2024年5月2日发(作者：)

清华大学综合论文训练

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A CITY IS NOT A TREE

城市不是树形结构

CHRISTOPHER ALEXANDER

The tree of my title is not a green tree with leaves. It is the name of an abstract

structure. I shall contrast 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.

我的题目中的“树”不是指那种有叶子的绿色的树，而是指一种抽象结构的名字。（通常叫

做“数形”。）我将把它与另一个更加复杂的叫做“半格”的抽象结构进行对照。为了使这

些抽象结构与城市的性质相结合，首先我需要做一种简单的区别。

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 of artificial cities.

我会把那些在一段较长的时间内或多或少自发兴起的城市叫做“自然的城市”。而将那些在

设计师和规划师设计下而形成的城市或者那部分的城市称为“人造的城市”。 锡耶纳，曼哈

顿，京都，利物浦都是自然的城市。莱维顿镇，昌迪加尔和英国的新城则是人造的城市。

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.

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今天，人们越来越广泛的认识到，人造的城市中缺少一些必要的因素。从人类的视角看来，

与那些拥有悠久历史的古老城市相比，我们这些现代人尝试人工创造的城市，是完全失败的。

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 for structures of sets.

数形与半格都是考虑一种思考一些很大数量的小的体系是如何构成一个大的复杂的系统的方

法。更通俗的说，他们都是集合的构造的名字。

In order to define such structures, let me first define the concept of a set. A set is a

collection of elements 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 of grass, cars, molecules,

houses, gardens, water pipes, the water molecules in them etc.

为了定义这种结构，首先定义一下“集合”的概念。“集合”是一个由于某些原因我们认为

具有同一属性的要素的收集。于是，作为设计者，我们关心物质的适于生活的城市以及它的

中轴线，我们必须限制我们自己去考虑那些物质的元素的集合，例如人人，草，汽车，分子，

房子，花园，水管以及其中的水分子等等。

When the elements of a set belong together because they co-operate or work

together somehow, we call the set of elements a system.

当集合里的元素因为他们相互合作或者因某些原因一起运转时，我们称这种集合为“系统”。

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 idly by 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 actually buy a

paper while they wait.

例如，在伯克利，赫斯特和欧几里德的拐弯处，有一个药房，在药房外边有个一个交通灯。 在

药房的入口里有个报栏，里面有每天的报纸。当红灯的时候，等待穿过街道的人们站在灯旁

边等待，也许他们没什么可做的，于是他们就看那些从他们站的地方可以看得到的报纸。 在

他们等待的时候，一些人只读标题，另一些人却会买一张报纸。

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This effect makes the newsrack and the traffic light interactive; the newsrack, the

newspapers on it, 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.

这种效果使得报栏和交通灯互相影响，放着报纸的报栏，从人们的口袋进入报栏的钱，在交

通灯前停下读报的人们，交通灯，那个使灯改变的电气推动，还有人们脚下的人行横道组成

了一个系统——他们全部一同运作。

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, form the 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

which includes it as a fixed invariant part.

从设计者的观点看来，这个系统中物质上不变的部分是最有趣的。报栏，交通灯和在它们之

间的人行道，以及他们之间的相互关系，形成这个系统的固定部分。正式这些固定部分形成

了可变部分的基础——人，报纸，钱和电脉冲——使他们能一同运作。我把这个固定的系统

定义为城市的一个单元。作为一个单元，它从把它自己的元素结合在一起的力量那里以及从

把它作为一个固定的不变的部分包括的更大的动态系统的连贯性那里取得它的连贯性。

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.

对于大部分的那些可以被看作是系统的容器并因此被认为是城市的重要的固定单元的子集来

说，我们通常选出一些作为典型的考虑。实际上，我认为无论某人的城市的映像是什么，它

都正好被他看作是单元的子集定义。

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 once the subsets are chosen, the collection has a definite

structure.

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现在，那些组成这样的一张图的子集合不再是无定形的。通常自动的，一旦子集被选出，仅

仅当子集中的关系是确定的时候，那些子集就会有一个确定的结构。

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.

为了理解这个结构，让我们暂时的抽象的思考，使用数字作为符号。让我们考虑一个只不过

由半打要素做成的简单结构，而不是思考在城市发生的真正的数百万个真实的粒子。给这些

要素贴上1，2，3，4，5，6 的标签。不包括 [1,2,3,4,5,6 ]的全集，空集[-]，以及单元素集

合[1],[2], [3],[4],[5],[6]，我们可以找到56 个不同的子集合由这6种元素构成的。

Suppose we now pick out certain of these 56 sets (just as we pick out certain sets

and call them units 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].

假定我们现在从这56个集合中选出某一个，（正如我们形成一个城市的描述的时候，我们选

出某些集合并把他们称为单元一样）。例如，我们选出了以下的子集合：[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].

这些设备之间可能的关系是什么？一些集合完全是较大的集合的一部分，例如[34]是[345]以

及[ 3456]的一部分。一些集合互相重叠，例如[123]与[234]。一些集合之间没有相同的元素

——比如，在[123]与[45]之间没有相同的元素。

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 with here. When the structure meets certain conditions it is called

a semilattice. When it meets other more restrictive conditions, it is called a tree.

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从这两种情况我们可以看出，这些选出的子集单独的作为一个整体的结构支持这些子集的集

合。这是我们关心的结构。当这些结构满足某些条件时，它被称为“半格”。当它满足其他

更限制性的条件时，它被叫为“树形”。

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.

