Introduction to Complexity Science, by Antonio Caperna

ISB SUMMER SCHOOL 2013: NEUROERGONOMICS AND URBAN PLACEMAKING

Introduction tocomplexity

Byy

Antonio Caperna

www.biourbanism.org

[email protected]

Antonio Caperna : Introduction to complexity


dKey words

complexity, determinism, system thinking, fractal, dynamic complex systemsy p y



INTRODUCTION



The science of the last 150 years has profoundly shaped our culture and our civilization

This has changed: Our Knowledge Our Knowledge how we look at ourselves how we think and feel, o e a d ee , how we view our social and political institutions, the findings of science have intentionally separated the process of forming mechanical models of physics from the process of feeling



An epistemological paradigm shift was called a "scientific revolution" by epistemologist revolution by epistemologist and historian of science Thomas Kuhn in his book The Structure of Scientific RevolutionsScientific Revolutions.A scientific revolution occurs, according to Kuhn, when scientists encounter anomalies that cannot

Kuhn used the duck-rabbit optical illusion to demonstrate the way in which a paradigm shift could cause one to see the same information in an

encounter anomalies that cannot be explained by the universally accepted paradigm within which scientific progress has thereto one to see the same information in an

entirely different way.p g

been made. The paradigm, in Kuhn's view, is not simply the current theory, but the entire worldview in which it exists, and all of the implications which come with it



The Cartesian method show aprioristic reduction and aprioristic analysis(Descartes 1637 pp 20-21)(Descartes, 1637, pp. 20 21).

analysing complex things into simple constituents (its parts)parts)understood a system in terms of its isolated partsPhenomena can be reduced to simple cause & effect relationships governed by linear lawsp g yrelationships are not important



Descartes’ mind-matter ontological d lidualism.

Mind and matter are separated substancessubstances.

This means that they have an independent existence and the pdifference between the two is infinite (see Descartes, 1642; Heidegger, 1962; Fuenmayor, 1985).Fuenmayor, 1985).



Epistemological paradigm shift

scientists encounter anomalies that t b l i d b th i ll cannot be explained by the universally

accepted paradigm within which scientific progress has thereto been made



Complexity scienceComplexity science



Shifting from the old paradigm to the l itcomplexity one

The reform in thinking is a key anthropological and historical problem. This implies a mental revolution of considerably greater proportions than the Copernican revolution. Never before in the history of humanity have theNever before in the history of humanity have the responsibilities of thinking weighed so crushingly on us.us.

(E. Morin)



Biourbanism aims to reformulate the epistemological foundation of architecture and urbanism, introducing the concepts of (hyper)complexity and biological roots of architecture.(hyper)complexity and biological roots of architecture.

Hypercomplexity refers to the methodological shift to the sciences of complexity an interdisciplinary model about adaptive complex complexity – an interdisciplinary model about adaptive complex systems and emerging phenomena.

i l i l f hi f h di l f h i l dBiological roots of architecture refers to the direct role of chemical and physical rules in the living systems, and the comeback of the Laws of form.

This leads to new and unexplored scenarios of research, both in theoretical terms as well as in design and technology.


Th M i f S t A h


The Meaning of a Systems Approach

A "systems approach" means to "approach" orA systems approach means to approach or "see" things (or phenomena) as systems

A system is "a group of interrelated, interdependent, or interacting l t f i ll ti it "elements forming a collective unity" (Collins English Dictionary, 1979, p.

1475)

"a complex whole" (The Concise Oxford Dictionary, 1976, p. 1174).



