A City is Not a Tree Complet

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'A City is not a Tree'

by Christopher Alexander

A CITY IS NOT A TREE

CHRISTOPHER ALEXANDER

The tree of my title is not a green tree with leaves. It is the name of an abstract structure. I shallcontrast it with another, more complex abstract structure called a semilattice. In order to relate

these abstract structures to the nature of the city, I must first make a simple distinction.

I want to call those cities which have arisen more or less spontaneously over many, many years

natural cities. And I shall call those cities and parts of cities which have been deliberately

created by designers and planners artificial cities. Siena, Liverpool, Kyoto, Manhattan are

examples of natural cities. Levittown, Chandigarh and the British New Towns are examples ofartificial cities.

It is more and more widely recognized today that there is some essential ingredient missing from

artificial cities. When compared with ancient cities that have acquired the patina of life, our

modern attempts to create cities artificially are, from a human point of view, entirely

unsuccessful.

Both the tree and the semilattice are ways of thinking about how a large collection of many small

systems goes to make up a large and complex system. More generally, they are both names forstructures of sets.

In order to define such structures, let me first define the concept of a set. A set is a collection ofelements which for some reason we think of as belonging together. Since, as designers, we are

concerned with the physical living city and its physical backbone, we must naturally restrict

ourselves to considering sets which are collections of material elements such as people, blades ofgrass, cars, molecules, houses, gardens, water pipes, the water molecules in them etc.
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When the elements of a set belong together because they co-operate or work together somehow,

we call the set of elements a system.

For example, in Berkeley at the corner of Hearst and Euclid, there is a drugstore, and outside the

drugstore a traffic light. In the entrance to the drugstore there is a newsrack where the day's

papers are displayed. When the light is red, people who are waiting to cross the street stand idlyby the light; and since they have nothing to do, they look at the papers displayed on the newsrack

which they can see from where they stand. Some of them just read the headlines, others actuallybuy a paper while they wait.

This effect makes the newsrack and the traffic light interactive; the newsrack, the newspapers onit, the money going from people's pockets to the dime slot, the people who stop at the light and

read papers, the traffic light, the electric impulses which make the lights change, and the

sidewalk which the people stand on form a system - they all work together.

From the designer's point of view, the physically unchanging part of this system is of special

interest. The newsrack, the traffic light and the sidewalk between them, related as they are, formthe fixed part of the system. It is the unchanging receptacle in which the changing parts of the

system - people, newspapers, money and electrical impulses - can work together. I define this

fixed part as a unit of the city. It derives its coherence as a unit both from the forces which hold

its own elements together and from the dynamic coherence of the larger living system whichincludes it as a fixed invariant part.

Of the many, many fixed concrete subsets of the city which are the receptacles for its systems

and can therefore be thought of as significant physical units, we usually single out a few for

special consideration. In fact, I claim that whatever picture of the city someone has is defined

precisely by the subsets he sees as units.

Now, a collection of subsets which goes to make up such a picture is not merely an amorphous

collection. Automatically, merely because relationships are established among the subsets oncethe subsets are chosen, the collection has a definite structure.

To understand this structure, let us think abstractly for a moment, using numbers as symbols.

Instead of talking about the real sets of millions of real particles which occur in the city, let us

consider a simpler structure made of just half a dozen elements. Label these elements 1,2,3,4,5,6.

Not including the full set [1,2,3,4,5,6], the empty set [-], and the one-element sets[1],[2],[3],C4],[5], [6], there are 56 different subsets we can pick from six elements.

Suppose we now pick out certain of these 56 sets (just as we pick out certain sets and call themunits when we form our picture of the city). Let us say, for example, that we pick the following

subsets: [123], [34], [45], [234], [345], [12345], [3456].

What are the possible relationships among these sets? Some sets will be entirely part of larger

sets, as [34] is part of [345] and [3456]. Some of the sets will overlap, like [123] and [234].

Some of the sets will be disjoint - that is, contain no elements in common like [123] and [45].


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diagram A diagram B

We can see these relationships displayed in two ways. Indiagram Aeach set chosen to be a unit

has a line drawn round it. Indiagram Bthe chosen sets are arranged in order of ascendingmagnitude, so that whenever one set contains another (as [345] contains [34], there is a vertical

path leading from one to the other. For the sake of clarity and visual economy, it is usual to draw

lines only between sets which have no further sets and lines between them; thus the line between

[34] and [345] and the line between [345] and [3456] make it unnecessary to draw a line between[34] and [3456].

Diagrams A & B redrawn byNikos Salingaros

As we see from these two representations, the choice of subsets alone endows the collection of

subsets as a whole with an overall structure. This is the structure which we are concerned withhere. When the structure meets certain conditions it is called a semilattice. When it meets other

more restrictive conditions, it is called a tree.

The semilattice axiom goes like this:A collection of sets forms a semilattice if and only if, when

two overlapping sets belong to the collection, the set of elements common to both also belongs to

the collection.

The structure illustrated in diagrams A and B is a semilattice. It satisfies the axiom since, for

instance, [234] and [345] both belong to the collection and their common part, [34], also belongs

to it. (As far as the city is concerned, this axiom states merely that wherever two units overlap,the area of overlap is itself a recognizable entity and hence a unit also. In the case of the

drugstore example, one unit consists of newsrack, sidewalk and traffic light. Another unit

consists of the drugstore itself, with its entry and the newsrack. The two units overlap in thenewsrack. Clearly this area of overlap is itself a recognizable unit and so satisfies the axiom

above which defines the characteristics of a semilattice.) The tree axiom states:A collection ofsets forms a tree if and only if, for any two sets that belong to the collection either one is wholly

contained in the other, or else they are wholly disjoint.
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diagram C diagram D

The structure illustrated indiagrams CandDis a tree. Since this axiom excludes the possibility

of overlapping sets, there is no way in which the semilattice axiom can be violated, so that everytree is a trivially simple semilattice.

Diagrams A & B redrawn byNikos Salingaros

However, in this chapter we are not so much concerned with the fact that a tree happens to be a

semilattice, but with the difference between trees and those more general semilattices which arenot trees because they do contain overlapping units. We are concerned with the difference

between structures in which no overlap occurs, and those structures in which overlap does occur.

It is not merely the overlap which makes the distinction between the two important. Still more

important is the fact that the semilattice is potentially a much more complex and subtle structure

than a tree. We may see just how much more complex a semilattice can be than a tree in thefollowing fact: a tree based on 20 elements can contain at most 19 further subsets of the 20,

while a semilattice based on the same 20 elements can contain more than 1,000,000 different

subsets.

