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ORIGINAL ARTICLE
Hyper-gourd theory: solving simultaneously the mysteriesin particle physics, biology, oncology, neurology, economics,and cosmology
Ken Naitoh
Received: 26 March 2012 / Accepted: 23 August 2012 / Published online: 21 September 2012
� ISAROB 2012
Abstract The inevitability of various particle masses for
hadrons, quarks, leptons, atoms, biological molecules,
liquid droplets of fossil fuel and water, living cells
including microorganisms and cancers, multi-cellar sys-
tems such as organs, neural systems, and the brain, stars,
galaxies, and the cosmos is synthetically revealed. This is
possible because each flexible particle is commonly gen-
erated by a mode in which a larger particle breaks up into
two smaller ones through a gourd shape with two lumps.
These masses, sizes, frequencies, and diversity dominated
by super-magic numbers including the silver ratio, in
fractal nature can be derived by the fusion of the quasi-
stability principle defined between absolute instability and
neutral stability, the indeterminacy principle extended for
quantum, statistical, and continuum mechanics, and the
spherical Lie group theory. The analyses also result in a
new mathematical definition of living beings and non-
living systems and further explain the standard network
patterns of various particles and also the relation between
information, structure, and function, because the proposed
theory based on gourds posits a new hyper-interdisciplinary
physics that explains a very wide range of scales, while the
Newton, Schrodinger, and Boltzmann equations describe
only a narrow range of scales.
Keywords Biological � Cosmic � Interdisciplinary �Subatomic � Quark
1 Introduction
There are still so many mysteries about non-living and
living systems from subatomic to cosmic scales, which are
related to the masses of subatomic particles, quantum
entanglement, the magic numbers, morphogenetic pro-
cesses, the standard circuit pattern of the neural network in
the brain, overall mechanism of cancer, fusion of left–right
symmetric and asymmetric organs, the definition of life,
side effects, functions of introns and junk, economic sys-
tems generated by the human brain, dark matter, and super-
cosmos outside our universe.
The reason why so many mysteries have not been
explained is related to the fact that the traditional Newton,
Schrodinger, and Boltzmann equations [1–5] can reveal only
a narrow range of scales, although each equation describes
several classes of conservation of mass, momentum,
moment, and energy. Super-interdisciplinary and supermulti-
scale physics, which synthesizes the whole span from the
pico- to the peta-scale, is necessary to go further.
Our previous researches [6, 7] offered some hypotheses
and predictions regarding these mysteries. One concerns
the function of introns and junk. Another concerns the left–
right asymmetric part inside the brain system, which brings
feelings of comfort. Later, some experimental researches
done by other people verified our hypotheses and predic-
tions [8, 9].
Here, we will reveal the mysteries above more intensively
and extensively. First, we will classify the natural processes
into three modes: breakup–collision, expansion–compression,
and excitatory–inhibitory process (acceleration–depression)
This work was presented in part at the 17th International Symposium
on Artificial Life and Robotics, Oita, Japan, January 19–21, 2012.
K. Naitoh (&)
Faculty of Science and Engineering, Waseda University,
3-4-1 Ookubo, Shinjuku, Tokyo 169-8555, Japan
e-mail: [email protected]
URL: http://www.k-naito.mech.waseda.ac.jp/;
https://www.wnp7.waseda.jp/Rdb/app/ip/ipi0211.html?lang_kbn=0
&kensaku_no=4181
123
Artif Life Robotics (2012) 17:275–286
DOI 10.1007/s10015-012-0056-y
(Fig. 1). We name the modes of breakup–collision, expan-
sion–compression, and excitatory–inhibitory process (accel-
eration–depression), as gourds I, II, and III, respectively. This
is because each one of the three modes has shape of gourd in
Fig. 2 or occurs after gourd shape. Breakup–collision mode
clearly shows a gourd shape having two kinks, while excit-
atory–inhibitory process that in chemical reaction apparently
has a gourd in connection pattern of two molecular particles at
collision timing. The mode of expansion–compression in
Fig. 1 also has a gourd shape of two kinks connected at later
stage of expansion as shown in the later section, although
earlier stage often shows only one kink. Nature is dominated
by gourds at rate-determining timing, rather than by strings or
spheres at equilibrium state. In short, our previous theoretical
models [6, 7, 10–13] are extended here and also we propose
here a physical theory that explains the fractal nature in the
gourds of the three models, although the fractal concept has
only been used in mathematics so far.
2 Methodology
2.1 Quasi-stability principle [7, 10–13]
Natural systems are essentially discontinuous in three-
dimensional space but relatively continuous in time,
because from the subatomic to the cosmic scale they con-
sist of particles such as quarks, hadrons, atoms, molecules,
fluid particles, cells, and stars. Accordingly, various natural
processes for non-living and living systems can approxi-
mately be described by the following momentum equation
systems:
dðnÞ
dtðnÞyi tð Þ ¼
X
j
fij yi; yj
� �þ ui or
oðnÞ
otðnÞyi t; xkð Þ ¼
X
j
fij yi; yj
� �þ ui;
ð1Þ
where yi, xk, t, n, fij, and ui denote physical quantities of
particles such as velocity, particle deformation rate, and
pressure, spatial coordinates, time, order of derivative,
function of yi and yj, and random disturbance related to
indeterminacy coming from the small number of particles,
respectively [7, 10–13]. Quasi-stability is defined as a
principle in which one part (one term) on the right-hand
side of Eq. 1 is zero, when disturbance of ui enters the
system. When at least one of the various terms of i or j for
fij is zero, the system is also quasi-stable against the dis-
turbance. Quasi-stability as it is used here lies between
neutral stability and an absolutely unstable condition. The
quasi-stability is different from meta-stability denoted in
thermo-physics, because this quasi-stability for momentum
is weaker than the meta-stability for energy conservation.
(One example of evidence is that the elimination of only
one term among various numerical error ones in a finite
difference equation derived with the Taylor series yields an
approximate solution for a physical phenomenon such as
the transition to turbulence [14, 15].)
It is emphasized here that traditional stability analyses
based on a mathematical variable transformation for matrix
diagonalization are meaningless for revealing the nature of
living beings, because life is not in mathematical space.
