PROPOLIS

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The Brunel Complexity Community Seminar,
Thursday, November 9, 2006 Complexity, Cities
and Planning Understanding and Modelling Cities
from the Ground Up Michael Batty University
College London

Centre for Advanced Spatial Analysis, University
College London
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• An Outline
• The Argument, A Message
• From Systems Sciences to Complexity Sciences
• Key Ideas Feedback, Nonlinearity, Path
  Dependence, Emergence
• Evolution, Connections, Emergence
• Four Examples Segregation and Cities, Transport
  Networks, Urban Growth, City-Size Distributions
• 5. Evolution and Prediction, Evolution and
  Design
• 6. A Sketch of a Case Study How Do We Use These
  Ideas?
• 7. Conclusions and Next Steps

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• The Argument, A Message
• The Mid 20thC Cities/Systems as Machines
• The Early 21stC Cities/Systems as Organisms
• A Switch from Designing Structures to Evolving
  Forms
• Structure to Behavior Form to Process
• A Slow March from Physicalism to Social Processes
• A Switch in Viewpoint what can be planned or
  designed
• A Switch top down to bottom up, from
  centralized to decentralized ways of how systems
  are built
• A Progression from Local to Global and back
  again, echoing the theme of yesterday but also a
  recurrent and important issue local actions
  generate global order and organization

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• Generative Social Science understanding systems
  only if you can evolve or grow them
• Let me tell you how we got from thinking of the
  world as machines to thinking of it as
  organisms, as behavior, a paradigm shift as
  deeply embedded now in physics as it is in
  sociology
• In a way this history resonates in many different
  areas of the sciences, social sciences, the
  arts, the humanities, the professions.
• But of course here I will explain it from my own
  perspective, notwithstanding that there are many
  others

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2. From Systems Sciences to Complexity
Sciences The origins of systems theory Systems
theory in the 1950s and 1960s Quantitative
social science, geography etc The Systems View
of Planning Cities as machines, designs as
controllers, top down command economy style
thinking But .there were seeds of a more
sophisticated view of physical and social systems
right from the beginning..
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In fact, the key leitmotiv of the movement was
bound up in the notion of complexity it was
the whole is greater than the sum of the
parts And it is paralleled in the arts and
elsewhere with similar clichés less is more
and more is different Straws in the wind The
precursors of complexity in the urban domain,
active then as now Chris Alexander and Jane
Jacobs let me tell you what they said and still
say as the world turns full circle to their point
of view. Alexander has worked on the bottom up
approach to design from the late 1950s as
reflected in his four volume magnum opus The
Nature of Order
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Jane Jacobs in the much neglected parts of her
book The Death and Life of Great American Cities
drew on Warren Weavers classification of science
into three types Problems of simplicity few
often no more than two variables being used to
explain everything Problems of disorganized
complexity problems of many variables being used
to explain everything through their interactions
in a mindless fashion Problems of organized
complexity where the seeming randomness of
interaction was anything but mindless it is
these latter types of problem that Jacobs argued
where the problems that faced the development and
planning of cities
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3. Key Ideas Feedback, Nonlinearity, Path
Dependence, Emergence OK, we could talk about
this stuff for ever but lets get up to date as
the 20th century wore on, gradually in my own
field, the top down paradigm came to be destroyed
the key milestones were things like No such
things as equilibrium, dynamics and time became
central with ideas about catastrophe,
bifurcation, chaos being explored Aggregate
models fell into disrepute, new data and software
changed our ability to simulate at different
scales.
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Out of all this came complexity theory first a
fusion of bottom up dynamics with new ways of
simulation Emphasizing the notion that novel
and surprising things should be explained rather
than the mechanistic routine structures of an
earlier age And there has been a shift too in
the kinds of systems that catch our interest a
shift from aggregates to bits, from wholes to
parts, from entire structures to one-off events
this is resonant with post modernism, and non
representational theory and all that sort of
stuff that people talk about in the mainstream
social sciences. There are many writings and
groups in this area but the Santa Fe Institute
represents a focus..
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• But first a very quick sketch of what complexity
  theory is a 3 minute primer
• Basic conundrums of complex systems
• Complex systems have too many variables to be
  able to use traditional methods to handle too
  many interactions
• The elements of complex systems are complex
  systems in their own right i.e. people,
  organizations
• Such systems are thus unpredictable
• The space of solutions is infinite the so
  called phase space and it cant be pinned down
  or traversed

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• Several ideas have become key
• The notion that dynamics temporal change is
  central and that feedback drives such systems
  usually positively as in population growth
• From the dynamics, surprising or novel change
  occurs which is unanticipated
• This change is emergence
• Complex systems are path dependent in that once
  set on a course of change, this make a difference
  thus history matters and systems are said to
  lock in to a process or pattern

