
probability demonstrates that combinations of large numbers of particles to the point of generating complex organisms require very long periods of time in comparison the age of
the universe is but the blink of an eye
2 The probabilities take on the largest numbers in correspondence with the most disordered
configurations
14
From ldquoCorriere della Serardquo october 2008 ldquoLa vita sulla Terra Cominciograve nei vulcani con un innesco chimicordquo 15
-Source Wikipedia
Pier Maria Boria Thermodynamics amp life
3 The most ordered combinations are those which characterize organic structures and the action
of an intelligent being is necessary to select order and conserve in time the favorable
combinations
4 The phrase ldquochance phenomenonrdquo is somewhat less intuitive than what ldquocommon senserdquo
would suggest In fact the Gaussian perspective implies that such phenomena are necessarily
associated with a program this program implies the existence of an objective around which
we have an increased concentration of events
5 In every case it is necessary to postulate the existence of an intelligent design without which
the configurations and the favorable events constitute events without any functional link
between themselves
6 The existence of life as a producer of negative entropy on a continuous basis (not cyclical) is a fact visible with our own eyes
All this leads us to support the existence of a Co-ordinating Entity which possesses life ldquoa
priorirdquo and which is capable of transmitting it to animals (animalis homo included) and vegetation It can be noted that the two living systems animal and vegetable complement each other in the
sense that the design requires that emissions from the first (CO2) are the nutrients for the second and the byproducts of the second (O2) are essential for the first the carbon and oxygen cycles look
like they have been designed According to the author there is only one explanation we are in the presence of the greatest
Design Physicist of all times God the Creator
This is what we call Him as Christians while Israelites call Him Jehovah the Ishmaelites
Allah the Masons GADU (Great Architect of the Universe) etc
In other terms
the Creation is a thermodynamic necessity
Amen
Pier Maria Boria Thermodynamics amp life
because
Te lt T2
Clausius called Entropy the ratio S = QT
Using current thinking we can say that the heat exchanged has performed a transformation in
that
∆S gt 0
12 A NUMERICAL APPLICATION
Now we do a simple numerical example using what we call the Clausius Calorimeter
consisting of an adiabatic calorimeter containing water and a warm body (a cube of copper)
Figure 13 ndash The Clausius Calorimeter
We postulate the following conditions
bull Starting temperature of water 300 K
bull Starting temperature of copper 400 K
bull Equilibrium temperature 310 K
bull Quantity of heat exchanged 30 J
Since as it is well known the elementary variation of entropy is
introducing the thermal capacity C (mass m multiplied by itrsquos specific heat c) of the bodies we have
13 ∙ ∙ ∙ and integrating for each of the two bodies we obtain
for the copper
Pier Maria Boria Thermodynamics amp life
4
∆
∙ 0255
for the water
∆
∙ +0033
More simply we obtain the thermal capacity of each body
∆
5090 0 5
∆
5010 5
and subsequently we can calculate the total variation in entropy of our closed system
∆ ∆ + ∆ 0142 + 0165 +0023 amp () 01
As a preview to the second law of Thermodynamics
In the equation 1) we found two addends of opposite sign each one representing a ldquolocalrdquo
variation of entropy it follows that even though the total entropy of the testing universe increases
we can have local variations of opposite sign3
In fact generally when we have a thermal transformation some mass increase in temperature
and the other decrease the heat exchanged is equal and we can say
∆ 0ℎ- lt 0∆ lt 0ℎ-
that is the cooled body decreased its own enthalpy in an opposite direction to that of overheating
(the meaning of indices is obvious)
This observation will soon be useful when talking about ldquoEntropy and Liferdquo
13 ANALOGY BETWEEN ENTROPY AND WEIGHT
The content of this paragraph is not essential for the purpose of this paper However we
consider it useful to complete the understanding of entropy
Amongst the physicists of the XIX century Zeuner (Germany 1828-1907) proposed an
interesting analogy between the gravitational potential energy of a weight P and the entropy of a
mass with a heat Q and a temperature T
With reference to Figure 14 we know that the potential energy (ie the mechanical work which can be performed) of the water mass of the reservoir is L = P ∆H
3 It seems rational to accept the popular statement according to which the entropy of the astronomical universe is
indefinitely increasing in spite of our lesser knowledge of the astronomical universe (see also the ldquoAnthropic Principlerdquo)
in any case pay attention not to confuse that with testing a closed universe
Pier Maria Boria Thermodynamics amp life
5
Figure 14 ndash System to transform gravitational potential energy into mechanical energy of a
motor shaft
Zeuner studied the work obtainable from a thermal motor capable of transforming heat into
work with a Carnot Cycle4 allowing the efficiency of the heatwork transformation to be expressed
exclusively in temperature terms (as opposed to quantity of heat) which leads us to our goal In fact as is widely known the efficiency of the Carnot Cycle is
T
T
T
TT 00 1minus=minus
=η
where T-T0 is the difference in temperature between ldquosourcerdquo and ldquocoolantrdquo
Consequently introducing the quantity of heat Q into the motor the mechanical work L obtainable will be
1 ∆ ∆2
or rather the expression that appears in Figure 4 where the entropy ∆QT is a factor of
proportionality analogous to the weight P where the change in height ∆H corresponds to the change in temperature ∆T which the motor is able to produce (from ∆rdquoT lt ∆rsquoT one has in
proportion LrdquoltLrsquo with the consequence that the residual internal energy after being depleted and not able to be transformed into work will be Urdquo gt Ursquo)
We can observe that a functional tie exists between Q and T such that by increasing Q T is
increased in direct proportion (considering as constant the specific heat of the mass which runs the
cycle with no latent heat exchange) and therefore given a particular initial entropy the work
obtainable depends exclusively on the ∆T achievable
A motor which expels heat at a lower temperature produces more mechanical work at equal
ldquoconsumptionrdquo this is the purpose of the comparison between the two thermal motors in Figure 15
4 A car run on petrol will produce an Otto Cycle one on diesel a Diesel Cycle an exothermic motor will produce a Rankin
Cycle etc
Pier Maria Boria Thermodynamics amp life
6
Figure 15 ndash Comparison between the mechanical work obtained from two identical thermal motors
functioning according to the Carnot cycle for two different exhaust temperatures
(T0rdquo in case A and T0rsquo in case B)
The point of view seen above and resumed in equation 2) seems favorable to the presence of
high values of entropy tout court to avoid erroneous generalizations it needs remember that Gibbs
says that the maximum energetic gain in thermal transformations that is to obtain the maximum
ldquofree energyrdquo G is to exploit the total energy (enthalpy) H of the active mass minimizing the
entropy at discharge In fact the Gibbs equation states that
2 3 ∙ ∆
where H represents the entalpy of the mass transformed
We stress that it is necessary to compare two cases with identical initial temperature (as in
Figure 41) and to consider that it is the factor ∆T which determines the efficiency of the transformation5
Sea water contains an enormous amount of thermal energy but at a temperature T (of the source) very near to T0 (that of the coolant) in other words rendering unusable the heat it contains
we can state that sea water contains a ldquolargerdquo amount of thermal energy but no practical possibility of making a thermal motor work (the thermal difference available is ldquopractically nilrdquo)
Exactly for this reason a boiler which burns a combustible fossil material capable of achieving ldquohighrdquo temperatures enabling it to provide water at 90 degC is to be considered the perpetrator of a
grave ldquothermodynamic crimerdquo That combustible could be used with more results for example in a
cogeneration plant where water at low temperature is a ldquowasterdquo product
5 Sources at high temperature are necessary to produce thermodynamic cycles with acceptable results Our car be it Otto
or Diesel develops a temperature of around 1500 degC in the combustion chamber and give us a mechanical efficiency at the
wheels of about 35 (approx 30 remains ldquointernal energyrdquo and is expelled to the exhaust The coolant temperature is
that of the atmosphere the remainder is transformed into heat by thermal loss and passive resistances and is dispersed
mainly by the radiator)
Pier Maria Boria Thermodynamics amp life
7
14 ENTROPY AND LIFE
Livio Gratton (Italian cosmologist from Trieste died in 1991 and considered the father of
Italian Astrophysics) observed that the phenomenon ldquoliferdquo contains something singular which does
not fit in with the mechanism described up to this point The appearance of life in an electromagnetically structured universe constitutes a singular moment which cannot be explained
technically In fact an organism is alive when within itself it produces transformations of negative
entropy (that is with ∆Slt0) which contradicts the second principle Let us observe a plant seed if it is alive in conditions expected in nature it germinates
spontaneously and grows capturing carbon from the atmosphere giving body to the plant and releasing oxygen through chlorophyll synthesis
A small wheat seedling recently sprouted amongst the snow germinates and grows warming itself up at the expense of the ground (who has not observed the molten snow round the seedling
The seedlings under a thin blanket of snow poke out and are clearly visible green seedlings on a
white blanket in the middle of a dark patch of earth free from that which surrounds them)
Naturally if we were to also consider the interaction of the plant with the quanta of solar
energy and the surrounding minerals we would find that the sum of transformations has generated
positive entropy (the affirmation that the entropy of the universe tends to increase without limits is
correct)
A living animal organism should it be injured is capable of healing itself the vis vitalis as
our ancestors called it produces such an effect while a dead animal organism remains injured and
decomposes with the passing of time (increase of disorder)
One could consider the possibility of turning to entropy to define the state of life or death
about which we periodically debate even in practical cases (Terry Schiavo Eluana Englarohellip) if the organism produces negative entropy it is alive in the opposite case it is nothellip
One could also suggest a crude experimental procedure of a slightly Hitlerian nature which would settle the matter once and for all consisting of injuring an organism that has a dubious state
of life to verify its reactions in one entropic direction or the otherhellip The vis vitalis departs even if all the mechanical organs would be perfectly functional we can
think of the so called cardiac arrest (a phrase that could be a savior for the corner of the art of medicine) One could certainly object that the arrest is the cause while the departure of the vis
vitalis is the effect who knows The only certainty is that with death an irreversible process starts with the production of positive entropy and we fall back into line with the second principle
In conclusion it can be said that the property of entropy is that of an increase in every
transformation that can be performed practically (like saying in every irreversible transformation)
except in the case of living organisms
How to produce heating of the plant at the expense of the surrounding masses and to increase
the order of the molecules to the point of ldquoforcingrdquo the carbon taken from the most formless state in
existence (that of gaseous CO2) to take on the shape of a trunk giving rise to transformations of
decreasing entropy
Also an ordinary refrigerator can produce a local decrease of entropy expending some
energy in the following figure we represent the energy transformations occurring in it at the end of
the transformation we have the temperatures marked with an asterisk after the energy Q leaves the
cool body to join the warmest body with the energy Q3 that is needed for the refrigerator to run6
6 The ratio (Q2+Q+Q3)Q3 is the widely known COP (Coefficient Of Performance) of the heat pumps
Pier Maria Boria Thermodynamics amp life
Figure 16 ndash Heat pumping in a refrigerator
In this sketch the external energy Q3 appears essential and the system is open the energy Q
increase its entropy gaining the temperature T2 entering the condensator Restarting the numerical example of the Clausius calorimeter we reconfirm Q=50 J as the
heat exchanged in this condition it is easy to verify that the water temperature decreases by 10 K while the copper increases by 90 K
Assuming COP=3 we have
final temperature of water T1 = 290 K
and for the copper T2 = 490+903 = 520 K
proceeding as above it follows that
for the copper
∆ 520400 0 5 ∙ 004 002
(
for the water
∆ 290300 5 ∙ 0034 0170
(
Therefore the quantity of transformed heat Q is subject to the variation
∆ ∆ + ∆ 002 0170 015 lt 0 ( ∶
thanks to the contribution of the external energy Q3 the exchanged heat decreases its entropy
Now we will see in what way nature does the heat pumping
Pier Maria Boria Thermodynamics amp life
9
Part 2 (of 4) Boltzmannrsquos Distribution
21 THE BOLTZMANNrsquoS DISTRIBUTION
We will reply to the question after having examined the second pillar on which we base this paper Boltzmannrsquos Distribution (Ludwig Boltzmann Austria 1844-1906)
As can also be seen in excellent web pages the disorganized vibrational velocity of the molecules of a gas (but also those of liquids and solids) at a given temperature take on values
which are continuously and randomly variable following a particular distribution represented graphically in Figure 21
Figure 21 ndash Probability distribution of the velocity of molecules of a gas as a function
of the velocity itself according to Boltzmannrsquos Statistic
It is thanks to this distribution discovered by Boltzmann that living nature vegetable and animal can perform local transformations with decreasing entropy the great masters have
thought up theoretical experiments based on devices capable of selecting molecules of colder gas having higher velocities than what is thought to be the average velocity of the molecules of the
warmer gas (Maxwell the demon Polvani the choosing porter Amerio the selecting valve) to allow them to pass from a lower temperature environment to another adjacent environment with
higher temperature in this way obtaining a transformation which locally invalidates the second
principle of thermodynamics
In Figure 22 it is possible to see that at every average velocity (considered) of the ldquowarmrdquo
molecules one can find a corresponding branch of the ldquocoldrdquo curve related to those particles that
should they pass to the warmer side could cause an increase in that average velocity and therefore
of the temperature
Pier Maria Boria Thermodynamics amp life
10
Figure 22 ndashThe Maxwell demon allows the passage from the colder to the warmer
environment only of the molecules which have a velocity higher than the
weighted average velocity of the warmer molecules
It is necessary to perform a sorting of the molecules one by one with mechanical means not
available to man while the experimental observations of the type reported above would suggest
that nature is capable of it operating at a molecular level in the realm of living organisms
In Figure 23 is represented the device which allows the ldquotheoretical experimentrdquo in the form
proposed by Prof Amerio of the Polytechnic of Milano (1955) Maxwell had proposed a ldquodemonrdquo
as selector of the molecules (1867) the selection device has been the object of particular attention
on the part of Szilard (1929) and later Bennet (1981) with the scope of correctly counting the
variation of entropy in the test universe and calculate the required energy for the selection
Figure 23 ndash The selective valve allows the passage from the colder to the warmer
environment only of the molecules which have a velocity higher than the
weighted average velocity of the warmer molecules as shown in Fig 22
Pier Maria Boria Thermodynamics amp life
These elementary applications of classic thermodynamics based on the concept of entropy
and on Bolzmannrsquos Distribution suggest to us that the phenomenon ldquoliferdquo is to be associated with a
ldquovis-vitalisrdquo external to the dissipative mechanism for which we have ample and daily experience
Obviously it is impossible for man to build a Maxwell device but in our research we have
found a very interesting observation by Jaques Monod (Nobel Prize in 1965) that confers the part of
demon to the natural enzymes7
According to this point of view we can convert the Figure 16 as follows
Figure 24 ndash The natural heat pumping performed by enzymes
and this sketch we consider as typical of the phenomenon ldquoliferdquo The role played by the vis-vitalis seems essential because the only electro-chemical energy
associated with enzymes are components easily deliverable in the biological laboratories but
nobody has been able to start life from these components8
There are those who attempt an approach to this argument with improper methods and with
arbitrary applications of the concept of probability which leads to theories that are devoid of the
required respect for a sound scientific doctrine
22 CONCLUSIONS FROM THE FIRST AND SECOND PART
Rivers of ink have been written about the origin of life to the point that it is possible to read
about the most bizarre theories that completely ignore that which is suggested by the Queen of
Physics Thermodynamics
Paleontology Biology extraterrestrials UFOs Cosmic Palingenesis and similar are all
stirred numbers equations concepts of probability principles of conservation etc are not used
7 Le hazard et la neacutecessiteacute 1970 ndash Arnoldo Mondadori Editore Spa ndash Milan ndash Pag 58
8 See the Stanley Miller experiment at the end of paragraph 54
Pier Maria Boria Thermodynamics amp life
12
correctly These are the only foundations possible for a correctly stated scientific discussion (there
is no adjective more abused than the term ldquoscientificrdquo)
The reader could (perhaps on a rainy Sunday) do some research on the ldquoprimordialrdquo soup (but
if it is not Knorr for whorsquos brand modestly in youth we made thermodynamics projects does not
taste good) on the ldquocosmic tankrdquo on the ldquotyping monkeysrdquo on the cycle of carbon and oxygen (in relation to the demonization of CO2) on the hydrological cycle (which is a substance that cannot
be ldquoconsumedrdquo as is currently heard said otherwise what cycle would it complete subjects often treated by substituting Science with ideology and making ample use of the principle of superior
authority (the ipse dixit of historical memory) upholding disjointed dogma but which are
politically correct
Sometimes one has the feeling of witnessing the squalid discourse of gossiping women by the fountain
It can be noted that in the observations made up to now we have practically not talked about energy whorsquos role in the economy of our discourse has been secondary Itrsquos the definition of the
entropy index state which changes the way to view the cosmos we would not talk of it if it were
possible to carry out reversible reactions
We would come to suspect that the irreversibility is a ldquodefectrdquo of the cosmos having the
function of forcing it to a gradual entropic enrichment (and therefore to a degeneration of energy)
such that the final form of all the energy available becomes one that is thermally and entropically
unusable therefore by virtue of what has been discussed at a certain point in the evolution of the
universe at a finite time it will not be possible to practically perform any thermodynamic cycle9
That is to say the thermal death of the universe
9 We will be further willing to suspect a decay of the cosmological properties correlated to the original sin Ah free
thought
Pier Maria Boria Thermodynamics amp life
13
Part 3 (of 4) Probability
31 PROBABILITY IN BOLTZMANNrsquoS STATISTICS
Boltzmann obtained the graph of the probability as a function of temperature postulating that
a certain number m of particles which are indistinguishable from each other (which we will call A
B C M) and a number n of possible states (a b c n) in which one or more particles (even if
m) can find themselves the presence of particles in each state could occur with different possibilities
If the identical particles are free to occupy the various states (as in the case of a gas) these could continuously exchange states between themselves (for example thanks to reciprocal impacts
as in Figure 23) whilst ldquoon averagerdquo maintaining a certain distribution subject to the conditions around them (for example temperature) a certain distribution of the possible configurations would
be typical of such conditions
Continuing with this example if by state of the particles we mean possessing a certain amount
of kinetic energy E associated with each molecule of a gas in a certain interval of values of energy
∆E there will be a stable quantity of molecules even if amongst themselves continues exchanges of
energy occur Therefore in the range of the same interval some particles enter and some leave
If for the sake of imagination in what follows particles will be considered as ldquoballsrdquo and
states as levels of energy the balls will represent the particles while the levels will represent an
interval of energy (∆E)
Let us start with a very simple case consisting of 3 particles (m=3) able to be hosted by two
levels (n=2) as illustrated in Figure 31
In the left column we see all the possible combinations In the central section we see that certain combinations repeat themselves in such a way that if the particles become indistinguishable
(column 3) they are to be considered the same amongst themselves Therefore three possibilities exist such that both the combinations 234 and 567 can occur
and only once for the combinations 1 and 8 If we ldquonormalizerdquo the possibility (expressing it in unitary or percentage terms) it assumes the
role of probability (ratio between favorable cases and possible cases) which we have done in the last column by expressing it in percentage terms as is common practice
Pier Maria Boria Thermodynamics amp life
14
Figure 31 ndash A rather simple case to demonstrate how given m=3 and n=2 it is possible to
have different probabilities for each combination
Pier Maria Boria Thermodynamics amp life
15
This allows us to draw the graph of Figure 32 where we can begin to see the
Boltzmann distribution forming
Figure 32 ndash The embryonic Boltzmann diagram increasing particles and the number of
possible states the envelope of the columns (in this particular case not yet)
acquires the characteristic asymmetric bell shape
Following in the footsteps of the great Ludwig we enter into systems which are numerically
more substantial three combinations of seven states with an arbitrary arrangement of four particles
as represented in Figure 33 the three combinations are equivalent because the particles are
indistinguishable by hypothesis
Pier Maria Boria Thermodynamics amp life
16
Figure 33 - The three configurations are equivalent if the four particles are indistinguishable
amongst themselves
Each of the n states can be associated with A B C etc (that is to each or more of the m
particles) and since a single particle can occupy each time a different state (and other particles
other states) m times the possible combinations C are ntimesntimesntimeshelliptimesn (m factors equal to n)
C = nm
We could also be convinced observing for example Figure 34 where it is assumed that n=5
(it looks like a musical stavehellip) and m=2 particles (therefore 52=25 combinations)
Pier Maria Boria Thermodynamics amp life
Figure 34 ndash Beyond the 25th beat the preceding configurations are repeated because A and B are
indistinguishable Within the range of the 25 possible configurations some are more favored
because they appear more frequently for example 6 and 22 9 and 25 etc The unoccupied
states are identified by a circle
As is fair to expect configuration 1 is least favored
Pier Maria Boria Thermodynamics amp life
18
We can arrive at the same result with a more practical method suitable also for very large
values of n and m which we will use as follows
It consists of a tabular method stolen from Combinatorial Analysis where for n and m equal to
various units it avoids the need to write hundreds or thousands of key strokes as used above
Let us take two rows and as many columns as there are states thereby obtaining a grid in
Figure 35 to verify what has been said above we have taken 2 rows and 5 columns (n=2 m=5)
Figure 35- With this grid we obtain the number of possible configurations
To further demonstrate we will build a grid for n=5 and m=4 as in Figure 36 where there are sufficient rows to progressively expose the number of particles (from 4 to 1 in the first box of
the first column of the occupancy numbers) and there are n columns
Pier Maria Boria Thermodynamics amp life
19
Figure 36 - Since 54= 625 there are 625 possible combinations the relative probabilities are
listed in the last column note the asymmetry
Pier Maria Boria Thermodynamics amp life
20
It is necessary to observe that in the figure the table of numbers of occupancy reminds
us not by chance of Tartagliarsquos Triangle while the Boltzmann type diagram that can be
associated shown in Figure 37 takes on an almost familiar shape
Figure 37 - Graphical representation of Figure 62 the bars are asymmetric
Pier Maria Boria Thermodynamics amp life
21
To provide an example and referring to Figure 36 we can see how it is possible to obtain 80
possibilities corresponding to his second line
If a box is occupied by 3 particles out of an available 4 the simple combinations of 4 objects
with 3 by 3 (as taught by the Combinatorial Analysis) are given by the binomial coefficient
6437 4
and the four possible groups of three numbers have five positions from which to choose From here 4times5=20 possibilities for the group of three numbers
The single remaining particle has the possibility of the four remaining locations and therefore has 1times4=4 possibilities
The product 20times4=80 gives us the total possibilities in the case that the particles arrange themselves in two groups one with three and one with a single particle and having five boxes
suitable It is easy to verify that we will obtain the same result considering first the single particle
having five boxes suitable (five possibilities 1x5=5) and after the three having the four remaining
(one is occupied by the single particle therefore 4x4=16 and 5x16=80)
Applying the procedure line by line it produces the results shown
Pier Maria Boria Thermodynamics amp life
22
Part 4 (of 4) Chance
41 CHANCE
A sharp-shooter shoots at a target with an excellent rifle he aims carefully chooses the
moment when his breathing will not interfere and the amount of force with which to pull the trigger so as not to move the barrel fires the shot and hits the bullrsquos-eye
Immediately afterwards he takes all the same precautions but the shot ends up being slightly off target it could have been a slight disturbance to his sight an involuntary variation in his
breathing an imperceptible abnormal movement of the finger a very slight unpredictable wind or who knows what else
The causes are many and imponderable slight if each is considered in itself but interacting differently each time ensuring that each shot has a different fate
This complex of innumerable causes of disturbance which are not controllable or predictable
and which not being able to take each into account one by one are called the Law of Probability
(Gaussrsquos Law)10
Probability for the reasons given and law thanks to Carl Friedrich Gauss (1777-1855) who
wrote an equation capable of taking into consideration in a global manner all those fleeting causes
so as to be able to predict with near accurate approximation how the shots will arrange themselves
percentage wise round the target with different distances from the bullseye The approximation will
be more accurate the greater the number of shots that are fired
Let us assume that the target is as represented in Figure 41 and is divided into two parts by
means of the section AB and that our sharpshooter fires many shots after which we count the
number of shots which hit the target in each half
Figure 41- The segmented target
If the reasons for the error are truly random (rifle without defects such that it does not tend to
deviate the shot systematically and neither does the sharpshooter have an analogous defect there is
10
The example of the sharpshooter was published by Engineer Mario Manaira in Ndeg 256 of ldquoJournal of Mechanicsrdquo
together with our first article concerning thermodynamics more than half a century ago (1961)
Pier Maria Boria Thermodynamics amp life
23
not a steady wind etc in other words there does not exist a cause which always influences with the
same bias called a systematic cause) we could note the following
1 The shots will be greater in number in the first band round the center
2 The shots will progressively decrease in number in the subsequent bands as these distance themselves further from the center until there are very few in the bands furthest away
3 The shots in the two halves right and left in any similar band will tend to have the same number and will even be identical if sufficient shots are fired
It is therefore possible to represent the phenomenon graphically as in the following figure
Figure 42 ndash The random distribution of the shots in each band and the Gaussian distribution that
would be obtained with an infinite number of shots fired
If the marksman were less capable the concentration of shots near the zero on the abscissa would reduce and the curve would flatten itself while maintaining the characteristics given and
represented in Figure 43 The first observation is that the maximum height of the curve constitutes the ldquotargetrdquo in other words the goal of the operation while the absence of systematic causes (in
antithesis of randomness) ensures the symmetry of the curve with respect to the vertical which
represents our target zero
Pier Maria Boria Thermodynamics amp life
24
Figure 43 - If the marksman is less skilled the Gaussian flattens
In the case of a systematic cause of error the curve loses its symmetry if we assume that the
test is performed with a constant wind from left to right the graph will take on the shape of Figure
44
Figure 44 ndash When the Gaussian is asymmetric it implies that the phenomenon is not ldquoentirely
randomrdquo11
Let us suppose now that our sharpshooter is blindfolded the target becomes very large and is
moved he will have to shoot blindly (randomly) left and right high and low Given that the Gauss
11
Gauss suggests that the analytical expression of the Law of Randomness is the function
2xey minus
=
where it can be seen that the curve is symmetrical with respect to the axis x=0 and decreasing both towards the left and
right of this line and has a maximum for x=0
It can be shown further that the area subtended is
π=int+infin
infinminus
minusdxe
x2
To ensure that this area is equal to unity as opposed to π appropriate steps can be taken which without
changing the general properties illustrated give the normalized Gaussrsquos Law
Pier Maria Boria Thermodynamics amp life
function still applies the probability curve will flatten itself maintaining the essential
characteristics in particular the two tails which will tend towards a tangent with the abscissa
tending towards infinity a maximum point a point of inflection and the other characteristics
illustrated in Figure 45
Figure 45 ndash Typical characteristics of a normalized Gaussian
Supposing once more that the Gauss function still applies it would be logical to expect a distribution with a curve that is so flat that it will be difficult to see a maximum point corresponding
to the center of the target it will be necessary to fire enough shots so as to occupy every position on the abscissa and to have hit with 100 certainty the bullrsquos-eye
This implies that everything is possible as long as an infinite number of shots are available
(using rhetorical language)
42 SOME PROPERTIES OF RANDOM EVENTS
The perplexities regarding the applicability of chance as referred to the blind sharpshooter
depend on the fact that the Gaussian assumes that programming has been applied to reach an
objective which implies that the operator is conscious of the objective an element which in this
case is absent
Both the existence of a program (the sharpshooter sets out to hit the bullrsquos-eye) and the
existence of an objective (the card with circles) appear to be essential to be able to talk about
chance
Another example let us imagine a machine programmed to produce a certain mechanical
piece the program is the design of the piece written in machine language and the objective is the production of the piece In mass production we will find that it is the case that despite the work
conditions being maintained the same each piece will be different to the other to the point that the pieces which exceed the tolerances (which would not allow them to be interchangeable) will be
rejected Innumerable examples could be presented identifying in every case these two characteristics
a program and an objective Statistics also operate in reverse from the measurement of a group of subjects it creates a bar
chart its envelope will be the curve of the random distribution It will give us the average of the values measured if the curve is symmetrical it will tell us that the phenomenon is not influenced by
systematic causes further it will tell us the value of the standard deviation etc
Pier Maria Boria Thermodynamics amp life
26
To fix this thought in our heads let us suppose that we want to study the average height of a
population of people who are male we make many measurements on many subjects creating bars
for every centimeter we will obtain a graph similar to Figure 46
Figure 46 ndash A practical application the Gaussian deduced from experimental measurements for
statistical purposes
In this statistical application where are the program and objective They are there they are
there they were contained in the information which the people naturally had at conception a
matter of genes and of DNA (an observation coherent with ldquoThe Kid Equationrdquo See the
ldquoIntroduction to Hyperspacerdquo12
)
These considerations lead us to think that the meaning of the word ldquochancerdquo commonly given
does not make sense that ldquochancerdquo does not exist and lead us to suspect that Anatole France had an
inspired guess when he said ldquochance is Godrsquos pseudonym when He does not want to sign his
namerdquo
This strongly agrees with what illustrious philosophers have been confirming for centuries
ldquoDeus absconditus estrdquo (Is XLV XV)
12
In our first volume ldquoCaro amico miohelliprdquo ndash Ed Pagine ndash 2010 In our second volume (ldquoVerba volant eqvuationes
manentrdquo) other considerations about a fundamental theorem of Genetics the Hardy Weinberg theorem
Pier Maria Boria Thermodynamics amp life
27
43 CHANCE amp PROBABILITY
We can now summarize some salient functions of Boltzmann and Gauss
Boltzmann
1 Deals with probability regarding the characteristics that can be assumed by many identical particles having a certain number of positions available (Dirac and Fermi deal
with particles which are distinguishable but the correct reference in our observations are the identical particles)
2 The function presents a maximum and aesthetically looks like a Gaussian but it is not symmetrical
3 It has only a single asymptote to the right of the maximum and its minimum at infinity coincides with zero the origin of the reference system
4 It is normalized so that the area subtended represents the total probability of 100
Gauss
1 Deals with chance and is applicable when an objective exists that is defined by a
program
2 The phenomenon ldquopurely by chancerdquo is represented by a curve that is symmetrical
about the axis x=0
3 The Gaussian has a maximum and no minimum at infinity
4 It possesses two asymptotes one to the right and one to the left of the maximum
5 Well defined values of probability can be associated with multiples of the standard deviation
6 It is normalized as for Boltzmannrsquos
44 THE EDDINGTONrsquoS PARADOX13
Eddingtonrsquos famous ldquoInfinite monkey theoremrdquo can be counted amongst the most discussed
paradoxes for the fact that it is often quoted by so called ldquoscientific popularizersrdquo The original assertion states ldquohellipa monkey hitting keys at random on a typewriter keyboard
for an infinite amount of times will almost surely type a given text such as the complete works of
William Shakespearerdquo
Having taken away the condition of an infinite amount of time the paradox remains acceptable
(from the moment we are able to demonstrate that a finite amount of time is sufficient) However
such a long period of time is necessary that the original statement could be seen as an hyperbolic
discussion
We have seen that random phenomena require a program in light of an objective In the case
of the typing monkeys the program could include the elimination of duplicate pages (actually the
identical pages as we will see below) and the objective could consist in the conservation of ldquogoodrdquo
pages arranged in the right sequence
Applying Boltzmannrsquos statistics let us assume that the typewriter has m=30 keys (we can think of ldquoblindrdquo keys without any writing and all identical) and that we want to write a book of
only 106
letters (a thousand typed pages) as we have observed in paragraph 31 all the possible combinations are
13
The reader can find all the details regarding these various arguments on the web
Pier Maria Boria Thermodynamics amp life
C = nm = (10
6)30
= (10)180
In other words there are 10180
possible configurations
Let us assume that the monkeys are capable of striking 10 keyssec (skilled typistshellip) the
time necessary would be
t = 10180
x 106 10 = 10
185 sec
Since we can count 1016 seconds in a billion years it is also possible to say that the time
required will be
10185
1016
= 10169
billion years (giga-years)
(let us remember that the big-bang has an age of ldquoonlyrdquo 14 billion years)
In reality the situation is even ldquoworserdquo in fact this calculation (which is generally accepted)
is wrong because we cannot talk about only thirty objects (the letters punctuation marks spaces between lines etc) to be arranged in 10
6 positions otherwise in each of 10180 configurations
obtainable we would find empty spaces up to 106-30 in each configuration
It is necessary to postulate that there are 106 letters to be arranged like conceding that the
monkeys have to insert 106 objects ie 10
6 key strokes In other words it is necessary that n = m =
106 and in this case the formula of the combinations gives us an astronomical value
6106 )10(===
mm mnC combinations
At a rhythm of 10 key strokes sec the time corresponds to
9899995005000616106 10sec101010)10(
6
equiv=sdotsdot=minust years
Figure 47 ndash Summary table of the probabilities according to Boltzmann
In realty the situation is even ldquoworserdquo still In fact in the calculation of the combinations duplicate configurations are not considered
(which necessarily must be considered as possible) in other words our monkeys could produce the same combinations several times (or two identical pages) anyway the duplications will be useless
in the compilation of our small book of only 106 letters
To this end we invoke chance (to attempt to appreciate the incidence of the repeating of
identical pages) and having constructed a Gaussian by arranging the frequency of identical pages we can reason as follows having produced all the astronomical combinations as above in the time
calculated (which we will call a cycle) the highest probability of identical pages is in pairs (which
Pier Maria Boria Thermodynamics amp life
29
we will assign the maximum position) then in threes and so on At infinity with a probability of
zero all the pages will be identical
It seems fair to presume that the standard deviation could be very large qualifying for a very
flat Gaussian and let us suppose that the pages to be rejected (one for the doubles two for the
triplets etc) are contained within the first standard deviation (as in Figure 48) then the duplicate pages to be thrown away would be about 68
Figure 48 ndash The postulated conditions (pages to be eliminated because they are duplicated equal
to the standard deviation) make 68 of the pages produced useless Iterating the cycle one could
consider the duplication of other pages however it can be demonstrated that the phenomenon
continues to imply finite times
How much does the required time increase to generalize we assume the length of a cycle to be of one unit and we identify with K the average cost of discarded pages (in the previous numerical
case K= 068) and then we observe Figure 49
Figure 49 ndash Having exhausted the first cycle identified by 1 the second of length K allows the
replacement of the duplicate pages produced in the first cycle the third of length K2 is used to
replace those produced in the second cycle and so on
The time necessary to complete the cycles required to eliminate the duplicates as they are produced will be given by the sum
suminfin
=0n
nK
which constitutes a geometric series
The Mathematical Analysis teaches us that such a series converges for 1ltK as is confirmed
in our case where it takes on the value 068
KS
minus=
1
1 and if K = 068 gives 1253
6801
1=
minus=S
Pier Maria Boria Thermodynamics amp life
30
Therefore multiplying by 3125 the time dedicated to complete a cycle (317middot105999989 billion
years) for the hypothesis made we also eliminate all the duplicate pages of our little book of 106
key strokes
Changing the value of K (always lt1) one obtains different multipliers but always of a finite
value let the reader imagine the time necessary to type all of Shakespearersquos works It must be highlighted that the monkey operation to be considered a success requires the
intervention of external intelligence capable of selecting the useful pages (like thought by Theory of
Information) and ordering them in the right sequence to obtain a final legible manuscript this
obvious necessity implies that negative entropy be introduced into the system as covered at the
beginning this is like a living being taking the trouble to ldquoput in orderrdquo otherwise the ldquopurely
randomrdquo work would be entirely useless because it will exclusively produce positive entropy
All experiments attempted by man with the goal of demonstrating the random production of
complex molecules (first building blocks of living organisms) have the defect of requiring an a
priori living system like man to arrange this production
When later chaotic physical-chemical conditions are created (temperature pressure
methane electrical arching etc) hoping to obtain that which Thermodynamics does not permit the
inventors of the moto perpetuo come to mind who never give up
The research on the ldquoprimordial souprdquo belongs to this type of experimentation a battle horse
of the followers of the ldquomaitre agrave penserrdquo of the last century and which regard in particular the laboratory experiments of Stanley Miller the goal of his research of a physical-chemical nature
was to recreate life it was an understandable but too ambitious of a project for a researcher The result was absolutely negative (Miller himself recognized it) however this last piece of information
is only whispered in scientific circles so that we still find genuine touts who speak with enthusiastic coram populo of the primordial soup and its miraculous effects14 with a self-assurance
that is truly shameful
45 CONCLUSION
On 4 July 2007 at the London Kinetics Museum a serious presentation of a perpetual motion
machine was scheduled a machine capable of supplying the user with a power greater than that
absorbed ldquoObviouslyrdquo the presentation was postponed due to ldquoa technical problemrdquo15
It would appear impossible but advocates convinced of such a motion exist and many
inventors submit patent after patent even though still in illo tempore Max Planck declared himself
to be contrary to such a possibility which violates the principles of Thermodynamics
Based on the reasoning we have developed regarding entropy probability and chance the
violation of such principles is implicit even in the attempts to obtain living organisms in a
laboratory (characterized as we have seen as being producers of negative entropy) and as such a
strong analogy can be seen between the advocates of perpetual motion and those aspiring to create
life
1 The correct application of Boltzmannrsquos statistics a phenomenon for which we call on
probability demonstrates that combinations of large numbers of particles to the point of generating complex organisms require very long periods of time in comparison the age of
the universe is but the blink of an eye
2 The probabilities take on the largest numbers in correspondence with the most disordered
configurations
14
From ldquoCorriere della Serardquo october 2008 ldquoLa vita sulla Terra Cominciograve nei vulcani con un innesco chimicordquo 15
-Source Wikipedia
Pier Maria Boria Thermodynamics amp life
3 The most ordered combinations are those which characterize organic structures and the action
of an intelligent being is necessary to select order and conserve in time the favorable
combinations
4 The phrase ldquochance phenomenonrdquo is somewhat less intuitive than what ldquocommon senserdquo
would suggest In fact the Gaussian perspective implies that such phenomena are necessarily
associated with a program this program implies the existence of an objective around which
we have an increased concentration of events
5 In every case it is necessary to postulate the existence of an intelligent design without which
the configurations and the favorable events constitute events without any functional link
between themselves
6 The existence of life as a producer of negative entropy on a continuous basis (not cyclical) is a fact visible with our own eyes
All this leads us to support the existence of a Co-ordinating Entity which possesses life ldquoa
priorirdquo and which is capable of transmitting it to animals (animalis homo included) and vegetation It can be noted that the two living systems animal and vegetable complement each other in the
sense that the design requires that emissions from the first (CO2) are the nutrients for the second and the byproducts of the second (O2) are essential for the first the carbon and oxygen cycles look
like they have been designed According to the author there is only one explanation we are in the presence of the greatest
Design Physicist of all times God the Creator
This is what we call Him as Christians while Israelites call Him Jehovah the Ishmaelites
Allah the Masons GADU (Great Architect of the Universe) etc
In other terms
the Creation is a thermodynamic necessity
Amen
Pier Maria Boria Thermodynamics amp life
4
∆
∙ 0255
for the water
∆
∙ +0033
More simply we obtain the thermal capacity of each body
∆
5090 0 5
∆
5010 5
and subsequently we can calculate the total variation in entropy of our closed system
∆ ∆ + ∆ 0142 + 0165 +0023 amp () 01
As a preview to the second law of Thermodynamics
In the equation 1) we found two addends of opposite sign each one representing a ldquolocalrdquo
variation of entropy it follows that even though the total entropy of the testing universe increases
we can have local variations of opposite sign3
In fact generally when we have a thermal transformation some mass increase in temperature
and the other decrease the heat exchanged is equal and we can say
∆ 0ℎ- lt 0∆ lt 0ℎ-
that is the cooled body decreased its own enthalpy in an opposite direction to that of overheating
(the meaning of indices is obvious)
This observation will soon be useful when talking about ldquoEntropy and Liferdquo
13 ANALOGY BETWEEN ENTROPY AND WEIGHT
The content of this paragraph is not essential for the purpose of this paper However we
consider it useful to complete the understanding of entropy
Amongst the physicists of the XIX century Zeuner (Germany 1828-1907) proposed an
interesting analogy between the gravitational potential energy of a weight P and the entropy of a
mass with a heat Q and a temperature T
With reference to Figure 14 we know that the potential energy (ie the mechanical work which can be performed) of the water mass of the reservoir is L = P ∆H
3 It seems rational to accept the popular statement according to which the entropy of the astronomical universe is
indefinitely increasing in spite of our lesser knowledge of the astronomical universe (see also the ldquoAnthropic Principlerdquo)
in any case pay attention not to confuse that with testing a closed universe
Pier Maria Boria Thermodynamics amp life
5
Figure 14 ndash System to transform gravitational potential energy into mechanical energy of a
motor shaft
Zeuner studied the work obtainable from a thermal motor capable of transforming heat into
work with a Carnot Cycle4 allowing the efficiency of the heatwork transformation to be expressed
exclusively in temperature terms (as opposed to quantity of heat) which leads us to our goal In fact as is widely known the efficiency of the Carnot Cycle is
T
T
T
TT 00 1minus=minus
=η
where T-T0 is the difference in temperature between ldquosourcerdquo and ldquocoolantrdquo
Consequently introducing the quantity of heat Q into the motor the mechanical work L obtainable will be
1 ∆ ∆2
or rather the expression that appears in Figure 4 where the entropy ∆QT is a factor of
proportionality analogous to the weight P where the change in height ∆H corresponds to the change in temperature ∆T which the motor is able to produce (from ∆rdquoT lt ∆rsquoT one has in
proportion LrdquoltLrsquo with the consequence that the residual internal energy after being depleted and not able to be transformed into work will be Urdquo gt Ursquo)
We can observe that a functional tie exists between Q and T such that by increasing Q T is
increased in direct proportion (considering as constant the specific heat of the mass which runs the
cycle with no latent heat exchange) and therefore given a particular initial entropy the work
obtainable depends exclusively on the ∆T achievable
A motor which expels heat at a lower temperature produces more mechanical work at equal
ldquoconsumptionrdquo this is the purpose of the comparison between the two thermal motors in Figure 15
4 A car run on petrol will produce an Otto Cycle one on diesel a Diesel Cycle an exothermic motor will produce a Rankin
Cycle etc
Pier Maria Boria Thermodynamics amp life
6
Figure 15 ndash Comparison between the mechanical work obtained from two identical thermal motors
functioning according to the Carnot cycle for two different exhaust temperatures
(T0rdquo in case A and T0rsquo in case B)
The point of view seen above and resumed in equation 2) seems favorable to the presence of
high values of entropy tout court to avoid erroneous generalizations it needs remember that Gibbs
says that the maximum energetic gain in thermal transformations that is to obtain the maximum
ldquofree energyrdquo G is to exploit the total energy (enthalpy) H of the active mass minimizing the
entropy at discharge In fact the Gibbs equation states that
2 3 ∙ ∆
where H represents the entalpy of the mass transformed
We stress that it is necessary to compare two cases with identical initial temperature (as in
Figure 41) and to consider that it is the factor ∆T which determines the efficiency of the transformation5
Sea water contains an enormous amount of thermal energy but at a temperature T (of the source) very near to T0 (that of the coolant) in other words rendering unusable the heat it contains
we can state that sea water contains a ldquolargerdquo amount of thermal energy but no practical possibility of making a thermal motor work (the thermal difference available is ldquopractically nilrdquo)
Exactly for this reason a boiler which burns a combustible fossil material capable of achieving ldquohighrdquo temperatures enabling it to provide water at 90 degC is to be considered the perpetrator of a
grave ldquothermodynamic crimerdquo That combustible could be used with more results for example in a
cogeneration plant where water at low temperature is a ldquowasterdquo product
5 Sources at high temperature are necessary to produce thermodynamic cycles with acceptable results Our car be it Otto
or Diesel develops a temperature of around 1500 degC in the combustion chamber and give us a mechanical efficiency at the
wheels of about 35 (approx 30 remains ldquointernal energyrdquo and is expelled to the exhaust The coolant temperature is
that of the atmosphere the remainder is transformed into heat by thermal loss and passive resistances and is dispersed
mainly by the radiator)
Pier Maria Boria Thermodynamics amp life
7
14 ENTROPY AND LIFE
Livio Gratton (Italian cosmologist from Trieste died in 1991 and considered the father of
Italian Astrophysics) observed that the phenomenon ldquoliferdquo contains something singular which does
not fit in with the mechanism described up to this point The appearance of life in an electromagnetically structured universe constitutes a singular moment which cannot be explained
technically In fact an organism is alive when within itself it produces transformations of negative
entropy (that is with ∆Slt0) which contradicts the second principle Let us observe a plant seed if it is alive in conditions expected in nature it germinates
spontaneously and grows capturing carbon from the atmosphere giving body to the plant and releasing oxygen through chlorophyll synthesis
A small wheat seedling recently sprouted amongst the snow germinates and grows warming itself up at the expense of the ground (who has not observed the molten snow round the seedling
The seedlings under a thin blanket of snow poke out and are clearly visible green seedlings on a
white blanket in the middle of a dark patch of earth free from that which surrounds them)
Naturally if we were to also consider the interaction of the plant with the quanta of solar
energy and the surrounding minerals we would find that the sum of transformations has generated
positive entropy (the affirmation that the entropy of the universe tends to increase without limits is
correct)
A living animal organism should it be injured is capable of healing itself the vis vitalis as
our ancestors called it produces such an effect while a dead animal organism remains injured and
decomposes with the passing of time (increase of disorder)
One could consider the possibility of turning to entropy to define the state of life or death
about which we periodically debate even in practical cases (Terry Schiavo Eluana Englarohellip) if the organism produces negative entropy it is alive in the opposite case it is nothellip
One could also suggest a crude experimental procedure of a slightly Hitlerian nature which would settle the matter once and for all consisting of injuring an organism that has a dubious state
of life to verify its reactions in one entropic direction or the otherhellip The vis vitalis departs even if all the mechanical organs would be perfectly functional we can
think of the so called cardiac arrest (a phrase that could be a savior for the corner of the art of medicine) One could certainly object that the arrest is the cause while the departure of the vis
vitalis is the effect who knows The only certainty is that with death an irreversible process starts with the production of positive entropy and we fall back into line with the second principle
In conclusion it can be said that the property of entropy is that of an increase in every
transformation that can be performed practically (like saying in every irreversible transformation)
except in the case of living organisms
How to produce heating of the plant at the expense of the surrounding masses and to increase
the order of the molecules to the point of ldquoforcingrdquo the carbon taken from the most formless state in
existence (that of gaseous CO2) to take on the shape of a trunk giving rise to transformations of
decreasing entropy
Also an ordinary refrigerator can produce a local decrease of entropy expending some
energy in the following figure we represent the energy transformations occurring in it at the end of
the transformation we have the temperatures marked with an asterisk after the energy Q leaves the
cool body to join the warmest body with the energy Q3 that is needed for the refrigerator to run6
6 The ratio (Q2+Q+Q3)Q3 is the widely known COP (Coefficient Of Performance) of the heat pumps
Pier Maria Boria Thermodynamics amp life
Figure 16 ndash Heat pumping in a refrigerator
In this sketch the external energy Q3 appears essential and the system is open the energy Q
increase its entropy gaining the temperature T2 entering the condensator Restarting the numerical example of the Clausius calorimeter we reconfirm Q=50 J as the
heat exchanged in this condition it is easy to verify that the water temperature decreases by 10 K while the copper increases by 90 K
Assuming COP=3 we have
final temperature of water T1 = 290 K
and for the copper T2 = 490+903 = 520 K
proceeding as above it follows that
for the copper
∆ 520400 0 5 ∙ 004 002
(
for the water
∆ 290300 5 ∙ 0034 0170
(
Therefore the quantity of transformed heat Q is subject to the variation
∆ ∆ + ∆ 002 0170 015 lt 0 ( ∶
thanks to the contribution of the external energy Q3 the exchanged heat decreases its entropy
Now we will see in what way nature does the heat pumping
Pier Maria Boria Thermodynamics amp life
9
Part 2 (of 4) Boltzmannrsquos Distribution
21 THE BOLTZMANNrsquoS DISTRIBUTION
We will reply to the question after having examined the second pillar on which we base this paper Boltzmannrsquos Distribution (Ludwig Boltzmann Austria 1844-1906)
As can also be seen in excellent web pages the disorganized vibrational velocity of the molecules of a gas (but also those of liquids and solids) at a given temperature take on values
which are continuously and randomly variable following a particular distribution represented graphically in Figure 21
Figure 21 ndash Probability distribution of the velocity of molecules of a gas as a function
of the velocity itself according to Boltzmannrsquos Statistic
It is thanks to this distribution discovered by Boltzmann that living nature vegetable and animal can perform local transformations with decreasing entropy the great masters have
thought up theoretical experiments based on devices capable of selecting molecules of colder gas having higher velocities than what is thought to be the average velocity of the molecules of the
warmer gas (Maxwell the demon Polvani the choosing porter Amerio the selecting valve) to allow them to pass from a lower temperature environment to another adjacent environment with
higher temperature in this way obtaining a transformation which locally invalidates the second
principle of thermodynamics
In Figure 22 it is possible to see that at every average velocity (considered) of the ldquowarmrdquo
molecules one can find a corresponding branch of the ldquocoldrdquo curve related to those particles that
should they pass to the warmer side could cause an increase in that average velocity and therefore
of the temperature
Pier Maria Boria Thermodynamics amp life
10
Figure 22 ndashThe Maxwell demon allows the passage from the colder to the warmer
environment only of the molecules which have a velocity higher than the
weighted average velocity of the warmer molecules
It is necessary to perform a sorting of the molecules one by one with mechanical means not
available to man while the experimental observations of the type reported above would suggest
that nature is capable of it operating at a molecular level in the realm of living organisms
In Figure 23 is represented the device which allows the ldquotheoretical experimentrdquo in the form
proposed by Prof Amerio of the Polytechnic of Milano (1955) Maxwell had proposed a ldquodemonrdquo
as selector of the molecules (1867) the selection device has been the object of particular attention
on the part of Szilard (1929) and later Bennet (1981) with the scope of correctly counting the
variation of entropy in the test universe and calculate the required energy for the selection
Figure 23 ndash The selective valve allows the passage from the colder to the warmer
environment only of the molecules which have a velocity higher than the
weighted average velocity of the warmer molecules as shown in Fig 22
Pier Maria Boria Thermodynamics amp life
These elementary applications of classic thermodynamics based on the concept of entropy
and on Bolzmannrsquos Distribution suggest to us that the phenomenon ldquoliferdquo is to be associated with a
ldquovis-vitalisrdquo external to the dissipative mechanism for which we have ample and daily experience
Obviously it is impossible for man to build a Maxwell device but in our research we have
found a very interesting observation by Jaques Monod (Nobel Prize in 1965) that confers the part of
demon to the natural enzymes7
According to this point of view we can convert the Figure 16 as follows
Figure 24 ndash The natural heat pumping performed by enzymes
and this sketch we consider as typical of the phenomenon ldquoliferdquo The role played by the vis-vitalis seems essential because the only electro-chemical energy
associated with enzymes are components easily deliverable in the biological laboratories but
nobody has been able to start life from these components8
There are those who attempt an approach to this argument with improper methods and with
arbitrary applications of the concept of probability which leads to theories that are devoid of the
required respect for a sound scientific doctrine
22 CONCLUSIONS FROM THE FIRST AND SECOND PART
Rivers of ink have been written about the origin of life to the point that it is possible to read
about the most bizarre theories that completely ignore that which is suggested by the Queen of
Physics Thermodynamics
Paleontology Biology extraterrestrials UFOs Cosmic Palingenesis and similar are all
stirred numbers equations concepts of probability principles of conservation etc are not used
7 Le hazard et la neacutecessiteacute 1970 ndash Arnoldo Mondadori Editore Spa ndash Milan ndash Pag 58
8 See the Stanley Miller experiment at the end of paragraph 54
Pier Maria Boria Thermodynamics amp life
12
correctly These are the only foundations possible for a correctly stated scientific discussion (there
is no adjective more abused than the term ldquoscientificrdquo)
The reader could (perhaps on a rainy Sunday) do some research on the ldquoprimordialrdquo soup (but
if it is not Knorr for whorsquos brand modestly in youth we made thermodynamics projects does not
taste good) on the ldquocosmic tankrdquo on the ldquotyping monkeysrdquo on the cycle of carbon and oxygen (in relation to the demonization of CO2) on the hydrological cycle (which is a substance that cannot
be ldquoconsumedrdquo as is currently heard said otherwise what cycle would it complete subjects often treated by substituting Science with ideology and making ample use of the principle of superior
authority (the ipse dixit of historical memory) upholding disjointed dogma but which are
politically correct
Sometimes one has the feeling of witnessing the squalid discourse of gossiping women by the fountain
It can be noted that in the observations made up to now we have practically not talked about energy whorsquos role in the economy of our discourse has been secondary Itrsquos the definition of the
entropy index state which changes the way to view the cosmos we would not talk of it if it were
possible to carry out reversible reactions
We would come to suspect that the irreversibility is a ldquodefectrdquo of the cosmos having the
function of forcing it to a gradual entropic enrichment (and therefore to a degeneration of energy)
such that the final form of all the energy available becomes one that is thermally and entropically
unusable therefore by virtue of what has been discussed at a certain point in the evolution of the
universe at a finite time it will not be possible to practically perform any thermodynamic cycle9
That is to say the thermal death of the universe
9 We will be further willing to suspect a decay of the cosmological properties correlated to the original sin Ah free
thought
Pier Maria Boria Thermodynamics amp life
13
Part 3 (of 4) Probability
31 PROBABILITY IN BOLTZMANNrsquoS STATISTICS
Boltzmann obtained the graph of the probability as a function of temperature postulating that
a certain number m of particles which are indistinguishable from each other (which we will call A
B C M) and a number n of possible states (a b c n) in which one or more particles (even if
m) can find themselves the presence of particles in each state could occur with different possibilities
If the identical particles are free to occupy the various states (as in the case of a gas) these could continuously exchange states between themselves (for example thanks to reciprocal impacts
as in Figure 23) whilst ldquoon averagerdquo maintaining a certain distribution subject to the conditions around them (for example temperature) a certain distribution of the possible configurations would
be typical of such conditions
Continuing with this example if by state of the particles we mean possessing a certain amount
of kinetic energy E associated with each molecule of a gas in a certain interval of values of energy
∆E there will be a stable quantity of molecules even if amongst themselves continues exchanges of
energy occur Therefore in the range of the same interval some particles enter and some leave
If for the sake of imagination in what follows particles will be considered as ldquoballsrdquo and
states as levels of energy the balls will represent the particles while the levels will represent an
interval of energy (∆E)
Let us start with a very simple case consisting of 3 particles (m=3) able to be hosted by two
levels (n=2) as illustrated in Figure 31
In the left column we see all the possible combinations In the central section we see that certain combinations repeat themselves in such a way that if the particles become indistinguishable
(column 3) they are to be considered the same amongst themselves Therefore three possibilities exist such that both the combinations 234 and 567 can occur
and only once for the combinations 1 and 8 If we ldquonormalizerdquo the possibility (expressing it in unitary or percentage terms) it assumes the
role of probability (ratio between favorable cases and possible cases) which we have done in the last column by expressing it in percentage terms as is common practice
Pier Maria Boria Thermodynamics amp life
14
Figure 31 ndash A rather simple case to demonstrate how given m=3 and n=2 it is possible to
have different probabilities for each combination
Pier Maria Boria Thermodynamics amp life
15
This allows us to draw the graph of Figure 32 where we can begin to see the
Boltzmann distribution forming
Figure 32 ndash The embryonic Boltzmann diagram increasing particles and the number of
possible states the envelope of the columns (in this particular case not yet)
acquires the characteristic asymmetric bell shape
Following in the footsteps of the great Ludwig we enter into systems which are numerically
more substantial three combinations of seven states with an arbitrary arrangement of four particles
as represented in Figure 33 the three combinations are equivalent because the particles are
indistinguishable by hypothesis
Pier Maria Boria Thermodynamics amp life
16
Figure 33 - The three configurations are equivalent if the four particles are indistinguishable
amongst themselves
Each of the n states can be associated with A B C etc (that is to each or more of the m
particles) and since a single particle can occupy each time a different state (and other particles
other states) m times the possible combinations C are ntimesntimesntimeshelliptimesn (m factors equal to n)
C = nm
We could also be convinced observing for example Figure 34 where it is assumed that n=5
(it looks like a musical stavehellip) and m=2 particles (therefore 52=25 combinations)
Pier Maria Boria Thermodynamics amp life
Figure 34 ndash Beyond the 25th beat the preceding configurations are repeated because A and B are
indistinguishable Within the range of the 25 possible configurations some are more favored
because they appear more frequently for example 6 and 22 9 and 25 etc The unoccupied
states are identified by a circle
As is fair to expect configuration 1 is least favored
Pier Maria Boria Thermodynamics amp life
18
We can arrive at the same result with a more practical method suitable also for very large
values of n and m which we will use as follows
It consists of a tabular method stolen from Combinatorial Analysis where for n and m equal to
various units it avoids the need to write hundreds or thousands of key strokes as used above
Let us take two rows and as many columns as there are states thereby obtaining a grid in
Figure 35 to verify what has been said above we have taken 2 rows and 5 columns (n=2 m=5)
Figure 35- With this grid we obtain the number of possible configurations
To further demonstrate we will build a grid for n=5 and m=4 as in Figure 36 where there are sufficient rows to progressively expose the number of particles (from 4 to 1 in the first box of
the first column of the occupancy numbers) and there are n columns
Pier Maria Boria Thermodynamics amp life
19
Figure 36 - Since 54= 625 there are 625 possible combinations the relative probabilities are
listed in the last column note the asymmetry
Pier Maria Boria Thermodynamics amp life
20
It is necessary to observe that in the figure the table of numbers of occupancy reminds
us not by chance of Tartagliarsquos Triangle while the Boltzmann type diagram that can be
associated shown in Figure 37 takes on an almost familiar shape
Figure 37 - Graphical representation of Figure 62 the bars are asymmetric
Pier Maria Boria Thermodynamics amp life
21
To provide an example and referring to Figure 36 we can see how it is possible to obtain 80
possibilities corresponding to his second line
If a box is occupied by 3 particles out of an available 4 the simple combinations of 4 objects
with 3 by 3 (as taught by the Combinatorial Analysis) are given by the binomial coefficient
6437 4
and the four possible groups of three numbers have five positions from which to choose From here 4times5=20 possibilities for the group of three numbers
The single remaining particle has the possibility of the four remaining locations and therefore has 1times4=4 possibilities
The product 20times4=80 gives us the total possibilities in the case that the particles arrange themselves in two groups one with three and one with a single particle and having five boxes
suitable It is easy to verify that we will obtain the same result considering first the single particle
having five boxes suitable (five possibilities 1x5=5) and after the three having the four remaining
(one is occupied by the single particle therefore 4x4=16 and 5x16=80)
Applying the procedure line by line it produces the results shown
Pier Maria Boria Thermodynamics amp life
22
Part 4 (of 4) Chance
41 CHANCE
A sharp-shooter shoots at a target with an excellent rifle he aims carefully chooses the
moment when his breathing will not interfere and the amount of force with which to pull the trigger so as not to move the barrel fires the shot and hits the bullrsquos-eye
Immediately afterwards he takes all the same precautions but the shot ends up being slightly off target it could have been a slight disturbance to his sight an involuntary variation in his
breathing an imperceptible abnormal movement of the finger a very slight unpredictable wind or who knows what else
The causes are many and imponderable slight if each is considered in itself but interacting differently each time ensuring that each shot has a different fate
This complex of innumerable causes of disturbance which are not controllable or predictable
and which not being able to take each into account one by one are called the Law of Probability
(Gaussrsquos Law)10
Probability for the reasons given and law thanks to Carl Friedrich Gauss (1777-1855) who
wrote an equation capable of taking into consideration in a global manner all those fleeting causes
so as to be able to predict with near accurate approximation how the shots will arrange themselves
percentage wise round the target with different distances from the bullseye The approximation will
be more accurate the greater the number of shots that are fired
Let us assume that the target is as represented in Figure 41 and is divided into two parts by
means of the section AB and that our sharpshooter fires many shots after which we count the
number of shots which hit the target in each half
Figure 41- The segmented target
If the reasons for the error are truly random (rifle without defects such that it does not tend to
deviate the shot systematically and neither does the sharpshooter have an analogous defect there is
10
The example of the sharpshooter was published by Engineer Mario Manaira in Ndeg 256 of ldquoJournal of Mechanicsrdquo
together with our first article concerning thermodynamics more than half a century ago (1961)
Pier Maria Boria Thermodynamics amp life
23
not a steady wind etc in other words there does not exist a cause which always influences with the
same bias called a systematic cause) we could note the following
1 The shots will be greater in number in the first band round the center
2 The shots will progressively decrease in number in the subsequent bands as these distance themselves further from the center until there are very few in the bands furthest away
3 The shots in the two halves right and left in any similar band will tend to have the same number and will even be identical if sufficient shots are fired
It is therefore possible to represent the phenomenon graphically as in the following figure
Figure 42 ndash The random distribution of the shots in each band and the Gaussian distribution that
would be obtained with an infinite number of shots fired
If the marksman were less capable the concentration of shots near the zero on the abscissa would reduce and the curve would flatten itself while maintaining the characteristics given and
represented in Figure 43 The first observation is that the maximum height of the curve constitutes the ldquotargetrdquo in other words the goal of the operation while the absence of systematic causes (in
antithesis of randomness) ensures the symmetry of the curve with respect to the vertical which
represents our target zero
Pier Maria Boria Thermodynamics amp life
24
Figure 43 - If the marksman is less skilled the Gaussian flattens
In the case of a systematic cause of error the curve loses its symmetry if we assume that the
test is performed with a constant wind from left to right the graph will take on the shape of Figure
44
Figure 44 ndash When the Gaussian is asymmetric it implies that the phenomenon is not ldquoentirely
randomrdquo11
Let us suppose now that our sharpshooter is blindfolded the target becomes very large and is
moved he will have to shoot blindly (randomly) left and right high and low Given that the Gauss
11
Gauss suggests that the analytical expression of the Law of Randomness is the function
2xey minus
=
where it can be seen that the curve is symmetrical with respect to the axis x=0 and decreasing both towards the left and
right of this line and has a maximum for x=0
It can be shown further that the area subtended is
π=int+infin
infinminus
minusdxe
x2
To ensure that this area is equal to unity as opposed to π appropriate steps can be taken which without
changing the general properties illustrated give the normalized Gaussrsquos Law
Pier Maria Boria Thermodynamics amp life
function still applies the probability curve will flatten itself maintaining the essential
characteristics in particular the two tails which will tend towards a tangent with the abscissa
tending towards infinity a maximum point a point of inflection and the other characteristics
illustrated in Figure 45
Figure 45 ndash Typical characteristics of a normalized Gaussian
Supposing once more that the Gauss function still applies it would be logical to expect a distribution with a curve that is so flat that it will be difficult to see a maximum point corresponding
to the center of the target it will be necessary to fire enough shots so as to occupy every position on the abscissa and to have hit with 100 certainty the bullrsquos-eye
This implies that everything is possible as long as an infinite number of shots are available
(using rhetorical language)
42 SOME PROPERTIES OF RANDOM EVENTS
The perplexities regarding the applicability of chance as referred to the blind sharpshooter
depend on the fact that the Gaussian assumes that programming has been applied to reach an
objective which implies that the operator is conscious of the objective an element which in this
case is absent
Both the existence of a program (the sharpshooter sets out to hit the bullrsquos-eye) and the
existence of an objective (the card with circles) appear to be essential to be able to talk about
chance
Another example let us imagine a machine programmed to produce a certain mechanical
piece the program is the design of the piece written in machine language and the objective is the production of the piece In mass production we will find that it is the case that despite the work
conditions being maintained the same each piece will be different to the other to the point that the pieces which exceed the tolerances (which would not allow them to be interchangeable) will be
rejected Innumerable examples could be presented identifying in every case these two characteristics
a program and an objective Statistics also operate in reverse from the measurement of a group of subjects it creates a bar
chart its envelope will be the curve of the random distribution It will give us the average of the values measured if the curve is symmetrical it will tell us that the phenomenon is not influenced by
systematic causes further it will tell us the value of the standard deviation etc
Pier Maria Boria Thermodynamics amp life
26
To fix this thought in our heads let us suppose that we want to study the average height of a
population of people who are male we make many measurements on many subjects creating bars
for every centimeter we will obtain a graph similar to Figure 46
Figure 46 ndash A practical application the Gaussian deduced from experimental measurements for
statistical purposes
In this statistical application where are the program and objective They are there they are
there they were contained in the information which the people naturally had at conception a
matter of genes and of DNA (an observation coherent with ldquoThe Kid Equationrdquo See the
ldquoIntroduction to Hyperspacerdquo12
)
These considerations lead us to think that the meaning of the word ldquochancerdquo commonly given
does not make sense that ldquochancerdquo does not exist and lead us to suspect that Anatole France had an
inspired guess when he said ldquochance is Godrsquos pseudonym when He does not want to sign his
namerdquo
This strongly agrees with what illustrious philosophers have been confirming for centuries
ldquoDeus absconditus estrdquo (Is XLV XV)
12
In our first volume ldquoCaro amico miohelliprdquo ndash Ed Pagine ndash 2010 In our second volume (ldquoVerba volant eqvuationes
manentrdquo) other considerations about a fundamental theorem of Genetics the Hardy Weinberg theorem
Pier Maria Boria Thermodynamics amp life
27
43 CHANCE amp PROBABILITY
We can now summarize some salient functions of Boltzmann and Gauss
Boltzmann
1 Deals with probability regarding the characteristics that can be assumed by many identical particles having a certain number of positions available (Dirac and Fermi deal
with particles which are distinguishable but the correct reference in our observations are the identical particles)
2 The function presents a maximum and aesthetically looks like a Gaussian but it is not symmetrical
3 It has only a single asymptote to the right of the maximum and its minimum at infinity coincides with zero the origin of the reference system
4 It is normalized so that the area subtended represents the total probability of 100
Gauss
1 Deals with chance and is applicable when an objective exists that is defined by a
program
2 The phenomenon ldquopurely by chancerdquo is represented by a curve that is symmetrical
about the axis x=0
3 The Gaussian has a maximum and no minimum at infinity
4 It possesses two asymptotes one to the right and one to the left of the maximum
5 Well defined values of probability can be associated with multiples of the standard deviation
6 It is normalized as for Boltzmannrsquos
44 THE EDDINGTONrsquoS PARADOX13
Eddingtonrsquos famous ldquoInfinite monkey theoremrdquo can be counted amongst the most discussed
paradoxes for the fact that it is often quoted by so called ldquoscientific popularizersrdquo The original assertion states ldquohellipa monkey hitting keys at random on a typewriter keyboard
for an infinite amount of times will almost surely type a given text such as the complete works of
William Shakespearerdquo
Having taken away the condition of an infinite amount of time the paradox remains acceptable
(from the moment we are able to demonstrate that a finite amount of time is sufficient) However
such a long period of time is necessary that the original statement could be seen as an hyperbolic
discussion
We have seen that random phenomena require a program in light of an objective In the case
of the typing monkeys the program could include the elimination of duplicate pages (actually the
identical pages as we will see below) and the objective could consist in the conservation of ldquogoodrdquo
pages arranged in the right sequence
Applying Boltzmannrsquos statistics let us assume that the typewriter has m=30 keys (we can think of ldquoblindrdquo keys without any writing and all identical) and that we want to write a book of
only 106
letters (a thousand typed pages) as we have observed in paragraph 31 all the possible combinations are
13
The reader can find all the details regarding these various arguments on the web
Pier Maria Boria Thermodynamics amp life
C = nm = (10
6)30
= (10)180
In other words there are 10180
possible configurations
Let us assume that the monkeys are capable of striking 10 keyssec (skilled typistshellip) the
time necessary would be
t = 10180
x 106 10 = 10
185 sec
Since we can count 1016 seconds in a billion years it is also possible to say that the time
required will be
10185
1016
= 10169
billion years (giga-years)
(let us remember that the big-bang has an age of ldquoonlyrdquo 14 billion years)
In reality the situation is even ldquoworserdquo in fact this calculation (which is generally accepted)
is wrong because we cannot talk about only thirty objects (the letters punctuation marks spaces between lines etc) to be arranged in 10
6 positions otherwise in each of 10180 configurations
obtainable we would find empty spaces up to 106-30 in each configuration
It is necessary to postulate that there are 106 letters to be arranged like conceding that the
monkeys have to insert 106 objects ie 10
6 key strokes In other words it is necessary that n = m =
106 and in this case the formula of the combinations gives us an astronomical value
6106 )10(===
mm mnC combinations
At a rhythm of 10 key strokes sec the time corresponds to
9899995005000616106 10sec101010)10(
6
equiv=sdotsdot=minust years
Figure 47 ndash Summary table of the probabilities according to Boltzmann
In realty the situation is even ldquoworserdquo still In fact in the calculation of the combinations duplicate configurations are not considered
(which necessarily must be considered as possible) in other words our monkeys could produce the same combinations several times (or two identical pages) anyway the duplications will be useless
in the compilation of our small book of only 106 letters
To this end we invoke chance (to attempt to appreciate the incidence of the repeating of
identical pages) and having constructed a Gaussian by arranging the frequency of identical pages we can reason as follows having produced all the astronomical combinations as above in the time
calculated (which we will call a cycle) the highest probability of identical pages is in pairs (which
Pier Maria Boria Thermodynamics amp life
29
we will assign the maximum position) then in threes and so on At infinity with a probability of
zero all the pages will be identical
It seems fair to presume that the standard deviation could be very large qualifying for a very
flat Gaussian and let us suppose that the pages to be rejected (one for the doubles two for the
triplets etc) are contained within the first standard deviation (as in Figure 48) then the duplicate pages to be thrown away would be about 68
Figure 48 ndash The postulated conditions (pages to be eliminated because they are duplicated equal
to the standard deviation) make 68 of the pages produced useless Iterating the cycle one could
consider the duplication of other pages however it can be demonstrated that the phenomenon
continues to imply finite times
How much does the required time increase to generalize we assume the length of a cycle to be of one unit and we identify with K the average cost of discarded pages (in the previous numerical
case K= 068) and then we observe Figure 49
Figure 49 ndash Having exhausted the first cycle identified by 1 the second of length K allows the
replacement of the duplicate pages produced in the first cycle the third of length K2 is used to
replace those produced in the second cycle and so on
The time necessary to complete the cycles required to eliminate the duplicates as they are produced will be given by the sum
suminfin
=0n
nK
which constitutes a geometric series
The Mathematical Analysis teaches us that such a series converges for 1ltK as is confirmed
in our case where it takes on the value 068
KS
minus=
1
1 and if K = 068 gives 1253
6801
1=
minus=S
Pier Maria Boria Thermodynamics amp life
30
Therefore multiplying by 3125 the time dedicated to complete a cycle (317middot105999989 billion
years) for the hypothesis made we also eliminate all the duplicate pages of our little book of 106
key strokes
Changing the value of K (always lt1) one obtains different multipliers but always of a finite
value let the reader imagine the time necessary to type all of Shakespearersquos works It must be highlighted that the monkey operation to be considered a success requires the
intervention of external intelligence capable of selecting the useful pages (like thought by Theory of
Information) and ordering them in the right sequence to obtain a final legible manuscript this
obvious necessity implies that negative entropy be introduced into the system as covered at the
beginning this is like a living being taking the trouble to ldquoput in orderrdquo otherwise the ldquopurely
randomrdquo work would be entirely useless because it will exclusively produce positive entropy
All experiments attempted by man with the goal of demonstrating the random production of
complex molecules (first building blocks of living organisms) have the defect of requiring an a
priori living system like man to arrange this production
When later chaotic physical-chemical conditions are created (temperature pressure
methane electrical arching etc) hoping to obtain that which Thermodynamics does not permit the
inventors of the moto perpetuo come to mind who never give up
The research on the ldquoprimordial souprdquo belongs to this type of experimentation a battle horse
of the followers of the ldquomaitre agrave penserrdquo of the last century and which regard in particular the laboratory experiments of Stanley Miller the goal of his research of a physical-chemical nature