2.2 Indeterminacy level
As shown above, various natural phenomena consist of
particles, i.e., discontinuity in space. This discontinuity of
particles leads to indeterminacy (stochasticity) for several
Fig. 1 Three modes
Fig. 2 Gourd shapes as two kinks connected
276 Artif Life Robotics (2012) 17:275–286
123
stages of phenomena, such as electron particles described by
the Schrodinger equation. An important point is that the level
of indeterminacy, i.e., degree of variation, varies according to
window scales for averaging (stochastic determinism win-
dow) and the number of particles. As an example, when the
system being analyzed consists of a smaller number of parti-
cles, the level of indeterminacy increases (Fig. 3).
Statistical mechanics based on the Liouville and Boltz-
mann equations [1] tells us that a very large window for
averaging the aggregation of a huge number of particles
brings deterministic continuum mechanics, whereas a small
window for a small number of particles leads to a sto-
chastic differential equation [15–18]. When a small win-
dow for averaging is used, physical quantities such as
mass, size, and velocity are defined with indeterminacy,
i.e., vagueness [10, 11, 15, 17, 18].
The baryons and mesons are constructed of only three and
two quarks, respectively. There are only two electrons inside
the smallest orbit around an atom. The number of carbon,
oxygen, and nitrogen particles inside a nitrogenous base is not
enough for continuum, because of the order of ten. These
small numbers of particles lead indeterminacy in the gov-
erning equations. On the other hand, a biological cell or a
liquid droplet of over 1 mm in size includes a lot of molecular
particles that result in deterministic governing equations.
The most important point is that a system of only one particle
is also deterministic, although such systems are of an infinitely
small number (see Appendix on the details of window of
averaging, indeterminacy level, and boundary conditions).
3 Breakup phenomena (Gourd Ia)
3.1 Size and weight
The breakup phenomena on various spatial scales com-
monly show the shape of a gourd having two lumps at the
time of breakup (Fig. 2). Thus, we can model the gourd
having two lumps using two flexible spheroids connected
as an approximation [7, 10–13, 19–22]. Here, we define a
parcel as a flexible spheroid (lump) having two long and
short radii a(t) and b(t) dependent on time t, for a quark or
lepton, the aggregation of some quarks, leptons, and hadrons
generated by a high energy experiment, the aggregation of
neutrons and protons in each child atom resulting from the
fission of a large atom such as a uranium 235, a nitrogenous
base in biological base pairs of nucleic acids hydrated with
a lot of water molecules, an amino acids hydrated, a bio-
logical cell just before division, a liquid droplet at breakup,
and a star (or dark matter) at breakup in the cosmos. The
parcel becomes a sphere of the radius rd (=[ab2]1/3) under
an equilibrium condition. The deformation rate c(t) is
defined as a(t)/b(t), while a sphere without deformation
corresponds to c = 1. Next, we derive a theory for
describing the deformations and motions of the two con-
nected spheroid parcels having two radii of rd1 and rd2
under equilibrium conditions and two deformation rates of
ck [k = 1, 2], while the size ratio of the two parcels is
defined by e = rd1/rd2.
We model the relative motion between the two parcels,
nonlinear convections inside the parcels, and the interfacial
force at the parcel surface. The interfacial force is evalu-
ated in the form of r/rm where m and r are constants and
r is the curvature of the parcel surface. Several types of
forces such as nuclear force, van der Waals force, surface
tension, Coulomb force, and the force of gravity can be
explained by varying m. The relation m = 1 implies the
surface tension of liquid. Mean density of the parcels is qL.
We assume that the convection flow inside a flexible
parcel is irrotational, i.e., potentially one. This potential
flow is applicable, because fluctuations entering the parcels
such as bases, cells, and atoms will be those of thermal
fluctuations with very high speeds, which are less dissi-
pative (fluctuation dissipation theorem). The potential
assumption is also valid for star breakups, because of their
large size and high speed. Breakup of subatomic particles
occurs with energy input of extremely high speeds at the
level of light.
Moreover, we must consider that a parcel is not often a
continuum, because the number of nucleons and water
molecules inside the parcels like atom and nitrogenous
base will be fewer than 1,000. Thus, this leads to a weak
indeterminacy of physical quantities such as deformation
rate and density.
Here, we derive the relation between the dimensionless
deformation rate ck (:ak/bk [k = 1, 2]) of each parcel
dependent on dimensionless time �t and the size ratio of two
parcels of e = rd1/rd2.
The stochastic governing equation having indeterminacy
can be written for momentum as
Fig. 3 Window for averaging
Artif Life Robotics (2012) 17:275–286 277
123
with, mci, mcj, msi, msj, Det, B0k, C0k, and E0k [for k =
1, 2], which are defined in Refs. [7, 10–13, 20–22], with
the parameter dst denotes random fluctuation. Equation 2 is
derived only by the above assumptions and also purely
mathematical transformation. The long derivation of Eq. 2
is in Refs. [7, 10] confirmed by the referees.
Next, we also define yi = ci – 1 as deviation from a
sphere. The momentum equation is
which is approximated by the first order of the Taylor
series [7, 10–13, 19–22].
It should be stressed that the indeterminacy caused by
the small number implies a slightly indeterminant (vague)
shape of parcel, which is weakly different from spheroid.
Thus, the present theory based on Eqs. 2 and 3 also
explains breakup processes of various shapes of parcels.
For each m, the quasi-stable size ratios of 1.0 and about
1.44 appear in Eq. 3, i.e., in the 1st-order term of the
Taylor series. It is stressed that a deformation disturbance
entering a particle, i.e., that for yi, leads to an asymmetric
size ratio around e = 1.44, while a disturbance of defor-
mation speed, dyi=d�ti, brings a symmetric ratio of 1.0.
The higher-order of the Taylor series for parcel 1 results in
d2yi
d�t2i
¼X1
k¼1
bk e; mð Þyk�1i
!dyi
d�ti
� �2
þX1
k¼1
ak e; mð Þyki þ f;
ð4Þ
where the last term on the right-hand side includes influ-
ences from parcel 2. Concrete functions for ak and bk can
be found using a computer program MATHEMATICA,
because of very long terms.