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• Complex systems are thus sensitive to initial
  conditions
• Novel change can be triggered by small events
  big changes can be triggered by small events
  such systems have tipping points a la Gladwell
• Such systems adapt and mutate and through
  feedback they show self organization at the level
  of their parts there is no hidden hand
• Self-organization depends on evolution and
  co-evolution which is competition, beyond
  Darwinism. Survival of the fittest elements is
  not as simple as we have assumed it to be

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Complex systems thus evolve from the bottom up
from their parts. They are unpredictable in this
sense. The bottom up paradigm is in contrast to
the top down although it is likely that this is a
gross simplification and that complex systems
manifest a combination of bottom up and top down
Ok, Enough of words, Let us look at some
examples, some pictures and I have three for
cities that illustrate a few of these
themes Four Examples Segregation and Cities,
Transport Networks, Urban Growth
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4. Evolution, Connections, Emergence Example 1
Segregation and Cities Schellings Model In
essence if we divide the population up into two
groups who basically will live peacefully along
side each other if no one group is in the
majority so a 50-50 balance is fine this model
shows that as soon as we get 51-49, the system
will unravel We get extreme segregation with
relatively mild preferences for living besides
ones own kind This was a model that goes back to
1969 and even before but has only come onto our
comprehension in the last 15 years ! As a result
of complexity theory
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• Schellings Model shows
• The idea of a fragile equilibrium
• The idea of tipping points
• The idea of a phase transition suddenly a
  system which is randomly mixed with a fragile
  balance falls apart with one change
• Small change leads to dramatic change
• Surprising and unexpected change - emergence
• Positive feedback
• Lets see how it works
• We start with a grid - lattice of points which
  exist in a space like a city and we populate this
  like a chess board