Systems ThinkingThe systems approach relates to considering wholes rather than parts taking all the interactions intorather than parts, taking all the interactions into account

General Systems Theory (GST)The interdisciplinary idea that systems of any typeThe interdisciplinary idea that systems of any type and in any specialism can all be described by a common set of ideas related to the holistic interactioncommon set of ideas related to the holistic interaction of the components. This nonlinear theory rejects the idea that system descriptions can be reduced to linear properties of disjoint parts.



complexity

disorganized complexity

life sciences



disorganized complexity In Weaver's view, disorganized complexity results from the particular system having a very large number of parts (millions of parts, or many more). Though the i t ti f th t i "di i d l it " it ti binteractions of the parts in a "disorganized complexity" situation can be seen as largely random, the properties of the system as a whole can be understood by using probability and statistical methods (example of disorganized complexity is a gas in a container)(example of disorganized complexity is a gas in a container)

Organized complexity in Weaver's view:Organized complexity, in Weaver s view:- the non-random interaction between the parts. - the coordinated system manifests properties not carried or dictated by individual partsparts- this form of complexity shows "emergent" phenomena / behaviour without any "guiding hand".- this system may be understood in its properties through modeling and simulationthis system may be understood in its properties through modeling and simulation (with computers)(example of organized complexity is an ants colony)


Complexity is hard to define!


Complexity is hard to define!

it has too many different definitions in different fields.y

Seth Lloyd’s paper: “Measures of Complexity: a non-” ff fexhaustive list” gives something like 42 different definitions

These different definitions are useful for measuring differentThese different definitions are useful for measuring different aspects of systems.


COMPLEXITY


COMPLEXITY

The interaction of many parts, giving rise to difficulties in linear or reductionist analysis due to the nonlinearity of the yinherent circular causation and feedback effects


A complex system involves a


A complex system involves anumber of elements, arrangedin structure(s) which can existon many scales.

These go through processes ofchange that are not describablechange that are not describableby a single rule nor arereducible to only one level of

l ti th l l ftexplanation, these levels ofteninclude features whoseemergence cannot be predictedfrom their current specifications.



A scientific approach structured around a new paradigm:

complex Systemscomplex Systems

Made of many non-identical elementst d b di i t ticonnected by diverse interactions

NETWORK



Common Principles of Complex Systems

components or agents Nonlinear interactions among components Nonlinear interactions among components No central control Emergent behaviors Emergent behaviors

• hierarchical organization• information processing• information processing• dynamics• evolution and learning• evolution and learning


Core Disciplines


Core Disciplines

Dynamics: The study of continually changing structure andDynamics: The study of continually changing structure and behavior of systems

Information: The study of representation, symbols, and communication

Computation: The study of how systems process p y y pinformation and act on the results

Evolution: The study of how systems adapt to constantly changing environments



Every complex system has a hierarchical structure; i e hierarchical structure; i.e., different processes are occurring on different scales or levels. C ti i t b th th Connections exist both on the same levels, and across levels (Mesarovic, Macko et al., 1970).

The same is true for a pattern language. The "language" generates a connective network by

Drawing an analogy with biological systems, the system works because

generates a connective network by which the ordering of nodes on one level creates nodes at a higher l l Thi ll th systems, the system works because

of the connections between subsystems (Passioura, 1979)

level. This process goes on all the way up, and all the way down in levels.



Goals:Goals:

Cross disciplinary insights into complex– Cross-disciplinary insights into complex systems

– General theory





COMPLEX SYSTEMSEXAMPLESEXAMPLES


“The construction and structure of graphs or networks is the key to

h i l ( b )

The construction and structure of graphs or networks is the key to understanding the complex world around us” (Barabási)

Metabolic NetworkNodes: chemicals (substrates)

Links: bio-chemical reactions

Neuronal Network



Social study

Sarah

Ralph

PeterJane

S ll ldSmall worlds



Each ant on its own is very simple, but the colony as a whole can work together cooperatively to accomplish very

complex tasks, without any central control; that is without any ant or group of antsthat is, without any ant or group of ants being in charge.

NetLogo



is a colony of army ants, building a bridge.

… them gradually adding themselves to the structure. Each ant is secreting chemicals to communicate with the other ants, and the whole bridge is b ilt ith t t l t lbuilt without any central control. this is a “decentralized, self-organizing

t ”system”



Another classic example of a example of a complex system i th b iis the brain

Here the individual simple d dua s p eagents are neuron(s?)neuron(s?)



