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Transcript of Introduction to Complexity Science, by Antonio Caperna, PhD
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Introduction tocomplexity
By
Antonio Caperna
www.biourbanism.org
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Key wor s
complexity, determinism, system thinking,fractal, dynamic complex systems
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INTRODUCTION
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The science of the last 150 years has profoundly shaped our
culture and our civilization
This has changed:
how we look at ourselves how we think and feel how we view our social and political institutions,
the findings of science have intentionally separated theprocess of forming mechanical models of physics from theprocess of feeling
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An epistemological paradigmshift was called a "scientific
"and historian of science Thomas Kuhn
in his book Th e S t r u c t u r e o f .
A scientific revolution occurs,according to Kuhn, when scientists
Kuhn used the duck-rabbit opticalillusion to demonstrate the way inwhich a paradigm shift could cause
be explained by the universallyaccepted paradigm within whichscientific ro ress has thereto
entirely different way.been made.The paradigm, in Kuhn's view, is not
simply the current theory, but theentire worldview in which it exists, andall of the implications which come withit
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The Cartesian method show aprioristic reduction and
aprioristic analysis-, , . .
analysing complex things into simple constituents (itsarts
understood a system in terms of its isolated partsPhenomena can be reduced to simple cause & effectrelationshi s overned b linear lawsrelationships are not important
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Descartes mind-matter ontologicalua sm.Mind and matter are separated
.
This means that they have anindependent existence and thedifference between the two is infinite(see Descartes, 1642; Heidegger, 1962;
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Epistemological paradigm shift
scientists encounter anomalies thatcanno e exp a ne y e un versa yaccepted paradigm within which scientific
progress has thereto been made
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Shifting from the old paradigm to thecomp ex y one
The reform in thinking is a key anthropological andhistorical problem. This implies a mental revolution
of considerably greater proportions than theCopernican revolution.
responsibilities of thinking weighed so crushingly on
us.
(E. Morin)
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Biourbanism aims to reformulate the epistemological foundation ofarchitecture and urbanism, introducing the concepts of
Hypercomplexity refers to the methodological shift to the sciences of
systems and emerging phenomena.
Bio ogica roots o arc itecture re ers to t e irect ro e o c emica anphysical rules in the living systems, and the comeback of the La w s o f f o r m .
This leads to new and unexplored scenarios of research, both in
theoretical terms as well as in design and technology.
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e ean ng o a ys ems pproac
" " " ""see" things (or phenomena) as systems
A system is"a group of interrelated, interdependent, or interacting
e emen s orm ng a co ec ve un y(Collins English Dictionary, 1979, p.
1475)
"a complex whole" (The Concise Oxford Dictionary, 1976, p. 1174).
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Systems ThinkingThe systems approach relates to considering wholes
,
account
General Systems Theory (GST)
and in any specialism can all be described by a
common set of ideas related to the holistic interaction
of the components. This nonlinear theory rejects the
idea that system descriptions can be reduced tolinear properties of disjoint parts.
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complexity
disorganizedcomplexity
life sciences
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disorganized complexityIn Weaver's view, disorganized complexity results from the particular system havinga very large number of parts (millions of parts, or many more). Though then erac ons o e par s n a sorganze compex y s ua on can e seen aslargely random, the properties of the system as a whole can be understood by
using probability and statistical methods
',
- the non-random interaction between the parts.- the coordinated system manifests properties not carried or dictated by individual
- this form of complexity shows "emergent" phenomena / behaviour without any"guiding hand".
- this s stemma be understood in its ro erties throu h modelin and simulation(with computers)(example of organized complexity is an ants colony)
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it has too man different definitions in different fields.
Seth Lloyds paper: Measures of Complexity: a non-exhaustive list gives something like 42 di erent de initions
aspects of systems.
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The interaction of
many parts, giving
rise to diff icultiesin linear or
reductionist
analysis due to thenonlinearity of the
inherent circular
causation andfeedback effects
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comp ex sys em nvo ves anumber of elements, arrangedin structure(s) which can exist
on many scales.