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The Basic Schelling Model from a fragile
balances start Black vote Republican, White vote
Democrat
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The Schelling Model from a random starting
point Black vote Republican, White vote Democrat
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The Basic Schelling Model with gaps for moving
White are Catholics, Black are Protestants
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Example 2 Connectivity in Cities In essence In
the early days of complexity theory, the focus
was on these ideas, which were contained in ideas
about emergence from the bottom up as seen in
chaos theory and fractals But more recently as
we have become concerned with interactions and
how we connect, network science has emerged. The
network is the icon of the post modern
age Initially this study took off from ideas
developed in the 1960s by the psychologist
Stanley Milgram which he called the small
world
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To illustrate these ideas, we use the
graph-theory to represent them as nodes and arcs
through Connectivity how many nodes are
connected, what is the density of connection
arcs/nodes etc. Reachability average path
length, degrees of connection, distance in
graphs Scaling the distribution of in-degrees
and out-degrees, how these scale, their frequency
v size Usually in networks, we can define links
between distant elements and we can define local
clusters. Small worlds are essentially systems
where you get the best of both worlds strong
local clusters but short average distances these
seem to characterise many types of network e.g.
social networks, transport
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An Example strong local clusters short cluster
distances but long average paths lengths
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Rewiring Take three cluster arcs and make them
long distance arcs
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We can also look at Network Growth Fixed Nodes,
Growing Links, and so on and there are strong
connections to percolation and epidemics which
can be applied to things like sprawl and
filtering in housing and job markets In terms
of London, very key that we have not built
certain links and we dont have a good
functioning small world.
The need for Cross Rail says it all. It is
impossible to travel across the city
efficiently..
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A good example is Berlin the removal of the
wall bringing isolated networks together Jake
Desyllas has measured its connectivity in his
thesis which uses space syntax.
Before
After
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Some of the most interesting developments are in
electronic space - in cyberspace not in real
space. Here is an early example of a naturally
evolving network the internet
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Example 3 Urban Growth at the Aggregate
Scale One of the best examples of emergence from
the bottom up is seen in the actual shape of
cities they grow from a multiplicity of small
decisions and grow to fill their space according
to certain densities here are some examples If
you look at cities at different scales then you
will see a kind of similarity or regularity
best seen in the retail hierarchy but also in the
hierarchy of streets. No one planned these
hierarchies they emerged naturally through
multiple markets and small scale actions. Large
scale actions tend to be rather minor in
comparison, Most cities are what Morris called
organically growing rather than planned.
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Fractal Britain
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These shapes scale regularly and this geometry is
called fractal one of the key signatures of
complex systems that grow from the bottom up
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Growth through time Washington DC-Baltimore
Las Vegas
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There is a wonderful model that lets us see how
such shapes grow from the bottom up it can be
used to show how all sorts of phenomena that are
hierarchical tree like in their self-similarity
grow and form order from essentially random
actions. The sorts of structures that are
produced are like this
Lets see how it works
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Other examples in cities
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One of the key things that characterizes all
these examples is that we are dealing with
dynamics, with time, with change, So with
equilibrium, in fact the equilibrium is always
fragile in fact these structures are what
physicists now call far from equilibrium. Even
disequilibrium has gone out of the window. In
fact the difference between machines and
organisms is that machine function in simple ways
and usually we have to design them to make them
change. Organisms have their own internal
dynamic. Of course there is an argument that
organisms are machines and vice versa - deus ex
machina but that is another story
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Example 4 City Size Distributions Macro
Stability and Micro Volatility If we rank cities
by size, then there is remarkable stability in
that their distribution follows an inverse power
law. Most distributions conform to a law that
says that city size is inversely
proportional to their rank r raised to some power
a which in the strict case is equal to 1 That is
. If we graph the relationship and
plot this on logarithmic scale then we get a
straight line. What is remarkable about this
relationships is that it seems to hold for all
city systems and for all times. It also is at
the basis of many other distributions such as
income, etc. It is called a scaling relation.
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Such relationships are fractal because they show
self-similarity at any scale. They are entirely
consistent with the city size data that we showed
earlier. The relations is called Zipfs Law after
the original populariser of these kinds of
scaling law Let us look at some
relations From Zipf
from our data reworked
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In fact, this stability is illusory for cities
change their rank very frequently but maintain
this order and it is hard to explain why this is
the case. A lot happens at the macro level but
competition seems to sort out city sizes so that
although they rise and fall rather quickly the
overall relationship of cities one to another in
terms of size is preserved. Here is an example
for the US for 1940 and 2000
Let me show you an example for the US urban
system from 1790 to 2000
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5. Evolution and Prediction, Evolution and
Design There are many implications for the way
we might intervene in cities but the key
conundrum is the one we face in genetics. Should
we interfere? Should we fine tune the
evolutionary process? Frankly I dont think we
have an answer to this. We are scared of
evolution..we find it so complex that word
again, that we are reluctant to disturb something
we dont understand at all well. Moreover the
idea of a city as a machine is one where we think
of it as parts that can be assembled. I have
shown, I think, albeit briefly, that this isnt
the way the world works.
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I am not going to say very much about what is in
many ways the essential theme of this talk that
complex evolving systems are unpredictable they
show emergence that we would like to understand
but usually cant. Its been said many times
before Rittel and Webber coined the term
Wicked Problems. We have a lifetime of
experience of this in planning. The 1960s! Ugh!
Transport systems, public housing and so on. In
fact, this new paradigm suggests that we should
back off a bit, that we should perhaps act as
others who evolve systems. Act piecemeal, slowly,
as Alexander and Jacobs have always
preached. Terry Farrell said it yesterday. Why
dont we just do it in bits and try to adapt it
in bits his example of the Euston-Marylebone
Road.
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In one sense, there is still hope that by
understanding through good theories and models,
we can get a handle on the fine tuning Let me
show you how we can take evolutionary models and
use them in design, in testing initial
conditions, implications of design and also
changing the rules Ill show you now very
quickly because time is short, such an example
where we can grow cities at different scales and
then also interfere with the rules, thinking
about prediction and design and understanding all
in one piece This is a message from this talk,
that understanding, prediction and design are not
separate really if we believe in the blind
watchmaker here goes
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6. A Sketch of a Case Study How Do We Use These
Ideas Movement in Cities What I want to do in
conclusion is show you that these sorts of ideas
are being used. In fact in many many areas of
social and public life, these sorts of theories
and models are being applied but even in our
own field Our work with the GLA on the Notting
Hill Carnival is an example. We essentially built
a model of how people and the parade and the
various events at the 2 day annual Carnival move
and cluster because there is a major problem of
public safety that has emerged as the event as
got bigger.
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The Practical Context a real problem of public
safety The Modeling Context what do we know
about pedestrian movement The idea of a movement
model pedestrians move randomly, constrained by
obstacles in the streets, responding to other
movement through flocking, responding to
congestion through dispersion, and generally
walking up an attraction surface which is based
on the routes for which pedestrians want to
actually walk. The model is built around these
notions but ,much data is absent we need to
generate it in several stages. We thus need to
build the model in several stages. We need to
ensure that the degree of control in the system
is central to the model.
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Let us launch two movies made from the model
First the Swarm Movie Second the Actual Walk
Movie
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7. Conclusions Where Do We Go From Here? Well
there is little doubt that time and dynamics has
come firmly onto the agenda and that we no
longer think of cities as being in equilibrium
this says a lot for planning that seeks end
states and I think it means that we need a
severe evaluation of the role of central
planning and government generally in modern
societies. Of course this is happening. I think
too that our concern for cities is rather narrow
and that much of what I have been describing is
taking place outside the narrow confines of the
kind of institutionalized planning that we are
focused on
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and About Complexity Applications tuning these
ideas to real problems . Recognizing the
growth of complexity theory as a major paradigm
for science admitting of unpredictability and
uncertainty, ambiguity and pluralism,
relativism The generic use of complexity
language in articulating social affairs, policy,
management and decision- making Complexity
theory as postmodernism and beyond the new
vocabulary based on physical metaphors
mobility, liquidity, fluidity and so on
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Read books on this stuff ESRI Press,
2005 The MIT Press, 2005
Edward Elgar, 2006 Another but longer PowerPoint
of this lecture with the example case study but
without the movies is at http//www.casa.ucl.ac.uk
/bartlett.ppt