The higher order of terms of the Taylor series obtained
with the statistical fluid dynamics model (Eq. 4) also
reveals the various super-magic numbers for the size ratios
of (Table 1). It is stressed that, although there are various
ratios in Table 1, the ratios are desultory or discontinuous.
We should recall that various values of m bring the same
quasi-stable ratios of 1.0 and about 1.44 for the first order
of the Taylor series, whereas the higher-order terms lead to
various other ratios. (The fractional Taylor series also show
quasi-stable ratios including about 1.44 and 1.0 in Table 1.)
The size and weight ratios of purines and pyrimidines in
DNA are often around 1.45, which is close to 1.44 related to
surface force in Table 1, while the size ratios of identical bases
in RNA is 1.0 related to convection in Table 1. Heavy chains
in immune globulins (IgX) have size ratios of about 1.5, while
the frequency ratio of small and large types of IgXs is also 1.5:
two types of large immune globulins (IgM and IgE) and three
small ones (IgG, IgD, and IgA) [7, 11–13, 16].
The largest amino acid is about three times larger than
the smallest one, which corresponds to 3.58 in the higher
order of the Taylor series for m = 1 in Table 1. It is well
known that there are several types of hydrogen-bond con-
nections [33, 34]. Thus, the several orders of the Taylor
series will also be related to the variety of hydrogen-bond
connections. (Liquid sprays such as water and fuel also
show about threefold variation of droplet sizes [7].)
The ratios of chromosomes in human beings are about
six times at maximum, which may be seen as 4.54 in the
higher order of the Taylor series for m = 1, 6.11 in the
higher order of the Taylor series for m = -1, or the ratios
over 4.0 for m [ 1. (This will be because of chromosomes
are related to covalent bond connection [20–22].)
These ratios of 1:1 and about 1:1.5 also correspond to those
of child atoms generated by the breakup of uranium 235. This
means that the probabilities of the size ratios of 1:1 and about
2:3 are relatively high, because uranium will have the shape of
a gourd with two kinks just before its breakup. (The effect of
special theory of relativity between mass and energy will not
influence for the size ratio of child atoms obtained after the
fission process of uranium 235 very much, because the effect
work on both two child atoms at an identical rate. Moreover,
impact of only one neutron to uranium will not produce fast
deformations of uranium at the later stage of fission.)
The halo structures such as H10 and M32 have the
number ratios of neutrons and protons over 2:3 [10, 20].
d2
d�t2i
ci ¼ mcid
d�tici
� �2
þmcjd
d�tjcj
� �2
þmsi c53�2
3m
i þ msj c53�2
3m
j
( ),Detþ dst for i ¼ 1; 2 j ¼ 1; 2 i 6¼ j½ � ð2Þ
d2yi
d�t2i
¼ � 2
3ð3� e3 � 2e2þmÞ dyi
d�ti
� �2
þ3ð3� e3Þmyi � 4e1þm dyj
d�tj
� �2
þ12e1þmmyj
" #,½3ðe3 þ 1Þ� þ d0st; ð3Þ
278 Artif Life Robotics (2012) 17:275–286
123
These number ratios will also be explained by the present
theory of the higher-order of accuracy.
Table 1 also reveals the magic numbers appearing in the
weight ratios in various atoms generated by cold fusion:
about 3.6, 2.1, and 1.8 [20, 21].
The constant m will often have values larger than 1.0 or
1.0 for subatomic forces such as those of nuclear force.
When m has a value between 1.3 and 3.0, the ratios of e are
between 1.0 and about 105, which correspond to the mass
ratios in very small particles including quarks and leptons
or those in the hadron classes of baryons and mesons. (It is
stressed that a weight ratio of about 2:3 is also observed in
dark matter [20, 21].)
If we redefine a parcel as an electron cloud, Eqs. 2–4
and Table 1 may also explain the mysterious electron
orbits such as 4f more unstable than 5p and 6s, because
quasi-stable ratios do not increase monotonously according
to increasing of the orders of the Taylor series, while those
are related to the energy levels of orbits. For examples, the
3rd and 8th orders of terms bring the relatively large quasi-
stable size ratios of about 3.58 and 4.54, whereas the 4th
and 5th orders lead to the relatively small ones of about
2.47 and 2.10. It will also be stressed that both the numbers
of electron orbits and the orders of the Taylor series
inducing various quasi-stable size ratios are about seven or
eight.
3.2 Permanent and tentative components inside parcels
Parcels can essentially include two types of components,
which are permanent and tentative ones. The permanent part
exists both before and after the breakup process, i.e., during
the whole processes including the breakup timing, while the
tentative part appears and shows important features only at
the time of breakup. In several cases of natural phenomena,
the permanent part is a one-dimensional string or ring, having
a mass proportional to the parcel size e. Parcels including
both tentative and permanent parts have a mass proportional
to e3. Some natural phenomena have no tentative part, in
which case only the permanent part is proportional to e3.
Let us examine the following examples. In biological
systems, these magic numbers of e explain those for bio-
logical molecules of one-dimensional strings and rings
such as nitrogenous bases, amino acids, and proteins,
whereas the values of e3 correspond to biological molecules
hydrated by water molecules. In subatomic processes, the
aggregation of baryons as permanent part is one-dimen-
sional, while the total mass including baryons, gluons, and
the quark condensation effect as tentative parts is three-
dimensional. The tentative part is similar to the immersed
mass in fluid dynamics. Pure droplets of water or fuel and
stars are three-dimensional because they only have the
permanent part.