This enormously greater variety is an index of the great structural complexity a semilattice can

have when compared with the structural simplicity of a tree. It is this lack of structuralcomplexity, characteristic of trees, which is crippling our conceptions of the city.

To demonstrate, let us look at some modern conceptions of the city, each of which I shall show

to be essentially a tree.
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Figure 1. Columbia, Maryland, Community Research and Development,

Inc.: Neighbourhoods,in clusters of five, form 'villages'. Transportation jovillages into a new town. The organization is a tree.

Figure 2. Greenbelt, Maryland, Clarence Stein: This

'garden city' has been broken down into superblocks.

Each superblock contains schools, parks and a number

of subsidiary groups of houses built around parking lots.The organization is a tree.

Figure 3.Greater London plan (1943), Abercrombieand Forshaw: The drawing depicts the structure

conceived by Abercrombie for London. It is made of alarge number of communities, each sharply separated

from all adjacent communities. Abercrombie writes,

'The proposal is to emphasize the identity of the existingcommunities, to increase their degree of segregation,

and where necessary to recognize them as separate and

definite entities.' And again, 'The communitiesthemselves consist of a series of sub-units, generally

with their own shops and schools, corresponding to the

neighbourhood units.' The city is conceived as a treewith two principal levels. The communities are thelarger units of the structure; the smaller sub-units are

neighbourhoods. There are no overlapping units. The

structure is a tree.
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Figure 4. Mesa City, Paolo Soleri: The organic shapesof Mesa City lead us, at a careless glance, to believe that

it is a richer structure than our more obviously rigid

examples. But when we look at it in detail we find

precisely the same principle of organization. Take,

particularly, the university centre. Here we find thecentre of the city divided into a university and a

residential quarter, which is itself divided into a numberof villages (actually apartment towers) for 4000

inhabitants, each again subdivided further and

surrounded by groups of still smaller dwelling units.

Figure 5. Tokyo plan, Kenzo Tange: This is a

beautiful example. The plan consists of a seriesof loops stretched across Tokyo Bay. There arefour major loops, each of which contains three

medium loops. In the second major loop, one

medium loop is the railway station and another

is the port. Otherwise, each medium loopcontains three minor loops which are residential

neighbourhoods, except in the third major loop

where one contains government offices andanother industrial offices.

Figure 6. Chandigarh (1951), Le Corbusier: The whole

city is served by a commercial centre in the middle,

linked to the administrative centre at the head. Twosubsidiary elongated commercial cores are strung out

along the maior arterial roads, running north-south.

Subsidiary to these are further administrative,

community and commercial centres, one for each of thecity's 20 sectors.
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Figure 7. Brasilia, Lucio Costa: The entire form pivots

about the central axis, and each of the two halves isserved by a single main artery. This main artery is in

turn fed by subsidiary arteries parallel to it. Finally,these are fed by the roads which surround the

superbiocks themselves. The structure is a tree.

Figure 8. Communitas, Percival and Paul

Goodman: Communitas is explicitly organizedas a tree: it is first divided into four concentricmajor zones, the innermost being a commercial

centre, the next a university, the third residential

and medical, and the fourth open country. Each

of these is further subdivided: the commercialcentre is represented as a great cylindrical

skyscraper, containing five layers: airport,

administration, light manufacture, shopping andamusement; and, at the bottom, railroads, buses

and mechanical services. The university is

divided into eight sectors comprising naturalhistory, zoos and aquariums, planetarium,science laboratories, plastic arts, music and

drama. The third concentric ring is divided into

neighbourhoods of 4000 people each, notconsisting of individual houses, but of

apartment blocks, each of these containing

individual dwelling units. Finally, the opencountry is divided into three segments: forest

preserves, agriculture and vacation lands. The

overall organization is a tree
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Figure 9.The most beautiful example of all Ihave kept until last, because it symbolizes the

problem perfectly. It appears in Hilberseimer's

bookThe Nature of Cities. He describes the fact

that certain Roman towns had their origin asmilitary camps, and then shows a picture of a

modern military encampment as a kind ofarchetypal form for the city. It is not possible to

have a structure which is a clearer tree. The

symbol is apt, for, of course, the organization of

the army was designed precisely in order tocreate discipline and rigidity. The photograph

on the [left] is Hilberseimer's own scheme for

the commercial area of a city based on the army

camp archetype.

Each of these structures, then, is a tree. Each unit in each tree that I have described, moreover, isthe fixed, unchanging residue of some system in the living city (just as a house is the residue of

the interactions between the members of a family, their emotions and their belongings; and a

freeway is the residue of movement and commercial exchange).

However, in every city there are thousands, even millions, of times as many more systems atwork whose physical residue does not appear as a unit in these tree structures. In the worst cases,the units which do appear fail to correspond to any living reality; and the real systems, whose

existence actually makes the city live, have been provided with no physical receptacle.

Neither the Columbia plan nor the Stein plan for example, corre

social realities. The physical layout of the plans, and the way thefunction suggests a hierarchy of stronger and stronger closed soc

groups, ranging from the whole city down to the family, each fo

associational ties of different strength.

In a traditional society, if we ask a man to name his best friends

ask each of these in turn to name their best friends, they will all each other so that they form a closed group. A village is made u

number of separate closed groups of this kind.

But today's social structure is utterly different. If we ask a man t

his friends and then ask them in turn to name their friends, they
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name different people, very likely unknown to the first person; tpeople would again name others, and so on outwards. There are

no closed groups of people in modern society. The reality of tod

structure is thick with overlap - the systems of friends and acqua

form a semilattice, not a tree (Figure 10).

Part II

The units of which an artificial city is made up are always organized to form a tree. So that we

get a really clear understanding of what this means, and shall better see its implications, let usdefine a tree once again. Whenever we have a tree structure, it means that within this structure no

piece of any unit is ever connected to other units, except through the medium of that unit as a

whole.

The enormity of this restriction is difficult to grasp. It is a little as though the members of a

family were not free to make friends outside the family, except when the family as a whole madea friendship.

In simplicity of structure the tree is comparable to the compulsive desire for neatness and order

that insists the candlesticks on a mantelpiece be perfectly straight and perfectly symmetrical

about the centre. The semilattice, by comparison, is the structure of a complex fabric; it is the

structure of living things, of great paintings and symphonies.

It must be emphasized, lest the orderly mind shrink in horror from anything that is not clearly

articulated and categorized in tree form, that the idea of overlap, ambiguity, multiplicity ofaspect and the semilattice are not less orderly than the rigid tree, but more so. They represent a

thicker, tougher, more subtle and more complex view of structure.