was to recreate life it was an understandable but too ambitious of a project for a researcher The result was absolutely negative (Miller himself recognized it) however this last piece of information
is only whispered in scientific circles so that we still find genuine touts who speak with enthusiastic coram populo of the primordial soup and its miraculous effects14 with a self-assurance
that is truly shameful
45 CONCLUSION
On 4 July 2007 at the London Kinetics Museum a serious presentation of a perpetual motion
machine was scheduled a machine capable of supplying the user with a power greater than that
absorbed ldquoObviouslyrdquo the presentation was postponed due to ldquoa technical problemrdquo15
It would appear impossible but advocates convinced of such a motion exist and many
inventors submit patent after patent even though still in illo tempore Max Planck declared himself
to be contrary to such a possibility which violates the principles of Thermodynamics
Based on the reasoning we have developed regarding entropy probability and chance the
violation of such principles is implicit even in the attempts to obtain living organisms in a
laboratory (characterized as we have seen as being producers of negative entropy) and as such a
strong analogy can be seen between the advocates of perpetual motion and those aspiring to create
life
1 The correct application of Boltzmannrsquos statistics a phenomenon for which we call on
probability demonstrates that combinations of large numbers of particles to the point of generating complex organisms require very long periods of time in comparison the age of
the universe is but the blink of an eye
2 The probabilities take on the largest numbers in correspondence with the most disordered
configurations
14
From ldquoCorriere della Serardquo october 2008 ldquoLa vita sulla Terra Cominciograve nei vulcani con un innesco chimicordquo 15
-Source Wikipedia
Pier Maria Boria Thermodynamics amp life
3 The most ordered combinations are those which characterize organic structures and the action
of an intelligent being is necessary to select order and conserve in time the favorable
combinations
4 The phrase ldquochance phenomenonrdquo is somewhat less intuitive than what ldquocommon senserdquo
would suggest In fact the Gaussian perspective implies that such phenomena are necessarily
associated with a program this program implies the existence of an objective around which
we have an increased concentration of events
5 In every case it is necessary to postulate the existence of an intelligent design without which
the configurations and the favorable events constitute events without any functional link
between themselves
6 The existence of life as a producer of negative entropy on a continuous basis (not cyclical) is a fact visible with our own eyes
All this leads us to support the existence of a Co-ordinating Entity which possesses life ldquoa
priorirdquo and which is capable of transmitting it to animals (animalis homo included) and vegetation It can be noted that the two living systems animal and vegetable complement each other in the
sense that the design requires that emissions from the first (CO2) are the nutrients for the second and the byproducts of the second (O2) are essential for the first the carbon and oxygen cycles look
like they have been designed According to the author there is only one explanation we are in the presence of the greatest
Design Physicist of all times God the Creator
This is what we call Him as Christians while Israelites call Him Jehovah the Ishmaelites
Allah the Masons GADU (Great Architect of the Universe) etc
In other terms
the Creation is a thermodynamic necessity
Amen
Pier Maria Boria Thermodynamics amp life
5
Figure 14 ndash System to transform gravitational potential energy into mechanical energy of a
motor shaft
Zeuner studied the work obtainable from a thermal motor capable of transforming heat into
work with a Carnot Cycle4 allowing the efficiency of the heatwork transformation to be expressed
exclusively in temperature terms (as opposed to quantity of heat) which leads us to our goal In fact as is widely known the efficiency of the Carnot Cycle is
T
T
T
TT 00 1minus=minus
=η
where T-T0 is the difference in temperature between ldquosourcerdquo and ldquocoolantrdquo
Consequently introducing the quantity of heat Q into the motor the mechanical work L obtainable will be
1 ∆ ∆2
or rather the expression that appears in Figure 4 where the entropy ∆QT is a factor of
proportionality analogous to the weight P where the change in height ∆H corresponds to the change in temperature ∆T which the motor is able to produce (from ∆rdquoT lt ∆rsquoT one has in
proportion LrdquoltLrsquo with the consequence that the residual internal energy after being depleted and not able to be transformed into work will be Urdquo gt Ursquo)
We can observe that a functional tie exists between Q and T such that by increasing Q T is
increased in direct proportion (considering as constant the specific heat of the mass which runs the
cycle with no latent heat exchange) and therefore given a particular initial entropy the work
obtainable depends exclusively on the ∆T achievable
A motor which expels heat at a lower temperature produces more mechanical work at equal
ldquoconsumptionrdquo this is the purpose of the comparison between the two thermal motors in Figure 15
4 A car run on petrol will produce an Otto Cycle one on diesel a Diesel Cycle an exothermic motor will produce a Rankin
Cycle etc
Pier Maria Boria Thermodynamics amp life
6
Figure 15 ndash Comparison between the mechanical work obtained from two identical thermal motors
functioning according to the Carnot cycle for two different exhaust temperatures
(T0rdquo in case A and T0rsquo in case B)
The point of view seen above and resumed in equation 2) seems favorable to the presence of
high values of entropy tout court to avoid erroneous generalizations it needs remember that Gibbs
says that the maximum energetic gain in thermal transformations that is to obtain the maximum
ldquofree energyrdquo G is to exploit the total energy (enthalpy) H of the active mass minimizing the
entropy at discharge In fact the Gibbs equation states that
2 3 ∙ ∆
where H represents the entalpy of the mass transformed
We stress that it is necessary to compare two cases with identical initial temperature (as in
Figure 41) and to consider that it is the factor ∆T which determines the efficiency of the transformation5
Sea water contains an enormous amount of thermal energy but at a temperature T (of the source) very near to T0 (that of the coolant) in other words rendering unusable the heat it contains
we can state that sea water contains a ldquolargerdquo amount of thermal energy but no practical possibility of making a thermal motor work (the thermal difference available is ldquopractically nilrdquo)
Exactly for this reason a boiler which burns a combustible fossil material capable of achieving ldquohighrdquo temperatures enabling it to provide water at 90 degC is to be considered the perpetrator of a
grave ldquothermodynamic crimerdquo That combustible could be used with more results for example in a
cogeneration plant where water at low temperature is a ldquowasterdquo product
5 Sources at high temperature are necessary to produce thermodynamic cycles with acceptable results Our car be it Otto
or Diesel develops a temperature of around 1500 degC in the combustion chamber and give us a mechanical efficiency at the
wheels of about 35 (approx 30 remains ldquointernal energyrdquo and is expelled to the exhaust The coolant temperature is
that of the atmosphere the remainder is transformed into heat by thermal loss and passive resistances and is dispersed
mainly by the radiator)
Pier Maria Boria Thermodynamics amp life
7
14 ENTROPY AND LIFE
Livio Gratton (Italian cosmologist from Trieste died in 1991 and considered the father of
Italian Astrophysics) observed that the phenomenon ldquoliferdquo contains something singular which does
not fit in with the mechanism described up to this point The appearance of life in an electromagnetically structured universe constitutes a singular moment which cannot be explained
technically In fact an organism is alive when within itself it produces transformations of negative
entropy (that is with ∆Slt0) which contradicts the second principle Let us observe a plant seed if it is alive in conditions expected in nature it germinates
spontaneously and grows capturing carbon from the atmosphere giving body to the plant and releasing oxygen through chlorophyll synthesis
A small wheat seedling recently sprouted amongst the snow germinates and grows warming itself up at the expense of the ground (who has not observed the molten snow round the seedling
The seedlings under a thin blanket of snow poke out and are clearly visible green seedlings on a
white blanket in the middle of a dark patch of earth free from that which surrounds them)
Naturally if we were to also consider the interaction of the plant with the quanta of solar
energy and the surrounding minerals we would find that the sum of transformations has generated
positive entropy (the affirmation that the entropy of the universe tends to increase without limits is
correct)
A living animal organism should it be injured is capable of healing itself the vis vitalis as
our ancestors called it produces such an effect while a dead animal organism remains injured and
decomposes with the passing of time (increase of disorder)
One could consider the possibility of turning to entropy to define the state of life or death
about which we periodically debate even in practical cases (Terry Schiavo Eluana Englarohellip) if the organism produces negative entropy it is alive in the opposite case it is nothellip
One could also suggest a crude experimental procedure of a slightly Hitlerian nature which would settle the matter once and for all consisting of injuring an organism that has a dubious state
of life to verify its reactions in one entropic direction or the otherhellip The vis vitalis departs even if all the mechanical organs would be perfectly functional we can
think of the so called cardiac arrest (a phrase that could be a savior for the corner of the art of medicine) One could certainly object that the arrest is the cause while the departure of the vis
vitalis is the effect who knows The only certainty is that with death an irreversible process starts with the production of positive entropy and we fall back into line with the second principle
In conclusion it can be said that the property of entropy is that of an increase in every
transformation that can be performed practically (like saying in every irreversible transformation)
except in the case of living organisms
How to produce heating of the plant at the expense of the surrounding masses and to increase
the order of the molecules to the point of ldquoforcingrdquo the carbon taken from the most formless state in
existence (that of gaseous CO2) to take on the shape of a trunk giving rise to transformations of
decreasing entropy
Also an ordinary refrigerator can produce a local decrease of entropy expending some
energy in the following figure we represent the energy transformations occurring in it at the end of
the transformation we have the temperatures marked with an asterisk after the energy Q leaves the
cool body to join the warmest body with the energy Q3 that is needed for the refrigerator to run6
6 The ratio (Q2+Q+Q3)Q3 is the widely known COP (Coefficient Of Performance) of the heat pumps
Pier Maria Boria Thermodynamics amp life
Figure 16 ndash Heat pumping in a refrigerator
In this sketch the external energy Q3 appears essential and the system is open the energy Q
increase its entropy gaining the temperature T2 entering the condensator Restarting the numerical example of the Clausius calorimeter we reconfirm Q=50 J as the
heat exchanged in this condition it is easy to verify that the water temperature decreases by 10 K while the copper increases by 90 K
Assuming COP=3 we have
final temperature of water T1 = 290 K
and for the copper T2 = 490+903 = 520 K
proceeding as above it follows that
for the copper
∆ 520400 0 5 ∙ 004 002
(
for the water
∆ 290300 5 ∙ 0034 0170
(
Therefore the quantity of transformed heat Q is subject to the variation
∆ ∆ + ∆ 002 0170 015 lt 0 ( ∶
thanks to the contribution of the external energy Q3 the exchanged heat decreases its entropy
Now we will see in what way nature does the heat pumping
Pier Maria Boria Thermodynamics amp life
9
Part 2 (of 4) Boltzmannrsquos Distribution
21 THE BOLTZMANNrsquoS DISTRIBUTION
We will reply to the question after having examined the second pillar on which we base this paper Boltzmannrsquos Distribution (Ludwig Boltzmann Austria 1844-1906)
As can also be seen in excellent web pages the disorganized vibrational velocity of the molecules of a gas (but also those of liquids and solids) at a given temperature take on values
which are continuously and randomly variable following a particular distribution represented graphically in Figure 21
Figure 21 ndash Probability distribution of the velocity of molecules of a gas as a function
of the velocity itself according to Boltzmannrsquos Statistic
It is thanks to this distribution discovered by Boltzmann that living nature vegetable and animal can perform local transformations with decreasing entropy the great masters have
thought up theoretical experiments based on devices capable of selecting molecules of colder gas having higher velocities than what is thought to be the average velocity of the molecules of the
warmer gas (Maxwell the demon Polvani the choosing porter Amerio the selecting valve) to allow them to pass from a lower temperature environment to another adjacent environment with
higher temperature in this way obtaining a transformation which locally invalidates the second
principle of thermodynamics
In Figure 22 it is possible to see that at every average velocity (considered) of the ldquowarmrdquo
molecules one can find a corresponding branch of the ldquocoldrdquo curve related to those particles that
should they pass to the warmer side could cause an increase in that average velocity and therefore
of the temperature
Pier Maria Boria Thermodynamics amp life
10
Figure 22 ndashThe Maxwell demon allows the passage from the colder to the warmer
environment only of the molecules which have a velocity higher than the
weighted average velocity of the warmer molecules
It is necessary to perform a sorting of the molecules one by one with mechanical means not
available to man while the experimental observations of the type reported above would suggest
that nature is capable of it operating at a molecular level in the realm of living organisms
In Figure 23 is represented the device which allows the ldquotheoretical experimentrdquo in the form
proposed by Prof Amerio of the Polytechnic of Milano (1955) Maxwell had proposed a ldquodemonrdquo
as selector of the molecules (1867) the selection device has been the object of particular attention
on the part of Szilard (1929) and later Bennet (1981) with the scope of correctly counting the
variation of entropy in the test universe and calculate the required energy for the selection
Figure 23 ndash The selective valve allows the passage from the colder to the warmer
environment only of the molecules which have a velocity higher than the
weighted average velocity of the warmer molecules as shown in Fig 22
Pier Maria Boria Thermodynamics amp life
These elementary applications of classic thermodynamics based on the concept of entropy
and on Bolzmannrsquos Distribution suggest to us that the phenomenon ldquoliferdquo is to be associated with a
ldquovis-vitalisrdquo external to the dissipative mechanism for which we have ample and daily experience
Obviously it is impossible for man to build a Maxwell device but in our research we have
found a very interesting observation by Jaques Monod (Nobel Prize in 1965) that confers the part of
demon to the natural enzymes7
According to this point of view we can convert the Figure 16 as follows
Figure 24 ndash The natural heat pumping performed by enzymes
and this sketch we consider as typical of the phenomenon ldquoliferdquo The role played by the vis-vitalis seems essential because the only electro-chemical energy
associated with enzymes are components easily deliverable in the biological laboratories but
nobody has been able to start life from these components8
There are those who attempt an approach to this argument with improper methods and with
arbitrary applications of the concept of probability which leads to theories that are devoid of the
required respect for a sound scientific doctrine
22 CONCLUSIONS FROM THE FIRST AND SECOND PART
Rivers of ink have been written about the origin of life to the point that it is possible to read
about the most bizarre theories that completely ignore that which is suggested by the Queen of
Physics Thermodynamics
Paleontology Biology extraterrestrials UFOs Cosmic Palingenesis and similar are all
stirred numbers equations concepts of probability principles of conservation etc are not used
7 Le hazard et la neacutecessiteacute 1970 ndash Arnoldo Mondadori Editore Spa ndash Milan ndash Pag 58
8 See the Stanley Miller experiment at the end of paragraph 54
Pier Maria Boria Thermodynamics amp life
12
correctly These are the only foundations possible for a correctly stated scientific discussion (there
is no adjective more abused than the term ldquoscientificrdquo)
The reader could (perhaps on a rainy Sunday) do some research on the ldquoprimordialrdquo soup (but
if it is not Knorr for whorsquos brand modestly in youth we made thermodynamics projects does not
taste good) on the ldquocosmic tankrdquo on the ldquotyping monkeysrdquo on the cycle of carbon and oxygen (in relation to the demonization of CO2) on the hydrological cycle (which is a substance that cannot
be ldquoconsumedrdquo as is currently heard said otherwise what cycle would it complete subjects often treated by substituting Science with ideology and making ample use of the principle of superior
authority (the ipse dixit of historical memory) upholding disjointed dogma but which are
politically correct
Sometimes one has the feeling of witnessing the squalid discourse of gossiping women by the fountain
It can be noted that in the observations made up to now we have practically not talked about energy whorsquos role in the economy of our discourse has been secondary Itrsquos the definition of the
entropy index state which changes the way to view the cosmos we would not talk of it if it were
possible to carry out reversible reactions
We would come to suspect that the irreversibility is a ldquodefectrdquo of the cosmos having the
function of forcing it to a gradual entropic enrichment (and therefore to a degeneration of energy)
such that the final form of all the energy available becomes one that is thermally and entropically
unusable therefore by virtue of what has been discussed at a certain point in the evolution of the
universe at a finite time it will not be possible to practically perform any thermodynamic cycle9
That is to say the thermal death of the universe
9 We will be further willing to suspect a decay of the cosmological properties correlated to the original sin Ah free
thought
Pier Maria Boria Thermodynamics amp life
13
Part 3 (of 4) Probability
31 PROBABILITY IN BOLTZMANNrsquoS STATISTICS
Boltzmann obtained the graph of the probability as a function of temperature postulating that
a certain number m of particles which are indistinguishable from each other (which we will call A
B C M) and a number n of possible states (a b c n) in which one or more particles (even if
m) can find themselves the presence of particles in each state could occur with different possibilities
If the identical particles are free to occupy the various states (as in the case of a gas) these could continuously exchange states between themselves (for example thanks to reciprocal impacts
as in Figure 23) whilst ldquoon averagerdquo maintaining a certain distribution subject to the conditions around them (for example temperature) a certain distribution of the possible configurations would
be typical of such conditions
Continuing with this example if by state of the particles we mean possessing a certain amount
of kinetic energy E associated with each molecule of a gas in a certain interval of values of energy
∆E there will be a stable quantity of molecules even if amongst themselves continues exchanges of
energy occur Therefore in the range of the same interval some particles enter and some leave
If for the sake of imagination in what follows particles will be considered as ldquoballsrdquo and
states as levels of energy the balls will represent the particles while the levels will represent an
interval of energy (∆E)
Let us start with a very simple case consisting of 3 particles (m=3) able to be hosted by two
levels (n=2) as illustrated in Figure 31
In the left column we see all the possible combinations In the central section we see that certain combinations repeat themselves in such a way that if the particles become indistinguishable
(column 3) they are to be considered the same amongst themselves Therefore three possibilities exist such that both the combinations 234 and 567 can occur
and only once for the combinations 1 and 8 If we ldquonormalizerdquo the possibility (expressing it in unitary or percentage terms) it assumes the
role of probability (ratio between favorable cases and possible cases) which we have done in the last column by expressing it in percentage terms as is common practice
Pier Maria Boria Thermodynamics amp life
14
Figure 31 ndash A rather simple case to demonstrate how given m=3 and n=2 it is possible to
have different probabilities for each combination
Pier Maria Boria Thermodynamics amp life
15
This allows us to draw the graph of Figure 32 where we can begin to see the
Boltzmann distribution forming
Figure 32 ndash The embryonic Boltzmann diagram increasing particles and the number of
possible states the envelope of the columns (in this particular case not yet)
acquires the characteristic asymmetric bell shape
Following in the footsteps of the great Ludwig we enter into systems which are numerically
more substantial three combinations of seven states with an arbitrary arrangement of four particles
as represented in Figure 33 the three combinations are equivalent because the particles are
indistinguishable by hypothesis
Pier Maria Boria Thermodynamics amp life
16
Figure 33 - The three configurations are equivalent if the four particles are indistinguishable
amongst themselves
Each of the n states can be associated with A B C etc (that is to each or more of the m
particles) and since a single particle can occupy each time a different state (and other particles
other states) m times the possible combinations C are ntimesntimesntimeshelliptimesn (m factors equal to n)
C = nm
We could also be convinced observing for example Figure 34 where it is assumed that n=5
(it looks like a musical stavehellip) and m=2 particles (therefore 52=25 combinations)
Pier Maria Boria Thermodynamics amp life
Figure 34 ndash Beyond the 25th beat the preceding configurations are repeated because A and B are
indistinguishable Within the range of the 25 possible configurations some are more favored
because they appear more frequently for example 6 and 22 9 and 25 etc The unoccupied
states are identified by a circle
As is fair to expect configuration 1 is least favored
Pier Maria Boria Thermodynamics amp life
18
We can arrive at the same result with a more practical method suitable also for very large
values of n and m which we will use as follows
It consists of a tabular method stolen from Combinatorial Analysis where for n and m equal to
various units it avoids the need to write hundreds or thousands of key strokes as used above
Let us take two rows and as many columns as there are states thereby obtaining a grid in
Figure 35 to verify what has been said above we have taken 2 rows and 5 columns (n=2 m=5)
Figure 35- With this grid we obtain the number of possible configurations
To further demonstrate we will build a grid for n=5 and m=4 as in Figure 36 where there are sufficient rows to progressively expose the number of particles (from 4 to 1 in the first box of
the first column of the occupancy numbers) and there are n columns
Pier Maria Boria Thermodynamics amp life
19
Figure 36 - Since 54= 625 there are 625 possible combinations the relative probabilities are
listed in the last column note the asymmetry
Pier Maria Boria Thermodynamics amp life
20
It is necessary to observe that in the figure the table of numbers of occupancy reminds
us not by chance of Tartagliarsquos Triangle while the Boltzmann type diagram that can be
associated shown in Figure 37 takes on an almost familiar shape
Figure 37 - Graphical representation of Figure 62 the bars are asymmetric
Pier Maria Boria Thermodynamics amp life
21
To provide an example and referring to Figure 36 we can see how it is possible to obtain 80
possibilities corresponding to his second line
If a box is occupied by 3 particles out of an available 4 the simple combinations of 4 objects
with 3 by 3 (as taught by the Combinatorial Analysis) are given by the binomial coefficient
6437 4
and the four possible groups of three numbers have five positions from which to choose From here 4times5=20 possibilities for the group of three numbers
The single remaining particle has the possibility of the four remaining locations and therefore has 1times4=4 possibilities
The product 20times4=80 gives us the total possibilities in the case that the particles arrange themselves in two groups one with three and one with a single particle and having five boxes
suitable It is easy to verify that we will obtain the same result considering first the single particle
having five boxes suitable (five possibilities 1x5=5) and after the three having the four remaining
(one is occupied by the single particle therefore 4x4=16 and 5x16=80)
Applying the procedure line by line it produces the results shown
Pier Maria Boria Thermodynamics amp life
22
Part 4 (of 4) Chance
41 CHANCE
A sharp-shooter shoots at a target with an excellent rifle he aims carefully chooses the
moment when his breathing will not interfere and the amount of force with which to pull the trigger so as not to move the barrel fires the shot and hits the bullrsquos-eye
Immediately afterwards he takes all the same precautions but the shot ends up being slightly off target it could have been a slight disturbance to his sight an involuntary variation in his
breathing an imperceptible abnormal movement of the finger a very slight unpredictable wind or who knows what else
The causes are many and imponderable slight if each is considered in itself but interacting differently each time ensuring that each shot has a different fate
This complex of innumerable causes of disturbance which are not controllable or predictable
and which not being able to take each into account one by one are called the Law of Probability
(Gaussrsquos Law)10
Probability for the reasons given and law thanks to Carl Friedrich Gauss (1777-1855) who
wrote an equation capable of taking into consideration in a global manner all those fleeting causes
so as to be able to predict with near accurate approximation how the shots will arrange themselves
percentage wise round the target with different distances from the bullseye The approximation will
be more accurate the greater the number of shots that are fired
Let us assume that the target is as represented in Figure 41 and is divided into two parts by
means of the section AB and that our sharpshooter fires many shots after which we count the
number of shots which hit the target in each half
Figure 41- The segmented target
If the reasons for the error are truly random (rifle without defects such that it does not tend to
deviate the shot systematically and neither does the sharpshooter have an analogous defect there is
10
The example of the sharpshooter was published by Engineer Mario Manaira in Ndeg 256 of ldquoJournal of Mechanicsrdquo
together with our first article concerning thermodynamics more than half a century ago (1961)
Pier Maria Boria Thermodynamics amp life
23
not a steady wind etc in other words there does not exist a cause which always influences with the
same bias called a systematic cause) we could note the following
1 The shots will be greater in number in the first band round the center
2 The shots will progressively decrease in number in the subsequent bands as these distance themselves further from the center until there are very few in the bands furthest away
3 The shots in the two halves right and left in any similar band will tend to have the same number and will even be identical if sufficient shots are fired
It is therefore possible to represent the phenomenon graphically as in the following figure
Figure 42 ndash The random distribution of the shots in each band and the Gaussian distribution that
would be obtained with an infinite number of shots fired
If the marksman were less capable the concentration of shots near the zero on the abscissa would reduce and the curve would flatten itself while maintaining the characteristics given and
represented in Figure 43 The first observation is that the maximum height of the curve constitutes the ldquotargetrdquo in other words the goal of the operation while the absence of systematic causes (in
antithesis of randomness) ensures the symmetry of the curve with respect to the vertical which
represents our target zero
Pier Maria Boria Thermodynamics amp life
24
Figure 43 - If the marksman is less skilled the Gaussian flattens
In the case of a systematic cause of error the curve loses its symmetry if we assume that the
test is performed with a constant wind from left to right the graph will take on the shape of Figure
44
Figure 44 ndash When the Gaussian is asymmetric it implies that the phenomenon is not ldquoentirely
randomrdquo11
Let us suppose now that our sharpshooter is blindfolded the target becomes very large and is
moved he will have to shoot blindly (randomly) left and right high and low Given that the Gauss
11
Gauss suggests that the analytical expression of the Law of Randomness is the function
2xey minus
=
where it can be seen that the curve is symmetrical with respect to the axis x=0 and decreasing both towards the left and
right of this line and has a maximum for x=0
It can be shown further that the area subtended is
π=int+infin
infinminus
minusdxe
x2
To ensure that this area is equal to unity as opposed to π appropriate steps can be taken which without
changing the general properties illustrated give the normalized Gaussrsquos Law
Pier Maria Boria Thermodynamics amp life
function still applies the probability curve will flatten itself maintaining the essential
characteristics in particular the two tails which will tend towards a tangent with the abscissa
tending towards infinity a maximum point a point of inflection and the other characteristics
illustrated in Figure 45
Figure 45 ndash Typical characteristics of a normalized Gaussian
Supposing once more that the Gauss function still applies it would be logical to expect a distribution with a curve that is so flat that it will be difficult to see a maximum point corresponding
to the center of the target it will be necessary to fire enough shots so as to occupy every position on the abscissa and to have hit with 100 certainty the bullrsquos-eye
This implies that everything is possible as long as an infinite number of shots are available
(using rhetorical language)
42 SOME PROPERTIES OF RANDOM EVENTS
The perplexities regarding the applicability of chance as referred to the blind sharpshooter
depend on the fact that the Gaussian assumes that programming has been applied to reach an
objective which implies that the operator is conscious of the objective an element which in this
case is absent
Both the existence of a program (the sharpshooter sets out to hit the bullrsquos-eye) and the
existence of an objective (the card with circles) appear to be essential to be able to talk about
chance
Another example let us imagine a machine programmed to produce a certain mechanical
piece the program is the design of the piece written in machine language and the objective is the production of the piece In mass production we will find that it is the case that despite the work
conditions being maintained the same each piece will be different to the other to the point that the pieces which exceed the tolerances (which would not allow them to be interchangeable) will be
rejected Innumerable examples could be presented identifying in every case these two characteristics
a program and an objective Statistics also operate in reverse from the measurement of a group of subjects it creates a bar
chart its envelope will be the curve of the random distribution It will give us the average of the values measured if the curve is symmetrical it will tell us that the phenomenon is not influenced by
systematic causes further it will tell us the value of the standard deviation etc
Pier Maria Boria Thermodynamics amp life
26
To fix this thought in our heads let us suppose that we want to study the average height of a
population of people who are male we make many measurements on many subjects creating bars
for every centimeter we will obtain a graph similar to Figure 46
Figure 46 ndash A practical application the Gaussian deduced from experimental measurements for
statistical purposes
In this statistical application where are the program and objective They are there they are
there they were contained in the information which the people naturally had at conception a
matter of genes and of DNA (an observation coherent with ldquoThe Kid Equationrdquo See the
ldquoIntroduction to Hyperspacerdquo12
)
These considerations lead us to think that the meaning of the word ldquochancerdquo commonly given
does not make sense that ldquochancerdquo does not exist and lead us to suspect that Anatole France had an
inspired guess when he said ldquochance is Godrsquos pseudonym when He does not want to sign his
namerdquo
This strongly agrees with what illustrious philosophers have been confirming for centuries
ldquoDeus absconditus estrdquo (Is XLV XV)
12
In our first volume ldquoCaro amico miohelliprdquo ndash Ed Pagine ndash 2010 In our second volume (ldquoVerba volant eqvuationes
manentrdquo) other considerations about a fundamental theorem of Genetics the Hardy Weinberg theorem
Pier Maria Boria Thermodynamics amp life
27
43 CHANCE amp PROBABILITY
We can now summarize some salient functions of Boltzmann and Gauss
Boltzmann
1 Deals with probability regarding the characteristics that can be assumed by many identical particles having a certain number of positions available (Dirac and Fermi deal
with particles which are distinguishable but the correct reference in our observations are the identical particles)
2 The function presents a maximum and aesthetically looks like a Gaussian but it is not symmetrical
3 It has only a single asymptote to the right of the maximum and its minimum at infinity coincides with zero the origin of the reference system
4 It is normalized so that the area subtended represents the total probability of 100
Gauss
1 Deals with chance and is applicable when an objective exists that is defined by a
program
2 The phenomenon ldquopurely by chancerdquo is represented by a curve that is symmetrical
about the axis x=0
3 The Gaussian has a maximum and no minimum at infinity
4 It possesses two asymptotes one to the right and one to the left of the maximum
5 Well defined values of probability can be associated with multiples of the standard deviation
6 It is normalized as for Boltzmannrsquos
44 THE EDDINGTONrsquoS PARADOX13
Eddingtonrsquos famous ldquoInfinite monkey theoremrdquo can be counted amongst the most discussed
paradoxes for the fact that it is often quoted by so called ldquoscientific popularizersrdquo The original assertion states ldquohellipa monkey hitting keys at random on a typewriter keyboard
for an infinite amount of times will almost surely type a given text such as the complete works of
William Shakespearerdquo
Having taken away the condition of an infinite amount of time the paradox remains acceptable
(from the moment we are able to demonstrate that a finite amount of time is sufficient) However
such a long period of time is necessary that the original statement could be seen as an hyperbolic
discussion
We have seen that random phenomena require a program in light of an objective In the case
of the typing monkeys the program could include the elimination of duplicate pages (actually the
identical pages as we will see below) and the objective could consist in the conservation of ldquogoodrdquo
pages arranged in the right sequence
Applying Boltzmannrsquos statistics let us assume that the typewriter has m=30 keys (we can think of ldquoblindrdquo keys without any writing and all identical) and that we want to write a book of
only 106
letters (a thousand typed pages) as we have observed in paragraph 31 all the possible combinations are
13
The reader can find all the details regarding these various arguments on the web
Pier Maria Boria Thermodynamics amp life
C = nm = (10
6)30
= (10)180
In other words there are 10180
possible configurations
Let us assume that the monkeys are capable of striking 10 keyssec (skilled typistshellip) the
time necessary would be
t = 10180
x 106 10 = 10
185 sec
Since we can count 1016 seconds in a billion years it is also possible to say that the time
required will be
10185
1016
= 10169
billion years (giga-years)
(let us remember that the big-bang has an age of ldquoonlyrdquo 14 billion years)
In reality the situation is even ldquoworserdquo in fact this calculation (which is generally accepted)
is wrong because we cannot talk about only thirty objects (the letters punctuation marks spaces between lines etc) to be arranged in 10
6 positions otherwise in each of 10180 configurations
obtainable we would find empty spaces up to 106-30 in each configuration
It is necessary to postulate that there are 106 letters to be arranged like conceding that the
monkeys have to insert 106 objects ie 10
6 key strokes In other words it is necessary that n = m =
106 and in this case the formula of the combinations gives us an astronomical value
6106 )10(===
mm mnC combinations
At a rhythm of 10 key strokes sec the time corresponds to
9899995005000616106 10sec101010)10(
6
equiv=sdotsdot=minust years
Figure 47 ndash Summary table of the probabilities according to Boltzmann
In realty the situation is even ldquoworserdquo still In fact in the calculation of the combinations duplicate configurations are not considered
(which necessarily must be considered as possible) in other words our monkeys could produce the same combinations several times (or two identical pages) anyway the duplications will be useless
in the compilation of our small book of only 106 letters
To this end we invoke chance (to attempt to appreciate the incidence of the repeating of
identical pages) and having constructed a Gaussian by arranging the frequency of identical pages we can reason as follows having produced all the astronomical combinations as above in the time
calculated (which we will call a cycle) the highest probability of identical pages is in pairs (which
Pier Maria Boria Thermodynamics amp life
29
we will assign the maximum position) then in threes and so on At infinity with a probability of
zero all the pages will be identical
It seems fair to presume that the standard deviation could be very large qualifying for a very
flat Gaussian and let us suppose that the pages to be rejected (one for the doubles two for the
triplets etc) are contained within the first standard deviation (as in Figure 48) then the duplicate pages to be thrown away would be about 68
Figure 48 ndash The postulated conditions (pages to be eliminated because they are duplicated equal
to the standard deviation) make 68 of the pages produced useless Iterating the cycle one could
consider the duplication of other pages however it can be demonstrated that the phenomenon
continues to imply finite times
How much does the required time increase to generalize we assume the length of a cycle to be of one unit and we identify with K the average cost of discarded pages (in the previous numerical
case K= 068) and then we observe Figure 49
Figure 49 ndash Having exhausted the first cycle identified by 1 the second of length K allows the
replacement of the duplicate pages produced in the first cycle the third of length K2 is used to
replace those produced in the second cycle and so on
The time necessary to complete the cycles required to eliminate the duplicates as they are produced will be given by the sum
suminfin
=0n
nK
which constitutes a geometric series
The Mathematical Analysis teaches us that such a series converges for 1ltK as is confirmed
in our case where it takes on the value 068
KS
minus=
1
1 and if K = 068 gives 1253
6801
1=
minus=S
Pier Maria Boria Thermodynamics amp life
30
Therefore multiplying by 3125 the time dedicated to complete a cycle (317middot105999989 billion
years) for the hypothesis made we also eliminate all the duplicate pages of our little book of 106
key strokes
Changing the value of K (always lt1) one obtains different multipliers but always of a finite
value let the reader imagine the time necessary to type all of Shakespearersquos works It must be highlighted that the monkey operation to be considered a success requires the
intervention of external intelligence capable of selecting the useful pages (like thought by Theory of
Information) and ordering them in the right sequence to obtain a final legible manuscript this
obvious necessity implies that negative entropy be introduced into the system as covered at the
beginning this is like a living being taking the trouble to ldquoput in orderrdquo otherwise the ldquopurely
randomrdquo work would be entirely useless because it will exclusively produce positive entropy
All experiments attempted by man with the goal of demonstrating the random production of
complex molecules (first building blocks of living organisms) have the defect of requiring an a
priori living system like man to arrange this production
When later chaotic physical-chemical conditions are created (temperature pressure
methane electrical arching etc) hoping to obtain that which Thermodynamics does not permit the
inventors of the moto perpetuo come to mind who never give up
The research on the ldquoprimordial souprdquo belongs to this type of experimentation a battle horse
of the followers of the ldquomaitre agrave penserrdquo of the last century and which regard in particular the laboratory experiments of Stanley Miller the goal of his research of a physical-chemical nature
was to recreate life it was an understandable but too ambitious of a project for a researcher The result was absolutely negative (Miller himself recognized it) however this last piece of information
is only whispered in scientific circles so that we still find genuine touts who speak with enthusiastic coram populo of the primordial soup and its miraculous effects14 with a self-assurance
that is truly shameful
45 CONCLUSION
On 4 July 2007 at the London Kinetics Museum a serious presentation of a perpetual motion
machine was scheduled a machine capable of supplying the user with a power greater than that
absorbed ldquoObviouslyrdquo the presentation was postponed due to ldquoa technical problemrdquo15
It would appear impossible but advocates convinced of such a motion exist and many
inventors submit patent after patent even though still in illo tempore Max Planck declared himself
to be contrary to such a possibility which violates the principles of Thermodynamics
Based on the reasoning we have developed regarding entropy probability and chance the
violation of such principles is implicit even in the attempts to obtain living organisms in a
laboratory (characterized as we have seen as being producers of negative entropy) and as such a
strong analogy can be seen between the advocates of perpetual motion and those aspiring to create
life
1 The correct application of Boltzmannrsquos statistics a phenomenon for which we call on
probability demonstrates that combinations of large numbers of particles to the point of generating complex organisms require very long periods of time in comparison the age of
the universe is but the blink of an eye
2 The probabilities take on the largest numbers in correspondence with the most disordered
configurations
14
From ldquoCorriere della Serardquo october 2008 ldquoLa vita sulla Terra Cominciograve nei vulcani con un innesco chimicordquo 15
-Source Wikipedia
Pier Maria Boria Thermodynamics amp life
3 The most ordered combinations are those which characterize organic structures and the action
of an intelligent being is necessary to select order and conserve in time the favorable
combinations
4 The phrase ldquochance phenomenonrdquo is somewhat less intuitive than what ldquocommon senserdquo
would suggest In fact the Gaussian perspective implies that such phenomena are necessarily
associated with a program this program implies the existence of an objective around which
we have an increased concentration of events
5 In every case it is necessary to postulate the existence of an intelligent design without which
the configurations and the favorable events constitute events without any functional link
between themselves
6 The existence of life as a producer of negative entropy on a continuous basis (not cyclical) is a fact visible with our own eyes
All this leads us to support the existence of a Co-ordinating Entity which possesses life ldquoa
priorirdquo and which is capable of transmitting it to animals (animalis homo included) and vegetation It can be noted that the two living systems animal and vegetable complement each other in the
sense that the design requires that emissions from the first (CO2) are the nutrients for the second and the byproducts of the second (O2) are essential for the first the carbon and oxygen cycles look
like they have been designed According to the author there is only one explanation we are in the presence of the greatest
Design Physicist of all times God the Creator
This is what we call Him as Christians while Israelites call Him Jehovah the Ishmaelites
Allah the Masons GADU (Great Architect of the Universe) etc
In other terms
the Creation is a thermodynamic necessity
Amen
Pier Maria Boria Thermodynamics amp life
6
Figure 15 ndash Comparison between the mechanical work obtained from two identical thermal motors
functioning according to the Carnot cycle for two different exhaust temperatures
(T0rdquo in case A and T0rsquo in case B)
The point of view seen above and resumed in equation 2) seems favorable to the presence of
high values of entropy tout court to avoid erroneous generalizations it needs remember that Gibbs
says that the maximum energetic gain in thermal transformations that is to obtain the maximum
ldquofree energyrdquo G is to exploit the total energy (enthalpy) H of the active mass minimizing the
entropy at discharge In fact the Gibbs equation states that
2 3 ∙ ∆
where H represents the entalpy of the mass transformed
We stress that it is necessary to compare two cases with identical initial temperature (as in
Figure 41) and to consider that it is the factor ∆T which determines the efficiency of the transformation5
Sea water contains an enormous amount of thermal energy but at a temperature T (of the source) very near to T0 (that of the coolant) in other words rendering unusable the heat it contains
we can state that sea water contains a ldquolargerdquo amount of thermal energy but no practical possibility of making a thermal motor work (the thermal difference available is ldquopractically nilrdquo)
Exactly for this reason a boiler which burns a combustible fossil material capable of achieving ldquohighrdquo temperatures enabling it to provide water at 90 degC is to be considered the perpetrator of a
grave ldquothermodynamic crimerdquo That combustible could be used with more results for example in a
cogeneration plant where water at low temperature is a ldquowasterdquo product
5 Sources at high temperature are necessary to produce thermodynamic cycles with acceptable results Our car be it Otto
or Diesel develops a temperature of around 1500 degC in the combustion chamber and give us a mechanical efficiency at the
wheels of about 35 (approx 30 remains ldquointernal energyrdquo and is expelled to the exhaust The coolant temperature is
that of the atmosphere the remainder is transformed into heat by thermal loss and passive resistances and is dispersed
mainly by the radiator)
Pier Maria Boria Thermodynamics amp life
7
14 ENTROPY AND LIFE
Livio Gratton (Italian cosmologist from Trieste died in 1991 and considered the father of
Italian Astrophysics) observed that the phenomenon ldquoliferdquo contains something singular which does
not fit in with the mechanism described up to this point The appearance of life in an electromagnetically structured universe constitutes a singular moment which cannot be explained
technically In fact an organism is alive when within itself it produces transformations of negative
entropy (that is with ∆Slt0) which contradicts the second principle Let us observe a plant seed if it is alive in conditions expected in nature it germinates
spontaneously and grows capturing carbon from the atmosphere giving body to the plant and releasing oxygen through chlorophyll synthesis
A small wheat seedling recently sprouted amongst the snow germinates and grows warming itself up at the expense of the ground (who has not observed the molten snow round the seedling
The seedlings under a thin blanket of snow poke out and are clearly visible green seedlings on a
white blanket in the middle of a dark patch of earth free from that which surrounds them)
Naturally if we were to also consider the interaction of the plant with the quanta of solar
energy and the surrounding minerals we would find that the sum of transformations has generated
positive entropy (the affirmation that the entropy of the universe tends to increase without limits is
correct)
A living animal organism should it be injured is capable of healing itself the vis vitalis as
our ancestors called it produces such an effect while a dead animal organism remains injured and
decomposes with the passing of time (increase of disorder)
One could consider the possibility of turning to entropy to define the state of life or death
about which we periodically debate even in practical cases (Terry Schiavo Eluana Englarohellip) if the organism produces negative entropy it is alive in the opposite case it is nothellip
One could also suggest a crude experimental procedure of a slightly Hitlerian nature which would settle the matter once and for all consisting of injuring an organism that has a dubious state
of life to verify its reactions in one entropic direction or the otherhellip The vis vitalis departs even if all the mechanical organs would be perfectly functional we can
think of the so called cardiac arrest (a phrase that could be a savior for the corner of the art of medicine) One could certainly object that the arrest is the cause while the departure of the vis
vitalis is the effect who knows The only certainty is that with death an irreversible process starts with the production of positive entropy and we fall back into line with the second principle
In conclusion it can be said that the property of entropy is that of an increase in every
transformation that can be performed practically (like saying in every irreversible transformation)
except in the case of living organisms
How to produce heating of the plant at the expense of the surrounding masses and to increase
the order of the molecules to the point of ldquoforcingrdquo the carbon taken from the most formless state in
existence (that of gaseous CO2) to take on the shape of a trunk giving rise to transformations of
decreasing entropy
Also an ordinary refrigerator can produce a local decrease of entropy expending some
energy in the following figure we represent the energy transformations occurring in it at the end of
the transformation we have the temperatures marked with an asterisk after the energy Q leaves the
cool body to join the warmest body with the energy Q3 that is needed for the refrigerator to run6
6 The ratio (Q2+Q+Q3)Q3 is the widely known COP (Coefficient Of Performance) of the heat pumps
Pier Maria Boria Thermodynamics amp life
Figure 16 ndash Heat pumping in a refrigerator
In this sketch the external energy Q3 appears essential and the system is open the energy Q
increase its entropy gaining the temperature T2 entering the condensator Restarting the numerical example of the Clausius calorimeter we reconfirm Q=50 J as the
heat exchanged in this condition it is easy to verify that the water temperature decreases by 10 K while the copper increases by 90 K
Assuming COP=3 we have
final temperature of water T1 = 290 K
and for the copper T2 = 490+903 = 520 K
proceeding as above it follows that
for the copper
∆ 520400 0 5 ∙ 004 002
(
for the water
∆ 290300 5 ∙ 0034 0170
(
Therefore the quantity of transformed heat Q is subject to the variation
∆ ∆ + ∆ 002 0170 015 lt 0 ( ∶
thanks to the contribution of the external energy Q3 the exchanged heat decreases its entropy
Now we will see in what way nature does the heat pumping
Pier Maria Boria Thermodynamics amp life
9
Part 2 (of 4) Boltzmannrsquos Distribution
21 THE BOLTZMANNrsquoS DISTRIBUTION
We will reply to the question after having examined the second pillar on which we base this paper Boltzmannrsquos Distribution (Ludwig Boltzmann Austria 1844-1906)
As can also be seen in excellent web pages the disorganized vibrational velocity of the molecules of a gas (but also those of liquids and solids) at a given temperature take on values
which are continuously and randomly variable following a particular distribution represented graphically in Figure 21
Figure 21 ndash Probability distribution of the velocity of molecules of a gas as a function
of the velocity itself according to Boltzmannrsquos Statistic
It is thanks to this distribution discovered by Boltzmann that living nature vegetable and animal can perform local transformations with decreasing entropy the great masters have
thought up theoretical experiments based on devices capable of selecting molecules of colder gas having higher velocities than what is thought to be the average velocity of the molecules of the
warmer gas (Maxwell the demon Polvani the choosing porter Amerio the selecting valve) to allow them to pass from a lower temperature environment to another adjacent environment with
higher temperature in this way obtaining a transformation which locally invalidates the second
principle of thermodynamics
In Figure 22 it is possible to see that at every average velocity (considered) of the ldquowarmrdquo
molecules one can find a corresponding branch of the ldquocoldrdquo curve related to those particles that
should they pass to the warmer side could cause an increase in that average velocity and therefore
of the temperature
Pier Maria Boria Thermodynamics amp life
10
Figure 22 ndashThe Maxwell demon allows the passage from the colder to the warmer
environment only of the molecules which have a velocity higher than the
weighted average velocity of the warmer molecules
It is necessary to perform a sorting of the molecules one by one with mechanical means not
available to man while the experimental observations of the type reported above would suggest
that nature is capable of it operating at a molecular level in the realm of living organisms
In Figure 23 is represented the device which allows the ldquotheoretical experimentrdquo in the form
proposed by Prof Amerio of the Polytechnic of Milano (1955) Maxwell had proposed a ldquodemonrdquo
as selector of the molecules (1867) the selection device has been the object of particular attention
on the part of Szilard (1929) and later Bennet (1981) with the scope of correctly counting the
variation of entropy in the test universe and calculate the required energy for the selection
Figure 23 ndash The selective valve allows the passage from the colder to the warmer
environment only of the molecules which have a velocity higher than the
weighted average velocity of the warmer molecules as shown in Fig 22
Pier Maria Boria Thermodynamics amp life
These elementary applications of classic thermodynamics based on the concept of entropy
and on Bolzmannrsquos Distribution suggest to us that the phenomenon ldquoliferdquo is to be associated with a
ldquovis-vitalisrdquo external to the dissipative mechanism for which we have ample and daily experience
Obviously it is impossible for man to build a Maxwell device but in our research we have
found a very interesting observation by Jaques Monod (Nobel Prize in 1965) that confers the part of
demon to the natural enzymes7
According to this point of view we can convert the Figure 16 as follows
Figure 24 ndash The natural heat pumping performed by enzymes
and this sketch we consider as typical of the phenomenon ldquoliferdquo The role played by the vis-vitalis seems essential because the only electro-chemical energy
associated with enzymes are components easily deliverable in the biological laboratories but
nobody has been able to start life from these components8
There are those who attempt an approach to this argument with improper methods and with
arbitrary applications of the concept of probability which leads to theories that are devoid of the
required respect for a sound scientific doctrine
22 CONCLUSIONS FROM THE FIRST AND SECOND PART
Rivers of ink have been written about the origin of life to the point that it is possible to read
about the most bizarre theories that completely ignore that which is suggested by the Queen of
Physics Thermodynamics
Paleontology Biology extraterrestrials UFOs Cosmic Palingenesis and similar are all
stirred numbers equations concepts of probability principles of conservation etc are not used
7 Le hazard et la neacutecessiteacute 1970 ndash Arnoldo Mondadori Editore Spa ndash Milan ndash Pag 58
8 See the Stanley Miller experiment at the end of paragraph 54
Pier Maria Boria Thermodynamics amp life
12
correctly These are the only foundations possible for a correctly stated scientific discussion (there
is no adjective more abused than the term ldquoscientificrdquo)
The reader could (perhaps on a rainy Sunday) do some research on the ldquoprimordialrdquo soup (but
if it is not Knorr for whorsquos brand modestly in youth we made thermodynamics projects does not
taste good) on the ldquocosmic tankrdquo on the ldquotyping monkeysrdquo on the cycle of carbon and oxygen (in relation to the demonization of CO2) on the hydrological cycle (which is a substance that cannot
be ldquoconsumedrdquo as is currently heard said otherwise what cycle would it complete subjects often treated by substituting Science with ideology and making ample use of the principle of superior
authority (the ipse dixit of historical memory) upholding disjointed dogma but which are
politically correct
Sometimes one has the feeling of witnessing the squalid discourse of gossiping women by the fountain
It can be noted that in the observations made up to now we have practically not talked about energy whorsquos role in the economy of our discourse has been secondary Itrsquos the definition of the
entropy index state which changes the way to view the cosmos we would not talk of it if it were
possible to carry out reversible reactions
We would come to suspect that the irreversibility is a ldquodefectrdquo of the cosmos having the
function of forcing it to a gradual entropic enrichment (and therefore to a degeneration of energy)
such that the final form of all the energy available becomes one that is thermally and entropically
unusable therefore by virtue of what has been discussed at a certain point in the evolution of the
universe at a finite time it will not be possible to practically perform any thermodynamic cycle9
That is to say the thermal death of the universe
9 We will be further willing to suspect a decay of the cosmological properties correlated to the original sin Ah free
thought
Pier Maria Boria Thermodynamics amp life
13
Part 3 (of 4) Probability
31 PROBABILITY IN BOLTZMANNrsquoS STATISTICS
Boltzmann obtained the graph of the probability as a function of temperature postulating that
a certain number m of particles which are indistinguishable from each other (which we will call A
B C M) and a number n of possible states (a b c n) in which one or more particles (even if
m) can find themselves the presence of particles in each state could occur with different possibilities
If the identical particles are free to occupy the various states (as in the case of a gas) these could continuously exchange states between themselves (for example thanks to reciprocal impacts
as in Figure 23) whilst ldquoon averagerdquo maintaining a certain distribution subject to the conditions around them (for example temperature) a certain distribution of the possible configurations would
be typical of such conditions
Continuing with this example if by state of the particles we mean possessing a certain amount
of kinetic energy E associated with each molecule of a gas in a certain interval of values of energy
∆E there will be a stable quantity of molecules even if amongst themselves continues exchanges of
energy occur Therefore in the range of the same interval some particles enter and some leave
If for the sake of imagination in what follows particles will be considered as ldquoballsrdquo and
states as levels of energy the balls will represent the particles while the levels will represent an
interval of energy (∆E)
Let us start with a very simple case consisting of 3 particles (m=3) able to be hosted by two
levels (n=2) as illustrated in Figure 31
In the left column we see all the possible combinations In the central section we see that certain combinations repeat themselves in such a way that if the particles become indistinguishable
(column 3) they are to be considered the same amongst themselves Therefore three possibilities exist such that both the combinations 234 and 567 can occur
and only once for the combinations 1 and 8 If we ldquonormalizerdquo the possibility (expressing it in unitary or percentage terms) it assumes the
role of probability (ratio between favorable cases and possible cases) which we have done in the last column by expressing it in percentage terms as is common practice
Pier Maria Boria Thermodynamics amp life
14
Figure 31 ndash A rather simple case to demonstrate how given m=3 and n=2 it is possible to
have different probabilities for each combination
Pier Maria Boria Thermodynamics amp life
15
This allows us to draw the graph of Figure 32 where we can begin to see the
Boltzmann distribution forming
Figure 32 ndash The embryonic Boltzmann diagram increasing particles and the number of
possible states the envelope of the columns (in this particular case not yet)
acquires the characteristic asymmetric bell shape
Following in the footsteps of the great Ludwig we enter into systems which are numerically
more substantial three combinations of seven states with an arbitrary arrangement of four particles
as represented in Figure 33 the three combinations are equivalent because the particles are
indistinguishable by hypothesis
Pier Maria Boria Thermodynamics amp life
16
Figure 33 - The three configurations are equivalent if the four particles are indistinguishable
amongst themselves
Each of the n states can be associated with A B C etc (that is to each or more of the m
particles) and since a single particle can occupy each time a different state (and other particles
other states) m times the possible combinations C are ntimesntimesntimeshelliptimesn (m factors equal to n)
C = nm
We could also be convinced observing for example Figure 34 where it is assumed that n=5
(it looks like a musical stavehellip) and m=2 particles (therefore 52=25 combinations)
Pier Maria Boria Thermodynamics amp life
Figure 34 ndash Beyond the 25th beat the preceding configurations are repeated because A and B are
indistinguishable Within the range of the 25 possible configurations some are more favored
because they appear more frequently for example 6 and 22 9 and 25 etc The unoccupied
states are identified by a circle
As is fair to expect configuration 1 is least favored
Pier Maria Boria Thermodynamics amp life
18
We can arrive at the same result with a more practical method suitable also for very large
values of n and m which we will use as follows
It consists of a tabular method stolen from Combinatorial Analysis where for n and m equal to
various units it avoids the need to write hundreds or thousands of key strokes as used above
Let us take two rows and as many columns as there are states thereby obtaining a grid in
Figure 35 to verify what has been said above we have taken 2 rows and 5 columns (n=2 m=5)
Figure 35- With this grid we obtain the number of possible configurations
To further demonstrate we will build a grid for n=5 and m=4 as in Figure 36 where there are sufficient rows to progressively expose the number of particles (from 4 to 1 in the first box of
the first column of the occupancy numbers) and there are n columns
Pier Maria Boria Thermodynamics amp life
19
Figure 36 - Since 54= 625 there are 625 possible combinations the relative probabilities are
listed in the last column note the asymmetry
Pier Maria Boria Thermodynamics amp life
20
It is necessary to observe that in the figure the table of numbers of occupancy reminds
us not by chance of Tartagliarsquos Triangle while the Boltzmann type diagram that can be
associated shown in Figure 37 takes on an almost familiar shape
Figure 37 - Graphical representation of Figure 62 the bars are asymmetric
Pier Maria Boria Thermodynamics amp life
21
To provide an example and referring to Figure 36 we can see how it is possible to obtain 80
possibilities corresponding to his second line
If a box is occupied by 3 particles out of an available 4 the simple combinations of 4 objects
with 3 by 3 (as taught by the Combinatorial Analysis) are given by the binomial coefficient
6437 4
and the four possible groups of three numbers have five positions from which to choose From here 4times5=20 possibilities for the group of three numbers
The single remaining particle has the possibility of the four remaining locations and therefore has 1times4=4 possibilities
The product 20times4=80 gives us the total possibilities in the case that the particles arrange themselves in two groups one with three and one with a single particle and having five boxes
suitable It is easy to verify that we will obtain the same result considering first the single particle
having five boxes suitable (five possibilities 1x5=5) and after the three having the four remaining
(one is occupied by the single particle therefore 4x4=16 and 5x16=80)
Applying the procedure line by line it produces the results shown
Pier Maria Boria Thermodynamics amp life
22
Part 4 (of 4) Chance
41 CHANCE
A sharp-shooter shoots at a target with an excellent rifle he aims carefully chooses the
moment when his breathing will not interfere and the amount of force with which to pull the trigger so as not to move the barrel fires the shot and hits the bullrsquos-eye
Immediately afterwards he takes all the same precautions but the shot ends up being slightly off target it could have been a slight disturbance to his sight an involuntary variation in his
breathing an imperceptible abnormal movement of the finger a very slight unpredictable wind or who knows what else
The causes are many and imponderable slight if each is considered in itself but interacting differently each time ensuring that each shot has a different fate
This complex of innumerable causes of disturbance which are not controllable or predictable
and which not being able to take each into account one by one are called the Law of Probability
(Gaussrsquos Law)10
Probability for the reasons given and law thanks to Carl Friedrich Gauss (1777-1855) who
wrote an equation capable of taking into consideration in a global manner all those fleeting causes
so as to be able to predict with near accurate approximation how the shots will arrange themselves
percentage wise round the target with different distances from the bullseye The approximation will
be more accurate the greater the number of shots that are fired
Let us assume that the target is as represented in Figure 41 and is divided into two parts by
means of the section AB and that our sharpshooter fires many shots after which we count the
number of shots which hit the target in each half
Figure 41- The segmented target
If the reasons for the error are truly random (rifle without defects such that it does not tend to
deviate the shot systematically and neither does the sharpshooter have an analogous defect there is
10
The example of the sharpshooter was published by Engineer Mario Manaira in Ndeg 256 of ldquoJournal of Mechanicsrdquo
together with our first article concerning thermodynamics more than half a century ago (1961)
Pier Maria Boria Thermodynamics amp life
23
not a steady wind etc in other words there does not exist a cause which always influences with the
same bias called a systematic cause) we could note the following
1 The shots will be greater in number in the first band round the center
2 The shots will progressively decrease in number in the subsequent bands as these distance themselves further from the center until there are very few in the bands furthest away
3 The shots in the two halves right and left in any similar band will tend to have the same number and will even be identical if sufficient shots are fired
It is therefore possible to represent the phenomenon graphically as in the following figure
Figure 42 ndash The random distribution of the shots in each band and the Gaussian distribution that
would be obtained with an infinite number of shots fired
If the marksman were less capable the concentration of shots near the zero on the abscissa would reduce and the curve would flatten itself while maintaining the characteristics given and
represented in Figure 43 The first observation is that the maximum height of the curve constitutes the ldquotargetrdquo in other words the goal of the operation while the absence of systematic causes (in
antithesis of randomness) ensures the symmetry of the curve with respect to the vertical which
represents our target zero
Pier Maria Boria Thermodynamics amp life
24
Figure 43 - If the marksman is less skilled the Gaussian flattens
In the case of a systematic cause of error the curve loses its symmetry if we assume that the
test is performed with a constant wind from left to right the graph will take on the shape of Figure
44
Figure 44 ndash When the Gaussian is asymmetric it implies that the phenomenon is not ldquoentirely
randomrdquo11
Let us suppose now that our sharpshooter is blindfolded the target becomes very large and is
moved he will have to shoot blindly (randomly) left and right high and low Given that the Gauss
11
Gauss suggests that the analytical expression of the Law of Randomness is the function
2xey minus
=
where it can be seen that the curve is symmetrical with respect to the axis x=0 and decreasing both towards the left and
right of this line and has a maximum for x=0
It can be shown further that the area subtended is
π=int+infin
infinminus
minusdxe
x2
To ensure that this area is equal to unity as opposed to π appropriate steps can be taken which without
changing the general properties illustrated give the normalized Gaussrsquos Law
Pier Maria Boria Thermodynamics amp life
function still applies the probability curve will flatten itself maintaining the essential
characteristics in particular the two tails which will tend towards a tangent with the abscissa
tending towards infinity a maximum point a point of inflection and the other characteristics
illustrated in Figure 45
Figure 45 ndash Typical characteristics of a normalized Gaussian
Supposing once more that the Gauss function still applies it would be logical to expect a distribution with a curve that is so flat that it will be difficult to see a maximum point corresponding
to the center of the target it will be necessary to fire enough shots so as to occupy every position on the abscissa and to have hit with 100 certainty the bullrsquos-eye
This implies that everything is possible as long as an infinite number of shots are available
(using rhetorical language)
42 SOME PROPERTIES OF RANDOM EVENTS
The perplexities regarding the applicability of chance as referred to the blind sharpshooter
depend on the fact that the Gaussian assumes that programming has been applied to reach an
objective which implies that the operator is conscious of the objective an element which in this
case is absent
Both the existence of a program (the sharpshooter sets out to hit the bullrsquos-eye) and the
existence of an objective (the card with circles) appear to be essential to be able to talk about
chance
Another example let us imagine a machine programmed to produce a certain mechanical
piece the program is the design of the piece written in machine language and the objective is the production of the piece In mass production we will find that it is the case that despite the work
conditions being maintained the same each piece will be different to the other to the point that the pieces which exceed the tolerances (which would not allow them to be interchangeable) will be
rejected Innumerable examples could be presented identifying in every case these two characteristics
a program and an objective Statistics also operate in reverse from the measurement of a group of subjects it creates a bar
chart its envelope will be the curve of the random distribution It will give us the average of the values measured if the curve is symmetrical it will tell us that the phenomenon is not influenced by
systematic causes further it will tell us the value of the standard deviation etc
Pier Maria Boria Thermodynamics amp life
26
To fix this thought in our heads let us suppose that we want to study the average height of a
population of people who are male we make many measurements on many subjects creating bars
for every centimeter we will obtain a graph similar to Figure 46
Figure 46 ndash A practical application the Gaussian deduced from experimental measurements for
statistical purposes
In this statistical application where are the program and objective They are there they are
there they were contained in the information which the people naturally had at conception a
matter of genes and of DNA (an observation coherent with ldquoThe Kid Equationrdquo See the
ldquoIntroduction to Hyperspacerdquo12
)
These considerations lead us to think that the meaning of the word ldquochancerdquo commonly given
does not make sense that ldquochancerdquo does not exist and lead us to suspect that Anatole France had an
inspired guess when he said ldquochance is Godrsquos pseudonym when He does not want to sign his
namerdquo
This strongly agrees with what illustrious philosophers have been confirming for centuries
ldquoDeus absconditus estrdquo (Is XLV XV)
12
In our first volume ldquoCaro amico miohelliprdquo ndash Ed Pagine ndash 2010 In our second volume (ldquoVerba volant eqvuationes
manentrdquo) other considerations about a fundamental theorem of Genetics the Hardy Weinberg theorem
Pier Maria Boria Thermodynamics amp life
27
43 CHANCE amp PROBABILITY
We can now summarize some salient functions of Boltzmann and Gauss
Boltzmann
1 Deals with probability regarding the characteristics that can be assumed by many identical particles having a certain number of positions available (Dirac and Fermi deal
with particles which are distinguishable but the correct reference in our observations are the identical particles)
2 The function presents a maximum and aesthetically looks like a Gaussian but it is not symmetrical
3 It has only a single asymptote to the right of the maximum and its minimum at infinity coincides with zero the origin of the reference system
4 It is normalized so that the area subtended represents the total probability of 100
Gauss
1 Deals with chance and is applicable when an objective exists that is defined by a
program
2 The phenomenon ldquopurely by chancerdquo is represented by a curve that is symmetrical
about the axis x=0
3 The Gaussian has a maximum and no minimum at infinity
4 It possesses two asymptotes one to the right and one to the left of the maximum
5 Well defined values of probability can be associated with multiples of the standard deviation
6 It is normalized as for Boltzmannrsquos
44 THE EDDINGTONrsquoS PARADOX13
Eddingtonrsquos famous ldquoInfinite monkey theoremrdquo can be counted amongst the most discussed
paradoxes for the fact that it is often quoted by so called ldquoscientific popularizersrdquo The original assertion states ldquohellipa monkey hitting keys at random on a typewriter keyboard
for an infinite amount of times will almost surely type a given text such as the complete works of
William Shakespearerdquo
Having taken away the condition of an infinite amount of time the paradox remains acceptable
(from the moment we are able to demonstrate that a finite amount of time is sufficient) However
such a long period of time is necessary that the original statement could be seen as an hyperbolic
discussion
We have seen that random phenomena require a program in light of an objective In the case
of the typing monkeys the program could include the elimination of duplicate pages (actually the
identical pages as we will see below) and the objective could consist in the conservation of ldquogoodrdquo
pages arranged in the right sequence
Applying Boltzmannrsquos statistics let us assume that the typewriter has m=30 keys (we can think of ldquoblindrdquo keys without any writing and all identical) and that we want to write a book of
only 106
letters (a thousand typed pages) as we have observed in paragraph 31 all the possible combinations are
13
The reader can find all the details regarding these various arguments on the web
Pier Maria Boria Thermodynamics amp life
C = nm = (10
6)30
= (10)180
In other words there are 10180
possible configurations
Let us assume that the monkeys are capable of striking 10 keyssec (skilled typistshellip) the
time necessary would be
t = 10180
x 106 10 = 10
185 sec
Since we can count 1016 seconds in a billion years it is also possible to say that the time
required will be
10185
1016
= 10169
billion years (giga-years)
(let us remember that the big-bang has an age of ldquoonlyrdquo 14 billion years)
In reality the situation is even ldquoworserdquo in fact this calculation (which is generally accepted)
is wrong because we cannot talk about only thirty objects (the letters punctuation marks spaces between lines etc) to be arranged in 10
6 positions otherwise in each of 10180 configurations
obtainable we would find empty spaces up to 106-30 in each configuration
It is necessary to postulate that there are 106 letters to be arranged like conceding that the
monkeys have to insert 106 objects ie 10
6 key strokes In other words it is necessary that n = m =
106 and in this case the formula of the combinations gives us an astronomical value
6106 )10(===
mm mnC combinations
At a rhythm of 10 key strokes sec the time corresponds to
9899995005000616106 10sec101010)10(
6
equiv=sdotsdot=minust years
Figure 47 ndash Summary table of the probabilities according to Boltzmann
In realty the situation is even ldquoworserdquo still In fact in the calculation of the combinations duplicate configurations are not considered
(which necessarily must be considered as possible) in other words our monkeys could produce the same combinations several times (or two identical pages) anyway the duplications will be useless
in the compilation of our small book of only 106 letters
To this end we invoke chance (to attempt to appreciate the incidence of the repeating of
identical pages) and having constructed a Gaussian by arranging the frequency of identical pages we can reason as follows having produced all the astronomical combinations as above in the time
calculated (which we will call a cycle) the highest probability of identical pages is in pairs (which
Pier Maria Boria Thermodynamics amp life
29
we will assign the maximum position) then in threes and so on At infinity with a probability of
zero all the pages will be identical
It seems fair to presume that the standard deviation could be very large qualifying for a very
flat Gaussian and let us suppose that the pages to be rejected (one for the doubles two for the
triplets etc) are contained within the first standard deviation (as in Figure 48) then the duplicate pages to be thrown away would be about 68
Figure 48 ndash The postulated conditions (pages to be eliminated because they are duplicated equal
to the standard deviation) make 68 of the pages produced useless Iterating the cycle one could
consider the duplication of other pages however it can be demonstrated that the phenomenon
continues to imply finite times
How much does the required time increase to generalize we assume the length of a cycle to be of one unit and we identify with K the average cost of discarded pages (in the previous numerical
case K= 068) and then we observe Figure 49
Figure 49 ndash Having exhausted the first cycle identified by 1 the second of length K allows the
replacement of the duplicate pages produced in the first cycle the third of length K2 is used to
replace those produced in the second cycle and so on
The time necessary to complete the cycles required to eliminate the duplicates as they are produced will be given by the sum
suminfin
=0n
nK
which constitutes a geometric series
The Mathematical Analysis teaches us that such a series converges for 1ltK as is confirmed
in our case where it takes on the value 068
KS
minus=
1
1 and if K = 068 gives 1253
6801
1=
minus=S
Pier Maria Boria Thermodynamics amp life
30
Therefore multiplying by 3125 the time dedicated to complete a cycle (317middot105999989 billion
years) for the hypothesis made we also eliminate all the duplicate pages of our little book of 106
key strokes
Changing the value of K (always lt1) one obtains different multipliers but always of a finite
value let the reader imagine the time necessary to type all of Shakespearersquos works It must be highlighted that the monkey operation to be considered a success requires the
intervention of external intelligence capable of selecting the useful pages (like thought by Theory of
Information) and ordering them in the right sequence to obtain a final legible manuscript this
obvious necessity implies that negative entropy be introduced into the system as covered at the
beginning this is like a living being taking the trouble to ldquoput in orderrdquo otherwise the ldquopurely
randomrdquo work would be entirely useless because it will exclusively produce positive entropy
All experiments attempted by man with the goal of demonstrating the random production of
complex molecules (first building blocks of living organisms) have the defect of requiring an a
priori living system like man to arrange this production
When later chaotic physical-chemical conditions are created (temperature pressure
methane electrical arching etc) hoping to obtain that which Thermodynamics does not permit the
inventors of the moto perpetuo come to mind who never give up
The research on the ldquoprimordial souprdquo belongs to this type of experimentation a battle horse
of the followers of the ldquomaitre agrave penserrdquo of the last century and which regard in particular the laboratory experiments of Stanley Miller the goal of his research of a physical-chemical nature
was to recreate life it was an understandable but too ambitious of a project for a researcher The result was absolutely negative (Miller himself recognized it) however this last piece of information
is only whispered in scientific circles so that we still find genuine touts who speak with enthusiastic coram populo of the primordial soup and its miraculous effects14 with a self-assurance
that is truly shameful
45 CONCLUSION
On 4 July 2007 at the London Kinetics Museum a serious presentation of a perpetual motion
machine was scheduled a machine capable of supplying the user with a power greater than that
absorbed ldquoObviouslyrdquo the presentation was postponed due to ldquoa technical problemrdquo15
It would appear impossible but advocates convinced of such a motion exist and many
inventors submit patent after patent even though still in illo tempore Max Planck declared himself
to be contrary to such a possibility which violates the principles of Thermodynamics
Based on the reasoning we have developed regarding entropy probability and chance the
violation of such principles is implicit even in the attempts to obtain living organisms in a
laboratory (characterized as we have seen as being producers of negative entropy) and as such a
strong analogy can be seen between the advocates of perpetual motion and those aspiring to create
life
1 The correct application of Boltzmannrsquos statistics a phenomenon for which we call on
probability demonstrates that combinations of large numbers of particles to the point of generating complex organisms require very long periods of time in comparison the age of
the universe is but the blink of an eye
2 The probabilities take on the largest numbers in correspondence with the most disordered
configurations
14
From ldquoCorriere della Serardquo october 2008 ldquoLa vita sulla Terra Cominciograve nei vulcani con un innesco chimicordquo 15
-Source Wikipedia
Pier Maria Boria Thermodynamics amp life
3 The most ordered combinations are those which characterize organic structures and the action
of an intelligent being is necessary to select order and conserve in time the favorable
combinations
4 The phrase ldquochance phenomenonrdquo is somewhat less intuitive than what ldquocommon senserdquo
would suggest In fact the Gaussian perspective implies that such phenomena are necessarily
associated with a program this program implies the existence of an objective around which
we have an increased concentration of events
5 In every case it is necessary to postulate the existence of an intelligent design without which
the configurations and the favorable events constitute events without any functional link
between themselves
6 The existence of life as a producer of negative entropy on a continuous basis (not cyclical) is a fact visible with our own eyes
All this leads us to support the existence of a Co-ordinating Entity which possesses life ldquoa
priorirdquo and which is capable of transmitting it to animals (animalis homo included) and vegetation It can be noted that the two living systems animal and vegetable complement each other in the
sense that the design requires that emissions from the first (CO2) are the nutrients for the second and the byproducts of the second (O2) are essential for the first the carbon and oxygen cycles look
like they have been designed According to the author there is only one explanation we are in the presence of the greatest
Design Physicist of all times God the Creator
This is what we call Him as Christians while Israelites call Him Jehovah the Ishmaelites
Allah the Masons GADU (Great Architect of the Universe) etc
In other terms
the Creation is a thermodynamic necessity
Amen
Pier Maria Boria Thermodynamics amp life
7
14 ENTROPY AND LIFE
Livio Gratton (Italian cosmologist from Trieste died in 1991 and considered the father of
Italian Astrophysics) observed that the phenomenon ldquoliferdquo contains something singular which does
not fit in with the mechanism described up to this point The appearance of life in an electromagnetically structured universe constitutes a singular moment which cannot be explained
technically In fact an organism is alive when within itself it produces transformations of negative
entropy (that is with ∆Slt0) which contradicts the second principle Let us observe a plant seed if it is alive in conditions expected in nature it germinates
spontaneously and grows capturing carbon from the atmosphere giving body to the plant and releasing oxygen through chlorophyll synthesis
A small wheat seedling recently sprouted amongst the snow germinates and grows warming itself up at the expense of the ground (who has not observed the molten snow round the seedling
The seedlings under a thin blanket of snow poke out and are clearly visible green seedlings on a
white blanket in the middle of a dark patch of earth free from that which surrounds them)