These go through processes of
by a single rule nor are
reducible to only one level of
exp ana on, ese eve s o eninclude features whoseemergence cannot be predictedfromthei current specifications.
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A scientific approach structured around a new paradigm:
Made of many non-identical elements
connec e y verse n erac ons
NETWORK
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Common Principles of Complex Systems
components or agents
No central control
hierarchical organization
dynamics
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behavior of systems
Information:The study of representation, symbols, andcommunication
Com utation:The study of how systems processinformation and act on the results
Evolution:The study of how systems adapt to constantlychanging environments
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Every complex system has a. .,
different processes are occurring
on different scales or levels.onnec ons ex s o on e
same levels, and across levels(Mesarovic, Macko et al., 1970).
The same is true for a patternlanguage. The "language"
Drawing an analogy with biological
which the ordering of nodes on
one level creates nodes at a higherof the connections betweensubsystems (Passioura, 1979)
eve . s process goes on a eway up, and all the way down inlevels.
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-systems
General theory
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COMPLEX SYSTEMS
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understanding the complex world around us (Barabsi)
Metabolic NetworkNodes: c em ca s su strates
Links:bio-chemical reactions
Neuronal Network
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Social study
Sarah
Ralph
PeterJane
ma wor s
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Each ant on its own is very simple, butthe colony as a whole can work togethercooperatively to accomplish very
complex tasks, without any centralcontrol;
,
being in charge.
NetLogo
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is a colony of army ants,building a bridge.
them gradually adding themselvesto the structure. Each ant is secretingchemicals to communicate with the
other ants, and the whole bridge isu w ou any cen ra con ro .this is a
decentralized, self-organizing
system
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Another classic
complex systems e ra n
Here theindividual sim leagents are
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The human brain consists ofabout 100 bill ion neurons
and 100 trillion connections
between those neurons.
Each neuron is relatively
brain). Somehow the hugeensemble of neurons andconnections gives rise to thecomplex behaviors we callcogn on or n e gence or
even creativity.
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shows .
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Brain imaging has shown thatthese neurons have organized themselvesinto different functional areas.us e e an s or erm es, neurons can se -organze n o compex
structures thathelp the species function and survive.
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here is an example of the kindof complex living structurebuilt by termites. Termitemound.
A ma or focus of com lexsystems is to understand
agents producecom lex behavior
without central control?
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The Termite Emulation of Regulatory
Mound Environments by Simulation
(TERMES) project at Loughborough
architecture of termite mounds, focusing inparticular on the Sandkings found in Africa.
The work is intended to "serve as both theoun aton or uture as c researc , an asinspiration for more tangible and immediateinnovations in architecture, structural and
"structures are "shaped to accommodateand regulate the exchanges of respiratorygases between the nest and atmosphere"an us prov e a po en a mo e ordeveloping sustainable building structuresfor humans. The website outlines the
research ro ect rovidin information onthe structure and functions of the mounds,as well as a discussion of their objectives,methods and simulation techniques.
https://scout.wisc.edu/archives/r22541
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It has often been said acity is like a living
organ sm n many ways,but to what extent do
cities actually resembleliving organisms, in theways they are structured,row, scale with size, and
operate? These andother questions form the
area of complex systemsresearch, which well look
course.
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Core Disciplines
Dynamics
Information
Evolution
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Dynamics
stud of how
systemsc ange over
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Crowd dynamics
Dynamics of
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Dynamical Systems Theory:- the branch of mathematics of how systems change over time
Differential equations Iterated maps
etc.
The dynamics of a system: the manner in which the systemchanges
Dynamical systems theory gives us a vocabulary and set of toolsfor describing dynamics
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If we knew exactly the laws of nature and thesituation of the universe at the init ial moment, we
could predict exactly the situation of that same
un verse a a succee ng momen .But even if it were the case that the natural laws had
no longer any secret for us, we could still only know .us to predict the succeeding situation with the sameapproximation, that is all we require, and we should
,
is governed by laws.But it is not always so;
conditions produce very great ones in the final
phenomena.