Table 1 Super-magic numbers
Values outside parentheses
mean the quasi-stable size ratios
of parcels, whereas values in
parentheses for m = 1 imply the
orders of the Taylor series
m = -3 m = -1 m = 1 m = 1.04 m = 1.3 m = 1.5 m = 2 m = 3
Convection
1 1 1 (1) 1 1 1 1 1
1.23 1.34 1.27 (2) 1.27 1.26 1.25 1.24 1.21
1.39 1.4 1.35 (3) 1.35 1.34 1.34 1.32 1.29
3.51 1.42 1.39 (4) 1.27 9 1030 10,321 256 16.1 4.36
1.42 1.43 1.4 (5) 1.38 1.38 1.37 1.36 1.33
4.22 1.41 (6) 9.08 9 1022 1,151 68.7 8.33 3.07
1.43 1.42 (7) 1.4 1.4 1.4 1.39 1.36
4.44 1.43 (8) 4.06 9 1022 1,033 64.4 8.02 2.86
1.44 1.43 (9) 1.41 1.41 1.41 1.4 1.38
4.5 2.82 9 1025 2,472 108.7 10.4 2.99
4.52 1.42 1.42 1.42 1.41 1.39
4.53 1.95 9 1034 37,325 553.6 23.5 4.25
1.43 1.43 1.43 1.42 1.4
Surface force
1.44 1.44 1.44 (1–9) 1.44 1.44 1.44 1.44 1.44
1.8 3.58 (3) 4.57 3.14
1.7 2.47 (4) 1.99
1.63 2.1 (5) 1.84
1.59 1.79 (7) 1.74
6.11 1.71 (8) 4.42
4.54 (8) 1.68
2.97
Artif Life Robotics (2012) 17:275–286 279
123
The group theory shows that one- and three-dimensional
spheres are in a group. This may support the idea that e and
e3 repeatedly appear in various natural particles (parcels),
while nature is relatively obviative to two-dimensional, e2.
(Many types of particles in nature take an axis such as that
of spheroid parcel, which is one-dimensional characteristic.
Thus, it is relatively difficult that aggregations of the par-
cels are two-dimensional.)
3.3 Discontinuity around m = 1
When the curvature is 1/r, we define the surface force as
one proportional to 1/rm. We can employ the simple form
of 1/rm, because we consider only the breakup timing of the
gourd having two lumps.
Let us think about the reason why discontinuous jumps
of size ratios in Table 1 can appear around m = 1. Taking
the r-integral of 1/rm as the potential, the functions dis-
continuously change for m increasing around 1.0. This may
be the reason why values of m a little larger than 1.0 dis-
continuously induce extremely large size ratios.
There are extremely large size ratios over 1030 in
Table 1 for 1.0 \ m \ 1.1. These very large ratios might
possibly correspond to the size ratios of vapor molecules
and water droplets produced at breakup and also to those of
subatomic particles and stars, or the very large or infinite
ratios for 1.0 \ m \ 1.1 may explain interaction between
particles at a infinite distance, i.e., the quantum
entanglement.
The potential flow assumption, irrotational flow one
without viscosity, is applicable even for very small sub-
atomic and molecular systems, because very high energy,
i.e., very high speed (in a very short period), is put for the
particle. Actually, energy at the level of sound speed is put
into the molecular system, while energy at the level of light
speed is put into the subatomic experiment, although the
period is very short.
3.4 Number of particle types and frequencies
The size asymmetry of around 3:2 of the main rings in
purines and pyrimidines naturally leads us to an asym-
metric number of types, i.e., ‘‘two’’ types of purines and
‘‘three’’ types of pyrimidines [7, 10–13]. The multiplicative
inverse of the asymmetric number of types is the size
asymmetry. This can be easily understood from the mass
conservation law, i.e., from the fact that the main rings of
purines have ‘‘nine’’ molecules of carbon and nitrogen,
while ‘‘six’’ molecules of carbon and nitrogen form the
main rings of pyrimidines. Accordingly, the number of
base types is proportional to the frequency of bases inside
RNA [7, 10–13]. In qualitative terms, the sizes and
molecular weights of the twenty types of amino acids are
also inversely proportional to the frequencies.
There are mesons with ‘‘two’’ quarks and baryons with
‘‘three’’. Therefore, an analysis based on Eqs. 2, 3, and 4
may also clarify the ratios in the elemental particles such as
quarks.
3.5 Relation between indeterminacy and quasi-stability
Our previous reports [7, 10–13, 19–22] support that the
quasi-stability weaker than the neutral stability controls the
natural particle sizes. Here, we will show another evidence.
The neutral stability demands that all of the terms of
momentum and deformation rate (position) in Eqs. 3 and 4
become zero, which leads to deterministic behavior,
whereas the quasi-stability permits that one term is not
zero, which brings indeterminate behavior. This quasi-
stability corresponds to the well-known indeterminacy
principle for quantum mechanics. Thus, the essential
indeterminacy principle in quantum mechanics [5] also
gives an evidence for the inevitability of the quasi-stability.
The hypothesis that both terms of momentum and position
can be deterministic is not true, because various natural
systems from subatomic to cosmic are in the quasi-
stability.
The reason why very small particles such as six quarks,
leptons, and gauge bosons cannot be taken out will also be
related to the indeterminacy, i.e., the quasi-stability.
4 Strings and rings produced by coalescence
(Gourd Ib)
4.1 Clover structure
An extremely large frequency ratio for purines and
pyrimdines in tRNA, say, far larger than 1.5, cannot produce
the stem in tRNA, because purine and pyrimidine pairs do
not easily form in the presence of only one type of base
[10–13, 16]. It is also known that, as purines and pyrimi-
dines in DNA have the same density, they form a pair at
each locus due to hydrogen bonding. Thus, this frequency
ratio of 1.0 for purines and pyrimidines cannot generate
loops in tRNA [10–13, 16]. This is the reason why a fre-
quency ratio between 1.0 and 1.5 for purines and pyrimi-
dines promotes clover structures having stems and loops
(Fig. 4). More complex structures such as rRNA can also
be explained by the above-mentioned dynamical mecha-
nism [10–13, 16]. Concavity and convexity, like thumbs in
RNAs, play an important function for grasping objects,
including nucleic acids and proteins. The ‘‘information’’
such as asymmetric frequency ratios between 1.0 and 1.5
induce ‘‘structures’’ such as convexoconcave shapes of
280 Artif Life Robotics (2012) 17:275–286
123
RNAs, which lead to ‘‘functions’’ such as grasping. (Dur-
ing differentiation and proliferation of the morphogenetic
process, repeats of symmetrical and asymmetrical cell sizes
also induce the structures of concavity and convexity in
multi-cellar systems, thereby leading to functional parts
such as arms and legs [11–13, 23, 24].)