半格的公理是这样的：当且仅当一个集合里包括的两个集合互相重叠，而且其中重叠的元素

也属于这个集合的时候，这个集合被称为一个“半格”。

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 the newsrack. 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 of sets 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.

在图解A和图解B中的结构是半格。例如，由于[234]以及[345]都属于这个集合，并且，他

们的共同部分，[34]，也属于它，因此这满足半格的定义。（就城市而言，这条公理仅仅表明

了无论两个单元如何重叠，重叠的地区本身也是一个被认识的实体并且作为一个单位而存在。

就药房例子而言，报栏，人行道和交通灯组成一个单位。另一个单位亲自由药房组成，带有

它的入口和报栏。两个单元的重叠部分为报栏。显然，这重叠的部分本身是一个可认识的单

位并且因此满足前面确定一个半格的特性的公理。）树形的定义是这样的：当且仅当一个集

合里包括的两个集合一个完全属于另一个，或者两个集合毫不相关的时候，这个集合被称为

一个“树形”。

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 are not 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.

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但是，在这个章节中，我们并不关心一个树形肯定是半格的这个事实，我们关心的是树形与

那些因为包含了相互重叠的单元的不是树形的更一般的半格之间的区别，我们关心的是没有

重叠发生的结构和那些有重叠的结构之间的区别。

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 the following 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.

那些造成如此区别的重叠的重要性不只如此，相对于树形来说，半格是一种潜在的更复杂微

妙的结构，这个事实更为重要。从上面的例子我们可以看出半格比树形更加复杂，一个基于

20个元素的数形最多含有19个深一层的子集，但一个基于这同样的20个元素的半格包含了

至少1,000,000个不同的子集。

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 structural complexity, characteristic of trees, which is crippling our

conceptions of the city.

与结构简单的树形相比，这种巨大的不同是一种半格的巨型结构负责性的指标。正是这种树

形特点上的结构复杂性的缺乏，使我们城市的概念大打折扣。

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

shall show to be essentially a tree.

例如，让我们看看一些现代概念的城市，他们中的每个本质上都是一个树形。

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Figure 1. Columbia, Maryland, Community Research

and Development, Inc.: Neighbourhoods, in clusters of

five, form 'villages'. Transportation joins the villages into

a new town. The organization is a tree.

图1、位于哥伦比亚的马里兰的社区研究和发展股份有限公

司：邻里关系，五个一体，形成了“乡村”的结构。交通系

统把这些乡村联系成为一个新城。这种结构是一个树形。

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.

图2、克拉伦斯·斯坦的马里兰绿化带：这个“花园城市”已

经被分解为大的街区。每个大街区包含学校，公园和许多位

于停车场附近的辅助建筑。这种组织形式是一种树形。

Figure 3. Greater London plan (1943), Abercrombie

and Forshaw: The drawing depicts the structure

conceived by Abercrombie for London. It is made of a

large number of communities, each sharply separated

from all adjacent communities. Abercrombie writes,

'The proposal is to emphasize the identity of the existing

communities, to increase their degree of segregation,

and where necessary to recognize them as separate

and definite entities.' And again, 'The communities

themselves consist of a series of sub-units, generally

with their own shops and schools, corresponding to the

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neighbourhood units.' The city is conceived as a tree

with two principal levels. The communities are the

larger units of the structure; the smaller sub-units are

neighbourhoods. There are no overlapping units. The

structure is a tree.

图3。由阿伯克龙比和福肖设计的大伦敦计划(1943)：一个由

阿伯克龙设计的描绘伦敦城市结构构思的图画。它由许多跟相

邻的社区明显分离的社区组成。阿伯克龙比写到，“这么做的

目的是为了强调现有的社区的独立性，增加他们的独立性，必

要的话，把他们看作是分离的特定的实体。”以及“这些社区

本身是由一系列的子单元组成的，通常是他们内部的商店和学

校，也是一种类似邻里关系的单元。”在两种基本的层面上，

城市被设计为一种树形的结构。社区是这种结构内大一些的元

素，而较小的元素是邻里关系。在整个结构中，没有有互相重

叠关系的元素存在，因此整个结构是一种树形结构。

Figure 4. Mesa City, Paolo Soleri: The organic shapes of

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 the

centre of the city divided into a university and a

residential quarter, which is itself divided into a number

of villages (actually apartment towers) for 4000

inhabitants, each again subdivided further and

surrounded by groups of still smaller dwelling units.

图4。 保罗的台地城市：乍一看来，台地城市的有机形状让

我们以为他比我们其他的刚性的城市更有丰富性。但是当我们

仔细看的时候就会发现，他们正是有着相同的组织原理的。大

学中心区就是一个例子，在那里我们看到，城市的中心区被分

成了一个大学区和一个居住区，这个居住区又被分成了许多村

落（实际上是一个个公寓楼），里面居住着4,000人，每个村

落又被进一步细分成更小的居住单元。

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

example. The plan consists of a series of loops

stretched across Tokyo Bay. There are four 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 loop contains three minor loops which are

residential neighbourhoods, except in the third major

loop where one contains government offices and

another industrial offices.