The human brain consists of about 100 billion neurons and 100 trillion connections between those neurons.

Each neuron is relatively simple (compared to the wholesimple (compared to the whole brain). Somehow the huge ensemble of neurons and connections gives rise to the complex behaviors we call “ iti ” “i t lli ”“cognition” or “intelligence” or even “creativity”.



Brain imagingBrain imaging shows ….

oooppppsss…oooppppsss…



Brain imaging has shown that these neurons have organized themselvesinto different functional areas.J t lik th t t it lf i i t lJust like the ants or termites, neurons can self-organize into complexstructures that help the species function and survive.



here is an example of the kind of complex living structurebuilt by termites. Termite ymound.

A major focus of complexA major focus of complex systems is to understand

How individually simpleHow individually simple agents produce complex behavior pwithout central control?



The Termite Emulation of Regulatory Mound Environments by Simulation (TERMES) project at LoughboroughUniversity seeks to understand the complexUniversity seeks to understand the complex architecture of termite mounds, focusing in particular on the Sandkings found in Africa. The work is intended to "serve as both the f d i f f b i h dfoundation for future basic research, and as inspiration for more tangible and immediate innovations in architecture, structural and environmental engineering." The termiteenvironmental engineering. The termite structures are "shaped to accommodate and regulate the exchanges of respiratory gases between the nest and atmosphere"

d th id t ti l d l fand thus provide a potential model for developing sustainable building structures for humans. The website outlines the research project, providing information onresearch project, providing information on the structure and functions of the mounds, as well as a discussion of their objectives, methods and simulation techniques.

https://scout.wisc.edu/archives/r22541



It has often been said a city is like a living

i iorganism in many ways, but to what extent do cities actually resemble living organisms, in the ways they are structured, grow, scale with size, and g , ,operate? These and other questions form the basis of a rapidly growingbasis of a rapidly growing area of complex systems research, which we’ll look at in detail later in theat in detail later in the course.



Core Disciplines

Dynamics

Informationo at o

ComputationComputation

Evolution



Dynamics

The general The general study of how ysystems hchange over

timetime



Crowd dynamics

Dynamics of stock pricesstock prices



Dynamical Systems Theory:- the branch of mathematics of how systems change over time CalculusCalculus Differential equations Iterated maps Algebraic topology Algebraic topology etc.

– The dynamics of a system: the manner in which the system changes– Dynamical systems theory gives us a vocabulary and set of tools for describing dynamics



“If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of that same

i t di tuniverse at a succeeding moment. But even if it were the case that the natural laws had no longer any secret for us, we could still only knowthe initial situation approximately If that enabledthe initial situation approximately. If that enabled us to predict the succeeding situation with the same approximation, that is all we require, and we should say that the phenomenon had been predicted that itsay that the phenomenon had been predicted, that it is governed by laws. But it is not always so; it may happen that small differences in the initialit may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous

Henri Poincaré, 1854 – 1912

A small error in the former will produce an enormous error in the latter.Prediction becomes impossible...”



“Sensitive dependence on initial conditions”

http://www.fws.gov/sacramento/ES_Kids/Mission-Blue-Butterfly/Images/mission-blue-butterfly_header.jpg

http://pmm.nasa.gov/sites/default/files/imageGallery/hurricane_depth.jpg



“Sensitive dependence on initial conditions”

NetLogo experiment



Chaos:

– One particular type of dynamics of a systemsystem

D fi d “ i i d d– Defined as “sensitive dependence on initial conditions”



• Weather and climate (the “butterfly effect”)

CHAOS IN NATUREa a d a ( bu y )

• Brain activity (EEG)



C OSCHAOS IN NATURE

• Heart activity (EKG)• Financial data



D t i i ti hDeterministic chaos

“The fact that the simple and deterministic equation [i.e., the Logistic Map] can possess dynamical trajectories which y jlook like some sort of random noise has disturbing practical implications implications. …This means that, even if we have a simple model in which all the parameters are

Lord Robert May (b. 1936)which all the parameters are determined exactly, long-term prediction is

th l i ibl ”nevertheless impossible”−− Robert May, 1976



Lorenz discovered that a small Lorenz discovered that a small change in the input to a certain system of equations resulted in

l l ha surprisingly large change in output.