Chromosomes in multi-cellar systems also have three-
dimensional repeat structures of concavity and convexity. It is
known that introns and junk are concave in shape, while exons
having the clear function of producing proteins are convex in
shape. (Several sequence data in the world-wide databases
may show a tendency of purines richer than pyrimidines in
RNA, which may be contradict to the above principle that
smaller bases are more. Non-coding RNA reported recently
may solve this contradiction. There may also be other
unknown RNAs which are rich with pyrimidines.)
4.2 Comfort
Human brain feels the golden and silver ratios of around 2:3 to
be comfortable. Thus, our previous reports predicted that there
will be about 2:3 ratios in the aggregations of neural cells of
the brain [7]. Recently, some researchers found the left–right
asymmetric part inside the habenular nucleus of the zebrafish
brain, which has size ratios between 1:1 and 1:2 [9]. It is
known that the habenular nucleus is related to fear, which is
the opposite feeling of comfort. Thus, the asymmetric size
ratios of neurons and networks inside the brain, which may be
induced by some different neurons such as GnRH neurons and
glia cells, also have sympathetic vibration with the asym-
metric ratios in picture images entering from the outside into
the eyes. The sympathetic vibration brings comfort.
Next, let us think about the musical scale inducing
comfortable music. Musical scale Perfect 5 uses the ratio of
2:3 for the sound frequencies, while perfect 4 employs 3:4.
Music also uses the magic numbers shown above. Then,
perfect 5 consists of ‘‘seven’’ half tones, while perfect 4 is
with ‘‘five’’ half tones. It is also stressed that the magic
numbers derived by Eq. 4 result in the ratio of 7:5 close to
the silver ratio, which is the rhythm used for Japanese
poems such as ‘‘haiku’’ and ‘‘tanka’’.
5 Aggregations generated by more coalescences
(Gourd Ic)
5.1 Inner asymmetry in cells and morphogenesis
Let us think about the morphogenetic process of the human
beings further. The starting point is colony of microor-
ganisms. Symmetric and asymmetric size ratios are also
observed at the cell level of microorganisms [10–13].
There are terminal cells and basal cells of different sizes
in the morphogenetic processes. This difference in cell size
also shows asymmetry [10–13]. Embryo stem (ES) cells
also show asymmetric cell divisions (differentiation) such
as a division to glial cells and neurons.
The left–right symmetric distribution of arms and legs is
observed in outward appearance, although the inner body,
including the heart and liver, is asymmetric. Outer cells
close to the surface move relatively easily in relation to the
absolute origin on the earth, because one part of the cell is
free without any connection to other cells. However, inner
cells receive forces from many directions due to the pres-
ence of other cells in a homogeneous field, making it dif-
ficult for them to move relative to the origin on the earth.
Therefore, inner cells deform relatively easily without any
translational motion of the gravity center.
Equations 3 and 4 explain this important characteristic
of the asymmetric division of inner cells and the symmetric
division of outer cells. This is because the asymmetric size
ratio of cells (the size ratio of about 1.45) is relatively
quasi-stable against the disturbance of deformation that
easily affects inner cells and also because the second term
on the right-hand side of Eqs. 3 and 4 implies cell defor-
mation. Outer cells divide into identical sizes of cells,
because the first term corresponds to the translational
motion of a cell [10–13].
5.2 Protons and neutrons in atoms
It is also well known that several atoms in nature have
number ratios of protons and neutrons between 1:1 and 2:3.
Here, let us examine the reason why larger atoms have
larger number ratios close to 2:3.
As shown above, the inner and outer parcels of baryons
determine whether the number ratio of neutrons and pro-
tons is asymmetric or symmetric, respectively [10, 11].
Larger aggregations of parcels such as thorium (Th),
which contains more baryons than helium (He), have more
Fig. 4 Schematic diagram of symmetric and asymmetric density
ratios in DNA and one leaf of tRNA
Artif Life Robotics (2012) 17:275–286 281
123
inner baryons, because the surface/volume ratio of the
aggregation becomes smaller as the size increases. More
inner baryons for larger atoms bring more asymmetric
number ratios of protons and neutrons [10, 11]. [Mysteri-
ously, the masses of stable protons and neutrons are almost
the same, while child atoms generated by fission of ura-
nium 235 and nitrogenous bases (pyrimidines and purines)
have a different weight ratio around 2:3. Some reasons are
shown in our previous reports [10–12]. There is the other
analogical evidence supporting the inevitability of the ratio
close to 1:1 for proton and neutron, that the Watson–Crick
pair of nitrogenous bases also has the asymmetric weight
ratio of about 2:3, whereas the weight ratio of the pair
including sugars inside DNA and RNA is close to 1:1
because of addition of sugar for each base.]
6 Repeats of breakup and coalescence (Gourd Id)
As shown above, one particle alone is deterministic without
indeterminacy, because of the Newton’s momentum
equation. Of course, systems having a number of particles
from three to several hundred can also be indeterminant,
when macroscopic modeling is done. Systems having more
particles may be approximated as a continuum, i.e.,
deterministic. Aggregation of a lot of small particles results
in a large particle at the next scale, which is close to a
sphere or a spheroid. The new large particle is determin-
istic again, because it is only one. (Two flexible particle
systems shown in Eq. 2 become deterministic when there
are no particles colliding to the two particle system as the
disturbance. If there are disturbance particles, the two
particle system is indeterminant.)
As an example, let us look at the biological system.
Only one DNA existing inside a cell is deterministic,
because DNA must accurately determine the structures and
functions of living beings. Two male and female DNAs for
mating filled with water can produce a weak diversity with
indeterminacy by crossing over. There are extremely large
numbers of genes, proteins, and water molecules inside a
cell, which leads to a continuum, i.e., the next deterministic
behaviors and sustainability during the cell’s life time.
Compartment of the large number of molecules due to cell
membrane leads to the determinacy as sustainability. The
loss of many molecules during the aging process results in
indeterminacy, instability, and death. (It is stressed that a
few electron orbits around atomic cores are indeterminant.
Stars are nearly deterministic, because weak gravity forces
lead to individual motion for each star.)