图5、Kenzo Tange的东京计划：这是一个美丽的例子。计划

由一系列横亘东京的环组成。有4个大环，其中每个环又包含

3个中等的环。在第2 个大环中，其中一个中等的环是火车站，

另一个是港口。其余的每个中等的环包含3个居住邻里关系的

小环，除了在第3 个主环内，一个包含政府办公室和另一个

是工业办公室之外。

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. Two

subsidiary 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

the city's 20 sectors.

图6：勒·柯布西埃的昌迪加尔( 1951)：整个城市的商业中

心设置在中间，与行政管理中心毗邻。附属的中心被向两端

拉长，一直沿着城市中心的南北向道路延伸。这些附属的中

心是进一步管理的社区和商业中心，城市中大约分作20个这

样的部分。

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Figure 7. Brasilia, Lucio Costa: The entire form pivots

about the central axis, and each of the two halves

is served 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.

图7，Lucio Costa的巴西利亚规划：整个形体围绕着中心

轴对称，城市的两半中都有一条主要交通干道穿过。这些

主干道是由一系列与之平行的附属道路辅助的。最终，这

些道路都被一些环绕着巨大街区的道路所辅助。整个结构

是一种树形。

Figure 8. Communitas, Percival and Paul

Goodman: Communitas is explicitly organized as a

tree: it is first divided into four concentric major

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 commercial centre

is represented as a great cylindrical skyscraper,

containing five layers: airport, administration, light

manufacture, shopping and amusement; and, at

the bottom, railroads, buses and mechanical

services. The university is divided into eight sectors

comprising natural history, zoos and aquariums,

planetarium, science laboratories, plastic arts,

music and drama. The third concentric ring is

divided into neighbourhoods of 4000 people each,

not consisting of individual houses, but of

apartment blocks, each of these containing

individual dwelling units. Finally, the open country is

divided into three segments: forest preserves,

agriculture and vacation lands. The overall

organization is a tree.

图8。珀西瓦尔和保罗的社区群：社区群作为一种树形明

确的组织：它被首先分成4个同心的主要区域，最内部作

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为商业中心，然后是一所大学，第三个是居住和医院区，

最外面的是开放郊区。这些中的每个被更进一步细分：商

业中心是一座巨大的圆柱体的摩天大厦，包括五层：飞机

场，管理层，轻工业层，购物和娱乐层；并且，在大厦的

底部，设有铁路，公共汽车和机械服务。大学分成8个部

分，包括博物学，动物学和水族馆，天文馆，科学实验室，

造型艺术馆，音乐部分和戏剧部分。 第3 同心圆分成每

个4000的，不是由单独的住宅，而是公寓街区组成的邻

近地区，其中每个都包含了独立的居住单元。最后，郊外

被分成3 部分：森林保护区，农业区和旅游区。总体的

组织是一种树形。

Figure most beautiful example of all I have

kept until last, because it symbolizes the problem

perfectly. It appears in Hilberseimer's book The

Nature of Cities. He describes the fact that certain

Roman towns had their origin as military camps,

and then shows a picture of a modern military

encampment as a kind of archetypal 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 to create 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.

图9、我把最美的例子放在了最后，因为它完美的阐述了

问题。它就是Hilberseimer书中的“自然城市”。他记录

了这样一个事实，某些古罗马的城市有一种军营的组织形

式，以及现代的军队都以一种城市原型的方式扎营的图

片。形成一个清楚的树形的结构是不可能的。符号只是一

部分，军队的组织是被设计来保证严格的纪律的。左面的

照片是Hilberseimer自己为基于军营原型的城市商业区

的设想。

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Each of these structures, then, is a tree. Each unit in each tree that I have described,

moreover, is the 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).

上面这些结构每个都是树形。在这些我已经描述过的每个树形里的每个单位都是变化的城市

里的固定的，不可改变的部分。就好比住宅是一个交互的家庭成员、他们的情感以及他们的

财产的固定部分，高速公路是移动于贸易交换的残余的固定部分一样。

However, in every city there are thousands, even millions, of times as many more

systems at work 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.

但是，在每座城市有数千，甚至数百万的不存在固定部分的物质体系的单位处于这些树形结

构内。从最糟的例子看来，这些不出现的单元不与任何活动的实体发生关系，这些使得车工

能使生存的实实在在的系统并没有任何物质的基础。

Neither the Columbia plan nor the Stein plan for example, corresponds to social

realities. The physical layout of the plans, and the way they function suggests a

hierarchy of stronger and stronger closed social groups, ranging from the whole city

down to the family, each formed by associational ties of different strength.

哥伦比亚计划和斯坦计划都不是相对于社会现实的。计划的实际布局，以及他们运作的方式

方法都表明了一种越来越坚固的关闭的社会团体的阶层，从整个城市一直到每个由不同辅助

力量形成的家庭都是这样。

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

friends and then ask each of these in turn to name their

best friends, they will all name each other so that they

form a closed group. A village is made up of a number

of separate closed groups of this kind.

在一个传统的社会里，我们要一个人评价他的最好的朋友然后

依次要求这些朋友中的每个评价他们的最好的朋友，他们将全

部给出一种以便使他们形成一个紧密的组的评价。一个村庄由

许多这种单独的紧密的组组成。

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But today's social structure is utterly different. If we ask a

man to name his friends and then ask them in turn to

name their friends, they will all name different people,

very likely unknown to the first person; these people

would again name others, and so on outwards. There

are virtually no closed groups of people in modern

society. The reality of today's social structure is thick with

overlap - the systems of friends and acquaintances form

a semilattice, not a tree (Figure 10).