Naturally if we were to also consider the interaction of the plant with the quanta of solar
energy and the surrounding minerals we would find that the sum of transformations has generated
positive entropy (the affirmation that the entropy of the universe tends to increase without limits is
correct)
A living animal organism should it be injured is capable of healing itself the vis vitalis as
our ancestors called it produces such an effect while a dead animal organism remains injured and
decomposes with the passing of time (increase of disorder)
One could consider the possibility of turning to entropy to define the state of life or death
about which we periodically debate even in practical cases (Terry Schiavo Eluana Englarohellip) if the organism produces negative entropy it is alive in the opposite case it is nothellip
One could also suggest a crude experimental procedure of a slightly Hitlerian nature which would settle the matter once and for all consisting of injuring an organism that has a dubious state
of life to verify its reactions in one entropic direction or the otherhellip The vis vitalis departs even if all the mechanical organs would be perfectly functional we can
think of the so called cardiac arrest (a phrase that could be a savior for the corner of the art of medicine) One could certainly object that the arrest is the cause while the departure of the vis
vitalis is the effect who knows The only certainty is that with death an irreversible process starts with the production of positive entropy and we fall back into line with the second principle
In conclusion it can be said that the property of entropy is that of an increase in every
transformation that can be performed practically (like saying in every irreversible transformation)
except in the case of living organisms
How to produce heating of the plant at the expense of the surrounding masses and to increase
the order of the molecules to the point of ldquoforcingrdquo the carbon taken from the most formless state in
existence (that of gaseous CO2) to take on the shape of a trunk giving rise to transformations of
decreasing entropy
Also an ordinary refrigerator can produce a local decrease of entropy expending some
energy in the following figure we represent the energy transformations occurring in it at the end of
the transformation we have the temperatures marked with an asterisk after the energy Q leaves the
cool body to join the warmest body with the energy Q3 that is needed for the refrigerator to run6
6 The ratio (Q2+Q+Q3)Q3 is the widely known COP (Coefficient Of Performance) of the heat pumps
Pier Maria Boria Thermodynamics amp life
Figure 16 ndash Heat pumping in a refrigerator
In this sketch the external energy Q3 appears essential and the system is open the energy Q
increase its entropy gaining the temperature T2 entering the condensator Restarting the numerical example of the Clausius calorimeter we reconfirm Q=50 J as the
heat exchanged in this condition it is easy to verify that the water temperature decreases by 10 K while the copper increases by 90 K
Assuming COP=3 we have
final temperature of water T1 = 290 K
and for the copper T2 = 490+903 = 520 K
proceeding as above it follows that
for the copper
∆ 520400 0 5 ∙ 004 002
(
for the water
∆ 290300 5 ∙ 0034 0170
(
Therefore the quantity of transformed heat Q is subject to the variation
∆ ∆ + ∆ 002 0170 015 lt 0 ( ∶
thanks to the contribution of the external energy Q3 the exchanged heat decreases its entropy
Now we will see in what way nature does the heat pumping
Pier Maria Boria Thermodynamics amp life
9
Part 2 (of 4) Boltzmannrsquos Distribution
21 THE BOLTZMANNrsquoS DISTRIBUTION
We will reply to the question after having examined the second pillar on which we base this paper Boltzmannrsquos Distribution (Ludwig Boltzmann Austria 1844-1906)
As can also be seen in excellent web pages the disorganized vibrational velocity of the molecules of a gas (but also those of liquids and solids) at a given temperature take on values
which are continuously and randomly variable following a particular distribution represented graphically in Figure 21
Figure 21 ndash Probability distribution of the velocity of molecules of a gas as a function
of the velocity itself according to Boltzmannrsquos Statistic
It is thanks to this distribution discovered by Boltzmann that living nature vegetable and animal can perform local transformations with decreasing entropy the great masters have
thought up theoretical experiments based on devices capable of selecting molecules of colder gas having higher velocities than what is thought to be the average velocity of the molecules of the
warmer gas (Maxwell the demon Polvani the choosing porter Amerio the selecting valve) to allow them to pass from a lower temperature environment to another adjacent environment with
higher temperature in this way obtaining a transformation which locally invalidates the second
principle of thermodynamics
In Figure 22 it is possible to see that at every average velocity (considered) of the ldquowarmrdquo
molecules one can find a corresponding branch of the ldquocoldrdquo curve related to those particles that
should they pass to the warmer side could cause an increase in that average velocity and therefore
of the temperature
Pier Maria Boria Thermodynamics amp life
10
Figure 22 ndashThe Maxwell demon allows the passage from the colder to the warmer
environment only of the molecules which have a velocity higher than the
weighted average velocity of the warmer molecules
It is necessary to perform a sorting of the molecules one by one with mechanical means not
available to man while the experimental observations of the type reported above would suggest
that nature is capable of it operating at a molecular level in the realm of living organisms
In Figure 23 is represented the device which allows the ldquotheoretical experimentrdquo in the form
proposed by Prof Amerio of the Polytechnic of Milano (1955) Maxwell had proposed a ldquodemonrdquo
as selector of the molecules (1867) the selection device has been the object of particular attention
on the part of Szilard (1929) and later Bennet (1981) with the scope of correctly counting the
variation of entropy in the test universe and calculate the required energy for the selection
Figure 23 ndash The selective valve allows the passage from the colder to the warmer
environment only of the molecules which have a velocity higher than the
weighted average velocity of the warmer molecules as shown in Fig 22
Pier Maria Boria Thermodynamics amp life
These elementary applications of classic thermodynamics based on the concept of entropy
and on Bolzmannrsquos Distribution suggest to us that the phenomenon ldquoliferdquo is to be associated with a
ldquovis-vitalisrdquo external to the dissipative mechanism for which we have ample and daily experience
Obviously it is impossible for man to build a Maxwell device but in our research we have
found a very interesting observation by Jaques Monod (Nobel Prize in 1965) that confers the part of
demon to the natural enzymes7
According to this point of view we can convert the Figure 16 as follows
Figure 24 ndash The natural heat pumping performed by enzymes
and this sketch we consider as typical of the phenomenon ldquoliferdquo The role played by the vis-vitalis seems essential because the only electro-chemical energy
associated with enzymes are components easily deliverable in the biological laboratories but
nobody has been able to start life from these components8
There are those who attempt an approach to this argument with improper methods and with
arbitrary applications of the concept of probability which leads to theories that are devoid of the
required respect for a sound scientific doctrine
22 CONCLUSIONS FROM THE FIRST AND SECOND PART
Rivers of ink have been written about the origin of life to the point that it is possible to read
about the most bizarre theories that completely ignore that which is suggested by the Queen of
Physics Thermodynamics
Paleontology Biology extraterrestrials UFOs Cosmic Palingenesis and similar are all
stirred numbers equations concepts of probability principles of conservation etc are not used
7 Le hazard et la neacutecessiteacute 1970 ndash Arnoldo Mondadori Editore Spa ndash Milan ndash Pag 58
8 See the Stanley Miller experiment at the end of paragraph 54
Pier Maria Boria Thermodynamics amp life
12
correctly These are the only foundations possible for a correctly stated scientific discussion (there
is no adjective more abused than the term ldquoscientificrdquo)
The reader could (perhaps on a rainy Sunday) do some research on the ldquoprimordialrdquo soup (but
if it is not Knorr for whorsquos brand modestly in youth we made thermodynamics projects does not
taste good) on the ldquocosmic tankrdquo on the ldquotyping monkeysrdquo on the cycle of carbon and oxygen (in relation to the demonization of CO2) on the hydrological cycle (which is a substance that cannot
be ldquoconsumedrdquo as is currently heard said otherwise what cycle would it complete subjects often treated by substituting Science with ideology and making ample use of the principle of superior
authority (the ipse dixit of historical memory) upholding disjointed dogma but which are
politically correct
Sometimes one has the feeling of witnessing the squalid discourse of gossiping women by the fountain
It can be noted that in the observations made up to now we have practically not talked about energy whorsquos role in the economy of our discourse has been secondary Itrsquos the definition of the
entropy index state which changes the way to view the cosmos we would not talk of it if it were
possible to carry out reversible reactions
We would come to suspect that the irreversibility is a ldquodefectrdquo of the cosmos having the
function of forcing it to a gradual entropic enrichment (and therefore to a degeneration of energy)
such that the final form of all the energy available becomes one that is thermally and entropically
unusable therefore by virtue of what has been discussed at a certain point in the evolution of the
universe at a finite time it will not be possible to practically perform any thermodynamic cycle9
That is to say the thermal death of the universe
9 We will be further willing to suspect a decay of the cosmological properties correlated to the original sin Ah free
thought
Pier Maria Boria Thermodynamics amp life
13
Part 3 (of 4) Probability
31 PROBABILITY IN BOLTZMANNrsquoS STATISTICS
Boltzmann obtained the graph of the probability as a function of temperature postulating that
a certain number m of particles which are indistinguishable from each other (which we will call A
B C M) and a number n of possible states (a b c n) in which one or more particles (even if
m) can find themselves the presence of particles in each state could occur with different possibilities
If the identical particles are free to occupy the various states (as in the case of a gas) these could continuously exchange states between themselves (for example thanks to reciprocal impacts
as in Figure 23) whilst ldquoon averagerdquo maintaining a certain distribution subject to the conditions around them (for example temperature) a certain distribution of the possible configurations would
be typical of such conditions
Continuing with this example if by state of the particles we mean possessing a certain amount
of kinetic energy E associated with each molecule of a gas in a certain interval of values of energy
∆E there will be a stable quantity of molecules even if amongst themselves continues exchanges of
energy occur Therefore in the range of the same interval some particles enter and some leave
If for the sake of imagination in what follows particles will be considered as ldquoballsrdquo and
states as levels of energy the balls will represent the particles while the levels will represent an
interval of energy (∆E)
Let us start with a very simple case consisting of 3 particles (m=3) able to be hosted by two
levels (n=2) as illustrated in Figure 31
In the left column we see all the possible combinations In the central section we see that certain combinations repeat themselves in such a way that if the particles become indistinguishable
(column 3) they are to be considered the same amongst themselves Therefore three possibilities exist such that both the combinations 234 and 567 can occur
and only once for the combinations 1 and 8 If we ldquonormalizerdquo the possibility (expressing it in unitary or percentage terms) it assumes the
role of probability (ratio between favorable cases and possible cases) which we have done in the last column by expressing it in percentage terms as is common practice
Pier Maria Boria Thermodynamics amp life
14
Figure 31 ndash A rather simple case to demonstrate how given m=3 and n=2 it is possible to
have different probabilities for each combination
Pier Maria Boria Thermodynamics amp life
15
This allows us to draw the graph of Figure 32 where we can begin to see the
Boltzmann distribution forming
Figure 32 ndash The embryonic Boltzmann diagram increasing particles and the number of
possible states the envelope of the columns (in this particular case not yet)
acquires the characteristic asymmetric bell shape
Following in the footsteps of the great Ludwig we enter into systems which are numerically
more substantial three combinations of seven states with an arbitrary arrangement of four particles
as represented in Figure 33 the three combinations are equivalent because the particles are
indistinguishable by hypothesis
Pier Maria Boria Thermodynamics amp life
16
Figure 33 - The three configurations are equivalent if the four particles are indistinguishable
amongst themselves
Each of the n states can be associated with A B C etc (that is to each or more of the m
particles) and since a single particle can occupy each time a different state (and other particles
other states) m times the possible combinations C are ntimesntimesntimeshelliptimesn (m factors equal to n)
C = nm
We could also be convinced observing for example Figure 34 where it is assumed that n=5
(it looks like a musical stavehellip) and m=2 particles (therefore 52=25 combinations)
Pier Maria Boria Thermodynamics amp life
Figure 34 ndash Beyond the 25th beat the preceding configurations are repeated because A and B are
indistinguishable Within the range of the 25 possible configurations some are more favored
because they appear more frequently for example 6 and 22 9 and 25 etc The unoccupied
states are identified by a circle
As is fair to expect configuration 1 is least favored
Pier Maria Boria Thermodynamics amp life
18
We can arrive at the same result with a more practical method suitable also for very large
values of n and m which we will use as follows
It consists of a tabular method stolen from Combinatorial Analysis where for n and m equal to
various units it avoids the need to write hundreds or thousands of key strokes as used above
Let us take two rows and as many columns as there are states thereby obtaining a grid in
Figure 35 to verify what has been said above we have taken 2 rows and 5 columns (n=2 m=5)
Figure 35- With this grid we obtain the number of possible configurations
To further demonstrate we will build a grid for n=5 and m=4 as in Figure 36 where there are sufficient rows to progressively expose the number of particles (from 4 to 1 in the first box of
the first column of the occupancy numbers) and there are n columns
Pier Maria Boria Thermodynamics amp life
19
Figure 36 - Since 54= 625 there are 625 possible combinations the relative probabilities are
listed in the last column note the asymmetry
Pier Maria Boria Thermodynamics amp life
20
It is necessary to observe that in the figure the table of numbers of occupancy reminds
us not by chance of Tartagliarsquos Triangle while the Boltzmann type diagram that can be
associated shown in Figure 37 takes on an almost familiar shape
Figure 37 - Graphical representation of Figure 62 the bars are asymmetric
Pier Maria Boria Thermodynamics amp life
21
To provide an example and referring to Figure 36 we can see how it is possible to obtain 80
possibilities corresponding to his second line
If a box is occupied by 3 particles out of an available 4 the simple combinations of 4 objects
with 3 by 3 (as taught by the Combinatorial Analysis) are given by the binomial coefficient
6437 4
and the four possible groups of three numbers have five positions from which to choose From here 4times5=20 possibilities for the group of three numbers
The single remaining particle has the possibility of the four remaining locations and therefore has 1times4=4 possibilities
The product 20times4=80 gives us the total possibilities in the case that the particles arrange themselves in two groups one with three and one with a single particle and having five boxes
suitable It is easy to verify that we will obtain the same result considering first the single particle
having five boxes suitable (five possibilities 1x5=5) and after the three having the four remaining
(one is occupied by the single particle therefore 4x4=16 and 5x16=80)
Applying the procedure line by line it produces the results shown
Pier Maria Boria Thermodynamics amp life
22
Part 4 (of 4) Chance
41 CHANCE
A sharp-shooter shoots at a target with an excellent rifle he aims carefully chooses the
moment when his breathing will not interfere and the amount of force with which to pull the trigger so as not to move the barrel fires the shot and hits the bullrsquos-eye
Immediately afterwards he takes all the same precautions but the shot ends up being slightly off target it could have been a slight disturbance to his sight an involuntary variation in his
breathing an imperceptible abnormal movement of the finger a very slight unpredictable wind or who knows what else
The causes are many and imponderable slight if each is considered in itself but interacting differently each time ensuring that each shot has a different fate
This complex of innumerable causes of disturbance which are not controllable or predictable
and which not being able to take each into account one by one are called the Law of Probability
(Gaussrsquos Law)10
Probability for the reasons given and law thanks to Carl Friedrich Gauss (1777-1855) who
wrote an equation capable of taking into consideration in a global manner all those fleeting causes
so as to be able to predict with near accurate approximation how the shots will arrange themselves
percentage wise round the target with different distances from the bullseye The approximation will
be more accurate the greater the number of shots that are fired
Let us assume that the target is as represented in Figure 41 and is divided into two parts by
means of the section AB and that our sharpshooter fires many shots after which we count the
number of shots which hit the target in each half
Figure 41- The segmented target
If the reasons for the error are truly random (rifle without defects such that it does not tend to
deviate the shot systematically and neither does the sharpshooter have an analogous defect there is
10
The example of the sharpshooter was published by Engineer Mario Manaira in Ndeg 256 of ldquoJournal of Mechanicsrdquo
together with our first article concerning thermodynamics more than half a century ago (1961)
Pier Maria Boria Thermodynamics amp life
23
not a steady wind etc in other words there does not exist a cause which always influences with the
same bias called a systematic cause) we could note the following
1 The shots will be greater in number in the first band round the center
2 The shots will progressively decrease in number in the subsequent bands as these distance themselves further from the center until there are very few in the bands furthest away
3 The shots in the two halves right and left in any similar band will tend to have the same number and will even be identical if sufficient shots are fired
It is therefore possible to represent the phenomenon graphically as in the following figure
Figure 42 ndash The random distribution of the shots in each band and the Gaussian distribution that
would be obtained with an infinite number of shots fired
If the marksman were less capable the concentration of shots near the zero on the abscissa would reduce and the curve would flatten itself while maintaining the characteristics given and
represented in Figure 43 The first observation is that the maximum height of the curve constitutes the ldquotargetrdquo in other words the goal of the operation while the absence of systematic causes (in
antithesis of randomness) ensures the symmetry of the curve with respect to the vertical which
represents our target zero
Pier Maria Boria Thermodynamics amp life
24
Figure 43 - If the marksman is less skilled the Gaussian flattens
In the case of a systematic cause of error the curve loses its symmetry if we assume that the
test is performed with a constant wind from left to right the graph will take on the shape of Figure
44
Figure 44 ndash When the Gaussian is asymmetric it implies that the phenomenon is not ldquoentirely
randomrdquo11
Let us suppose now that our sharpshooter is blindfolded the target becomes very large and is
moved he will have to shoot blindly (randomly) left and right high and low Given that the Gauss
11
Gauss suggests that the analytical expression of the Law of Randomness is the function
2xey minus
=
where it can be seen that the curve is symmetrical with respect to the axis x=0 and decreasing both towards the left and
right of this line and has a maximum for x=0
It can be shown further that the area subtended is
π=int+infin
infinminus
minusdxe
x2
To ensure that this area is equal to unity as opposed to π appropriate steps can be taken which without
changing the general properties illustrated give the normalized Gaussrsquos Law
Pier Maria Boria Thermodynamics amp life
function still applies the probability curve will flatten itself maintaining the essential
characteristics in particular the two tails which will tend towards a tangent with the abscissa
tending towards infinity a maximum point a point of inflection and the other characteristics
illustrated in Figure 45
Figure 45 ndash Typical characteristics of a normalized Gaussian
Supposing once more that the Gauss function still applies it would be logical to expect a distribution with a curve that is so flat that it will be difficult to see a maximum point corresponding
to the center of the target it will be necessary to fire enough shots so as to occupy every position on the abscissa and to have hit with 100 certainty the bullrsquos-eye
This implies that everything is possible as long as an infinite number of shots are available
(using rhetorical language)
42 SOME PROPERTIES OF RANDOM EVENTS
The perplexities regarding the applicability of chance as referred to the blind sharpshooter
depend on the fact that the Gaussian assumes that programming has been applied to reach an
objective which implies that the operator is conscious of the objective an element which in this
case is absent
Both the existence of a program (the sharpshooter sets out to hit the bullrsquos-eye) and the
existence of an objective (the card with circles) appear to be essential to be able to talk about
chance
Another example let us imagine a machine programmed to produce a certain mechanical
piece the program is the design of the piece written in machine language and the objective is the production of the piece In mass production we will find that it is the case that despite the work
conditions being maintained the same each piece will be different to the other to the point that the pieces which exceed the tolerances (which would not allow them to be interchangeable) will be
rejected Innumerable examples could be presented identifying in every case these two characteristics
a program and an objective Statistics also operate in reverse from the measurement of a group of subjects it creates a bar
chart its envelope will be the curve of the random distribution It will give us the average of the values measured if the curve is symmetrical it will tell us that the phenomenon is not influenced by
systematic causes further it will tell us the value of the standard deviation etc
Pier Maria Boria Thermodynamics amp life
26
To fix this thought in our heads let us suppose that we want to study the average height of a
population of people who are male we make many measurements on many subjects creating bars
for every centimeter we will obtain a graph similar to Figure 46
Figure 46 ndash A practical application the Gaussian deduced from experimental measurements for
statistical purposes
In this statistical application where are the program and objective They are there they are
there they were contained in the information which the people naturally had at conception a
matter of genes and of DNA (an observation coherent with ldquoThe Kid Equationrdquo See the
ldquoIntroduction to Hyperspacerdquo12
)
These considerations lead us to think that the meaning of the word ldquochancerdquo commonly given
does not make sense that ldquochancerdquo does not exist and lead us to suspect that Anatole France had an
inspired guess when he said ldquochance is Godrsquos pseudonym when He does not want to sign his
namerdquo
This strongly agrees with what illustrious philosophers have been confirming for centuries
ldquoDeus absconditus estrdquo (Is XLV XV)
12
In our first volume ldquoCaro amico miohelliprdquo ndash Ed Pagine ndash 2010 In our second volume (ldquoVerba volant eqvuationes
manentrdquo) other considerations about a fundamental theorem of Genetics the Hardy Weinberg theorem
Pier Maria Boria Thermodynamics amp life
27
43 CHANCE amp PROBABILITY
We can now summarize some salient functions of Boltzmann and Gauss
Boltzmann
1 Deals with probability regarding the characteristics that can be assumed by many identical particles having a certain number of positions available (Dirac and Fermi deal
with particles which are distinguishable but the correct reference in our observations are the identical particles)
2 The function presents a maximum and aesthetically looks like a Gaussian but it is not symmetrical
3 It has only a single asymptote to the right of the maximum and its minimum at infinity coincides with zero the origin of the reference system
4 It is normalized so that the area subtended represents the total probability of 100
Gauss
1 Deals with chance and is applicable when an objective exists that is defined by a
program
2 The phenomenon ldquopurely by chancerdquo is represented by a curve that is symmetrical
about the axis x=0
3 The Gaussian has a maximum and no minimum at infinity
4 It possesses two asymptotes one to the right and one to the left of the maximum
5 Well defined values of probability can be associated with multiples of the standard deviation
6 It is normalized as for Boltzmannrsquos
44 THE EDDINGTONrsquoS PARADOX13
Eddingtonrsquos famous ldquoInfinite monkey theoremrdquo can be counted amongst the most discussed
paradoxes for the fact that it is often quoted by so called ldquoscientific popularizersrdquo The original assertion states ldquohellipa monkey hitting keys at random on a typewriter keyboard
for an infinite amount of times will almost surely type a given text such as the complete works of
William Shakespearerdquo
Having taken away the condition of an infinite amount of time the paradox remains acceptable
(from the moment we are able to demonstrate that a finite amount of time is sufficient) However
such a long period of time is necessary that the original statement could be seen as an hyperbolic
discussion
We have seen that random phenomena require a program in light of an objective In the case
of the typing monkeys the program could include the elimination of duplicate pages (actually the
identical pages as we will see below) and the objective could consist in the conservation of ldquogoodrdquo
pages arranged in the right sequence
Applying Boltzmannrsquos statistics let us assume that the typewriter has m=30 keys (we can think of ldquoblindrdquo keys without any writing and all identical) and that we want to write a book of
only 106
letters (a thousand typed pages) as we have observed in paragraph 31 all the possible combinations are
13
The reader can find all the details regarding these various arguments on the web
Pier Maria Boria Thermodynamics amp life
C = nm = (10
6)30
= (10)180
In other words there are 10180
possible configurations
Let us assume that the monkeys are capable of striking 10 keyssec (skilled typistshellip) the
time necessary would be
t = 10180
x 106 10 = 10
185 sec
Since we can count 1016 seconds in a billion years it is also possible to say that the time
required will be
10185
1016
= 10169
billion years (giga-years)
(let us remember that the big-bang has an age of ldquoonlyrdquo 14 billion years)
In reality the situation is even ldquoworserdquo in fact this calculation (which is generally accepted)
is wrong because we cannot talk about only thirty objects (the letters punctuation marks spaces between lines etc) to be arranged in 10
6 positions otherwise in each of 10180 configurations
obtainable we would find empty spaces up to 106-30 in each configuration
It is necessary to postulate that there are 106 letters to be arranged like conceding that the
monkeys have to insert 106 objects ie 10
6 key strokes In other words it is necessary that n = m =
106 and in this case the formula of the combinations gives us an astronomical value
6106 )10(===
mm mnC combinations
At a rhythm of 10 key strokes sec the time corresponds to
9899995005000616106 10sec101010)10(
6
equiv=sdotsdot=minust years
Figure 47 ndash Summary table of the probabilities according to Boltzmann
In realty the situation is even ldquoworserdquo still In fact in the calculation of the combinations duplicate configurations are not considered
(which necessarily must be considered as possible) in other words our monkeys could produce the same combinations several times (or two identical pages) anyway the duplications will be useless
in the compilation of our small book of only 106 letters
To this end we invoke chance (to attempt to appreciate the incidence of the repeating of
identical pages) and having constructed a Gaussian by arranging the frequency of identical pages we can reason as follows having produced all the astronomical combinations as above in the time
calculated (which we will call a cycle) the highest probability of identical pages is in pairs (which
Pier Maria Boria Thermodynamics amp life
29
we will assign the maximum position) then in threes and so on At infinity with a probability of
zero all the pages will be identical
It seems fair to presume that the standard deviation could be very large qualifying for a very
flat Gaussian and let us suppose that the pages to be rejected (one for the doubles two for the
triplets etc) are contained within the first standard deviation (as in Figure 48) then the duplicate pages to be thrown away would be about 68
Figure 48 ndash The postulated conditions (pages to be eliminated because they are duplicated equal
to the standard deviation) make 68 of the pages produced useless Iterating the cycle one could
consider the duplication of other pages however it can be demonstrated that the phenomenon
continues to imply finite times
How much does the required time increase to generalize we assume the length of a cycle to be of one unit and we identify with K the average cost of discarded pages (in the previous numerical
case K= 068) and then we observe Figure 49
Figure 49 ndash Having exhausted the first cycle identified by 1 the second of length K allows the
replacement of the duplicate pages produced in the first cycle the third of length K2 is used to
replace those produced in the second cycle and so on
The time necessary to complete the cycles required to eliminate the duplicates as they are produced will be given by the sum
suminfin
=0n
nK
which constitutes a geometric series
The Mathematical Analysis teaches us that such a series converges for 1ltK as is confirmed
in our case where it takes on the value 068
KS
minus=
1
1 and if K = 068 gives 1253
6801
1=
minus=S
Pier Maria Boria Thermodynamics amp life
30
Therefore multiplying by 3125 the time dedicated to complete a cycle (317middot105999989 billion
years) for the hypothesis made we also eliminate all the duplicate pages of our little book of 106
key strokes
Changing the value of K (always lt1) one obtains different multipliers but always of a finite
value let the reader imagine the time necessary to type all of Shakespearersquos works It must be highlighted that the monkey operation to be considered a success requires the
intervention of external intelligence capable of selecting the useful pages (like thought by Theory of
Information) and ordering them in the right sequence to obtain a final legible manuscript this
obvious necessity implies that negative entropy be introduced into the system as covered at the
beginning this is like a living being taking the trouble to ldquoput in orderrdquo otherwise the ldquopurely
randomrdquo work would be entirely useless because it will exclusively produce positive entropy
All experiments attempted by man with the goal of demonstrating the random production of
complex molecules (first building blocks of living organisms) have the defect of requiring an a
priori living system like man to arrange this production
When later chaotic physical-chemical conditions are created (temperature pressure
methane electrical arching etc) hoping to obtain that which Thermodynamics does not permit the
inventors of the moto perpetuo come to mind who never give up
The research on the ldquoprimordial souprdquo belongs to this type of experimentation a battle horse
of the followers of the ldquomaitre agrave penserrdquo of the last century and which regard in particular the laboratory experiments of Stanley Miller the goal of his research of a physical-chemical nature
was to recreate life it was an understandable but too ambitious of a project for a researcher The result was absolutely negative (Miller himself recognized it) however this last piece of information
is only whispered in scientific circles so that we still find genuine touts who speak with enthusiastic coram populo of the primordial soup and its miraculous effects14 with a self-assurance
that is truly shameful
45 CONCLUSION
On 4 July 2007 at the London Kinetics Museum a serious presentation of a perpetual motion
machine was scheduled a machine capable of supplying the user with a power greater than that
absorbed ldquoObviouslyrdquo the presentation was postponed due to ldquoa technical problemrdquo15
It would appear impossible but advocates convinced of such a motion exist and many
inventors submit patent after patent even though still in illo tempore Max Planck declared himself
to be contrary to such a possibility which violates the principles of Thermodynamics
Based on the reasoning we have developed regarding entropy probability and chance the
violation of such principles is implicit even in the attempts to obtain living organisms in a
laboratory (characterized as we have seen as being producers of negative entropy) and as such a
strong analogy can be seen between the advocates of perpetual motion and those aspiring to create
life
1 The correct application of Boltzmannrsquos statistics a phenomenon for which we call on
probability demonstrates that combinations of large numbers of particles to the point of generating complex organisms require very long periods of time in comparison the age of
the universe is but the blink of an eye
2 The probabilities take on the largest numbers in correspondence with the most disordered
configurations
14
From ldquoCorriere della Serardquo october 2008 ldquoLa vita sulla Terra Cominciograve nei vulcani con un innesco chimicordquo 15
-Source Wikipedia
Pier Maria Boria Thermodynamics amp life
3 The most ordered combinations are those which characterize organic structures and the action
of an intelligent being is necessary to select order and conserve in time the favorable
combinations
4 The phrase ldquochance phenomenonrdquo is somewhat less intuitive than what ldquocommon senserdquo
would suggest In fact the Gaussian perspective implies that such phenomena are necessarily
associated with a program this program implies the existence of an objective around which
we have an increased concentration of events
5 In every case it is necessary to postulate the existence of an intelligent design without which
the configurations and the favorable events constitute events without any functional link
between themselves
6 The existence of life as a producer of negative entropy on a continuous basis (not cyclical) is a fact visible with our own eyes
All this leads us to support the existence of a Co-ordinating Entity which possesses life ldquoa
priorirdquo and which is capable of transmitting it to animals (animalis homo included) and vegetation It can be noted that the two living systems animal and vegetable complement each other in the
sense that the design requires that emissions from the first (CO2) are the nutrients for the second and the byproducts of the second (O2) are essential for the first the carbon and oxygen cycles look
like they have been designed According to the author there is only one explanation we are in the presence of the greatest
Design Physicist of all times God the Creator
This is what we call Him as Christians while Israelites call Him Jehovah the Ishmaelites
Allah the Masons GADU (Great Architect of the Universe) etc
In other terms
the Creation is a thermodynamic necessity
Amen
Pier Maria Boria Thermodynamics amp life
Figure 16 ndash Heat pumping in a refrigerator
In this sketch the external energy Q3 appears essential and the system is open the energy Q
increase its entropy gaining the temperature T2 entering the condensator Restarting the numerical example of the Clausius calorimeter we reconfirm Q=50 J as the
heat exchanged in this condition it is easy to verify that the water temperature decreases by 10 K while the copper increases by 90 K
Assuming COP=3 we have
final temperature of water T1 = 290 K
and for the copper T2 = 490+903 = 520 K
proceeding as above it follows that
for the copper
∆ 520400 0 5 ∙ 004 002
(
for the water
∆ 290300 5 ∙ 0034 0170
(
Therefore the quantity of transformed heat Q is subject to the variation
∆ ∆ + ∆ 002 0170 015 lt 0 ( ∶
thanks to the contribution of the external energy Q3 the exchanged heat decreases its entropy
Now we will see in what way nature does the heat pumping
Pier Maria Boria Thermodynamics amp life
9
Part 2 (of 4) Boltzmannrsquos Distribution
21 THE BOLTZMANNrsquoS DISTRIBUTION
We will reply to the question after having examined the second pillar on which we base this paper Boltzmannrsquos Distribution (Ludwig Boltzmann Austria 1844-1906)
As can also be seen in excellent web pages the disorganized vibrational velocity of the molecules of a gas (but also those of liquids and solids) at a given temperature take on values
which are continuously and randomly variable following a particular distribution represented graphically in Figure 21
Figure 21 ndash Probability distribution of the velocity of molecules of a gas as a function
of the velocity itself according to Boltzmannrsquos Statistic
It is thanks to this distribution discovered by Boltzmann that living nature vegetable and animal can perform local transformations with decreasing entropy the great masters have
thought up theoretical experiments based on devices capable of selecting molecules of colder gas having higher velocities than what is thought to be the average velocity of the molecules of the
warmer gas (Maxwell the demon Polvani the choosing porter Amerio the selecting valve) to allow them to pass from a lower temperature environment to another adjacent environment with
higher temperature in this way obtaining a transformation which locally invalidates the second
principle of thermodynamics
In Figure 22 it is possible to see that at every average velocity (considered) of the ldquowarmrdquo
molecules one can find a corresponding branch of the ldquocoldrdquo curve related to those particles that
should they pass to the warmer side could cause an increase in that average velocity and therefore
of the temperature
Pier Maria Boria Thermodynamics amp life
10
Figure 22 ndashThe Maxwell demon allows the passage from the colder to the warmer
environment only of the molecules which have a velocity higher than the
weighted average velocity of the warmer molecules
It is necessary to perform a sorting of the molecules one by one with mechanical means not
available to man while the experimental observations of the type reported above would suggest
that nature is capable of it operating at a molecular level in the realm of living organisms
In Figure 23 is represented the device which allows the ldquotheoretical experimentrdquo in the form
proposed by Prof Amerio of the Polytechnic of Milano (1955) Maxwell had proposed a ldquodemonrdquo
as selector of the molecules (1867) the selection device has been the object of particular attention
on the part of Szilard (1929) and later Bennet (1981) with the scope of correctly counting the
variation of entropy in the test universe and calculate the required energy for the selection
Figure 23 ndash The selective valve allows the passage from the colder to the warmer
environment only of the molecules which have a velocity higher than the
weighted average velocity of the warmer molecules as shown in Fig 22
Pier Maria Boria Thermodynamics amp life
These elementary applications of classic thermodynamics based on the concept of entropy
and on Bolzmannrsquos Distribution suggest to us that the phenomenon ldquoliferdquo is to be associated with a
ldquovis-vitalisrdquo external to the dissipative mechanism for which we have ample and daily experience
Obviously it is impossible for man to build a Maxwell device but in our research we have
found a very interesting observation by Jaques Monod (Nobel Prize in 1965) that confers the part of
demon to the natural enzymes7
According to this point of view we can convert the Figure 16 as follows
Figure 24 ndash The natural heat pumping performed by enzymes
and this sketch we consider as typical of the phenomenon ldquoliferdquo The role played by the vis-vitalis seems essential because the only electro-chemical energy
associated with enzymes are components easily deliverable in the biological laboratories but
nobody has been able to start life from these components8
There are those who attempt an approach to this argument with improper methods and with
arbitrary applications of the concept of probability which leads to theories that are devoid of the
required respect for a sound scientific doctrine
22 CONCLUSIONS FROM THE FIRST AND SECOND PART
Rivers of ink have been written about the origin of life to the point that it is possible to read
about the most bizarre theories that completely ignore that which is suggested by the Queen of
Physics Thermodynamics
Paleontology Biology extraterrestrials UFOs Cosmic Palingenesis and similar are all
stirred numbers equations concepts of probability principles of conservation etc are not used
7 Le hazard et la neacutecessiteacute 1970 ndash Arnoldo Mondadori Editore Spa ndash Milan ndash Pag 58
8 See the Stanley Miller experiment at the end of paragraph 54
Pier Maria Boria Thermodynamics amp life
12
correctly These are the only foundations possible for a correctly stated scientific discussion (there
is no adjective more abused than the term ldquoscientificrdquo)
The reader could (perhaps on a rainy Sunday) do some research on the ldquoprimordialrdquo soup (but
if it is not Knorr for whorsquos brand modestly in youth we made thermodynamics projects does not
taste good) on the ldquocosmic tankrdquo on the ldquotyping monkeysrdquo on the cycle of carbon and oxygen (in relation to the demonization of CO2) on the hydrological cycle (which is a substance that cannot
be ldquoconsumedrdquo as is currently heard said otherwise what cycle would it complete subjects often treated by substituting Science with ideology and making ample use of the principle of superior
authority (the ipse dixit of historical memory) upholding disjointed dogma but which are
politically correct
Sometimes one has the feeling of witnessing the squalid discourse of gossiping women by the fountain
It can be noted that in the observations made up to now we have practically not talked about energy whorsquos role in the economy of our discourse has been secondary Itrsquos the definition of the
entropy index state which changes the way to view the cosmos we would not talk of it if it were
possible to carry out reversible reactions
We would come to suspect that the irreversibility is a ldquodefectrdquo of the cosmos having the
function of forcing it to a gradual entropic enrichment (and therefore to a degeneration of energy)
such that the final form of all the energy available becomes one that is thermally and entropically
unusable therefore by virtue of what has been discussed at a certain point in the evolution of the
universe at a finite time it will not be possible to practically perform any thermodynamic cycle9
That is to say the thermal death of the universe
9 We will be further willing to suspect a decay of the cosmological properties correlated to the original sin Ah free
thought
Pier Maria Boria Thermodynamics amp life
13
Part 3 (of 4) Probability
31 PROBABILITY IN BOLTZMANNrsquoS STATISTICS
Boltzmann obtained the graph of the probability as a function of temperature postulating that
a certain number m of particles which are indistinguishable from each other (which we will call A
B C M) and a number n of possible states (a b c n) in which one or more particles (even if
m) can find themselves the presence of particles in each state could occur with different possibilities
If the identical particles are free to occupy the various states (as in the case of a gas) these could continuously exchange states between themselves (for example thanks to reciprocal impacts
as in Figure 23) whilst ldquoon averagerdquo maintaining a certain distribution subject to the conditions around them (for example temperature) a certain distribution of the possible configurations would
be typical of such conditions
Continuing with this example if by state of the particles we mean possessing a certain amount
of kinetic energy E associated with each molecule of a gas in a certain interval of values of energy
∆E there will be a stable quantity of molecules even if amongst themselves continues exchanges of
energy occur Therefore in the range of the same interval some particles enter and some leave
If for the sake of imagination in what follows particles will be considered as ldquoballsrdquo and
states as levels of energy the balls will represent the particles while the levels will represent an
interval of energy (∆E)
Let us start with a very simple case consisting of 3 particles (m=3) able to be hosted by two
levels (n=2) as illustrated in Figure 31
In the left column we see all the possible combinations In the central section we see that certain combinations repeat themselves in such a way that if the particles become indistinguishable
(column 3) they are to be considered the same amongst themselves Therefore three possibilities exist such that both the combinations 234 and 567 can occur
and only once for the combinations 1 and 8 If we ldquonormalizerdquo the possibility (expressing it in unitary or percentage terms) it assumes the
role of probability (ratio between favorable cases and possible cases) which we have done in the last column by expressing it in percentage terms as is common practice
Pier Maria Boria Thermodynamics amp life
14
Figure 31 ndash A rather simple case to demonstrate how given m=3 and n=2 it is possible to
have different probabilities for each combination
Pier Maria Boria Thermodynamics amp life
15
This allows us to draw the graph of Figure 32 where we can begin to see the
Boltzmann distribution forming
Figure 32 ndash The embryonic Boltzmann diagram increasing particles and the number of
possible states the envelope of the columns (in this particular case not yet)
acquires the characteristic asymmetric bell shape
Following in the footsteps of the great Ludwig we enter into systems which are numerically
more substantial three combinations of seven states with an arbitrary arrangement of four particles
as represented in Figure 33 the three combinations are equivalent because the particles are
indistinguishable by hypothesis
Pier Maria Boria Thermodynamics amp life
16
Figure 33 - The three configurations are equivalent if the four particles are indistinguishable
amongst themselves
Each of the n states can be associated with A B C etc (that is to each or more of the m
particles) and since a single particle can occupy each time a different state (and other particles
other states) m times the possible combinations C are ntimesntimesntimeshelliptimesn (m factors equal to n)
C = nm
We could also be convinced observing for example Figure 34 where it is assumed that n=5
(it looks like a musical stavehellip) and m=2 particles (therefore 52=25 combinations)
Pier Maria Boria Thermodynamics amp life
Figure 34 ndash Beyond the 25th beat the preceding configurations are repeated because A and B are
indistinguishable Within the range of the 25 possible configurations some are more favored
because they appear more frequently for example 6 and 22 9 and 25 etc The unoccupied
states are identified by a circle
As is fair to expect configuration 1 is least favored
Pier Maria Boria Thermodynamics amp life
18
We can arrive at the same result with a more practical method suitable also for very large
values of n and m which we will use as follows
It consists of a tabular method stolen from Combinatorial Analysis where for n and m equal to
various units it avoids the need to write hundreds or thousands of key strokes as used above
Let us take two rows and as many columns as there are states thereby obtaining a grid in
Figure 35 to verify what has been said above we have taken 2 rows and 5 columns (n=2 m=5)
Figure 35- With this grid we obtain the number of possible configurations
To further demonstrate we will build a grid for n=5 and m=4 as in Figure 36 where there are sufficient rows to progressively expose the number of particles (from 4 to 1 in the first box of
the first column of the occupancy numbers) and there are n columns
Pier Maria Boria Thermodynamics amp life
19
Figure 36 - Since 54= 625 there are 625 possible combinations the relative probabilities are
listed in the last column note the asymmetry
Pier Maria Boria Thermodynamics amp life
20
It is necessary to observe that in the figure the table of numbers of occupancy reminds
us not by chance of Tartagliarsquos Triangle while the Boltzmann type diagram that can be
associated shown in Figure 37 takes on an almost familiar shape
Figure 37 - Graphical representation of Figure 62 the bars are asymmetric
Pier Maria Boria Thermodynamics amp life
21
To provide an example and referring to Figure 36 we can see how it is possible to obtain 80
possibilities corresponding to his second line
If a box is occupied by 3 particles out of an available 4 the simple combinations of 4 objects
with 3 by 3 (as taught by the Combinatorial Analysis) are given by the binomial coefficient
6437 4
and the four possible groups of three numbers have five positions from which to choose From here 4times5=20 possibilities for the group of three numbers
The single remaining particle has the possibility of the four remaining locations and therefore has 1times4=4 possibilities
The product 20times4=80 gives us the total possibilities in the case that the particles arrange themselves in two groups one with three and one with a single particle and having five boxes
suitable It is easy to verify that we will obtain the same result considering first the single particle
having five boxes suitable (five possibilities 1x5=5) and after the three having the four remaining
(one is occupied by the single particle therefore 4x4=16 and 5x16=80)
Applying the procedure line by line it produces the results shown
Pier Maria Boria Thermodynamics amp life
22
Part 4 (of 4) Chance
41 CHANCE
A sharp-shooter shoots at a target with an excellent rifle he aims carefully chooses the
moment when his breathing will not interfere and the amount of force with which to pull the trigger so as not to move the barrel fires the shot and hits the bullrsquos-eye
Immediately afterwards he takes all the same precautions but the shot ends up being slightly off target it could have been a slight disturbance to his sight an involuntary variation in his
breathing an imperceptible abnormal movement of the finger a very slight unpredictable wind or who knows what else
The causes are many and imponderable slight if each is considered in itself but interacting differently each time ensuring that each shot has a different fate
This complex of innumerable causes of disturbance which are not controllable or predictable
and which not being able to take each into account one by one are called the Law of Probability
(Gaussrsquos Law)10
Probability for the reasons given and law thanks to Carl Friedrich Gauss (1777-1855) who
wrote an equation capable of taking into consideration in a global manner all those fleeting causes
so as to be able to predict with near accurate approximation how the shots will arrange themselves
percentage wise round the target with different distances from the bullseye The approximation will
be more accurate the greater the number of shots that are fired
Let us assume that the target is as represented in Figure 41 and is divided into two parts by
means of the section AB and that our sharpshooter fires many shots after which we count the
number of shots which hit the target in each half
Figure 41- The segmented target
If the reasons for the error are truly random (rifle without defects such that it does not tend to
deviate the shot systematically and neither does the sharpshooter have an analogous defect there is
10
The example of the sharpshooter was published by Engineer Mario Manaira in Ndeg 256 of ldquoJournal of Mechanicsrdquo
together with our first article concerning thermodynamics more than half a century ago (1961)
Pier Maria Boria Thermodynamics amp life
23
not a steady wind etc in other words there does not exist a cause which always influences with the
same bias called a systematic cause) we could note the following
1 The shots will be greater in number in the first band round the center
2 The shots will progressively decrease in number in the subsequent bands as these distance themselves further from the center until there are very few in the bands furthest away
3 The shots in the two halves right and left in any similar band will tend to have the same number and will even be identical if sufficient shots are fired
It is therefore possible to represent the phenomenon graphically as in the following figure
Figure 42 ndash The random distribution of the shots in each band and the Gaussian distribution that
would be obtained with an infinite number of shots fired
If the marksman were less capable the concentration of shots near the zero on the abscissa would reduce and the curve would flatten itself while maintaining the characteristics given and
represented in Figure 43 The first observation is that the maximum height of the curve constitutes the ldquotargetrdquo in other words the goal of the operation while the absence of systematic causes (in
antithesis of randomness) ensures the symmetry of the curve with respect to the vertical which
represents our target zero
Pier Maria Boria Thermodynamics amp life
24
Figure 43 - If the marksman is less skilled the Gaussian flattens
In the case of a systematic cause of error the curve loses its symmetry if we assume that the
test is performed with a constant wind from left to right the graph will take on the shape of Figure
44
Figure 44 ndash When the Gaussian is asymmetric it implies that the phenomenon is not ldquoentirely
randomrdquo11
Let us suppose now that our sharpshooter is blindfolded the target becomes very large and is
moved he will have to shoot blindly (randomly) left and right high and low Given that the Gauss
11
Gauss suggests that the analytical expression of the Law of Randomness is the function
2xey minus
=
where it can be seen that the curve is symmetrical with respect to the axis x=0 and decreasing both towards the left and
right of this line and has a maximum for x=0
It can be shown further that the area subtended is
π=int+infin
infinminus
minusdxe
x2
To ensure that this area is equal to unity as opposed to π appropriate steps can be taken which without
changing the general properties illustrated give the normalized Gaussrsquos Law
Pier Maria Boria Thermodynamics amp life
function still applies the probability curve will flatten itself maintaining the essential
characteristics in particular the two tails which will tend towards a tangent with the abscissa
tending towards infinity a maximum point a point of inflection and the other characteristics
illustrated in Figure 45
Figure 45 ndash Typical characteristics of a normalized Gaussian
Supposing once more that the Gauss function still applies it would be logical to expect a distribution with a curve that is so flat that it will be difficult to see a maximum point corresponding
to the center of the target it will be necessary to fire enough shots so as to occupy every position on the abscissa and to have hit with 100 certainty the bullrsquos-eye
This implies that everything is possible as long as an infinite number of shots are available
(using rhetorical language)
42 SOME PROPERTIES OF RANDOM EVENTS
The perplexities regarding the applicability of chance as referred to the blind sharpshooter
depend on the fact that the Gaussian assumes that programming has been applied to reach an
objective which implies that the operator is conscious of the objective an element which in this
case is absent
Both the existence of a program (the sharpshooter sets out to hit the bullrsquos-eye) and the
existence of an objective (the card with circles) appear to be essential to be able to talk about
chance
Another example let us imagine a machine programmed to produce a certain mechanical
piece the program is the design of the piece written in machine language and the objective is the production of the piece In mass production we will find that it is the case that despite the work
conditions being maintained the same each piece will be different to the other to the point that the pieces which exceed the tolerances (which would not allow them to be interchangeable) will be
rejected Innumerable examples could be presented identifying in every case these two characteristics
a program and an objective Statistics also operate in reverse from the measurement of a group of subjects it creates a bar
chart its envelope will be the curve of the random distribution It will give us the average of the values measured if the curve is symmetrical it will tell us that the phenomenon is not influenced by
systematic causes further it will tell us the value of the standard deviation etc
Pier Maria Boria Thermodynamics amp life
26
To fix this thought in our heads let us suppose that we want to study the average height of a
population of people who are male we make many measurements on many subjects creating bars
for every centimeter we will obtain a graph similar to Figure 46
Figure 46 ndash A practical application the Gaussian deduced from experimental measurements for
statistical purposes
In this statistical application where are the program and objective They are there they are
there they were contained in the information which the people naturally had at conception a
matter of genes and of DNA (an observation coherent with ldquoThe Kid Equationrdquo See the
ldquoIntroduction to Hyperspacerdquo12
)
These considerations lead us to think that the meaning of the word ldquochancerdquo commonly given
does not make sense that ldquochancerdquo does not exist and lead us to suspect that Anatole France had an
inspired guess when he said ldquochance is Godrsquos pseudonym when He does not want to sign his
namerdquo
This strongly agrees with what illustrious philosophers have been confirming for centuries
ldquoDeus absconditus estrdquo (Is XLV XV)
12
In our first volume ldquoCaro amico miohelliprdquo ndash Ed Pagine ndash 2010 In our second volume (ldquoVerba volant eqvuationes
manentrdquo) other considerations about a fundamental theorem of Genetics the Hardy Weinberg theorem
Pier Maria Boria Thermodynamics amp life
27
43 CHANCE amp PROBABILITY
We can now summarize some salient functions of Boltzmann and Gauss
Boltzmann
1 Deals with probability regarding the characteristics that can be assumed by many identical particles having a certain number of positions available (Dirac and Fermi deal
with particles which are distinguishable but the correct reference in our observations are the identical particles)
2 The function presents a maximum and aesthetically looks like a Gaussian but it is not symmetrical
3 It has only a single asymptote to the right of the maximum and its minimum at infinity coincides with zero the origin of the reference system
4 It is normalized so that the area subtended represents the total probability of 100
Gauss
1 Deals with chance and is applicable when an objective exists that is defined by a
program
2 The phenomenon ldquopurely by chancerdquo is represented by a curve that is symmetrical
about the axis x=0
3 The Gaussian has a maximum and no minimum at infinity
4 It possesses two asymptotes one to the right and one to the left of the maximum
5 Well defined values of probability can be associated with multiples of the standard deviation
6 It is normalized as for Boltzmannrsquos
44 THE EDDINGTONrsquoS PARADOX13
Eddingtonrsquos famous ldquoInfinite monkey theoremrdquo can be counted amongst the most discussed
paradoxes for the fact that it is often quoted by so called ldquoscientific popularizersrdquo The original assertion states ldquohellipa monkey hitting keys at random on a typewriter keyboard
for an infinite amount of times will almost surely type a given text such as the complete works of
William Shakespearerdquo
Having taken away the condition of an infinite amount of time the paradox remains acceptable
(from the moment we are able to demonstrate that a finite amount of time is sufficient) However
such a long period of time is necessary that the original statement could be seen as an hyperbolic
discussion
We have seen that random phenomena require a program in light of an objective In the case
of the typing monkeys the program could include the elimination of duplicate pages (actually the
identical pages as we will see below) and the objective could consist in the conservation of ldquogoodrdquo
pages arranged in the right sequence
Applying Boltzmannrsquos statistics let us assume that the typewriter has m=30 keys (we can think of ldquoblindrdquo keys without any writing and all identical) and that we want to write a book of
only 106
letters (a thousand typed pages) as we have observed in paragraph 31 all the possible combinations are
13
The reader can find all the details regarding these various arguments on the web
Pier Maria Boria Thermodynamics amp life
C = nm = (10
6)30
= (10)180
In other words there are 10180
possible configurations
Let us assume that the monkeys are capable of striking 10 keyssec (skilled typistshellip) the
time necessary would be
t = 10180
x 106 10 = 10
185 sec
Since we can count 1016 seconds in a billion years it is also possible to say that the time
required will be
10185
1016
= 10169
billion years (giga-years)
(let us remember that the big-bang has an age of ldquoonlyrdquo 14 billion years)
In reality the situation is even ldquoworserdquo in fact this calculation (which is generally accepted)
is wrong because we cannot talk about only thirty objects (the letters punctuation marks spaces between lines etc) to be arranged in 10
6 positions otherwise in each of 10180 configurations
obtainable we would find empty spaces up to 106-30 in each configuration
It is necessary to postulate that there are 106 letters to be arranged like conceding that the
monkeys have to insert 106 objects ie 10
6 key strokes In other words it is necessary that n = m =
106 and in this case the formula of the combinations gives us an astronomical value
6106 )10(===
mm mnC combinations
At a rhythm of 10 key strokes sec the time corresponds to
9899995005000616106 10sec101010)10(
6
equiv=sdotsdot=minust years
Figure 47 ndash Summary table of the probabilities according to Boltzmann
In realty the situation is even ldquoworserdquo still In fact in the calculation of the combinations duplicate configurations are not considered
(which necessarily must be considered as possible) in other words our monkeys could produce the same combinations several times (or two identical pages) anyway the duplications will be useless
in the compilation of our small book of only 106 letters
To this end we invoke chance (to attempt to appreciate the incidence of the repeating of
identical pages) and having constructed a Gaussian by arranging the frequency of identical pages we can reason as follows having produced all the astronomical combinations as above in the time
calculated (which we will call a cycle) the highest probability of identical pages is in pairs (which
Pier Maria Boria Thermodynamics amp life
29
we will assign the maximum position) then in threes and so on At infinity with a probability of
zero all the pages will be identical
It seems fair to presume that the standard deviation could be very large qualifying for a very
flat Gaussian and let us suppose that the pages to be rejected (one for the doubles two for the
triplets etc) are contained within the first standard deviation (as in Figure 48) then the duplicate pages to be thrown away would be about 68
Figure 48 ndash The postulated conditions (pages to be eliminated because they are duplicated equal
to the standard deviation) make 68 of the pages produced useless Iterating the cycle one could
consider the duplication of other pages however it can be demonstrated that the phenomenon
continues to imply finite times
How much does the required time increase to generalize we assume the length of a cycle to be of one unit and we identify with K the average cost of discarded pages (in the previous numerical
case K= 068) and then we observe Figure 49
Figure 49 ndash Having exhausted the first cycle identified by 1 the second of length K allows the
replacement of the duplicate pages produced in the first cycle the third of length K2 is used to
replace those produced in the second cycle and so on
The time necessary to complete the cycles required to eliminate the duplicates as they are produced will be given by the sum
suminfin
=0n
nK
which constitutes a geometric series
The Mathematical Analysis teaches us that such a series converges for 1ltK as is confirmed
in our case where it takes on the value 068
KS
minus=
1
1 and if K = 068 gives 1253
6801
1=
minus=S
Pier Maria Boria Thermodynamics amp life
30
Therefore multiplying by 3125 the time dedicated to complete a cycle (317middot105999989 billion
years) for the hypothesis made we also eliminate all the duplicate pages of our little book of 106
key strokes
Changing the value of K (always lt1) one obtains different multipliers but always of a finite
value let the reader imagine the time necessary to type all of Shakespearersquos works It must be highlighted that the monkey operation to be considered a success requires the
intervention of external intelligence capable of selecting the useful pages (like thought by Theory of
Information) and ordering them in the right sequence to obtain a final legible manuscript this
obvious necessity implies that negative entropy be introduced into the system as covered at the
beginning this is like a living being taking the trouble to ldquoput in orderrdquo otherwise the ldquopurely
randomrdquo work would be entirely useless because it will exclusively produce positive entropy
All experiments attempted by man with the goal of demonstrating the random production of
complex molecules (first building blocks of living organisms) have the defect of requiring an a
priori living system like man to arrange this production
When later chaotic physical-chemical conditions are created (temperature pressure
methane electrical arching etc) hoping to obtain that which Thermodynamics does not permit the
inventors of the moto perpetuo come to mind who never give up
The research on the ldquoprimordial souprdquo belongs to this type of experimentation a battle horse
of the followers of the ldquomaitre agrave penserrdquo of the last century and which regard in particular the laboratory experiments of Stanley Miller the goal of his research of a physical-chemical nature
was to recreate life it was an understandable but too ambitious of a project for a researcher The result was absolutely negative (Miller himself recognized it) however this last piece of information
is only whispered in scientific circles so that we still find genuine touts who speak with enthusiastic coram populo of the primordial soup and its miraculous effects14 with a self-assurance
that is truly shameful
45 CONCLUSION
On 4 July 2007 at the London Kinetics Museum a serious presentation of a perpetual motion
machine was scheduled a machine capable of supplying the user with a power greater than that
absorbed ldquoObviouslyrdquo the presentation was postponed due to ldquoa technical problemrdquo15
It would appear impossible but advocates convinced of such a motion exist and many
inventors submit patent after patent even though still in illo tempore Max Planck declared himself
to be contrary to such a possibility which violates the principles of Thermodynamics
Based on the reasoning we have developed regarding entropy probability and chance the
violation of such principles is implicit even in the attempts to obtain living organisms in a
laboratory (characterized as we have seen as being producers of negative entropy) and as such a
strong analogy can be seen between the advocates of perpetual motion and those aspiring to create
life
1 The correct application of Boltzmannrsquos statistics a phenomenon for which we call on
probability demonstrates that combinations of large numbers of particles to the point of generating complex organisms require very long periods of time in comparison the age of
the universe is but the blink of an eye
2 The probabilities take on the largest numbers in correspondence with the most disordered
configurations
14
From ldquoCorriere della Serardquo october 2008 ldquoLa vita sulla Terra Cominciograve nei vulcani con un innesco chimicordquo 15
-Source Wikipedia
Pier Maria Boria Thermodynamics amp life
3 The most ordered combinations are those which characterize organic structures and the action
of an intelligent being is necessary to select order and conserve in time the favorable
combinations
4 The phrase ldquochance phenomenonrdquo is somewhat less intuitive than what ldquocommon senserdquo
would suggest In fact the Gaussian perspective implies that such phenomena are necessarily
associated with a program this program implies the existence of an objective around which
we have an increased concentration of events
5 In every case it is necessary to postulate the existence of an intelligent design without which
the configurations and the favorable events constitute events without any functional link
between themselves
6 The existence of life as a producer of negative entropy on a continuous basis (not cyclical) is a fact visible with our own eyes
All this leads us to support the existence of a Co-ordinating Entity which possesses life ldquoa
priorirdquo and which is capable of transmitting it to animals (animalis homo included) and vegetation It can be noted that the two living systems animal and vegetable complement each other in the
sense that the design requires that emissions from the first (CO2) are the nutrients for the second and the byproducts of the second (O2) are essential for the first the carbon and oxygen cycles look
like they have been designed According to the author there is only one explanation we are in the presence of the greatest
Design Physicist of all times God the Creator
This is what we call Him as Christians while Israelites call Him Jehovah the Ishmaelites
Allah the Masons GADU (Great Architect of the Universe) etc
In other terms
the Creation is a thermodynamic necessity
Amen
Pier Maria Boria Thermodynamics amp life
9
Part 2 (of 4) Boltzmannrsquos Distribution
21 THE BOLTZMANNrsquoS DISTRIBUTION
We will reply to the question after having examined the second pillar on which we base this paper Boltzmannrsquos Distribution (Ludwig Boltzmann Austria 1844-1906)
As can also be seen in excellent web pages the disorganized vibrational velocity of the molecules of a gas (but also those of liquids and solids) at a given temperature take on values
which are continuously and randomly variable following a particular distribution represented graphically in Figure 21
Figure 21 ndash Probability distribution of the velocity of molecules of a gas as a function
of the velocity itself according to Boltzmannrsquos Statistic
It is thanks to this distribution discovered by Boltzmann that living nature vegetable and animal can perform local transformations with decreasing entropy the great masters have
thought up theoretical experiments based on devices capable of selecting molecules of colder gas having higher velocities than what is thought to be the average velocity of the molecules of the
warmer gas (Maxwell the demon Polvani the choosing porter Amerio the selecting valve) to allow them to pass from a lower temperature environment to another adjacent environment with
higher temperature in this way obtaining a transformation which locally invalidates the second
principle of thermodynamics
In Figure 22 it is possible to see that at every average velocity (considered) of the ldquowarmrdquo
molecules one can find a corresponding branch of the ldquocoldrdquo curve related to those particles that
should they pass to the warmer side could cause an increase in that average velocity and therefore
of the temperature
Pier Maria Boria Thermodynamics amp life
10
Figure 22 ndashThe Maxwell demon allows the passage from the colder to the warmer
environment only of the molecules which have a velocity higher than the
weighted average velocity of the warmer molecules
It is necessary to perform a sorting of the molecules one by one with mechanical means not
available to man while the experimental observations of the type reported above would suggest
that nature is capable of it operating at a molecular level in the realm of living organisms
In Figure 23 is represented the device which allows the ldquotheoretical experimentrdquo in the form
proposed by Prof Amerio of the Polytechnic of Milano (1955) Maxwell had proposed a ldquodemonrdquo
as selector of the molecules (1867) the selection device has been the object of particular attention
on the part of Szilard (1929) and later Bennet (1981) with the scope of correctly counting the
variation of entropy in the test universe and calculate the required energy for the selection
Figure 23 ndash The selective valve allows the passage from the colder to the warmer
environment only of the molecules which have a velocity higher than the
weighted average velocity of the warmer molecules as shown in Fig 22
Pier Maria Boria Thermodynamics amp life
These elementary applications of classic thermodynamics based on the concept of entropy
and on Bolzmannrsquos Distribution suggest to us that the phenomenon ldquoliferdquo is to be associated with a
ldquovis-vitalisrdquo external to the dissipative mechanism for which we have ample and daily experience
Obviously it is impossible for man to build a Maxwell device but in our research we have
found a very interesting observation by Jaques Monod (Nobel Prize in 1965) that confers the part of
demon to the natural enzymes7
According to this point of view we can convert the Figure 16 as follows
Figure 24 ndash The natural heat pumping performed by enzymes
and this sketch we consider as typical of the phenomenon ldquoliferdquo The role played by the vis-vitalis seems essential because the only electro-chemical energy
associated with enzymes are components easily deliverable in the biological laboratories but
nobody has been able to start life from these components8
There are those who attempt an approach to this argument with improper methods and with
arbitrary applications of the concept of probability which leads to theories that are devoid of the
required respect for a sound scientific doctrine
22 CONCLUSIONS FROM THE FIRST AND SECOND PART
Rivers of ink have been written about the origin of life to the point that it is possible to read
about the most bizarre theories that completely ignore that which is suggested by the Queen of
Physics Thermodynamics
Paleontology Biology extraterrestrials UFOs Cosmic Palingenesis and similar are all
stirred numbers equations concepts of probability principles of conservation etc are not used
7 Le hazard et la neacutecessiteacute 1970 ndash Arnoldo Mondadori Editore Spa ndash Milan ndash Pag 58
8 See the Stanley Miller experiment at the end of paragraph 54
Pier Maria Boria Thermodynamics amp life
12
correctly These are the only foundations possible for a correctly stated scientific discussion (there
is no adjective more abused than the term ldquoscientificrdquo)
The reader could (perhaps on a rainy Sunday) do some research on the ldquoprimordialrdquo soup (but
if it is not Knorr for whorsquos brand modestly in youth we made thermodynamics projects does not
taste good) on the ldquocosmic tankrdquo on the ldquotyping monkeysrdquo on the cycle of carbon and oxygen (in relation to the demonization of CO2) on the hydrological cycle (which is a substance that cannot
be ldquoconsumedrdquo as is currently heard said otherwise what cycle would it complete subjects often treated by substituting Science with ideology and making ample use of the principle of superior
authority (the ipse dixit of historical memory) upholding disjointed dogma but which are
politically correct
Sometimes one has the feeling of witnessing the squalid discourse of gossiping women by the fountain
It can be noted that in the observations made up to now we have practically not talked about energy whorsquos role in the economy of our discourse has been secondary Itrsquos the definition of the
entropy index state which changes the way to view the cosmos we would not talk of it if it were
possible to carry out reversible reactions
We would come to suspect that the irreversibility is a ldquodefectrdquo of the cosmos having the
function of forcing it to a gradual entropic enrichment (and therefore to a degeneration of energy)
such that the final form of all the energy available becomes one that is thermally and entropically
unusable therefore by virtue of what has been discussed at a certain point in the evolution of the
universe at a finite time it will not be possible to practically perform any thermodynamic cycle9
That is to say the thermal death of the universe
9 We will be further willing to suspect a decay of the cosmological properties correlated to the original sin Ah free
thought
Pier Maria Boria Thermodynamics amp life
13
Part 3 (of 4) Probability
31 PROBABILITY IN BOLTZMANNrsquoS STATISTICS
Boltzmann obtained the graph of the probability as a function of temperature postulating that
a certain number m of particles which are indistinguishable from each other (which we will call A
B C M) and a number n of possible states (a b c n) in which one or more particles (even if
m) can find themselves the presence of particles in each state could occur with different possibilities
If the identical particles are free to occupy the various states (as in the case of a gas) these could continuously exchange states between themselves (for example thanks to reciprocal impacts
as in Figure 23) whilst ldquoon averagerdquo maintaining a certain distribution subject to the conditions around them (for example temperature) a certain distribution of the possible configurations would
be typical of such conditions
Continuing with this example if by state of the particles we mean possessing a certain amount
of kinetic energy E associated with each molecule of a gas in a certain interval of values of energy
∆E there will be a stable quantity of molecules even if amongst themselves continues exchanges of
energy occur Therefore in the range of the same interval some particles enter and some leave
If for the sake of imagination in what follows particles will be considered as ldquoballsrdquo and
states as levels of energy the balls will represent the particles while the levels will represent an
interval of energy (∆E)
Let us start with a very simple case consisting of 3 particles (m=3) able to be hosted by two
levels (n=2) as illustrated in Figure 31
In the left column we see all the possible combinations In the central section we see that certain combinations repeat themselves in such a way that if the particles become indistinguishable
(column 3) they are to be considered the same amongst themselves Therefore three possibilities exist such that both the combinations 234 and 567 can occur
and only once for the combinations 1 and 8 If we ldquonormalizerdquo the possibility (expressing it in unitary or percentage terms) it assumes the
role of probability (ratio between favorable cases and possible cases) which we have done in the last column by expressing it in percentage terms as is common practice
Pier Maria Boria Thermodynamics amp life
14
Figure 31 ndash A rather simple case to demonstrate how given m=3 and n=2 it is possible to
have different probabilities for each combination
Pier Maria Boria Thermodynamics amp life
15
This allows us to draw the graph of Figure 32 where we can begin to see the
Boltzmann distribution forming
Figure 32 ndash The embryonic Boltzmann diagram increasing particles and the number of
possible states the envelope of the columns (in this particular case not yet)
acquires the characteristic asymmetric bell shape
Following in the footsteps of the great Ludwig we enter into systems which are numerically
more substantial three combinations of seven states with an arbitrary arrangement of four particles
as represented in Figure 33 the three combinations are equivalent because the particles are
indistinguishable by hypothesis
Pier Maria Boria Thermodynamics amp life
16
Figure 33 - The three configurations are equivalent if the four particles are indistinguishable
amongst themselves
Each of the n states can be associated with A B C etc (that is to each or more of the m
particles) and since a single particle can occupy each time a different state (and other particles
other states) m times the possible combinations C are ntimesntimesntimeshelliptimesn (m factors equal to n)
C = nm
We could also be convinced observing for example Figure 34 where it is assumed that n=5
(it looks like a musical stavehellip) and m=2 particles (therefore 52=25 combinations)
Pier Maria Boria Thermodynamics amp life
Figure 34 ndash Beyond the 25th beat the preceding configurations are repeated because A and B are
indistinguishable Within the range of the 25 possible configurations some are more favored
because they appear more frequently for example 6 and 22 9 and 25 etc The unoccupied
states are identified by a circle
As is fair to expect configuration 1 is least favored
Pier Maria Boria Thermodynamics amp life
18
We can arrive at the same result with a more practical method suitable also for very large
values of n and m which we will use as follows
It consists of a tabular method stolen from Combinatorial Analysis where for n and m equal to
various units it avoids the need to write hundreds or thousands of key strokes as used above
Let us take two rows and as many columns as there are states thereby obtaining a grid in
Figure 35 to verify what has been said above we have taken 2 rows and 5 columns (n=2 m=5)
Figure 35- With this grid we obtain the number of possible configurations
To further demonstrate we will build a grid for n=5 and m=4 as in Figure 36 where there are sufficient rows to progressively expose the number of particles (from 4 to 1 in the first box of
the first column of the occupancy numbers) and there are n columns
Pier Maria Boria Thermodynamics amp life
19
Figure 36 - Since 54= 625 there are 625 possible combinations the relative probabilities are
listed in the last column note the asymmetry
Pier Maria Boria Thermodynamics amp life
20
It is necessary to observe that in the figure the table of numbers of occupancy reminds
us not by chance of Tartagliarsquos Triangle while the Boltzmann type diagram that can be
associated shown in Figure 37 takes on an almost familiar shape
Figure 37 - Graphical representation of Figure 62 the bars are asymmetric
Pier Maria Boria Thermodynamics amp life
21
To provide an example and referring to Figure 36 we can see how it is possible to obtain 80
possibilities corresponding to his second line
If a box is occupied by 3 particles out of an available 4 the simple combinations of 4 objects
with 3 by 3 (as taught by the Combinatorial Analysis) are given by the binomial coefficient
6437 4
and the four possible groups of three numbers have five positions from which to choose From here 4times5=20 possibilities for the group of three numbers
The single remaining particle has the possibility of the four remaining locations and therefore has 1times4=4 possibilities
The product 20times4=80 gives us the total possibilities in the case that the particles arrange themselves in two groups one with three and one with a single particle and having five boxes
suitable It is easy to verify that we will obtain the same result considering first the single particle
having five boxes suitable (five possibilities 1x5=5) and after the three having the four remaining
(one is occupied by the single particle therefore 4x4=16 and 5x16=80)
Applying the procedure line by line it produces the results shown
Pier Maria Boria Thermodynamics amp life
22
Part 4 (of 4) Chance
41 CHANCE
A sharp-shooter shoots at a target with an excellent rifle he aims carefully chooses the
moment when his breathing will not interfere and the amount of force with which to pull the trigger so as not to move the barrel fires the shot and hits the bullrsquos-eye
Immediately afterwards he takes all the same precautions but the shot ends up being slightly off target it could have been a slight disturbance to his sight an involuntary variation in his
breathing an imperceptible abnormal movement of the finger a very slight unpredictable wind or who knows what else
The causes are many and imponderable slight if each is considered in itself but interacting differently each time ensuring that each shot has a different fate
This complex of innumerable causes of disturbance which are not controllable or predictable
and which not being able to take each into account one by one are called the Law of Probability
(Gaussrsquos Law)10
Probability for the reasons given and law thanks to Carl Friedrich Gauss (1777-1855) who
wrote an equation capable of taking into consideration in a global manner all those fleeting causes
so as to be able to predict with near accurate approximation how the shots will arrange themselves
percentage wise round the target with different distances from the bullseye The approximation will
be more accurate the greater the number of shots that are fired
Let us assume that the target is as represented in Figure 41 and is divided into two parts by
means of the section AB and that our sharpshooter fires many shots after which we count the
number of shots which hit the target in each half
Figure 41- The segmented target
If the reasons for the error are truly random (rifle without defects such that it does not tend to
deviate the shot systematically and neither does the sharpshooter have an analogous defect there is
10
The example of the sharpshooter was published by Engineer Mario Manaira in Ndeg 256 of ldquoJournal of Mechanicsrdquo
together with our first article concerning thermodynamics more than half a century ago (1961)
Pier Maria Boria Thermodynamics amp life
23
not a steady wind etc in other words there does not exist a cause which always influences with the
same bias called a systematic cause) we could note the following
1 The shots will be greater in number in the first band round the center
2 The shots will progressively decrease in number in the subsequent bands as these distance themselves further from the center until there are very few in the bands furthest away
