Introduction to Complexity Science, by Antonio Caperna, PhD

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ISB SUMMER SCHOOL 2013: NEUROERGONOMICS AND URBAN PLACEMAKING

Introduction tocomplexity

By

Antonio Caperna

www.biourbanism.org

[email protected]

Antonio Caperna : Introduction to complexity


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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


ISB SUMMER SCHOOL 2013 NEUROERGONOMICS AND URBAN PLACEMAKING


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Another classic

complex systems e ra n

Here theindividual sim leagents are


ISB SUMMER SCHOOL 2013 NEUROERGONOMICS AND URBAN PLACEMAKING


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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



ercep ua an ys o og ca esponses o ac son


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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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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



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.



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


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Introduction to Complexity Science, by Antonio Caperna, PhD