但是今天的社会结构完全不同。如果我们让一个人评价她的朋

友，然后依次要他们朋友反过来评价，他们将都评价一些完全

不同的人，每个人好像都不知道前一个人的；这些人再次将评

价其它人，一直向外扩散。在现代社会方面实际上没有像过去

的社会那些紧密而单一的组。今天的社会结构的现实充满重叠

——朋友和相识的人的系统形成一个半格，而不是一个树形（图

10）。

In the natural city, even the house on a long street (not in some little cluster) is a

more accurate acknowledgement of the fact that your friends live not next door,

but far away, and can only be reached by bus or car. In this respect Manhattan has

more overlap in it than Greenbelt. And though one can argue that in Greenbelt,

too, friends are only minutes away by car, one must then ask: since certain groups

have been emphasized by the physical units of the physical structure, why are just

these the most irrelevant ones?

在自然的城市中，即使，一个长长的街道边的房子相当准确，你的朋友并非就在隔壁，而是

在远方，并且只能乘公共汽车或者小汽车到达。与绿化带相比较，曼哈顿在这方面有更多的

重叠的现象。即使一个人也在绿化带也能了解这些，朋友并不远，坐汽车仅仅只有数分钟，

但是他也会问：既然某些组已经被物质结构中的单元强调过了，为什么这些只是最不相关的

一些呢？

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 us define 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.

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组成人造城市的单位通常会被组织成“树形”的结构。为了我们能够得到一个真正清晰的理

解它的含义，让我们再一次定义“树形”。任何一个树形结构都意味着在这个结构内部没有

任何单位于别的单位相连，除了通过那种把单位作为一个整体媒介之外。

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 made a friendship.

这种巨大的限制并不容易理解。它有一点类似于这样的情况，一个家庭内的成员不能自由的

在家庭之外交朋友，除非家庭作为一个整体去发展友谊。

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.

在简单的结构中，树形可以看作是一种强烈的追求整洁和秩序的欲望，这种欲望要求壁炉上

的烛台完全的笔直和中心对称。而半格则是一种相对复杂的构造，它是那种活的东西，类似

于伟大的绘画和交响乐。

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 of aspect 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.

重叠的、含糊的、多样性的视角与半格并不是比严格的树形显得更加有序，这一点必须得到

强调，以免有序的思想害怕树形的不清楚的分类和关系而收缩。他们表现出的是一种更加厚

重的、坚忍的、更加微妙的和复杂的看待结构的视角。

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

conceptions, shows itself to be a semilattice.

现在，让我们来看一些自然的城市，他们没有收到人为的概念的影响，因此表现成为一种半

格。

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 she recommends be broken down into 29 separate neighbourhoods.

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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 which actually exist for the

people in such a neighbourhood, do the physical units defined by these various

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 discussion. The units

corresponding to different kinds of centres for the single neighbourhood of Waterloo

Road are shown in Figure 11.

声势的社会结构并不能由一个树形所正确的反应的主要视角已经由卢斯的米德尔斯布勒在发

展规划所阐述。她建议把米德尔斯布勒这个200,000人口的城市分成29个分离的邻里关系系

统。通过确定最尖锐的建筑类型收入和工作类型的缺乏发生的地点的方法，她调查了选出的

29个邻里关系，然后，她问自己，“如果我们调查在这样一个邻里关系里，真正为了人们而

存在的社会系统，那些被这样的社会系统所定义的物质单元会属于同一个空间上的邻里关系

么？”她自己的答案是否定的。她所调查的每一个社会系统都是类似的。他们是由一些种类

的中心节点，再加上使用这些中心的人所构成的。她明确指出的是小学、中学、青年俱乐部、

成年俱乐部、邮局、蔬菜摊以及食品店。这些中心的使用者都是从某个空间领域或者空间单

元来的。这些空间单元是整个社会系统的物质剩余，并且因此在此讨论中作为一个组里的单

元。这些单元都与滑铁卢的一个邻里关系中不同种类的中心想呼应。

The hard outline is the boundary of the so-called

neighbourhood itself. The white circle stands for

the youth club, and the small solid rings stand for

areas where its members live. The ringed spot is

the adult club, and the homes of its members

form the unit marked by dashed boundaries. The

white square is the post office, and the dotted

line marks the unit which contains its users. The

secondary 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.

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所谓邻近地区它自己的边界是一个坚固轮廓。白色的圈

支持着青年俱乐部，并且固定的小环支持着成员住的地

区。被画出的点是成年人的俱乐部，它的成员的家形成

被虚线的边界标出的单位。白色的广场是邮局，并且虚

线标明包含它的用户的单位。中学在里面有三角形的点

标出。还有它的子集，它形成以小圆点短划线为特征的

系统。

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

coincide. Yet neither are they disjoint. They

overlap.

这样如你所见，不同的单位不会重合。然而，两者都不

是完全独立的。他们之间会有重叠。

We cannot get an adequate picture of what Middlesbrough is, or of what it ought

to be, in terms of 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 other neighbourhoods through the

medium of the neighbourhoods to which they themselves belong. Ruth Glass herself

shows clearly that this is not the case.