A small error in the former will roduce an enormous
Henri Poincar, 1854 1912
error in the latter.Prediction becomes impossible...
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Sensitive dependence on initial conditions
http://www.fws.gov/sacramento/ES_Kids/Mi
ssion-Blue-Butterfly/Images/mission-blue-butterfly_header.jpg
http://pmm.nasa.gov/sites/default/files/imageGallery/hurricane_depth.jpg
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Sensitive dependence on initial conditions
NetLogo experiment
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Chaos:
One particular type of dynamics of a
De ne as sensitive dependence oninitial conditions
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Weather and climate the butterfl effectCHAOS IN NATURE
Brain activity (EEG)
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CHAOS IN NATURE
Heart activity (EKG) Financial data
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e erm n s c c aos
The fact that the simple anddeterministic equation [i.e., theLogistic Map] can possess
d namical tra ectories whichlook like some sort of randomnoise has disturbing practical
.
This means that, even if wehave a simple model in
Lord Robert May (b. 1936)
determined exactly, long-term prediction isnever e ess mposs e Robert May, 1976
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change in the input to a certainsystem of equations resulted ina surprising y arge c ange inoutput.
Lord Robert May (b. 1936)
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Chaos: Seemingly random behavior with sensitiveepen ence on n t a con t ons
,that, when iterated, can display chaos (depending on the valueofR).
Deterministic chaos: Perfect prediction, a la Laplacese ermn s c c oc wor unverse , s mposs e, even n
principle, if were looking at a chaotic system.
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Universality in ChaosW i e c aotic systems are not pre icta e in etai , a
wide class of chaotic systems has highly predictable,
.
How can we understand this universality?
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og s c map. urca on agram
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Significance of dynamics and chaos for complex systems
Complex, unpredictable behavior from simple, deterministic
rules
Dynamics gives us a vocabulary for describing complex
There are fundamental limits to detailed rediction
At the same time there is universality: Order in Chaos
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Antonio Caperna PhDAntonio Caperna : Introduction to complexity
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NETWORK
interdisciplinary academic field whichs u es compex ne wor s suc as,information networks, biological networks,cognitive and semantic networks, and
.The field draws on theories and methodsincluding graph theory from mathematics,
,
mining and information visualization fromcomputer science, inferential modeling from,
sociology.The National Research Council defines
network science as "the stud of networkrepresentations of physical, biological, andsocial phenomena leading to predictivemodels of these henomena
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The term fractal describe suchobjects, was coined by the
,from the Latin root for fractured.
Mandelbrots goal was todevelop a mathematical theory
of roughness to better describe
the natural world.
He brought together the work ofdifferent mathematicians in different
Geometry.
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"fractal" from the Latin fractus or"to break"
is an object or quantity that
displays self-similarity on allscales.
of the simplest fractals is self-similarity: the shape is made of.
copies are similar to the whole:same shape but different size
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The Koch curve is a classiciterated fractal curve.It is a theoretical constructthat is made by iterativelyscaling a starting segment.
- each new se ment isscaled by 1/3 into 4 newpieces laid end to endwith 2 middle piecesleaning toward each
other between the othertwo pieces,
Whereas the animation only
shows a few iterations, thetheoretical curve is scaled inthis way infinitely.
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"Fractal Geometry plays two roles. Itis the geometry of deterministic
c aos an can a so escr e e
geometry of mountains, clouds and
galaxies." - Benoit Mandelbrot
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One of the largest relationships with real-life is the similarity betweenfractals and objects in nature. The resemblance many fractals and their
- .Mathematical formulas are used to model self similar natural forms. Thepattern is repeated at a large scale and patterns evolve to mimic large
.
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Trees show self-similarity atdifferent scales
Plant roots
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ea e ns are rac a
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Gloucester, cathedral, chiostro
Granada : Alhambra
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ne o e more rva app ca ons o rac a s stheir visual effect.
Not only do fractals have a stunning aesthetic
the eye, but they also have a way to trick themind.
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Plan of a non-fractal modernist city.