Let us now look at the ways in which the natural, when unconstrained by artificial conceptions,

shows itself to be a semilattice.

A major aspect of the city's social structure which a tree can never mirror properly is illustrated

by Ruth Glass's redevelopment plan for Middlesbrough, England, a city of 200,000 which sherecommends be broken down into 29 separate neighbourhoods. After picking her 29

neighbourhoods by determining where the sharpest discontinuities of building type, income and

job type occur, she asks herself the question: 'If we examine some of the social systems whichactually exist for the people in such a neighbourhood, do the physical units defined by thesevarious social systems all define the same spatial neighbourhood?' Her own answer to this

question is no. Each of the social systems she examines is a nodal system. It is made of some sort

of central node, plus the people who use this centre. Specifically she takes elementary schools,secondary schools, youth clubs, adult clubs, post offices, greengrocers and grocers selling sugar.Each of these centres draws its users from a certain spatial area or spatial unit. This spatial unit is

the physical residue of the social system as a whole, and is therefore a unit in the terms of this


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discussion. The units corresponding to different kinds of centres for the single neighbourhood of

Waterloo Road are shown inFigure 11.

The hard outline is the boundary of the so-calledneighbourhood itself. The white circle stands for

the youth club, and the small solid rings stand forareas where its members live. The ringed spot is

the adult club, and the homes of its membersform the unit marked by dashed boundaries. The

white square is the post office, and the dotted line

marks the unit which contains its users. Thesecondary school is marked by the spot with a

white triangle in it. Together with its pupils, it

forms the system marked by the dot-dashed line.

As you can see at once, the different units do not

coincide. Yet neither are they disjoint. Theyoverlap.

We cannot get an adequate picture of what Middlesbrough is, or of what it ought to be, in termsof 29 large and conveniently integral Chunks called neighbourhoods. When we describe the city

in terms of neighbourhoods, we implicitly assume that the smaller elements within any one of

these neighbourhoods belong together so tightly that they only interact with elements in otherneighbourhoods through the medium of the neighbourhoods to which they themselves belong.

Ruth Glass herself shows clearly that this is not the case.

Next to Figure 11 are two representations of theWaterloo neighbourhood. For the sake of

argument I have broken it into a number of small

areas.Figure 12shows how these pieces stick

together in fact, andFigure 13shows how theredevelopment plan pretends they stick together.

There is nothing in the nature of the various centres which says that their catchment areas shouldbe the same. Their natures are different. Therefore the units they define are different. The natural

city of Middlesbrough was faithful to the semilattice structure of the units. Only in the artificial-

tree conception of the city are their natural, proper and necessary overlaps destroyed.
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Consider the separation of pedestrians from

moving vehicles, a tree concept proposed by Le

Corbusier, Louis Kahn and many others. At a

very crude level of thought this is obviously a

good idea. Yet the urban taxi can function only

because pedestrians and vehicles are not strictlyseparated. The cruising taxi needs a fast stream

of traffic so that it can cover a large area to besure of finding a passenger. The pedestrian

needs to be able to hail the taxi from any point in

the pedestrian world, and to be able to get out toany part of the pedestrian world to which he

wants to go. The system which contains the

taxicabs needs to overlap both the fast vehicular

traffic system and the system of pedestriancirculation. In Manhattan pedestrians and

vehicles do share certain parts of the city, andthe necessary overlap is guaranteed (Figure 14).

Anotherfavourite concept of the CIAM theorists and others is the separation of recreation from

everything else. This has crystallized in our real cities in the form of playgrounds. Theplayground, asphalted and fenced in, is nothing but a pictorial acknowledgment of the fact that

'play' exists as an isolated concept in our minds. It has nothing to do with the life of play itself.

Few self-respecting children will even play in a playground.

Play itself, the play that children practise, goes on somewhere different every day. One day it

may be indoors, another day in a friendly gas station, another day down by the river, another day

in a derelict building, another day on a construction site which has been abandoned for theweekend. Each of these play activities, and the objects it requires, forms a system. It is not true

that these systems exist in isolation, cut off from the other systems of the city. The differentsystems overlap one another, and they overlap many other systems besides. The units, the

physical places recognized as play places, must do the same.

In a natural city this is what happens. Play takes place in a thousand places it fills the interstices

of adult life. As they play, children become full of their surroundings. How can children become

filled with their surroundings in a fenced enclosure! They cannot.

A similar kind of mistake occurs in trees like that of Goodman's Communitas or Soleri's Mesa

City, which separate the university from the rest of the city. Again, this has actually beenrealized in the common American form of the isolated campus.

What is the reason for drawing a line in the city so that everything within the boundary is

university, and everything outside is nonuniversity? It is conceptually clear. But does itcorrespond to the realities of university life? Certainly it is not the structure which occurs in

nonartificial university cities.
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There are always many systems of activitywhere university life and city life overlap: pub-

crawling, coffee-drinking, the movies, walking

from place to place. In some cases whole

departments may be actively involved in the life

of the city's inhabitants (the hospital-cum-medical school is an example). In Cambridge, a

natural city where university and city havegrown together gradually, the physical units

overlap because they are the physical residues of

city systems and university systems whichoverlap (Figure 15).

Let us look next at the hierarchy of urban cores realized in Brasilia, Chandigarh, the MARS planfor London and, most recently, in the Manhattan Lincoln Center, where various performing arts

serving the population of greater New York have been gathered together to form just one core.

Does a concert hall ask to be next to an opera house? Can the two feed on one another? Will

anybody ever visit them both, gluttonously, in a single evening, or even buy tickets from one

after going to a performance in the other? In Vienna, London, Paris, each of the performing artshas found its own place, because all are not mixed randomly. Each has created its own familiar

section of the city. In Manhattan itself, Carnegie Hall and the Metropolitan Opera House were

not built side by side. Each found its own place, and now creates its own atmosphere. Theinfluence of each overlaps the parts of the city which have been made unique to it.

The only reason that these functions have all been brought together in Lincoln Center is that the

concept of performing art links them to one another.

But this tree, and the idea of a single hierarchy of urban cores which is its parent, do notilluminate the relations between art and city life. They are merely born of the mania every

simple-minded person has for putting things with the same name into the same basket.

The total separation of work from housing, started by Tony Garnier in his industrial city, then

incorporated in the 1929 Athens Charter, is now found in every artificial city and accepted

everywhere where zoning is enforced. Is this a sound principle? It is easy to see how badconditions at the beginning of the century prompted planners to try to get the dirty factories out

of residential areas. But the separation misses a variety of systems which require, for their

sustenance, little parts of both.