我们不可能得到一张确切的图画来说明米德尔斯布勒是什么，或者它应该是什么，就29个大

的和方便的不可缺少的被称作使邻里空间的块而言。当我们就邻近地区而言描述城市时， 我

们含蓄的假设在任意邻里空间内的小元素属于一个如此紧密以致于他们与其他邻里空间内的

元素发生作用的时候，只通过他们自己属于的邻近空间。卢斯本人清楚的表明了情况不是如

此。

Next to Figure 11 are two representations of the Waterloo

neighbourhood. For the sake of argument I have broken

it into a number of small areas. Figure 12 shows how

these pieces stick together in fact, and Figure 13 shows

how the redevelopment plan pretends they stick

together.

图11下面的是两个那些滑铁卢邻近地区的图片。为了说明问题，

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我已经把它毁坏成为许多小的领域。 图12 显示怎样这些片实

际上都是连在一起的，图13 显示那些重新规划计划是怎样假装

的把他们连在一起。

There is nothing in the nature of the various centres which says that their catchment

areas should be 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.

没有什么具有的性质说那些不同的中心的重叠地区应该相同。他们的本性不同。因此他们确

定的单元是不同的。自然的米德尔斯布勒市对单位的半格结构是忠实的。只在城市的人造树

的概念里他们的自然的，适当的和必要的重叠会遭到破坏。

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

strictly separated. The cruising taxi needs a fast stream of

traffic so that it can cover a large area to be sure 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 to any 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 pedestrian circulation. In

Manhattan pedestrians and vehicles do share certain

parts of the city, and the necessary overlap is

guaranteed (Figure 14).

从把行人从移动车辆中分离的考虑来说，树形的概念是被勒·柯

布西耶，路易斯卡恩还有很多其它人提出的。在那个非常早期

的水平下，这显而易见是一种好想法。然而仅仅在行人和车辆

没被严格分开的情况下，都市的出租车才能起作用。这些巡游

的出租车需要组成一个很快很高效的交通体系，才能在一个很

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大的范围内寻找旅客。行人需要能在行人世界内的任何一点召

唤出租车，能从步行体系中的任何他想要出去的一点出去。那

个包含出租小汽车的系统需要重叠的覆盖快的交通车辆体系和

行人步行的体系。在曼哈顿，行人和车辆确实分享城市的不同

部分，并且必要重叠部分也被保证了(图14)。

Another·favourite 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. The playground, 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.

CIAM理论家另一个喜欢的概念是从其他一切事务中分离的娱乐。这些已经以运动场的形式在

我们真正的城市里形成结晶。那些有篱笆围着的沥青的运动场，不过是那些行为最为孤立的

我们内心的概念的形态存在的事实的图片形式。这种行为跟它自己的生活无关。很少会有自

尊的孩子将在一座运动场里出现。

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 the weekend. 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 different systems overlap one another,

and they overlap many other systems besides. The units, the physical places

recognized as play places, must do the same.

这种孩子们实践的行动本身，每天在不同的某处发生着。有一天它可能在屋里，改天在一个

友好的加油站，改天在那条河旁边，或者在一座被废弃的大楼，在已经被抛弃的一个建筑工

地上度周末。每个这种行为活动和它要求的目的，形成一个系统。这些系统并不是在从其他

系统中隔离中存在的。不同的系统彼此重叠，而且除了跟其他的系统重叠之外，他们本身也

重叠。这些被认为是行为上演的地方物质的单元，一定是相同的。

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.

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在一座自然的城市是这样发生的。行为进行在许多的地方以至于可以填补那些成年人的生活

的间隙内。他们进行的时候，周围到处都是孩子。孩子竟然能在一个围住的地方充满他们的

环境！但是成年人不能。

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 been realized in the common American form of the isolated campus.

一种相似的错误发生在那种古德慢的社区里和梭勒里的台地城市的树形里，把大学与其余的

城市分开。再一次的，这实际上已经普遍的在美国的被孤立的大学校园里实现。

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 it correspond to the realities of university life? Certainly it is not the

structure which occurs in nonartificial university cities.

在城市里画一条区别大学以及非大学的线的原因是什么？观点是很清楚的。但是它符合大学

生活的现实吗？当然这不是在非人造城市的大学里发生的结构。

There are always many systems of activity where

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 have

grown together gradually, the physical units overlap

because they are the physical residues of city systems

and university systems which overlap (Figure 15).

总会有许多大学生活和城市生活重叠活动的系统：比如逛酒店，

喝咖啡喝酒，看电影，到处散步。有时候整个部门可能动态的

涉及城市的居民的生活(医学院附属的医院就是一个例子)。在剑

桥，大学和城市已经一同逐渐增长的一座自然的城市， 物质部

分相互重叠，因为他们是重叠(图15) 的城市系统和大学系统的

物质剩余。

Let us look next at the hierarchy of urban cores realized in Brasilia, Chandigarh, the

MARS plan for London and, most recently, in the Manhattan Lincoln Center, where

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various performing arts serving the population of greater New York have been

gathered together to form just one core.

让我们进一步地看着在巴西利亚的都市核心的阶层，还有昌迪加尔，伦敦内的MARS计划，

以及在曼哈顿林肯大厦内，在那里为大纽约巨大人口服务的各种各样的表演艺术聚集形成一

个唯一的核心。

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 arts has 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. The

influence of each overlaps the parts of the city which have been made unique to it.