Therefore, further thought experiments based on the
indeterminacy level mentioned above may reveal the total
numbers of macroscopic groups of bio-molecules inside
human beings, including presently unknown ones. The
death rate of children will be between 10 and 0.1 %,
although the rate depends on economical situation of each
country. This may imply that the total number of macro-
scopic molecular groups inside healthy human beings is
between 10 and 1,000. (We find that at least six macro-
scopic molecular groups are necessary for living beings
[10–12, 25–29].)
Moreover, if the total numbers and types of macroscopic
molecular groups are revealed between 10 and 1,000 in detail,
the present indeterminacy level analysis may bring a new
insight for medicines such as those after becoming cancer.
7 Expansion and compression (Gourd II)
Other natural phenomena such as the morphogenetic and
aging process are in the topological mode of expansion and
compression. This mode is like a gourd expanding, which
has two spherical parts and a duct for suction.
An example of the gourd expanding is unborn baby
inside mother, in which two spherical parts correspond to
head and body. Our unsteady three-dimensional flow sim-
ulations obtained by solving the stochastic Navier–Stokes
equation qualitatively revealed the three-dimensional
structure of the morphogenetic processes of human beings,
including organs and the brain [30]. The morphogenetic
process of the main blood vessels inside the brain was also
simulated [31]. The computational simulations demonstrate
left–right asymmetric organs in the inner region of the
body, while symmetric organs and parts are relatively
outside the body. The simulation results also support the
principle of inner asymmetry and outer symmetry obtained
in the foregoing sections by the quasi-stability principle
(Eq. 3). Moreover, the simulation results also show another
principle of early symmetry and later asymmetry [27].
(Compression with shrinking will correspond to death,
because compression process is very unstable as seen in
turbulence increase during the compression stage of piston
engine.)
Our universe may also be expanding. If there are no
super-universes outside our universe, our one is symmetric.
8 Excitatory and inhibitory mode (Gourd III)
8.1 Self-replication
Our previous reports clarified the minimum excitatory
network of chemical reactions necessary for biological
self-replication [12]. The minimum system has four types
of macroscopic molecular groups: two information groups
x11 and x12 and two functional molecular groups x21 and
x22 (Fig. 5) [12]. This four-stroke system in Fig. 5 works
282 Artif Life Robotics (2012) 17:275–286
123
as a closed loop. Microorganisms including bacteria and
archaea and cancer cells basically employ this network of
the four molecular groups, because of a monotonic increase
without any depression. Emphasis is placed on the fact that
Fig. 5 shows a new, concrete, mathematical definition of
life. We can topologically see the symmetric and asym-
metric circles of reaction networks in Fig. 5, which also
have gourd shapes connected with symmetric and asym-
metric lumps. These gourds may commonly appear in both
parcels in a base-pair and those in the network, because
both are related to interaction of particles at the rate-
determining stage. Fusion of asymmetric and symmetric
size ratios of molecules (bipolarity of sizes of 1:1 and about
2:3) will naturally result in the fusion of asymmetrical and
symmetrical network patterns (bipolarity of topology).
Complementary pairs of RNA such as double-strand
RNA (dsRNA), i.e., only one molecular group, may form
the simplest excitatory cycle. However, information and a
catalytic function are undetached in this type of system,
because each strand of dsRNA has both of them. This leads
to the fact that the dsRNA and DNA suitable for stabilizing
information is not conducive to the production of various
functions for inducing multi-cellar systems having com-
plex geometries. Thus, living beings select the detachment
of information and function.
8.2 Morphogenetic and economic processes
The main temporal mystery is the standard clock, i.e., the basic
molecular instrument regulating the biological rhythm com-
mon to the cell cycle, proliferation and differentiation induced
by the stem cell cycle, neural pulse, neural network, and cir-
cadian clock. In order to generate the standard clock, at least
two more inhibitory molecules (molecular groups) of infor-
mation and function should be added to depress a monotonous
increase in DNA [10, 26, 27, 29].
Here, we define x13 and x23 as the other molecular groups
for inhibitory factors repressing reactions. These two groups
are incorporated in the four groups of x11, x12, x21, and x22,
because today’s cells, the morphogenetic processes of multi-
cellar systems, and neural systems use negative controllers
such as Oct-4 and SOX2 for producing tissues and organs [32].
This leads to a macroscopic model having six types of
molecular groups, or in other words, a six-stroke engine
(Fig. 6a). We can describe the densities of the six molecular
groups at generation N after the mother cell generation in the
morphogenetic process, by the following equations.
xNþ11i � xN
1i ¼ ai1xN1i � xN
21; i ¼ 1; 2; 3ð ÞxNþ1
2i � xN2i ¼ ai2d xN
1i � nixN23
� �� xN
22; i ¼ 1; 2; 3ð Þ;ð5Þ
where xij � xkm denotes the smaller value among xij and
xkm and also where d(x) denotes the larger value of x or 0,
i.e., max (x, 0) [25–27]. Statistical mechanics inevitably
leads to the mathematical form on the right-hand side in
Eq. 5, because of collision probability.
Numerical solutions for Eq. 5 show about a sevenfold beat
cycleofdensities formolecular groupson average,whilevarying
the parameters in Eq. 5 results in four- to tenfold beat cycles.
An important point is that the actual morphogenetic pro-
cesses show about seven-beat cycles of molecular densities
[25–29]. Another example may be that, in the morphogenetic
processes, both human beings and giraffes have ‘‘seven’’ neck
bones. These facts provide substantiating evidence for Eq. 5.
8.3 Neural network
Equation 5 will also reveal the standard topology of the cor-
tical neural circuit (network), the integration mechanism of
brain functions, the neural system for muscle control, and the
chemical reaction network inside a neuron [28].
Figure 6b shows the standard pattern for neural net-
works, which includes inputs and outputs. For the network,
six variables of xij (i = 1–2, j = 1–3) are redefined as the
activation level of neurons, related to the density of mol-
ecules and amount of total energy inside the neurons.
Fig. 5 Four-stroke molecular engine
Artif Life Robotics (2012) 17:275–286 283
123
There are two sides in Fig. 6b, one for inputs and the other
for outputs, which correspond to information and functional
molecules in Eq. 5 and Fig. 6a. The upside-down topology of
inputs and outputs in Fig. 6b will also be possible.