Plan of unrealistically ordered fractal city
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Traditional urban
characterized by
fractal interfaces Cobweb(Batty and Longley,
1994; Bovill, 1996;
Aerial
ran auser, .
The simplest definition
Chinese
town
structure that shows
complexity at any
magnification
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N= reduction factor from previous level = 3M= number of copies of previous level = 4
Dimension
D = lo M lo N
Log 4 / log 3 ~1.26
This version of fractal dimension iscalled H au s d o r f f D im e n s i o n ,after the German mathematicianFelix Hausdorff
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Cantor set in seven iterations
Fractal Dimension
D = log M / log N
N= reduction factor from previous level = 2M= number of copies of previous level = 3
Log 2 / log 3 ~ 0.63
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Broccoli. D = 2.66
The alveoli of a lung form a fractalsurface close to 3
Surface of human brain.D = 2.79
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ercep ua an ys o og ca esponses o ac son
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ercep ua an ys o og ca esponses o ac son
Pollock's Fractals(Richard P. Taylor, Branka Spehar, Paul Van Donkelaar, and Caroline M. Hagerhall)
Examples of natural scenery (leftcolumn) and poured paintings (rightcolumn).
Top: Clouds and Pollock's paintingUntitled (1945) are fractal patternswith low D values D=1.3 and 1.10respectively).
'o om: ores an o oc spainting ...
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ercep ua an ys o og ca esponses o ac son
Pollock's Fractals(Richard P. Taylor, Branka Spehar, Paul Van Donkelaar, and Caroline M. Hagerhall)
our preliminary experiments provide a fascinating insightinto the i m p a c t t h a t a r t m i g h t h a v e o n t h e p e r ce p t u a l ,
.
e x p l o r e t h e p o s s ib i l i t y o f i n c o r p o r a t i n g f r a c t a l a r t i n t o ,
t h e v i su a l c h a r a c t e r i s t i c s o f a r t i f i c i a l e n v i r o n m e n t s t o
t h e p o s i t i v e r e sp o n s es
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rac a ana ys s n a ys ems o ogy approac o cancer
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rac a ana ys s n a ys ems o ogy approac o cancer
M. Bizzarri1, A. Giuliani2, A. Cucina3, F. D Anselmi3, A. M. Soto#, and C. Sonnenschein#1 Dep.t of Experimental Medicine, Univesity La Sapienza, Roma, Italy2 Istituto Superiore di Sanit, Roma, Italy
, , ,# Tufts University School of Medicine. Department of Anatomy and Cellular Biology and Programin Cell, Molecular and Developmental Biology. Boston, MA 02111. USA
They- sketch a general frame for a systemic cancer appreciation-fractal analysis in the construction of a reliable phase space for cancer
development.
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CONCLUSION
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CONCLUSION
- cancer can be reversed by both physical as well chemical morphogeneticfactors belonging to different embryonic morphogenetic fields.
- rediscovery of the morphogenetic field as a major protagonist in ontogenicand phylogenic change. Indeed, in our view, morphogenetic field effects revertcancer phenotypic traits through the induction of dramatic shape changes.
o ca on o rac a parame ers g g s a para e c ange n
thermodynamics constraints.Thus, it stands to reason that such modifications might be followed by remarkable, ,
behavior
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responsibility towards all the shapes and spaces of the world, in which we
try, first theoretically and then practically, and then again in handicraft and
,processes that govern and give a shape to the buildings of the world, in
order to allow each place to become a living structure, and the whole
wor , n s en reness, a eau u p ace
this is the only idea of architecture really making sense.
Christopher Alexander, The Nature of Order
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REFERENCES
Weaver, Warren (1948). " Sc i en c e a n d Com p l e x i t y ".AmericanScientist36 (4): 53644. PMID 18882675. Retrieved 2007-11-21
Johnson, Steven (2001). Em e r g e n c e : t h e c o n n e c t e d l i v e s o f a n t s ,b r a i n s , c i t i e s , a n d s o f t w a r e . New York: Scribner. p. 46. ISBN 0-684-86875-X
Complexity: A Guided Tour, by Melanie Mitchell
Antonio Caperna : Introduction to complexity