一个音乐厅需要紧挨着一个歌剧院吗？在他们两个能够彼此供给么？会不会有人一次参观他

们两个，或者在同一个个晚上里，或者在买票从他们中的一个逛到另一个？在维也纳，伦敦，

巴黎内，每一种表演艺术都在发现它自己地方，因为他们全部都不会混合。每一个都会形成

他自己的城市的熟悉的部分。在曼哈顿本身，卡内基大厦和大都市的歌剧厅都没有被肩并肩

的建造。他们每一个都建立勒它自己的地方，并且在那里营造它自己的气氛。城市的每一个

重叠的部分的影响都已经成为了独特而不可复制的。

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.

把这些功能一起放在林肯大厦内的唯一的原因就是由于表演艺术的概念把他们和彼此连结起

来。

But this tree, and the idea of a single hierarchy of urban cores which is its parent, do

not illuminate 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.

但是这些树形，以及作为他们的父母的都市核心的单独层次的想法，都没有在城市与艺术之

间表现出关系。他们仅仅出现于一些头脑简单的人把相同的名字放进相同的篮的癫狂的想法。

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

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easy to see how bad conditions 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.

以托尼加尼尔在他工业城市内启动，然后在1929 雅典特许证内合并的居住出发的工作的总分

离的原则，现在正在在一切人造城市内建立并且接受。这是一个正确的原则吗？很容易看出

的是，在世纪之初的不良状态是怎样促使计划者努力在居民点之外得到工厂的。但是这种分

离错过了很多不同的要求两个小的部分适合他们的支持。

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 one manages 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.

最后，让我们检查城市的细分进孤立的团体。正如我们已经在阿伯克龙比的伦敦计划里看到

的一样，它自己就是一个树形结构。在一座更大的城市的个别的团体没有现实成为一个起作

用的单位。如同在许多巨大的城市一样，在伦敦内，几乎没有人去设法找到接近他的家的适

合他的工作。在一个社区的人们在很可能在另一个社区的一家工厂工作。

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 by Abercrombie'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.

于是有很多成千上万个工人工作场所系统，每个包括个人和他们工作在里的工厂，他们穿过

阿伯克龙比确定的树形的边界。这些单元的存在，和他们重叠的自然，表明伦敦的生活系统

形成一个半格。只在规划师的心里，它才会是一个树形。

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 has relatively 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

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systems must be anchored in physically recognizable units of the city which can

then be taxed.

我们迄今不能给给出任何物质的表达的事实有一个至关重要的结果。在目前形势下，无论什

么时候工人和他的工作场所属于分别管理的行政当局，包含工作场所的社区会收巨大的税款

但是却没有什么能花掉国家的税收的。工人居住的社区，如果它是主要用于居住的，只能收

来很少的税款，然而却有非常大的负担需要承受学校，医院等等。显然，为了解决这种不公

平的情况，工人和工作场所系统一定要固定在能被征税的城市的可认识的单位上。

It might be argued that, even though the individual communities of a great city

have no functional 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, in the political complexity of a modern city, even this is

suspect.

可能可以证明的是，即使巨大城市的个别社区在他们的居民的生活中没有职能的重要性， 他

们仍然是最方便管理的单位，并且因此应该被在他们的目前的树形组织里留下。但是，在一

座政治复杂的现代城市里，这也是有问题的。

Edward Banfield, in his book Political Influence, gives a detailed account of the

patterns of influence and control that have actually led to decisions in Chicago. He

shows that, although the lines 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 is interested in the matter,

who has what at stake, who has what favours to trade with whom.

爱德华班菲尔德，在他的《政治影响》内，详细描述了实际上影响并控制在芝加哥内的决定

方式。他所显示的是，虽然管理和执行的是一种树形的正式结构，但这些一系列的正式影响

和授权很大程度上受到作为每座新城市的问题出现的控制的的影响。这些线索取决于那些对

事情感兴趣的人，那些在危急中有东西的人，那些与其他人有交易的人。

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 one problem 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 is semilattice-like.

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这并不正规的第二种结构，在第一种的范围内运行，是真正控制公共活动的。当一个问题替

换另一个时，它通常会每周都发生变化，甚至每小时也会发生变化。没有人的势力范围完全

在单一的一个超越性的控制之下，都随着那些问题变化每个人都是处于不同的影响下。虽然

在市长办公室内的组织系统图是一个树形，但是真实的控制和权力的运行是一个好比半格的

形状。

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 they are 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?

那么现在，为什么会有那么多设计者把城市设想为树形，即使那些自然结构在每件事上都是

半格的？是因为他们相信一个树形结构将更好地服务于城市的人民，所以他们才如此有意识

的做了吗？或者他们这么做是因为他们不能起到任何的帮助，或者因为他们被一种精神习惯

困住，或许甚至被他们思考的方式所困住——因为他们不可能围绕一个半格在任何精神形式

方面的复杂性，因为他们的思想有着压倒一切的倾向性把城市看为树形，无论在哪里，也逃

不出树形的概念？

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 form intuitively accessible structures, cannot achieve

the complexity of the semilattice in a single mental act.

我将努力使你确信正是由于这第二种原因，所以树形会被提议并且作为城市的结构来得到建

造——也就是说，设计者，被限制在他们以直觉感到可达到的建筑的中心结构的设计者，不

可能取得在一单个精神行动方面的复杂的半格。

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 your mind'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 two large and more

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egg-shaped objects - the watermelon and the football. Some of you will be aware

of both.