Lord Robert May (b. 1936)



Chaos: Seemingly random behavior with sensitive d d i iti l ditidependence on initial conditions

Logistic map: A simple completely deterministic equationLogistic map: A simple, completely deterministic equation that, when iterated, can display chaos (depending on the value of R).)

Deterministic chaos: Perfect prediction, a la Laplace’s d t i i ti “ l k k i ” i i ibl ideterministic “clockwork universe”, is impossible, even in principle, if we’re looking at a chaotic system.



Universality in ChaosWhil h i di bl i d il While chaotic systems are not predictable in detail, a wide class of chaotic systems has highly predictable, “universal” propertiesuniversal properties.

How can we understand this universality?



L i ti Bif ti diLogistic map. Bifurcation diagram



Significance of dynamics and chaos for complex systems

Complex, unpredictable behavior from simple, deterministic rules

Dynamics gives us a vocabulary for describing complex behaviorbehavior

There are fundamental limits to detailed predictionp

At the same time there is universality: “Order in Chaos”


ISB SUMMER SCHOOL 2012: NEUROERGONOMICS AND URBAN DESIGN

Antonio Caperna PhDAntonio Caperna : Introduction to complexity


NETWORK

interdisciplinary academic field which t di l t k hstudies complex networks such as,

information networks, biological networks, cognitive and semantic networks, and social networkssocial networks. The field draws on theories and methods including graph theory from mathematics, statistical mechanics from physics datastatistical mechanics from physics, data mining and information visualization from computer science, inferential modeling from statistics and social structure fromstatistics, and social structure from sociology. The National Research Council defines network science as "the study of networknetwork science as the study of network representations of physical, biological, and social phenomena leading to predictive models of these phenomena”p



The term fractal describe such objects, was coined by the mathematician Benoit Mandelbrotmathematician Benoit Mandelbrot, from the Latin root for “fractured”.

Mandelbrot’s goal was to develop a mathematical “theory of roughness” to better describe the natural world.

He brought together the work of different mathematicians in different fields to create the field of Fractalfields to create the field of FractalGeometry.



"fractal" from the Latin fractus or "to break"

is an object or quantity that displays self-similarity on all

lscales.

The geometric characterizationThe geometric characterization of the simplest fractals is self-similarity: the shape is made of smaller copies of itself Thesmaller copies of itself. The copies are similar to the whole: same shape but different size



The Koch curve is a classic iterated fractal curve. It is a theoretical construct that is made by iteratively scaling a starting segment. - each new segment is g

scaled by 1/3 into 4 new pieces laid end to end with 2 middle pieces leaning toward each other between the other two pieces,

Whereas the animation only shows a few iterations, the ,theoretical curve is scaled in this way infinitely.



"Fractal Geometry plays two roles. It is the geometry of deterministic h d it l d ib thchaos and it can also describe the

geometry of mountains, clouds and galaxies." - Benoit Mandelbrot



One of the largest relationships with real-life is the similarity between fractals and objects in nature. The resemblance many fractals and their natural counter-parts is so large that it cannot be overlookednatural counter parts is so large that it cannot be overlooked. Mathematical formulas are used to model self similar natural forms. The pattern is repeated at a large scale and patterns evolve to mimic large scale real world objectsscale real world objects.



Trees show self-similarity atdifferent scales

Plant roots


World wide web


World wide web

L f V i F t lLeaf Veins are Fractal



Gloucester, cathedral, chiostro

Granada : Alhambra



O f th t i i l li ti f f t l iOne of the more trivial applications of fractals is their visual effect.

Not only do fractals have a stunning aesthetic value, that is, they are remarkably pleasing tovalue, that is, they are remarkably pleasing to the eye, but they also have a way to trick the mind.mind.