Finally, let us examine the subdivision of the city into isolated communities. As we have seen in

the Abercrombie plan for London, this is itself a tree structure. The individual community in a

greater city has no reality as a functioning unit. In London, as in any great city, almost no onemanages to find work which suits him near his home. People in one community work in a factory

which is very likely to be in another community.
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There are therefore many hundreds of thousands of worker-workplace systems, each consisting

of individuals plus the factory they work in, which cut across the boundaries defined byAbercrombie's tree. The existence of these units, and their overlapping nature, indicates that the

living systems of London form a semilattice. Only in the planner's mind has it become a tree.

The fact that we have so far failed to give this any physical expression has a vital consequence.As things are, whenever the worker and his workplace belong to separately administered

municipalities, the community which contains the workplace collects huge taxes and hasrelatively little on which to spend the tax revenue. The community where the worker lives, if it is

mainly residential, collects only little in the way of taxes and yet has great additional burdens on

its purse in the form of schools, hospitals, etc. Clearly, to resolve this inequity, the worker-workplace systems must be anchored in physically recognizable units of the city which can then

be taxed.

It might be argued that, even though the individual communities of a great city have nofunctional significance in the lives of their inhabitants, they are still the most convenient

administrative units, and should therefore be left in their present tree organization. However, inthe political complexity of a modern city, even this is suspect.

Edward Banfield, in his bookPolitical Influence, gives a detailed account of the patterns of

influence and control that have actually led to decisions in Chicago. He shows that, although thelines of administrative and executive control have a formal structure which is a tree, these formal

chains of influence and authority are entirely overshadowed by the ad hoc lines of control which

arise naturally as each new city problem presents itself. These ad hoc lines depend on who isinterested in the matter, who has what at stake, who has what favours to trade with whom.

This second structure, which is informal, working within the framework of the first, is what

really controls public action. It varies from week to week, even from hour to hour, as oneproblem replaces another. Nobody's sphere of influence is entirely under the control of any one

superior; each person is under different influences as the problems change. Although the

organization chart in the Mayor's office is a tree, the actual control and exercise of authority issemilattice-like.

Now, why is it that so many designers have conceived cities as trees when the natural structure is

in every case a semilattice? Have they done so deliberately, in the belief that a tree structure will

serve the people of the city better? Or have they done it because they cannot help it, because theyare trapped by a mental habit, perhaps even trapped by the way the mind works - because they

cannot encompass the complexity of a semilattice in any convenient mental form, because the

mind has an overwhelming predisposition to see trees wherever it looks and cannot escape the

tree conception?

I shall try to convince you that it is for this second reason that trees are being proposed and built

as cities - that is, because designers, limited as they must be by the capacity of the mind to formintuitively accessible structures, cannot achieve the complexity of the semilattice in a single

mental act.


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Let me begin with an example. Suppose I ask you to remember the following four objects: an

orange, a watermelon, a football and a tennis ball. How will you keep them in your mind, in yourmind's eye? However you do it, you will do it by grouping them. Some of you will take the two

fruits together, the orange and the watermelon, and the two sports balls together, the football and

the tennis ball. Those of you who tend to think in terms of physical shape may group them

differently, taking the two small spheres together - the orange and the tennis ball and the twolarge and more egg-shaped objects - the watermelon and the football. Some of you will be aware

of both.

Let us make a diagram of these groupings

(Figure 16). Either grouping taken by itself is atree structure. The two together are a semilattice.

Now let us try and visualize these groupings in

the mind's eye. I think you will find that you

cannot visualize all four sets simultaneously -because they overlap. You can visualize one pair

of sets and then the other, and you can alternatebetween the two pairs extremely fast, so that youmay deceive yourself into thinking you can

visualize them all together. But in truth, you

cannot conceive all four sets at once in a singlemental act. You cannot bring the semilattice

structure into a visualizable form for a single

mental act. In a single mental act you can only

visualize a tree.

This is the problem we face as designers. While we are not, perhaps, necessarily occupied with

the problem of total visualization in a single mental act, the principle is still the same. The tree isaccessible mentally and easy to deal with. The semilattice is hard to keep before the mind's eye

and therefore hard to deal with.

It is known today that grouping and categorization are among the most primitive psychological

processes. Modern psychology treats thought as a process of fitting new situations into existingslots and pigeonholes in the mind. Just as you cannot put a physical thing into more than one

physical pigeonhole at once, so, by analogy, the processes of thought prevent you from putting a

mental construct into more than one mental category at once. Study of the origin of these

processes suggests that they stem essentially from the organism's need to reduce the complexityof its environment by establishing barriers between the different events that it encounters.

It is for this reason - because the mind's first function is to reduce the ambiguity and overlap in aconfusing situation and because, to this end, it is endowed with a basic intolerance for ambiguity

- that structures like the city, which do require overlapping sets within them, are nevertheless

persistently conceived as trees.

The same rigidity dogs even perception of physical patterns. In experiments by Huggins and

myself at Harvard, we showed people patterns whose internal units overlapped, and found that
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they almost always invent a way of seeing the patterns as a tree - even when the semilattice view

of the patterns would have helped them perform the task of experimentation which was beforethem.

The most startling proof that people tend to

conceive even physical patterns as trees is foundin some experiments of Sir Frederick Bartlett.

He showed people a pattern for about a quarterof a second and then asked them to draw what

they had seen. Many people, unable to grasp the

full complexity of the pattern they had seen,simplified the patterns by cutting out the

overlap. InFigure 17, the original is shown on

the left, with two fairly typical redrawn versions

to the right of it. In the redrawn versions thecircles are separated from the rest; the overlap

between triangles and circles disappears.

These experiments suggest strongly that people have an underlying tendency, when faced by a

complex organization, to reorganize it mentally in terms of non-overlapping units. Thecomplexity of the semilattice is replaced by the simpler and more easily grasped tree form.

You are no doubt wondering by now what a city looks like which is a semilattice, but not a tree. Imust confess that I cannot yet show you plans or sketches. It is not enough merely to make a

demonstration of overlap - the overlap must be the right overlap. This is doubly important

because it is so tempting to make plans in which overlap occurs for its own sake. This is

essentially what the high- density 'life-filled' city plans of recent years do. But overlap alone does

not give structure. It can also give chaos. A garbage can is full of overlap. To have structure, youmust have the right overlap, and this is for us almost certainly different from the old overlap

which we observe in historic cities. As the relationships between functions change, so thesystems which need to overlap in order to receive these relationships must also change. The

recreation of old kinds of overlap will be inappropriate, and chaotic instead of structured.