让我从一个例子开始。假定我要你记得如下的四个物体：一个橙子，一个西瓜，一个足球和

一个网球。你将怎样在你的头脑里记住他们，或者在想象中？无论怎样你做，你通过把他们

归类来记住他们。一些人将把两个水果放在一起，橙和西瓜，并且把两个运动球类放在一起，

足球和网球。那些倾向依据物质的形状归类的人将会得到不同的结果，他们把两个小的球放

在一起——橙和网球，并把两个更大的物体放在一起——西瓜和足球。一些人可能会有这两

种方法。

Let us make a diagram of these groupings (Figure

16). Either grouping taken by itself is a tree

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 alternate

between the two pairs extremely fast, so that you

may deceive yourself into thinking you can

visualize them all together. But in truth, you

cannot conceive all four sets at once in a single

mental 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.

让我们做一张这些集团(图16)的图解。两种组合方式中

的任何一个单独来说是一个树形结构。但这两个放在一

起则是一个半格结构。现在让我们想办法想象这些集

团。我认为你将发现你不能同时设想全部四种情况——

因为他们之间会有重叠。你能设想两个然后确定另外两

个，并且你能强烈迅速地在二对之间交替， 以便你能

使自己以为你能共同的想象他们。实际上，在一个单独

的人类行为中，你是不能设想全部四个情况的。你是不

能使半格结构形成一个单独的精神行动。 在一次单个

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的精神行动里你只能想象一个树形。

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 is accessible mentally and easy to deal with. The semilattice

is hard to keep before the mind's eye and therefore hard to deal with.

这是我们作为设计者面对的问题。或许当我们并不必要的解决在一个行为中一起设想的问题

时，原则仍然是相同的。树形是容易达到并且容易处理的。半格结构是很难在思维里设想出

来的，因此很难处理。

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 existing slots 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 complexity of its

environment by establishing barriers between the different events that it encounters.

分类和归类是在最原始的心理过程，在今天这一点勿庸置疑。现代心理学把想法当作一个在

的头脑里把新的事务放入现有的文件分类架基础里的过程。正象你不能同时把一件物质的东

西放进超过一个的物质的文件分类架一样，人们思考问题的方法的过程阻止他们同时把精神

结构放进超过一个精神分类架上。研究的那些思考的过程的起源显示，这种思考的方式起源

于人们通过建立屏障减少外部环境的不同的事件的复杂性的需要。

It is for this reason - because the mind's first function is to reduce the ambiguity and

overlap in a confusing 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.

正是由于这个原因，因为那些思考的第一个功能是降低那些意义含糊并且在一种混乱的形势

内重叠，因为这些意义含糊的结构在意识中是不能容忍的——就像那些城市的结构，他们确

实在它们内部是有重叠的，被这样坚持的设想为树形结构。

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 they almost always invent a way of seeing the patterns

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as a tree - even when the semilattice view of the patterns would have helped them

perform the task of experimentation which was before them.

同样的僵硬也出现在物质图案的感觉里。在哈金斯和我自己的在哈佛的实验过程中，我们发

现人们总是会形成内部单元重叠的图案，并且发现他们经常发明一种把图案视为一棵树的方

式——即使当半格的视角可能可以帮助他们展现他们面前的实验的任务的时候也是如此。

The most startling proof that people tend to

conceive even physical patterns as trees is

found in some experiments of Sir Frederick

Bartlett. He showed people a pattern for about a

quarter of 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. In Figure 17, the original is shown on

the left, with two fairly typical redrawn versions to

the right of it. In the redrawn versions the circles

are separated from the rest; the overlap

between triangles and circles disappears.

最令人震惊的证明倾向于设想物质图案为树形的证据

是由在一些弗雷德里克·巴特利特先生的实验发现的。

他让人看一个模式适合大约一秒的四分之一秒之后，要

他们画出他们所看见的东西。很多不能掌握他们已经看

见的图案的充分的复杂性的人，通过删去重叠的部分来

简化图案。在图17，原物被在左边显示，右边是两个

相当典型的重画的版本。 在重画的版本里圈与其余分

离；在三角形和圈之间的重叠部分消失了。

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. The complexity of the semilattice is replaced by the simpler

and more easily grasped tree form.

这些经历强烈暗示着当面对一个复杂的组织的时候，精神上就会以非重叠的单位而言改组，

人有这样一种基本的趋势。 半格的复杂性在于简单和更容易抓住树形用以替换。

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You are no doubt wondering by now what a city looks like which is a semilattice, but

not a tree. I must 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, you must 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 the

systems 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.

现在你应该对于一座城市看起来象是一个“半格”，而不是某种“树形”没有疑问了，但是

必须承认我不能让你看相关的图纸或者草图。仅仅示范出一些重叠是足够的——重叠一定得

是是正确的重叠。这非常非常的重要是因为做那种重叠刚好发生在他们自己的范围内的规划

是如此的有诱惑力。这基本上就是那些近年来为一种高的密度城市做的规划。但是重叠不会

独自变得有组织，它也能变得十分混乱。一个垃圾箱就充满重叠。为了变得有组织，你必须

有正确的重叠，并且这是对于我们来说是相当不同的，与我们在一些古老的城市里面观察到

的重叠相比。随着在功能之间的关系变化，为了形成某种关系而需要互相重叠的系统还必须

改变。老式的这种重叠是不适当的，混乱的，而不是有组织的。

One can perhaps make the physical consequences of

overlap more comprehensible by means of an image.