3 The shots in the two halves right and left in any similar band will tend to have the same number and will even be identical if sufficient shots are fired
It is therefore possible to represent the phenomenon graphically as in the following figure
Figure 42 ndash The random distribution of the shots in each band and the Gaussian distribution that
would be obtained with an infinite number of shots fired
If the marksman were less capable the concentration of shots near the zero on the abscissa would reduce and the curve would flatten itself while maintaining the characteristics given and
represented in Figure 43 The first observation is that the maximum height of the curve constitutes the ldquotargetrdquo in other words the goal of the operation while the absence of systematic causes (in
antithesis of randomness) ensures the symmetry of the curve with respect to the vertical which
represents our target zero
Pier Maria Boria Thermodynamics amp life
24
Figure 43 - If the marksman is less skilled the Gaussian flattens
In the case of a systematic cause of error the curve loses its symmetry if we assume that the
test is performed with a constant wind from left to right the graph will take on the shape of Figure
44
Figure 44 ndash When the Gaussian is asymmetric it implies that the phenomenon is not ldquoentirely
randomrdquo11
Let us suppose now that our sharpshooter is blindfolded the target becomes very large and is
moved he will have to shoot blindly (randomly) left and right high and low Given that the Gauss
11
Gauss suggests that the analytical expression of the Law of Randomness is the function
2xey minus
=
where it can be seen that the curve is symmetrical with respect to the axis x=0 and decreasing both towards the left and
right of this line and has a maximum for x=0
It can be shown further that the area subtended is
π=int+infin
infinminus
minusdxe
x2
To ensure that this area is equal to unity as opposed to π appropriate steps can be taken which without
changing the general properties illustrated give the normalized Gaussrsquos Law
Pier Maria Boria Thermodynamics amp life
function still applies the probability curve will flatten itself maintaining the essential
characteristics in particular the two tails which will tend towards a tangent with the abscissa
tending towards infinity a maximum point a point of inflection and the other characteristics
illustrated in Figure 45
Figure 45 ndash Typical characteristics of a normalized Gaussian
Supposing once more that the Gauss function still applies it would be logical to expect a distribution with a curve that is so flat that it will be difficult to see a maximum point corresponding
to the center of the target it will be necessary to fire enough shots so as to occupy every position on the abscissa and to have hit with 100 certainty the bullrsquos-eye
This implies that everything is possible as long as an infinite number of shots are available
(using rhetorical language)
42 SOME PROPERTIES OF RANDOM EVENTS
The perplexities regarding the applicability of chance as referred to the blind sharpshooter
depend on the fact that the Gaussian assumes that programming has been applied to reach an
objective which implies that the operator is conscious of the objective an element which in this
case is absent
Both the existence of a program (the sharpshooter sets out to hit the bullrsquos-eye) and the
existence of an objective (the card with circles) appear to be essential to be able to talk about
chance
Another example let us imagine a machine programmed to produce a certain mechanical
piece the program is the design of the piece written in machine language and the objective is the production of the piece In mass production we will find that it is the case that despite the work
conditions being maintained the same each piece will be different to the other to the point that the pieces which exceed the tolerances (which would not allow them to be interchangeable) will be
rejected Innumerable examples could be presented identifying in every case these two characteristics
a program and an objective Statistics also operate in reverse from the measurement of a group of subjects it creates a bar
chart its envelope will be the curve of the random distribution It will give us the average of the values measured if the curve is symmetrical it will tell us that the phenomenon is not influenced by
systematic causes further it will tell us the value of the standard deviation etc
Pier Maria Boria Thermodynamics amp life
26
To fix this thought in our heads let us suppose that we want to study the average height of a
population of people who are male we make many measurements on many subjects creating bars
for every centimeter we will obtain a graph similar to Figure 46
Figure 46 ndash A practical application the Gaussian deduced from experimental measurements for
statistical purposes
In this statistical application where are the program and objective They are there they are
there they were contained in the information which the people naturally had at conception a
matter of genes and of DNA (an observation coherent with ldquoThe Kid Equationrdquo See the
ldquoIntroduction to Hyperspacerdquo12
)
These considerations lead us to think that the meaning of the word ldquochancerdquo commonly given
does not make sense that ldquochancerdquo does not exist and lead us to suspect that Anatole France had an
inspired guess when he said ldquochance is Godrsquos pseudonym when He does not want to sign his
namerdquo
This strongly agrees with what illustrious philosophers have been confirming for centuries
ldquoDeus absconditus estrdquo (Is XLV XV)
12
In our first volume ldquoCaro amico miohelliprdquo ndash Ed Pagine ndash 2010 In our second volume (ldquoVerba volant eqvuationes
manentrdquo) other considerations about a fundamental theorem of Genetics the Hardy Weinberg theorem
Pier Maria Boria Thermodynamics amp life
27
43 CHANCE amp PROBABILITY
We can now summarize some salient functions of Boltzmann and Gauss
Boltzmann
1 Deals with probability regarding the characteristics that can be assumed by many identical particles having a certain number of positions available (Dirac and Fermi deal
with particles which are distinguishable but the correct reference in our observations are the identical particles)
2 The function presents a maximum and aesthetically looks like a Gaussian but it is not symmetrical
3 It has only a single asymptote to the right of the maximum and its minimum at infinity coincides with zero the origin of the reference system
4 It is normalized so that the area subtended represents the total probability of 100
Gauss
1 Deals with chance and is applicable when an objective exists that is defined by a
program
2 The phenomenon ldquopurely by chancerdquo is represented by a curve that is symmetrical
about the axis x=0
3 The Gaussian has a maximum and no minimum at infinity
4 It possesses two asymptotes one to the right and one to the left of the maximum
5 Well defined values of probability can be associated with multiples of the standard deviation
6 It is normalized as for Boltzmannrsquos
44 THE EDDINGTONrsquoS PARADOX13
Eddingtonrsquos famous ldquoInfinite monkey theoremrdquo can be counted amongst the most discussed
paradoxes for the fact that it is often quoted by so called ldquoscientific popularizersrdquo The original assertion states ldquohellipa monkey hitting keys at random on a typewriter keyboard
for an infinite amount of times will almost surely type a given text such as the complete works of
William Shakespearerdquo
Having taken away the condition of an infinite amount of time the paradox remains acceptable
(from the moment we are able to demonstrate that a finite amount of time is sufficient) However
such a long period of time is necessary that the original statement could be seen as an hyperbolic
discussion
We have seen that random phenomena require a program in light of an objective In the case
of the typing monkeys the program could include the elimination of duplicate pages (actually the
identical pages as we will see below) and the objective could consist in the conservation of ldquogoodrdquo
pages arranged in the right sequence
Applying Boltzmannrsquos statistics let us assume that the typewriter has m=30 keys (we can think of ldquoblindrdquo keys without any writing and all identical) and that we want to write a book of
only 106
letters (a thousand typed pages) as we have observed in paragraph 31 all the possible combinations are
13
The reader can find all the details regarding these various arguments on the web
Pier Maria Boria Thermodynamics amp life
C = nm = (10
6)30
= (10)180
In other words there are 10180
possible configurations
Let us assume that the monkeys are capable of striking 10 keyssec (skilled typistshellip) the
time necessary would be
t = 10180
x 106 10 = 10
185 sec
Since we can count 1016 seconds in a billion years it is also possible to say that the time
required will be
10185
1016
= 10169
billion years (giga-years)
(let us remember that the big-bang has an age of ldquoonlyrdquo 14 billion years)
In reality the situation is even ldquoworserdquo in fact this calculation (which is generally accepted)
is wrong because we cannot talk about only thirty objects (the letters punctuation marks spaces between lines etc) to be arranged in 10
6 positions otherwise in each of 10180 configurations
obtainable we would find empty spaces up to 106-30 in each configuration
It is necessary to postulate that there are 106 letters to be arranged like conceding that the
monkeys have to insert 106 objects ie 10
6 key strokes In other words it is necessary that n = m =
106 and in this case the formula of the combinations gives us an astronomical value
6106 )10(===
mm mnC combinations
At a rhythm of 10 key strokes sec the time corresponds to
9899995005000616106 10sec101010)10(
6
equiv=sdotsdot=minust years
Figure 47 ndash Summary table of the probabilities according to Boltzmann
In realty the situation is even ldquoworserdquo still In fact in the calculation of the combinations duplicate configurations are not considered
(which necessarily must be considered as possible) in other words our monkeys could produce the same combinations several times (or two identical pages) anyway the duplications will be useless
in the compilation of our small book of only 106 letters
To this end we invoke chance (to attempt to appreciate the incidence of the repeating of
identical pages) and having constructed a Gaussian by arranging the frequency of identical pages we can reason as follows having produced all the astronomical combinations as above in the time
calculated (which we will call a cycle) the highest probability of identical pages is in pairs (which
Pier Maria Boria Thermodynamics amp life
29
we will assign the maximum position) then in threes and so on At infinity with a probability of
zero all the pages will be identical
It seems fair to presume that the standard deviation could be very large qualifying for a very
flat Gaussian and let us suppose that the pages to be rejected (one for the doubles two for the
triplets etc) are contained within the first standard deviation (as in Figure 48) then the duplicate pages to be thrown away would be about 68
Figure 48 ndash The postulated conditions (pages to be eliminated because they are duplicated equal
to the standard deviation) make 68 of the pages produced useless Iterating the cycle one could
consider the duplication of other pages however it can be demonstrated that the phenomenon
continues to imply finite times
How much does the required time increase to generalize we assume the length of a cycle to be of one unit and we identify with K the average cost of discarded pages (in the previous numerical
case K= 068) and then we observe Figure 49
Figure 49 ndash Having exhausted the first cycle identified by 1 the second of length K allows the
replacement of the duplicate pages produced in the first cycle the third of length K2 is used to
replace those produced in the second cycle and so on
The time necessary to complete the cycles required to eliminate the duplicates as they are produced will be given by the sum
suminfin
=0n
nK
which constitutes a geometric series
The Mathematical Analysis teaches us that such a series converges for 1ltK as is confirmed
in our case where it takes on the value 068
KS
minus=
1
1 and if K = 068 gives 1253
6801
1=
minus=S
Pier Maria Boria Thermodynamics amp life
30
Therefore multiplying by 3125 the time dedicated to complete a cycle (317middot105999989 billion
years) for the hypothesis made we also eliminate all the duplicate pages of our little book of 106
key strokes
Changing the value of K (always lt1) one obtains different multipliers but always of a finite
value let the reader imagine the time necessary to type all of Shakespearersquos works It must be highlighted that the monkey operation to be considered a success requires the
intervention of external intelligence capable of selecting the useful pages (like thought by Theory of
Information) and ordering them in the right sequence to obtain a final legible manuscript this
obvious necessity implies that negative entropy be introduced into the system as covered at the
beginning this is like a living being taking the trouble to ldquoput in orderrdquo otherwise the ldquopurely
randomrdquo work would be entirely useless because it will exclusively produce positive entropy
All experiments attempted by man with the goal of demonstrating the random production of
complex molecules (first building blocks of living organisms) have the defect of requiring an a
priori living system like man to arrange this production
When later chaotic physical-chemical conditions are created (temperature pressure
methane electrical arching etc) hoping to obtain that which Thermodynamics does not permit the
inventors of the moto perpetuo come to mind who never give up
The research on the ldquoprimordial souprdquo belongs to this type of experimentation a battle horse
of the followers of the ldquomaitre agrave penserrdquo of the last century and which regard in particular the laboratory experiments of Stanley Miller the goal of his research of a physical-chemical nature
was to recreate life it was an understandable but too ambitious of a project for a researcher The result was absolutely negative (Miller himself recognized it) however this last piece of information
is only whispered in scientific circles so that we still find genuine touts who speak with enthusiastic coram populo of the primordial soup and its miraculous effects14 with a self-assurance
that is truly shameful
45 CONCLUSION
On 4 July 2007 at the London Kinetics Museum a serious presentation of a perpetual motion
machine was scheduled a machine capable of supplying the user with a power greater than that
absorbed ldquoObviouslyrdquo the presentation was postponed due to ldquoa technical problemrdquo15
It would appear impossible but advocates convinced of such a motion exist and many
inventors submit patent after patent even though still in illo tempore Max Planck declared himself
to be contrary to such a possibility which violates the principles of Thermodynamics
Based on the reasoning we have developed regarding entropy probability and chance the
violation of such principles is implicit even in the attempts to obtain living organisms in a
laboratory (characterized as we have seen as being producers of negative entropy) and as such a
strong analogy can be seen between the advocates of perpetual motion and those aspiring to create
life
1 The correct application of Boltzmannrsquos statistics a phenomenon for which we call on
probability demonstrates that combinations of large numbers of particles to the point of generating complex organisms require very long periods of time in comparison the age of
the universe is but the blink of an eye
2 The probabilities take on the largest numbers in correspondence with the most disordered
configurations
14
From ldquoCorriere della Serardquo october 2008 ldquoLa vita sulla Terra Cominciograve nei vulcani con un innesco chimicordquo 15
-Source Wikipedia
Pier Maria Boria Thermodynamics amp life
3 The most ordered combinations are those which characterize organic structures and the action
of an intelligent being is necessary to select order and conserve in time the favorable
combinations
4 The phrase ldquochance phenomenonrdquo is somewhat less intuitive than what ldquocommon senserdquo
would suggest In fact the Gaussian perspective implies that such phenomena are necessarily
associated with a program this program implies the existence of an objective around which
we have an increased concentration of events
5 In every case it is necessary to postulate the existence of an intelligent design without which
the configurations and the favorable events constitute events without any functional link
between themselves
6 The existence of life as a producer of negative entropy on a continuous basis (not cyclical) is a fact visible with our own eyes
All this leads us to support the existence of a Co-ordinating Entity which possesses life ldquoa
priorirdquo and which is capable of transmitting it to animals (animalis homo included) and vegetation It can be noted that the two living systems animal and vegetable complement each other in the
sense that the design requires that emissions from the first (CO2) are the nutrients for the second and the byproducts of the second (O2) are essential for the first the carbon and oxygen cycles look
like they have been designed According to the author there is only one explanation we are in the presence of the greatest
Design Physicist of all times God the Creator
This is what we call Him as Christians while Israelites call Him Jehovah the Ishmaelites
Allah the Masons GADU (Great Architect of the Universe) etc
In other terms
the Creation is a thermodynamic necessity
Amen
Pier Maria Boria Thermodynamics amp life
10
Figure 22 ndashThe Maxwell demon allows the passage from the colder to the warmer
environment only of the molecules which have a velocity higher than the
weighted average velocity of the warmer molecules
It is necessary to perform a sorting of the molecules one by one with mechanical means not
available to man while the experimental observations of the type reported above would suggest
that nature is capable of it operating at a molecular level in the realm of living organisms
In Figure 23 is represented the device which allows the ldquotheoretical experimentrdquo in the form
proposed by Prof Amerio of the Polytechnic of Milano (1955) Maxwell had proposed a ldquodemonrdquo
as selector of the molecules (1867) the selection device has been the object of particular attention
on the part of Szilard (1929) and later Bennet (1981) with the scope of correctly counting the
variation of entropy in the test universe and calculate the required energy for the selection
Figure 23 ndash The selective valve allows the passage from the colder to the warmer
environment only of the molecules which have a velocity higher than the
weighted average velocity of the warmer molecules as shown in Fig 22
Pier Maria Boria Thermodynamics amp life
These elementary applications of classic thermodynamics based on the concept of entropy
and on Bolzmannrsquos Distribution suggest to us that the phenomenon ldquoliferdquo is to be associated with a
ldquovis-vitalisrdquo external to the dissipative mechanism for which we have ample and daily experience
Obviously it is impossible for man to build a Maxwell device but in our research we have
found a very interesting observation by Jaques Monod (Nobel Prize in 1965) that confers the part of
demon to the natural enzymes7
According to this point of view we can convert the Figure 16 as follows
Figure 24 ndash The natural heat pumping performed by enzymes
and this sketch we consider as typical of the phenomenon ldquoliferdquo The role played by the vis-vitalis seems essential because the only electro-chemical energy
associated with enzymes are components easily deliverable in the biological laboratories but
nobody has been able to start life from these components8
There are those who attempt an approach to this argument with improper methods and with
arbitrary applications of the concept of probability which leads to theories that are devoid of the
required respect for a sound scientific doctrine
22 CONCLUSIONS FROM THE FIRST AND SECOND PART
Rivers of ink have been written about the origin of life to the point that it is possible to read
about the most bizarre theories that completely ignore that which is suggested by the Queen of
Physics Thermodynamics
Paleontology Biology extraterrestrials UFOs Cosmic Palingenesis and similar are all
stirred numbers equations concepts of probability principles of conservation etc are not used
7 Le hazard et la neacutecessiteacute 1970 ndash Arnoldo Mondadori Editore Spa ndash Milan ndash Pag 58
8 See the Stanley Miller experiment at the end of paragraph 54
Pier Maria Boria Thermodynamics amp life
12
correctly These are the only foundations possible for a correctly stated scientific discussion (there
is no adjective more abused than the term ldquoscientificrdquo)
The reader could (perhaps on a rainy Sunday) do some research on the ldquoprimordialrdquo soup (but
if it is not Knorr for whorsquos brand modestly in youth we made thermodynamics projects does not
taste good) on the ldquocosmic tankrdquo on the ldquotyping monkeysrdquo on the cycle of carbon and oxygen (in relation to the demonization of CO2) on the hydrological cycle (which is a substance that cannot
be ldquoconsumedrdquo as is currently heard said otherwise what cycle would it complete subjects often treated by substituting Science with ideology and making ample use of the principle of superior
authority (the ipse dixit of historical memory) upholding disjointed dogma but which are
politically correct
Sometimes one has the feeling of witnessing the squalid discourse of gossiping women by the fountain
It can be noted that in the observations made up to now we have practically not talked about energy whorsquos role in the economy of our discourse has been secondary Itrsquos the definition of the
entropy index state which changes the way to view the cosmos we would not talk of it if it were
possible to carry out reversible reactions
We would come to suspect that the irreversibility is a ldquodefectrdquo of the cosmos having the
function of forcing it to a gradual entropic enrichment (and therefore to a degeneration of energy)
such that the final form of all the energy available becomes one that is thermally and entropically
unusable therefore by virtue of what has been discussed at a certain point in the evolution of the
universe at a finite time it will not be possible to practically perform any thermodynamic cycle9
That is to say the thermal death of the universe
9 We will be further willing to suspect a decay of the cosmological properties correlated to the original sin Ah free
thought
Pier Maria Boria Thermodynamics amp life
13
Part 3 (of 4) Probability
31 PROBABILITY IN BOLTZMANNrsquoS STATISTICS
Boltzmann obtained the graph of the probability as a function of temperature postulating that
a certain number m of particles which are indistinguishable from each other (which we will call A
B C M) and a number n of possible states (a b c n) in which one or more particles (even if
m) can find themselves the presence of particles in each state could occur with different possibilities
If the identical particles are free to occupy the various states (as in the case of a gas) these could continuously exchange states between themselves (for example thanks to reciprocal impacts
as in Figure 23) whilst ldquoon averagerdquo maintaining a certain distribution subject to the conditions around them (for example temperature) a certain distribution of the possible configurations would
be typical of such conditions
Continuing with this example if by state of the particles we mean possessing a certain amount
of kinetic energy E associated with each molecule of a gas in a certain interval of values of energy
∆E there will be a stable quantity of molecules even if amongst themselves continues exchanges of
energy occur Therefore in the range of the same interval some particles enter and some leave
If for the sake of imagination in what follows particles will be considered as ldquoballsrdquo and
states as levels of energy the balls will represent the particles while the levels will represent an
interval of energy (∆E)
Let us start with a very simple case consisting of 3 particles (m=3) able to be hosted by two
levels (n=2) as illustrated in Figure 31
In the left column we see all the possible combinations In the central section we see that certain combinations repeat themselves in such a way that if the particles become indistinguishable
(column 3) they are to be considered the same amongst themselves Therefore three possibilities exist such that both the combinations 234 and 567 can occur
and only once for the combinations 1 and 8 If we ldquonormalizerdquo the possibility (expressing it in unitary or percentage terms) it assumes the
role of probability (ratio between favorable cases and possible cases) which we have done in the last column by expressing it in percentage terms as is common practice
Pier Maria Boria Thermodynamics amp life
14
Figure 31 ndash A rather simple case to demonstrate how given m=3 and n=2 it is possible to
have different probabilities for each combination
Pier Maria Boria Thermodynamics amp life
15
This allows us to draw the graph of Figure 32 where we can begin to see the
Boltzmann distribution forming
Figure 32 ndash The embryonic Boltzmann diagram increasing particles and the number of
possible states the envelope of the columns (in this particular case not yet)
acquires the characteristic asymmetric bell shape
Following in the footsteps of the great Ludwig we enter into systems which are numerically
more substantial three combinations of seven states with an arbitrary arrangement of four particles
as represented in Figure 33 the three combinations are equivalent because the particles are
indistinguishable by hypothesis
Pier Maria Boria Thermodynamics amp life
16
Figure 33 - The three configurations are equivalent if the four particles are indistinguishable
amongst themselves
Each of the n states can be associated with A B C etc (that is to each or more of the m
particles) and since a single particle can occupy each time a different state (and other particles
other states) m times the possible combinations C are ntimesntimesntimeshelliptimesn (m factors equal to n)
C = nm
We could also be convinced observing for example Figure 34 where it is assumed that n=5
(it looks like a musical stavehellip) and m=2 particles (therefore 52=25 combinations)
Pier Maria Boria Thermodynamics amp life
Figure 34 ndash Beyond the 25th beat the preceding configurations are repeated because A and B are
indistinguishable Within the range of the 25 possible configurations some are more favored
because they appear more frequently for example 6 and 22 9 and 25 etc The unoccupied
states are identified by a circle
As is fair to expect configuration 1 is least favored
Pier Maria Boria Thermodynamics amp life
18
We can arrive at the same result with a more practical method suitable also for very large
values of n and m which we will use as follows
It consists of a tabular method stolen from Combinatorial Analysis where for n and m equal to
various units it avoids the need to write hundreds or thousands of key strokes as used above
Let us take two rows and as many columns as there are states thereby obtaining a grid in
Figure 35 to verify what has been said above we have taken 2 rows and 5 columns (n=2 m=5)
Figure 35- With this grid we obtain the number of possible configurations
To further demonstrate we will build a grid for n=5 and m=4 as in Figure 36 where there are sufficient rows to progressively expose the number of particles (from 4 to 1 in the first box of
the first column of the occupancy numbers) and there are n columns
Pier Maria Boria Thermodynamics amp life
19
Figure 36 - Since 54= 625 there are 625 possible combinations the relative probabilities are
listed in the last column note the asymmetry
Pier Maria Boria Thermodynamics amp life
20
It is necessary to observe that in the figure the table of numbers of occupancy reminds
us not by chance of Tartagliarsquos Triangle while the Boltzmann type diagram that can be
associated shown in Figure 37 takes on an almost familiar shape
Figure 37 - Graphical representation of Figure 62 the bars are asymmetric
Pier Maria Boria Thermodynamics amp life
21
To provide an example and referring to Figure 36 we can see how it is possible to obtain 80
possibilities corresponding to his second line
If a box is occupied by 3 particles out of an available 4 the simple combinations of 4 objects
with 3 by 3 (as taught by the Combinatorial Analysis) are given by the binomial coefficient
6437 4
and the four possible groups of three numbers have five positions from which to choose From here 4times5=20 possibilities for the group of three numbers
The single remaining particle has the possibility of the four remaining locations and therefore has 1times4=4 possibilities
The product 20times4=80 gives us the total possibilities in the case that the particles arrange themselves in two groups one with three and one with a single particle and having five boxes
suitable It is easy to verify that we will obtain the same result considering first the single particle
having five boxes suitable (five possibilities 1x5=5) and after the three having the four remaining
(one is occupied by the single particle therefore 4x4=16 and 5x16=80)
Applying the procedure line by line it produces the results shown
Pier Maria Boria Thermodynamics amp life
22
Part 4 (of 4) Chance
41 CHANCE
A sharp-shooter shoots at a target with an excellent rifle he aims carefully chooses the
moment when his breathing will not interfere and the amount of force with which to pull the trigger so as not to move the barrel fires the shot and hits the bullrsquos-eye
Immediately afterwards he takes all the same precautions but the shot ends up being slightly off target it could have been a slight disturbance to his sight an involuntary variation in his
breathing an imperceptible abnormal movement of the finger a very slight unpredictable wind or who knows what else
The causes are many and imponderable slight if each is considered in itself but interacting differently each time ensuring that each shot has a different fate
This complex of innumerable causes of disturbance which are not controllable or predictable
and which not being able to take each into account one by one are called the Law of Probability
(Gaussrsquos Law)10
Probability for the reasons given and law thanks to Carl Friedrich Gauss (1777-1855) who
wrote an equation capable of taking into consideration in a global manner all those fleeting causes
so as to be able to predict with near accurate approximation how the shots will arrange themselves
percentage wise round the target with different distances from the bullseye The approximation will
be more accurate the greater the number of shots that are fired
Let us assume that the target is as represented in Figure 41 and is divided into two parts by
means of the section AB and that our sharpshooter fires many shots after which we count the
number of shots which hit the target in each half
Figure 41- The segmented target
If the reasons for the error are truly random (rifle without defects such that it does not tend to
deviate the shot systematically and neither does the sharpshooter have an analogous defect there is
10
The example of the sharpshooter was published by Engineer Mario Manaira in Ndeg 256 of ldquoJournal of Mechanicsrdquo
together with our first article concerning thermodynamics more than half a century ago (1961)
Pier Maria Boria Thermodynamics amp life
23
not a steady wind etc in other words there does not exist a cause which always influences with the
same bias called a systematic cause) we could note the following
1 The shots will be greater in number in the first band round the center
2 The shots will progressively decrease in number in the subsequent bands as these distance themselves further from the center until there are very few in the bands furthest away
3 The shots in the two halves right and left in any similar band will tend to have the same number and will even be identical if sufficient shots are fired
It is therefore possible to represent the phenomenon graphically as in the following figure
Figure 42 ndash The random distribution of the shots in each band and the Gaussian distribution that
would be obtained with an infinite number of shots fired
If the marksman were less capable the concentration of shots near the zero on the abscissa would reduce and the curve would flatten itself while maintaining the characteristics given and
represented in Figure 43 The first observation is that the maximum height of the curve constitutes the ldquotargetrdquo in other words the goal of the operation while the absence of systematic causes (in
antithesis of randomness) ensures the symmetry of the curve with respect to the vertical which
represents our target zero
Pier Maria Boria Thermodynamics amp life
24
Figure 43 - If the marksman is less skilled the Gaussian flattens
In the case of a systematic cause of error the curve loses its symmetry if we assume that the
test is performed with a constant wind from left to right the graph will take on the shape of Figure
44
Figure 44 ndash When the Gaussian is asymmetric it implies that the phenomenon is not ldquoentirely
randomrdquo11
Let us suppose now that our sharpshooter is blindfolded the target becomes very large and is
moved he will have to shoot blindly (randomly) left and right high and low Given that the Gauss
11
Gauss suggests that the analytical expression of the Law of Randomness is the function
2xey minus
=
where it can be seen that the curve is symmetrical with respect to the axis x=0 and decreasing both towards the left and
right of this line and has a maximum for x=0
It can be shown further that the area subtended is
π=int+infin
infinminus
minusdxe
x2
To ensure that this area is equal to unity as opposed to π appropriate steps can be taken which without
changing the general properties illustrated give the normalized Gaussrsquos Law
Pier Maria Boria Thermodynamics amp life
function still applies the probability curve will flatten itself maintaining the essential
characteristics in particular the two tails which will tend towards a tangent with the abscissa
tending towards infinity a maximum point a point of inflection and the other characteristics
illustrated in Figure 45
Figure 45 ndash Typical characteristics of a normalized Gaussian
Supposing once more that the Gauss function still applies it would be logical to expect a distribution with a curve that is so flat that it will be difficult to see a maximum point corresponding
to the center of the target it will be necessary to fire enough shots so as to occupy every position on the abscissa and to have hit with 100 certainty the bullrsquos-eye
This implies that everything is possible as long as an infinite number of shots are available
(using rhetorical language)
42 SOME PROPERTIES OF RANDOM EVENTS
The perplexities regarding the applicability of chance as referred to the blind sharpshooter
depend on the fact that the Gaussian assumes that programming has been applied to reach an
objective which implies that the operator is conscious of the objective an element which in this
case is absent
Both the existence of a program (the sharpshooter sets out to hit the bullrsquos-eye) and the
existence of an objective (the card with circles) appear to be essential to be able to talk about
chance
Another example let us imagine a machine programmed to produce a certain mechanical
piece the program is the design of the piece written in machine language and the objective is the production of the piece In mass production we will find that it is the case that despite the work
conditions being maintained the same each piece will be different to the other to the point that the pieces which exceed the tolerances (which would not allow them to be interchangeable) will be
rejected Innumerable examples could be presented identifying in every case these two characteristics
a program and an objective Statistics also operate in reverse from the measurement of a group of subjects it creates a bar
chart its envelope will be the curve of the random distribution It will give us the average of the values measured if the curve is symmetrical it will tell us that the phenomenon is not influenced by
systematic causes further it will tell us the value of the standard deviation etc
Pier Maria Boria Thermodynamics amp life
26
To fix this thought in our heads let us suppose that we want to study the average height of a
population of people who are male we make many measurements on many subjects creating bars
for every centimeter we will obtain a graph similar to Figure 46
Figure 46 ndash A practical application the Gaussian deduced from experimental measurements for
statistical purposes
In this statistical application where are the program and objective They are there they are
there they were contained in the information which the people naturally had at conception a
matter of genes and of DNA (an observation coherent with ldquoThe Kid Equationrdquo See the
ldquoIntroduction to Hyperspacerdquo12
)
These considerations lead us to think that the meaning of the word ldquochancerdquo commonly given
does not make sense that ldquochancerdquo does not exist and lead us to suspect that Anatole France had an
inspired guess when he said ldquochance is Godrsquos pseudonym when He does not want to sign his
namerdquo
This strongly agrees with what illustrious philosophers have been confirming for centuries
ldquoDeus absconditus estrdquo (Is XLV XV)
12
In our first volume ldquoCaro amico miohelliprdquo ndash Ed Pagine ndash 2010 In our second volume (ldquoVerba volant eqvuationes
manentrdquo) other considerations about a fundamental theorem of Genetics the Hardy Weinberg theorem
Pier Maria Boria Thermodynamics amp life
27
43 CHANCE amp PROBABILITY
We can now summarize some salient functions of Boltzmann and Gauss
Boltzmann
1 Deals with probability regarding the characteristics that can be assumed by many identical particles having a certain number of positions available (Dirac and Fermi deal
with particles which are distinguishable but the correct reference in our observations are the identical particles)
2 The function presents a maximum and aesthetically looks like a Gaussian but it is not symmetrical
3 It has only a single asymptote to the right of the maximum and its minimum at infinity coincides with zero the origin of the reference system
4 It is normalized so that the area subtended represents the total probability of 100
Gauss
1 Deals with chance and is applicable when an objective exists that is defined by a
program
2 The phenomenon ldquopurely by chancerdquo is represented by a curve that is symmetrical
about the axis x=0
3 The Gaussian has a maximum and no minimum at infinity
4 It possesses two asymptotes one to the right and one to the left of the maximum
5 Well defined values of probability can be associated with multiples of the standard deviation
6 It is normalized as for Boltzmannrsquos
44 THE EDDINGTONrsquoS PARADOX13
Eddingtonrsquos famous ldquoInfinite monkey theoremrdquo can be counted amongst the most discussed
paradoxes for the fact that it is often quoted by so called ldquoscientific popularizersrdquo The original assertion states ldquohellipa monkey hitting keys at random on a typewriter keyboard
for an infinite amount of times will almost surely type a given text such as the complete works of
William Shakespearerdquo
Having taken away the condition of an infinite amount of time the paradox remains acceptable
(from the moment we are able to demonstrate that a finite amount of time is sufficient) However
such a long period of time is necessary that the original statement could be seen as an hyperbolic
discussion
We have seen that random phenomena require a program in light of an objective In the case
of the typing monkeys the program could include the elimination of duplicate pages (actually the
identical pages as we will see below) and the objective could consist in the conservation of ldquogoodrdquo
pages arranged in the right sequence
Applying Boltzmannrsquos statistics let us assume that the typewriter has m=30 keys (we can think of ldquoblindrdquo keys without any writing and all identical) and that we want to write a book of
only 106
letters (a thousand typed pages) as we have observed in paragraph 31 all the possible combinations are
13
The reader can find all the details regarding these various arguments on the web
Pier Maria Boria Thermodynamics amp life
C = nm = (10
6)30
= (10)180
In other words there are 10180
possible configurations
Let us assume that the monkeys are capable of striking 10 keyssec (skilled typistshellip) the
time necessary would be
t = 10180
x 106 10 = 10
185 sec
Since we can count 1016 seconds in a billion years it is also possible to say that the time
required will be
10185
1016
= 10169
billion years (giga-years)
(let us remember that the big-bang has an age of ldquoonlyrdquo 14 billion years)
In reality the situation is even ldquoworserdquo in fact this calculation (which is generally accepted)
is wrong because we cannot talk about only thirty objects (the letters punctuation marks spaces between lines etc) to be arranged in 10
6 positions otherwise in each of 10180 configurations
obtainable we would find empty spaces up to 106-30 in each configuration
It is necessary to postulate that there are 106 letters to be arranged like conceding that the
monkeys have to insert 106 objects ie 10
6 key strokes In other words it is necessary that n = m =
106 and in this case the formula of the combinations gives us an astronomical value
6106 )10(===
mm mnC combinations
At a rhythm of 10 key strokes sec the time corresponds to
9899995005000616106 10sec101010)10(
6
equiv=sdotsdot=minust years
Figure 47 ndash Summary table of the probabilities according to Boltzmann
In realty the situation is even ldquoworserdquo still In fact in the calculation of the combinations duplicate configurations are not considered
(which necessarily must be considered as possible) in other words our monkeys could produce the same combinations several times (or two identical pages) anyway the duplications will be useless
in the compilation of our small book of only 106 letters
To this end we invoke chance (to attempt to appreciate the incidence of the repeating of
identical pages) and having constructed a Gaussian by arranging the frequency of identical pages we can reason as follows having produced all the astronomical combinations as above in the time
calculated (which we will call a cycle) the highest probability of identical pages is in pairs (which
Pier Maria Boria Thermodynamics amp life
29
we will assign the maximum position) then in threes and so on At infinity with a probability of
zero all the pages will be identical
It seems fair to presume that the standard deviation could be very large qualifying for a very
flat Gaussian and let us suppose that the pages to be rejected (one for the doubles two for the
triplets etc) are contained within the first standard deviation (as in Figure 48) then the duplicate pages to be thrown away would be about 68
Figure 48 ndash The postulated conditions (pages to be eliminated because they are duplicated equal
to the standard deviation) make 68 of the pages produced useless Iterating the cycle one could
consider the duplication of other pages however it can be demonstrated that the phenomenon
continues to imply finite times
How much does the required time increase to generalize we assume the length of a cycle to be of one unit and we identify with K the average cost of discarded pages (in the previous numerical
case K= 068) and then we observe Figure 49
Figure 49 ndash Having exhausted the first cycle identified by 1 the second of length K allows the
replacement of the duplicate pages produced in the first cycle the third of length K2 is used to
replace those produced in the second cycle and so on
The time necessary to complete the cycles required to eliminate the duplicates as they are produced will be given by the sum
suminfin
=0n
nK
which constitutes a geometric series
The Mathematical Analysis teaches us that such a series converges for 1ltK as is confirmed
in our case where it takes on the value 068
KS
minus=
1
1 and if K = 068 gives 1253
6801
1=
minus=S
Pier Maria Boria Thermodynamics amp life
30
Therefore multiplying by 3125 the time dedicated to complete a cycle (317middot105999989 billion
years) for the hypothesis made we also eliminate all the duplicate pages of our little book of 106
key strokes
Changing the value of K (always lt1) one obtains different multipliers but always of a finite
value let the reader imagine the time necessary to type all of Shakespearersquos works It must be highlighted that the monkey operation to be considered a success requires the
intervention of external intelligence capable of selecting the useful pages (like thought by Theory of
Information) and ordering them in the right sequence to obtain a final legible manuscript this
obvious necessity implies that negative entropy be introduced into the system as covered at the
beginning this is like a living being taking the trouble to ldquoput in orderrdquo otherwise the ldquopurely
randomrdquo work would be entirely useless because it will exclusively produce positive entropy
All experiments attempted by man with the goal of demonstrating the random production of
complex molecules (first building blocks of living organisms) have the defect of requiring an a
priori living system like man to arrange this production
When later chaotic physical-chemical conditions are created (temperature pressure
methane electrical arching etc) hoping to obtain that which Thermodynamics does not permit the
inventors of the moto perpetuo come to mind who never give up
The research on the ldquoprimordial souprdquo belongs to this type of experimentation a battle horse
of the followers of the ldquomaitre agrave penserrdquo of the last century and which regard in particular the laboratory experiments of Stanley Miller the goal of his research of a physical-chemical nature
was to recreate life it was an understandable but too ambitious of a project for a researcher The result was absolutely negative (Miller himself recognized it) however this last piece of information
is only whispered in scientific circles so that we still find genuine touts who speak with enthusiastic coram populo of the primordial soup and its miraculous effects14 with a self-assurance
that is truly shameful
45 CONCLUSION
On 4 July 2007 at the London Kinetics Museum a serious presentation of a perpetual motion
machine was scheduled a machine capable of supplying the user with a power greater than that
absorbed ldquoObviouslyrdquo the presentation was postponed due to ldquoa technical problemrdquo15
It would appear impossible but advocates convinced of such a motion exist and many
inventors submit patent after patent even though still in illo tempore Max Planck declared himself
to be contrary to such a possibility which violates the principles of Thermodynamics
Based on the reasoning we have developed regarding entropy probability and chance the
violation of such principles is implicit even in the attempts to obtain living organisms in a
laboratory (characterized as we have seen as being producers of negative entropy) and as such a
strong analogy can be seen between the advocates of perpetual motion and those aspiring to create
life
1 The correct application of Boltzmannrsquos statistics a phenomenon for which we call on
probability demonstrates that combinations of large numbers of particles to the point of generating complex organisms require very long periods of time in comparison the age of
the universe is but the blink of an eye
2 The probabilities take on the largest numbers in correspondence with the most disordered
configurations
14
From ldquoCorriere della Serardquo october 2008 ldquoLa vita sulla Terra Cominciograve nei vulcani con un innesco chimicordquo 15
-Source Wikipedia
Pier Maria Boria Thermodynamics amp life
3 The most ordered combinations are those which characterize organic structures and the action
of an intelligent being is necessary to select order and conserve in time the favorable
combinations
4 The phrase ldquochance phenomenonrdquo is somewhat less intuitive than what ldquocommon senserdquo
would suggest In fact the Gaussian perspective implies that such phenomena are necessarily
associated with a program this program implies the existence of an objective around which
we have an increased concentration of events
5 In every case it is necessary to postulate the existence of an intelligent design without which
the configurations and the favorable events constitute events without any functional link
between themselves
6 The existence of life as a producer of negative entropy on a continuous basis (not cyclical) is a fact visible with our own eyes
All this leads us to support the existence of a Co-ordinating Entity which possesses life ldquoa
priorirdquo and which is capable of transmitting it to animals (animalis homo included) and vegetation It can be noted that the two living systems animal and vegetable complement each other in the
sense that the design requires that emissions from the first (CO2) are the nutrients for the second and the byproducts of the second (O2) are essential for the first the carbon and oxygen cycles look
like they have been designed According to the author there is only one explanation we are in the presence of the greatest
Design Physicist of all times God the Creator
This is what we call Him as Christians while Israelites call Him Jehovah the Ishmaelites
Allah the Masons GADU (Great Architect of the Universe) etc
In other terms
the Creation is a thermodynamic necessity
Amen
Pier Maria Boria Thermodynamics amp life
These elementary applications of classic thermodynamics based on the concept of entropy
and on Bolzmannrsquos Distribution suggest to us that the phenomenon ldquoliferdquo is to be associated with a
ldquovis-vitalisrdquo external to the dissipative mechanism for which we have ample and daily experience
Obviously it is impossible for man to build a Maxwell device but in our research we have
found a very interesting observation by Jaques Monod (Nobel Prize in 1965) that confers the part of
demon to the natural enzymes7
According to this point of view we can convert the Figure 16 as follows
Figure 24 ndash The natural heat pumping performed by enzymes
and this sketch we consider as typical of the phenomenon ldquoliferdquo The role played by the vis-vitalis seems essential because the only electro-chemical energy
associated with enzymes are components easily deliverable in the biological laboratories but
nobody has been able to start life from these components8
There are those who attempt an approach to this argument with improper methods and with
arbitrary applications of the concept of probability which leads to theories that are devoid of the
required respect for a sound scientific doctrine
22 CONCLUSIONS FROM THE FIRST AND SECOND PART
Rivers of ink have been written about the origin of life to the point that it is possible to read
about the most bizarre theories that completely ignore that which is suggested by the Queen of
Physics Thermodynamics
Paleontology Biology extraterrestrials UFOs Cosmic Palingenesis and similar are all
stirred numbers equations concepts of probability principles of conservation etc are not used
7 Le hazard et la neacutecessiteacute 1970 ndash Arnoldo Mondadori Editore Spa ndash Milan ndash Pag 58
8 See the Stanley Miller experiment at the end of paragraph 54
Pier Maria Boria Thermodynamics amp life
12
correctly These are the only foundations possible for a correctly stated scientific discussion (there
is no adjective more abused than the term ldquoscientificrdquo)
The reader could (perhaps on a rainy Sunday) do some research on the ldquoprimordialrdquo soup (but
if it is not Knorr for whorsquos brand modestly in youth we made thermodynamics projects does not
taste good) on the ldquocosmic tankrdquo on the ldquotyping monkeysrdquo on the cycle of carbon and oxygen (in relation to the demonization of CO2) on the hydrological cycle (which is a substance that cannot
be ldquoconsumedrdquo as is currently heard said otherwise what cycle would it complete subjects often treated by substituting Science with ideology and making ample use of the principle of superior
authority (the ipse dixit of historical memory) upholding disjointed dogma but which are
politically correct
Sometimes one has the feeling of witnessing the squalid discourse of gossiping women by the fountain
It can be noted that in the observations made up to now we have practically not talked about energy whorsquos role in the economy of our discourse has been secondary Itrsquos the definition of the
entropy index state which changes the way to view the cosmos we would not talk of it if it were
possible to carry out reversible reactions
We would come to suspect that the irreversibility is a ldquodefectrdquo of the cosmos having the
function of forcing it to a gradual entropic enrichment (and therefore to a degeneration of energy)
such that the final form of all the energy available becomes one that is thermally and entropically
unusable therefore by virtue of what has been discussed at a certain point in the evolution of the
universe at a finite time it will not be possible to practically perform any thermodynamic cycle9
That is to say the thermal death of the universe
9 We will be further willing to suspect a decay of the cosmological properties correlated to the original sin Ah free
thought
Pier Maria Boria Thermodynamics amp life
13
Part 3 (of 4) Probability
31 PROBABILITY IN BOLTZMANNrsquoS STATISTICS
Boltzmann obtained the graph of the probability as a function of temperature postulating that
a certain number m of particles which are indistinguishable from each other (which we will call A
B C M) and a number n of possible states (a b c n) in which one or more particles (even if
m) can find themselves the presence of particles in each state could occur with different possibilities
If the identical particles are free to occupy the various states (as in the case of a gas) these could continuously exchange states between themselves (for example thanks to reciprocal impacts
as in Figure 23) whilst ldquoon averagerdquo maintaining a certain distribution subject to the conditions around them (for example temperature) a certain distribution of the possible configurations would
be typical of such conditions
Continuing with this example if by state of the particles we mean possessing a certain amount
of kinetic energy E associated with each molecule of a gas in a certain interval of values of energy
∆E there will be a stable quantity of molecules even if amongst themselves continues exchanges of
energy occur Therefore in the range of the same interval some particles enter and some leave
If for the sake of imagination in what follows particles will be considered as ldquoballsrdquo and
states as levels of energy the balls will represent the particles while the levels will represent an
interval of energy (∆E)
Let us start with a very simple case consisting of 3 particles (m=3) able to be hosted by two
levels (n=2) as illustrated in Figure 31
In the left column we see all the possible combinations In the central section we see that certain combinations repeat themselves in such a way that if the particles become indistinguishable
(column 3) they are to be considered the same amongst themselves Therefore three possibilities exist such that both the combinations 234 and 567 can occur
and only once for the combinations 1 and 8 If we ldquonormalizerdquo the possibility (expressing it in unitary or percentage terms) it assumes the
role of probability (ratio between favorable cases and possible cases) which we have done in the last column by expressing it in percentage terms as is common practice
Pier Maria Boria Thermodynamics amp life
14
Figure 31 ndash A rather simple case to demonstrate how given m=3 and n=2 it is possible to
have different probabilities for each combination
Pier Maria Boria Thermodynamics amp life
15
This allows us to draw the graph of Figure 32 where we can begin to see the
Boltzmann distribution forming
Figure 32 ndash The embryonic Boltzmann diagram increasing particles and the number of
possible states the envelope of the columns (in this particular case not yet)
acquires the characteristic asymmetric bell shape
Following in the footsteps of the great Ludwig we enter into systems which are numerically
more substantial three combinations of seven states with an arbitrary arrangement of four particles
as represented in Figure 33 the three combinations are equivalent because the particles are
indistinguishable by hypothesis
Pier Maria Boria Thermodynamics amp life
16
Figure 33 - The three configurations are equivalent if the four particles are indistinguishable
amongst themselves
Each of the n states can be associated with A B C etc (that is to each or more of the m
particles) and since a single particle can occupy each time a different state (and other particles
other states) m times the possible combinations C are ntimesntimesntimeshelliptimesn (m factors equal to n)
C = nm
We could also be convinced observing for example Figure 34 where it is assumed that n=5
(it looks like a musical stavehellip) and m=2 particles (therefore 52=25 combinations)
Pier Maria Boria Thermodynamics amp life
Figure 34 ndash Beyond the 25th beat the preceding configurations are repeated because A and B are
indistinguishable Within the range of the 25 possible configurations some are more favored
because they appear more frequently for example 6 and 22 9 and 25 etc The unoccupied
states are identified by a circle
As is fair to expect configuration 1 is least favored
Pier Maria Boria Thermodynamics amp life
18
We can arrive at the same result with a more practical method suitable also for very large
values of n and m which we will use as follows
It consists of a tabular method stolen from Combinatorial Analysis where for n and m equal to
various units it avoids the need to write hundreds or thousands of key strokes as used above
Let us take two rows and as many columns as there are states thereby obtaining a grid in
Figure 35 to verify what has been said above we have taken 2 rows and 5 columns (n=2 m=5)
Figure 35- With this grid we obtain the number of possible configurations
To further demonstrate we will build a grid for n=5 and m=4 as in Figure 36 where there are sufficient rows to progressively expose the number of particles (from 4 to 1 in the first box of
the first column of the occupancy numbers) and there are n columns
Pier Maria Boria Thermodynamics amp life
19
Figure 36 - Since 54= 625 there are 625 possible combinations the relative probabilities are
listed in the last column note the asymmetry
Pier Maria Boria Thermodynamics amp life
20
It is necessary to observe that in the figure the table of numbers of occupancy reminds
us not by chance of Tartagliarsquos Triangle while the Boltzmann type diagram that can be
associated shown in Figure 37 takes on an almost familiar shape
Figure 37 - Graphical representation of Figure 62 the bars are asymmetric
Pier Maria Boria Thermodynamics amp life
21
To provide an example and referring to Figure 36 we can see how it is possible to obtain 80
possibilities corresponding to his second line
If a box is occupied by 3 particles out of an available 4 the simple combinations of 4 objects
with 3 by 3 (as taught by the Combinatorial Analysis) are given by the binomial coefficient
6437 4
and the four possible groups of three numbers have five positions from which to choose From here 4times5=20 possibilities for the group of three numbers
The single remaining particle has the possibility of the four remaining locations and therefore has 1times4=4 possibilities
The product 20times4=80 gives us the total possibilities in the case that the particles arrange themselves in two groups one with three and one with a single particle and having five boxes
suitable It is easy to verify that we will obtain the same result considering first the single particle
having five boxes suitable (five possibilities 1x5=5) and after the three having the four remaining
(one is occupied by the single particle therefore 4x4=16 and 5x16=80)
Applying the procedure line by line it produces the results shown
Pier Maria Boria Thermodynamics amp life
22
Part 4 (of 4) Chance
41 CHANCE
A sharp-shooter shoots at a target with an excellent rifle he aims carefully chooses the
moment when his breathing will not interfere and the amount of force with which to pull the trigger so as not to move the barrel fires the shot and hits the bullrsquos-eye
Immediately afterwards he takes all the same precautions but the shot ends up being slightly off target it could have been a slight disturbance to his sight an involuntary variation in his
breathing an imperceptible abnormal movement of the finger a very slight unpredictable wind or who knows what else
The causes are many and imponderable slight if each is considered in itself but interacting differently each time ensuring that each shot has a different fate
This complex of innumerable causes of disturbance which are not controllable or predictable
and which not being able to take each into account one by one are called the Law of Probability
(Gaussrsquos Law)10
Probability for the reasons given and law thanks to Carl Friedrich Gauss (1777-1855) who
wrote an equation capable of taking into consideration in a global manner all those fleeting causes
so as to be able to predict with near accurate approximation how the shots will arrange themselves
percentage wise round the target with different distances from the bullseye The approximation will
be more accurate the greater the number of shots that are fired
Let us assume that the target is as represented in Figure 41 and is divided into two parts by
means of the section AB and that our sharpshooter fires many shots after which we count the
number of shots which hit the target in each half
Figure 41- The segmented target
If the reasons for the error are truly random (rifle without defects such that it does not tend to
deviate the shot systematically and neither does the sharpshooter have an analogous defect there is
10
The example of the sharpshooter was published by Engineer Mario Manaira in Ndeg 256 of ldquoJournal of Mechanicsrdquo
together with our first article concerning thermodynamics more than half a century ago (1961)
Pier Maria Boria Thermodynamics amp life
23
not a steady wind etc in other words there does not exist a cause which always influences with the
same bias called a systematic cause) we could note the following
1 The shots will be greater in number in the first band round the center
2 The shots will progressively decrease in number in the subsequent bands as these distance themselves further from the center until there are very few in the bands furthest away
3 The shots in the two halves right and left in any similar band will tend to have the same number and will even be identical if sufficient shots are fired
It is therefore possible to represent the phenomenon graphically as in the following figure
Figure 42 ndash The random distribution of the shots in each band and the Gaussian distribution that
would be obtained with an infinite number of shots fired
If the marksman were less capable the concentration of shots near the zero on the abscissa would reduce and the curve would flatten itself while maintaining the characteristics given and
represented in Figure 43 The first observation is that the maximum height of the curve constitutes the ldquotargetrdquo in other words the goal of the operation while the absence of systematic causes (in
antithesis of randomness) ensures the symmetry of the curve with respect to the vertical which
represents our target zero
Pier Maria Boria Thermodynamics amp life
24
Figure 43 - If the marksman is less skilled the Gaussian flattens
In the case of a systematic cause of error the curve loses its symmetry if we assume that the
test is performed with a constant wind from left to right the graph will take on the shape of Figure
44
Figure 44 ndash When the Gaussian is asymmetric it implies that the phenomenon is not ldquoentirely
randomrdquo11
Let us suppose now that our sharpshooter is blindfolded the target becomes very large and is
moved he will have to shoot blindly (randomly) left and right high and low Given that the Gauss
11
Gauss suggests that the analytical expression of the Law of Randomness is the function
2xey minus
=
where it can be seen that the curve is symmetrical with respect to the axis x=0 and decreasing both towards the left and
right of this line and has a maximum for x=0
It can be shown further that the area subtended is
π=int+infin
infinminus
minusdxe
x2
To ensure that this area is equal to unity as opposed to π appropriate steps can be taken which without
changing the general properties illustrated give the normalized Gaussrsquos Law
Pier Maria Boria Thermodynamics amp life
function still applies the probability curve will flatten itself maintaining the essential
characteristics in particular the two tails which will tend towards a tangent with the abscissa
tending towards infinity a maximum point a point of inflection and the other characteristics
illustrated in Figure 45
Figure 45 ndash Typical characteristics of a normalized Gaussian
Supposing once more that the Gauss function still applies it would be logical to expect a distribution with a curve that is so flat that it will be difficult to see a maximum point corresponding
to the center of the target it will be necessary to fire enough shots so as to occupy every position on the abscissa and to have hit with 100 certainty the bullrsquos-eye
This implies that everything is possible as long as an infinite number of shots are available
(using rhetorical language)
42 SOME PROPERTIES OF RANDOM EVENTS
The perplexities regarding the applicability of chance as referred to the blind sharpshooter
depend on the fact that the Gaussian assumes that programming has been applied to reach an
objective which implies that the operator is conscious of the objective an element which in this
case is absent
Both the existence of a program (the sharpshooter sets out to hit the bullrsquos-eye) and the
existence of an objective (the card with circles) appear to be essential to be able to talk about
chance
Another example let us imagine a machine programmed to produce a certain mechanical
piece the program is the design of the piece written in machine language and the objective is the production of the piece In mass production we will find that it is the case that despite the work
conditions being maintained the same each piece will be different to the other to the point that the pieces which exceed the tolerances (which would not allow them to be interchangeable) will be
rejected Innumerable examples could be presented identifying in every case these two characteristics
a program and an objective Statistics also operate in reverse from the measurement of a group of subjects it creates a bar
chart its envelope will be the curve of the random distribution It will give us the average of the values measured if the curve is symmetrical it will tell us that the phenomenon is not influenced by
systematic causes further it will tell us the value of the standard deviation etc
Pier Maria Boria Thermodynamics amp life
26
To fix this thought in our heads let us suppose that we want to study the average height of a
population of people who are male we make many measurements on many subjects creating bars
for every centimeter we will obtain a graph similar to Figure 46
Figure 46 ndash A practical application the Gaussian deduced from experimental measurements for
statistical purposes
In this statistical application where are the program and objective They are there they are
there they were contained in the information which the people naturally had at conception a
matter of genes and of DNA (an observation coherent with ldquoThe Kid Equationrdquo See the
ldquoIntroduction to Hyperspacerdquo12
)
These considerations lead us to think that the meaning of the word ldquochancerdquo commonly given
does not make sense that ldquochancerdquo does not exist and lead us to suspect that Anatole France had an
inspired guess when he said ldquochance is Godrsquos pseudonym when He does not want to sign his
namerdquo
This strongly agrees with what illustrious philosophers have been confirming for centuries
ldquoDeus absconditus estrdquo (Is XLV XV)
12
In our first volume ldquoCaro amico miohelliprdquo ndash Ed Pagine ndash 2010 In our second volume (ldquoVerba volant eqvuationes
manentrdquo) other considerations about a fundamental theorem of Genetics the Hardy Weinberg theorem
Pier Maria Boria Thermodynamics amp life
27
43 CHANCE amp PROBABILITY
We can now summarize some salient functions of Boltzmann and Gauss
Boltzmann
1 Deals with probability regarding the characteristics that can be assumed by many identical particles having a certain number of positions available (Dirac and Fermi deal
with particles which are distinguishable but the correct reference in our observations are the identical particles)
2 The function presents a maximum and aesthetically looks like a Gaussian but it is not symmetrical
3 It has only a single asymptote to the right of the maximum and its minimum at infinity coincides with zero the origin of the reference system
4 It is normalized so that the area subtended represents the total probability of 100
Gauss
1 Deals with chance and is applicable when an objective exists that is defined by a
program
2 The phenomenon ldquopurely by chancerdquo is represented by a curve that is symmetrical
about the axis x=0
3 The Gaussian has a maximum and no minimum at infinity
4 It possesses two asymptotes one to the right and one to the left of the maximum
5 Well defined values of probability can be associated with multiples of the standard deviation
6 It is normalized as for Boltzmannrsquos
44 THE EDDINGTONrsquoS PARADOX13
Eddingtonrsquos famous ldquoInfinite monkey theoremrdquo can be counted amongst the most discussed
paradoxes for the fact that it is often quoted by so called ldquoscientific popularizersrdquo The original assertion states ldquohellipa monkey hitting keys at random on a typewriter keyboard
for an infinite amount of times will almost surely type a given text such as the complete works of
William Shakespearerdquo
Having taken away the condition of an infinite amount of time the paradox remains acceptable
(from the moment we are able to demonstrate that a finite amount of time is sufficient) However
such a long period of time is necessary that the original statement could be seen as an hyperbolic
discussion
We have seen that random phenomena require a program in light of an objective In the case
of the typing monkeys the program could include the elimination of duplicate pages (actually the
identical pages as we will see below) and the objective could consist in the conservation of ldquogoodrdquo
pages arranged in the right sequence
Applying Boltzmannrsquos statistics let us assume that the typewriter has m=30 keys (we can think of ldquoblindrdquo keys without any writing and all identical) and that we want to write a book of
only 106
letters (a thousand typed pages) as we have observed in paragraph 31 all the possible combinations are
13
The reader can find all the details regarding these various arguments on the web
Pier Maria Boria Thermodynamics amp life
C = nm = (10
6)30
= (10)180
In other words there are 10180
possible configurations
Let us assume that the monkeys are capable of striking 10 keyssec (skilled typistshellip) the
time necessary would be
t = 10180
x 106 10 = 10
185 sec
Since we can count 1016 seconds in a billion years it is also possible to say that the time
required will be
10185
1016
= 10169
billion years (giga-years)
(let us remember that the big-bang has an age of ldquoonlyrdquo 14 billion years)
In reality the situation is even ldquoworserdquo in fact this calculation (which is generally accepted)
is wrong because we cannot talk about only thirty objects (the letters punctuation marks spaces between lines etc) to be arranged in 10
6 positions otherwise in each of 10180 configurations
obtainable we would find empty spaces up to 106-30 in each configuration
It is necessary to postulate that there are 106 letters to be arranged like conceding that the
monkeys have to insert 106 objects ie 10
6 key strokes In other words it is necessary that n = m =
106 and in this case the formula of the combinations gives us an astronomical value
6106 )10(===
mm mnC combinations
At a rhythm of 10 key strokes sec the time corresponds to
9899995005000616106 10sec101010)10(
6
equiv=sdotsdot=minust years
Figure 47 ndash Summary table of the probabilities according to Boltzmann
In realty the situation is even ldquoworserdquo still In fact in the calculation of the combinations duplicate configurations are not considered
(which necessarily must be considered as possible) in other words our monkeys could produce the same combinations several times (or two identical pages) anyway the duplications will be useless
in the compilation of our small book of only 106 letters
To this end we invoke chance (to attempt to appreciate the incidence of the repeating of
identical pages) and having constructed a Gaussian by arranging the frequency of identical pages we can reason as follows having produced all the astronomical combinations as above in the time
calculated (which we will call a cycle) the highest probability of identical pages is in pairs (which
Pier Maria Boria Thermodynamics amp life
29
we will assign the maximum position) then in threes and so on At infinity with a probability of
zero all the pages will be identical
It seems fair to presume that the standard deviation could be very large qualifying for a very
flat Gaussian and let us suppose that the pages to be rejected (one for the doubles two for the
triplets etc) are contained within the first standard deviation (as in Figure 48) then the duplicate pages to be thrown away would be about 68
Figure 48 ndash The postulated conditions (pages to be eliminated because they are duplicated equal
to the standard deviation) make 68 of the pages produced useless Iterating the cycle one could
consider the duplication of other pages however it can be demonstrated that the phenomenon
continues to imply finite times
How much does the required time increase to generalize we assume the length of a cycle to be of one unit and we identify with K the average cost of discarded pages (in the previous numerical
case K= 068) and then we observe Figure 49
Figure 49 ndash Having exhausted the first cycle identified by 1 the second of length K allows the
replacement of the duplicate pages produced in the first cycle the third of length K2 is used to
replace those produced in the second cycle and so on
The time necessary to complete the cycles required to eliminate the duplicates as they are produced will be given by the sum
suminfin
=0n
nK
which constitutes a geometric series
The Mathematical Analysis teaches us that such a series converges for 1ltK as is confirmed
in our case where it takes on the value 068
KS
minus=
1
1 and if K = 068 gives 1253
6801
1=
minus=S
Pier Maria Boria Thermodynamics amp life
30
Therefore multiplying by 3125 the time dedicated to complete a cycle (317middot105999989 billion
years) for the hypothesis made we also eliminate all the duplicate pages of our little book of 106
key strokes
Changing the value of K (always lt1) one obtains different multipliers but always of a finite
value let the reader imagine the time necessary to type all of Shakespearersquos works It must be highlighted that the monkey operation to be considered a success requires the
intervention of external intelligence capable of selecting the useful pages (like thought by Theory of
Information) and ordering them in the right sequence to obtain a final legible manuscript this
obvious necessity implies that negative entropy be introduced into the system as covered at the
beginning this is like a living being taking the trouble to ldquoput in orderrdquo otherwise the ldquopurely
randomrdquo work would be entirely useless because it will exclusively produce positive entropy
All experiments attempted by man with the goal of demonstrating the random production of
complex molecules (first building blocks of living organisms) have the defect of requiring an a
priori living system like man to arrange this production
When later chaotic physical-chemical conditions are created (temperature pressure
methane electrical arching etc) hoping to obtain that which Thermodynamics does not permit the
inventors of the moto perpetuo come to mind who never give up
The research on the ldquoprimordial souprdquo belongs to this type of experimentation a battle horse
of the followers of the ldquomaitre agrave penserrdquo of the last century and which regard in particular the laboratory experiments of Stanley Miller the goal of his research of a physical-chemical nature
was to recreate life it was an understandable but too ambitious of a project for a researcher The result was absolutely negative (Miller himself recognized it) however this last piece of information
is only whispered in scientific circles so that we still find genuine touts who speak with enthusiastic coram populo of the primordial soup and its miraculous effects14 with a self-assurance
that is truly shameful
45 CONCLUSION
On 4 July 2007 at the London Kinetics Museum a serious presentation of a perpetual motion
machine was scheduled a machine capable of supplying the user with a power greater than that
absorbed ldquoObviouslyrdquo the presentation was postponed due to ldquoa technical problemrdquo15
It would appear impossible but advocates convinced of such a motion exist and many
inventors submit patent after patent even though still in illo tempore Max Planck declared himself
to be contrary to such a possibility which violates the principles of Thermodynamics
Based on the reasoning we have developed regarding entropy probability and chance the
violation of such principles is implicit even in the attempts to obtain living organisms in a
laboratory (characterized as we have seen as being producers of negative entropy) and as such a
strong analogy can be seen between the advocates of perpetual motion and those aspiring to create
life
1 The correct application of Boltzmannrsquos statistics a phenomenon for which we call on
probability demonstrates that combinations of large numbers of particles to the point of generating complex organisms require very long periods of time in comparison the age of
the universe is but the blink of an eye
2 The probabilities take on the largest numbers in correspondence with the most disordered
configurations
14
From ldquoCorriere della Serardquo october 2008 ldquoLa vita sulla Terra Cominciograve nei vulcani con un innesco chimicordquo 15
-Source Wikipedia
Pier Maria Boria Thermodynamics amp life
3 The most ordered combinations are those which characterize organic structures and the action
of an intelligent being is necessary to select order and conserve in time the favorable
combinations
4 The phrase ldquochance phenomenonrdquo is somewhat less intuitive than what ldquocommon senserdquo
would suggest In fact the Gaussian perspective implies that such phenomena are necessarily
associated with a program this program implies the existence of an objective around which
we have an increased concentration of events
5 In every case it is necessary to postulate the existence of an intelligent design without which
the configurations and the favorable events constitute events without any functional link
between themselves
6 The existence of life as a producer of negative entropy on a continuous basis (not cyclical) is a fact visible with our own eyes
All this leads us to support the existence of a Co-ordinating Entity which possesses life ldquoa
priorirdquo and which is capable of transmitting it to animals (animalis homo included) and vegetation It can be noted that the two living systems animal and vegetable complement each other in the
sense that the design requires that emissions from the first (CO2) are the nutrients for the second and the byproducts of the second (O2) are essential for the first the carbon and oxygen cycles look
like they have been designed According to the author there is only one explanation we are in the presence of the greatest
Design Physicist of all times God the Creator
This is what we call Him as Christians while Israelites call Him Jehovah the Ishmaelites
Allah the Masons GADU (Great Architect of the Universe) etc
In other terms
the Creation is a thermodynamic necessity
Amen
Pier Maria Boria Thermodynamics amp life
12
correctly These are the only foundations possible for a correctly stated scientific discussion (there
is no adjective more abused than the term ldquoscientificrdquo)
The reader could (perhaps on a rainy Sunday) do some research on the ldquoprimordialrdquo soup (but
if it is not Knorr for whorsquos brand modestly in youth we made thermodynamics projects does not
taste good) on the ldquocosmic tankrdquo on the ldquotyping monkeysrdquo on the cycle of carbon and oxygen (in relation to the demonization of CO2) on the hydrological cycle (which is a substance that cannot
be ldquoconsumedrdquo as is currently heard said otherwise what cycle would it complete subjects often treated by substituting Science with ideology and making ample use of the principle of superior
authority (the ipse dixit of historical memory) upholding disjointed dogma but which are
politically correct
Sometimes one has the feeling of witnessing the squalid discourse of gossiping women by the fountain
It can be noted that in the observations made up to now we have practically not talked about energy whorsquos role in the economy of our discourse has been secondary Itrsquos the definition of the
entropy index state which changes the way to view the cosmos we would not talk of it if it were
possible to carry out reversible reactions
We would come to suspect that the irreversibility is a ldquodefectrdquo of the cosmos having the
function of forcing it to a gradual entropic enrichment (and therefore to a degeneration of energy)
such that the final form of all the energy available becomes one that is thermally and entropically
unusable therefore by virtue of what has been discussed at a certain point in the evolution of the
universe at a finite time it will not be possible to practically perform any thermodynamic cycle9
That is to say the thermal death of the universe
9 We will be further willing to suspect a decay of the cosmological properties correlated to the original sin Ah free
thought
Pier Maria Boria Thermodynamics amp life
13
Part 3 (of 4) Probability
31 PROBABILITY IN BOLTZMANNrsquoS STATISTICS
Boltzmann obtained the graph of the probability as a function of temperature postulating that
a certain number m of particles which are indistinguishable from each other (which we will call A
B C M) and a number n of possible states (a b c n) in which one or more particles (even if
m) can find themselves the presence of particles in each state could occur with different possibilities
If the identical particles are free to occupy the various states (as in the case of a gas) these could continuously exchange states between themselves (for example thanks to reciprocal impacts
as in Figure 23) whilst ldquoon averagerdquo maintaining a certain distribution subject to the conditions around them (for example temperature) a certain distribution of the possible configurations would
be typical of such conditions
Continuing with this example if by state of the particles we mean possessing a certain amount
of kinetic energy E associated with each molecule of a gas in a certain interval of values of energy
∆E there will be a stable quantity of molecules even if amongst themselves continues exchanges of
energy occur Therefore in the range of the same interval some particles enter and some leave
If for the sake of imagination in what follows particles will be considered as ldquoballsrdquo and
states as levels of energy the balls will represent the particles while the levels will represent an
interval of energy (∆E)
Let us start with a very simple case consisting of 3 particles (m=3) able to be hosted by two
levels (n=2) as illustrated in Figure 31
In the left column we see all the possible combinations In the central section we see that certain combinations repeat themselves in such a way that if the particles become indistinguishable
(column 3) they are to be considered the same amongst themselves Therefore three possibilities exist such that both the combinations 234 and 567 can occur
and only once for the combinations 1 and 8 If we ldquonormalizerdquo the possibility (expressing it in unitary or percentage terms) it assumes the
role of probability (ratio between favorable cases and possible cases) which we have done in the last column by expressing it in percentage terms as is common practice
Pier Maria Boria Thermodynamics amp life
14
Figure 31 ndash A rather simple case to demonstrate how given m=3 and n=2 it is possible to
have different probabilities for each combination
Pier Maria Boria Thermodynamics amp life
15
This allows us to draw the graph of Figure 32 where we can begin to see the
Boltzmann distribution forming
Figure 32 ndash The embryonic Boltzmann diagram increasing particles and the number of
possible states the envelope of the columns (in this particular case not yet)
acquires the characteristic asymmetric bell shape
Following in the footsteps of the great Ludwig we enter into systems which are numerically
more substantial three combinations of seven states with an arbitrary arrangement of four particles
as represented in Figure 33 the three combinations are equivalent because the particles are
indistinguishable by hypothesis
Pier Maria Boria Thermodynamics amp life
16
Figure 33 - The three configurations are equivalent if the four particles are indistinguishable
amongst themselves
Each of the n states can be associated with A B C etc (that is to each or more of the m
particles) and since a single particle can occupy each time a different state (and other particles
other states) m times the possible combinations C are ntimesntimesntimeshelliptimesn (m factors equal to n)
C = nm
We could also be convinced observing for example Figure 34 where it is assumed that n=5
(it looks like a musical stavehellip) and m=2 particles (therefore 52=25 combinations)
Pier Maria Boria Thermodynamics amp life
Figure 34 ndash Beyond the 25th beat the preceding configurations are repeated because A and B are
indistinguishable Within the range of the 25 possible configurations some are more favored
because they appear more frequently for example 6 and 22 9 and 25 etc The unoccupied
states are identified by a circle
As is fair to expect configuration 1 is least favored
Pier Maria Boria Thermodynamics amp life
18
We can arrive at the same result with a more practical method suitable also for very large
values of n and m which we will use as follows
It consists of a tabular method stolen from Combinatorial Analysis where for n and m equal to
various units it avoids the need to write hundreds or thousands of key strokes as used above
Let us take two rows and as many columns as there are states thereby obtaining a grid in
Figure 35 to verify what has been said above we have taken 2 rows and 5 columns (n=2 m=5)
Figure 35- With this grid we obtain the number of possible configurations
To further demonstrate we will build a grid for n=5 and m=4 as in Figure 36 where there are sufficient rows to progressively expose the number of particles (from 4 to 1 in the first box of
the first column of the occupancy numbers) and there are n columns
Pier Maria Boria Thermodynamics amp life
19
Figure 36 - Since 54= 625 there are 625 possible combinations the relative probabilities are
listed in the last column note the asymmetry
Pier Maria Boria Thermodynamics amp life
20
It is necessary to observe that in the figure the table of numbers of occupancy reminds
us not by chance of Tartagliarsquos Triangle while the Boltzmann type diagram that can be
associated shown in Figure 37 takes on an almost familiar shape