One can perhaps make the physical consequences

of overlap more comprehensible by means of animage. The painting illustrated is a work by

Simon Nicholson (Figure 18). The fascination of

this painting lies in the fact that, although

constructed of rather few simple triangularelements, these elements unite in many different

ways to form the large units of the painting - in

such a way indeed that, if we make a completeinventory of the perceived units in the painting,

we find that each triangle enters into four or five

completely different kinds of unit, none

contained in the others, yet all overlapping in that
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triangle.

Thus, if we number the triangles and pick out the

sets of triangles which appear as strong visual

units, we get the semilattice shown inFigure 19.

Three and 5 form a unit because they worktogether as a rectangle; 2 and 4 because they

form a parallelogram; 5 and 6 because they are

both dark and pointing the same way; 6 and 7

because one is the ghost of the other shiftedsideways; 4 and 7 because they are symmetrical

with one another; 4 and 6 because they form

another rectangle; 4 and 5 because they form a

sort of Z; 2 and 3 because they form a ratherthinner kind of Z; 1 and 7 because they are at

opposite corners; 1 and 2 because they are a

rectangle; 3 and 4 because they point the sameway as 5 and 6, and form a sort of off-centre

reflection; 3 and 6 because they enclose 4 and 5;

1 and S because they enclose 2, 3 and 4. I haveonly listed the units of two triangles. The larger

units are even more complex. The white is more

complex still and is not even included in thediagram because it is harder to be sure of its

elementary pieces.

The painting is significant, not so much because it has overlap in it (many paintings have overlap

in them), but rather because this painting has nothing else in it except overlap. It is only the factof the overlap, and the resulting multiplicity of aspects which the forms present, that makes thepainting fascinating. It seems almost as though the painter had made an explicit attempt, as I

have done, to single out overlap as a vital generator of structure.

All the artificial cities I have described have the structure of a tree rather than the semilattice

structure of the Nicholson painting. Yet it is the painting, and other images like it, which must be

our vehicles for thought. And when we wish to be precise, the semilattice, being part of a largebranch of modern mathematics, is a powerfu1 way of exploring the structure of these images. It

is the semilattice we must look for, not the tree.

When we think in terms of trees we are trading the humanity and richness of the living city for aconceptual simplicity which benefits only designers, planners, administrators and developers.

Every time a piece of a city is torn out, and a tree made to replace the semilattice that was there

before, the city takes a further step toward dissociation.

In any organized object, extreme compartmentalization and the dissociation of internal elements

are the first signs of coming destruction. In a society, dissociation is anarchy. In a Person,dissociation is the mark of schizophrenia and impending suicide. An ominous example of city-
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wide dissociation is the separation of retired people from the rest of urban life, caused by the

growth of desert cities for the old like Sun City, Arizona. This separation isonly possible underthe influence of treelike thought.

It not only takes from the young the company of those who have lived long, but worse, it causes

the same rift inside each individual life. As you pass into Sun City, and into old age, your tieswith your own past will be unacknowledged, lost and therefore broken. Your youth will no

longer be alive in your old age - the two will be dissociated; your own life will be cut in two.

For the human mind, the tree is the easiest vehicle for complex thoughts. But the city is not,

cannot and must not be a tree. The city is a receptacle for life. If the receptacle severs the overlapof the strands of life within it, because it is a tree, it will be like a bowl full of razor blades on

edge, ready to cut up whatever is entrusted to it. In such a receptacle life will be cut to pieces. If

we make cities which are trees, they will cut our life within to pieces.


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A critique of design theory and method as presently applied to city design

[This article was originally published under the title 'If the City is not a Tree, nor is it a System'

in

Planning OutlookNew Series, Volume Sixteen, Spring 1975, pp 4 -18]

Most people seem to agree that modern cities are pretty awful. We can be persuaded to enjoyaspects of them, such as thrilling new structures which win design awards, or the feeling ofmovement on new communication systems, but most of the time they are just plain boring, dull,

and tawdry; tinged with a sense of 'welfare' that it's all we can afford. Wherever one goes one

sees the same standard answers; stereotyped housing blocks, neat soulless shopping centres, or

schools, fire stations or churches (which might be interchangeable), and standard amounts of'public open space' (ugh!). At the centre of the city there is more standard kit - television mast,

faceless tower and slab blocks, and regulation neon signs (when there's electricity) to whoop it

up a bit.

Critics, casting around for people to blame latch on to the planner as the villain. He's

unimaginative. His thinking is stuck in a rut of neighbourhoods, zoning, densities, and plotratios. His view of the city is far too simplistic for such a complex machine. We must match the

complexity of the city with more complex multi-purpose and intricate development, so we try

complex schemes - and what happens? Despite a plethora of ideas and conferences, despite agreat deal of endeavour and architectural ingenuity, the plans and sketches which seem to show

such high promise turn out to be yet another collection of pedestrian bridges, car park ramps, and

plastic paving surrounding anonymous building blocks. We still seem unable to match the life

and liveliness of 'real cities'.

Consequently critics have turned their attention to querying the planner's method of operationwhich requires him to make such assumptions. The problem, they suggest, is not that city

planners are inherently simplistic but that the design process they operate forces them to make

simplistic assumptions. For example Christopher Alexander (1966) argues that much of people's

dissatisfaction with the modern city stems from their artificial organisation into hierarchicalgroupings of facilities which, he suggests, are based not on the way people use the city, but on

the way designers conceive the process of design and apply it to the design of a city. Similarly,

Maurice Ash (1969) condemns town planners for what he regards as their attempt to organisepeople and facilities into idealised patterns based on what he asserts is an unproven theory of

settlement hierarchy. Like Ash, Melvin Webber (1968/69) argues that the philosophy of town

planning is not founded on social realities. Instead, he suggests, city planners have defined their

problems and solutions in idealised terms because they adopted the design style of the parentprofessions of engineering and architecture, and therefore adopted their design assumptions.

What is design? What are its assumptions?

Herbert Simon (1969)has called design the 'science of the artificial' because it is an artificialcreation to catalyse the requirements of man with those of his environment. It can be defined as

the ordering of relations between components in order to satisfy predetermined objectives. As a
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process it can only start when the problem has been defined in terms of objectives to be satisfied;

that is when the various aspects or component parts of the problem which together needsatisfying have been identified. The solution represents a synthesis which should satisfy the

requirements of each component and the problem as a whole. It is this process of synthesis that I

would define asDesign: a process in which the designer is an innovator, an inventor of solutions.

Investigations into the way designers design show that they go through a series of definite stages.