Plan of a non-fractal modernist city.

Plan of unrealistically ordered fractal city



Traditional urban geometry isgeometry is characterized by fractal interfaces

Cobweb(Batty and Longley, 1994; Bovill, 1996; Frankha ser 1994)

Aerial view of

Frankhauser, 1994). The simplest definition of a fractal is a view of

Chinese town

of a fractal is a structure that shows complexity at any magnification



Fractal DimensionFractal DimensionN = reduction factor from previous level = 3M = number of copies of previous level = 4

DimensionD = log M / log N og / og

Log 4 / log 3 ~1.26g / g

This version of fractal dimension is s e s o o acta d e s o scalled Hausdorff Dimension,after the German mathematician Felix Hausdorff



Cantor set in seven iterations

Fractal DimensionD = log M / log N

N = reduction factor from previous level = 2M = number of copies of previous level = 3

Log 2 / log 3 ~ 0.63



Broccoli. D = 2.66

The alveoli of a lung form a fractal surface close to 3

Surface of human brain.D = 2.79


Perceptual and Physiological Responses to Jackson


Perceptual and Physiological Responses to Jackson Pollock's Fractals(Richard P. Taylor, Branka Spehar, Paul Van Donkelaar, and Caroline M. Hagerhall)

Examples of natural scenery (left column) and poured paintings (right column).

Top: Clouds and Pollock's painting Untitled (1945) are fractal patterns with low D values (D=1.3 and 1.10 (respectively).

Bottom: A forest and Pollock's Bottom: A forest and Pollock's painting ...


Perceptual and Physiological Responses to Jackson


Perceptual and Physiological Responses to Jackson Pollock's Fractals(Richard P. Taylor, Branka Spehar, Paul Van Donkelaar, and Caroline M. Hagerhall)

… our preliminary experiments provide a fascinating insight into the impact that art might have on the perceptual, physiological and neurological condition of the observer physiological and neurological condition of the observer.

… explore the possibility of incorporating fractal art into the interior and exterior of buildings in order to adapt the interior and exterior of buildings, in order to adapt the visual characteristics of artificial environments to the positive responses


Fractal analysis in a Systems Biology approach to cancer


Fractal analysis in a Systems Biology approach to cancerM. 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 Sanità, Roma, Italy3 Dept of Surgery Pietro Valdoni Univesity La Sapienza Roma Italy3 Dept of Surgery Pietro Valdoni, Univesity La Sapienza, 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- highlight the relevance of the shape of cells and tissues as studied by highlight the relevance of the shape of cells and tissues as studied by fractal analysis in the construction of a reliable phase space for cancerdevelopment.



CONCLUSION

- cancer can be reversed by both physical as well chemical morphogenetic factors 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 revert cancer phenotypic traits through the induction of dramatic shape changes.

M difi ti f f t l t hi hli ht ll l h iModification of fractal parameters highlights a parallel change in thermodynamics constraints. Thus, it stands to reason that such modifications might be followed by remarkable changes in cell proliferation patterns metabolism as well as tissue differentiatingchanges in cell proliferation patterns, metabolism, as well as tissue differentiatingbehavior



“I imagine a new role for us architects, in which we take more seriously ourI imagine a new role for us architects, in which we take more seriously our 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 arts to help the various societies of the planet to take control over thearts, to help the various societies of the planet to take control over the 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

orld in its entireness a bea tif l place [ ]world, in its entireness, a beautiful place […]… this is the only idea of architecture really making sense.

Christopher Alexander, The Nature of Order



REFERENCES

Weaver, Warren (1948). "Science and Complexity". American Scientist 36 (4): 536–44. PMID 18882675. Retrieved 2007-11-21

Johnson, Steven (2001). Emergence: the connected lives of ants, brains, cities, and software. New York: Scribner. p. 46. ISBN 0-684-86875-X

Complexity: A Guided Tour, by Melanie Mitchell


Introduction to Complexity Science, by Antonio Caperna

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