Figure 37 - Graphical representation of Figure 62 the bars are asymmetric
Pier Maria Boria Thermodynamics amp life
21
To provide an example and referring to Figure 36 we can see how it is possible to obtain 80
possibilities corresponding to his second line
If a box is occupied by 3 particles out of an available 4 the simple combinations of 4 objects
with 3 by 3 (as taught by the Combinatorial Analysis) are given by the binomial coefficient
6437 4
and the four possible groups of three numbers have five positions from which to choose From here 4times5=20 possibilities for the group of three numbers
The single remaining particle has the possibility of the four remaining locations and therefore has 1times4=4 possibilities
The product 20times4=80 gives us the total possibilities in the case that the particles arrange themselves in two groups one with three and one with a single particle and having five boxes
suitable It is easy to verify that we will obtain the same result considering first the single particle
having five boxes suitable (five possibilities 1x5=5) and after the three having the four remaining
(one is occupied by the single particle therefore 4x4=16 and 5x16=80)
Applying the procedure line by line it produces the results shown
Pier Maria Boria Thermodynamics amp life
22
Part 4 (of 4) Chance
41 CHANCE
A sharp-shooter shoots at a target with an excellent rifle he aims carefully chooses the
moment when his breathing will not interfere and the amount of force with which to pull the trigger so as not to move the barrel fires the shot and hits the bullrsquos-eye
Immediately afterwards he takes all the same precautions but the shot ends up being slightly off target it could have been a slight disturbance to his sight an involuntary variation in his
breathing an imperceptible abnormal movement of the finger a very slight unpredictable wind or who knows what else
The causes are many and imponderable slight if each is considered in itself but interacting differently each time ensuring that each shot has a different fate
This complex of innumerable causes of disturbance which are not controllable or predictable
and which not being able to take each into account one by one are called the Law of Probability
(Gaussrsquos Law)10
Probability for the reasons given and law thanks to Carl Friedrich Gauss (1777-1855) who
wrote an equation capable of taking into consideration in a global manner all those fleeting causes
so as to be able to predict with near accurate approximation how the shots will arrange themselves
percentage wise round the target with different distances from the bullseye The approximation will
be more accurate the greater the number of shots that are fired
Let us assume that the target is as represented in Figure 41 and is divided into two parts by
means of the section AB and that our sharpshooter fires many shots after which we count the
number of shots which hit the target in each half
Figure 41- The segmented target
If the reasons for the error are truly random (rifle without defects such that it does not tend to
deviate the shot systematically and neither does the sharpshooter have an analogous defect there is
10
The example of the sharpshooter was published by Engineer Mario Manaira in Ndeg 256 of ldquoJournal of Mechanicsrdquo
together with our first article concerning thermodynamics more than half a century ago (1961)
Pier Maria Boria Thermodynamics amp life
23
not a steady wind etc in other words there does not exist a cause which always influences with the
same bias called a systematic cause) we could note the following
1 The shots will be greater in number in the first band round the center
2 The shots will progressively decrease in number in the subsequent bands as these distance themselves further from the center until there are very few in the bands furthest away
3 The shots in the two halves right and left in any similar band will tend to have the same number and will even be identical if sufficient shots are fired
It is therefore possible to represent the phenomenon graphically as in the following figure
Figure 42 ndash The random distribution of the shots in each band and the Gaussian distribution that
would be obtained with an infinite number of shots fired
If the marksman were less capable the concentration of shots near the zero on the abscissa would reduce and the curve would flatten itself while maintaining the characteristics given and
represented in Figure 43 The first observation is that the maximum height of the curve constitutes the ldquotargetrdquo in other words the goal of the operation while the absence of systematic causes (in
antithesis of randomness) ensures the symmetry of the curve with respect to the vertical which
represents our target zero
Pier Maria Boria Thermodynamics amp life
24
Figure 43 - If the marksman is less skilled the Gaussian flattens
In the case of a systematic cause of error the curve loses its symmetry if we assume that the
test is performed with a constant wind from left to right the graph will take on the shape of Figure
44
Figure 44 ndash When the Gaussian is asymmetric it implies that the phenomenon is not ldquoentirely
randomrdquo11
Let us suppose now that our sharpshooter is blindfolded the target becomes very large and is
moved he will have to shoot blindly (randomly) left and right high and low Given that the Gauss
11
Gauss suggests that the analytical expression of the Law of Randomness is the function
2xey minus
=
where it can be seen that the curve is symmetrical with respect to the axis x=0 and decreasing both towards the left and
right of this line and has a maximum for x=0
It can be shown further that the area subtended is
π=int+infin
infinminus
minusdxe
x2
To ensure that this area is equal to unity as opposed to π appropriate steps can be taken which without
changing the general properties illustrated give the normalized Gaussrsquos Law
Pier Maria Boria Thermodynamics amp life
function still applies the probability curve will flatten itself maintaining the essential
characteristics in particular the two tails which will tend towards a tangent with the abscissa
tending towards infinity a maximum point a point of inflection and the other characteristics
illustrated in Figure 45
Figure 45 ndash Typical characteristics of a normalized Gaussian
Supposing once more that the Gauss function still applies it would be logical to expect a distribution with a curve that is so flat that it will be difficult to see a maximum point corresponding
to the center of the target it will be necessary to fire enough shots so as to occupy every position on the abscissa and to have hit with 100 certainty the bullrsquos-eye
This implies that everything is possible as long as an infinite number of shots are available
(using rhetorical language)
42 SOME PROPERTIES OF RANDOM EVENTS
The perplexities regarding the applicability of chance as referred to the blind sharpshooter
depend on the fact that the Gaussian assumes that programming has been applied to reach an
objective which implies that the operator is conscious of the objective an element which in this
case is absent
Both the existence of a program (the sharpshooter sets out to hit the bullrsquos-eye) and the
existence of an objective (the card with circles) appear to be essential to be able to talk about
chance
Another example let us imagine a machine programmed to produce a certain mechanical
piece the program is the design of the piece written in machine language and the objective is the production of the piece In mass production we will find that it is the case that despite the work
conditions being maintained the same each piece will be different to the other to the point that the pieces which exceed the tolerances (which would not allow them to be interchangeable) will be
rejected Innumerable examples could be presented identifying in every case these two characteristics
a program and an objective Statistics also operate in reverse from the measurement of a group of subjects it creates a bar
chart its envelope will be the curve of the random distribution It will give us the average of the values measured if the curve is symmetrical it will tell us that the phenomenon is not influenced by
systematic causes further it will tell us the value of the standard deviation etc
Pier Maria Boria Thermodynamics amp life
26
To fix this thought in our heads let us suppose that we want to study the average height of a
population of people who are male we make many measurements on many subjects creating bars
for every centimeter we will obtain a graph similar to Figure 46
Figure 46 ndash A practical application the Gaussian deduced from experimental measurements for
statistical purposes
In this statistical application where are the program and objective They are there they are
there they were contained in the information which the people naturally had at conception a
matter of genes and of DNA (an observation coherent with ldquoThe Kid Equationrdquo See the
ldquoIntroduction to Hyperspacerdquo12
)
These considerations lead us to think that the meaning of the word ldquochancerdquo commonly given
does not make sense that ldquochancerdquo does not exist and lead us to suspect that Anatole France had an
inspired guess when he said ldquochance is Godrsquos pseudonym when He does not want to sign his
namerdquo
This strongly agrees with what illustrious philosophers have been confirming for centuries
ldquoDeus absconditus estrdquo (Is XLV XV)
12
In our first volume ldquoCaro amico miohelliprdquo ndash Ed Pagine ndash 2010 In our second volume (ldquoVerba volant eqvuationes
manentrdquo) other considerations about a fundamental theorem of Genetics the Hardy Weinberg theorem
Pier Maria Boria Thermodynamics amp life
27
43 CHANCE amp PROBABILITY
We can now summarize some salient functions of Boltzmann and Gauss
Boltzmann
1 Deals with probability regarding the characteristics that can be assumed by many identical particles having a certain number of positions available (Dirac and Fermi deal
with particles which are distinguishable but the correct reference in our observations are the identical particles)
2 The function presents a maximum and aesthetically looks like a Gaussian but it is not symmetrical
3 It has only a single asymptote to the right of the maximum and its minimum at infinity coincides with zero the origin of the reference system
4 It is normalized so that the area subtended represents the total probability of 100
Gauss
1 Deals with chance and is applicable when an objective exists that is defined by a
program
2 The phenomenon ldquopurely by chancerdquo is represented by a curve that is symmetrical
about the axis x=0
3 The Gaussian has a maximum and no minimum at infinity
4 It possesses two asymptotes one to the right and one to the left of the maximum
5 Well defined values of probability can be associated with multiples of the standard deviation
6 It is normalized as for Boltzmannrsquos
44 THE EDDINGTONrsquoS PARADOX13
Eddingtonrsquos famous ldquoInfinite monkey theoremrdquo can be counted amongst the most discussed
paradoxes for the fact that it is often quoted by so called ldquoscientific popularizersrdquo The original assertion states ldquohellipa monkey hitting keys at random on a typewriter keyboard
for an infinite amount of times will almost surely type a given text such as the complete works of
William Shakespearerdquo
Having taken away the condition of an infinite amount of time the paradox remains acceptable
(from the moment we are able to demonstrate that a finite amount of time is sufficient) However
such a long period of time is necessary that the original statement could be seen as an hyperbolic
discussion
We have seen that random phenomena require a program in light of an objective In the case
of the typing monkeys the program could include the elimination of duplicate pages (actually the
identical pages as we will see below) and the objective could consist in the conservation of ldquogoodrdquo
pages arranged in the right sequence
Applying Boltzmannrsquos statistics let us assume that the typewriter has m=30 keys (we can think of ldquoblindrdquo keys without any writing and all identical) and that we want to write a book of
only 106
letters (a thousand typed pages) as we have observed in paragraph 31 all the possible combinations are
13
The reader can find all the details regarding these various arguments on the web
Pier Maria Boria Thermodynamics amp life
C = nm = (10
6)30
= (10)180
In other words there are 10180
possible configurations
Let us assume that the monkeys are capable of striking 10 keyssec (skilled typistshellip) the
time necessary would be
t = 10180
x 106 10 = 10
185 sec
Since we can count 1016 seconds in a billion years it is also possible to say that the time
required will be
10185
1016
= 10169
billion years (giga-years)
(let us remember that the big-bang has an age of ldquoonlyrdquo 14 billion years)
In reality the situation is even ldquoworserdquo in fact this calculation (which is generally accepted)
is wrong because we cannot talk about only thirty objects (the letters punctuation marks spaces between lines etc) to be arranged in 10
6 positions otherwise in each of 10180 configurations
obtainable we would find empty spaces up to 106-30 in each configuration
It is necessary to postulate that there are 106 letters to be arranged like conceding that the
monkeys have to insert 106 objects ie 10
6 key strokes In other words it is necessary that n = m =
106 and in this case the formula of the combinations gives us an astronomical value
6106 )10(===
mm mnC combinations
At a rhythm of 10 key strokes sec the time corresponds to
9899995005000616106 10sec101010)10(
6
equiv=sdotsdot=minust years
Figure 47 ndash Summary table of the probabilities according to Boltzmann
In realty the situation is even ldquoworserdquo still In fact in the calculation of the combinations duplicate configurations are not considered
(which necessarily must be considered as possible) in other words our monkeys could produce the same combinations several times (or two identical pages) anyway the duplications will be useless
in the compilation of our small book of only 106 letters
To this end we invoke chance (to attempt to appreciate the incidence of the repeating of
identical pages) and having constructed a Gaussian by arranging the frequency of identical pages we can reason as follows having produced all the astronomical combinations as above in the time
calculated (which we will call a cycle) the highest probability of identical pages is in pairs (which
Pier Maria Boria Thermodynamics amp life
29
we will assign the maximum position) then in threes and so on At infinity with a probability of
zero all the pages will be identical
It seems fair to presume that the standard deviation could be very large qualifying for a very
flat Gaussian and let us suppose that the pages to be rejected (one for the doubles two for the
triplets etc) are contained within the first standard deviation (as in Figure 48) then the duplicate pages to be thrown away would be about 68
Figure 48 ndash The postulated conditions (pages to be eliminated because they are duplicated equal
to the standard deviation) make 68 of the pages produced useless Iterating the cycle one could
consider the duplication of other pages however it can be demonstrated that the phenomenon
continues to imply finite times
How much does the required time increase to generalize we assume the length of a cycle to be of one unit and we identify with K the average cost of discarded pages (in the previous numerical
case K= 068) and then we observe Figure 49
Figure 49 ndash Having exhausted the first cycle identified by 1 the second of length K allows the
replacement of the duplicate pages produced in the first cycle the third of length K2 is used to
replace those produced in the second cycle and so on
The time necessary to complete the cycles required to eliminate the duplicates as they are produced will be given by the sum
suminfin
=0n
nK
which constitutes a geometric series
The Mathematical Analysis teaches us that such a series converges for 1ltK as is confirmed
in our case where it takes on the value 068
KS
minus=
1
1 and if K = 068 gives 1253
6801
1=
minus=S
Pier Maria Boria Thermodynamics amp life
30
Therefore multiplying by 3125 the time dedicated to complete a cycle (317middot105999989 billion
years) for the hypothesis made we also eliminate all the duplicate pages of our little book of 106
key strokes
Changing the value of K (always lt1) one obtains different multipliers but always of a finite
value let the reader imagine the time necessary to type all of Shakespearersquos works It must be highlighted that the monkey operation to be considered a success requires the
intervention of external intelligence capable of selecting the useful pages (like thought by Theory of
Information) and ordering them in the right sequence to obtain a final legible manuscript this
obvious necessity implies that negative entropy be introduced into the system as covered at the
beginning this is like a living being taking the trouble to ldquoput in orderrdquo otherwise the ldquopurely
randomrdquo work would be entirely useless because it will exclusively produce positive entropy
All experiments attempted by man with the goal of demonstrating the random production of
complex molecules (first building blocks of living organisms) have the defect of requiring an a
priori living system like man to arrange this production
When later chaotic physical-chemical conditions are created (temperature pressure
methane electrical arching etc) hoping to obtain that which Thermodynamics does not permit the
inventors of the moto perpetuo come to mind who never give up
The research on the ldquoprimordial souprdquo belongs to this type of experimentation a battle horse
of the followers of the ldquomaitre agrave penserrdquo of the last century and which regard in particular the laboratory experiments of Stanley Miller the goal of his research of a physical-chemical nature
was to recreate life it was an understandable but too ambitious of a project for a researcher The result was absolutely negative (Miller himself recognized it) however this last piece of information
is only whispered in scientific circles so that we still find genuine touts who speak with enthusiastic coram populo of the primordial soup and its miraculous effects14 with a self-assurance
that is truly shameful
45 CONCLUSION
On 4 July 2007 at the London Kinetics Museum a serious presentation of a perpetual motion
machine was scheduled a machine capable of supplying the user with a power greater than that
absorbed ldquoObviouslyrdquo the presentation was postponed due to ldquoa technical problemrdquo15
It would appear impossible but advocates convinced of such a motion exist and many
inventors submit patent after patent even though still in illo tempore Max Planck declared himself
to be contrary to such a possibility which violates the principles of Thermodynamics
Based on the reasoning we have developed regarding entropy probability and chance the
violation of such principles is implicit even in the attempts to obtain living organisms in a
laboratory (characterized as we have seen as being producers of negative entropy) and as such a
strong analogy can be seen between the advocates of perpetual motion and those aspiring to create
life
1 The correct application of Boltzmannrsquos statistics a phenomenon for which we call on
probability demonstrates that combinations of large numbers of particles to the point of generating complex organisms require very long periods of time in comparison the age of
the universe is but the blink of an eye
2 The probabilities take on the largest numbers in correspondence with the most disordered
configurations
14
From ldquoCorriere della Serardquo october 2008 ldquoLa vita sulla Terra Cominciograve nei vulcani con un innesco chimicordquo 15
-Source Wikipedia
Pier Maria Boria Thermodynamics amp life
3 The most ordered combinations are those which characterize organic structures and the action
of an intelligent being is necessary to select order and conserve in time the favorable
combinations
4 The phrase ldquochance phenomenonrdquo is somewhat less intuitive than what ldquocommon senserdquo
would suggest In fact the Gaussian perspective implies that such phenomena are necessarily
associated with a program this program implies the existence of an objective around which
we have an increased concentration of events
5 In every case it is necessary to postulate the existence of an intelligent design without which
the configurations and the favorable events constitute events without any functional link
between themselves
6 The existence of life as a producer of negative entropy on a continuous basis (not cyclical) is a fact visible with our own eyes
All this leads us to support the existence of a Co-ordinating Entity which possesses life ldquoa
priorirdquo and which is capable of transmitting it to animals (animalis homo included) and vegetation It can be noted that the two living systems animal and vegetable complement each other in the
sense that the design requires that emissions from the first (CO2) are the nutrients for the second and the byproducts of the second (O2) are essential for the first the carbon and oxygen cycles look
like they have been designed According to the author there is only one explanation we are in the presence of the greatest
Design Physicist of all times God the Creator
This is what we call Him as Christians while Israelites call Him Jehovah the Ishmaelites
Allah the Masons GADU (Great Architect of the Universe) etc
In other terms
the Creation is a thermodynamic necessity
Amen
Pier Maria Boria Thermodynamics amp life
13
Part 3 (of 4) Probability
31 PROBABILITY IN BOLTZMANNrsquoS STATISTICS
Boltzmann obtained the graph of the probability as a function of temperature postulating that
a certain number m of particles which are indistinguishable from each other (which we will call A
B C M) and a number n of possible states (a b c n) in which one or more particles (even if
m) can find themselves the presence of particles in each state could occur with different possibilities
If the identical particles are free to occupy the various states (as in the case of a gas) these could continuously exchange states between themselves (for example thanks to reciprocal impacts
as in Figure 23) whilst ldquoon averagerdquo maintaining a certain distribution subject to the conditions around them (for example temperature) a certain distribution of the possible configurations would
be typical of such conditions
Continuing with this example if by state of the particles we mean possessing a certain amount
of kinetic energy E associated with each molecule of a gas in a certain interval of values of energy
∆E there will be a stable quantity of molecules even if amongst themselves continues exchanges of
energy occur Therefore in the range of the same interval some particles enter and some leave
If for the sake of imagination in what follows particles will be considered as ldquoballsrdquo and
states as levels of energy the balls will represent the particles while the levels will represent an
interval of energy (∆E)
Let us start with a very simple case consisting of 3 particles (m=3) able to be hosted by two
levels (n=2) as illustrated in Figure 31
In the left column we see all the possible combinations In the central section we see that certain combinations repeat themselves in such a way that if the particles become indistinguishable
(column 3) they are to be considered the same amongst themselves Therefore three possibilities exist such that both the combinations 234 and 567 can occur
and only once for the combinations 1 and 8 If we ldquonormalizerdquo the possibility (expressing it in unitary or percentage terms) it assumes the
role of probability (ratio between favorable cases and possible cases) which we have done in the last column by expressing it in percentage terms as is common practice
Pier Maria Boria Thermodynamics amp life
14
Figure 31 ndash A rather simple case to demonstrate how given m=3 and n=2 it is possible to
have different probabilities for each combination
Pier Maria Boria Thermodynamics amp life
15
This allows us to draw the graph of Figure 32 where we can begin to see the
Boltzmann distribution forming
Figure 32 ndash The embryonic Boltzmann diagram increasing particles and the number of
possible states the envelope of the columns (in this particular case not yet)
acquires the characteristic asymmetric bell shape
Following in the footsteps of the great Ludwig we enter into systems which are numerically
more substantial three combinations of seven states with an arbitrary arrangement of four particles
as represented in Figure 33 the three combinations are equivalent because the particles are
indistinguishable by hypothesis
Pier Maria Boria Thermodynamics amp life
16
Figure 33 - The three configurations are equivalent if the four particles are indistinguishable
amongst themselves
Each of the n states can be associated with A B C etc (that is to each or more of the m
particles) and since a single particle can occupy each time a different state (and other particles
other states) m times the possible combinations C are ntimesntimesntimeshelliptimesn (m factors equal to n)
C = nm
We could also be convinced observing for example Figure 34 where it is assumed that n=5
(it looks like a musical stavehellip) and m=2 particles (therefore 52=25 combinations)
Pier Maria Boria Thermodynamics amp life
Figure 34 ndash Beyond the 25th beat the preceding configurations are repeated because A and B are
indistinguishable Within the range of the 25 possible configurations some are more favored
because they appear more frequently for example 6 and 22 9 and 25 etc The unoccupied
states are identified by a circle
As is fair to expect configuration 1 is least favored
Pier Maria Boria Thermodynamics amp life
18
We can arrive at the same result with a more practical method suitable also for very large
values of n and m which we will use as follows
It consists of a tabular method stolen from Combinatorial Analysis where for n and m equal to
various units it avoids the need to write hundreds or thousands of key strokes as used above
Let us take two rows and as many columns as there are states thereby obtaining a grid in
Figure 35 to verify what has been said above we have taken 2 rows and 5 columns (n=2 m=5)
Figure 35- With this grid we obtain the number of possible configurations
To further demonstrate we will build a grid for n=5 and m=4 as in Figure 36 where there are sufficient rows to progressively expose the number of particles (from 4 to 1 in the first box of
the first column of the occupancy numbers) and there are n columns
Pier Maria Boria Thermodynamics amp life
19
Figure 36 - Since 54= 625 there are 625 possible combinations the relative probabilities are
listed in the last column note the asymmetry
Pier Maria Boria Thermodynamics amp life
20
It is necessary to observe that in the figure the table of numbers of occupancy reminds
us not by chance of Tartagliarsquos Triangle while the Boltzmann type diagram that can be
associated shown in Figure 37 takes on an almost familiar shape
Figure 37 - Graphical representation of Figure 62 the bars are asymmetric
Pier Maria Boria Thermodynamics amp life
21
To provide an example and referring to Figure 36 we can see how it is possible to obtain 80
possibilities corresponding to his second line
If a box is occupied by 3 particles out of an available 4 the simple combinations of 4 objects
with 3 by 3 (as taught by the Combinatorial Analysis) are given by the binomial coefficient
6437 4
and the four possible groups of three numbers have five positions from which to choose From here 4times5=20 possibilities for the group of three numbers
The single remaining particle has the possibility of the four remaining locations and therefore has 1times4=4 possibilities
The product 20times4=80 gives us the total possibilities in the case that the particles arrange themselves in two groups one with three and one with a single particle and having five boxes
suitable It is easy to verify that we will obtain the same result considering first the single particle
having five boxes suitable (five possibilities 1x5=5) and after the three having the four remaining
(one is occupied by the single particle therefore 4x4=16 and 5x16=80)
Applying the procedure line by line it produces the results shown
Pier Maria Boria Thermodynamics amp life
22
Part 4 (of 4) Chance
41 CHANCE
A sharp-shooter shoots at a target with an excellent rifle he aims carefully chooses the
moment when his breathing will not interfere and the amount of force with which to pull the trigger so as not to move the barrel fires the shot and hits the bullrsquos-eye
Immediately afterwards he takes all the same precautions but the shot ends up being slightly off target it could have been a slight disturbance to his sight an involuntary variation in his
breathing an imperceptible abnormal movement of the finger a very slight unpredictable wind or who knows what else
The causes are many and imponderable slight if each is considered in itself but interacting differently each time ensuring that each shot has a different fate
This complex of innumerable causes of disturbance which are not controllable or predictable
and which not being able to take each into account one by one are called the Law of Probability
(Gaussrsquos Law)10
Probability for the reasons given and law thanks to Carl Friedrich Gauss (1777-1855) who
wrote an equation capable of taking into consideration in a global manner all those fleeting causes
so as to be able to predict with near accurate approximation how the shots will arrange themselves
percentage wise round the target with different distances from the bullseye The approximation will
be more accurate the greater the number of shots that are fired
Let us assume that the target is as represented in Figure 41 and is divided into two parts by
means of the section AB and that our sharpshooter fires many shots after which we count the
number of shots which hit the target in each half
Figure 41- The segmented target
If the reasons for the error are truly random (rifle without defects such that it does not tend to
deviate the shot systematically and neither does the sharpshooter have an analogous defect there is
10
The example of the sharpshooter was published by Engineer Mario Manaira in Ndeg 256 of ldquoJournal of Mechanicsrdquo
together with our first article concerning thermodynamics more than half a century ago (1961)
Pier Maria Boria Thermodynamics amp life
23
not a steady wind etc in other words there does not exist a cause which always influences with the
same bias called a systematic cause) we could note the following
1 The shots will be greater in number in the first band round the center
2 The shots will progressively decrease in number in the subsequent bands as these distance themselves further from the center until there are very few in the bands furthest away
3 The shots in the two halves right and left in any similar band will tend to have the same number and will even be identical if sufficient shots are fired
It is therefore possible to represent the phenomenon graphically as in the following figure
Figure 42 ndash The random distribution of the shots in each band and the Gaussian distribution that
would be obtained with an infinite number of shots fired
If the marksman were less capable the concentration of shots near the zero on the abscissa would reduce and the curve would flatten itself while maintaining the characteristics given and
represented in Figure 43 The first observation is that the maximum height of the curve constitutes the ldquotargetrdquo in other words the goal of the operation while the absence of systematic causes (in
antithesis of randomness) ensures the symmetry of the curve with respect to the vertical which
represents our target zero
Pier Maria Boria Thermodynamics amp life
24
Figure 43 - If the marksman is less skilled the Gaussian flattens
In the case of a systematic cause of error the curve loses its symmetry if we assume that the
test is performed with a constant wind from left to right the graph will take on the shape of Figure
44
Figure 44 ndash When the Gaussian is asymmetric it implies that the phenomenon is not ldquoentirely
randomrdquo11
Let us suppose now that our sharpshooter is blindfolded the target becomes very large and is
moved he will have to shoot blindly (randomly) left and right high and low Given that the Gauss
11
Gauss suggests that the analytical expression of the Law of Randomness is the function
2xey minus
=
where it can be seen that the curve is symmetrical with respect to the axis x=0 and decreasing both towards the left and
right of this line and has a maximum for x=0
It can be shown further that the area subtended is
π=int+infin
infinminus
minusdxe
x2
To ensure that this area is equal to unity as opposed to π appropriate steps can be taken which without
changing the general properties illustrated give the normalized Gaussrsquos Law
Pier Maria Boria Thermodynamics amp life
function still applies the probability curve will flatten itself maintaining the essential
characteristics in particular the two tails which will tend towards a tangent with the abscissa
tending towards infinity a maximum point a point of inflection and the other characteristics
illustrated in Figure 45
Figure 45 ndash Typical characteristics of a normalized Gaussian
Supposing once more that the Gauss function still applies it would be logical to expect a distribution with a curve that is so flat that it will be difficult to see a maximum point corresponding
to the center of the target it will be necessary to fire enough shots so as to occupy every position on the abscissa and to have hit with 100 certainty the bullrsquos-eye
This implies that everything is possible as long as an infinite number of shots are available
(using rhetorical language)
42 SOME PROPERTIES OF RANDOM EVENTS
The perplexities regarding the applicability of chance as referred to the blind sharpshooter
depend on the fact that the Gaussian assumes that programming has been applied to reach an
objective which implies that the operator is conscious of the objective an element which in this
case is absent
Both the existence of a program (the sharpshooter sets out to hit the bullrsquos-eye) and the
existence of an objective (the card with circles) appear to be essential to be able to talk about
chance
Another example let us imagine a machine programmed to produce a certain mechanical
piece the program is the design of the piece written in machine language and the objective is the production of the piece In mass production we will find that it is the case that despite the work
conditions being maintained the same each piece will be different to the other to the point that the pieces which exceed the tolerances (which would not allow them to be interchangeable) will be
rejected Innumerable examples could be presented identifying in every case these two characteristics
a program and an objective Statistics also operate in reverse from the measurement of a group of subjects it creates a bar
chart its envelope will be the curve of the random distribution It will give us the average of the values measured if the curve is symmetrical it will tell us that the phenomenon is not influenced by
systematic causes further it will tell us the value of the standard deviation etc
Pier Maria Boria Thermodynamics amp life
26
To fix this thought in our heads let us suppose that we want to study the average height of a
population of people who are male we make many measurements on many subjects creating bars
for every centimeter we will obtain a graph similar to Figure 46
Figure 46 ndash A practical application the Gaussian deduced from experimental measurements for
statistical purposes
In this statistical application where are the program and objective They are there they are
there they were contained in the information which the people naturally had at conception a
matter of genes and of DNA (an observation coherent with ldquoThe Kid Equationrdquo See the
ldquoIntroduction to Hyperspacerdquo12
)
These considerations lead us to think that the meaning of the word ldquochancerdquo commonly given
does not make sense that ldquochancerdquo does not exist and lead us to suspect that Anatole France had an
inspired guess when he said ldquochance is Godrsquos pseudonym when He does not want to sign his
namerdquo
This strongly agrees with what illustrious philosophers have been confirming for centuries
ldquoDeus absconditus estrdquo (Is XLV XV)
12
In our first volume ldquoCaro amico miohelliprdquo ndash Ed Pagine ndash 2010 In our second volume (ldquoVerba volant eqvuationes
manentrdquo) other considerations about a fundamental theorem of Genetics the Hardy Weinberg theorem
Pier Maria Boria Thermodynamics amp life
27
43 CHANCE amp PROBABILITY
We can now summarize some salient functions of Boltzmann and Gauss
Boltzmann
1 Deals with probability regarding the characteristics that can be assumed by many identical particles having a certain number of positions available (Dirac and Fermi deal
with particles which are distinguishable but the correct reference in our observations are the identical particles)
2 The function presents a maximum and aesthetically looks like a Gaussian but it is not symmetrical
3 It has only a single asymptote to the right of the maximum and its minimum at infinity coincides with zero the origin of the reference system
4 It is normalized so that the area subtended represents the total probability of 100
Gauss
1 Deals with chance and is applicable when an objective exists that is defined by a
program
2 The phenomenon ldquopurely by chancerdquo is represented by a curve that is symmetrical
about the axis x=0
3 The Gaussian has a maximum and no minimum at infinity
4 It possesses two asymptotes one to the right and one to the left of the maximum
5 Well defined values of probability can be associated with multiples of the standard deviation
6 It is normalized as for Boltzmannrsquos
44 THE EDDINGTONrsquoS PARADOX13
Eddingtonrsquos famous ldquoInfinite monkey theoremrdquo can be counted amongst the most discussed
paradoxes for the fact that it is often quoted by so called ldquoscientific popularizersrdquo The original assertion states ldquohellipa monkey hitting keys at random on a typewriter keyboard
for an infinite amount of times will almost surely type a given text such as the complete works of
William Shakespearerdquo
Having taken away the condition of an infinite amount of time the paradox remains acceptable
(from the moment we are able to demonstrate that a finite amount of time is sufficient) However
such a long period of time is necessary that the original statement could be seen as an hyperbolic
discussion
We have seen that random phenomena require a program in light of an objective In the case
of the typing monkeys the program could include the elimination of duplicate pages (actually the
identical pages as we will see below) and the objective could consist in the conservation of ldquogoodrdquo
pages arranged in the right sequence
Applying Boltzmannrsquos statistics let us assume that the typewriter has m=30 keys (we can think of ldquoblindrdquo keys without any writing and all identical) and that we want to write a book of
only 106
letters (a thousand typed pages) as we have observed in paragraph 31 all the possible combinations are
13
The reader can find all the details regarding these various arguments on the web
Pier Maria Boria Thermodynamics amp life
C = nm = (10
6)30
= (10)180
In other words there are 10180
possible configurations
Let us assume that the monkeys are capable of striking 10 keyssec (skilled typistshellip) the
time necessary would be
t = 10180
x 106 10 = 10
185 sec
Since we can count 1016 seconds in a billion years it is also possible to say that the time
required will be
10185
1016
= 10169
billion years (giga-years)
(let us remember that the big-bang has an age of ldquoonlyrdquo 14 billion years)
In reality the situation is even ldquoworserdquo in fact this calculation (which is generally accepted)
is wrong because we cannot talk about only thirty objects (the letters punctuation marks spaces between lines etc) to be arranged in 10
6 positions otherwise in each of 10180 configurations
obtainable we would find empty spaces up to 106-30 in each configuration
It is necessary to postulate that there are 106 letters to be arranged like conceding that the
monkeys have to insert 106 objects ie 10
6 key strokes In other words it is necessary that n = m =
106 and in this case the formula of the combinations gives us an astronomical value
6106 )10(===
mm mnC combinations
At a rhythm of 10 key strokes sec the time corresponds to
9899995005000616106 10sec101010)10(
6
equiv=sdotsdot=minust years
Figure 47 ndash Summary table of the probabilities according to Boltzmann
In realty the situation is even ldquoworserdquo still In fact in the calculation of the combinations duplicate configurations are not considered
(which necessarily must be considered as possible) in other words our monkeys could produce the same combinations several times (or two identical pages) anyway the duplications will be useless
in the compilation of our small book of only 106 letters
To this end we invoke chance (to attempt to appreciate the incidence of the repeating of
identical pages) and having constructed a Gaussian by arranging the frequency of identical pages we can reason as follows having produced all the astronomical combinations as above in the time
calculated (which we will call a cycle) the highest probability of identical pages is in pairs (which
Pier Maria Boria Thermodynamics amp life
29
we will assign the maximum position) then in threes and so on At infinity with a probability of
zero all the pages will be identical
It seems fair to presume that the standard deviation could be very large qualifying for a very
flat Gaussian and let us suppose that the pages to be rejected (one for the doubles two for the
triplets etc) are contained within the first standard deviation (as in Figure 48) then the duplicate pages to be thrown away would be about 68
Figure 48 ndash The postulated conditions (pages to be eliminated because they are duplicated equal
to the standard deviation) make 68 of the pages produced useless Iterating the cycle one could
consider the duplication of other pages however it can be demonstrated that the phenomenon
continues to imply finite times
How much does the required time increase to generalize we assume the length of a cycle to be of one unit and we identify with K the average cost of discarded pages (in the previous numerical
case K= 068) and then we observe Figure 49
Figure 49 ndash Having exhausted the first cycle identified by 1 the second of length K allows the
replacement of the duplicate pages produced in the first cycle the third of length K2 is used to
replace those produced in the second cycle and so on
The time necessary to complete the cycles required to eliminate the duplicates as they are produced will be given by the sum
suminfin
=0n
nK
which constitutes a geometric series
The Mathematical Analysis teaches us that such a series converges for 1ltK as is confirmed
in our case where it takes on the value 068
KS
minus=
1
1 and if K = 068 gives 1253
6801
1=
minus=S
Pier Maria Boria Thermodynamics amp life
30
Therefore multiplying by 3125 the time dedicated to complete a cycle (317middot105999989 billion
years) for the hypothesis made we also eliminate all the duplicate pages of our little book of 106
key strokes
Changing the value of K (always lt1) one obtains different multipliers but always of a finite
value let the reader imagine the time necessary to type all of Shakespearersquos works It must be highlighted that the monkey operation to be considered a success requires the
intervention of external intelligence capable of selecting the useful pages (like thought by Theory of
Information) and ordering them in the right sequence to obtain a final legible manuscript this
obvious necessity implies that negative entropy be introduced into the system as covered at the
beginning this is like a living being taking the trouble to ldquoput in orderrdquo otherwise the ldquopurely
randomrdquo work would be entirely useless because it will exclusively produce positive entropy
All experiments attempted by man with the goal of demonstrating the random production of
complex molecules (first building blocks of living organisms) have the defect of requiring an a
priori living system like man to arrange this production
When later chaotic physical-chemical conditions are created (temperature pressure
methane electrical arching etc) hoping to obtain that which Thermodynamics does not permit the
inventors of the moto perpetuo come to mind who never give up
The research on the ldquoprimordial souprdquo belongs to this type of experimentation a battle horse
of the followers of the ldquomaitre agrave penserrdquo of the last century and which regard in particular the laboratory experiments of Stanley Miller the goal of his research of a physical-chemical nature
was to recreate life it was an understandable but too ambitious of a project for a researcher The result was absolutely negative (Miller himself recognized it) however this last piece of information
is only whispered in scientific circles so that we still find genuine touts who speak with enthusiastic coram populo of the primordial soup and its miraculous effects14 with a self-assurance
that is truly shameful
45 CONCLUSION
On 4 July 2007 at the London Kinetics Museum a serious presentation of a perpetual motion
machine was scheduled a machine capable of supplying the user with a power greater than that
absorbed ldquoObviouslyrdquo the presentation was postponed due to ldquoa technical problemrdquo15
It would appear impossible but advocates convinced of such a motion exist and many
inventors submit patent after patent even though still in illo tempore Max Planck declared himself
to be contrary to such a possibility which violates the principles of Thermodynamics
Based on the reasoning we have developed regarding entropy probability and chance the
violation of such principles is implicit even in the attempts to obtain living organisms in a
laboratory (characterized as we have seen as being producers of negative entropy) and as such a
strong analogy can be seen between the advocates of perpetual motion and those aspiring to create
life
1 The correct application of Boltzmannrsquos statistics a phenomenon for which we call on
probability demonstrates that combinations of large numbers of particles to the point of generating complex organisms require very long periods of time in comparison the age of
the universe is but the blink of an eye
2 The probabilities take on the largest numbers in correspondence with the most disordered
configurations
14
From ldquoCorriere della Serardquo october 2008 ldquoLa vita sulla Terra Cominciograve nei vulcani con un innesco chimicordquo 15
-Source Wikipedia
Pier Maria Boria Thermodynamics amp life
3 The most ordered combinations are those which characterize organic structures and the action
of an intelligent being is necessary to select order and conserve in time the favorable
combinations
4 The phrase ldquochance phenomenonrdquo is somewhat less intuitive than what ldquocommon senserdquo
would suggest In fact the Gaussian perspective implies that such phenomena are necessarily
associated with a program this program implies the existence of an objective around which
we have an increased concentration of events
5 In every case it is necessary to postulate the existence of an intelligent design without which
the configurations and the favorable events constitute events without any functional link
between themselves
6 The existence of life as a producer of negative entropy on a continuous basis (not cyclical) is a fact visible with our own eyes
All this leads us to support the existence of a Co-ordinating Entity which possesses life ldquoa
priorirdquo and which is capable of transmitting it to animals (animalis homo included) and vegetation It can be noted that the two living systems animal and vegetable complement each other in the
sense that the design requires that emissions from the first (CO2) are the nutrients for the second and the byproducts of the second (O2) are essential for the first the carbon and oxygen cycles look
like they have been designed According to the author there is only one explanation we are in the presence of the greatest
Design Physicist of all times God the Creator
This is what we call Him as Christians while Israelites call Him Jehovah the Ishmaelites
Allah the Masons GADU (Great Architect of the Universe) etc
In other terms
the Creation is a thermodynamic necessity
Amen
Pier Maria Boria Thermodynamics amp life
14
Figure 31 ndash A rather simple case to demonstrate how given m=3 and n=2 it is possible to
have different probabilities for each combination
Pier Maria Boria Thermodynamics amp life
15
This allows us to draw the graph of Figure 32 where we can begin to see the
Boltzmann distribution forming
Figure 32 ndash The embryonic Boltzmann diagram increasing particles and the number of
possible states the envelope of the columns (in this particular case not yet)
acquires the characteristic asymmetric bell shape
Following in the footsteps of the great Ludwig we enter into systems which are numerically
more substantial three combinations of seven states with an arbitrary arrangement of four particles
as represented in Figure 33 the three combinations are equivalent because the particles are
indistinguishable by hypothesis
Pier Maria Boria Thermodynamics amp life
16
Figure 33 - The three configurations are equivalent if the four particles are indistinguishable
amongst themselves
Each of the n states can be associated with A B C etc (that is to each or more of the m
particles) and since a single particle can occupy each time a different state (and other particles
other states) m times the possible combinations C are ntimesntimesntimeshelliptimesn (m factors equal to n)
C = nm
We could also be convinced observing for example Figure 34 where it is assumed that n=5
(it looks like a musical stavehellip) and m=2 particles (therefore 52=25 combinations)
Pier Maria Boria Thermodynamics amp life
Figure 34 ndash Beyond the 25th beat the preceding configurations are repeated because A and B are
indistinguishable Within the range of the 25 possible configurations some are more favored
because they appear more frequently for example 6 and 22 9 and 25 etc The unoccupied
states are identified by a circle
As is fair to expect configuration 1 is least favored
Pier Maria Boria Thermodynamics amp life
18
We can arrive at the same result with a more practical method suitable also for very large
values of n and m which we will use as follows
It consists of a tabular method stolen from Combinatorial Analysis where for n and m equal to
various units it avoids the need to write hundreds or thousands of key strokes as used above
Let us take two rows and as many columns as there are states thereby obtaining a grid in
Figure 35 to verify what has been said above we have taken 2 rows and 5 columns (n=2 m=5)
Figure 35- With this grid we obtain the number of possible configurations
To further demonstrate we will build a grid for n=5 and m=4 as in Figure 36 where there are sufficient rows to progressively expose the number of particles (from 4 to 1 in the first box of
the first column of the occupancy numbers) and there are n columns
Pier Maria Boria Thermodynamics amp life
19
Figure 36 - Since 54= 625 there are 625 possible combinations the relative probabilities are
listed in the last column note the asymmetry
Pier Maria Boria Thermodynamics amp life
20
It is necessary to observe that in the figure the table of numbers of occupancy reminds
us not by chance of Tartagliarsquos Triangle while the Boltzmann type diagram that can be
associated shown in Figure 37 takes on an almost familiar shape
Figure 37 - Graphical representation of Figure 62 the bars are asymmetric
Pier Maria Boria Thermodynamics amp life
21
To provide an example and referring to Figure 36 we can see how it is possible to obtain 80
possibilities corresponding to his second line
If a box is occupied by 3 particles out of an available 4 the simple combinations of 4 objects
with 3 by 3 (as taught by the Combinatorial Analysis) are given by the binomial coefficient
6437 4
and the four possible groups of three numbers have five positions from which to choose From here 4times5=20 possibilities for the group of three numbers
The single remaining particle has the possibility of the four remaining locations and therefore has 1times4=4 possibilities
The product 20times4=80 gives us the total possibilities in the case that the particles arrange themselves in two groups one with three and one with a single particle and having five boxes
suitable It is easy to verify that we will obtain the same result considering first the single particle
having five boxes suitable (five possibilities 1x5=5) and after the three having the four remaining
(one is occupied by the single particle therefore 4x4=16 and 5x16=80)
Applying the procedure line by line it produces the results shown
Pier Maria Boria Thermodynamics amp life
22
Part 4 (of 4) Chance
41 CHANCE
A sharp-shooter shoots at a target with an excellent rifle he aims carefully chooses the
moment when his breathing will not interfere and the amount of force with which to pull the trigger so as not to move the barrel fires the shot and hits the bullrsquos-eye
Immediately afterwards he takes all the same precautions but the shot ends up being slightly off target it could have been a slight disturbance to his sight an involuntary variation in his
breathing an imperceptible abnormal movement of the finger a very slight unpredictable wind or who knows what else
The causes are many and imponderable slight if each is considered in itself but interacting differently each time ensuring that each shot has a different fate
This complex of innumerable causes of disturbance which are not controllable or predictable
and which not being able to take each into account one by one are called the Law of Probability
(Gaussrsquos Law)10
Probability for the reasons given and law thanks to Carl Friedrich Gauss (1777-1855) who
wrote an equation capable of taking into consideration in a global manner all those fleeting causes
so as to be able to predict with near accurate approximation how the shots will arrange themselves
percentage wise round the target with different distances from the bullseye The approximation will
be more accurate the greater the number of shots that are fired
Let us assume that the target is as represented in Figure 41 and is divided into two parts by
means of the section AB and that our sharpshooter fires many shots after which we count the
number of shots which hit the target in each half
Figure 41- The segmented target
If the reasons for the error are truly random (rifle without defects such that it does not tend to
deviate the shot systematically and neither does the sharpshooter have an analogous defect there is
10
The example of the sharpshooter was published by Engineer Mario Manaira in Ndeg 256 of ldquoJournal of Mechanicsrdquo
together with our first article concerning thermodynamics more than half a century ago (1961)
Pier Maria Boria Thermodynamics amp life
23
not a steady wind etc in other words there does not exist a cause which always influences with the
same bias called a systematic cause) we could note the following
1 The shots will be greater in number in the first band round the center
2 The shots will progressively decrease in number in the subsequent bands as these distance themselves further from the center until there are very few in the bands furthest away
3 The shots in the two halves right and left in any similar band will tend to have the same number and will even be identical if sufficient shots are fired
It is therefore possible to represent the phenomenon graphically as in the following figure
Figure 42 ndash The random distribution of the shots in each band and the Gaussian distribution that
would be obtained with an infinite number of shots fired
If the marksman were less capable the concentration of shots near the zero on the abscissa would reduce and the curve would flatten itself while maintaining the characteristics given and
represented in Figure 43 The first observation is that the maximum height of the curve constitutes the ldquotargetrdquo in other words the goal of the operation while the absence of systematic causes (in
antithesis of randomness) ensures the symmetry of the curve with respect to the vertical which
represents our target zero
Pier Maria Boria Thermodynamics amp life
24
Figure 43 - If the marksman is less skilled the Gaussian flattens
In the case of a systematic cause of error the curve loses its symmetry if we assume that the
test is performed with a constant wind from left to right the graph will take on the shape of Figure
44
Figure 44 ndash When the Gaussian is asymmetric it implies that the phenomenon is not ldquoentirely
randomrdquo11
Let us suppose now that our sharpshooter is blindfolded the target becomes very large and is
moved he will have to shoot blindly (randomly) left and right high and low Given that the Gauss
11
Gauss suggests that the analytical expression of the Law of Randomness is the function
2xey minus
=
where it can be seen that the curve is symmetrical with respect to the axis x=0 and decreasing both towards the left and
right of this line and has a maximum for x=0
It can be shown further that the area subtended is
π=int+infin
infinminus
minusdxe
x2
To ensure that this area is equal to unity as opposed to π appropriate steps can be taken which without
changing the general properties illustrated give the normalized Gaussrsquos Law
Pier Maria Boria Thermodynamics amp life
function still applies the probability curve will flatten itself maintaining the essential
characteristics in particular the two tails which will tend towards a tangent with the abscissa
tending towards infinity a maximum point a point of inflection and the other characteristics
illustrated in Figure 45
Figure 45 ndash Typical characteristics of a normalized Gaussian
Supposing once more that the Gauss function still applies it would be logical to expect a distribution with a curve that is so flat that it will be difficult to see a maximum point corresponding
to the center of the target it will be necessary to fire enough shots so as to occupy every position on the abscissa and to have hit with 100 certainty the bullrsquos-eye
This implies that everything is possible as long as an infinite number of shots are available
(using rhetorical language)
42 SOME PROPERTIES OF RANDOM EVENTS
The perplexities regarding the applicability of chance as referred to the blind sharpshooter
depend on the fact that the Gaussian assumes that programming has been applied to reach an
objective which implies that the operator is conscious of the objective an element which in this
case is absent
Both the existence of a program (the sharpshooter sets out to hit the bullrsquos-eye) and the
existence of an objective (the card with circles) appear to be essential to be able to talk about
chance
Another example let us imagine a machine programmed to produce a certain mechanical
piece the program is the design of the piece written in machine language and the objective is the production of the piece In mass production we will find that it is the case that despite the work
conditions being maintained the same each piece will be different to the other to the point that the pieces which exceed the tolerances (which would not allow them to be interchangeable) will be
rejected Innumerable examples could be presented identifying in every case these two characteristics
a program and an objective Statistics also operate in reverse from the measurement of a group of subjects it creates a bar
chart its envelope will be the curve of the random distribution It will give us the average of the values measured if the curve is symmetrical it will tell us that the phenomenon is not influenced by
systematic causes further it will tell us the value of the standard deviation etc
Pier Maria Boria Thermodynamics amp life
26
To fix this thought in our heads let us suppose that we want to study the average height of a
population of people who are male we make many measurements on many subjects creating bars
for every centimeter we will obtain a graph similar to Figure 46
Figure 46 ndash A practical application the Gaussian deduced from experimental measurements for
statistical purposes
In this statistical application where are the program and objective They are there they are
there they were contained in the information which the people naturally had at conception a
matter of genes and of DNA (an observation coherent with ldquoThe Kid Equationrdquo See the
ldquoIntroduction to Hyperspacerdquo12
)
These considerations lead us to think that the meaning of the word ldquochancerdquo commonly given
does not make sense that ldquochancerdquo does not exist and lead us to suspect that Anatole France had an
inspired guess when he said ldquochance is Godrsquos pseudonym when He does not want to sign his
namerdquo
This strongly agrees with what illustrious philosophers have been confirming for centuries
ldquoDeus absconditus estrdquo (Is XLV XV)
12
In our first volume ldquoCaro amico miohelliprdquo ndash Ed Pagine ndash 2010 In our second volume (ldquoVerba volant eqvuationes
manentrdquo) other considerations about a fundamental theorem of Genetics the Hardy Weinberg theorem
Pier Maria Boria Thermodynamics amp life
27
43 CHANCE amp PROBABILITY
We can now summarize some salient functions of Boltzmann and Gauss
Boltzmann
1 Deals with probability regarding the characteristics that can be assumed by many identical particles having a certain number of positions available (Dirac and Fermi deal
with particles which are distinguishable but the correct reference in our observations are the identical particles)
2 The function presents a maximum and aesthetically looks like a Gaussian but it is not symmetrical
3 It has only a single asymptote to the right of the maximum and its minimum at infinity coincides with zero the origin of the reference system
4 It is normalized so that the area subtended represents the total probability of 100
Gauss
1 Deals with chance and is applicable when an objective exists that is defined by a
program
2 The phenomenon ldquopurely by chancerdquo is represented by a curve that is symmetrical
about the axis x=0
3 The Gaussian has a maximum and no minimum at infinity
4 It possesses two asymptotes one to the right and one to the left of the maximum
5 Well defined values of probability can be associated with multiples of the standard deviation
6 It is normalized as for Boltzmannrsquos
44 THE EDDINGTONrsquoS PARADOX13
Eddingtonrsquos famous ldquoInfinite monkey theoremrdquo can be counted amongst the most discussed
paradoxes for the fact that it is often quoted by so called ldquoscientific popularizersrdquo The original assertion states ldquohellipa monkey hitting keys at random on a typewriter keyboard
for an infinite amount of times will almost surely type a given text such as the complete works of
William Shakespearerdquo
Having taken away the condition of an infinite amount of time the paradox remains acceptable
(from the moment we are able to demonstrate that a finite amount of time is sufficient) However
such a long period of time is necessary that the original statement could be seen as an hyperbolic
discussion
We have seen that random phenomena require a program in light of an objective In the case
of the typing monkeys the program could include the elimination of duplicate pages (actually the
identical pages as we will see below) and the objective could consist in the conservation of ldquogoodrdquo
pages arranged in the right sequence
Applying Boltzmannrsquos statistics let us assume that the typewriter has m=30 keys (we can think of ldquoblindrdquo keys without any writing and all identical) and that we want to write a book of
only 106
letters (a thousand typed pages) as we have observed in paragraph 31 all the possible combinations are
13
The reader can find all the details regarding these various arguments on the web
Pier Maria Boria Thermodynamics amp life
C = nm = (10
6)30
= (10)180
In other words there are 10180
possible configurations
Let us assume that the monkeys are capable of striking 10 keyssec (skilled typistshellip) the
time necessary would be
t = 10180
x 106 10 = 10
185 sec
Since we can count 1016 seconds in a billion years it is also possible to say that the time
required will be
10185
1016
= 10169
billion years (giga-years)
(let us remember that the big-bang has an age of ldquoonlyrdquo 14 billion years)
In reality the situation is even ldquoworserdquo in fact this calculation (which is generally accepted)
is wrong because we cannot talk about only thirty objects (the letters punctuation marks spaces between lines etc) to be arranged in 10
6 positions otherwise in each of 10180 configurations
obtainable we would find empty spaces up to 106-30 in each configuration
It is necessary to postulate that there are 106 letters to be arranged like conceding that the
monkeys have to insert 106 objects ie 10
6 key strokes In other words it is necessary that n = m =
106 and in this case the formula of the combinations gives us an astronomical value
6106 )10(===
mm mnC combinations
At a rhythm of 10 key strokes sec the time corresponds to
9899995005000616106 10sec101010)10(
6
equiv=sdotsdot=minust years
Figure 47 ndash Summary table of the probabilities according to Boltzmann
In realty the situation is even ldquoworserdquo still In fact in the calculation of the combinations duplicate configurations are not considered
(which necessarily must be considered as possible) in other words our monkeys could produce the same combinations several times (or two identical pages) anyway the duplications will be useless
in the compilation of our small book of only 106 letters
To this end we invoke chance (to attempt to appreciate the incidence of the repeating of
identical pages) and having constructed a Gaussian by arranging the frequency of identical pages we can reason as follows having produced all the astronomical combinations as above in the time
calculated (which we will call a cycle) the highest probability of identical pages is in pairs (which
Pier Maria Boria Thermodynamics amp life
29
we will assign the maximum position) then in threes and so on At infinity with a probability of
zero all the pages will be identical
It seems fair to presume that the standard deviation could be very large qualifying for a very
flat Gaussian and let us suppose that the pages to be rejected (one for the doubles two for the
triplets etc) are contained within the first standard deviation (as in Figure 48) then the duplicate pages to be thrown away would be about 68
Figure 48 ndash The postulated conditions (pages to be eliminated because they are duplicated equal
to the standard deviation) make 68 of the pages produced useless Iterating the cycle one could
consider the duplication of other pages however it can be demonstrated that the phenomenon
continues to imply finite times
How much does the required time increase to generalize we assume the length of a cycle to be of one unit and we identify with K the average cost of discarded pages (in the previous numerical
case K= 068) and then we observe Figure 49
Figure 49 ndash Having exhausted the first cycle identified by 1 the second of length K allows the
replacement of the duplicate pages produced in the first cycle the third of length K2 is used to
replace those produced in the second cycle and so on
The time necessary to complete the cycles required to eliminate the duplicates as they are produced will be given by the sum
suminfin
=0n
nK
which constitutes a geometric series
The Mathematical Analysis teaches us that such a series converges for 1ltK as is confirmed
in our case where it takes on the value 068
KS
minus=
1
1 and if K = 068 gives 1253
6801
1=
minus=S
Pier Maria Boria Thermodynamics amp life
30
Therefore multiplying by 3125 the time dedicated to complete a cycle (317middot105999989 billion
years) for the hypothesis made we also eliminate all the duplicate pages of our little book of 106
key strokes
Changing the value of K (always lt1) one obtains different multipliers but always of a finite
value let the reader imagine the time necessary to type all of Shakespearersquos works It must be highlighted that the monkey operation to be considered a success requires the
intervention of external intelligence capable of selecting the useful pages (like thought by Theory of
Information) and ordering them in the right sequence to obtain a final legible manuscript this
obvious necessity implies that negative entropy be introduced into the system as covered at the
beginning this is like a living being taking the trouble to ldquoput in orderrdquo otherwise the ldquopurely
randomrdquo work would be entirely useless because it will exclusively produce positive entropy
All experiments attempted by man with the goal of demonstrating the random production of
complex molecules (first building blocks of living organisms) have the defect of requiring an a
priori living system like man to arrange this production
When later chaotic physical-chemical conditions are created (temperature pressure
methane electrical arching etc) hoping to obtain that which Thermodynamics does not permit the
inventors of the moto perpetuo come to mind who never give up
The research on the ldquoprimordial souprdquo belongs to this type of experimentation a battle horse
of the followers of the ldquomaitre agrave penserrdquo of the last century and which regard in particular the laboratory experiments of Stanley Miller the goal of his research of a physical-chemical nature
was to recreate life it was an understandable but too ambitious of a project for a researcher The result was absolutely negative (Miller himself recognized it) however this last piece of information
is only whispered in scientific circles so that we still find genuine touts who speak with enthusiastic coram populo of the primordial soup and its miraculous effects14 with a self-assurance
that is truly shameful
45 CONCLUSION
On 4 July 2007 at the London Kinetics Museum a serious presentation of a perpetual motion
machine was scheduled a machine capable of supplying the user with a power greater than that
absorbed ldquoObviouslyrdquo the presentation was postponed due to ldquoa technical problemrdquo15
It would appear impossible but advocates convinced of such a motion exist and many
inventors submit patent after patent even though still in illo tempore Max Planck declared himself
to be contrary to such a possibility which violates the principles of Thermodynamics
Based on the reasoning we have developed regarding entropy probability and chance the
violation of such principles is implicit even in the attempts to obtain living organisms in a
laboratory (characterized as we have seen as being producers of negative entropy) and as such a
strong analogy can be seen between the advocates of perpetual motion and those aspiring to create
life
1 The correct application of Boltzmannrsquos statistics a phenomenon for which we call on
probability demonstrates that combinations of large numbers of particles to the point of generating complex organisms require very long periods of time in comparison the age of
the universe is but the blink of an eye
2 The probabilities take on the largest numbers in correspondence with the most disordered
configurations
14
From ldquoCorriere della Serardquo october 2008 ldquoLa vita sulla Terra Cominciograve nei vulcani con un innesco chimicordquo 15
-Source Wikipedia
Pier Maria Boria Thermodynamics amp life
3 The most ordered combinations are those which characterize organic structures and the action
of an intelligent being is necessary to select order and conserve in time the favorable
combinations
4 The phrase ldquochance phenomenonrdquo is somewhat less intuitive than what ldquocommon senserdquo
would suggest In fact the Gaussian perspective implies that such phenomena are necessarily
associated with a program this program implies the existence of an objective around which
we have an increased concentration of events
5 In every case it is necessary to postulate the existence of an intelligent design without which
the configurations and the favorable events constitute events without any functional link
between themselves
6 The existence of life as a producer of negative entropy on a continuous basis (not cyclical) is a fact visible with our own eyes
All this leads us to support the existence of a Co-ordinating Entity which possesses life ldquoa
priorirdquo and which is capable of transmitting it to animals (animalis homo included) and vegetation It can be noted that the two living systems animal and vegetable complement each other in the
sense that the design requires that emissions from the first (CO2) are the nutrients for the second and the byproducts of the second (O2) are essential for the first the carbon and oxygen cycles look
like they have been designed According to the author there is only one explanation we are in the presence of the greatest
Design Physicist of all times God the Creator
This is what we call Him as Christians while Israelites call Him Jehovah the Ishmaelites
Allah the Masons GADU (Great Architect of the Universe) etc
In other terms
the Creation is a thermodynamic necessity
Amen
Pier Maria Boria Thermodynamics amp life
15
This allows us to draw the graph of Figure 32 where we can begin to see the
Boltzmann distribution forming
Figure 32 ndash The embryonic Boltzmann diagram increasing particles and the number of
possible states the envelope of the columns (in this particular case not yet)
acquires the characteristic asymmetric bell shape
Following in the footsteps of the great Ludwig we enter into systems which are numerically
more substantial three combinations of seven states with an arbitrary arrangement of four particles
as represented in Figure 33 the three combinations are equivalent because the particles are
indistinguishable by hypothesis
Pier Maria Boria Thermodynamics amp life
16
Figure 33 - The three configurations are equivalent if the four particles are indistinguishable
amongst themselves
Each of the n states can be associated with A B C etc (that is to each or more of the m
particles) and since a single particle can occupy each time a different state (and other particles
other states) m times the possible combinations C are ntimesntimesntimeshelliptimesn (m factors equal to n)
C = nm
We could also be convinced observing for example Figure 34 where it is assumed that n=5
(it looks like a musical stavehellip) and m=2 particles (therefore 52=25 combinations)
Pier Maria Boria Thermodynamics amp life
Figure 34 ndash Beyond the 25th beat the preceding configurations are repeated because A and B are
indistinguishable Within the range of the 25 possible configurations some are more favored
because they appear more frequently for example 6 and 22 9 and 25 etc The unoccupied
states are identified by a circle
As is fair to expect configuration 1 is least favored
Pier Maria Boria Thermodynamics amp life
18
We can arrive at the same result with a more practical method suitable also for very large
values of n and m which we will use as follows
It consists of a tabular method stolen from Combinatorial Analysis where for n and m equal to
various units it avoids the need to write hundreds or thousands of key strokes as used above
Let us take two rows and as many columns as there are states thereby obtaining a grid in
Figure 35 to verify what has been said above we have taken 2 rows and 5 columns (n=2 m=5)
Figure 35- With this grid we obtain the number of possible configurations
To further demonstrate we will build a grid for n=5 and m=4 as in Figure 36 where there are sufficient rows to progressively expose the number of particles (from 4 to 1 in the first box of
the first column of the occupancy numbers) and there are n columns
Pier Maria Boria Thermodynamics amp life
19
Figure 36 - Since 54= 625 there are 625 possible combinations the relative probabilities are
listed in the last column note the asymmetry
Pier Maria Boria Thermodynamics amp life
20
It is necessary to observe that in the figure the table of numbers of occupancy reminds
us not by chance of Tartagliarsquos Triangle while the Boltzmann type diagram that can be
associated shown in Figure 37 takes on an almost familiar shape
Figure 37 - Graphical representation of Figure 62 the bars are asymmetric
Pier Maria Boria Thermodynamics amp life
21
To provide an example and referring to Figure 36 we can see how it is possible to obtain 80
possibilities corresponding to his second line
If a box is occupied by 3 particles out of an available 4 the simple combinations of 4 objects
with 3 by 3 (as taught by the Combinatorial Analysis) are given by the binomial coefficient
6437 4
and the four possible groups of three numbers have five positions from which to choose From here 4times5=20 possibilities for the group of three numbers
The single remaining particle has the possibility of the four remaining locations and therefore has 1times4=4 possibilities
The product 20times4=80 gives us the total possibilities in the case that the particles arrange themselves in two groups one with three and one with a single particle and having five boxes
suitable It is easy to verify that we will obtain the same result considering first the single particle
having five boxes suitable (five possibilities 1x5=5) and after the three having the four remaining
(one is occupied by the single particle therefore 4x4=16 and 5x16=80)
Applying the procedure line by line it produces the results shown
Pier Maria Boria Thermodynamics amp life
22
Part 4 (of 4) Chance
41 CHANCE
A sharp-shooter shoots at a target with an excellent rifle he aims carefully chooses the
moment when his breathing will not interfere and the amount of force with which to pull the trigger so as not to move the barrel fires the shot and hits the bullrsquos-eye
Immediately afterwards he takes all the same precautions but the shot ends up being slightly off target it could have been a slight disturbance to his sight an involuntary variation in his
breathing an imperceptible abnormal movement of the finger a very slight unpredictable wind or who knows what else
The causes are many and imponderable slight if each is considered in itself but interacting differently each time ensuring that each shot has a different fate
This complex of innumerable causes of disturbance which are not controllable or predictable
and which not being able to take each into account one by one are called the Law of Probability
(Gaussrsquos Law)10
Probability for the reasons given and law thanks to Carl Friedrich Gauss (1777-1855) who
wrote an equation capable of taking into consideration in a global manner all those fleeting causes
so as to be able to predict with near accurate approximation how the shots will arrange themselves
percentage wise round the target with different distances from the bullseye The approximation will
be more accurate the greater the number of shots that are fired
Let us assume that the target is as represented in Figure 41 and is divided into two parts by
means of the section AB and that our sharpshooter fires many shots after which we count the
number of shots which hit the target in each half
Figure 41- The segmented target
If the reasons for the error are truly random (rifle without defects such that it does not tend to
deviate the shot systematically and neither does the sharpshooter have an analogous defect there is
10
The example of the sharpshooter was published by Engineer Mario Manaira in Ndeg 256 of ldquoJournal of Mechanicsrdquo
together with our first article concerning thermodynamics more than half a century ago (1961)
Pier Maria Boria Thermodynamics amp life
23
not a steady wind etc in other words there does not exist a cause which always influences with the
same bias called a systematic cause) we could note the following
1 The shots will be greater in number in the first band round the center
2 The shots will progressively decrease in number in the subsequent bands as these distance themselves further from the center until there are very few in the bands furthest away
3 The shots in the two halves right and left in any similar band will tend to have the same number and will even be identical if sufficient shots are fired
It is therefore possible to represent the phenomenon graphically as in the following figure
Figure 42 ndash The random distribution of the shots in each band and the Gaussian distribution that
would be obtained with an infinite number of shots fired
If the marksman were less capable the concentration of shots near the zero on the abscissa would reduce and the curve would flatten itself while maintaining the characteristics given and
represented in Figure 43 The first observation is that the maximum height of the curve constitutes the ldquotargetrdquo in other words the goal of the operation while the absence of systematic causes (in
antithesis of randomness) ensures the symmetry of the curve with respect to the vertical which
represents our target zero
Pier Maria Boria Thermodynamics amp life
24
Figure 43 - If the marksman is less skilled the Gaussian flattens
In the case of a systematic cause of error the curve loses its symmetry if we assume that the
test is performed with a constant wind from left to right the graph will take on the shape of Figure
44
Figure 44 ndash When the Gaussian is asymmetric it implies that the phenomenon is not ldquoentirely
randomrdquo11
Let us suppose now that our sharpshooter is blindfolded the target becomes very large and is
moved he will have to shoot blindly (randomly) left and right high and low Given that the Gauss
11
Gauss suggests that the analytical expression of the Law of Randomness is the function
2xey minus
=
where it can be seen that the curve is symmetrical with respect to the axis x=0 and decreasing both towards the left and
right of this line and has a maximum for x=0
It can be shown further that the area subtended is
π=int+infin
infinminus
minusdxe
x2
To ensure that this area is equal to unity as opposed to π appropriate steps can be taken which without
changing the general properties illustrated give the normalized Gaussrsquos Law
Pier Maria Boria Thermodynamics amp life
function still applies the probability curve will flatten itself maintaining the essential
characteristics in particular the two tails which will tend towards a tangent with the abscissa
tending towards infinity a maximum point a point of inflection and the other characteristics
illustrated in Figure 45
Figure 45 ndash Typical characteristics of a normalized Gaussian
Supposing once more that the Gauss function still applies it would be logical to expect a distribution with a curve that is so flat that it will be difficult to see a maximum point corresponding
to the center of the target it will be necessary to fire enough shots so as to occupy every position on the abscissa and to have hit with 100 certainty the bullrsquos-eye
This implies that everything is possible as long as an infinite number of shots are available
(using rhetorical language)
42 SOME PROPERTIES OF RANDOM EVENTS
The perplexities regarding the applicability of chance as referred to the blind sharpshooter
depend on the fact that the Gaussian assumes that programming has been applied to reach an
objective which implies that the operator is conscious of the objective an element which in this
case is absent
Both the existence of a program (the sharpshooter sets out to hit the bullrsquos-eye) and the
existence of an objective (the card with circles) appear to be essential to be able to talk about
chance
Another example let us imagine a machine programmed to produce a certain mechanical
piece the program is the design of the piece written in machine language and the objective is the production of the piece In mass production we will find that it is the case that despite the work
conditions being maintained the same each piece will be different to the other to the point that the pieces which exceed the tolerances (which would not allow them to be interchangeable) will be
rejected Innumerable examples could be presented identifying in every case these two characteristics
a program and an objective Statistics also operate in reverse from the measurement of a group of subjects it creates a bar
chart its envelope will be the curve of the random distribution It will give us the average of the values measured if the curve is symmetrical it will tell us that the phenomenon is not influenced by
systematic causes further it will tell us the value of the standard deviation etc
Pier Maria Boria Thermodynamics amp life
26
To fix this thought in our heads let us suppose that we want to study the average height of a
population of people who are male we make many measurements on many subjects creating bars
for every centimeter we will obtain a graph similar to Figure 46
Figure 46 ndash A practical application the Gaussian deduced from experimental measurements for
statistical purposes
In this statistical application where are the program and objective They are there they are
there they were contained in the information which the people naturally had at conception a
matter of genes and of DNA (an observation coherent with ldquoThe Kid Equationrdquo See the
ldquoIntroduction to Hyperspacerdquo12
)
These considerations lead us to think that the meaning of the word ldquochancerdquo commonly given
does not make sense that ldquochancerdquo does not exist and lead us to suspect that Anatole France had an
inspired guess when he said ldquochance is Godrsquos pseudonym when He does not want to sign his
namerdquo
This strongly agrees with what illustrious philosophers have been confirming for centuries
ldquoDeus absconditus estrdquo (Is XLV XV)
12
In our first volume ldquoCaro amico miohelliprdquo ndash Ed Pagine ndash 2010 In our second volume (ldquoVerba volant eqvuationes
manentrdquo) other considerations about a fundamental theorem of Genetics the Hardy Weinberg theorem
Pier Maria Boria Thermodynamics amp life
27
43 CHANCE amp PROBABILITY
We can now summarize some salient functions of Boltzmann and Gauss
Boltzmann
1 Deals with probability regarding the characteristics that can be assumed by many identical particles having a certain number of positions available (Dirac and Fermi deal
with particles which are distinguishable but the correct reference in our observations are the identical particles)
2 The function presents a maximum and aesthetically looks like a Gaussian but it is not symmetrical
3 It has only a single asymptote to the right of the maximum and its minimum at infinity coincides with zero the origin of the reference system
4 It is normalized so that the area subtended represents the total probability of 100
Gauss
1 Deals with chance and is applicable when an objective exists that is defined by a
program
2 The phenomenon ldquopurely by chancerdquo is represented by a curve that is symmetrical
about the axis x=0
3 The Gaussian has a maximum and no minimum at infinity
4 It possesses two asymptotes one to the right and one to the left of the maximum
5 Well defined values of probability can be associated with multiples of the standard deviation
6 It is normalized as for Boltzmannrsquos
44 THE EDDINGTONrsquoS PARADOX13
Eddingtonrsquos famous ldquoInfinite monkey theoremrdquo can be counted amongst the most discussed
paradoxes for the fact that it is often quoted by so called ldquoscientific popularizersrdquo The original assertion states ldquohellipa monkey hitting keys at random on a typewriter keyboard
for an infinite amount of times will almost surely type a given text such as the complete works of
William Shakespearerdquo
Having taken away the condition of an infinite amount of time the paradox remains acceptable
(from the moment we are able to demonstrate that a finite amount of time is sufficient) However
such a long period of time is necessary that the original statement could be seen as an hyperbolic
discussion
We have seen that random phenomena require a program in light of an objective In the case
of the typing monkeys the program could include the elimination of duplicate pages (actually the
identical pages as we will see below) and the objective could consist in the conservation of ldquogoodrdquo