The first is concerned with clarifying the problem by breaking it down into its component partsor functions and identifying their requirements. The second is to gather 'like' components

together into 'sets' (i.e. collections of elements which are thought to have something in common).

The third stage is to link those components which work together into a system (i.e. a set ofcomponents which are linked together in order to perform a function). The aim is to create what

Alexander calls 'good fit' between problem and solution.1

For example, imagine designing a house. You break it down into the kind of rooms, or better stillactivities, which are required, such as sleeping, cooking, sitting etc. [fig. 1]. You analyse those

activities which have common or related features (for instance requiring service) and group themas sets [fig. 2]. Then you link those components which require inter-connection (e.g. cooking toeating) into a system [fig. 3]. Structuring the solutions you try to satisfy the known wants and

functions involved, by making enough space for the different activities to be accommodated;

trying to ensure that those activities which are most linked are put in the closest relationship. Butno matter how objective you attempt to be your image or idea of how each part, and the whole,

might function, look and feel will also greatly influence any solution you propose. Consequently,

although the design process must attempt to be objective, in most cases it will also reflect the

designer's own philosophy and values. You can only put forward solutions which you think aresatisfactory.2

Fig.1 ComponentsFig.2 Components grouped to form

a 'set'
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Fig.3 Components linked to form a

'system'

Examining the design process, the fundamental point emerges that designers create systems. Ofall the stages in the design process this is the one where he uses his expertise - this is what the

client pays for. Whereas the client should be concerned with helping to define the various parts

of the problem, and possibly their grouping into sets, the designer is responsible for ordering the

relationships in the system, or between systems and sub-systems, to satisfy functional andaesthetic requirements. The links which make the system are designed to maintain equilibrium

between the components, future change being controlled by the links. Consequently, the designer

is in a very powerful position. He is creating frameworks relative to the way he thinks theyshould be. When he creates a system he is not only providing opportunities, but also constraints.

His design will stabilise a set of relationships allowing only changes acceptable to the structure.

Consequently he must be sure that the relationships he sees are valid, and the links he creates areneeded. Identification of a set does not automatically make it a system; it is the links that create

the system.

Summarising, the design process would seem to rest on four assumptions:

1. That the problem can be defined, in terms of agreeable objectives.

2. That the components can be isolated and their requirements analysed.

3. That there is a 'best-fit' relationship.

4. That the end product can be achieved in reality, because design takes account of the

variables in the control of the designer and client.

Thus in engineering and architecture the aim is to produce an artifact which satisfies a client'sknown requirements. The operational style assumes that a client's requirements can be identifiedand arranged into a rational ordered solution to satisfy agreed objectives. Although the design

can have built-in 'flexibility' there is an overriding assumption of stability, such that there areascertainable and agreeable goals based on common values (held by client and designer); thatany change will like-wise conform to existing values; that a 'best-fit' arrangement can be found to

meet these goals and that controls can be agreed which will allow the plan to be implemented.

The application of design principles in town planning


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Although the assumptions underlying design would seem questionable if applied to city

planning, their application by city planners is clearly seen in many recent planning reportsparticularly for New Towns and new Cities. For example, consider the report for the new city in

Central Lancashire (for which a Development Corporation was appointed early in 1971).3

In that study an attempt is made to identify all the facilities that the population will require in a'large' city, and economic levels of provision are ascribed to each facility based on population

thresholds [fig. 4]. Facilities are then grouped into sets, which create a hierarchy of 'communities'

[fig. 4].

play areadoctors

surgery

public housecorner shop

nursery

schoolcreche

primary

school

meeting

room

playgroundcafe

post office

clinicprotestant

church

branchlibrary

health centre

catholicchurch

public park

industrial

estate

bankarts centre

secondary

schoolassembly

hall

restaurantmarket

hotel

sports centregpo

central

librarytown hall

swimming

poolgolf course

dance hallcinema

varietystores

night club

museumbowling

alley

technicalcollege

coll, of arts

& crafts

regional

park

zooart gallery

law courtstheatre

botanical

gardensspecialised

shops

concerthall

reference

library

county

admin.

officessports

stadium

indust.

retraining

centrepolytechnic


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Fig. 4 Facilities relative to population thresholds (Central Lancashire: Study for a C

Each grouping is assumed to work as a system and becomes a sub-system in a city wide system,

which is itself organised for ease of traffic movement[fig.6]. The assumption is that a city can be

rationalised on the basis of the provision of economic facilities and movement patterns to thosefacilities[fig.7], that people move to their nearest centre providing the particular facilities they

require, and that facilities having similar economic thresholds are best located in areas havingcongruent boundaries. Functions and movement are brought into a 'best-fit' relationship based on

assumed likely behaviour patterns, as in any other engineering or architectural product. The cityhas been treated as if it were a system and designed as such. The plan is presented as an

aesthetically and mathematically coherent solution to the problem of designing a city and all its

major functions.

3 Township

2 District

1

Neighbourhood

Like the architect and engineer, the city planner has designed his plans around the assumed needsof his client, in this case the people (sic. 'Planning is for People'), ordering and arranging the

various facilities in locations and groups thought to be best suited to the clients' demands. Thecity has been treated as an artifact, so that, even though it is ostensibly designed for growth andchange, growth is assumed to take place in roughly equi-size units up to some finite level, each

phase being regarded as a rationally planned unit and taking its place within the ordering

framework of the whole city system. As Alexander has shown, this approach, whereby the city isdesigned as 'a tree'[fig. 8]in which all facilities are treated as subsystems having an

hierarchically ordered relationship within a single system, is a common to the design of new

cities throughout the world.4
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Dispersal Movement Pattern


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Fig. 7 Assumed transport modes to facilities (Central Lancashire: Study for a City)


25/31

The planner, like the architect and the engineer, has assumed that similar functions serving

similar needs can be grouped, and that these groupings and arrangements reflect generally agreedforms of social organisation and social objectives. But can there be generally agreed forms of

social organisation or social objectives except at the most abstract level? It is really possible to

list the people's requirements except at the most minimum or basic level? Is it valid to assume

that the agencies who provide for the multiplicity of people's requirements can be expected toconform to some overall pattern based on assumed optimum standards of provision, which once

achieved will hold good for the foreseeable future?