The most important point is that the present equation
(Eq. 5) and Fig. 6 describe the essential physics underlying
the network of neural cells and the molecular network
inside a neuron, whereas the Hodgkin–Huxley (H–H)
model describes only the outer electrical quantities such as
electron flow and voltage for a single neuron. (It should be
added that some variations modified from the network
pattern in Fig. 6 and Eq. 5 are also possible, by varying the
arbitrary constants and also by adding more molecular
types except for x13 and x23.)
It is stressed that the equation generated by the six groups
for describing the seven-beat cycle on average (Eq. 5) also
shows a quasi-stable feature for healthy conditions, whereas
an unstable condition will be for sickness [10].
Circadian clock of about 24–25 h are also seven times the
fundamental temperature oscillation of about 3.5 h [28, 29].
Equation 5 is an ordinary differential one that eliminates
spatial variations of quantities, because the spatial diffusion
of molecules and cells is relatively fast in comparison with
temporal oscillations and also because a lot of molecules
move between cells.
Moreover, emphasis is placed on the fact that the cycles
of boom and bust appearing in economic and social sys-
tems are also the seven-beat on average, because economic
systems are produced by human brains. Flux and reflux of
companies and capital can also be clarified by the present
analysis. (For standard neural network systems, the initial
conditions or inputs may be inputs from outside networks.
The initial inputs can be included on the right-hand side of
Eqs. 5 and 6 by the Delta function.)
8.4 Total energy limit
The model (Eq. 5) in the previous sections was derived
under the assumption of an infinite energy supply. How-
ever, energy supplied for molecular networks, cell colo-
nies, organs, neural networks, or economic systems will be
limited, because the surface-to-volume ratio of each system
decreases according to an increase in the number of mol-
ecules, cells, neurons, or populations, leading to a condi-
tion of insufficient energy. Thus, a new energy restriction
term should be added to Eq. 5, which results in Eq. 6 [28].
xNþ1ij� xN
ij¼ aijðxN
1j � bijxN23Þ � xN
2i � eij ½xNij �
q;
xij� 0; xN1j � bij xN
23� 0 ði ¼ 1� 2; j ¼ 1;�3Þ; ð6Þ
where q [ 2 is set in case that the symbol � is defined as
product, whereas q [ 1 if the symbol � means smaller
value among two.
Let us solve the time-dependent process including
morphogenesis and aging processes by using Eq. 6.
Numerical solutions for the equation extended with total
energy limit show a transition to sick situation such as
cancer in the aging process of the human beings including
the brain, i.e., a mysterious transition from chaotic oscil-
lation at 2nd stage to periodic one at 3rd stage, while the
vibration amplitude keeps a constant level (Fig. 7).
This limitation on the total mass and energy is also
evident in today’s economic systems, because a huge
amount of information travels at the very high speed of
light through the worldwide internet, whereas the speed of
cargo shipment is still at the sonic level. This unbalance
between information and objects may induce very complex
oscillations and economic crisis, which do not have the
sevenfold beat mentioned above.
8.5 Higher pressure for evolution and self-organization
The scenario described above by Eqs. 5 and 6 for a universal
network pattern in fractal nature can reveal the reason why
living beings from the pre-biotic process to multi-cellar sys-
tems can be induced stably in a self-organizing manner.
Random processes cannot generate the present living system
having complex chemical reaction processes.
Fig. 6 Six-stroke engines for morphogenetic processes and neural
systems
284 Artif Life Robotics (2012) 17:275–286
123
9 Conclusion
This approach solves mysterious problems concerning the
origin of life, evolution, molecular biology, microbiology,
system biology, morphogenesis, economics, medicine,
brain science, subatomic theories, high energy physics, and
cosmology.
The proposed theory based on gourds at rate-determin-
ing stage posits a new hyper-interdisciplinary physics that
explains a very wide range of scales, while the Newton,
Schrodinger, and Boltzmann equations describe only a
narrow range of scales. Analysis based on gourd shapes at
rate-determining timing shows a new paradigm, whereas
superstring theories based strings or spheres will mainly
reveal at equilibrium state (Fig. 8). Quasi-stability princi-
ple is extremely important for various phenomena and
stages.
Acknowledgments This article is part of the outcome of research
performed under a Waseda university Grant for special research
project (2009B-206). The author thanks Mr. Hiromi Inoue and Mr.
Kenji Hashimoto of Waseda University for their help on this study.
Appendix
Various window sizes for spatial averaging, which are
smaller than those for continuum approximations such as
the Boltzmann and Navier–Stokes equations (deterministic
equations) describing inner analytical domains vary the
indeterminacy levels (degrees of vagueness for physical
quantities such as parcel shape, density, pressure, and
temperature). We should show a way, which determines
the window size for averaging. This can be done using
boundary and initial conditions, because these conditions
are also indeterminant due to existing in the outer unknown
region. Basically, the indeterminacy level of physical
quantities in inner region is set to be identical to that of
initial and boundary conditions. Several examples on the
indeterminacy level are reported in our previous reports
[10, 11, 15–21, 28].