pages arranged in the right sequence
Applying Boltzmannrsquos statistics let us assume that the typewriter has m=30 keys (we can think of ldquoblindrdquo keys without any writing and all identical) and that we want to write a book of
only 106
letters (a thousand typed pages) as we have observed in paragraph 31 all the possible combinations are
13
The reader can find all the details regarding these various arguments on the web
Pier Maria Boria Thermodynamics amp life
C = nm = (10
6)30
= (10)180
In other words there are 10180
possible configurations
Let us assume that the monkeys are capable of striking 10 keyssec (skilled typistshellip) the
time necessary would be
t = 10180
x 106 10 = 10
185 sec
Since we can count 1016 seconds in a billion years it is also possible to say that the time
required will be
10185
1016
= 10169
billion years (giga-years)
(let us remember that the big-bang has an age of ldquoonlyrdquo 14 billion years)
In reality the situation is even ldquoworserdquo in fact this calculation (which is generally accepted)
is wrong because we cannot talk about only thirty objects (the letters punctuation marks spaces between lines etc) to be arranged in 10
6 positions otherwise in each of 10180 configurations
obtainable we would find empty spaces up to 106-30 in each configuration
It is necessary to postulate that there are 106 letters to be arranged like conceding that the
monkeys have to insert 106 objects ie 10
6 key strokes In other words it is necessary that n = m =
106 and in this case the formula of the combinations gives us an astronomical value
6106 )10(===
mm mnC combinations
At a rhythm of 10 key strokes sec the time corresponds to
9899995005000616106 10sec101010)10(
6
equiv=sdotsdot=minust years
Figure 47 ndash Summary table of the probabilities according to Boltzmann
In realty the situation is even ldquoworserdquo still In fact in the calculation of the combinations duplicate configurations are not considered
(which necessarily must be considered as possible) in other words our monkeys could produce the same combinations several times (or two identical pages) anyway the duplications will be useless
in the compilation of our small book of only 106 letters
To this end we invoke chance (to attempt to appreciate the incidence of the repeating of
identical pages) and having constructed a Gaussian by arranging the frequency of identical pages we can reason as follows having produced all the astronomical combinations as above in the time
calculated (which we will call a cycle) the highest probability of identical pages is in pairs (which
Pier Maria Boria Thermodynamics amp life
29
we will assign the maximum position) then in threes and so on At infinity with a probability of
zero all the pages will be identical
It seems fair to presume that the standard deviation could be very large qualifying for a very
flat Gaussian and let us suppose that the pages to be rejected (one for the doubles two for the
triplets etc) are contained within the first standard deviation (as in Figure 48) then the duplicate pages to be thrown away would be about 68
Figure 48 ndash The postulated conditions (pages to be eliminated because they are duplicated equal
to the standard deviation) make 68 of the pages produced useless Iterating the cycle one could
consider the duplication of other pages however it can be demonstrated that the phenomenon
continues to imply finite times
How much does the required time increase to generalize we assume the length of a cycle to be of one unit and we identify with K the average cost of discarded pages (in the previous numerical
case K= 068) and then we observe Figure 49
Figure 49 ndash Having exhausted the first cycle identified by 1 the second of length K allows the
replacement of the duplicate pages produced in the first cycle the third of length K2 is used to
replace those produced in the second cycle and so on
The time necessary to complete the cycles required to eliminate the duplicates as they are produced will be given by the sum
suminfin
=0n
nK
which constitutes a geometric series
The Mathematical Analysis teaches us that such a series converges for 1ltK as is confirmed
in our case where it takes on the value 068
KS
minus=
1
1 and if K = 068 gives 1253
6801
1=
minus=S
Pier Maria Boria Thermodynamics amp life
30
Therefore multiplying by 3125 the time dedicated to complete a cycle (317middot105999989 billion
years) for the hypothesis made we also eliminate all the duplicate pages of our little book of 106
key strokes
Changing the value of K (always lt1) one obtains different multipliers but always of a finite
value let the reader imagine the time necessary to type all of Shakespearersquos works It must be highlighted that the monkey operation to be considered a success requires the
intervention of external intelligence capable of selecting the useful pages (like thought by Theory of
Information) and ordering them in the right sequence to obtain a final legible manuscript this
obvious necessity implies that negative entropy be introduced into the system as covered at the
beginning this is like a living being taking the trouble to ldquoput in orderrdquo otherwise the ldquopurely
randomrdquo work would be entirely useless because it will exclusively produce positive entropy
All experiments attempted by man with the goal of demonstrating the random production of
complex molecules (first building blocks of living organisms) have the defect of requiring an a
priori living system like man to arrange this production
When later chaotic physical-chemical conditions are created (temperature pressure
methane electrical arching etc) hoping to obtain that which Thermodynamics does not permit the
inventors of the moto perpetuo come to mind who never give up
The research on the ldquoprimordial souprdquo belongs to this type of experimentation a battle horse
of the followers of the ldquomaitre agrave penserrdquo of the last century and which regard in particular the laboratory experiments of Stanley Miller the goal of his research of a physical-chemical nature
was to recreate life it was an understandable but too ambitious of a project for a researcher The result was absolutely negative (Miller himself recognized it) however this last piece of information
is only whispered in scientific circles so that we still find genuine touts who speak with enthusiastic coram populo of the primordial soup and its miraculous effects14 with a self-assurance
that is truly shameful
45 CONCLUSION
On 4 July 2007 at the London Kinetics Museum a serious presentation of a perpetual motion
machine was scheduled a machine capable of supplying the user with a power greater than that
absorbed ldquoObviouslyrdquo the presentation was postponed due to ldquoa technical problemrdquo15
It would appear impossible but advocates convinced of such a motion exist and many
inventors submit patent after patent even though still in illo tempore Max Planck declared himself
to be contrary to such a possibility which violates the principles of Thermodynamics
Based on the reasoning we have developed regarding entropy probability and chance the
violation of such principles is implicit even in the attempts to obtain living organisms in a
laboratory (characterized as we have seen as being producers of negative entropy) and as such a
strong analogy can be seen between the advocates of perpetual motion and those aspiring to create
life
1 The correct application of Boltzmannrsquos statistics a phenomenon for which we call on
probability demonstrates that combinations of large numbers of particles to the point of generating complex organisms require very long periods of time in comparison the age of
the universe is but the blink of an eye
2 The probabilities take on the largest numbers in correspondence with the most disordered
configurations
14
From ldquoCorriere della Serardquo october 2008 ldquoLa vita sulla Terra Cominciograve nei vulcani con un innesco chimicordquo 15
-Source Wikipedia
Pier Maria Boria Thermodynamics amp life
3 The most ordered combinations are those which characterize organic structures and the action
of an intelligent being is necessary to select order and conserve in time the favorable
combinations
4 The phrase ldquochance phenomenonrdquo is somewhat less intuitive than what ldquocommon senserdquo
would suggest In fact the Gaussian perspective implies that such phenomena are necessarily
associated with a program this program implies the existence of an objective around which
we have an increased concentration of events
5 In every case it is necessary to postulate the existence of an intelligent design without which
the configurations and the favorable events constitute events without any functional link
between themselves
6 The existence of life as a producer of negative entropy on a continuous basis (not cyclical) is a fact visible with our own eyes
All this leads us to support the existence of a Co-ordinating Entity which possesses life ldquoa
priorirdquo and which is capable of transmitting it to animals (animalis homo included) and vegetation It can be noted that the two living systems animal and vegetable complement each other in the
sense that the design requires that emissions from the first (CO2) are the nutrients for the second and the byproducts of the second (O2) are essential for the first the carbon and oxygen cycles look
like they have been designed According to the author there is only one explanation we are in the presence of the greatest
Design Physicist of all times God the Creator
This is what we call Him as Christians while Israelites call Him Jehovah the Ishmaelites
Allah the Masons GADU (Great Architect of the Universe) etc
In other terms
the Creation is a thermodynamic necessity
Amen
Pier Maria Boria Thermodynamics amp life
16
Figure 33 - The three configurations are equivalent if the four particles are indistinguishable
amongst themselves
Each of the n states can be associated with A B C etc (that is to each or more of the m
particles) and since a single particle can occupy each time a different state (and other particles
other states) m times the possible combinations C are ntimesntimesntimeshelliptimesn (m factors equal to n)
C = nm
We could also be convinced observing for example Figure 34 where it is assumed that n=5
(it looks like a musical stavehellip) and m=2 particles (therefore 52=25 combinations)
Pier Maria Boria Thermodynamics amp life
Figure 34 ndash Beyond the 25th beat the preceding configurations are repeated because A and B are
indistinguishable Within the range of the 25 possible configurations some are more favored
because they appear more frequently for example 6 and 22 9 and 25 etc The unoccupied
states are identified by a circle
As is fair to expect configuration 1 is least favored
Pier Maria Boria Thermodynamics amp life
18
We can arrive at the same result with a more practical method suitable also for very large
values of n and m which we will use as follows
It consists of a tabular method stolen from Combinatorial Analysis where for n and m equal to
various units it avoids the need to write hundreds or thousands of key strokes as used above
Let us take two rows and as many columns as there are states thereby obtaining a grid in
Figure 35 to verify what has been said above we have taken 2 rows and 5 columns (n=2 m=5)
Figure 35- With this grid we obtain the number of possible configurations
To further demonstrate we will build a grid for n=5 and m=4 as in Figure 36 where there are sufficient rows to progressively expose the number of particles (from 4 to 1 in the first box of
the first column of the occupancy numbers) and there are n columns
Pier Maria Boria Thermodynamics amp life
19
Figure 36 - Since 54= 625 there are 625 possible combinations the relative probabilities are
listed in the last column note the asymmetry
Pier Maria Boria Thermodynamics amp life
20
It is necessary to observe that in the figure the table of numbers of occupancy reminds
us not by chance of Tartagliarsquos Triangle while the Boltzmann type diagram that can be
associated shown in Figure 37 takes on an almost familiar shape
Figure 37 - Graphical representation of Figure 62 the bars are asymmetric
Pier Maria Boria Thermodynamics amp life
21
To provide an example and referring to Figure 36 we can see how it is possible to obtain 80
possibilities corresponding to his second line
If a box is occupied by 3 particles out of an available 4 the simple combinations of 4 objects
with 3 by 3 (as taught by the Combinatorial Analysis) are given by the binomial coefficient
6437 4
and the four possible groups of three numbers have five positions from which to choose From here 4times5=20 possibilities for the group of three numbers
The single remaining particle has the possibility of the four remaining locations and therefore has 1times4=4 possibilities
The product 20times4=80 gives us the total possibilities in the case that the particles arrange themselves in two groups one with three and one with a single particle and having five boxes
suitable It is easy to verify that we will obtain the same result considering first the single particle
having five boxes suitable (five possibilities 1x5=5) and after the three having the four remaining
(one is occupied by the single particle therefore 4x4=16 and 5x16=80)
Applying the procedure line by line it produces the results shown
Pier Maria Boria Thermodynamics amp life
22
Part 4 (of 4) Chance
41 CHANCE
A sharp-shooter shoots at a target with an excellent rifle he aims carefully chooses the
moment when his breathing will not interfere and the amount of force with which to pull the trigger so as not to move the barrel fires the shot and hits the bullrsquos-eye
Immediately afterwards he takes all the same precautions but the shot ends up being slightly off target it could have been a slight disturbance to his sight an involuntary variation in his
breathing an imperceptible abnormal movement of the finger a very slight unpredictable wind or who knows what else
The causes are many and imponderable slight if each is considered in itself but interacting differently each time ensuring that each shot has a different fate
This complex of innumerable causes of disturbance which are not controllable or predictable
and which not being able to take each into account one by one are called the Law of Probability
(Gaussrsquos Law)10
Probability for the reasons given and law thanks to Carl Friedrich Gauss (1777-1855) who
wrote an equation capable of taking into consideration in a global manner all those fleeting causes
so as to be able to predict with near accurate approximation how the shots will arrange themselves
percentage wise round the target with different distances from the bullseye The approximation will
be more accurate the greater the number of shots that are fired
Let us assume that the target is as represented in Figure 41 and is divided into two parts by
means of the section AB and that our sharpshooter fires many shots after which we count the
number of shots which hit the target in each half
Figure 41- The segmented target
If the reasons for the error are truly random (rifle without defects such that it does not tend to
deviate the shot systematically and neither does the sharpshooter have an analogous defect there is
10
The example of the sharpshooter was published by Engineer Mario Manaira in Ndeg 256 of ldquoJournal of Mechanicsrdquo
together with our first article concerning thermodynamics more than half a century ago (1961)
Pier Maria Boria Thermodynamics amp life
23
not a steady wind etc in other words there does not exist a cause which always influences with the
same bias called a systematic cause) we could note the following
1 The shots will be greater in number in the first band round the center
2 The shots will progressively decrease in number in the subsequent bands as these distance themselves further from the center until there are very few in the bands furthest away
3 The shots in the two halves right and left in any similar band will tend to have the same number and will even be identical if sufficient shots are fired
It is therefore possible to represent the phenomenon graphically as in the following figure
Figure 42 ndash The random distribution of the shots in each band and the Gaussian distribution that
would be obtained with an infinite number of shots fired
If the marksman were less capable the concentration of shots near the zero on the abscissa would reduce and the curve would flatten itself while maintaining the characteristics given and
represented in Figure 43 The first observation is that the maximum height of the curve constitutes the ldquotargetrdquo in other words the goal of the operation while the absence of systematic causes (in
antithesis of randomness) ensures the symmetry of the curve with respect to the vertical which
represents our target zero
Pier Maria Boria Thermodynamics amp life
24
Figure 43 - If the marksman is less skilled the Gaussian flattens
In the case of a systematic cause of error the curve loses its symmetry if we assume that the
test is performed with a constant wind from left to right the graph will take on the shape of Figure
44
Figure 44 ndash When the Gaussian is asymmetric it implies that the phenomenon is not ldquoentirely
randomrdquo11
Let us suppose now that our sharpshooter is blindfolded the target becomes very large and is
moved he will have to shoot blindly (randomly) left and right high and low Given that the Gauss
11
Gauss suggests that the analytical expression of the Law of Randomness is the function
2xey minus
=
where it can be seen that the curve is symmetrical with respect to the axis x=0 and decreasing both towards the left and
right of this line and has a maximum for x=0
It can be shown further that the area subtended is
π=int+infin
infinminus
minusdxe
x2
To ensure that this area is equal to unity as opposed to π appropriate steps can be taken which without
changing the general properties illustrated give the normalized Gaussrsquos Law
Pier Maria Boria Thermodynamics amp life
function still applies the probability curve will flatten itself maintaining the essential
characteristics in particular the two tails which will tend towards a tangent with the abscissa
tending towards infinity a maximum point a point of inflection and the other characteristics
illustrated in Figure 45
Figure 45 ndash Typical characteristics of a normalized Gaussian
Supposing once more that the Gauss function still applies it would be logical to expect a distribution with a curve that is so flat that it will be difficult to see a maximum point corresponding
to the center of the target it will be necessary to fire enough shots so as to occupy every position on the abscissa and to have hit with 100 certainty the bullrsquos-eye
This implies that everything is possible as long as an infinite number of shots are available
(using rhetorical language)
42 SOME PROPERTIES OF RANDOM EVENTS
The perplexities regarding the applicability of chance as referred to the blind sharpshooter
depend on the fact that the Gaussian assumes that programming has been applied to reach an
objective which implies that the operator is conscious of the objective an element which in this
case is absent
Both the existence of a program (the sharpshooter sets out to hit the bullrsquos-eye) and the
existence of an objective (the card with circles) appear to be essential to be able to talk about
chance
Another example let us imagine a machine programmed to produce a certain mechanical
piece the program is the design of the piece written in machine language and the objective is the production of the piece In mass production we will find that it is the case that despite the work
conditions being maintained the same each piece will be different to the other to the point that the pieces which exceed the tolerances (which would not allow them to be interchangeable) will be
rejected Innumerable examples could be presented identifying in every case these two characteristics
a program and an objective Statistics also operate in reverse from the measurement of a group of subjects it creates a bar
chart its envelope will be the curve of the random distribution It will give us the average of the values measured if the curve is symmetrical it will tell us that the phenomenon is not influenced by
systematic causes further it will tell us the value of the standard deviation etc
Pier Maria Boria Thermodynamics amp life
26
To fix this thought in our heads let us suppose that we want to study the average height of a
population of people who are male we make many measurements on many subjects creating bars
for every centimeter we will obtain a graph similar to Figure 46
Figure 46 ndash A practical application the Gaussian deduced from experimental measurements for
statistical purposes
In this statistical application where are the program and objective They are there they are
there they were contained in the information which the people naturally had at conception a
matter of genes and of DNA (an observation coherent with ldquoThe Kid Equationrdquo See the
ldquoIntroduction to Hyperspacerdquo12
)
These considerations lead us to think that the meaning of the word ldquochancerdquo commonly given
does not make sense that ldquochancerdquo does not exist and lead us to suspect that Anatole France had an
inspired guess when he said ldquochance is Godrsquos pseudonym when He does not want to sign his
namerdquo
This strongly agrees with what illustrious philosophers have been confirming for centuries
ldquoDeus absconditus estrdquo (Is XLV XV)
12
In our first volume ldquoCaro amico miohelliprdquo ndash Ed Pagine ndash 2010 In our second volume (ldquoVerba volant eqvuationes
manentrdquo) other considerations about a fundamental theorem of Genetics the Hardy Weinberg theorem
Pier Maria Boria Thermodynamics amp life
27
43 CHANCE amp PROBABILITY
We can now summarize some salient functions of Boltzmann and Gauss
Boltzmann
1 Deals with probability regarding the characteristics that can be assumed by many identical particles having a certain number of positions available (Dirac and Fermi deal
with particles which are distinguishable but the correct reference in our observations are the identical particles)
2 The function presents a maximum and aesthetically looks like a Gaussian but it is not symmetrical
3 It has only a single asymptote to the right of the maximum and its minimum at infinity coincides with zero the origin of the reference system
4 It is normalized so that the area subtended represents the total probability of 100
Gauss
1 Deals with chance and is applicable when an objective exists that is defined by a
program
2 The phenomenon ldquopurely by chancerdquo is represented by a curve that is symmetrical
about the axis x=0
3 The Gaussian has a maximum and no minimum at infinity
4 It possesses two asymptotes one to the right and one to the left of the maximum
5 Well defined values of probability can be associated with multiples of the standard deviation
6 It is normalized as for Boltzmannrsquos
44 THE EDDINGTONrsquoS PARADOX13
Eddingtonrsquos famous ldquoInfinite monkey theoremrdquo can be counted amongst the most discussed
paradoxes for the fact that it is often quoted by so called ldquoscientific popularizersrdquo The original assertion states ldquohellipa monkey hitting keys at random on a typewriter keyboard
for an infinite amount of times will almost surely type a given text such as the complete works of
William Shakespearerdquo
Having taken away the condition of an infinite amount of time the paradox remains acceptable
(from the moment we are able to demonstrate that a finite amount of time is sufficient) However
such a long period of time is necessary that the original statement could be seen as an hyperbolic
discussion
We have seen that random phenomena require a program in light of an objective In the case
of the typing monkeys the program could include the elimination of duplicate pages (actually the
identical pages as we will see below) and the objective could consist in the conservation of ldquogoodrdquo
pages arranged in the right sequence
Applying Boltzmannrsquos statistics let us assume that the typewriter has m=30 keys (we can think of ldquoblindrdquo keys without any writing and all identical) and that we want to write a book of
only 106
letters (a thousand typed pages) as we have observed in paragraph 31 all the possible combinations are
13
The reader can find all the details regarding these various arguments on the web
Pier Maria Boria Thermodynamics amp life
C = nm = (10
6)30
= (10)180
In other words there are 10180
possible configurations
Let us assume that the monkeys are capable of striking 10 keyssec (skilled typistshellip) the
time necessary would be
t = 10180
x 106 10 = 10
185 sec
Since we can count 1016 seconds in a billion years it is also possible to say that the time
required will be
10185
1016
= 10169
billion years (giga-years)
(let us remember that the big-bang has an age of ldquoonlyrdquo 14 billion years)
In reality the situation is even ldquoworserdquo in fact this calculation (which is generally accepted)
is wrong because we cannot talk about only thirty objects (the letters punctuation marks spaces between lines etc) to be arranged in 10
6 positions otherwise in each of 10180 configurations
obtainable we would find empty spaces up to 106-30 in each configuration
It is necessary to postulate that there are 106 letters to be arranged like conceding that the
monkeys have to insert 106 objects ie 10
6 key strokes In other words it is necessary that n = m =
106 and in this case the formula of the combinations gives us an astronomical value
6106 )10(===
mm mnC combinations
At a rhythm of 10 key strokes sec the time corresponds to
9899995005000616106 10sec101010)10(
6
equiv=sdotsdot=minust years
Figure 47 ndash Summary table of the probabilities according to Boltzmann
In realty the situation is even ldquoworserdquo still In fact in the calculation of the combinations duplicate configurations are not considered
(which necessarily must be considered as possible) in other words our monkeys could produce the same combinations several times (or two identical pages) anyway the duplications will be useless
in the compilation of our small book of only 106 letters
To this end we invoke chance (to attempt to appreciate the incidence of the repeating of
identical pages) and having constructed a Gaussian by arranging the frequency of identical pages we can reason as follows having produced all the astronomical combinations as above in the time
calculated (which we will call a cycle) the highest probability of identical pages is in pairs (which
Pier Maria Boria Thermodynamics amp life
29
we will assign the maximum position) then in threes and so on At infinity with a probability of
zero all the pages will be identical
It seems fair to presume that the standard deviation could be very large qualifying for a very
flat Gaussian and let us suppose that the pages to be rejected (one for the doubles two for the
triplets etc) are contained within the first standard deviation (as in Figure 48) then the duplicate pages to be thrown away would be about 68
Figure 48 ndash The postulated conditions (pages to be eliminated because they are duplicated equal
to the standard deviation) make 68 of the pages produced useless Iterating the cycle one could
consider the duplication of other pages however it can be demonstrated that the phenomenon
continues to imply finite times
How much does the required time increase to generalize we assume the length of a cycle to be of one unit and we identify with K the average cost of discarded pages (in the previous numerical
case K= 068) and then we observe Figure 49
Figure 49 ndash Having exhausted the first cycle identified by 1 the second of length K allows the
replacement of the duplicate pages produced in the first cycle the third of length K2 is used to
replace those produced in the second cycle and so on
The time necessary to complete the cycles required to eliminate the duplicates as they are produced will be given by the sum
suminfin
=0n
nK
which constitutes a geometric series
The Mathematical Analysis teaches us that such a series converges for 1ltK as is confirmed
in our case where it takes on the value 068
KS
minus=
1
1 and if K = 068 gives 1253
6801
1=
minus=S
Pier Maria Boria Thermodynamics amp life
30
Therefore multiplying by 3125 the time dedicated to complete a cycle (317middot105999989 billion
years) for the hypothesis made we also eliminate all the duplicate pages of our little book of 106
key strokes
Changing the value of K (always lt1) one obtains different multipliers but always of a finite
value let the reader imagine the time necessary to type all of Shakespearersquos works It must be highlighted that the monkey operation to be considered a success requires the
intervention of external intelligence capable of selecting the useful pages (like thought by Theory of
Information) and ordering them in the right sequence to obtain a final legible manuscript this
obvious necessity implies that negative entropy be introduced into the system as covered at the
beginning this is like a living being taking the trouble to ldquoput in orderrdquo otherwise the ldquopurely
randomrdquo work would be entirely useless because it will exclusively produce positive entropy
All experiments attempted by man with the goal of demonstrating the random production of
complex molecules (first building blocks of living organisms) have the defect of requiring an a
priori living system like man to arrange this production
When later chaotic physical-chemical conditions are created (temperature pressure
methane electrical arching etc) hoping to obtain that which Thermodynamics does not permit the
inventors of the moto perpetuo come to mind who never give up
The research on the ldquoprimordial souprdquo belongs to this type of experimentation a battle horse
of the followers of the ldquomaitre agrave penserrdquo of the last century and which regard in particular the laboratory experiments of Stanley Miller the goal of his research of a physical-chemical nature
was to recreate life it was an understandable but too ambitious of a project for a researcher The result was absolutely negative (Miller himself recognized it) however this last piece of information
is only whispered in scientific circles so that we still find genuine touts who speak with enthusiastic coram populo of the primordial soup and its miraculous effects14 with a self-assurance
that is truly shameful
45 CONCLUSION
On 4 July 2007 at the London Kinetics Museum a serious presentation of a perpetual motion
machine was scheduled a machine capable of supplying the user with a power greater than that
absorbed ldquoObviouslyrdquo the presentation was postponed due to ldquoa technical problemrdquo15
It would appear impossible but advocates convinced of such a motion exist and many
inventors submit patent after patent even though still in illo tempore Max Planck declared himself
to be contrary to such a possibility which violates the principles of Thermodynamics
Based on the reasoning we have developed regarding entropy probability and chance the
violation of such principles is implicit even in the attempts to obtain living organisms in a
laboratory (characterized as we have seen as being producers of negative entropy) and as such a
strong analogy can be seen between the advocates of perpetual motion and those aspiring to create
life
1 The correct application of Boltzmannrsquos statistics a phenomenon for which we call on
probability demonstrates that combinations of large numbers of particles to the point of generating complex organisms require very long periods of time in comparison the age of
the universe is but the blink of an eye
2 The probabilities take on the largest numbers in correspondence with the most disordered
configurations
14
From ldquoCorriere della Serardquo october 2008 ldquoLa vita sulla Terra Cominciograve nei vulcani con un innesco chimicordquo 15
-Source Wikipedia
Pier Maria Boria Thermodynamics amp life
3 The most ordered combinations are those which characterize organic structures and the action
of an intelligent being is necessary to select order and conserve in time the favorable
combinations
4 The phrase ldquochance phenomenonrdquo is somewhat less intuitive than what ldquocommon senserdquo
would suggest In fact the Gaussian perspective implies that such phenomena are necessarily
associated with a program this program implies the existence of an objective around which
we have an increased concentration of events
5 In every case it is necessary to postulate the existence of an intelligent design without which
the configurations and the favorable events constitute events without any functional link
between themselves
6 The existence of life as a producer of negative entropy on a continuous basis (not cyclical) is a fact visible with our own eyes
All this leads us to support the existence of a Co-ordinating Entity which possesses life ldquoa
priorirdquo and which is capable of transmitting it to animals (animalis homo included) and vegetation It can be noted that the two living systems animal and vegetable complement each other in the
sense that the design requires that emissions from the first (CO2) are the nutrients for the second and the byproducts of the second (O2) are essential for the first the carbon and oxygen cycles look
like they have been designed According to the author there is only one explanation we are in the presence of the greatest
Design Physicist of all times God the Creator
This is what we call Him as Christians while Israelites call Him Jehovah the Ishmaelites
Allah the Masons GADU (Great Architect of the Universe) etc
In other terms
the Creation is a thermodynamic necessity
Amen
Pier Maria Boria Thermodynamics amp life
Figure 34 ndash Beyond the 25th beat the preceding configurations are repeated because A and B are
indistinguishable Within the range of the 25 possible configurations some are more favored
because they appear more frequently for example 6 and 22 9 and 25 etc The unoccupied
states are identified by a circle
As is fair to expect configuration 1 is least favored
Pier Maria Boria Thermodynamics amp life
18
We can arrive at the same result with a more practical method suitable also for very large
values of n and m which we will use as follows
It consists of a tabular method stolen from Combinatorial Analysis where for n and m equal to
various units it avoids the need to write hundreds or thousands of key strokes as used above
Let us take two rows and as many columns as there are states thereby obtaining a grid in
Figure 35 to verify what has been said above we have taken 2 rows and 5 columns (n=2 m=5)
Figure 35- With this grid we obtain the number of possible configurations
To further demonstrate we will build a grid for n=5 and m=4 as in Figure 36 where there are sufficient rows to progressively expose the number of particles (from 4 to 1 in the first box of
the first column of the occupancy numbers) and there are n columns
Pier Maria Boria Thermodynamics amp life
19
Figure 36 - Since 54= 625 there are 625 possible combinations the relative probabilities are
listed in the last column note the asymmetry
Pier Maria Boria Thermodynamics amp life
20
It is necessary to observe that in the figure the table of numbers of occupancy reminds
us not by chance of Tartagliarsquos Triangle while the Boltzmann type diagram that can be
associated shown in Figure 37 takes on an almost familiar shape
Figure 37 - Graphical representation of Figure 62 the bars are asymmetric
Pier Maria Boria Thermodynamics amp life
21
To provide an example and referring to Figure 36 we can see how it is possible to obtain 80
possibilities corresponding to his second line
If a box is occupied by 3 particles out of an available 4 the simple combinations of 4 objects
with 3 by 3 (as taught by the Combinatorial Analysis) are given by the binomial coefficient
6437 4
and the four possible groups of three numbers have five positions from which to choose From here 4times5=20 possibilities for the group of three numbers
The single remaining particle has the possibility of the four remaining locations and therefore has 1times4=4 possibilities
The product 20times4=80 gives us the total possibilities in the case that the particles arrange themselves in two groups one with three and one with a single particle and having five boxes
suitable It is easy to verify that we will obtain the same result considering first the single particle
having five boxes suitable (five possibilities 1x5=5) and after the three having the four remaining
(one is occupied by the single particle therefore 4x4=16 and 5x16=80)
Applying the procedure line by line it produces the results shown
Pier Maria Boria Thermodynamics amp life
22
Part 4 (of 4) Chance
41 CHANCE
A sharp-shooter shoots at a target with an excellent rifle he aims carefully chooses the
moment when his breathing will not interfere and the amount of force with which to pull the trigger so as not to move the barrel fires the shot and hits the bullrsquos-eye
Immediately afterwards he takes all the same precautions but the shot ends up being slightly off target it could have been a slight disturbance to his sight an involuntary variation in his
breathing an imperceptible abnormal movement of the finger a very slight unpredictable wind or who knows what else
The causes are many and imponderable slight if each is considered in itself but interacting differently each time ensuring that each shot has a different fate
This complex of innumerable causes of disturbance which are not controllable or predictable
and which not being able to take each into account one by one are called the Law of Probability
(Gaussrsquos Law)10
Probability for the reasons given and law thanks to Carl Friedrich Gauss (1777-1855) who
wrote an equation capable of taking into consideration in a global manner all those fleeting causes
so as to be able to predict with near accurate approximation how the shots will arrange themselves
percentage wise round the target with different distances from the bullseye The approximation will
be more accurate the greater the number of shots that are fired
Let us assume that the target is as represented in Figure 41 and is divided into two parts by
means of the section AB and that our sharpshooter fires many shots after which we count the
number of shots which hit the target in each half
Figure 41- The segmented target
If the reasons for the error are truly random (rifle without defects such that it does not tend to
deviate the shot systematically and neither does the sharpshooter have an analogous defect there is
10
The example of the sharpshooter was published by Engineer Mario Manaira in Ndeg 256 of ldquoJournal of Mechanicsrdquo
together with our first article concerning thermodynamics more than half a century ago (1961)
Pier Maria Boria Thermodynamics amp life
23
not a steady wind etc in other words there does not exist a cause which always influences with the
same bias called a systematic cause) we could note the following
1 The shots will be greater in number in the first band round the center
2 The shots will progressively decrease in number in the subsequent bands as these distance themselves further from the center until there are very few in the bands furthest away
3 The shots in the two halves right and left in any similar band will tend to have the same number and will even be identical if sufficient shots are fired
It is therefore possible to represent the phenomenon graphically as in the following figure
Figure 42 ndash The random distribution of the shots in each band and the Gaussian distribution that
would be obtained with an infinite number of shots fired
If the marksman were less capable the concentration of shots near the zero on the abscissa would reduce and the curve would flatten itself while maintaining the characteristics given and
represented in Figure 43 The first observation is that the maximum height of the curve constitutes the ldquotargetrdquo in other words the goal of the operation while the absence of systematic causes (in
antithesis of randomness) ensures the symmetry of the curve with respect to the vertical which
represents our target zero
Pier Maria Boria Thermodynamics amp life
24
Figure 43 - If the marksman is less skilled the Gaussian flattens
In the case of a systematic cause of error the curve loses its symmetry if we assume that the
test is performed with a constant wind from left to right the graph will take on the shape of Figure
44
Figure 44 ndash When the Gaussian is asymmetric it implies that the phenomenon is not ldquoentirely
randomrdquo11
Let us suppose now that our sharpshooter is blindfolded the target becomes very large and is
moved he will have to shoot blindly (randomly) left and right high and low Given that the Gauss
11
Gauss suggests that the analytical expression of the Law of Randomness is the function
2xey minus
=
where it can be seen that the curve is symmetrical with respect to the axis x=0 and decreasing both towards the left and
right of this line and has a maximum for x=0
It can be shown further that the area subtended is
π=int+infin
infinminus
minusdxe
x2
To ensure that this area is equal to unity as opposed to π appropriate steps can be taken which without
changing the general properties illustrated give the normalized Gaussrsquos Law
Pier Maria Boria Thermodynamics amp life
function still applies the probability curve will flatten itself maintaining the essential
characteristics in particular the two tails which will tend towards a tangent with the abscissa
tending towards infinity a maximum point a point of inflection and the other characteristics
illustrated in Figure 45
Figure 45 ndash Typical characteristics of a normalized Gaussian
Supposing once more that the Gauss function still applies it would be logical to expect a distribution with a curve that is so flat that it will be difficult to see a maximum point corresponding
to the center of the target it will be necessary to fire enough shots so as to occupy every position on the abscissa and to have hit with 100 certainty the bullrsquos-eye
This implies that everything is possible as long as an infinite number of shots are available
(using rhetorical language)
42 SOME PROPERTIES OF RANDOM EVENTS
The perplexities regarding the applicability of chance as referred to the blind sharpshooter
depend on the fact that the Gaussian assumes that programming has been applied to reach an
objective which implies that the operator is conscious of the objective an element which in this
case is absent
Both the existence of a program (the sharpshooter sets out to hit the bullrsquos-eye) and the
existence of an objective (the card with circles) appear to be essential to be able to talk about
chance
Another example let us imagine a machine programmed to produce a certain mechanical
piece the program is the design of the piece written in machine language and the objective is the production of the piece In mass production we will find that it is the case that despite the work
conditions being maintained the same each piece will be different to the other to the point that the pieces which exceed the tolerances (which would not allow them to be interchangeable) will be
rejected Innumerable examples could be presented identifying in every case these two characteristics
a program and an objective Statistics also operate in reverse from the measurement of a group of subjects it creates a bar
chart its envelope will be the curve of the random distribution It will give us the average of the values measured if the curve is symmetrical it will tell us that the phenomenon is not influenced by
systematic causes further it will tell us the value of the standard deviation etc
Pier Maria Boria Thermodynamics amp life
26
To fix this thought in our heads let us suppose that we want to study the average height of a
population of people who are male we make many measurements on many subjects creating bars
for every centimeter we will obtain a graph similar to Figure 46
Figure 46 ndash A practical application the Gaussian deduced from experimental measurements for
statistical purposes
In this statistical application where are the program and objective They are there they are
there they were contained in the information which the people naturally had at conception a
matter of genes and of DNA (an observation coherent with ldquoThe Kid Equationrdquo See the
ldquoIntroduction to Hyperspacerdquo12
)
These considerations lead us to think that the meaning of the word ldquochancerdquo commonly given
does not make sense that ldquochancerdquo does not exist and lead us to suspect that Anatole France had an
inspired guess when he said ldquochance is Godrsquos pseudonym when He does not want to sign his
namerdquo
This strongly agrees with what illustrious philosophers have been confirming for centuries
ldquoDeus absconditus estrdquo (Is XLV XV)
12
In our first volume ldquoCaro amico miohelliprdquo ndash Ed Pagine ndash 2010 In our second volume (ldquoVerba volant eqvuationes
manentrdquo) other considerations about a fundamental theorem of Genetics the Hardy Weinberg theorem
Pier Maria Boria Thermodynamics amp life
27
43 CHANCE amp PROBABILITY
We can now summarize some salient functions of Boltzmann and Gauss
Boltzmann
1 Deals with probability regarding the characteristics that can be assumed by many identical particles having a certain number of positions available (Dirac and Fermi deal
with particles which are distinguishable but the correct reference in our observations are the identical particles)
2 The function presents a maximum and aesthetically looks like a Gaussian but it is not symmetrical
3 It has only a single asymptote to the right of the maximum and its minimum at infinity coincides with zero the origin of the reference system
4 It is normalized so that the area subtended represents the total probability of 100
Gauss
1 Deals with chance and is applicable when an objective exists that is defined by a
program
2 The phenomenon ldquopurely by chancerdquo is represented by a curve that is symmetrical
about the axis x=0
3 The Gaussian has a maximum and no minimum at infinity
4 It possesses two asymptotes one to the right and one to the left of the maximum
5 Well defined values of probability can be associated with multiples of the standard deviation
6 It is normalized as for Boltzmannrsquos
44 THE EDDINGTONrsquoS PARADOX13
Eddingtonrsquos famous ldquoInfinite monkey theoremrdquo can be counted amongst the most discussed
paradoxes for the fact that it is often quoted by so called ldquoscientific popularizersrdquo The original assertion states ldquohellipa monkey hitting keys at random on a typewriter keyboard
for an infinite amount of times will almost surely type a given text such as the complete works of
William Shakespearerdquo
Having taken away the condition of an infinite amount of time the paradox remains acceptable
(from the moment we are able to demonstrate that a finite amount of time is sufficient) However
such a long period of time is necessary that the original statement could be seen as an hyperbolic
discussion
We have seen that random phenomena require a program in light of an objective In the case
of the typing monkeys the program could include the elimination of duplicate pages (actually the
identical pages as we will see below) and the objective could consist in the conservation of ldquogoodrdquo
pages arranged in the right sequence
Applying Boltzmannrsquos statistics let us assume that the typewriter has m=30 keys (we can think of ldquoblindrdquo keys without any writing and all identical) and that we want to write a book of
only 106
letters (a thousand typed pages) as we have observed in paragraph 31 all the possible combinations are
13
The reader can find all the details regarding these various arguments on the web
Pier Maria Boria Thermodynamics amp life
C = nm = (10
6)30
= (10)180
In other words there are 10180
possible configurations
Let us assume that the monkeys are capable of striking 10 keyssec (skilled typistshellip) the
time necessary would be
t = 10180
x 106 10 = 10
185 sec
Since we can count 1016 seconds in a billion years it is also possible to say that the time
required will be
10185
1016
= 10169
billion years (giga-years)
(let us remember that the big-bang has an age of ldquoonlyrdquo 14 billion years)
In reality the situation is even ldquoworserdquo in fact this calculation (which is generally accepted)
is wrong because we cannot talk about only thirty objects (the letters punctuation marks spaces between lines etc) to be arranged in 10
6 positions otherwise in each of 10180 configurations
obtainable we would find empty spaces up to 106-30 in each configuration
It is necessary to postulate that there are 106 letters to be arranged like conceding that the
monkeys have to insert 106 objects ie 10
6 key strokes In other words it is necessary that n = m =
106 and in this case the formula of the combinations gives us an astronomical value
6106 )10(===
mm mnC combinations
At a rhythm of 10 key strokes sec the time corresponds to
9899995005000616106 10sec101010)10(
6
equiv=sdotsdot=minust years
Figure 47 ndash Summary table of the probabilities according to Boltzmann
In realty the situation is even ldquoworserdquo still In fact in the calculation of the combinations duplicate configurations are not considered
(which necessarily must be considered as possible) in other words our monkeys could produce the same combinations several times (or two identical pages) anyway the duplications will be useless
in the compilation of our small book of only 106 letters
To this end we invoke chance (to attempt to appreciate the incidence of the repeating of
identical pages) and having constructed a Gaussian by arranging the frequency of identical pages we can reason as follows having produced all the astronomical combinations as above in the time
calculated (which we will call a cycle) the highest probability of identical pages is in pairs (which
Pier Maria Boria Thermodynamics amp life
29
we will assign the maximum position) then in threes and so on At infinity with a probability of
zero all the pages will be identical
It seems fair to presume that the standard deviation could be very large qualifying for a very
flat Gaussian and let us suppose that the pages to be rejected (one for the doubles two for the
triplets etc) are contained within the first standard deviation (as in Figure 48) then the duplicate pages to be thrown away would be about 68
Figure 48 ndash The postulated conditions (pages to be eliminated because they are duplicated equal
to the standard deviation) make 68 of the pages produced useless Iterating the cycle one could
consider the duplication of other pages however it can be demonstrated that the phenomenon
continues to imply finite times
How much does the required time increase to generalize we assume the length of a cycle to be of one unit and we identify with K the average cost of discarded pages (in the previous numerical
case K= 068) and then we observe Figure 49
Figure 49 ndash Having exhausted the first cycle identified by 1 the second of length K allows the
replacement of the duplicate pages produced in the first cycle the third of length K2 is used to
replace those produced in the second cycle and so on
The time necessary to complete the cycles required to eliminate the duplicates as they are produced will be given by the sum
suminfin
=0n
nK
which constitutes a geometric series
The Mathematical Analysis teaches us that such a series converges for 1ltK as is confirmed
in our case where it takes on the value 068
KS
minus=
1
1 and if K = 068 gives 1253
6801
1=
minus=S
Pier Maria Boria Thermodynamics amp life
30
Therefore multiplying by 3125 the time dedicated to complete a cycle (317middot105999989 billion
years) for the hypothesis made we also eliminate all the duplicate pages of our little book of 106
key strokes
Changing the value of K (always lt1) one obtains different multipliers but always of a finite
value let the reader imagine the time necessary to type all of Shakespearersquos works It must be highlighted that the monkey operation to be considered a success requires the
intervention of external intelligence capable of selecting the useful pages (like thought by Theory of
Information) and ordering them in the right sequence to obtain a final legible manuscript this
obvious necessity implies that negative entropy be introduced into the system as covered at the
beginning this is like a living being taking the trouble to ldquoput in orderrdquo otherwise the ldquopurely
randomrdquo work would be entirely useless because it will exclusively produce positive entropy
All experiments attempted by man with the goal of demonstrating the random production of
complex molecules (first building blocks of living organisms) have the defect of requiring an a
priori living system like man to arrange this production
When later chaotic physical-chemical conditions are created (temperature pressure
methane electrical arching etc) hoping to obtain that which Thermodynamics does not permit the
inventors of the moto perpetuo come to mind who never give up
The research on the ldquoprimordial souprdquo belongs to this type of experimentation a battle horse
of the followers of the ldquomaitre agrave penserrdquo of the last century and which regard in particular the laboratory experiments of Stanley Miller the goal of his research of a physical-chemical nature
was to recreate life it was an understandable but too ambitious of a project for a researcher The result was absolutely negative (Miller himself recognized it) however this last piece of information
is only whispered in scientific circles so that we still find genuine touts who speak with enthusiastic coram populo of the primordial soup and its miraculous effects14 with a self-assurance
that is truly shameful
45 CONCLUSION
On 4 July 2007 at the London Kinetics Museum a serious presentation of a perpetual motion
machine was scheduled a machine capable of supplying the user with a power greater than that
absorbed ldquoObviouslyrdquo the presentation was postponed due to ldquoa technical problemrdquo15
It would appear impossible but advocates convinced of such a motion exist and many
inventors submit patent after patent even though still in illo tempore Max Planck declared himself
to be contrary to such a possibility which violates the principles of Thermodynamics
Based on the reasoning we have developed regarding entropy probability and chance the
violation of such principles is implicit even in the attempts to obtain living organisms in a
laboratory (characterized as we have seen as being producers of negative entropy) and as such a
strong analogy can be seen between the advocates of perpetual motion and those aspiring to create
life
1 The correct application of Boltzmannrsquos statistics a phenomenon for which we call on
probability demonstrates that combinations of large numbers of particles to the point of generating complex organisms require very long periods of time in comparison the age of
the universe is but the blink of an eye
2 The probabilities take on the largest numbers in correspondence with the most disordered
configurations
14
From ldquoCorriere della Serardquo october 2008 ldquoLa vita sulla Terra Cominciograve nei vulcani con un innesco chimicordquo 15
-Source Wikipedia
Pier Maria Boria Thermodynamics amp life
3 The most ordered combinations are those which characterize organic structures and the action
of an intelligent being is necessary to select order and conserve in time the favorable
combinations
4 The phrase ldquochance phenomenonrdquo is somewhat less intuitive than what ldquocommon senserdquo
would suggest In fact the Gaussian perspective implies that such phenomena are necessarily
associated with a program this program implies the existence of an objective around which
we have an increased concentration of events
5 In every case it is necessary to postulate the existence of an intelligent design without which
the configurations and the favorable events constitute events without any functional link
between themselves
6 The existence of life as a producer of negative entropy on a continuous basis (not cyclical) is a fact visible with our own eyes
All this leads us to support the existence of a Co-ordinating Entity which possesses life ldquoa
priorirdquo and which is capable of transmitting it to animals (animalis homo included) and vegetation It can be noted that the two living systems animal and vegetable complement each other in the
sense that the design requires that emissions from the first (CO2) are the nutrients for the second and the byproducts of the second (O2) are essential for the first the carbon and oxygen cycles look
like they have been designed According to the author there is only one explanation we are in the presence of the greatest
Design Physicist of all times God the Creator
This is what we call Him as Christians while Israelites call Him Jehovah the Ishmaelites
Allah the Masons GADU (Great Architect of the Universe) etc
In other terms
the Creation is a thermodynamic necessity
Amen
Pier Maria Boria Thermodynamics amp life
18
We can arrive at the same result with a more practical method suitable also for very large
values of n and m which we will use as follows
It consists of a tabular method stolen from Combinatorial Analysis where for n and m equal to
various units it avoids the need to write hundreds or thousands of key strokes as used above
Let us take two rows and as many columns as there are states thereby obtaining a grid in
Figure 35 to verify what has been said above we have taken 2 rows and 5 columns (n=2 m=5)
Figure 35- With this grid we obtain the number of possible configurations
To further demonstrate we will build a grid for n=5 and m=4 as in Figure 36 where there are sufficient rows to progressively expose the number of particles (from 4 to 1 in the first box of
the first column of the occupancy numbers) and there are n columns
Pier Maria Boria Thermodynamics amp life
19
Figure 36 - Since 54= 625 there are 625 possible combinations the relative probabilities are
listed in the last column note the asymmetry
Pier Maria Boria Thermodynamics amp life
20
It is necessary to observe that in the figure the table of numbers of occupancy reminds
us not by chance of Tartagliarsquos Triangle while the Boltzmann type diagram that can be
associated shown in Figure 37 takes on an almost familiar shape
Figure 37 - Graphical representation of Figure 62 the bars are asymmetric
Pier Maria Boria Thermodynamics amp life
21
To provide an example and referring to Figure 36 we can see how it is possible to obtain 80
possibilities corresponding to his second line
If a box is occupied by 3 particles out of an available 4 the simple combinations of 4 objects
with 3 by 3 (as taught by the Combinatorial Analysis) are given by the binomial coefficient
6437 4
and the four possible groups of three numbers have five positions from which to choose From here 4times5=20 possibilities for the group of three numbers
The single remaining particle has the possibility of the four remaining locations and therefore has 1times4=4 possibilities
The product 20times4=80 gives us the total possibilities in the case that the particles arrange themselves in two groups one with three and one with a single particle and having five boxes
suitable It is easy to verify that we will obtain the same result considering first the single particle
having five boxes suitable (five possibilities 1x5=5) and after the three having the four remaining
(one is occupied by the single particle therefore 4x4=16 and 5x16=80)
Applying the procedure line by line it produces the results shown
Pier Maria Boria Thermodynamics amp life
22
Part 4 (of 4) Chance
41 CHANCE
A sharp-shooter shoots at a target with an excellent rifle he aims carefully chooses the
moment when his breathing will not interfere and the amount of force with which to pull the trigger so as not to move the barrel fires the shot and hits the bullrsquos-eye
Immediately afterwards he takes all the same precautions but the shot ends up being slightly off target it could have been a slight disturbance to his sight an involuntary variation in his
breathing an imperceptible abnormal movement of the finger a very slight unpredictable wind or who knows what else
The causes are many and imponderable slight if each is considered in itself but interacting differently each time ensuring that each shot has a different fate
This complex of innumerable causes of disturbance which are not controllable or predictable
and which not being able to take each into account one by one are called the Law of Probability
(Gaussrsquos Law)10
Probability for the reasons given and law thanks to Carl Friedrich Gauss (1777-1855) who
wrote an equation capable of taking into consideration in a global manner all those fleeting causes
so as to be able to predict with near accurate approximation how the shots will arrange themselves
percentage wise round the target with different distances from the bullseye The approximation will
be more accurate the greater the number of shots that are fired
Let us assume that the target is as represented in Figure 41 and is divided into two parts by
means of the section AB and that our sharpshooter fires many shots after which we count the
number of shots which hit the target in each half
Figure 41- The segmented target
If the reasons for the error are truly random (rifle without defects such that it does not tend to
deviate the shot systematically and neither does the sharpshooter have an analogous defect there is
10
The example of the sharpshooter was published by Engineer Mario Manaira in Ndeg 256 of ldquoJournal of Mechanicsrdquo
together with our first article concerning thermodynamics more than half a century ago (1961)
Pier Maria Boria Thermodynamics amp life
23
not a steady wind etc in other words there does not exist a cause which always influences with the
same bias called a systematic cause) we could note the following
1 The shots will be greater in number in the first band round the center
2 The shots will progressively decrease in number in the subsequent bands as these distance themselves further from the center until there are very few in the bands furthest away
3 The shots in the two halves right and left in any similar band will tend to have the same number and will even be identical if sufficient shots are fired
It is therefore possible to represent the phenomenon graphically as in the following figure
Figure 42 ndash The random distribution of the shots in each band and the Gaussian distribution that
would be obtained with an infinite number of shots fired
If the marksman were less capable the concentration of shots near the zero on the abscissa would reduce and the curve would flatten itself while maintaining the characteristics given and
represented in Figure 43 The first observation is that the maximum height of the curve constitutes the ldquotargetrdquo in other words the goal of the operation while the absence of systematic causes (in
antithesis of randomness) ensures the symmetry of the curve with respect to the vertical which
represents our target zero
Pier Maria Boria Thermodynamics amp life
24
Figure 43 - If the marksman is less skilled the Gaussian flattens
In the case of a systematic cause of error the curve loses its symmetry if we assume that the
test is performed with a constant wind from left to right the graph will take on the shape of Figure
44
Figure 44 ndash When the Gaussian is asymmetric it implies that the phenomenon is not ldquoentirely
randomrdquo11
Let us suppose now that our sharpshooter is blindfolded the target becomes very large and is
moved he will have to shoot blindly (randomly) left and right high and low Given that the Gauss
11
Gauss suggests that the analytical expression of the Law of Randomness is the function
2xey minus
=
where it can be seen that the curve is symmetrical with respect to the axis x=0 and decreasing both towards the left and
right of this line and has a maximum for x=0
It can be shown further that the area subtended is
π=int+infin
infinminus
minusdxe
x2
To ensure that this area is equal to unity as opposed to π appropriate steps can be taken which without
changing the general properties illustrated give the normalized Gaussrsquos Law
Pier Maria Boria Thermodynamics amp life
function still applies the probability curve will flatten itself maintaining the essential
characteristics in particular the two tails which will tend towards a tangent with the abscissa
tending towards infinity a maximum point a point of inflection and the other characteristics
illustrated in Figure 45
Figure 45 ndash Typical characteristics of a normalized Gaussian
Supposing once more that the Gauss function still applies it would be logical to expect a distribution with a curve that is so flat that it will be difficult to see a maximum point corresponding
to the center of the target it will be necessary to fire enough shots so as to occupy every position on the abscissa and to have hit with 100 certainty the bullrsquos-eye
This implies that everything is possible as long as an infinite number of shots are available
(using rhetorical language)
42 SOME PROPERTIES OF RANDOM EVENTS
The perplexities regarding the applicability of chance as referred to the blind sharpshooter
depend on the fact that the Gaussian assumes that programming has been applied to reach an
objective which implies that the operator is conscious of the objective an element which in this
case is absent
Both the existence of a program (the sharpshooter sets out to hit the bullrsquos-eye) and the
existence of an objective (the card with circles) appear to be essential to be able to talk about
chance
Another example let us imagine a machine programmed to produce a certain mechanical
piece the program is the design of the piece written in machine language and the objective is the production of the piece In mass production we will find that it is the case that despite the work
conditions being maintained the same each piece will be different to the other to the point that the pieces which exceed the tolerances (which would not allow them to be interchangeable) will be
rejected Innumerable examples could be presented identifying in every case these two characteristics
a program and an objective Statistics also operate in reverse from the measurement of a group of subjects it creates a bar
chart its envelope will be the curve of the random distribution It will give us the average of the values measured if the curve is symmetrical it will tell us that the phenomenon is not influenced by
systematic causes further it will tell us the value of the standard deviation etc
Pier Maria Boria Thermodynamics amp life
26
To fix this thought in our heads let us suppose that we want to study the average height of a
population of people who are male we make many measurements on many subjects creating bars
for every centimeter we will obtain a graph similar to Figure 46
Figure 46 ndash A practical application the Gaussian deduced from experimental measurements for
statistical purposes
In this statistical application where are the program and objective They are there they are
there they were contained in the information which the people naturally had at conception a
matter of genes and of DNA (an observation coherent with ldquoThe Kid Equationrdquo See the
ldquoIntroduction to Hyperspacerdquo12
)
These considerations lead us to think that the meaning of the word ldquochancerdquo commonly given
does not make sense that ldquochancerdquo does not exist and lead us to suspect that Anatole France had an
inspired guess when he said ldquochance is Godrsquos pseudonym when He does not want to sign his
namerdquo
This strongly agrees with what illustrious philosophers have been confirming for centuries
ldquoDeus absconditus estrdquo (Is XLV XV)
12
In our first volume ldquoCaro amico miohelliprdquo ndash Ed Pagine ndash 2010 In our second volume (ldquoVerba volant eqvuationes
manentrdquo) other considerations about a fundamental theorem of Genetics the Hardy Weinberg theorem
Pier Maria Boria Thermodynamics amp life
27
43 CHANCE amp PROBABILITY
We can now summarize some salient functions of Boltzmann and Gauss
Boltzmann
1 Deals with probability regarding the characteristics that can be assumed by many identical particles having a certain number of positions available (Dirac and Fermi deal
with particles which are distinguishable but the correct reference in our observations are the identical particles)
2 The function presents a maximum and aesthetically looks like a Gaussian but it is not symmetrical
3 It has only a single asymptote to the right of the maximum and its minimum at infinity coincides with zero the origin of the reference system
4 It is normalized so that the area subtended represents the total probability of 100
Gauss
1 Deals with chance and is applicable when an objective exists that is defined by a
program
2 The phenomenon ldquopurely by chancerdquo is represented by a curve that is symmetrical
about the axis x=0
3 The Gaussian has a maximum and no minimum at infinity
4 It possesses two asymptotes one to the right and one to the left of the maximum
5 Well defined values of probability can be associated with multiples of the standard deviation
6 It is normalized as for Boltzmannrsquos
44 THE EDDINGTONrsquoS PARADOX13
Eddingtonrsquos famous ldquoInfinite monkey theoremrdquo can be counted amongst the most discussed
paradoxes for the fact that it is often quoted by so called ldquoscientific popularizersrdquo The original assertion states ldquohellipa monkey hitting keys at random on a typewriter keyboard
for an infinite amount of times will almost surely type a given text such as the complete works of
William Shakespearerdquo
Having taken away the condition of an infinite amount of time the paradox remains acceptable
(from the moment we are able to demonstrate that a finite amount of time is sufficient) However
such a long period of time is necessary that the original statement could be seen as an hyperbolic
discussion
We have seen that random phenomena require a program in light of an objective In the case
of the typing monkeys the program could include the elimination of duplicate pages (actually the
identical pages as we will see below) and the objective could consist in the conservation of ldquogoodrdquo
pages arranged in the right sequence
Applying Boltzmannrsquos statistics let us assume that the typewriter has m=30 keys (we can think of ldquoblindrdquo keys without any writing and all identical) and that we want to write a book of
only 106
letters (a thousand typed pages) as we have observed in paragraph 31 all the possible combinations are
13
The reader can find all the details regarding these various arguments on the web
Pier Maria Boria Thermodynamics amp life
C = nm = (10
6)30
= (10)180
In other words there are 10180
possible configurations
Let us assume that the monkeys are capable of striking 10 keyssec (skilled typistshellip) the
time necessary would be
t = 10180
x 106 10 = 10
185 sec
Since we can count 1016 seconds in a billion years it is also possible to say that the time
required will be
10185
1016
= 10169
billion years (giga-years)
(let us remember that the big-bang has an age of ldquoonlyrdquo 14 billion years)
In reality the situation is even ldquoworserdquo in fact this calculation (which is generally accepted)
is wrong because we cannot talk about only thirty objects (the letters punctuation marks spaces between lines etc) to be arranged in 10
6 positions otherwise in each of 10180 configurations
obtainable we would find empty spaces up to 106-30 in each configuration
It is necessary to postulate that there are 106 letters to be arranged like conceding that the
monkeys have to insert 106 objects ie 10
6 key strokes In other words it is necessary that n = m =
106 and in this case the formula of the combinations gives us an astronomical value
6106 )10(===
mm mnC combinations
At a rhythm of 10 key strokes sec the time corresponds to
9899995005000616106 10sec101010)10(
6
equiv=sdotsdot=minust years
Figure 47 ndash Summary table of the probabilities according to Boltzmann
In realty the situation is even ldquoworserdquo still In fact in the calculation of the combinations duplicate configurations are not considered
(which necessarily must be considered as possible) in other words our monkeys could produce the same combinations several times (or two identical pages) anyway the duplications will be useless
in the compilation of our small book of only 106 letters
To this end we invoke chance (to attempt to appreciate the incidence of the repeating of
identical pages) and having constructed a Gaussian by arranging the frequency of identical pages we can reason as follows having produced all the astronomical combinations as above in the time
calculated (which we will call a cycle) the highest probability of identical pages is in pairs (which
Pier Maria Boria Thermodynamics amp life
29
we will assign the maximum position) then in threes and so on At infinity with a probability of
zero all the pages will be identical
It seems fair to presume that the standard deviation could be very large qualifying for a very
flat Gaussian and let us suppose that the pages to be rejected (one for the doubles two for the
triplets etc) are contained within the first standard deviation (as in Figure 48) then the duplicate pages to be thrown away would be about 68
Figure 48 ndash The postulated conditions (pages to be eliminated because they are duplicated equal
to the standard deviation) make 68 of the pages produced useless Iterating the cycle one could
consider the duplication of other pages however it can be demonstrated that the phenomenon
continues to imply finite times
How much does the required time increase to generalize we assume the length of a cycle to be of one unit and we identify with K the average cost of discarded pages (in the previous numerical
case K= 068) and then we observe Figure 49
Figure 49 ndash Having exhausted the first cycle identified by 1 the second of length K allows the
replacement of the duplicate pages produced in the first cycle the third of length K2 is used to
replace those produced in the second cycle and so on
The time necessary to complete the cycles required to eliminate the duplicates as they are produced will be given by the sum
suminfin
=0n
nK
which constitutes a geometric series
The Mathematical Analysis teaches us that such a series converges for 1ltK as is confirmed
in our case where it takes on the value 068
KS
minus=
1
1 and if K = 068 gives 1253
6801
1=
minus=S
Pier Maria Boria Thermodynamics amp life
30
Therefore multiplying by 3125 the time dedicated to complete a cycle (317middot105999989 billion
years) for the hypothesis made we also eliminate all the duplicate pages of our little book of 106
key strokes
Changing the value of K (always lt1) one obtains different multipliers but always of a finite
value let the reader imagine the time necessary to type all of Shakespearersquos works It must be highlighted that the monkey operation to be considered a success requires the
intervention of external intelligence capable of selecting the useful pages (like thought by Theory of
Information) and ordering them in the right sequence to obtain a final legible manuscript this
obvious necessity implies that negative entropy be introduced into the system as covered at the
beginning this is like a living being taking the trouble to ldquoput in orderrdquo otherwise the ldquopurely
randomrdquo work would be entirely useless because it will exclusively produce positive entropy
All experiments attempted by man with the goal of demonstrating the random production of
complex molecules (first building blocks of living organisms) have the defect of requiring an a
priori living system like man to arrange this production
When later chaotic physical-chemical conditions are created (temperature pressure
methane electrical arching etc) hoping to obtain that which Thermodynamics does not permit the
inventors of the moto perpetuo come to mind who never give up
The research on the ldquoprimordial souprdquo belongs to this type of experimentation a battle horse
of the followers of the ldquomaitre agrave penserrdquo of the last century and which regard in particular the laboratory experiments of Stanley Miller the goal of his research of a physical-chemical nature
was to recreate life it was an understandable but too ambitious of a project for a researcher The result was absolutely negative (Miller himself recognized it) however this last piece of information
is only whispered in scientific circles so that we still find genuine touts who speak with enthusiastic coram populo of the primordial soup and its miraculous effects14 with a self-assurance
that is truly shameful
45 CONCLUSION
On 4 July 2007 at the London Kinetics Museum a serious presentation of a perpetual motion
machine was scheduled a machine capable of supplying the user with a power greater than that
absorbed ldquoObviouslyrdquo the presentation was postponed due to ldquoa technical problemrdquo15
It would appear impossible but advocates convinced of such a motion exist and many
inventors submit patent after patent even though still in illo tempore Max Planck declared himself
to be contrary to such a possibility which violates the principles of Thermodynamics
Based on the reasoning we have developed regarding entropy probability and chance the
violation of such principles is implicit even in the attempts to obtain living organisms in a
laboratory (characterized as we have seen as being producers of negative entropy) and as such a
strong analogy can be seen between the advocates of perpetual motion and those aspiring to create
life
1 The correct application of Boltzmannrsquos statistics a phenomenon for which we call on
probability demonstrates that combinations of large numbers of particles to the point of generating complex organisms require very long periods of time in comparison the age of
the universe is but the blink of an eye
2 The probabilities take on the largest numbers in correspondence with the most disordered
configurations
14
From ldquoCorriere della Serardquo october 2008 ldquoLa vita sulla Terra Cominciograve nei vulcani con un innesco chimicordquo 15
-Source Wikipedia
Pier Maria Boria Thermodynamics amp life
3 The most ordered combinations are those which characterize organic structures and the action
of an intelligent being is necessary to select order and conserve in time the favorable
combinations
4 The phrase ldquochance phenomenonrdquo is somewhat less intuitive than what ldquocommon senserdquo
would suggest In fact the Gaussian perspective implies that such phenomena are necessarily
associated with a program this program implies the existence of an objective around which
we have an increased concentration of events
5 In every case it is necessary to postulate the existence of an intelligent design without which
the configurations and the favorable events constitute events without any functional link
between themselves
6 The existence of life as a producer of negative entropy on a continuous basis (not cyclical) is a fact visible with our own eyes
All this leads us to support the existence of a Co-ordinating Entity which possesses life ldquoa
priorirdquo and which is capable of transmitting it to animals (animalis homo included) and vegetation It can be noted that the two living systems animal and vegetable complement each other in the
sense that the design requires that emissions from the first (CO2) are the nutrients for the second and the byproducts of the second (O2) are essential for the first the carbon and oxygen cycles look
like they have been designed According to the author there is only one explanation we are in the presence of the greatest
Design Physicist of all times God the Creator
This is what we call Him as Christians while Israelites call Him Jehovah the Ishmaelites
Allah the Masons GADU (Great Architect of the Universe) etc
In other terms
the Creation is a thermodynamic necessity
Amen
Pier Maria Boria Thermodynamics amp life
19
Figure 36 - Since 54= 625 there are 625 possible combinations the relative probabilities are
listed in the last column note the asymmetry
Pier Maria Boria Thermodynamics amp life
20
It is necessary to observe that in the figure the table of numbers of occupancy reminds
us not by chance of Tartagliarsquos Triangle while the Boltzmann type diagram that can be
associated shown in Figure 37 takes on an almost familiar shape
Figure 37 - Graphical representation of Figure 62 the bars are asymmetric
Pier Maria Boria Thermodynamics amp life
21
To provide an example and referring to Figure 36 we can see how it is possible to obtain 80
possibilities corresponding to his second line
If a box is occupied by 3 particles out of an available 4 the simple combinations of 4 objects
with 3 by 3 (as taught by the Combinatorial Analysis) are given by the binomial coefficient
6437 4
and the four possible groups of three numbers have five positions from which to choose From here 4times5=20 possibilities for the group of three numbers
The single remaining particle has the possibility of the four remaining locations and therefore has 1times4=4 possibilities
The product 20times4=80 gives us the total possibilities in the case that the particles arrange themselves in two groups one with three and one with a single particle and having five boxes
suitable It is easy to verify that we will obtain the same result considering first the single particle
having five boxes suitable (five possibilities 1x5=5) and after the three having the four remaining
(one is occupied by the single particle therefore 4x4=16 and 5x16=80)
Applying the procedure line by line it produces the results shown
Pier Maria Boria Thermodynamics amp life
22
Part 4 (of 4) Chance
41 CHANCE
A sharp-shooter shoots at a target with an excellent rifle he aims carefully chooses the
moment when his breathing will not interfere and the amount of force with which to pull the trigger so as not to move the barrel fires the shot and hits the bullrsquos-eye
Immediately afterwards he takes all the same precautions but the shot ends up being slightly off target it could have been a slight disturbance to his sight an involuntary variation in his
breathing an imperceptible abnormal movement of the finger a very slight unpredictable wind or who knows what else
The causes are many and imponderable slight if each is considered in itself but interacting differently each time ensuring that each shot has a different fate
This complex of innumerable causes of disturbance which are not controllable or predictable
and which not being able to take each into account one by one are called the Law of Probability
(Gaussrsquos Law)10
Probability for the reasons given and law thanks to Carl Friedrich Gauss (1777-1855) who
wrote an equation capable of taking into consideration in a global manner all those fleeting causes
so as to be able to predict with near accurate approximation how the shots will arrange themselves
percentage wise round the target with different distances from the bullseye The approximation will
be more accurate the greater the number of shots that are fired
Let us assume that the target is as represented in Figure 41 and is divided into two parts by
means of the section AB and that our sharpshooter fires many shots after which we count the
number of shots which hit the target in each half
Figure 41- The segmented target
If the reasons for the error are truly random (rifle without defects such that it does not tend to
deviate the shot systematically and neither does the sharpshooter have an analogous defect there is
10
The example of the sharpshooter was published by Engineer Mario Manaira in Ndeg 256 of ldquoJournal of Mechanicsrdquo
together with our first article concerning thermodynamics more than half a century ago (1961)
Pier Maria Boria Thermodynamics amp life
23
not a steady wind etc in other words there does not exist a cause which always influences with the
same bias called a systematic cause) we could note the following
1 The shots will be greater in number in the first band round the center
2 The shots will progressively decrease in number in the subsequent bands as these distance themselves further from the center until there are very few in the bands furthest away
3 The shots in the two halves right and left in any similar band will tend to have the same number and will even be identical if sufficient shots are fired
It is therefore possible to represent the phenomenon graphically as in the following figure
Figure 42 ndash The random distribution of the shots in each band and the Gaussian distribution that
would be obtained with an infinite number of shots fired
If the marksman were less capable the concentration of shots near the zero on the abscissa would reduce and the curve would flatten itself while maintaining the characteristics given and
represented in Figure 43 The first observation is that the maximum height of the curve constitutes the ldquotargetrdquo in other words the goal of the operation while the absence of systematic causes (in
antithesis of randomness) ensures the symmetry of the curve with respect to the vertical which
represents our target zero
Pier Maria Boria Thermodynamics amp life
24
Figure 43 - If the marksman is less skilled the Gaussian flattens
In the case of a systematic cause of error the curve loses its symmetry if we assume that the
test is performed with a constant wind from left to right the graph will take on the shape of Figure
44
Figure 44 ndash When the Gaussian is asymmetric it implies that the phenomenon is not ldquoentirely
randomrdquo11
Let us suppose now that our sharpshooter is blindfolded the target becomes very large and is
moved he will have to shoot blindly (randomly) left and right high and low Given that the Gauss
11
Gauss suggests that the analytical expression of the Law of Randomness is the function
2xey minus
=
where it can be seen that the curve is symmetrical with respect to the axis x=0 and decreasing both towards the left and
right of this line and has a maximum for x=0
It can be shown further that the area subtended is
π=int+infin
infinminus
minusdxe
x2
To ensure that this area is equal to unity as opposed to π appropriate steps can be taken which without
changing the general properties illustrated give the normalized Gaussrsquos Law
Pier Maria Boria Thermodynamics amp life
function still applies the probability curve will flatten itself maintaining the essential
characteristics in particular the two tails which will tend towards a tangent with the abscissa
tending towards infinity a maximum point a point of inflection and the other characteristics
illustrated in Figure 45
Figure 45 ndash Typical characteristics of a normalized Gaussian
Supposing once more that the Gauss function still applies it would be logical to expect a distribution with a curve that is so flat that it will be difficult to see a maximum point corresponding
to the center of the target it will be necessary to fire enough shots so as to occupy every position on the abscissa and to have hit with 100 certainty the bullrsquos-eye
This implies that everything is possible as long as an infinite number of shots are available
(using rhetorical language)
42 SOME PROPERTIES OF RANDOM EVENTS
The perplexities regarding the applicability of chance as referred to the blind sharpshooter
depend on the fact that the Gaussian assumes that programming has been applied to reach an
objective which implies that the operator is conscious of the objective an element which in this
case is absent
Both the existence of a program (the sharpshooter sets out to hit the bullrsquos-eye) and the
existence of an objective (the card with circles) appear to be essential to be able to talk about
chance
Another example let us imagine a machine programmed to produce a certain mechanical
piece the program is the design of the piece written in machine language and the objective is the production of the piece In mass production we will find that it is the case that despite the work
conditions being maintained the same each piece will be different to the other to the point that the pieces which exceed the tolerances (which would not allow them to be interchangeable) will be
rejected Innumerable examples could be presented identifying in every case these two characteristics
a program and an objective Statistics also operate in reverse from the measurement of a group of subjects it creates a bar
chart its envelope will be the curve of the random distribution It will give us the average of the values measured if the curve is symmetrical it will tell us that the phenomenon is not influenced by