Criticism of Planners' design approach

Here then is the nub of the criticism. Because the city planner adopted the operational style of the

engineer and architect, he was forced to work on similar assumptions; that he was producing an

artifact representing the known requirements of 'the people', that these could be identified and

once identified would remain relatively stable, and that there was some rational arrangement ofthe city which would be satisfactory not only for the present but also for the future. As Webber

suggests, the city planner adopted the assumptions of the engineer designing public worksincluding:

1. That social organisation and social objectives will remain stable during the timeperiod under review;

2. that there is a society wide consensus on city development goals;

3. that these goals are stable, future goals will be like present goals and that they are

knowable by professionals."5

Furthermore the adoption of the architectural / engineering design style assumed the need for asimilar approach to implementation, whereby "the sorts of deliberate outcomes accomplished in

the centralised decision setting of engineer client relationship, or centrally controlled government

enterprise" could be extended to the market place.6

In place of the 'real world' of multipleownerships and multiple power, an 'ideal world' was required where the planner could play the

role of designer for the people, represented by a statutory authority, knowing that his plan could

be implemented. As Webber points out, the planners produced a remarkably inventive set of

controls - the technical standard (providing minimum levels of quality), the master plan (settingforth overall system design) and the land use regulation (which constrained the locational

decisions of individual establishments). But these methods only allow the 'negative' controls of

stopping 'unsatisfactory' development.

In Britain the Government went further by providing powers which allowed 'creative' planning -

the Comprehensive Development Area (1944) and the New Town (1946), and subsidised localauthority housing (1919). In each case the relevant authority could draw up plans and, through its


26/31

powers of land ownership and finance, could implement its proposals. The trouble is that almost

all 'creative' planning has been used for the poorer sections of the community, particularlythrough the use of subsidised housing for estate development and comprehensive redevelopment

of slum areas, and for overspill to New Towns and Town Expansion schemes. The better off,

including those who were once worse off but have joined the 'private sector', can afford to move

out of the clutches of the 'creative' planner with his concepts of rationally ordered communities.The car-borne mother doesn't have to move where the Gravity Model suggests she should go -

the bus-borne mother has no choice!

Thus critics are suggesting that the stereotyped planned environment is not so much a product of

poor imagination on the part of city planners, as a product of the idea of designing cities as ifthey were a public works artifact. As a consequence of centralised design, instead of catering for

the variety of people's aspirations, there has been a tendency to reduce people's needs to

formalistic models where the quality of life and environment which comes from individual

innovation is squeezed out in order to safeguard 'the public interest'. The city planners' admirabledesire to ensure that people have a satisfactory minimum of facilities far too often seems to

produce stereotyped results where minima become maxima. All too often it is for one class ofsociety: what Maurice Ash calls 'an alliance with poverty'.7

The idea that the city can be designedas a coherent system made up of a rational arrangement of subsystems is a static concept. Thepursuit of city wide equilibrium for whatever high ideals, will result in its stagnation, decline and

eventual death.

The design of cities

How then should city planners approach the design of cities? Should they drop the

architect/engineering design style, as implied by Webber, and concentrate on social and

economic policy? Should they seek to design more complex city structures like the semi-lattic

advocated by Alexander?

Whatever the objectives of city planning should be, I do not think we can find another design

style (like Bruce Archer, I believe that "the logical act of designing is largely independent of thething designed"8). Nor do I believe it is possible to 'design in' complexity or deliberately create

semi-lattices; for as Alexander has shown (1966) design is inherently concerned with

rationalisation and simplification of the parts of the problem into a hierarchical arrangement. Soif we can only design in one way, and we cannot design complexity, how can we create complex

satisfying cities?

I believe the answer lies in a paradox set by Peter Levin in his paper 'Decision making in Urban

Design' (1966). He suggested "perhaps it is a valid aim to try deliberately to achieve a situation

in which the functioning of the system is as independent as possible of the design. The design, inother words, should have the minimum effect on human organisation and activities."9 But, as we

have seen designers derive their designs from the functioning of the system. Furthermore I don't

think you can design a system unrelated to its function. Thus the paradox: but only a paradox so

long as the city is regarded as a system.

The city is not a system


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Looked at from the viewpoint of its development and operation, the city is not a single system.

Rather it is a multiplicity of systems under the control of a multiplicity of agencies. Theseagencies, both public and private, provide and operate facilities [fig. 9] and both the agencies'

attitude to provision and the people's demand for provision is subject to change. Some facilities

will grow and others will die without the city planner having much say. Consequently, although

he may attempt to design his city plans on the basis of linkages between activity systems, and theuse the people make of them, he cannot implement and maintain his plan unless he has autocratic

powers to stabilise the world he has attempted to create. Without autocratic powers, which I am

sure few people will be prepared to accord, the city planner is wasting his time designing the cityas a system. As Margaret Willis has suggested "the narrow and restricted approach of what is

primarily a physical plan, and that is devised for the most part independently of the agencies that

actually build and administer a town shows the limitation of this type of planning in trying tomeet social realities".10 She quotes Professor Peter Wilmot, ". . . If city planning is to respect

social criteria, it must increasingly enable the design to work",11 that is work through the

agencies which develop and operate the city. As these agencies cannot be welded and subsumed

within a single comprehensive system, the city is better regarded as a set of semi-independent

systems with each agency responsible for the design and positive direction of its own system[fig. 10].

Examples of Agencies :

1. Education Committee

2. Welfare Committee3. Ind Coope

4. Express Dairy

5. Water Board6. Bus Company

Fig. 9. Examples of Agencies

which 'develop' a city

Fig.10 The city a number of separate system

based on agencies

Although this might appear as an advocation of 'non-plan', it is not. Rather it is a plea for design

being applied only where it is valid. The areas each agency controls are only semi-independent

[fig. 11]. To the extent they do not affect other activity areas they should be free to plan and

develop themselves. To the extent they are linked to others they should be subject to supra-

planning. Almost all activity systems are linked to others, albeit in a transient fashion, throughpolicies for land and the infrastructure which serves it. These links provide the framework of

constraints and opportunities within which the multifarious agencies work. The design of plansand policies for these links (the 'public' area as opposed to the 'private' area of an agency's own

sphere) is the city planner's field'12 [fig. 12].


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Fig.11 Interrelationship of systems: 'Public'

and 'Private' space

Fig.12 Planners design and control the

overlap between systems -The 'Public

space'.

It is a more limited area than he attempts to design at present, but it is none the less positive. Thecity planner can continue to manage and control the spatial organisation distribution,arrangement and visual quality of land use through his development control powers over links

between activity systems. He should be concerned with the positive design of public areas and

resources as a framework for semi-independent agencies.

