Introduction to Complexity Science, by Antonio Caperna

ISB SUMMER SCHOOL 2013: NEUROERGONOMICS AND URBAN PLACEMAKING
Introduction to
complexity
Byy
Antonio Caperna
www.biourbanism.org
antonio.caperna@biourbanism.org
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 epistemologistrevolution 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 parts
Phenomena can be reduced to simple cause & effect
relationships governed by linear lawsp g y
relationships are not important

Descartes’ mind-matter ontological
d lidualism.
Mind and matter are separated
substancessubstances.
This means that they have an
independent existence and thep
difference 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 llcannot 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 complexcomplexity – 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 Thinking
The 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 they
inherent circular
causation and
feedback effects

A complex system involves a
A complex system involves a
number of elements, arranged
in structure(s) which can exist
on many scales.
These go through processes of
change that are not describablechange that are not describable
by a single rule nor are
reducible to only one level of
l ti th l l ftexplanation, these levels often
include features whose
emergence cannot be predicted
from their current specifications.

A scientific approach structured around a new paradigm:
complex Systemscomplex Systems
Made of many non-identical elements
t 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 processp y y p
information and act on the results
Evolution: The study of how systems adapt to constantly
changing environments

Every complex system has a
hierarchical structure; i ehierarchical structure; i.e.,
different processes are occurring
on different scales or levels.
C ti i t b th thConnections 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 SYSTEMS
EXAMPLESEXAMPLES

“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 Network
Nodes: chemicals (substrates)
Links: bio-chemical reactions
Neuronal Network

Social study
Sarah
Ralph
Peter
Jane
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 aexample of a
complex system
i th b iis the brain
Here the
individual simpled dua s p e
agents 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 themselves
into 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 complex
structures that help the species function and survive.

here is an example of the kind
of complex living structure
built by termites. Termitey
mound.
A major focus of complexA major focus of complex
systems is to understand
How individually simpleHow individually simple
agents produce
complex behaviorp
without central control?

The Termite Emulation of Regulatory
Mound Environments by Simulation
(TERMES) project at Loughborough
University 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, andg , ,
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 generalThe general
study of howy
systems
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 know
the 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/Mi
ssion-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 NATURE
a 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 whichy j
look like some sort of random
noise has disturbing practical
implicationsimplications. …
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 smallLorenz 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 Chaos
Whil h i di bl i d ilWhile 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 Fractal
Geometry.

"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 isg
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 at
different 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 Dimension
N = reduction factor from previous level = 3
M = number of copies of previous level = 4
Dimension
D = log M / log Nog / og
Log 4 / log 3 ~1.26g / g
This version of fractal dimension iss e s o o acta d e s o s
called Hausdorff Dimension,
after the German mathematician
Felix Hausdorff

Cantor set in seven iterations
Fractal Dimension
D = log M / log N
N = reduction factor from previous level = 2
M = 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
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'sBottom: A forest and Pollock's
painting ...

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 observerphysiological and neurological condition of the observer.
… explore the possibility of incorporating fractal art into
the interior and exterior of buildings in order to adaptthe 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 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, Italy
2 Istituto Superiore di Sanità, Roma, Italy
3 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 Program
in 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 byhighlight the relevance of the shape of cells and tissues as studied by
fractal analysis in the construction of a reliable phase space for cancer
development.

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 ontogenic
and 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 differentiating
behavior

“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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