systematic causes further it will tell us the value of the standard deviation etc
Pier Maria Boria Thermodynamics amp life
26
To fix this thought in our heads let us suppose that we want to study the average height of a
population of people who are male we make many measurements on many subjects creating bars
for every centimeter we will obtain a graph similar to Figure 46
Figure 46 ndash A practical application the Gaussian deduced from experimental measurements for
statistical purposes
In this statistical application where are the program and objective They are there they are
there they were contained in the information which the people naturally had at conception a
matter of genes and of DNA (an observation coherent with ldquoThe Kid Equationrdquo See the
ldquoIntroduction to Hyperspacerdquo12
)
These considerations lead us to think that the meaning of the word ldquochancerdquo commonly given
does not make sense that ldquochancerdquo does not exist and lead us to suspect that Anatole France had an
inspired guess when he said ldquochance is Godrsquos pseudonym when He does not want to sign his
namerdquo
This strongly agrees with what illustrious philosophers have been confirming for centuries
ldquoDeus absconditus estrdquo (Is XLV XV)
12
In our first volume ldquoCaro amico miohelliprdquo ndash Ed Pagine ndash 2010 In our second volume (ldquoVerba volant eqvuationes
manentrdquo) other considerations about a fundamental theorem of Genetics the Hardy Weinberg theorem
Pier Maria Boria Thermodynamics amp life
27
43 CHANCE amp PROBABILITY
We can now summarize some salient functions of Boltzmann and Gauss
Boltzmann
1 Deals with probability regarding the characteristics that can be assumed by many identical particles having a certain number of positions available (Dirac and Fermi deal
with particles which are distinguishable but the correct reference in our observations are the identical particles)
2 The function presents a maximum and aesthetically looks like a Gaussian but it is not symmetrical
3 It has only a single asymptote to the right of the maximum and its minimum at infinity coincides with zero the origin of the reference system
4 It is normalized so that the area subtended represents the total probability of 100
Gauss
1 Deals with chance and is applicable when an objective exists that is defined by a
program
2 The phenomenon ldquopurely by chancerdquo is represented by a curve that is symmetrical
about the axis x=0
3 The Gaussian has a maximum and no minimum at infinity
4 It possesses two asymptotes one to the right and one to the left of the maximum
5 Well defined values of probability can be associated with multiples of the standard deviation
6 It is normalized as for Boltzmannrsquos
44 THE EDDINGTONrsquoS PARADOX13
Eddingtonrsquos famous ldquoInfinite monkey theoremrdquo can be counted amongst the most discussed
paradoxes for the fact that it is often quoted by so called ldquoscientific popularizersrdquo The original assertion states ldquohellipa monkey hitting keys at random on a typewriter keyboard
for an infinite amount of times will almost surely type a given text such as the complete works of
William Shakespearerdquo
Having taken away the condition of an infinite amount of time the paradox remains acceptable
(from the moment we are able to demonstrate that a finite amount of time is sufficient) However
such a long period of time is necessary that the original statement could be seen as an hyperbolic
discussion
We have seen that random phenomena require a program in light of an objective In the case
of the typing monkeys the program could include the elimination of duplicate pages (actually the
identical pages as we will see below) and the objective could consist in the conservation of ldquogoodrdquo
pages arranged in the right sequence
Applying Boltzmannrsquos statistics let us assume that the typewriter has m=30 keys (we can think of ldquoblindrdquo keys without any writing and all identical) and that we want to write a book of
only 106
letters (a thousand typed pages) as we have observed in paragraph 31 all the possible combinations are
13
The reader can find all the details regarding these various arguments on the web
Pier Maria Boria Thermodynamics amp life
C = nm = (10
6)30
= (10)180
In other words there are 10180
possible configurations
Let us assume that the monkeys are capable of striking 10 keyssec (skilled typistshellip) the
time necessary would be
t = 10180
x 106 10 = 10
185 sec
Since we can count 1016 seconds in a billion years it is also possible to say that the time
required will be
10185
1016
= 10169
billion years (giga-years)
(let us remember that the big-bang has an age of ldquoonlyrdquo 14 billion years)
In reality the situation is even ldquoworserdquo in fact this calculation (which is generally accepted)
is wrong because we cannot talk about only thirty objects (the letters punctuation marks spaces between lines etc) to be arranged in 10
6 positions otherwise in each of 10180 configurations
obtainable we would find empty spaces up to 106-30 in each configuration
It is necessary to postulate that there are 106 letters to be arranged like conceding that the
monkeys have to insert 106 objects ie 10
6 key strokes In other words it is necessary that n = m =
106 and in this case the formula of the combinations gives us an astronomical value
6106 )10(===
mm mnC combinations
At a rhythm of 10 key strokes sec the time corresponds to
9899995005000616106 10sec101010)10(
6
equiv=sdotsdot=minust years
Figure 47 ndash Summary table of the probabilities according to Boltzmann
In realty the situation is even ldquoworserdquo still In fact in the calculation of the combinations duplicate configurations are not considered
(which necessarily must be considered as possible) in other words our monkeys could produce the same combinations several times (or two identical pages) anyway the duplications will be useless
in the compilation of our small book of only 106 letters
To this end we invoke chance (to attempt to appreciate the incidence of the repeating of
identical pages) and having constructed a Gaussian by arranging the frequency of identical pages we can reason as follows having produced all the astronomical combinations as above in the time
calculated (which we will call a cycle) the highest probability of identical pages is in pairs (which
Pier Maria Boria Thermodynamics amp life
29
we will assign the maximum position) then in threes and so on At infinity with a probability of
zero all the pages will be identical
It seems fair to presume that the standard deviation could be very large qualifying for a very
flat Gaussian and let us suppose that the pages to be rejected (one for the doubles two for the
triplets etc) are contained within the first standard deviation (as in Figure 48) then the duplicate pages to be thrown away would be about 68
Figure 48 ndash The postulated conditions (pages to be eliminated because they are duplicated equal
to the standard deviation) make 68 of the pages produced useless Iterating the cycle one could
consider the duplication of other pages however it can be demonstrated that the phenomenon
continues to imply finite times
How much does the required time increase to generalize we assume the length of a cycle to be of one unit and we identify with K the average cost of discarded pages (in the previous numerical
case K= 068) and then we observe Figure 49
Figure 49 ndash Having exhausted the first cycle identified by 1 the second of length K allows the
replacement of the duplicate pages produced in the first cycle the third of length K2 is used to
replace those produced in the second cycle and so on
The time necessary to complete the cycles required to eliminate the duplicates as they are produced will be given by the sum
suminfin
=0n
nK
which constitutes a geometric series
The Mathematical Analysis teaches us that such a series converges for 1ltK as is confirmed
in our case where it takes on the value 068
KS
minus=
1
1 and if K = 068 gives 1253
6801
1=
minus=S
Pier Maria Boria Thermodynamics amp life
30
Therefore multiplying by 3125 the time dedicated to complete a cycle (317middot105999989 billion
years) for the hypothesis made we also eliminate all the duplicate pages of our little book of 106
key strokes
Changing the value of K (always lt1) one obtains different multipliers but always of a finite
value let the reader imagine the time necessary to type all of Shakespearersquos works It must be highlighted that the monkey operation to be considered a success requires the
intervention of external intelligence capable of selecting the useful pages (like thought by Theory of
Information) and ordering them in the right sequence to obtain a final legible manuscript this
obvious necessity implies that negative entropy be introduced into the system as covered at the
beginning this is like a living being taking the trouble to ldquoput in orderrdquo otherwise the ldquopurely
randomrdquo work would be entirely useless because it will exclusively produce positive entropy
All experiments attempted by man with the goal of demonstrating the random production of
complex molecules (first building blocks of living organisms) have the defect of requiring an a
priori living system like man to arrange this production
When later chaotic physical-chemical conditions are created (temperature pressure
methane electrical arching etc) hoping to obtain that which Thermodynamics does not permit the
inventors of the moto perpetuo come to mind who never give up
The research on the ldquoprimordial souprdquo belongs to this type of experimentation a battle horse
of the followers of the ldquomaitre agrave penserrdquo of the last century and which regard in particular the laboratory experiments of Stanley Miller the goal of his research of a physical-chemical nature
was to recreate life it was an understandable but too ambitious of a project for a researcher The result was absolutely negative (Miller himself recognized it) however this last piece of information
is only whispered in scientific circles so that we still find genuine touts who speak with enthusiastic coram populo of the primordial soup and its miraculous effects14 with a self-assurance
that is truly shameful
45 CONCLUSION
On 4 July 2007 at the London Kinetics Museum a serious presentation of a perpetual motion
machine was scheduled a machine capable of supplying the user with a power greater than that
absorbed ldquoObviouslyrdquo the presentation was postponed due to ldquoa technical problemrdquo15
It would appear impossible but advocates convinced of such a motion exist and many
inventors submit patent after patent even though still in illo tempore Max Planck declared himself
to be contrary to such a possibility which violates the principles of Thermodynamics
Based on the reasoning we have developed regarding entropy probability and chance the
violation of such principles is implicit even in the attempts to obtain living organisms in a
laboratory (characterized as we have seen as being producers of negative entropy) and as such a
strong analogy can be seen between the advocates of perpetual motion and those aspiring to create
life
1 The correct application of Boltzmannrsquos statistics a phenomenon for which we call on
probability demonstrates that combinations of large numbers of particles to the point of generating complex organisms require very long periods of time in comparison the age of
the universe is but the blink of an eye
2 The probabilities take on the largest numbers in correspondence with the most disordered
configurations
14
From ldquoCorriere della Serardquo october 2008 ldquoLa vita sulla Terra Cominciograve nei vulcani con un innesco chimicordquo 15
-Source Wikipedia
Pier Maria Boria Thermodynamics amp life
3 The most ordered combinations are those which characterize organic structures and the action
of an intelligent being is necessary to select order and conserve in time the favorable
combinations
4 The phrase ldquochance phenomenonrdquo is somewhat less intuitive than what ldquocommon senserdquo
would suggest In fact the Gaussian perspective implies that such phenomena are necessarily
associated with a program this program implies the existence of an objective around which
we have an increased concentration of events
5 In every case it is necessary to postulate the existence of an intelligent design without which
the configurations and the favorable events constitute events without any functional link
between themselves
6 The existence of life as a producer of negative entropy on a continuous basis (not cyclical) is a fact visible with our own eyes
All this leads us to support the existence of a Co-ordinating Entity which possesses life ldquoa
priorirdquo and which is capable of transmitting it to animals (animalis homo included) and vegetation It can be noted that the two living systems animal and vegetable complement each other in the
sense that the design requires that emissions from the first (CO2) are the nutrients for the second and the byproducts of the second (O2) are essential for the first the carbon and oxygen cycles look
like they have been designed According to the author there is only one explanation we are in the presence of the greatest
Design Physicist of all times God the Creator
This is what we call Him as Christians while Israelites call Him Jehovah the Ishmaelites
Allah the Masons GADU (Great Architect of the Universe) etc
In other terms
the Creation is a thermodynamic necessity
Amen
Pier Maria Boria Thermodynamics amp life
20
It is necessary to observe that in the figure the table of numbers of occupancy reminds
us not by chance of Tartagliarsquos Triangle while the Boltzmann type diagram that can be
associated shown in Figure 37 takes on an almost familiar shape
Figure 37 - Graphical representation of Figure 62 the bars are asymmetric
Pier Maria Boria Thermodynamics amp life
21
To provide an example and referring to Figure 36 we can see how it is possible to obtain 80
possibilities corresponding to his second line
If a box is occupied by 3 particles out of an available 4 the simple combinations of 4 objects
with 3 by 3 (as taught by the Combinatorial Analysis) are given by the binomial coefficient
6437 4
and the four possible groups of three numbers have five positions from which to choose From here 4times5=20 possibilities for the group of three numbers
The single remaining particle has the possibility of the four remaining locations and therefore has 1times4=4 possibilities
The product 20times4=80 gives us the total possibilities in the case that the particles arrange themselves in two groups one with three and one with a single particle and having five boxes
suitable It is easy to verify that we will obtain the same result considering first the single particle
having five boxes suitable (five possibilities 1x5=5) and after the three having the four remaining
(one is occupied by the single particle therefore 4x4=16 and 5x16=80)
Applying the procedure line by line it produces the results shown
Pier Maria Boria Thermodynamics amp life
22
Part 4 (of 4) Chance
41 CHANCE
A sharp-shooter shoots at a target with an excellent rifle he aims carefully chooses the
moment when his breathing will not interfere and the amount of force with which to pull the trigger so as not to move the barrel fires the shot and hits the bullrsquos-eye
Immediately afterwards he takes all the same precautions but the shot ends up being slightly off target it could have been a slight disturbance to his sight an involuntary variation in his
breathing an imperceptible abnormal movement of the finger a very slight unpredictable wind or who knows what else
The causes are many and imponderable slight if each is considered in itself but interacting differently each time ensuring that each shot has a different fate
This complex of innumerable causes of disturbance which are not controllable or predictable
and which not being able to take each into account one by one are called the Law of Probability
(Gaussrsquos Law)10
Probability for the reasons given and law thanks to Carl Friedrich Gauss (1777-1855) who
wrote an equation capable of taking into consideration in a global manner all those fleeting causes
so as to be able to predict with near accurate approximation how the shots will arrange themselves
percentage wise round the target with different distances from the bullseye The approximation will
be more accurate the greater the number of shots that are fired
Let us assume that the target is as represented in Figure 41 and is divided into two parts by
means of the section AB and that our sharpshooter fires many shots after which we count the
number of shots which hit the target in each half
Figure 41- The segmented target
If the reasons for the error are truly random (rifle without defects such that it does not tend to
deviate the shot systematically and neither does the sharpshooter have an analogous defect there is
10
The example of the sharpshooter was published by Engineer Mario Manaira in Ndeg 256 of ldquoJournal of Mechanicsrdquo
together with our first article concerning thermodynamics more than half a century ago (1961)
Pier Maria Boria Thermodynamics amp life
23
not a steady wind etc in other words there does not exist a cause which always influences with the
same bias called a systematic cause) we could note the following
1 The shots will be greater in number in the first band round the center
2 The shots will progressively decrease in number in the subsequent bands as these distance themselves further from the center until there are very few in the bands furthest away
3 The shots in the two halves right and left in any similar band will tend to have the same number and will even be identical if sufficient shots are fired
It is therefore possible to represent the phenomenon graphically as in the following figure
Figure 42 ndash The random distribution of the shots in each band and the Gaussian distribution that
would be obtained with an infinite number of shots fired
If the marksman were less capable the concentration of shots near the zero on the abscissa would reduce and the curve would flatten itself while maintaining the characteristics given and
represented in Figure 43 The first observation is that the maximum height of the curve constitutes the ldquotargetrdquo in other words the goal of the operation while the absence of systematic causes (in
antithesis of randomness) ensures the symmetry of the curve with respect to the vertical which
represents our target zero
Pier Maria Boria Thermodynamics amp life
24
Figure 43 - If the marksman is less skilled the Gaussian flattens
In the case of a systematic cause of error the curve loses its symmetry if we assume that the
test is performed with a constant wind from left to right the graph will take on the shape of Figure
44
Figure 44 ndash When the Gaussian is asymmetric it implies that the phenomenon is not ldquoentirely
randomrdquo11
Let us suppose now that our sharpshooter is blindfolded the target becomes very large and is
moved he will have to shoot blindly (randomly) left and right high and low Given that the Gauss
11
Gauss suggests that the analytical expression of the Law of Randomness is the function
2xey minus
=
where it can be seen that the curve is symmetrical with respect to the axis x=0 and decreasing both towards the left and
right of this line and has a maximum for x=0
It can be shown further that the area subtended is
π=int+infin
infinminus
minusdxe
x2
To ensure that this area is equal to unity as opposed to π appropriate steps can be taken which without
changing the general properties illustrated give the normalized Gaussrsquos Law
Pier Maria Boria Thermodynamics amp life
function still applies the probability curve will flatten itself maintaining the essential
characteristics in particular the two tails which will tend towards a tangent with the abscissa
tending towards infinity a maximum point a point of inflection and the other characteristics
illustrated in Figure 45
Figure 45 ndash Typical characteristics of a normalized Gaussian
Supposing once more that the Gauss function still applies it would be logical to expect a distribution with a curve that is so flat that it will be difficult to see a maximum point corresponding
to the center of the target it will be necessary to fire enough shots so as to occupy every position on the abscissa and to have hit with 100 certainty the bullrsquos-eye
This implies that everything is possible as long as an infinite number of shots are available
(using rhetorical language)
42 SOME PROPERTIES OF RANDOM EVENTS
The perplexities regarding the applicability of chance as referred to the blind sharpshooter
depend on the fact that the Gaussian assumes that programming has been applied to reach an
objective which implies that the operator is conscious of the objective an element which in this
case is absent
Both the existence of a program (the sharpshooter sets out to hit the bullrsquos-eye) and the
existence of an objective (the card with circles) appear to be essential to be able to talk about
chance
Another example let us imagine a machine programmed to produce a certain mechanical
piece the program is the design of the piece written in machine language and the objective is the production of the piece In mass production we will find that it is the case that despite the work
conditions being maintained the same each piece will be different to the other to the point that the pieces which exceed the tolerances (which would not allow them to be interchangeable) will be
rejected Innumerable examples could be presented identifying in every case these two characteristics
a program and an objective Statistics also operate in reverse from the measurement of a group of subjects it creates a bar
chart its envelope will be the curve of the random distribution It will give us the average of the values measured if the curve is symmetrical it will tell us that the phenomenon is not influenced by
systematic causes further it will tell us the value of the standard deviation etc
Pier Maria Boria Thermodynamics amp life
26
To fix this thought in our heads let us suppose that we want to study the average height of a
population of people who are male we make many measurements on many subjects creating bars
for every centimeter we will obtain a graph similar to Figure 46
Figure 46 ndash A practical application the Gaussian deduced from experimental measurements for
statistical purposes
In this statistical application where are the program and objective They are there they are
there they were contained in the information which the people naturally had at conception a
matter of genes and of DNA (an observation coherent with ldquoThe Kid Equationrdquo See the
ldquoIntroduction to Hyperspacerdquo12
)
These considerations lead us to think that the meaning of the word ldquochancerdquo commonly given
does not make sense that ldquochancerdquo does not exist and lead us to suspect that Anatole France had an
inspired guess when he said ldquochance is Godrsquos pseudonym when He does not want to sign his
namerdquo
This strongly agrees with what illustrious philosophers have been confirming for centuries
ldquoDeus absconditus estrdquo (Is XLV XV)
12
In our first volume ldquoCaro amico miohelliprdquo ndash Ed Pagine ndash 2010 In our second volume (ldquoVerba volant eqvuationes
manentrdquo) other considerations about a fundamental theorem of Genetics the Hardy Weinberg theorem
Pier Maria Boria Thermodynamics amp life
27
43 CHANCE amp PROBABILITY
We can now summarize some salient functions of Boltzmann and Gauss
Boltzmann
1 Deals with probability regarding the characteristics that can be assumed by many identical particles having a certain number of positions available (Dirac and Fermi deal
with particles which are distinguishable but the correct reference in our observations are the identical particles)
2 The function presents a maximum and aesthetically looks like a Gaussian but it is not symmetrical
3 It has only a single asymptote to the right of the maximum and its minimum at infinity coincides with zero the origin of the reference system
4 It is normalized so that the area subtended represents the total probability of 100
Gauss
1 Deals with chance and is applicable when an objective exists that is defined by a
program
2 The phenomenon ldquopurely by chancerdquo is represented by a curve that is symmetrical
about the axis x=0
3 The Gaussian has a maximum and no minimum at infinity
4 It possesses two asymptotes one to the right and one to the left of the maximum
5 Well defined values of probability can be associated with multiples of the standard deviation
6 It is normalized as for Boltzmannrsquos
44 THE EDDINGTONrsquoS PARADOX13
Eddingtonrsquos famous ldquoInfinite monkey theoremrdquo can be counted amongst the most discussed
paradoxes for the fact that it is often quoted by so called ldquoscientific popularizersrdquo The original assertion states ldquohellipa monkey hitting keys at random on a typewriter keyboard
for an infinite amount of times will almost surely type a given text such as the complete works of
William Shakespearerdquo
Having taken away the condition of an infinite amount of time the paradox remains acceptable
(from the moment we are able to demonstrate that a finite amount of time is sufficient) However
such a long period of time is necessary that the original statement could be seen as an hyperbolic
discussion
We have seen that random phenomena require a program in light of an objective In the case
of the typing monkeys the program could include the elimination of duplicate pages (actually the
identical pages as we will see below) and the objective could consist in the conservation of ldquogoodrdquo
pages arranged in the right sequence
Applying Boltzmannrsquos statistics let us assume that the typewriter has m=30 keys (we can think of ldquoblindrdquo keys without any writing and all identical) and that we want to write a book of
only 106
letters (a thousand typed pages) as we have observed in paragraph 31 all the possible combinations are
13
The reader can find all the details regarding these various arguments on the web
Pier Maria Boria Thermodynamics amp life
C = nm = (10
6)30
= (10)180
In other words there are 10180
possible configurations
Let us assume that the monkeys are capable of striking 10 keyssec (skilled typistshellip) the
time necessary would be
t = 10180
x 106 10 = 10
185 sec
Since we can count 1016 seconds in a billion years it is also possible to say that the time
required will be
10185
1016
= 10169
billion years (giga-years)
(let us remember that the big-bang has an age of ldquoonlyrdquo 14 billion years)
In reality the situation is even ldquoworserdquo in fact this calculation (which is generally accepted)
is wrong because we cannot talk about only thirty objects (the letters punctuation marks spaces between lines etc) to be arranged in 10
6 positions otherwise in each of 10180 configurations
obtainable we would find empty spaces up to 106-30 in each configuration
It is necessary to postulate that there are 106 letters to be arranged like conceding that the
monkeys have to insert 106 objects ie 10
6 key strokes In other words it is necessary that n = m =
106 and in this case the formula of the combinations gives us an astronomical value
6106 )10(===
mm mnC combinations
At a rhythm of 10 key strokes sec the time corresponds to
9899995005000616106 10sec101010)10(
6
equiv=sdotsdot=minust years
Figure 47 ndash Summary table of the probabilities according to Boltzmann
In realty the situation is even ldquoworserdquo still In fact in the calculation of the combinations duplicate configurations are not considered
(which necessarily must be considered as possible) in other words our monkeys could produce the same combinations several times (or two identical pages) anyway the duplications will be useless
in the compilation of our small book of only 106 letters
To this end we invoke chance (to attempt to appreciate the incidence of the repeating of
identical pages) and having constructed a Gaussian by arranging the frequency of identical pages we can reason as follows having produced all the astronomical combinations as above in the time
calculated (which we will call a cycle) the highest probability of identical pages is in pairs (which
Pier Maria Boria Thermodynamics amp life
29
we will assign the maximum position) then in threes and so on At infinity with a probability of
zero all the pages will be identical
It seems fair to presume that the standard deviation could be very large qualifying for a very
flat Gaussian and let us suppose that the pages to be rejected (one for the doubles two for the
triplets etc) are contained within the first standard deviation (as in Figure 48) then the duplicate pages to be thrown away would be about 68
Figure 48 ndash The postulated conditions (pages to be eliminated because they are duplicated equal
to the standard deviation) make 68 of the pages produced useless Iterating the cycle one could
consider the duplication of other pages however it can be demonstrated that the phenomenon
continues to imply finite times
How much does the required time increase to generalize we assume the length of a cycle to be of one unit and we identify with K the average cost of discarded pages (in the previous numerical
case K= 068) and then we observe Figure 49
Figure 49 ndash Having exhausted the first cycle identified by 1 the second of length K allows the
replacement of the duplicate pages produced in the first cycle the third of length K2 is used to
replace those produced in the second cycle and so on
The time necessary to complete the cycles required to eliminate the duplicates as they are produced will be given by the sum
suminfin
=0n
nK
which constitutes a geometric series
The Mathematical Analysis teaches us that such a series converges for 1ltK as is confirmed
in our case where it takes on the value 068
KS
minus=
1
1 and if K = 068 gives 1253
6801
1=
minus=S
Pier Maria Boria Thermodynamics amp life
30
Therefore multiplying by 3125 the time dedicated to complete a cycle (317middot105999989 billion
years) for the hypothesis made we also eliminate all the duplicate pages of our little book of 106
key strokes
Changing the value of K (always lt1) one obtains different multipliers but always of a finite
value let the reader imagine the time necessary to type all of Shakespearersquos works It must be highlighted that the monkey operation to be considered a success requires the
intervention of external intelligence capable of selecting the useful pages (like thought by Theory of
Information) and ordering them in the right sequence to obtain a final legible manuscript this
obvious necessity implies that negative entropy be introduced into the system as covered at the
beginning this is like a living being taking the trouble to ldquoput in orderrdquo otherwise the ldquopurely
randomrdquo work would be entirely useless because it will exclusively produce positive entropy
All experiments attempted by man with the goal of demonstrating the random production of
complex molecules (first building blocks of living organisms) have the defect of requiring an a
priori living system like man to arrange this production
When later chaotic physical-chemical conditions are created (temperature pressure
methane electrical arching etc) hoping to obtain that which Thermodynamics does not permit the
inventors of the moto perpetuo come to mind who never give up
The research on the ldquoprimordial souprdquo belongs to this type of experimentation a battle horse
of the followers of the ldquomaitre agrave penserrdquo of the last century and which regard in particular the laboratory experiments of Stanley Miller the goal of his research of a physical-chemical nature
was to recreate life it was an understandable but too ambitious of a project for a researcher The result was absolutely negative (Miller himself recognized it) however this last piece of information
is only whispered in scientific circles so that we still find genuine touts who speak with enthusiastic coram populo of the primordial soup and its miraculous effects14 with a self-assurance
that is truly shameful
45 CONCLUSION
On 4 July 2007 at the London Kinetics Museum a serious presentation of a perpetual motion
machine was scheduled a machine capable of supplying the user with a power greater than that
absorbed ldquoObviouslyrdquo the presentation was postponed due to ldquoa technical problemrdquo15
It would appear impossible but advocates convinced of such a motion exist and many
inventors submit patent after patent even though still in illo tempore Max Planck declared himself
to be contrary to such a possibility which violates the principles of Thermodynamics
Based on the reasoning we have developed regarding entropy probability and chance the
violation of such principles is implicit even in the attempts to obtain living organisms in a
laboratory (characterized as we have seen as being producers of negative entropy) and as such a
strong analogy can be seen between the advocates of perpetual motion and those aspiring to create
life
1 The correct application of Boltzmannrsquos statistics a phenomenon for which we call on
probability demonstrates that combinations of large numbers of particles to the point of generating complex organisms require very long periods of time in comparison the age of
the universe is but the blink of an eye
2 The probabilities take on the largest numbers in correspondence with the most disordered
configurations
14
From ldquoCorriere della Serardquo october 2008 ldquoLa vita sulla Terra Cominciograve nei vulcani con un innesco chimicordquo 15
-Source Wikipedia
Pier Maria Boria Thermodynamics amp life
3 The most ordered combinations are those which characterize organic structures and the action
of an intelligent being is necessary to select order and conserve in time the favorable
combinations
4 The phrase ldquochance phenomenonrdquo is somewhat less intuitive than what ldquocommon senserdquo
would suggest In fact the Gaussian perspective implies that such phenomena are necessarily
associated with a program this program implies the existence of an objective around which
we have an increased concentration of events
5 In every case it is necessary to postulate the existence of an intelligent design without which
the configurations and the favorable events constitute events without any functional link
between themselves
6 The existence of life as a producer of negative entropy on a continuous basis (not cyclical) is a fact visible with our own eyes
All this leads us to support the existence of a Co-ordinating Entity which possesses life ldquoa
priorirdquo and which is capable of transmitting it to animals (animalis homo included) and vegetation It can be noted that the two living systems animal and vegetable complement each other in the
sense that the design requires that emissions from the first (CO2) are the nutrients for the second and the byproducts of the second (O2) are essential for the first the carbon and oxygen cycles look
like they have been designed According to the author there is only one explanation we are in the presence of the greatest
Design Physicist of all times God the Creator
This is what we call Him as Christians while Israelites call Him Jehovah the Ishmaelites
Allah the Masons GADU (Great Architect of the Universe) etc
In other terms
the Creation is a thermodynamic necessity
Amen
Pier Maria Boria Thermodynamics amp life
21
To provide an example and referring to Figure 36 we can see how it is possible to obtain 80
possibilities corresponding to his second line
If a box is occupied by 3 particles out of an available 4 the simple combinations of 4 objects
with 3 by 3 (as taught by the Combinatorial Analysis) are given by the binomial coefficient
6437 4
and the four possible groups of three numbers have five positions from which to choose From here 4times5=20 possibilities for the group of three numbers
The single remaining particle has the possibility of the four remaining locations and therefore has 1times4=4 possibilities
The product 20times4=80 gives us the total possibilities in the case that the particles arrange themselves in two groups one with three and one with a single particle and having five boxes
suitable It is easy to verify that we will obtain the same result considering first the single particle
having five boxes suitable (five possibilities 1x5=5) and after the three having the four remaining
(one is occupied by the single particle therefore 4x4=16 and 5x16=80)
Applying the procedure line by line it produces the results shown
Pier Maria Boria Thermodynamics amp life
22
Part 4 (of 4) Chance
41 CHANCE
A sharp-shooter shoots at a target with an excellent rifle he aims carefully chooses the
moment when his breathing will not interfere and the amount of force with which to pull the trigger so as not to move the barrel fires the shot and hits the bullrsquos-eye
Immediately afterwards he takes all the same precautions but the shot ends up being slightly off target it could have been a slight disturbance to his sight an involuntary variation in his
breathing an imperceptible abnormal movement of the finger a very slight unpredictable wind or who knows what else
The causes are many and imponderable slight if each is considered in itself but interacting differently each time ensuring that each shot has a different fate
This complex of innumerable causes of disturbance which are not controllable or predictable
and which not being able to take each into account one by one are called the Law of Probability
(Gaussrsquos Law)10
Probability for the reasons given and law thanks to Carl Friedrich Gauss (1777-1855) who
wrote an equation capable of taking into consideration in a global manner all those fleeting causes
so as to be able to predict with near accurate approximation how the shots will arrange themselves
percentage wise round the target with different distances from the bullseye The approximation will
be more accurate the greater the number of shots that are fired
Let us assume that the target is as represented in Figure 41 and is divided into two parts by
means of the section AB and that our sharpshooter fires many shots after which we count the
number of shots which hit the target in each half
Figure 41- The segmented target
If the reasons for the error are truly random (rifle without defects such that it does not tend to
deviate the shot systematically and neither does the sharpshooter have an analogous defect there is
10
The example of the sharpshooter was published by Engineer Mario Manaira in Ndeg 256 of ldquoJournal of Mechanicsrdquo
together with our first article concerning thermodynamics more than half a century ago (1961)
Pier Maria Boria Thermodynamics amp life
23
not a steady wind etc in other words there does not exist a cause which always influences with the
same bias called a systematic cause) we could note the following
1 The shots will be greater in number in the first band round the center
2 The shots will progressively decrease in number in the subsequent bands as these distance themselves further from the center until there are very few in the bands furthest away
3 The shots in the two halves right and left in any similar band will tend to have the same number and will even be identical if sufficient shots are fired
It is therefore possible to represent the phenomenon graphically as in the following figure
Figure 42 ndash The random distribution of the shots in each band and the Gaussian distribution that
would be obtained with an infinite number of shots fired
If the marksman were less capable the concentration of shots near the zero on the abscissa would reduce and the curve would flatten itself while maintaining the characteristics given and
represented in Figure 43 The first observation is that the maximum height of the curve constitutes the ldquotargetrdquo in other words the goal of the operation while the absence of systematic causes (in
antithesis of randomness) ensures the symmetry of the curve with respect to the vertical which
represents our target zero
Pier Maria Boria Thermodynamics amp life
24
Figure 43 - If the marksman is less skilled the Gaussian flattens
In the case of a systematic cause of error the curve loses its symmetry if we assume that the
test is performed with a constant wind from left to right the graph will take on the shape of Figure
44
Figure 44 ndash When the Gaussian is asymmetric it implies that the phenomenon is not ldquoentirely
randomrdquo11
Let us suppose now that our sharpshooter is blindfolded the target becomes very large and is
moved he will have to shoot blindly (randomly) left and right high and low Given that the Gauss
11
Gauss suggests that the analytical expression of the Law of Randomness is the function
2xey minus
=
where it can be seen that the curve is symmetrical with respect to the axis x=0 and decreasing both towards the left and
right of this line and has a maximum for x=0
It can be shown further that the area subtended is
π=int+infin
infinminus
minusdxe
x2
To ensure that this area is equal to unity as opposed to π appropriate steps can be taken which without
changing the general properties illustrated give the normalized Gaussrsquos Law
Pier Maria Boria Thermodynamics amp life
function still applies the probability curve will flatten itself maintaining the essential
characteristics in particular the two tails which will tend towards a tangent with the abscissa
tending towards infinity a maximum point a point of inflection and the other characteristics
illustrated in Figure 45
Figure 45 ndash Typical characteristics of a normalized Gaussian
Supposing once more that the Gauss function still applies it would be logical to expect a distribution with a curve that is so flat that it will be difficult to see a maximum point corresponding
to the center of the target it will be necessary to fire enough shots so as to occupy every position on the abscissa and to have hit with 100 certainty the bullrsquos-eye
This implies that everything is possible as long as an infinite number of shots are available
(using rhetorical language)
42 SOME PROPERTIES OF RANDOM EVENTS
The perplexities regarding the applicability of chance as referred to the blind sharpshooter
depend on the fact that the Gaussian assumes that programming has been applied to reach an
objective which implies that the operator is conscious of the objective an element which in this
case is absent
Both the existence of a program (the sharpshooter sets out to hit the bullrsquos-eye) and the
existence of an objective (the card with circles) appear to be essential to be able to talk about
chance
Another example let us imagine a machine programmed to produce a certain mechanical
piece the program is the design of the piece written in machine language and the objective is the production of the piece In mass production we will find that it is the case that despite the work
conditions being maintained the same each piece will be different to the other to the point that the pieces which exceed the tolerances (which would not allow them to be interchangeable) will be
rejected Innumerable examples could be presented identifying in every case these two characteristics
a program and an objective Statistics also operate in reverse from the measurement of a group of subjects it creates a bar
chart its envelope will be the curve of the random distribution It will give us the average of the values measured if the curve is symmetrical it will tell us that the phenomenon is not influenced by
systematic causes further it will tell us the value of the standard deviation etc
Pier Maria Boria Thermodynamics amp life
26
To fix this thought in our heads let us suppose that we want to study the average height of a
population of people who are male we make many measurements on many subjects creating bars
for every centimeter we will obtain a graph similar to Figure 46
Figure 46 ndash A practical application the Gaussian deduced from experimental measurements for
statistical purposes
In this statistical application where are the program and objective They are there they are
there they were contained in the information which the people naturally had at conception a
matter of genes and of DNA (an observation coherent with ldquoThe Kid Equationrdquo See the
ldquoIntroduction to Hyperspacerdquo12
)
These considerations lead us to think that the meaning of the word ldquochancerdquo commonly given
does not make sense that ldquochancerdquo does not exist and lead us to suspect that Anatole France had an
inspired guess when he said ldquochance is Godrsquos pseudonym when He does not want to sign his
namerdquo
This strongly agrees with what illustrious philosophers have been confirming for centuries
ldquoDeus absconditus estrdquo (Is XLV XV)
12
In our first volume ldquoCaro amico miohelliprdquo ndash Ed Pagine ndash 2010 In our second volume (ldquoVerba volant eqvuationes
manentrdquo) other considerations about a fundamental theorem of Genetics the Hardy Weinberg theorem
Pier Maria Boria Thermodynamics amp life
27
43 CHANCE amp PROBABILITY
We can now summarize some salient functions of Boltzmann and Gauss
Boltzmann
1 Deals with probability regarding the characteristics that can be assumed by many identical particles having a certain number of positions available (Dirac and Fermi deal
with particles which are distinguishable but the correct reference in our observations are the identical particles)
2 The function presents a maximum and aesthetically looks like a Gaussian but it is not symmetrical
3 It has only a single asymptote to the right of the maximum and its minimum at infinity coincides with zero the origin of the reference system
4 It is normalized so that the area subtended represents the total probability of 100
Gauss
1 Deals with chance and is applicable when an objective exists that is defined by a
program
2 The phenomenon ldquopurely by chancerdquo is represented by a curve that is symmetrical
about the axis x=0
3 The Gaussian has a maximum and no minimum at infinity
4 It possesses two asymptotes one to the right and one to the left of the maximum
5 Well defined values of probability can be associated with multiples of the standard deviation
6 It is normalized as for Boltzmannrsquos
44 THE EDDINGTONrsquoS PARADOX13
Eddingtonrsquos famous ldquoInfinite monkey theoremrdquo can be counted amongst the most discussed
paradoxes for the fact that it is often quoted by so called ldquoscientific popularizersrdquo The original assertion states ldquohellipa monkey hitting keys at random on a typewriter keyboard
for an infinite amount of times will almost surely type a given text such as the complete works of
William Shakespearerdquo
Having taken away the condition of an infinite amount of time the paradox remains acceptable
(from the moment we are able to demonstrate that a finite amount of time is sufficient) However
such a long period of time is necessary that the original statement could be seen as an hyperbolic
discussion
We have seen that random phenomena require a program in light of an objective In the case
of the typing monkeys the program could include the elimination of duplicate pages (actually the
identical pages as we will see below) and the objective could consist in the conservation of ldquogoodrdquo
pages arranged in the right sequence
Applying Boltzmannrsquos statistics let us assume that the typewriter has m=30 keys (we can think of ldquoblindrdquo keys without any writing and all identical) and that we want to write a book of
only 106
letters (a thousand typed pages) as we have observed in paragraph 31 all the possible combinations are
13
The reader can find all the details regarding these various arguments on the web
Pier Maria Boria Thermodynamics amp life
C = nm = (10
6)30
= (10)180
In other words there are 10180
possible configurations
Let us assume that the monkeys are capable of striking 10 keyssec (skilled typistshellip) the
time necessary would be
t = 10180
x 106 10 = 10
185 sec
Since we can count 1016 seconds in a billion years it is also possible to say that the time
required will be
10185
1016
= 10169
billion years (giga-years)
(let us remember that the big-bang has an age of ldquoonlyrdquo 14 billion years)
In reality the situation is even ldquoworserdquo in fact this calculation (which is generally accepted)
is wrong because we cannot talk about only thirty objects (the letters punctuation marks spaces between lines etc) to be arranged in 10
6 positions otherwise in each of 10180 configurations
obtainable we would find empty spaces up to 106-30 in each configuration
It is necessary to postulate that there are 106 letters to be arranged like conceding that the
monkeys have to insert 106 objects ie 10
6 key strokes In other words it is necessary that n = m =
106 and in this case the formula of the combinations gives us an astronomical value
6106 )10(===
mm mnC combinations
At a rhythm of 10 key strokes sec the time corresponds to
9899995005000616106 10sec101010)10(
6
equiv=sdotsdot=minust years
Figure 47 ndash Summary table of the probabilities according to Boltzmann
In realty the situation is even ldquoworserdquo still In fact in the calculation of the combinations duplicate configurations are not considered
(which necessarily must be considered as possible) in other words our monkeys could produce the same combinations several times (or two identical pages) anyway the duplications will be useless
in the compilation of our small book of only 106 letters
To this end we invoke chance (to attempt to appreciate the incidence of the repeating of
identical pages) and having constructed a Gaussian by arranging the frequency of identical pages we can reason as follows having produced all the astronomical combinations as above in the time
calculated (which we will call a cycle) the highest probability of identical pages is in pairs (which
Pier Maria Boria Thermodynamics amp life
29
we will assign the maximum position) then in threes and so on At infinity with a probability of
zero all the pages will be identical
It seems fair to presume that the standard deviation could be very large qualifying for a very
flat Gaussian and let us suppose that the pages to be rejected (one for the doubles two for the
triplets etc) are contained within the first standard deviation (as in Figure 48) then the duplicate pages to be thrown away would be about 68
Figure 48 ndash The postulated conditions (pages to be eliminated because they are duplicated equal
to the standard deviation) make 68 of the pages produced useless Iterating the cycle one could
consider the duplication of other pages however it can be demonstrated that the phenomenon
continues to imply finite times
How much does the required time increase to generalize we assume the length of a cycle to be of one unit and we identify with K the average cost of discarded pages (in the previous numerical
case K= 068) and then we observe Figure 49
Figure 49 ndash Having exhausted the first cycle identified by 1 the second of length K allows the
replacement of the duplicate pages produced in the first cycle the third of length K2 is used to
replace those produced in the second cycle and so on
The time necessary to complete the cycles required to eliminate the duplicates as they are produced will be given by the sum
suminfin
=0n
nK
which constitutes a geometric series
The Mathematical Analysis teaches us that such a series converges for 1ltK as is confirmed
in our case where it takes on the value 068
KS
minus=
1
1 and if K = 068 gives 1253
6801
1=
minus=S
Pier Maria Boria Thermodynamics amp life
30
Therefore multiplying by 3125 the time dedicated to complete a cycle (317middot105999989 billion
years) for the hypothesis made we also eliminate all the duplicate pages of our little book of 106
key strokes
Changing the value of K (always lt1) one obtains different multipliers but always of a finite
value let the reader imagine the time necessary to type all of Shakespearersquos works It must be highlighted that the monkey operation to be considered a success requires the
intervention of external intelligence capable of selecting the useful pages (like thought by Theory of
Information) and ordering them in the right sequence to obtain a final legible manuscript this
obvious necessity implies that negative entropy be introduced into the system as covered at the
beginning this is like a living being taking the trouble to ldquoput in orderrdquo otherwise the ldquopurely
randomrdquo work would be entirely useless because it will exclusively produce positive entropy
All experiments attempted by man with the goal of demonstrating the random production of
complex molecules (first building blocks of living organisms) have the defect of requiring an a
priori living system like man to arrange this production
When later chaotic physical-chemical conditions are created (temperature pressure
methane electrical arching etc) hoping to obtain that which Thermodynamics does not permit the
inventors of the moto perpetuo come to mind who never give up
The research on the ldquoprimordial souprdquo belongs to this type of experimentation a battle horse
of the followers of the ldquomaitre agrave penserrdquo of the last century and which regard in particular the laboratory experiments of Stanley Miller the goal of his research of a physical-chemical nature
was to recreate life it was an understandable but too ambitious of a project for a researcher The result was absolutely negative (Miller himself recognized it) however this last piece of information
is only whispered in scientific circles so that we still find genuine touts who speak with enthusiastic coram populo of the primordial soup and its miraculous effects14 with a self-assurance
that is truly shameful
45 CONCLUSION
On 4 July 2007 at the London Kinetics Museum a serious presentation of a perpetual motion
machine was scheduled a machine capable of supplying the user with a power greater than that
absorbed ldquoObviouslyrdquo the presentation was postponed due to ldquoa technical problemrdquo15
It would appear impossible but advocates convinced of such a motion exist and many
inventors submit patent after patent even though still in illo tempore Max Planck declared himself
to be contrary to such a possibility which violates the principles of Thermodynamics
Based on the reasoning we have developed regarding entropy probability and chance the
violation of such principles is implicit even in the attempts to obtain living organisms in a
laboratory (characterized as we have seen as being producers of negative entropy) and as such a
strong analogy can be seen between the advocates of perpetual motion and those aspiring to create
life
1 The correct application of Boltzmannrsquos statistics a phenomenon for which we call on
probability demonstrates that combinations of large numbers of particles to the point of generating complex organisms require very long periods of time in comparison the age of
the universe is but the blink of an eye
2 The probabilities take on the largest numbers in correspondence with the most disordered
configurations
14
From ldquoCorriere della Serardquo october 2008 ldquoLa vita sulla Terra Cominciograve nei vulcani con un innesco chimicordquo 15
-Source Wikipedia
Pier Maria Boria Thermodynamics amp life
3 The most ordered combinations are those which characterize organic structures and the action
of an intelligent being is necessary to select order and conserve in time the favorable
combinations
4 The phrase ldquochance phenomenonrdquo is somewhat less intuitive than what ldquocommon senserdquo
would suggest In fact the Gaussian perspective implies that such phenomena are necessarily
associated with a program this program implies the existence of an objective around which
we have an increased concentration of events
5 In every case it is necessary to postulate the existence of an intelligent design without which
the configurations and the favorable events constitute events without any functional link
between themselves
6 The existence of life as a producer of negative entropy on a continuous basis (not cyclical) is a fact visible with our own eyes
All this leads us to support the existence of a Co-ordinating Entity which possesses life ldquoa
priorirdquo and which is capable of transmitting it to animals (animalis homo included) and vegetation It can be noted that the two living systems animal and vegetable complement each other in the
sense that the design requires that emissions from the first (CO2) are the nutrients for the second and the byproducts of the second (O2) are essential for the first the carbon and oxygen cycles look
like they have been designed According to the author there is only one explanation we are in the presence of the greatest
Design Physicist of all times God the Creator
This is what we call Him as Christians while Israelites call Him Jehovah the Ishmaelites
Allah the Masons GADU (Great Architect of the Universe) etc
In other terms
the Creation is a thermodynamic necessity
Amen
Pier Maria Boria Thermodynamics amp life
22
Part 4 (of 4) Chance
41 CHANCE
A sharp-shooter shoots at a target with an excellent rifle he aims carefully chooses the
moment when his breathing will not interfere and the amount of force with which to pull the trigger so as not to move the barrel fires the shot and hits the bullrsquos-eye
Immediately afterwards he takes all the same precautions but the shot ends up being slightly off target it could have been a slight disturbance to his sight an involuntary variation in his
breathing an imperceptible abnormal movement of the finger a very slight unpredictable wind or who knows what else
The causes are many and imponderable slight if each is considered in itself but interacting differently each time ensuring that each shot has a different fate
This complex of innumerable causes of disturbance which are not controllable or predictable
and which not being able to take each into account one by one are called the Law of Probability
(Gaussrsquos Law)10
Probability for the reasons given and law thanks to Carl Friedrich Gauss (1777-1855) who
wrote an equation capable of taking into consideration in a global manner all those fleeting causes
so as to be able to predict with near accurate approximation how the shots will arrange themselves
percentage wise round the target with different distances from the bullseye The approximation will
be more accurate the greater the number of shots that are fired
Let us assume that the target is as represented in Figure 41 and is divided into two parts by
means of the section AB and that our sharpshooter fires many shots after which we count the
number of shots which hit the target in each half
Figure 41- The segmented target
If the reasons for the error are truly random (rifle without defects such that it does not tend to
deviate the shot systematically and neither does the sharpshooter have an analogous defect there is
10
The example of the sharpshooter was published by Engineer Mario Manaira in Ndeg 256 of ldquoJournal of Mechanicsrdquo
together with our first article concerning thermodynamics more than half a century ago (1961)
Pier Maria Boria Thermodynamics amp life
23
not a steady wind etc in other words there does not exist a cause which always influences with the
same bias called a systematic cause) we could note the following
1 The shots will be greater in number in the first band round the center
2 The shots will progressively decrease in number in the subsequent bands as these distance themselves further from the center until there are very few in the bands furthest away
3 The shots in the two halves right and left in any similar band will tend to have the same number and will even be identical if sufficient shots are fired
It is therefore possible to represent the phenomenon graphically as in the following figure
Figure 42 ndash The random distribution of the shots in each band and the Gaussian distribution that
would be obtained with an infinite number of shots fired
If the marksman were less capable the concentration of shots near the zero on the abscissa would reduce and the curve would flatten itself while maintaining the characteristics given and
represented in Figure 43 The first observation is that the maximum height of the curve constitutes the ldquotargetrdquo in other words the goal of the operation while the absence of systematic causes (in
antithesis of randomness) ensures the symmetry of the curve with respect to the vertical which
represents our target zero
Pier Maria Boria Thermodynamics amp life
24
Figure 43 - If the marksman is less skilled the Gaussian flattens
In the case of a systematic cause of error the curve loses its symmetry if we assume that the
test is performed with a constant wind from left to right the graph will take on the shape of Figure
44
Figure 44 ndash When the Gaussian is asymmetric it implies that the phenomenon is not ldquoentirely
randomrdquo11
Let us suppose now that our sharpshooter is blindfolded the target becomes very large and is
moved he will have to shoot blindly (randomly) left and right high and low Given that the Gauss
11
Gauss suggests that the analytical expression of the Law of Randomness is the function
2xey minus
=
where it can be seen that the curve is symmetrical with respect to the axis x=0 and decreasing both towards the left and
right of this line and has a maximum for x=0
It can be shown further that the area subtended is
π=int+infin
infinminus
minusdxe
x2
To ensure that this area is equal to unity as opposed to π appropriate steps can be taken which without
changing the general properties illustrated give the normalized Gaussrsquos Law
Pier Maria Boria Thermodynamics amp life
function still applies the probability curve will flatten itself maintaining the essential
characteristics in particular the two tails which will tend towards a tangent with the abscissa
tending towards infinity a maximum point a point of inflection and the other characteristics
illustrated in Figure 45
Figure 45 ndash Typical characteristics of a normalized Gaussian
Supposing once more that the Gauss function still applies it would be logical to expect a distribution with a curve that is so flat that it will be difficult to see a maximum point corresponding
to the center of the target it will be necessary to fire enough shots so as to occupy every position on the abscissa and to have hit with 100 certainty the bullrsquos-eye
This implies that everything is possible as long as an infinite number of shots are available
(using rhetorical language)
42 SOME PROPERTIES OF RANDOM EVENTS
The perplexities regarding the applicability of chance as referred to the blind sharpshooter
depend on the fact that the Gaussian assumes that programming has been applied to reach an
objective which implies that the operator is conscious of the objective an element which in this
case is absent
Both the existence of a program (the sharpshooter sets out to hit the bullrsquos-eye) and the
existence of an objective (the card with circles) appear to be essential to be able to talk about
chance
Another example let us imagine a machine programmed to produce a certain mechanical
piece the program is the design of the piece written in machine language and the objective is the production of the piece In mass production we will find that it is the case that despite the work
conditions being maintained the same each piece will be different to the other to the point that the pieces which exceed the tolerances (which would not allow them to be interchangeable) will be
rejected Innumerable examples could be presented identifying in every case these two characteristics
a program and an objective Statistics also operate in reverse from the measurement of a group of subjects it creates a bar
chart its envelope will be the curve of the random distribution It will give us the average of the values measured if the curve is symmetrical it will tell us that the phenomenon is not influenced by
systematic causes further it will tell us the value of the standard deviation etc
Pier Maria Boria Thermodynamics amp life
26
To fix this thought in our heads let us suppose that we want to study the average height of a
population of people who are male we make many measurements on many subjects creating bars
for every centimeter we will obtain a graph similar to Figure 46
Figure 46 ndash A practical application the Gaussian deduced from experimental measurements for
statistical purposes
In this statistical application where are the program and objective They are there they are
there they were contained in the information which the people naturally had at conception a
matter of genes and of DNA (an observation coherent with ldquoThe Kid Equationrdquo See the
ldquoIntroduction to Hyperspacerdquo12
)
These considerations lead us to think that the meaning of the word ldquochancerdquo commonly given
does not make sense that ldquochancerdquo does not exist and lead us to suspect that Anatole France had an
inspired guess when he said ldquochance is Godrsquos pseudonym when He does not want to sign his
namerdquo
This strongly agrees with what illustrious philosophers have been confirming for centuries
ldquoDeus absconditus estrdquo (Is XLV XV)
12
In our first volume ldquoCaro amico miohelliprdquo ndash Ed Pagine ndash 2010 In our second volume (ldquoVerba volant eqvuationes
manentrdquo) other considerations about a fundamental theorem of Genetics the Hardy Weinberg theorem
Pier Maria Boria Thermodynamics amp life
27
43 CHANCE amp PROBABILITY
We can now summarize some salient functions of Boltzmann and Gauss
Boltzmann
1 Deals with probability regarding the characteristics that can be assumed by many identical particles having a certain number of positions available (Dirac and Fermi deal
with particles which are distinguishable but the correct reference in our observations are the identical particles)
2 The function presents a maximum and aesthetically looks like a Gaussian but it is not symmetrical
3 It has only a single asymptote to the right of the maximum and its minimum at infinity coincides with zero the origin of the reference system
4 It is normalized so that the area subtended represents the total probability of 100
Gauss
1 Deals with chance and is applicable when an objective exists that is defined by a
program
2 The phenomenon ldquopurely by chancerdquo is represented by a curve that is symmetrical
about the axis x=0
3 The Gaussian has a maximum and no minimum at infinity
4 It possesses two asymptotes one to the right and one to the left of the maximum
5 Well defined values of probability can be associated with multiples of the standard deviation
6 It is normalized as for Boltzmannrsquos
44 THE EDDINGTONrsquoS PARADOX13
Eddingtonrsquos famous ldquoInfinite monkey theoremrdquo can be counted amongst the most discussed
paradoxes for the fact that it is often quoted by so called ldquoscientific popularizersrdquo The original assertion states ldquohellipa monkey hitting keys at random on a typewriter keyboard
for an infinite amount of times will almost surely type a given text such as the complete works of
William Shakespearerdquo
Having taken away the condition of an infinite amount of time the paradox remains acceptable
(from the moment we are able to demonstrate that a finite amount of time is sufficient) However
such a long period of time is necessary that the original statement could be seen as an hyperbolic
discussion
We have seen that random phenomena require a program in light of an objective In the case
of the typing monkeys the program could include the elimination of duplicate pages (actually the
identical pages as we will see below) and the objective could consist in the conservation of ldquogoodrdquo
pages arranged in the right sequence
Applying Boltzmannrsquos statistics let us assume that the typewriter has m=30 keys (we can think of ldquoblindrdquo keys without any writing and all identical) and that we want to write a book of
only 106
letters (a thousand typed pages) as we have observed in paragraph 31 all the possible combinations are
13
The reader can find all the details regarding these various arguments on the web
Pier Maria Boria Thermodynamics amp life
C = nm = (10
6)30
= (10)180
In other words there are 10180
possible configurations
Let us assume that the monkeys are capable of striking 10 keyssec (skilled typistshellip) the
time necessary would be
t = 10180
x 106 10 = 10
185 sec
Since we can count 1016 seconds in a billion years it is also possible to say that the time
required will be
10185
1016
= 10169
billion years (giga-years)
(let us remember that the big-bang has an age of ldquoonlyrdquo 14 billion years)
In reality the situation is even ldquoworserdquo in fact this calculation (which is generally accepted)
is wrong because we cannot talk about only thirty objects (the letters punctuation marks spaces between lines etc) to be arranged in 10
6 positions otherwise in each of 10180 configurations
obtainable we would find empty spaces up to 106-30 in each configuration
It is necessary to postulate that there are 106 letters to be arranged like conceding that the
monkeys have to insert 106 objects ie 10
6 key strokes In other words it is necessary that n = m =
106 and in this case the formula of the combinations gives us an astronomical value
6106 )10(===
mm mnC combinations
At a rhythm of 10 key strokes sec the time corresponds to
9899995005000616106 10sec101010)10(
6
equiv=sdotsdot=minust years
Figure 47 ndash Summary table of the probabilities according to Boltzmann
In realty the situation is even ldquoworserdquo still In fact in the calculation of the combinations duplicate configurations are not considered
(which necessarily must be considered as possible) in other words our monkeys could produce the same combinations several times (or two identical pages) anyway the duplications will be useless
in the compilation of our small book of only 106 letters
To this end we invoke chance (to attempt to appreciate the incidence of the repeating of
identical pages) and having constructed a Gaussian by arranging the frequency of identical pages we can reason as follows having produced all the astronomical combinations as above in the time
calculated (which we will call a cycle) the highest probability of identical pages is in pairs (which
Pier Maria Boria Thermodynamics amp life
29
we will assign the maximum position) then in threes and so on At infinity with a probability of
zero all the pages will be identical
It seems fair to presume that the standard deviation could be very large qualifying for a very
flat Gaussian and let us suppose that the pages to be rejected (one for the doubles two for the
triplets etc) are contained within the first standard deviation (as in Figure 48) then the duplicate pages to be thrown away would be about 68
Figure 48 ndash The postulated conditions (pages to be eliminated because they are duplicated equal
to the standard deviation) make 68 of the pages produced useless Iterating the cycle one could
consider the duplication of other pages however it can be demonstrated that the phenomenon
continues to imply finite times
How much does the required time increase to generalize we assume the length of a cycle to be of one unit and we identify with K the average cost of discarded pages (in the previous numerical
case K= 068) and then we observe Figure 49
Figure 49 ndash Having exhausted the first cycle identified by 1 the second of length K allows the
replacement of the duplicate pages produced in the first cycle the third of length K2 is used to
replace those produced in the second cycle and so on
The time necessary to complete the cycles required to eliminate the duplicates as they are produced will be given by the sum
suminfin
=0n
nK
which constitutes a geometric series
The Mathematical Analysis teaches us that such a series converges for 1ltK as is confirmed
in our case where it takes on the value 068
KS
minus=
1
1 and if K = 068 gives 1253
6801
1=
minus=S
Pier Maria Boria Thermodynamics amp life
30
Therefore multiplying by 3125 the time dedicated to complete a cycle (317middot105999989 billion
years) for the hypothesis made we also eliminate all the duplicate pages of our little book of 106
key strokes
Changing the value of K (always lt1) one obtains different multipliers but always of a finite
value let the reader imagine the time necessary to type all of Shakespearersquos works It must be highlighted that the monkey operation to be considered a success requires the
intervention of external intelligence capable of selecting the useful pages (like thought by Theory of
Information) and ordering them in the right sequence to obtain a final legible manuscript this
obvious necessity implies that negative entropy be introduced into the system as covered at the
beginning this is like a living being taking the trouble to ldquoput in orderrdquo otherwise the ldquopurely
randomrdquo work would be entirely useless because it will exclusively produce positive entropy
All experiments attempted by man with the goal of demonstrating the random production of
complex molecules (first building blocks of living organisms) have the defect of requiring an a
priori living system like man to arrange this production
When later chaotic physical-chemical conditions are created (temperature pressure
methane electrical arching etc) hoping to obtain that which Thermodynamics does not permit the
inventors of the moto perpetuo come to mind who never give up
The research on the ldquoprimordial souprdquo belongs to this type of experimentation a battle horse
of the followers of the ldquomaitre agrave penserrdquo of the last century and which regard in particular the laboratory experiments of Stanley Miller the goal of his research of a physical-chemical nature
was to recreate life it was an understandable but too ambitious of a project for a researcher The result was absolutely negative (Miller himself recognized it) however this last piece of information
is only whispered in scientific circles so that we still find genuine touts who speak with enthusiastic coram populo of the primordial soup and its miraculous effects14 with a self-assurance
that is truly shameful
45 CONCLUSION
On 4 July 2007 at the London Kinetics Museum a serious presentation of a perpetual motion
machine was scheduled a machine capable of supplying the user with a power greater than that
absorbed ldquoObviouslyrdquo the presentation was postponed due to ldquoa technical problemrdquo15
It would appear impossible but advocates convinced of such a motion exist and many
inventors submit patent after patent even though still in illo tempore Max Planck declared himself
to be contrary to such a possibility which violates the principles of Thermodynamics
Based on the reasoning we have developed regarding entropy probability and chance the
violation of such principles is implicit even in the attempts to obtain living organisms in a
laboratory (characterized as we have seen as being producers of negative entropy) and as such a
strong analogy can be seen between the advocates of perpetual motion and those aspiring to create
life
1 The correct application of Boltzmannrsquos statistics a phenomenon for which we call on
probability demonstrates that combinations of large numbers of particles to the point of generating complex organisms require very long periods of time in comparison the age of
the universe is but the blink of an eye
2 The probabilities take on the largest numbers in correspondence with the most disordered
configurations
14
From ldquoCorriere della Serardquo october 2008 ldquoLa vita sulla Terra Cominciograve nei vulcani con un innesco chimicordquo 15
-Source Wikipedia
Pier Maria Boria Thermodynamics amp life
3 The most ordered combinations are those which characterize organic structures and the action
of an intelligent being is necessary to select order and conserve in time the favorable
combinations
4 The phrase ldquochance phenomenonrdquo is somewhat less intuitive than what ldquocommon senserdquo
would suggest In fact the Gaussian perspective implies that such phenomena are necessarily
associated with a program this program implies the existence of an objective around which
we have an increased concentration of events
5 In every case it is necessary to postulate the existence of an intelligent design without which
the configurations and the favorable events constitute events without any functional link
between themselves
6 The existence of life as a producer of negative entropy on a continuous basis (not cyclical) is a fact visible with our own eyes
All this leads us to support the existence of a Co-ordinating Entity which possesses life ldquoa
priorirdquo and which is capable of transmitting it to animals (animalis homo included) and vegetation It can be noted that the two living systems animal and vegetable complement each other in the
sense that the design requires that emissions from the first (CO2) are the nutrients for the second and the byproducts of the second (O2) are essential for the first the carbon and oxygen cycles look
like they have been designed According to the author there is only one explanation we are in the presence of the greatest
Design Physicist of all times God the Creator
This is what we call Him as Christians while Israelites call Him Jehovah the Ishmaelites
Allah the Masons GADU (Great Architect of the Universe) etc
In other terms
the Creation is a thermodynamic necessity
Amen
Pier Maria Boria Thermodynamics amp life
23
not a steady wind etc in other words there does not exist a cause which always influences with the
same bias called a systematic cause) we could note the following
1 The shots will be greater in number in the first band round the center
2 The shots will progressively decrease in number in the subsequent bands as these distance themselves further from the center until there are very few in the bands furthest away
3 The shots in the two halves right and left in any similar band will tend to have the same number and will even be identical if sufficient shots are fired
It is therefore possible to represent the phenomenon graphically as in the following figure
Figure 42 ndash The random distribution of the shots in each band and the Gaussian distribution that
would be obtained with an infinite number of shots fired
If the marksman were less capable the concentration of shots near the zero on the abscissa would reduce and the curve would flatten itself while maintaining the characteristics given and
represented in Figure 43 The first observation is that the maximum height of the curve constitutes the ldquotargetrdquo in other words the goal of the operation while the absence of systematic causes (in
antithesis of randomness) ensures the symmetry of the curve with respect to the vertical which
represents our target zero
Pier Maria Boria Thermodynamics amp life
24
Figure 43 - If the marksman is less skilled the Gaussian flattens
In the case of a systematic cause of error the curve loses its symmetry if we assume that the
test is performed with a constant wind from left to right the graph will take on the shape of Figure
44
Figure 44 ndash When the Gaussian is asymmetric it implies that the phenomenon is not ldquoentirely
randomrdquo11
Let us suppose now that our sharpshooter is blindfolded the target becomes very large and is
moved he will have to shoot blindly (randomly) left and right high and low Given that the Gauss
11
Gauss suggests that the analytical expression of the Law of Randomness is the function
2xey minus
=
where it can be seen that the curve is symmetrical with respect to the axis x=0 and decreasing both towards the left and
right of this line and has a maximum for x=0
It can be shown further that the area subtended is
π=int+infin
infinminus
minusdxe
x2
To ensure that this area is equal to unity as opposed to π appropriate steps can be taken which without
changing the general properties illustrated give the normalized Gaussrsquos Law
Pier Maria Boria Thermodynamics amp life
function still applies the probability curve will flatten itself maintaining the essential
characteristics in particular the two tails which will tend towards a tangent with the abscissa
tending towards infinity a maximum point a point of inflection and the other characteristics
illustrated in Figure 45
Figure 45 ndash Typical characteristics of a normalized Gaussian
Supposing once more that the Gauss function still applies it would be logical to expect a distribution with a curve that is so flat that it will be difficult to see a maximum point corresponding
to the center of the target it will be necessary to fire enough shots so as to occupy every position on the abscissa and to have hit with 100 certainty the bullrsquos-eye
This implies that everything is possible as long as an infinite number of shots are available
(using rhetorical language)
42 SOME PROPERTIES OF RANDOM EVENTS
The perplexities regarding the applicability of chance as referred to the blind sharpshooter
depend on the fact that the Gaussian assumes that programming has been applied to reach an
objective which implies that the operator is conscious of the objective an element which in this
case is absent
Both the existence of a program (the sharpshooter sets out to hit the bullrsquos-eye) and the
existence of an objective (the card with circles) appear to be essential to be able to talk about
chance
Another example let us imagine a machine programmed to produce a certain mechanical
piece the program is the design of the piece written in machine language and the objective is the production of the piece In mass production we will find that it is the case that despite the work
conditions being maintained the same each piece will be different to the other to the point that the pieces which exceed the tolerances (which would not allow them to be interchangeable) will be
rejected Innumerable examples could be presented identifying in every case these two characteristics
a program and an objective Statistics also operate in reverse from the measurement of a group of subjects it creates a bar
chart its envelope will be the curve of the random distribution It will give us the average of the values measured if the curve is symmetrical it will tell us that the phenomenon is not influenced by
systematic causes further it will tell us the value of the standard deviation etc
Pier Maria Boria Thermodynamics amp life
26
To fix this thought in our heads let us suppose that we want to study the average height of a
population of people who are male we make many measurements on many subjects creating bars
for every centimeter we will obtain a graph similar to Figure 46
Figure 46 ndash A practical application the Gaussian deduced from experimental measurements for
statistical purposes
In this statistical application where are the program and objective They are there they are
there they were contained in the information which the people naturally had at conception a
matter of genes and of DNA (an observation coherent with ldquoThe Kid Equationrdquo See the
ldquoIntroduction to Hyperspacerdquo12
)
These considerations lead us to think that the meaning of the word ldquochancerdquo commonly given
does not make sense that ldquochancerdquo does not exist and lead us to suspect that Anatole France had an
inspired guess when he said ldquochance is Godrsquos pseudonym when He does not want to sign his
namerdquo
This strongly agrees with what illustrious philosophers have been confirming for centuries
ldquoDeus absconditus estrdquo (Is XLV XV)
12
In our first volume ldquoCaro amico miohelliprdquo ndash Ed Pagine ndash 2010 In our second volume (ldquoVerba volant eqvuationes
manentrdquo) other considerations about a fundamental theorem of Genetics the Hardy Weinberg theorem
Pier Maria Boria Thermodynamics amp life
27
43 CHANCE amp PROBABILITY
We can now summarize some salient functions of Boltzmann and Gauss
Boltzmann
1 Deals with probability regarding the characteristics that can be assumed by many identical particles having a certain number of positions available (Dirac and Fermi deal
with particles which are distinguishable but the correct reference in our observations are the identical particles)
2 The function presents a maximum and aesthetically looks like a Gaussian but it is not symmetrical
3 It has only a single asymptote to the right of the maximum and its minimum at infinity coincides with zero the origin of the reference system
4 It is normalized so that the area subtended represents the total probability of 100
Gauss
1 Deals with chance and is applicable when an objective exists that is defined by a
program
2 The phenomenon ldquopurely by chancerdquo is represented by a curve that is symmetrical
about the axis x=0
3 The Gaussian has a maximum and no minimum at infinity
4 It possesses two asymptotes one to the right and one to the left of the maximum
5 Well defined values of probability can be associated with multiples of the standard deviation
6 It is normalized as for Boltzmannrsquos
44 THE EDDINGTONrsquoS PARADOX13
Eddingtonrsquos famous ldquoInfinite monkey theoremrdquo can be counted amongst the most discussed
paradoxes for the fact that it is often quoted by so called ldquoscientific popularizersrdquo The original assertion states ldquohellipa monkey hitting keys at random on a typewriter keyboard
for an infinite amount of times will almost surely type a given text such as the complete works of
William Shakespearerdquo
Having taken away the condition of an infinite amount of time the paradox remains acceptable
(from the moment we are able to demonstrate that a finite amount of time is sufficient) However
such a long period of time is necessary that the original statement could be seen as an hyperbolic
discussion
We have seen that random phenomena require a program in light of an objective In the case
of the typing monkeys the program could include the elimination of duplicate pages (actually the
identical pages as we will see below) and the objective could consist in the conservation of ldquogoodrdquo
pages arranged in the right sequence
Applying Boltzmannrsquos statistics let us assume that the typewriter has m=30 keys (we can think of ldquoblindrdquo keys without any writing and all identical) and that we want to write a book of
only 106
letters (a thousand typed pages) as we have observed in paragraph 31 all the possible combinations are
13
The reader can find all the details regarding these various arguments on the web
Pier Maria Boria Thermodynamics amp life
C = nm = (10
6)30
= (10)180
In other words there are 10180
possible configurations
Let us assume that the monkeys are capable of striking 10 keyssec (skilled typistshellip) the
time necessary would be
t = 10180
x 106 10 = 10
185 sec
Since we can count 1016 seconds in a billion years it is also possible to say that the time
required will be
10185
1016
= 10169
billion years (giga-years)
(let us remember that the big-bang has an age of ldquoonlyrdquo 14 billion years)
In reality the situation is even ldquoworserdquo in fact this calculation (which is generally accepted)
is wrong because we cannot talk about only thirty objects (the letters punctuation marks spaces between lines etc) to be arranged in 10
6 positions otherwise in each of 10180 configurations
obtainable we would find empty spaces up to 106-30 in each configuration
It is necessary to postulate that there are 106 letters to be arranged like conceding that the
monkeys have to insert 106 objects ie 10
6 key strokes In other words it is necessary that n = m =
106 and in this case the formula of the combinations gives us an astronomical value
6106 )10(===
mm mnC combinations
At a rhythm of 10 key strokes sec the time corresponds to
9899995005000616106 10sec101010)10(
6
equiv=sdotsdot=minust years
Figure 47 ndash Summary table of the probabilities according to Boltzmann
In realty the situation is even ldquoworserdquo still In fact in the calculation of the combinations duplicate configurations are not considered
(which necessarily must be considered as possible) in other words our monkeys could produce the same combinations several times (or two identical pages) anyway the duplications will be useless
in the compilation of our small book of only 106 letters
To this end we invoke chance (to attempt to appreciate the incidence of the repeating of
identical pages) and having constructed a Gaussian by arranging the frequency of identical pages we can reason as follows having produced all the astronomical combinations as above in the time
calculated (which we will call a cycle) the highest probability of identical pages is in pairs (which
Pier Maria Boria Thermodynamics amp life
29
we will assign the maximum position) then in threes and so on At infinity with a probability of