Given that each agency will create a rational design solution to its own problem but would no

longer be subject to some supra-rationality of how the various activities should best fit together,complexity would be created in the way it occurs in normal cities. Instead of the city being cut

up in discreet neighbourhoods around centres with congruent catchment areas for each activity

system, each activity system would arrange itself to suit its own demands. Alexander's 'semi-

lattice' would result from activity systems solving their problems in their way. Levin suggeststhat making the function of the city independent of overall design should provide freedom and

choice: "A choice of nearby schools for a child, a choice of convenient shops for a housewife, a

choice of nearby friends to call on in an emergency, and a choice of routes to work."13

As hesuggests this might involve some over-provision of facilities (an anathema to the city planner?),

but surely that would be no bad thing for the consumer. We might actually get away from the

stereotyped standardised world that seems the only end product available from present citydesign.

I believe that 'Planning is for People' is in fact a static and paternalistic concept which serves to

reduce the quality of life and the environment in which it is lived. City Planning must provide theopportunity for people to enhance their own lives. Andrew Kopkind quoted Catherine Bauer as

saying "the worst kind of dictatorship is the kind that gives people what they want, the kind inwhich you can't tell you're being controlled." As he comments, "if that is one of the possible

futures it is too important to be left only to the planners."14

REFERENCES


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1 See Christopher Alexander 'Notes on the Synthesis of Form'.

2 In the introduction to Design Methods in Architecture. Anthony Ward queries the 'objective'

approach to design which suggests that the nature of design is independent of the thing designed

and suggests that perhaps the way a designer goes about designing something does affect the

thing that is designed (p. 12). He suggests that "if we are to contribute significantly to thedevelopment of design method, we have no alternative but to make explicit the philosophical

premises upon which we base our conclusions. Otherwise the logical nature of our task willremain impenetrable." This suggests the beginning of an acceptance by the architectural design

theorists that the designer cannot be wholly objective; that there is a place for the subjective as

preached by one of the foremost Architectural theorists, Goodhart-Rendall, in the 1930's: "Manymodern theorists of architecture, by refusing to let the (design) process disappear from sight,

have observed with dismay or neglected to observe that there is then no architecture at the end of

it." Goodhart-Rendell (1934). This all echoes the plea of the German philosopher Karl

Mannheim (1966) for designers and decision makers to be more self aware and thus gain greaterfreedom.

3 Robert Matthew, Johnson-Marshall and Partners: Central Lancashire, Study for a City. 1964.

4 Christopher Alexander:A City is not a Tree. 1966.

5 Melvin Webber: Planning in an Environment of Change Part I, Town Planning Review October1968, p. 192.

6 ibid. Part II January 1969, p. 284.

7 Maurice Ash:Regions of Tomorrow 1964.

8 Bruce Archer: The Structure of the Design Process in 'Design Methods in Architecture' (ed. A.Ward and G. Broadbent, AA Paper No. 4 1969).

9 Peter Levin:Decision Making in Urban Design B.R.S. 1966, p.11.

10 Margaret Willis: Sociological Aspects of Urban Structure Town Planning Review, January1969, p. 305.

11 Peter Wilmot: Social Research & New Communities Journal of the American Institute of

Planners Nov. 1967.

12 See Fumihiko Maki:Linkage in Collective Form in 'Investigations in Collective Form' 1964.Also Jane Jacobs:Death and Life of Great AmericanCities (1961).

13 Peter Levin: op. cit. p. 11.

14 Andrew Kopkind: 'The Future Planners' in 'America the Mixed Curse' 1969.


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Figures 4, 5, 6 and 7 are based on diagrams from 'Central Lancashire, Study for a City' (1967)

and are published by kind permission ofRMJM(formerly Robert Matthew, Johnson-Marshalland Partners).

Selected Bibliography

ALEXANDER, CHRISTOPHER

A City is not a Tree in Human Identity in the Urban Environment (ed. Bell & Tyrwhitt). Penguin,

1973

Notes on the Synthesis of Form; Harvard University Press, 1964

ASH, MAURICE

Regions of Tomorrow. Evelyn Adams & Mackay, 1969.

GOODHART-RENDELL, L

Fine Art. Clarendon Press, 1934

JACOBS, JANE

Death & Life of Great American Cities. Penguin, 1973.

LEVIN, PETER

Decision Making in Urban Design. Building Research Station Design Series No.49, 1966.

MAKI, FUMIHIKO

Investigations in Collective Form. Washington State University. 1964.

MANNHEIM, KARL

Ideology & Utopia. Routledge, 1966

MINISTRY OF HOUSING AND LOCAL GOVERNMENT

Central Lancashire: Study for a City. HMSO, 1967.

SIMON, HERBERT

The Sciences of the Artificial. M.I.T., 1969.

WARD, A. and BROADBENT, G.Design Methods in Architecture. Architectural Association Paper No.4, Lund Humphries, 1969.

WEBBER, MELVINPlanning in an Environment of Change. Town Planning Review, October 1968 and January 1969.

WILLIS, MARGARET

Sociological Aspects of' Urban Structure. Town Planning Review, January 1969.
http://www.rmjm.com/http://www.rmjm.com/http://www.rmjm.com/http://www.rmjm.com/


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Nikos A. Salingaros,

Division of Mathematics

University of Texas at San Antonio

San Antonio, Texas 78249

Abstract. Scientific principles applied to city form help to understand the role of various typesof urban connectivity. The degree of "life" in a city or region of a city is tied to the complexity of

visual, geometrical, and path connections. There is an optimal distribution of connection lengthsin a living city, and violating this distribution removes life from the urban environment.

Alternative parcellations of a living city reveal the complex structure that is required to generate

human contact, which is the basis for city life. These results are compared to the work ofChristopher Alexander.

Dr. Nikos A. Salingaros is Professor of Mathematics at the University of Texas at San Antonio,

has a Ph. D. in theoretical physics from the State University of New York at Stony Brook, andhas made contributions to mathematical physics, field theory, and thermonuclear fusion. He isthe author of more than seventy scientific publications, and has served as associate editor for two

journals, and referees for fourteen others.

Since 1983, he has been learning from and working with architectural theorist Christopher

Alexander. This interaction has inspired an entirely new direction of research, which usesmathematics to describe aspects of nature that are traditionally regarded as being in the domain

of art. These phenomena have so far eluded a scientific explanation. Dr. Salingaros is applying

insights gained from complex physical systems to architecture and urbanism. His latest

publications combine ideas from complexity theory, fractals, and thermodynamics to develop amathematical theory of structural form. The same ideas apply to architecture as well as to other

complex systems, be they urban regions or biological organisms. From this work, a new picture

of urban and architectural form emerges; one that is more consistent with natural structures. As aresult, it is now possible to connect mathematically the built environment with the natural

environment.

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