References
1. Hirschfelder JO, Curtiss CF, Bird RB (1964) Molecular theory of
gases and liquids. Willey, New York
2. Aris R (1989) Vectors, tensors, and the basic equations of fluid
mechanics. Dover, New York
3. Tatsumi T (1982) Fluid dynamics. Baifukan, Tokyo
4. Landau ED, Lifshitz EM (2004) Fluid mechanics, 2nd edn.
Butterworth-Heinemann Elsevier, Oxford
5. Landau ED, Lifshitz EM (1981) Quantum mechanics, 3rd edn.
Butterworth-Heinemann Elsevier, Oxford
6. Naitoh K (1998) Introns for accelerating quasi-macroevolution.
JSME Int J Ser C 41(3):398–405
7. Naitoh K (2001) Cyto-fluid dynamic theory. Jpn J Ind Appl Math
18-1:75–105 (also in Naitoh K (1999) Oil Gas Sci Technol 54-2)
8. Hirotsune S, Yoshida N, Chen A, Garrett L, Sugiyama F,
Takahashi S, Yagami K, Wynshaw-Boris A, Yoshiki A (2003)
An expressed pseudogene regulates the messenger-RNA stability
of its homologous coding gene. Nature 423:91–96
9. Aizawa H, Bianco IH, Hamaoka T, Miyashita T, Uemura O,
Concha ML, Russell C, Wilson SW, Okamoto H et al (2005)
Laterotopic representation of left-right information onto the
dorso-ventral axis of a zebrafish midbrain target nucleus. Curr
Biol 15(8):238–243
10. Naitoh K (2012) Spatiotemporal structure: common to subatomic
systems, biological processes, and economic cycles. J Phys Conf
Ser 344 (also in Naitoh K (2011) A force theory. RIMS Kok-
yuroku 1724:176–185)
11. Naitoh K (2010) Onto-biology. Artif Life Robot 15:117–127
12. Naitoh K (2008) Stochastic determinism. artificial life and robotics
13:10–17 (also in Naitoh K (2008) Onto-biology: inevitability
of five bases and twenty amino-acids. In: Proceedings of 13th
international conference on biomedial engineering (ICBME),
Singapore. Springer, Berlin)
13. Naitoh K (2006) Gene engine and machine engine. Springer,
Tokyo
14. Naitoh K, Kuwahara K (1992) Large eddy simulation and direct
simulation of compressible turbulence and combusting flows
in engines based on the BI-SCALES method. Fluid Dyn Res 10:
299–325
Fig. 7 Transition to sick condition as the 3rd stage in the aging
process of the human being including the brain
Newton eq.
Boltzmann eq.
Shroedinger eq.
Subatomic Theories
Hyper-gourd theory: [for rate-determining stages based on quasi -stability and statistic fluid mechanics]
[Mainly analyses for equilibrium states]
Fig. 8 Hyper-gourd theory as warp and traditional equations as weft
Artif Life Robotics (2012) 17:275–286 285
123
15. Naitoh K, Shimiya H (2011) Stochastic determinism capturing
the transition point from laminar flow to turbulence. Jpn J Ind
Appl Math 28(1):3–14 (also in Naitoh K, Nakagawa Y, Shimiya
H (2008) Stochastic determinism approach for simulating the
transition points in internal flows with various inlet disturbances.
In: Proceedings of 5th international conference on computational
fluid dynamics, (ICCFD5) and computational fluid dynamics.
Springer, and in proceedings of 6th international symposium on
turbulence and shear flow phenomena (TSFP6), 2009)
16. Naitoh K (2010) Onto-biology: a design diagram of life, rather
than its birthplace in the cosmos. J Cosmol 5:999–1007
17. Naitoh K (2011) Stochastic determinism: revealing the critical
Reynolds number in pipe and fast phase transition. In: Proceed-
ings of 10th international symposium on experimental and
computational aerothermodynamics of internal flows (ISAIF),
Paper no. ISAIF10-045, 2011
18. Naitoh K, Noda A, Kimura S, Shimiya H, Maeguchi H (2010)
Transition to turbulence and laminarization clarified by stochastic
determinism. In: Proceedings of 8th international symposium on
engineering turbulence modeling and measurements (ETMM8),
vol 775, Marseille
19. Naitoh K (2012) Hyper-gourd theory. In: Proceedings of 17th
international symposium on artificial life and robotics (AROB17)
20. Naitoh K (2011) Quasi-stability theory: explaining the inevita-
bility of the Magic numbers at various stages from subatomic to
biological. In: Proceedings of 15th Nordic and Baltic conference
on biomedical engineering and biophysics, IFMBE proceedings,
vol 34, Denmark, pp 211–214 (also in Naitoh K (2011) Quasi-
stability theory: explaining the inevitability of the Magic numbers
at various stages. Proceedings of ISB2011, Brussels)
21. Naitoh K (2011) The inevitability of biological molecules con-
nected by covalent and hydrogen bonds. In: Proceedings of
European IFMBE conference, IFMBE proceedings, vol 37,
pp 251–254
22. Naitoh K, Hashimoto K, Inoue H (2011) The inevitability of the
biological molecules. Artif Life Robot 16
23. Naitoh K (2011) The engine: inducing the ontogenesis. In: Pro-
ceedings of 15th Nordic and Baltic conference on biomedical
engineering and biophysics, IFMBE proceedings, vol 34, Den-
mark, pp 215–218
24. Naitoh K (2008) Physics underling topobiology: space–time
structure underlying the morphogenetic process. In: Proceedings
of 13th international conference on biomedial engineering,
(ICBME). Springer, Singapore (2008)
25. Naitoh K (2011) Morphogenic economics. Jpn J Ind Appl Math 28:1
26. Naitoh K (2011) The universal bio-circuit: underlying normal and
abnormal reaction networks including cancer. In: Proceedings of
European IFMBE conference, IFMBE proceedings, vol 37,
Budapest, pp 247–250
27. Naitoh K (2011) Onto-oncology: a mathematical physics under-
lying the proliferation, differentiation, apoptosis, and homeostasis
in normal and abnormal morphogenesis and neural system. In:
Proceedings of 15th Nordic and Baltic conference on biomedical
engineering and biophysics, IFMBE proceedings, vol 34,
Denmark. pp 29–32
28. Naitoh K (2011) Onto-neurology. In: Proceedings of JSST2011,
international conference modeling and simulation technology,
Tokyo, pp 322–327
29. Naitoh K (2009) Onto-biology: clarifying also the standard clock
for pre-biotic process, stem-cell, organs, brain, and societies. Proc
CBEE, Singapore
30. Naitoh K (2008) Engine for cerebral development, artificial life
robotics, vol 18. Springer, Berlin
31. Naitoh K, Kawanobe H (2012) Engine for brain development.
Artif Life Robot 16:482–485
32. Takahashi K, Yamanaka S (2006) Induction of pluripotent stem
cells from mouse embryonic and adult fibroblast cultures by
defined factors. Cell 126:663–676
33. Nishio M (2004) Weak hydrogen bonds. Encyclopedia of
supramolecular chemistry. Marcel Dekker, USA, pp 1576–1585
34. Umezawa Y, Nishio M (2005) The CH/Pai hydrogenbond. Seitai
no Kagaku 56(6):632–638
286 Artif Life Robotics (2012) 17:275–286
123