zero all the pages will be identical
It seems fair to presume that the standard deviation could be very large qualifying for a very
flat Gaussian and let us suppose that the pages to be rejected (one for the doubles two for the
triplets etc) are contained within the first standard deviation (as in Figure 48) then the duplicate pages to be thrown away would be about 68
Figure 48 ndash The postulated conditions (pages to be eliminated because they are duplicated equal
to the standard deviation) make 68 of the pages produced useless Iterating the cycle one could
consider the duplication of other pages however it can be demonstrated that the phenomenon
continues to imply finite times
How much does the required time increase to generalize we assume the length of a cycle to be of one unit and we identify with K the average cost of discarded pages (in the previous numerical
case K= 068) and then we observe Figure 49
Figure 49 ndash Having exhausted the first cycle identified by 1 the second of length K allows the
replacement of the duplicate pages produced in the first cycle the third of length K2 is used to
replace those produced in the second cycle and so on
The time necessary to complete the cycles required to eliminate the duplicates as they are produced will be given by the sum
suminfin
=0n
nK
which constitutes a geometric series
The Mathematical Analysis teaches us that such a series converges for 1ltK as is confirmed
in our case where it takes on the value 068
KS
minus=
1
1 and if K = 068 gives 1253
6801
1=
minus=S
Pier Maria Boria Thermodynamics amp life
30
Therefore multiplying by 3125 the time dedicated to complete a cycle (317middot105999989 billion
years) for the hypothesis made we also eliminate all the duplicate pages of our little book of 106
key strokes
Changing the value of K (always lt1) one obtains different multipliers but always of a finite
value let the reader imagine the time necessary to type all of Shakespearersquos works It must be highlighted that the monkey operation to be considered a success requires the
intervention of external intelligence capable of selecting the useful pages (like thought by Theory of
Information) and ordering them in the right sequence to obtain a final legible manuscript this
obvious necessity implies that negative entropy be introduced into the system as covered at the
beginning this is like a living being taking the trouble to ldquoput in orderrdquo otherwise the ldquopurely
randomrdquo work would be entirely useless because it will exclusively produce positive entropy
All experiments attempted by man with the goal of demonstrating the random production of
complex molecules (first building blocks of living organisms) have the defect of requiring an a
priori living system like man to arrange this production
When later chaotic physical-chemical conditions are created (temperature pressure
methane electrical arching etc) hoping to obtain that which Thermodynamics does not permit the
inventors of the moto perpetuo come to mind who never give up
The research on the ldquoprimordial souprdquo belongs to this type of experimentation a battle horse
of the followers of the ldquomaitre agrave penserrdquo of the last century and which regard in particular the laboratory experiments of Stanley Miller the goal of his research of a physical-chemical nature
was to recreate life it was an understandable but too ambitious of a project for a researcher The result was absolutely negative (Miller himself recognized it) however this last piece of information
is only whispered in scientific circles so that we still find genuine touts who speak with enthusiastic coram populo of the primordial soup and its miraculous effects14 with a self-assurance
that is truly shameful
45 CONCLUSION
On 4 July 2007 at the London Kinetics Museum a serious presentation of a perpetual motion
machine was scheduled a machine capable of supplying the user with a power greater than that
absorbed ldquoObviouslyrdquo the presentation was postponed due to ldquoa technical problemrdquo15
It would appear impossible but advocates convinced of such a motion exist and many
inventors submit patent after patent even though still in illo tempore Max Planck declared himself
to be contrary to such a possibility which violates the principles of Thermodynamics
Based on the reasoning we have developed regarding entropy probability and chance the
violation of such principles is implicit even in the attempts to obtain living organisms in a
laboratory (characterized as we have seen as being producers of negative entropy) and as such a
strong analogy can be seen between the advocates of perpetual motion and those aspiring to create
life
1 The correct application of Boltzmannrsquos statistics a phenomenon for which we call on
probability demonstrates that combinations of large numbers of particles to the point of generating complex organisms require very long periods of time in comparison the age of
the universe is but the blink of an eye
2 The probabilities take on the largest numbers in correspondence with the most disordered
configurations
14
From ldquoCorriere della Serardquo october 2008 ldquoLa vita sulla Terra Cominciograve nei vulcani con un innesco chimicordquo 15
-Source Wikipedia
Pier Maria Boria Thermodynamics amp life
3 The most ordered combinations are those which characterize organic structures and the action
of an intelligent being is necessary to select order and conserve in time the favorable
combinations
4 The phrase ldquochance phenomenonrdquo is somewhat less intuitive than what ldquocommon senserdquo
would suggest In fact the Gaussian perspective implies that such phenomena are necessarily
associated with a program this program implies the existence of an objective around which
we have an increased concentration of events
5 In every case it is necessary to postulate the existence of an intelligent design without which
the configurations and the favorable events constitute events without any functional link
between themselves
6 The existence of life as a producer of negative entropy on a continuous basis (not cyclical) is a fact visible with our own eyes
All this leads us to support the existence of a Co-ordinating Entity which possesses life ldquoa
priorirdquo and which is capable of transmitting it to animals (animalis homo included) and vegetation It can be noted that the two living systems animal and vegetable complement each other in the
sense that the design requires that emissions from the first (CO2) are the nutrients for the second and the byproducts of the second (O2) are essential for the first the carbon and oxygen cycles look
like they have been designed According to the author there is only one explanation we are in the presence of the greatest
Design Physicist of all times God the Creator
This is what we call Him as Christians while Israelites call Him Jehovah the Ishmaelites
Allah the Masons GADU (Great Architect of the Universe) etc
In other terms
the Creation is a thermodynamic necessity
Amen
Pier Maria Boria Thermodynamics amp life
24
Figure 43 - If the marksman is less skilled the Gaussian flattens
In the case of a systematic cause of error the curve loses its symmetry if we assume that the
test is performed with a constant wind from left to right the graph will take on the shape of Figure
44
Figure 44 ndash When the Gaussian is asymmetric it implies that the phenomenon is not ldquoentirely
randomrdquo11
Let us suppose now that our sharpshooter is blindfolded the target becomes very large and is
moved he will have to shoot blindly (randomly) left and right high and low Given that the Gauss
11
Gauss suggests that the analytical expression of the Law of Randomness is the function
2xey minus
=
where it can be seen that the curve is symmetrical with respect to the axis x=0 and decreasing both towards the left and
right of this line and has a maximum for x=0
It can be shown further that the area subtended is
π=int+infin
infinminus
minusdxe
x2
To ensure that this area is equal to unity as opposed to π appropriate steps can be taken which without
changing the general properties illustrated give the normalized Gaussrsquos Law
Pier Maria Boria Thermodynamics amp life
function still applies the probability curve will flatten itself maintaining the essential
characteristics in particular the two tails which will tend towards a tangent with the abscissa
tending towards infinity a maximum point a point of inflection and the other characteristics
illustrated in Figure 45
Figure 45 ndash Typical characteristics of a normalized Gaussian
Supposing once more that the Gauss function still applies it would be logical to expect a distribution with a curve that is so flat that it will be difficult to see a maximum point corresponding
to the center of the target it will be necessary to fire enough shots so as to occupy every position on the abscissa and to have hit with 100 certainty the bullrsquos-eye
This implies that everything is possible as long as an infinite number of shots are available
(using rhetorical language)
42 SOME PROPERTIES OF RANDOM EVENTS
The perplexities regarding the applicability of chance as referred to the blind sharpshooter
depend on the fact that the Gaussian assumes that programming has been applied to reach an
objective which implies that the operator is conscious of the objective an element which in this
case is absent
Both the existence of a program (the sharpshooter sets out to hit the bullrsquos-eye) and the
existence of an objective (the card with circles) appear to be essential to be able to talk about
chance
Another example let us imagine a machine programmed to produce a certain mechanical
piece the program is the design of the piece written in machine language and the objective is the production of the piece In mass production we will find that it is the case that despite the work
conditions being maintained the same each piece will be different to the other to the point that the pieces which exceed the tolerances (which would not allow them to be interchangeable) will be
rejected Innumerable examples could be presented identifying in every case these two characteristics
a program and an objective Statistics also operate in reverse from the measurement of a group of subjects it creates a bar
chart its envelope will be the curve of the random distribution It will give us the average of the values measured if the curve is symmetrical it will tell us that the phenomenon is not influenced by
systematic causes further it will tell us the value of the standard deviation etc
Pier Maria Boria Thermodynamics amp life
26
To fix this thought in our heads let us suppose that we want to study the average height of a
population of people who are male we make many measurements on many subjects creating bars
for every centimeter we will obtain a graph similar to Figure 46
Figure 46 ndash A practical application the Gaussian deduced from experimental measurements for
statistical purposes
In this statistical application where are the program and objective They are there they are
there they were contained in the information which the people naturally had at conception a
matter of genes and of DNA (an observation coherent with ldquoThe Kid Equationrdquo See the
ldquoIntroduction to Hyperspacerdquo12
)
These considerations lead us to think that the meaning of the word ldquochancerdquo commonly given
does not make sense that ldquochancerdquo does not exist and lead us to suspect that Anatole France had an
inspired guess when he said ldquochance is Godrsquos pseudonym when He does not want to sign his
namerdquo
This strongly agrees with what illustrious philosophers have been confirming for centuries
ldquoDeus absconditus estrdquo (Is XLV XV)
12
In our first volume ldquoCaro amico miohelliprdquo ndash Ed Pagine ndash 2010 In our second volume (ldquoVerba volant eqvuationes
manentrdquo) other considerations about a fundamental theorem of Genetics the Hardy Weinberg theorem
Pier Maria Boria Thermodynamics amp life
27
43 CHANCE amp PROBABILITY
We can now summarize some salient functions of Boltzmann and Gauss
Boltzmann
1 Deals with probability regarding the characteristics that can be assumed by many identical particles having a certain number of positions available (Dirac and Fermi deal
with particles which are distinguishable but the correct reference in our observations are the identical particles)
2 The function presents a maximum and aesthetically looks like a Gaussian but it is not symmetrical
3 It has only a single asymptote to the right of the maximum and its minimum at infinity coincides with zero the origin of the reference system
4 It is normalized so that the area subtended represents the total probability of 100
Gauss
1 Deals with chance and is applicable when an objective exists that is defined by a
program
2 The phenomenon ldquopurely by chancerdquo is represented by a curve that is symmetrical
about the axis x=0
3 The Gaussian has a maximum and no minimum at infinity
4 It possesses two asymptotes one to the right and one to the left of the maximum
5 Well defined values of probability can be associated with multiples of the standard deviation
6 It is normalized as for Boltzmannrsquos
44 THE EDDINGTONrsquoS PARADOX13
Eddingtonrsquos famous ldquoInfinite monkey theoremrdquo can be counted amongst the most discussed
paradoxes for the fact that it is often quoted by so called ldquoscientific popularizersrdquo The original assertion states ldquohellipa monkey hitting keys at random on a typewriter keyboard
for an infinite amount of times will almost surely type a given text such as the complete works of
William Shakespearerdquo
Having taken away the condition of an infinite amount of time the paradox remains acceptable
(from the moment we are able to demonstrate that a finite amount of time is sufficient) However
such a long period of time is necessary that the original statement could be seen as an hyperbolic
discussion
We have seen that random phenomena require a program in light of an objective In the case
of the typing monkeys the program could include the elimination of duplicate pages (actually the
identical pages as we will see below) and the objective could consist in the conservation of ldquogoodrdquo
pages arranged in the right sequence
Applying Boltzmannrsquos statistics let us assume that the typewriter has m=30 keys (we can think of ldquoblindrdquo keys without any writing and all identical) and that we want to write a book of
only 106
letters (a thousand typed pages) as we have observed in paragraph 31 all the possible combinations are
13
The reader can find all the details regarding these various arguments on the web
Pier Maria Boria Thermodynamics amp life
C = nm = (10
6)30
= (10)180
In other words there are 10180
possible configurations
Let us assume that the monkeys are capable of striking 10 keyssec (skilled typistshellip) the
time necessary would be
t = 10180
x 106 10 = 10
185 sec
Since we can count 1016 seconds in a billion years it is also possible to say that the time
required will be
10185
1016
= 10169
billion years (giga-years)
(let us remember that the big-bang has an age of ldquoonlyrdquo 14 billion years)
In reality the situation is even ldquoworserdquo in fact this calculation (which is generally accepted)
is wrong because we cannot talk about only thirty objects (the letters punctuation marks spaces between lines etc) to be arranged in 10
6 positions otherwise in each of 10180 configurations
obtainable we would find empty spaces up to 106-30 in each configuration
It is necessary to postulate that there are 106 letters to be arranged like conceding that the
monkeys have to insert 106 objects ie 10
6 key strokes In other words it is necessary that n = m =
106 and in this case the formula of the combinations gives us an astronomical value
6106 )10(===
mm mnC combinations
At a rhythm of 10 key strokes sec the time corresponds to
9899995005000616106 10sec101010)10(
6
equiv=sdotsdot=minust years
Figure 47 ndash Summary table of the probabilities according to Boltzmann
In realty the situation is even ldquoworserdquo still In fact in the calculation of the combinations duplicate configurations are not considered
(which necessarily must be considered as possible) in other words our monkeys could produce the same combinations several times (or two identical pages) anyway the duplications will be useless
in the compilation of our small book of only 106 letters
To this end we invoke chance (to attempt to appreciate the incidence of the repeating of
identical pages) and having constructed a Gaussian by arranging the frequency of identical pages we can reason as follows having produced all the astronomical combinations as above in the time
calculated (which we will call a cycle) the highest probability of identical pages is in pairs (which
Pier Maria Boria Thermodynamics amp life
29
we will assign the maximum position) then in threes and so on At infinity with a probability of
zero all the pages will be identical
It seems fair to presume that the standard deviation could be very large qualifying for a very
flat Gaussian and let us suppose that the pages to be rejected (one for the doubles two for the
triplets etc) are contained within the first standard deviation (as in Figure 48) then the duplicate pages to be thrown away would be about 68
Figure 48 ndash The postulated conditions (pages to be eliminated because they are duplicated equal
to the standard deviation) make 68 of the pages produced useless Iterating the cycle one could
consider the duplication of other pages however it can be demonstrated that the phenomenon
continues to imply finite times
How much does the required time increase to generalize we assume the length of a cycle to be of one unit and we identify with K the average cost of discarded pages (in the previous numerical
case K= 068) and then we observe Figure 49
Figure 49 ndash Having exhausted the first cycle identified by 1 the second of length K allows the
replacement of the duplicate pages produced in the first cycle the third of length K2 is used to
replace those produced in the second cycle and so on
The time necessary to complete the cycles required to eliminate the duplicates as they are produced will be given by the sum
suminfin
=0n
nK
which constitutes a geometric series
The Mathematical Analysis teaches us that such a series converges for 1ltK as is confirmed
in our case where it takes on the value 068
KS
minus=
1
1 and if K = 068 gives 1253
6801
1=
minus=S
Pier Maria Boria Thermodynamics amp life
30
Therefore multiplying by 3125 the time dedicated to complete a cycle (317middot105999989 billion
years) for the hypothesis made we also eliminate all the duplicate pages of our little book of 106
key strokes
Changing the value of K (always lt1) one obtains different multipliers but always of a finite
value let the reader imagine the time necessary to type all of Shakespearersquos works It must be highlighted that the monkey operation to be considered a success requires the
intervention of external intelligence capable of selecting the useful pages (like thought by Theory of
Information) and ordering them in the right sequence to obtain a final legible manuscript this
obvious necessity implies that negative entropy be introduced into the system as covered at the
beginning this is like a living being taking the trouble to ldquoput in orderrdquo otherwise the ldquopurely
randomrdquo work would be entirely useless because it will exclusively produce positive entropy
All experiments attempted by man with the goal of demonstrating the random production of
complex molecules (first building blocks of living organisms) have the defect of requiring an a
priori living system like man to arrange this production
When later chaotic physical-chemical conditions are created (temperature pressure
methane electrical arching etc) hoping to obtain that which Thermodynamics does not permit the
inventors of the moto perpetuo come to mind who never give up
The research on the ldquoprimordial souprdquo belongs to this type of experimentation a battle horse
of the followers of the ldquomaitre agrave penserrdquo of the last century and which regard in particular the laboratory experiments of Stanley Miller the goal of his research of a physical-chemical nature
was to recreate life it was an understandable but too ambitious of a project for a researcher The result was absolutely negative (Miller himself recognized it) however this last piece of information
is only whispered in scientific circles so that we still find genuine touts who speak with enthusiastic coram populo of the primordial soup and its miraculous effects14 with a self-assurance
that is truly shameful
45 CONCLUSION
On 4 July 2007 at the London Kinetics Museum a serious presentation of a perpetual motion
machine was scheduled a machine capable of supplying the user with a power greater than that
absorbed ldquoObviouslyrdquo the presentation was postponed due to ldquoa technical problemrdquo15
It would appear impossible but advocates convinced of such a motion exist and many
inventors submit patent after patent even though still in illo tempore Max Planck declared himself
to be contrary to such a possibility which violates the principles of Thermodynamics
Based on the reasoning we have developed regarding entropy probability and chance the
violation of such principles is implicit even in the attempts to obtain living organisms in a
laboratory (characterized as we have seen as being producers of negative entropy) and as such a
strong analogy can be seen between the advocates of perpetual motion and those aspiring to create
life
1 The correct application of Boltzmannrsquos statistics a phenomenon for which we call on
probability demonstrates that combinations of large numbers of particles to the point of generating complex organisms require very long periods of time in comparison the age of
the universe is but the blink of an eye
2 The probabilities take on the largest numbers in correspondence with the most disordered
configurations
14
From ldquoCorriere della Serardquo october 2008 ldquoLa vita sulla Terra Cominciograve nei vulcani con un innesco chimicordquo 15
-Source Wikipedia
Pier Maria Boria Thermodynamics amp life
3 The most ordered combinations are those which characterize organic structures and the action
of an intelligent being is necessary to select order and conserve in time the favorable
combinations
4 The phrase ldquochance phenomenonrdquo is somewhat less intuitive than what ldquocommon senserdquo
would suggest In fact the Gaussian perspective implies that such phenomena are necessarily
associated with a program this program implies the existence of an objective around which
we have an increased concentration of events
5 In every case it is necessary to postulate the existence of an intelligent design without which
the configurations and the favorable events constitute events without any functional link
between themselves
6 The existence of life as a producer of negative entropy on a continuous basis (not cyclical) is a fact visible with our own eyes
All this leads us to support the existence of a Co-ordinating Entity which possesses life ldquoa
priorirdquo and which is capable of transmitting it to animals (animalis homo included) and vegetation It can be noted that the two living systems animal and vegetable complement each other in the
sense that the design requires that emissions from the first (CO2) are the nutrients for the second and the byproducts of the second (O2) are essential for the first the carbon and oxygen cycles look
like they have been designed According to the author there is only one explanation we are in the presence of the greatest
Design Physicist of all times God the Creator
This is what we call Him as Christians while Israelites call Him Jehovah the Ishmaelites
Allah the Masons GADU (Great Architect of the Universe) etc
In other terms
the Creation is a thermodynamic necessity
Amen
Pier Maria Boria Thermodynamics amp life
function still applies the probability curve will flatten itself maintaining the essential
characteristics in particular the two tails which will tend towards a tangent with the abscissa
tending towards infinity a maximum point a point of inflection and the other characteristics
illustrated in Figure 45
Figure 45 ndash Typical characteristics of a normalized Gaussian
Supposing once more that the Gauss function still applies it would be logical to expect a distribution with a curve that is so flat that it will be difficult to see a maximum point corresponding
to the center of the target it will be necessary to fire enough shots so as to occupy every position on the abscissa and to have hit with 100 certainty the bullrsquos-eye
This implies that everything is possible as long as an infinite number of shots are available
(using rhetorical language)
42 SOME PROPERTIES OF RANDOM EVENTS
The perplexities regarding the applicability of chance as referred to the blind sharpshooter
depend on the fact that the Gaussian assumes that programming has been applied to reach an
objective which implies that the operator is conscious of the objective an element which in this
case is absent
Both the existence of a program (the sharpshooter sets out to hit the bullrsquos-eye) and the
existence of an objective (the card with circles) appear to be essential to be able to talk about
chance
Another example let us imagine a machine programmed to produce a certain mechanical
piece the program is the design of the piece written in machine language and the objective is the production of the piece In mass production we will find that it is the case that despite the work
conditions being maintained the same each piece will be different to the other to the point that the pieces which exceed the tolerances (which would not allow them to be interchangeable) will be
rejected Innumerable examples could be presented identifying in every case these two characteristics
a program and an objective Statistics also operate in reverse from the measurement of a group of subjects it creates a bar
chart its envelope will be the curve of the random distribution It will give us the average of the values measured if the curve is symmetrical it will tell us that the phenomenon is not influenced by
systematic causes further it will tell us the value of the standard deviation etc
Pier Maria Boria Thermodynamics amp life
26
To fix this thought in our heads let us suppose that we want to study the average height of a
population of people who are male we make many measurements on many subjects creating bars
for every centimeter we will obtain a graph similar to Figure 46
Figure 46 ndash A practical application the Gaussian deduced from experimental measurements for
statistical purposes
In this statistical application where are the program and objective They are there they are
there they were contained in the information which the people naturally had at conception a
matter of genes and of DNA (an observation coherent with ldquoThe Kid Equationrdquo See the
ldquoIntroduction to Hyperspacerdquo12
)
These considerations lead us to think that the meaning of the word ldquochancerdquo commonly given
does not make sense that ldquochancerdquo does not exist and lead us to suspect that Anatole France had an
inspired guess when he said ldquochance is Godrsquos pseudonym when He does not want to sign his
namerdquo
This strongly agrees with what illustrious philosophers have been confirming for centuries
ldquoDeus absconditus estrdquo (Is XLV XV)
12
In our first volume ldquoCaro amico miohelliprdquo ndash Ed Pagine ndash 2010 In our second volume (ldquoVerba volant eqvuationes
manentrdquo) other considerations about a fundamental theorem of Genetics the Hardy Weinberg theorem
Pier Maria Boria Thermodynamics amp life
27
43 CHANCE amp PROBABILITY
We can now summarize some salient functions of Boltzmann and Gauss
Boltzmann
1 Deals with probability regarding the characteristics that can be assumed by many identical particles having a certain number of positions available (Dirac and Fermi deal
with particles which are distinguishable but the correct reference in our observations are the identical particles)
2 The function presents a maximum and aesthetically looks like a Gaussian but it is not symmetrical
3 It has only a single asymptote to the right of the maximum and its minimum at infinity coincides with zero the origin of the reference system
4 It is normalized so that the area subtended represents the total probability of 100
Gauss
1 Deals with chance and is applicable when an objective exists that is defined by a
program
2 The phenomenon ldquopurely by chancerdquo is represented by a curve that is symmetrical
about the axis x=0
3 The Gaussian has a maximum and no minimum at infinity
4 It possesses two asymptotes one to the right and one to the left of the maximum
5 Well defined values of probability can be associated with multiples of the standard deviation
6 It is normalized as for Boltzmannrsquos
44 THE EDDINGTONrsquoS PARADOX13
Eddingtonrsquos famous ldquoInfinite monkey theoremrdquo can be counted amongst the most discussed
paradoxes for the fact that it is often quoted by so called ldquoscientific popularizersrdquo The original assertion states ldquohellipa monkey hitting keys at random on a typewriter keyboard
for an infinite amount of times will almost surely type a given text such as the complete works of
William Shakespearerdquo
Having taken away the condition of an infinite amount of time the paradox remains acceptable
(from the moment we are able to demonstrate that a finite amount of time is sufficient) However
such a long period of time is necessary that the original statement could be seen as an hyperbolic
discussion
We have seen that random phenomena require a program in light of an objective In the case
of the typing monkeys the program could include the elimination of duplicate pages (actually the
identical pages as we will see below) and the objective could consist in the conservation of ldquogoodrdquo
pages arranged in the right sequence
Applying Boltzmannrsquos statistics let us assume that the typewriter has m=30 keys (we can think of ldquoblindrdquo keys without any writing and all identical) and that we want to write a book of
only 106
letters (a thousand typed pages) as we have observed in paragraph 31 all the possible combinations are
13
The reader can find all the details regarding these various arguments on the web
Pier Maria Boria Thermodynamics amp life
C = nm = (10
6)30
= (10)180
In other words there are 10180
possible configurations
Let us assume that the monkeys are capable of striking 10 keyssec (skilled typistshellip) the
time necessary would be
t = 10180
x 106 10 = 10
185 sec
Since we can count 1016 seconds in a billion years it is also possible to say that the time
required will be
10185
1016
= 10169
billion years (giga-years)
(let us remember that the big-bang has an age of ldquoonlyrdquo 14 billion years)
In reality the situation is even ldquoworserdquo in fact this calculation (which is generally accepted)
is wrong because we cannot talk about only thirty objects (the letters punctuation marks spaces between lines etc) to be arranged in 10
6 positions otherwise in each of 10180 configurations
obtainable we would find empty spaces up to 106-30 in each configuration
It is necessary to postulate that there are 106 letters to be arranged like conceding that the
monkeys have to insert 106 objects ie 10
6 key strokes In other words it is necessary that n = m =
106 and in this case the formula of the combinations gives us an astronomical value
6106 )10(===
mm mnC combinations
At a rhythm of 10 key strokes sec the time corresponds to
9899995005000616106 10sec101010)10(
6
equiv=sdotsdot=minust years
Figure 47 ndash Summary table of the probabilities according to Boltzmann
In realty the situation is even ldquoworserdquo still In fact in the calculation of the combinations duplicate configurations are not considered
(which necessarily must be considered as possible) in other words our monkeys could produce the same combinations several times (or two identical pages) anyway the duplications will be useless
in the compilation of our small book of only 106 letters
To this end we invoke chance (to attempt to appreciate the incidence of the repeating of
identical pages) and having constructed a Gaussian by arranging the frequency of identical pages we can reason as follows having produced all the astronomical combinations as above in the time
calculated (which we will call a cycle) the highest probability of identical pages is in pairs (which
Pier Maria Boria Thermodynamics amp life
29
we will assign the maximum position) then in threes and so on At infinity with a probability of
zero all the pages will be identical
It seems fair to presume that the standard deviation could be very large qualifying for a very
flat Gaussian and let us suppose that the pages to be rejected (one for the doubles two for the
triplets etc) are contained within the first standard deviation (as in Figure 48) then the duplicate pages to be thrown away would be about 68
Figure 48 ndash The postulated conditions (pages to be eliminated because they are duplicated equal
to the standard deviation) make 68 of the pages produced useless Iterating the cycle one could
consider the duplication of other pages however it can be demonstrated that the phenomenon
continues to imply finite times
How much does the required time increase to generalize we assume the length of a cycle to be of one unit and we identify with K the average cost of discarded pages (in the previous numerical
case K= 068) and then we observe Figure 49
Figure 49 ndash Having exhausted the first cycle identified by 1 the second of length K allows the
replacement of the duplicate pages produced in the first cycle the third of length K2 is used to
replace those produced in the second cycle and so on
The time necessary to complete the cycles required to eliminate the duplicates as they are produced will be given by the sum
suminfin
=0n
nK
which constitutes a geometric series
The Mathematical Analysis teaches us that such a series converges for 1ltK as is confirmed
in our case where it takes on the value 068
KS
minus=
1
1 and if K = 068 gives 1253
6801
1=
minus=S
Pier Maria Boria Thermodynamics amp life
30
Therefore multiplying by 3125 the time dedicated to complete a cycle (317middot105999989 billion
years) for the hypothesis made we also eliminate all the duplicate pages of our little book of 106
key strokes
Changing the value of K (always lt1) one obtains different multipliers but always of a finite
value let the reader imagine the time necessary to type all of Shakespearersquos works It must be highlighted that the monkey operation to be considered a success requires the
intervention of external intelligence capable of selecting the useful pages (like thought by Theory of
Information) and ordering them in the right sequence to obtain a final legible manuscript this
obvious necessity implies that negative entropy be introduced into the system as covered at the
beginning this is like a living being taking the trouble to ldquoput in orderrdquo otherwise the ldquopurely
randomrdquo work would be entirely useless because it will exclusively produce positive entropy
All experiments attempted by man with the goal of demonstrating the random production of
complex molecules (first building blocks of living organisms) have the defect of requiring an a
priori living system like man to arrange this production
When later chaotic physical-chemical conditions are created (temperature pressure
methane electrical arching etc) hoping to obtain that which Thermodynamics does not permit the
inventors of the moto perpetuo come to mind who never give up
The research on the ldquoprimordial souprdquo belongs to this type of experimentation a battle horse
of the followers of the ldquomaitre agrave penserrdquo of the last century and which regard in particular the laboratory experiments of Stanley Miller the goal of his research of a physical-chemical nature
was to recreate life it was an understandable but too ambitious of a project for a researcher The result was absolutely negative (Miller himself recognized it) however this last piece of information
is only whispered in scientific circles so that we still find genuine touts who speak with enthusiastic coram populo of the primordial soup and its miraculous effects14 with a self-assurance
that is truly shameful
45 CONCLUSION
On 4 July 2007 at the London Kinetics Museum a serious presentation of a perpetual motion
machine was scheduled a machine capable of supplying the user with a power greater than that
absorbed ldquoObviouslyrdquo the presentation was postponed due to ldquoa technical problemrdquo15
It would appear impossible but advocates convinced of such a motion exist and many
inventors submit patent after patent even though still in illo tempore Max Planck declared himself
to be contrary to such a possibility which violates the principles of Thermodynamics
Based on the reasoning we have developed regarding entropy probability and chance the
violation of such principles is implicit even in the attempts to obtain living organisms in a
laboratory (characterized as we have seen as being producers of negative entropy) and as such a
strong analogy can be seen between the advocates of perpetual motion and those aspiring to create
life
1 The correct application of Boltzmannrsquos statistics a phenomenon for which we call on
probability demonstrates that combinations of large numbers of particles to the point of generating complex organisms require very long periods of time in comparison the age of
the universe is but the blink of an eye
2 The probabilities take on the largest numbers in correspondence with the most disordered
configurations
14
From ldquoCorriere della Serardquo october 2008 ldquoLa vita sulla Terra Cominciograve nei vulcani con un innesco chimicordquo 15
-Source Wikipedia
Pier Maria Boria Thermodynamics amp life
3 The most ordered combinations are those which characterize organic structures and the action
of an intelligent being is necessary to select order and conserve in time the favorable
combinations
4 The phrase ldquochance phenomenonrdquo is somewhat less intuitive than what ldquocommon senserdquo
would suggest In fact the Gaussian perspective implies that such phenomena are necessarily
associated with a program this program implies the existence of an objective around which
we have an increased concentration of events
5 In every case it is necessary to postulate the existence of an intelligent design without which
the configurations and the favorable events constitute events without any functional link
between themselves
6 The existence of life as a producer of negative entropy on a continuous basis (not cyclical) is a fact visible with our own eyes
All this leads us to support the existence of a Co-ordinating Entity which possesses life ldquoa
priorirdquo and which is capable of transmitting it to animals (animalis homo included) and vegetation It can be noted that the two living systems animal and vegetable complement each other in the
sense that the design requires that emissions from the first (CO2) are the nutrients for the second and the byproducts of the second (O2) are essential for the first the carbon and oxygen cycles look
like they have been designed According to the author there is only one explanation we are in the presence of the greatest
Design Physicist of all times God the Creator
This is what we call Him as Christians while Israelites call Him Jehovah the Ishmaelites
Allah the Masons GADU (Great Architect of the Universe) etc
In other terms
the Creation is a thermodynamic necessity
Amen
Pier Maria Boria Thermodynamics amp life
26
To fix this thought in our heads let us suppose that we want to study the average height of a
population of people who are male we make many measurements on many subjects creating bars
for every centimeter we will obtain a graph similar to Figure 46
Figure 46 ndash A practical application the Gaussian deduced from experimental measurements for
statistical purposes
In this statistical application where are the program and objective They are there they are
there they were contained in the information which the people naturally had at conception a
matter of genes and of DNA (an observation coherent with ldquoThe Kid Equationrdquo See the
ldquoIntroduction to Hyperspacerdquo12
)
These considerations lead us to think that the meaning of the word ldquochancerdquo commonly given
does not make sense that ldquochancerdquo does not exist and lead us to suspect that Anatole France had an
inspired guess when he said ldquochance is Godrsquos pseudonym when He does not want to sign his
namerdquo
This strongly agrees with what illustrious philosophers have been confirming for centuries
ldquoDeus absconditus estrdquo (Is XLV XV)
12
In our first volume ldquoCaro amico miohelliprdquo ndash Ed Pagine ndash 2010 In our second volume (ldquoVerba volant eqvuationes
manentrdquo) other considerations about a fundamental theorem of Genetics the Hardy Weinberg theorem
Pier Maria Boria Thermodynamics amp life
27
43 CHANCE amp PROBABILITY
We can now summarize some salient functions of Boltzmann and Gauss
Boltzmann
1 Deals with probability regarding the characteristics that can be assumed by many identical particles having a certain number of positions available (Dirac and Fermi deal
with particles which are distinguishable but the correct reference in our observations are the identical particles)
2 The function presents a maximum and aesthetically looks like a Gaussian but it is not symmetrical
3 It has only a single asymptote to the right of the maximum and its minimum at infinity coincides with zero the origin of the reference system
4 It is normalized so that the area subtended represents the total probability of 100
Gauss
1 Deals with chance and is applicable when an objective exists that is defined by a
program
2 The phenomenon ldquopurely by chancerdquo is represented by a curve that is symmetrical
about the axis x=0
3 The Gaussian has a maximum and no minimum at infinity
4 It possesses two asymptotes one to the right and one to the left of the maximum
5 Well defined values of probability can be associated with multiples of the standard deviation
6 It is normalized as for Boltzmannrsquos
44 THE EDDINGTONrsquoS PARADOX13
Eddingtonrsquos famous ldquoInfinite monkey theoremrdquo can be counted amongst the most discussed
paradoxes for the fact that it is often quoted by so called ldquoscientific popularizersrdquo The original assertion states ldquohellipa monkey hitting keys at random on a typewriter keyboard
for an infinite amount of times will almost surely type a given text such as the complete works of
William Shakespearerdquo
Having taken away the condition of an infinite amount of time the paradox remains acceptable
(from the moment we are able to demonstrate that a finite amount of time is sufficient) However
such a long period of time is necessary that the original statement could be seen as an hyperbolic
discussion
We have seen that random phenomena require a program in light of an objective In the case
of the typing monkeys the program could include the elimination of duplicate pages (actually the
identical pages as we will see below) and the objective could consist in the conservation of ldquogoodrdquo
pages arranged in the right sequence
Applying Boltzmannrsquos statistics let us assume that the typewriter has m=30 keys (we can think of ldquoblindrdquo keys without any writing and all identical) and that we want to write a book of
only 106
letters (a thousand typed pages) as we have observed in paragraph 31 all the possible combinations are
13
The reader can find all the details regarding these various arguments on the web
Pier Maria Boria Thermodynamics amp life
C = nm = (10
6)30
= (10)180
In other words there are 10180
possible configurations
Let us assume that the monkeys are capable of striking 10 keyssec (skilled typistshellip) the
time necessary would be
t = 10180
x 106 10 = 10
185 sec
Since we can count 1016 seconds in a billion years it is also possible to say that the time
required will be
10185
1016
= 10169
billion years (giga-years)
(let us remember that the big-bang has an age of ldquoonlyrdquo 14 billion years)
In reality the situation is even ldquoworserdquo in fact this calculation (which is generally accepted)
is wrong because we cannot talk about only thirty objects (the letters punctuation marks spaces between lines etc) to be arranged in 10
6 positions otherwise in each of 10180 configurations
obtainable we would find empty spaces up to 106-30 in each configuration
It is necessary to postulate that there are 106 letters to be arranged like conceding that the
monkeys have to insert 106 objects ie 10
6 key strokes In other words it is necessary that n = m =
106 and in this case the formula of the combinations gives us an astronomical value
6106 )10(===
mm mnC combinations
At a rhythm of 10 key strokes sec the time corresponds to
9899995005000616106 10sec101010)10(
6
equiv=sdotsdot=minust years
Figure 47 ndash Summary table of the probabilities according to Boltzmann
In realty the situation is even ldquoworserdquo still In fact in the calculation of the combinations duplicate configurations are not considered
(which necessarily must be considered as possible) in other words our monkeys could produce the same combinations several times (or two identical pages) anyway the duplications will be useless
in the compilation of our small book of only 106 letters
To this end we invoke chance (to attempt to appreciate the incidence of the repeating of
identical pages) and having constructed a Gaussian by arranging the frequency of identical pages we can reason as follows having produced all the astronomical combinations as above in the time
calculated (which we will call a cycle) the highest probability of identical pages is in pairs (which
Pier Maria Boria Thermodynamics amp life
29
we will assign the maximum position) then in threes and so on At infinity with a probability of
zero all the pages will be identical
It seems fair to presume that the standard deviation could be very large qualifying for a very
flat Gaussian and let us suppose that the pages to be rejected (one for the doubles two for the
triplets etc) are contained within the first standard deviation (as in Figure 48) then the duplicate pages to be thrown away would be about 68
Figure 48 ndash The postulated conditions (pages to be eliminated because they are duplicated equal
to the standard deviation) make 68 of the pages produced useless Iterating the cycle one could
consider the duplication of other pages however it can be demonstrated that the phenomenon
continues to imply finite times
How much does the required time increase to generalize we assume the length of a cycle to be of one unit and we identify with K the average cost of discarded pages (in the previous numerical
case K= 068) and then we observe Figure 49
Figure 49 ndash Having exhausted the first cycle identified by 1 the second of length K allows the
replacement of the duplicate pages produced in the first cycle the third of length K2 is used to
replace those produced in the second cycle and so on
The time necessary to complete the cycles required to eliminate the duplicates as they are produced will be given by the sum
suminfin
=0n
nK
which constitutes a geometric series
The Mathematical Analysis teaches us that such a series converges for 1ltK as is confirmed
in our case where it takes on the value 068
KS
minus=
1
1 and if K = 068 gives 1253
6801
1=
minus=S
Pier Maria Boria Thermodynamics amp life
30
Therefore multiplying by 3125 the time dedicated to complete a cycle (317middot105999989 billion
years) for the hypothesis made we also eliminate all the duplicate pages of our little book of 106
key strokes
Changing the value of K (always lt1) one obtains different multipliers but always of a finite
value let the reader imagine the time necessary to type all of Shakespearersquos works It must be highlighted that the monkey operation to be considered a success requires the
intervention of external intelligence capable of selecting the useful pages (like thought by Theory of
Information) and ordering them in the right sequence to obtain a final legible manuscript this
obvious necessity implies that negative entropy be introduced into the system as covered at the
beginning this is like a living being taking the trouble to ldquoput in orderrdquo otherwise the ldquopurely
randomrdquo work would be entirely useless because it will exclusively produce positive entropy
All experiments attempted by man with the goal of demonstrating the random production of
complex molecules (first building blocks of living organisms) have the defect of requiring an a
priori living system like man to arrange this production
When later chaotic physical-chemical conditions are created (temperature pressure
methane electrical arching etc) hoping to obtain that which Thermodynamics does not permit the
inventors of the moto perpetuo come to mind who never give up
The research on the ldquoprimordial souprdquo belongs to this type of experimentation a battle horse
of the followers of the ldquomaitre agrave penserrdquo of the last century and which regard in particular the laboratory experiments of Stanley Miller the goal of his research of a physical-chemical nature
was to recreate life it was an understandable but too ambitious of a project for a researcher The result was absolutely negative (Miller himself recognized it) however this last piece of information
is only whispered in scientific circles so that we still find genuine touts who speak with enthusiastic coram populo of the primordial soup and its miraculous effects14 with a self-assurance
that is truly shameful
45 CONCLUSION
On 4 July 2007 at the London Kinetics Museum a serious presentation of a perpetual motion
machine was scheduled a machine capable of supplying the user with a power greater than that
absorbed ldquoObviouslyrdquo the presentation was postponed due to ldquoa technical problemrdquo15
It would appear impossible but advocates convinced of such a motion exist and many
inventors submit patent after patent even though still in illo tempore Max Planck declared himself
to be contrary to such a possibility which violates the principles of Thermodynamics
Based on the reasoning we have developed regarding entropy probability and chance the
violation of such principles is implicit even in the attempts to obtain living organisms in a
laboratory (characterized as we have seen as being producers of negative entropy) and as such a
strong analogy can be seen between the advocates of perpetual motion and those aspiring to create
life
1 The correct application of Boltzmannrsquos statistics a phenomenon for which we call on
probability demonstrates that combinations of large numbers of particles to the point of generating complex organisms require very long periods of time in comparison the age of
the universe is but the blink of an eye
2 The probabilities take on the largest numbers in correspondence with the most disordered
configurations
14
From ldquoCorriere della Serardquo october 2008 ldquoLa vita sulla Terra Cominciograve nei vulcani con un innesco chimicordquo 15
-Source Wikipedia
Pier Maria Boria Thermodynamics amp life
3 The most ordered combinations are those which characterize organic structures and the action
of an intelligent being is necessary to select order and conserve in time the favorable
combinations
4 The phrase ldquochance phenomenonrdquo is somewhat less intuitive than what ldquocommon senserdquo
would suggest In fact the Gaussian perspective implies that such phenomena are necessarily
associated with a program this program implies the existence of an objective around which
we have an increased concentration of events
5 In every case it is necessary to postulate the existence of an intelligent design without which
the configurations and the favorable events constitute events without any functional link
between themselves
6 The existence of life as a producer of negative entropy on a continuous basis (not cyclical) is a fact visible with our own eyes
All this leads us to support the existence of a Co-ordinating Entity which possesses life ldquoa
priorirdquo and which is capable of transmitting it to animals (animalis homo included) and vegetation It can be noted that the two living systems animal and vegetable complement each other in the
sense that the design requires that emissions from the first (CO2) are the nutrients for the second and the byproducts of the second (O2) are essential for the first the carbon and oxygen cycles look
like they have been designed According to the author there is only one explanation we are in the presence of the greatest
Design Physicist of all times God the Creator
This is what we call Him as Christians while Israelites call Him Jehovah the Ishmaelites
Allah the Masons GADU (Great Architect of the Universe) etc
In other terms
the Creation is a thermodynamic necessity
Amen
Pier Maria Boria Thermodynamics amp life
27
43 CHANCE amp PROBABILITY
We can now summarize some salient functions of Boltzmann and Gauss
Boltzmann
1 Deals with probability regarding the characteristics that can be assumed by many identical particles having a certain number of positions available (Dirac and Fermi deal
with particles which are distinguishable but the correct reference in our observations are the identical particles)
2 The function presents a maximum and aesthetically looks like a Gaussian but it is not symmetrical
3 It has only a single asymptote to the right of the maximum and its minimum at infinity coincides with zero the origin of the reference system
4 It is normalized so that the area subtended represents the total probability of 100
Gauss
1 Deals with chance and is applicable when an objective exists that is defined by a
program
2 The phenomenon ldquopurely by chancerdquo is represented by a curve that is symmetrical
about the axis x=0
3 The Gaussian has a maximum and no minimum at infinity
4 It possesses two asymptotes one to the right and one to the left of the maximum
5 Well defined values of probability can be associated with multiples of the standard deviation
6 It is normalized as for Boltzmannrsquos
44 THE EDDINGTONrsquoS PARADOX13
Eddingtonrsquos famous ldquoInfinite monkey theoremrdquo can be counted amongst the most discussed
paradoxes for the fact that it is often quoted by so called ldquoscientific popularizersrdquo The original assertion states ldquohellipa monkey hitting keys at random on a typewriter keyboard
for an infinite amount of times will almost surely type a given text such as the complete works of
William Shakespearerdquo
Having taken away the condition of an infinite amount of time the paradox remains acceptable
(from the moment we are able to demonstrate that a finite amount of time is sufficient) However
such a long period of time is necessary that the original statement could be seen as an hyperbolic
discussion
We have seen that random phenomena require a program in light of an objective In the case
of the typing monkeys the program could include the elimination of duplicate pages (actually the
identical pages as we will see below) and the objective could consist in the conservation of ldquogoodrdquo
pages arranged in the right sequence
Applying Boltzmannrsquos statistics let us assume that the typewriter has m=30 keys (we can think of ldquoblindrdquo keys without any writing and all identical) and that we want to write a book of
only 106
letters (a thousand typed pages) as we have observed in paragraph 31 all the possible combinations are
13
The reader can find all the details regarding these various arguments on the web
Pier Maria Boria Thermodynamics amp life
C = nm = (10
6)30
= (10)180
In other words there are 10180
possible configurations
Let us assume that the monkeys are capable of striking 10 keyssec (skilled typistshellip) the
time necessary would be
t = 10180
x 106 10 = 10
185 sec
Since we can count 1016 seconds in a billion years it is also possible to say that the time
required will be
10185
1016
= 10169
billion years (giga-years)
(let us remember that the big-bang has an age of ldquoonlyrdquo 14 billion years)
In reality the situation is even ldquoworserdquo in fact this calculation (which is generally accepted)
is wrong because we cannot talk about only thirty objects (the letters punctuation marks spaces between lines etc) to be arranged in 10
6 positions otherwise in each of 10180 configurations
obtainable we would find empty spaces up to 106-30 in each configuration
It is necessary to postulate that there are 106 letters to be arranged like conceding that the
monkeys have to insert 106 objects ie 10
6 key strokes In other words it is necessary that n = m =
106 and in this case the formula of the combinations gives us an astronomical value
6106 )10(===
mm mnC combinations
At a rhythm of 10 key strokes sec the time corresponds to
9899995005000616106 10sec101010)10(
6
equiv=sdotsdot=minust years
Figure 47 ndash Summary table of the probabilities according to Boltzmann
In realty the situation is even ldquoworserdquo still In fact in the calculation of the combinations duplicate configurations are not considered
(which necessarily must be considered as possible) in other words our monkeys could produce the same combinations several times (or two identical pages) anyway the duplications will be useless
in the compilation of our small book of only 106 letters
To this end we invoke chance (to attempt to appreciate the incidence of the repeating of
identical pages) and having constructed a Gaussian by arranging the frequency of identical pages we can reason as follows having produced all the astronomical combinations as above in the time
calculated (which we will call a cycle) the highest probability of identical pages is in pairs (which
Pier Maria Boria Thermodynamics amp life
29
we will assign the maximum position) then in threes and so on At infinity with a probability of
zero all the pages will be identical
It seems fair to presume that the standard deviation could be very large qualifying for a very
flat Gaussian and let us suppose that the pages to be rejected (one for the doubles two for the
triplets etc) are contained within the first standard deviation (as in Figure 48) then the duplicate pages to be thrown away would be about 68
Figure 48 ndash The postulated conditions (pages to be eliminated because they are duplicated equal
to the standard deviation) make 68 of the pages produced useless Iterating the cycle one could
consider the duplication of other pages however it can be demonstrated that the phenomenon
continues to imply finite times
How much does the required time increase to generalize we assume the length of a cycle to be of one unit and we identify with K the average cost of discarded pages (in the previous numerical
case K= 068) and then we observe Figure 49
Figure 49 ndash Having exhausted the first cycle identified by 1 the second of length K allows the
replacement of the duplicate pages produced in the first cycle the third of length K2 is used to
replace those produced in the second cycle and so on
The time necessary to complete the cycles required to eliminate the duplicates as they are produced will be given by the sum
suminfin
=0n
nK
which constitutes a geometric series
The Mathematical Analysis teaches us that such a series converges for 1ltK as is confirmed
in our case where it takes on the value 068
KS
minus=
1
1 and if K = 068 gives 1253
6801
1=
minus=S
Pier Maria Boria Thermodynamics amp life
30
Therefore multiplying by 3125 the time dedicated to complete a cycle (317middot105999989 billion
years) for the hypothesis made we also eliminate all the duplicate pages of our little book of 106
key strokes
Changing the value of K (always lt1) one obtains different multipliers but always of a finite
value let the reader imagine the time necessary to type all of Shakespearersquos works It must be highlighted that the monkey operation to be considered a success requires the
intervention of external intelligence capable of selecting the useful pages (like thought by Theory of
Information) and ordering them in the right sequence to obtain a final legible manuscript this
obvious necessity implies that negative entropy be introduced into the system as covered at the
beginning this is like a living being taking the trouble to ldquoput in orderrdquo otherwise the ldquopurely
randomrdquo work would be entirely useless because it will exclusively produce positive entropy
All experiments attempted by man with the goal of demonstrating the random production of
complex molecules (first building blocks of living organisms) have the defect of requiring an a
priori living system like man to arrange this production
When later chaotic physical-chemical conditions are created (temperature pressure
methane electrical arching etc) hoping to obtain that which Thermodynamics does not permit the
inventors of the moto perpetuo come to mind who never give up
The research on the ldquoprimordial souprdquo belongs to this type of experimentation a battle horse
of the followers of the ldquomaitre agrave penserrdquo of the last century and which regard in particular the laboratory experiments of Stanley Miller the goal of his research of a physical-chemical nature
was to recreate life it was an understandable but too ambitious of a project for a researcher The result was absolutely negative (Miller himself recognized it) however this last piece of information
is only whispered in scientific circles so that we still find genuine touts who speak with enthusiastic coram populo of the primordial soup and its miraculous effects14 with a self-assurance
that is truly shameful
45 CONCLUSION
On 4 July 2007 at the London Kinetics Museum a serious presentation of a perpetual motion
machine was scheduled a machine capable of supplying the user with a power greater than that
absorbed ldquoObviouslyrdquo the presentation was postponed due to ldquoa technical problemrdquo15
It would appear impossible but advocates convinced of such a motion exist and many
inventors submit patent after patent even though still in illo tempore Max Planck declared himself
to be contrary to such a possibility which violates the principles of Thermodynamics
Based on the reasoning we have developed regarding entropy probability and chance the
violation of such principles is implicit even in the attempts to obtain living organisms in a
laboratory (characterized as we have seen as being producers of negative entropy) and as such a
strong analogy can be seen between the advocates of perpetual motion and those aspiring to create
life
1 The correct application of Boltzmannrsquos statistics a phenomenon for which we call on
probability demonstrates that combinations of large numbers of particles to the point of generating complex organisms require very long periods of time in comparison the age of
the universe is but the blink of an eye
2 The probabilities take on the largest numbers in correspondence with the most disordered
configurations
14
From ldquoCorriere della Serardquo october 2008 ldquoLa vita sulla Terra Cominciograve nei vulcani con un innesco chimicordquo 15
-Source Wikipedia
Pier Maria Boria Thermodynamics amp life
3 The most ordered combinations are those which characterize organic structures and the action
of an intelligent being is necessary to select order and conserve in time the favorable
combinations
4 The phrase ldquochance phenomenonrdquo is somewhat less intuitive than what ldquocommon senserdquo
would suggest In fact the Gaussian perspective implies that such phenomena are necessarily
associated with a program this program implies the existence of an objective around which
we have an increased concentration of events
5 In every case it is necessary to postulate the existence of an intelligent design without which
the configurations and the favorable events constitute events without any functional link
between themselves
6 The existence of life as a producer of negative entropy on a continuous basis (not cyclical) is a fact visible with our own eyes
All this leads us to support the existence of a Co-ordinating Entity which possesses life ldquoa
priorirdquo and which is capable of transmitting it to animals (animalis homo included) and vegetation It can be noted that the two living systems animal and vegetable complement each other in the
sense that the design requires that emissions from the first (CO2) are the nutrients for the second and the byproducts of the second (O2) are essential for the first the carbon and oxygen cycles look
like they have been designed According to the author there is only one explanation we are in the presence of the greatest
Design Physicist of all times God the Creator
This is what we call Him as Christians while Israelites call Him Jehovah the Ishmaelites
Allah the Masons GADU (Great Architect of the Universe) etc
In other terms
the Creation is a thermodynamic necessity
Amen
Pier Maria Boria Thermodynamics amp life
C = nm = (10
6)30
= (10)180
In other words there are 10180
possible configurations
Let us assume that the monkeys are capable of striking 10 keyssec (skilled typistshellip) the
time necessary would be
t = 10180
x 106 10 = 10
185 sec
Since we can count 1016 seconds in a billion years it is also possible to say that the time
required will be
10185
1016
= 10169
billion years (giga-years)
(let us remember that the big-bang has an age of ldquoonlyrdquo 14 billion years)
In reality the situation is even ldquoworserdquo in fact this calculation (which is generally accepted)
is wrong because we cannot talk about only thirty objects (the letters punctuation marks spaces between lines etc) to be arranged in 10
6 positions otherwise in each of 10180 configurations
obtainable we would find empty spaces up to 106-30 in each configuration
It is necessary to postulate that there are 106 letters to be arranged like conceding that the
monkeys have to insert 106 objects ie 10
6 key strokes In other words it is necessary that n = m =
106 and in this case the formula of the combinations gives us an astronomical value
6106 )10(===
mm mnC combinations
At a rhythm of 10 key strokes sec the time corresponds to
9899995005000616106 10sec101010)10(
6
equiv=sdotsdot=minust years
Figure 47 ndash Summary table of the probabilities according to Boltzmann
In realty the situation is even ldquoworserdquo still In fact in the calculation of the combinations duplicate configurations are not considered
(which necessarily must be considered as possible) in other words our monkeys could produce the same combinations several times (or two identical pages) anyway the duplications will be useless
in the compilation of our small book of only 106 letters
To this end we invoke chance (to attempt to appreciate the incidence of the repeating of
identical pages) and having constructed a Gaussian by arranging the frequency of identical pages we can reason as follows having produced all the astronomical combinations as above in the time
calculated (which we will call a cycle) the highest probability of identical pages is in pairs (which
Pier Maria Boria Thermodynamics amp life
29
we will assign the maximum position) then in threes and so on At infinity with a probability of
zero all the pages will be identical
It seems fair to presume that the standard deviation could be very large qualifying for a very
flat Gaussian and let us suppose that the pages to be rejected (one for the doubles two for the
triplets etc) are contained within the first standard deviation (as in Figure 48) then the duplicate pages to be thrown away would be about 68
Figure 48 ndash The postulated conditions (pages to be eliminated because they are duplicated equal
to the standard deviation) make 68 of the pages produced useless Iterating the cycle one could
consider the duplication of other pages however it can be demonstrated that the phenomenon
continues to imply finite times
How much does the required time increase to generalize we assume the length of a cycle to be of one unit and we identify with K the average cost of discarded pages (in the previous numerical
case K= 068) and then we observe Figure 49
Figure 49 ndash Having exhausted the first cycle identified by 1 the second of length K allows the
replacement of the duplicate pages produced in the first cycle the third of length K2 is used to
replace those produced in the second cycle and so on
The time necessary to complete the cycles required to eliminate the duplicates as they are produced will be given by the sum
suminfin
=0n
nK
which constitutes a geometric series
The Mathematical Analysis teaches us that such a series converges for 1ltK as is confirmed
in our case where it takes on the value 068
KS
minus=
1
1 and if K = 068 gives 1253
6801
1=
minus=S
Pier Maria Boria Thermodynamics amp life
30
Therefore multiplying by 3125 the time dedicated to complete a cycle (317middot105999989 billion
years) for the hypothesis made we also eliminate all the duplicate pages of our little book of 106
key strokes
Changing the value of K (always lt1) one obtains different multipliers but always of a finite
value let the reader imagine the time necessary to type all of Shakespearersquos works It must be highlighted that the monkey operation to be considered a success requires the
intervention of external intelligence capable of selecting the useful pages (like thought by Theory of
Information) and ordering them in the right sequence to obtain a final legible manuscript this
obvious necessity implies that negative entropy be introduced into the system as covered at the
beginning this is like a living being taking the trouble to ldquoput in orderrdquo otherwise the ldquopurely
randomrdquo work would be entirely useless because it will exclusively produce positive entropy
All experiments attempted by man with the goal of demonstrating the random production of
complex molecules (first building blocks of living organisms) have the defect of requiring an a
priori living system like man to arrange this production
When later chaotic physical-chemical conditions are created (temperature pressure
methane electrical arching etc) hoping to obtain that which Thermodynamics does not permit the
inventors of the moto perpetuo come to mind who never give up
The research on the ldquoprimordial souprdquo belongs to this type of experimentation a battle horse
of the followers of the ldquomaitre agrave penserrdquo of the last century and which regard in particular the laboratory experiments of Stanley Miller the goal of his research of a physical-chemical nature
was to recreate life it was an understandable but too ambitious of a project for a researcher The result was absolutely negative (Miller himself recognized it) however this last piece of information
is only whispered in scientific circles so that we still find genuine touts who speak with enthusiastic coram populo of the primordial soup and its miraculous effects14 with a self-assurance
that is truly shameful
45 CONCLUSION
On 4 July 2007 at the London Kinetics Museum a serious presentation of a perpetual motion
machine was scheduled a machine capable of supplying the user with a power greater than that
absorbed ldquoObviouslyrdquo the presentation was postponed due to ldquoa technical problemrdquo15
It would appear impossible but advocates convinced of such a motion exist and many
inventors submit patent after patent even though still in illo tempore Max Planck declared himself
to be contrary to such a possibility which violates the principles of Thermodynamics
Based on the reasoning we have developed regarding entropy probability and chance the
violation of such principles is implicit even in the attempts to obtain living organisms in a
laboratory (characterized as we have seen as being producers of negative entropy) and as such a
strong analogy can be seen between the advocates of perpetual motion and those aspiring to create
life
1 The correct application of Boltzmannrsquos statistics a phenomenon for which we call on
probability demonstrates that combinations of large numbers of particles to the point of generating complex organisms require very long periods of time in comparison the age of
the universe is but the blink of an eye
2 The probabilities take on the largest numbers in correspondence with the most disordered
configurations
14
From ldquoCorriere della Serardquo october 2008 ldquoLa vita sulla Terra Cominciograve nei vulcani con un innesco chimicordquo 15
-Source Wikipedia
Pier Maria Boria Thermodynamics amp life
3 The most ordered combinations are those which characterize organic structures and the action
of an intelligent being is necessary to select order and conserve in time the favorable
combinations
4 The phrase ldquochance phenomenonrdquo is somewhat less intuitive than what ldquocommon senserdquo
would suggest In fact the Gaussian perspective implies that such phenomena are necessarily
associated with a program this program implies the existence of an objective around which
we have an increased concentration of events
5 In every case it is necessary to postulate the existence of an intelligent design without which
the configurations and the favorable events constitute events without any functional link
between themselves
6 The existence of life as a producer of negative entropy on a continuous basis (not cyclical) is a fact visible with our own eyes
All this leads us to support the existence of a Co-ordinating Entity which possesses life ldquoa
priorirdquo and which is capable of transmitting it to animals (animalis homo included) and vegetation It can be noted that the two living systems animal and vegetable complement each other in the
sense that the design requires that emissions from the first (CO2) are the nutrients for the second and the byproducts of the second (O2) are essential for the first the carbon and oxygen cycles look
like they have been designed According to the author there is only one explanation we are in the presence of the greatest
Design Physicist of all times God the Creator
This is what we call Him as Christians while Israelites call Him Jehovah the Ishmaelites
Allah the Masons GADU (Great Architect of the Universe) etc
In other terms
the Creation is a thermodynamic necessity
Amen
Pier Maria Boria Thermodynamics amp life
29
we will assign the maximum position) then in threes and so on At infinity with a probability of
zero all the pages will be identical
It seems fair to presume that the standard deviation could be very large qualifying for a very
flat Gaussian and let us suppose that the pages to be rejected (one for the doubles two for the
triplets etc) are contained within the first standard deviation (as in Figure 48) then the duplicate pages to be thrown away would be about 68
Figure 48 ndash The postulated conditions (pages to be eliminated because they are duplicated equal
to the standard deviation) make 68 of the pages produced useless Iterating the cycle one could
consider the duplication of other pages however it can be demonstrated that the phenomenon
continues to imply finite times
How much does the required time increase to generalize we assume the length of a cycle to be of one unit and we identify with K the average cost of discarded pages (in the previous numerical
case K= 068) and then we observe Figure 49
Figure 49 ndash Having exhausted the first cycle identified by 1 the second of length K allows the
replacement of the duplicate pages produced in the first cycle the third of length K2 is used to
replace those produced in the second cycle and so on
The time necessary to complete the cycles required to eliminate the duplicates as they are produced will be given by the sum
suminfin
=0n
nK
which constitutes a geometric series
The Mathematical Analysis teaches us that such a series converges for 1ltK as is confirmed
in our case where it takes on the value 068
KS
minus=
1
1 and if K = 068 gives 1253
6801
1=
minus=S
Pier Maria Boria Thermodynamics amp life
30
Therefore multiplying by 3125 the time dedicated to complete a cycle (317middot105999989 billion
years) for the hypothesis made we also eliminate all the duplicate pages of our little book of 106
key strokes
Changing the value of K (always lt1) one obtains different multipliers but always of a finite
value let the reader imagine the time necessary to type all of Shakespearersquos works It must be highlighted that the monkey operation to be considered a success requires the
intervention of external intelligence capable of selecting the useful pages (like thought by Theory of
Information) and ordering them in the right sequence to obtain a final legible manuscript this
obvious necessity implies that negative entropy be introduced into the system as covered at the
beginning this is like a living being taking the trouble to ldquoput in orderrdquo otherwise the ldquopurely
randomrdquo work would be entirely useless because it will exclusively produce positive entropy
All experiments attempted by man with the goal of demonstrating the random production of
complex molecules (first building blocks of living organisms) have the defect of requiring an a
priori living system like man to arrange this production
When later chaotic physical-chemical conditions are created (temperature pressure
methane electrical arching etc) hoping to obtain that which Thermodynamics does not permit the
inventors of the moto perpetuo come to mind who never give up
The research on the ldquoprimordial souprdquo belongs to this type of experimentation a battle horse
of the followers of the ldquomaitre agrave penserrdquo of the last century and which regard in particular the laboratory experiments of Stanley Miller the goal of his research of a physical-chemical nature
was to recreate life it was an understandable but too ambitious of a project for a researcher The result was absolutely negative (Miller himself recognized it) however this last piece of information
is only whispered in scientific circles so that we still find genuine touts who speak with enthusiastic coram populo of the primordial soup and its miraculous effects14 with a self-assurance
that is truly shameful
45 CONCLUSION
On 4 July 2007 at the London Kinetics Museum a serious presentation of a perpetual motion
machine was scheduled a machine capable of supplying the user with a power greater than that
absorbed ldquoObviouslyrdquo the presentation was postponed due to ldquoa technical problemrdquo15
It would appear impossible but advocates convinced of such a motion exist and many
inventors submit patent after patent even though still in illo tempore Max Planck declared himself
to be contrary to such a possibility which violates the principles of Thermodynamics
Based on the reasoning we have developed regarding entropy probability and chance the
violation of such principles is implicit even in the attempts to obtain living organisms in a
laboratory (characterized as we have seen as being producers of negative entropy) and as such a
strong analogy can be seen between the advocates of perpetual motion and those aspiring to create
life
1 The correct application of Boltzmannrsquos statistics a phenomenon for which we call on
probability demonstrates that combinations of large numbers of particles to the point of generating complex organisms require very long periods of time in comparison the age of
the universe is but the blink of an eye
2 The probabilities take on the largest numbers in correspondence with the most disordered
configurations
14
From ldquoCorriere della Serardquo october 2008 ldquoLa vita sulla Terra Cominciograve nei vulcani con un innesco chimicordquo 15
-Source Wikipedia
Pier Maria Boria Thermodynamics amp life
3 The most ordered combinations are those which characterize organic structures and the action
of an intelligent being is necessary to select order and conserve in time the favorable
combinations
4 The phrase ldquochance phenomenonrdquo is somewhat less intuitive than what ldquocommon senserdquo
would suggest In fact the Gaussian perspective implies that such phenomena are necessarily
associated with a program this program implies the existence of an objective around which
we have an increased concentration of events
5 In every case it is necessary to postulate the existence of an intelligent design without which
the configurations and the favorable events constitute events without any functional link
between themselves
6 The existence of life as a producer of negative entropy on a continuous basis (not cyclical) is a fact visible with our own eyes
All this leads us to support the existence of a Co-ordinating Entity which possesses life ldquoa
priorirdquo and which is capable of transmitting it to animals (animalis homo included) and vegetation It can be noted that the two living systems animal and vegetable complement each other in the
sense that the design requires that emissions from the first (CO2) are the nutrients for the second and the byproducts of the second (O2) are essential for the first the carbon and oxygen cycles look
like they have been designed According to the author there is only one explanation we are in the presence of the greatest
Design Physicist of all times God the Creator
This is what we call Him as Christians while Israelites call Him Jehovah the Ishmaelites
Allah the Masons GADU (Great Architect of the Universe) etc
In other terms
the Creation is a thermodynamic necessity
Amen
Pier Maria Boria Thermodynamics amp life
30
Therefore multiplying by 3125 the time dedicated to complete a cycle (317middot105999989 billion
years) for the hypothesis made we also eliminate all the duplicate pages of our little book of 106
key strokes
Changing the value of K (always lt1) one obtains different multipliers but always of a finite
value let the reader imagine the time necessary to type all of Shakespearersquos works It must be highlighted that the monkey operation to be considered a success requires the
intervention of external intelligence capable of selecting the useful pages (like thought by Theory of
Information) and ordering them in the right sequence to obtain a final legible manuscript this
obvious necessity implies that negative entropy be introduced into the system as covered at the
beginning this is like a living being taking the trouble to ldquoput in orderrdquo otherwise the ldquopurely
randomrdquo work would be entirely useless because it will exclusively produce positive entropy
All experiments attempted by man with the goal of demonstrating the random production of
complex molecules (first building blocks of living organisms) have the defect of requiring an a
priori living system like man to arrange this production
When later chaotic physical-chemical conditions are created (temperature pressure
methane electrical arching etc) hoping to obtain that which Thermodynamics does not permit the
inventors of the moto perpetuo come to mind who never give up
The research on the ldquoprimordial souprdquo belongs to this type of experimentation a battle horse
of the followers of the ldquomaitre agrave penserrdquo of the last century and which regard in particular the laboratory experiments of Stanley Miller the goal of his research of a physical-chemical nature
was to recreate life it was an understandable but too ambitious of a project for a researcher The result was absolutely negative (Miller himself recognized it) however this last piece of information
is only whispered in scientific circles so that we still find genuine touts who speak with enthusiastic coram populo of the primordial soup and its miraculous effects14 with a self-assurance
that is truly shameful
45 CONCLUSION
On 4 July 2007 at the London Kinetics Museum a serious presentation of a perpetual motion
machine was scheduled a machine capable of supplying the user with a power greater than that
absorbed ldquoObviouslyrdquo the presentation was postponed due to ldquoa technical problemrdquo15
It would appear impossible but advocates convinced of such a motion exist and many
inventors submit patent after patent even though still in illo tempore Max Planck declared himself
to be contrary to such a possibility which violates the principles of Thermodynamics
Based on the reasoning we have developed regarding entropy probability and chance the
violation of such principles is implicit even in the attempts to obtain living organisms in a
laboratory (characterized as we have seen as being producers of negative entropy) and as such a
strong analogy can be seen between the advocates of perpetual motion and those aspiring to create
life
1 The correct application of Boltzmannrsquos statistics a phenomenon for which we call on
probability demonstrates that combinations of large numbers of particles to the point of generating complex organisms require very long periods of time in comparison the age of
the universe is but the blink of an eye
2 The probabilities take on the largest numbers in correspondence with the most disordered
configurations
14
From ldquoCorriere della Serardquo october 2008 ldquoLa vita sulla Terra Cominciograve nei vulcani con un innesco chimicordquo 15
-Source Wikipedia
Pier Maria Boria Thermodynamics amp life
3 The most ordered combinations are those which characterize organic structures and the action
of an intelligent being is necessary to select order and conserve in time the favorable
combinations
4 The phrase ldquochance phenomenonrdquo is somewhat less intuitive than what ldquocommon senserdquo
would suggest In fact the Gaussian perspective implies that such phenomena are necessarily
associated with a program this program implies the existence of an objective around which
we have an increased concentration of events
5 In every case it is necessary to postulate the existence of an intelligent design without which
the configurations and the favorable events constitute events without any functional link
between themselves
6 The existence of life as a producer of negative entropy on a continuous basis (not cyclical) is a fact visible with our own eyes
All this leads us to support the existence of a Co-ordinating Entity which possesses life ldquoa
priorirdquo and which is capable of transmitting it to animals (animalis homo included) and vegetation It can be noted that the two living systems animal and vegetable complement each other in the
sense that the design requires that emissions from the first (CO2) are the nutrients for the second and the byproducts of the second (O2) are essential for the first the carbon and oxygen cycles look
like they have been designed According to the author there is only one explanation we are in the presence of the greatest
Design Physicist of all times God the Creator
This is what we call Him as Christians while Israelites call Him Jehovah the Ishmaelites
Allah the Masons GADU (Great Architect of the Universe) etc
In other terms
the Creation is a thermodynamic necessity
Amen
Pier Maria Boria Thermodynamics amp life
3 The most ordered combinations are those which characterize organic structures and the action
of an intelligent being is necessary to select order and conserve in time the favorable
combinations
4 The phrase ldquochance phenomenonrdquo is somewhat less intuitive than what ldquocommon senserdquo
would suggest In fact the Gaussian perspective implies that such phenomena are necessarily
associated with a program this program implies the existence of an objective around which
we have an increased concentration of events
5 In every case it is necessary to postulate the existence of an intelligent design without which
the configurations and the favorable events constitute events without any functional link
between themselves
6 The existence of life as a producer of negative entropy on a continuous basis (not cyclical) is a fact visible with our own eyes
All this leads us to support the existence of a Co-ordinating Entity which possesses life ldquoa
priorirdquo and which is capable of transmitting it to animals (animalis homo included) and vegetation It can be noted that the two living systems animal and vegetable complement each other in the
sense that the design requires that emissions from the first (CO2) are the nutrients for the second and the byproducts of the second (O2) are essential for the first the carbon and oxygen cycles look
like they have been designed According to the author there is only one explanation we are in the presence of the greatest
Design Physicist of all times God the Creator
This is what we call Him as Christians while Israelites call Him Jehovah the Ishmaelites
Allah the Masons GADU (Great Architect of the Universe) etc
In other terms
the Creation is a thermodynamic necessity
Amen