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

triangular elements, 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 complete

inventory 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 triangle.

人们或许能通过理解一幅图像而使重叠的物理结果变得更可以

理解。下面这幅画是由西蒙·尼科尔森( 图18) 创作的一件作品。

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这画的魅力在于，虽然只用了很少的简单三角形元素，但是这

些简单的三角形元素却以相当多的不同的方法来组成图画里较

大的单位。在这样的一种方式那的确定之内。如果我们总结一

下这些所有的单元的目录的话，我们会发现每个基本的三角形

单位会参加4个或者5个完全不同种类的大的单位，基本的三

角形元素之间没有互相包含的关系，然而所有的较大的组合都

会重叠为基本的三角形。

Thus, if we number the triangles and pick out the sets of

triangles which appear as strong visual units, we get the

semilattice shown in Figure 19.

因此，我们给三角形编号和并且把三角形的集合作为强烈的视

觉元素提出来分析的话，我们就会得到了一种半格结构，如图

19所表现的。

Three and 5 form a unit because they work together 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

shifted sideways; 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 rather thinner 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

same way 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 have only 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 the diagram because it is harder to be sure

of its elementary pieces.

3和5组成一个单位因为他们作为一个长方形一同工作； 2和4

是因为他们形成一个平行四边形；5和6因为他们都是黑的且有

指相同的方向；6和7则是因为他们互为变种；4和7是因为他

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们相互匀称而组成一个单位；4和6因为他们形成另一个长方形；

4和5因为他们形成某种Z字形；2和3因为他们形成一种瘦得

多的Z字型；1和7因为他们在对角；1和2因为他们是一个长

方形；3和4因为他们与5和6指向同样的方向，然后形成一种

非中心的对称；3和6是因为他们与4和5互补；1和S是因为

他们与2，3和4互补。 我只列举两个三角形的集合为例。更

大的集合将会更加复杂。色彩仍然是更复杂的，并且甚至没有

包括在图解里，因为我确信对它的大量分析是很难的。

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 fact of the overlap, and the resulting multiplicity of aspects

which the forms present, that makes the painting 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.

这副画是比较典型的，因为尽管在它内部有重叠出现，（许多的画内部都会有重叠出现，）

但是更是因为它的内部除了重叠之外就没有别的东西了。它完全就是一种重叠现象的表现，

是一种多种视角展现形式的结果，这使这副画像是具有了魔力。它好像几乎就是作者的一种

思想的体现，作者做的就是把生活中的典型的重复的例子全部挑出来。

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 large branch of modern mathematics, is a

powerful way of exploring the structure of these images. It is the semilattice we must

look for, not the tree.

我已经描述的全部的人造城市都接近一种树形的结构，而不是尼科尔森画的半格机理的结构。

然而是那幅画，连同其余类似的图画，被认为是我们思维的一般方法。并且当我们希望思想

变得更加准确时，半格，作为一个现代数学的大的分支的一部分，是一种探索这些图像的结

构的有力的方式。这就是我们为什么必须寻找半格，而不是树形的原因。

When we think in terms of trees we are trading the humanity and richness of the

living city for a conceptual simplicity which benefits only designers, planners,

administrators and developers. Every time a piece of a city is turn out, and a tree

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made to replace the semilattice that was there before, the city takes a further step

toward dissociation.

当我们用一组树形的方法来进行思考的时候，我们往往会把我们的人性、我们所居住的城市

的财富看成是一种只会对设计师、规划师和管理者有好处的简单的概念来思考。每当城市的

一部分被规划的时候，树形结构被规划者用来取代本该是半格结构的体系，这样，城市就向

着分裂又前进了一步。

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-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 is only possible under the influence of treelike

thought.

在任何有组织的对象中，趋向毁灭的第一个标志就是极端的区分和相互有关的元素的分裂。

对于一个社会来说，分裂会造成无政府的后果。对于一个人来说，分裂是精神分裂和趋向自

杀的一种标志。这方面的一个恐怖的例子是，把退休的人们从都市生活的其他部分割裂出去，

就像亚里桑那的太阳城那样的老年人的城市。这种分裂是只可能在树形思想的影响下发生的。

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 ties with 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.

它不仅仅只将那些长寿的人群从年轻的人中分裂出去，更糟的是，它在每个个人的生活里面

引起相同的分裂。当你在太阳城里，进入老年的时候，你以及你的过去将不会被世人承认，

并且因此被遗弃，被破坏。在你老年的时候，你将不会享受到年轻时候的生活，——这两个

时代将被分离；你自己的生活将被分裂为两份。

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 overlap of 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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清华大学综合论文训练

翻译部分

对人类智力来说，树形是达到复杂的思想的最容易的方法。但是城市不是这样的，她不能并

且也不可能是一棵树形。城市将永远是一个生活的容器。如果容器因为一种树形的结构，切

断生活内在的重叠以至于使生活搁浅，那么它将使一个表面都是刀片的球形，随时准备割裂

任何生活在这个城市中的生活。在这样的容器中，生命将被割裂，摧毁。也就是说，如果我

们认为城市是一种树形的结构，那么他们将会把我们的生活撕裂。

Originally published in:

Architectural Forum, Vol 122, No 1, April 1965, pp 58-62 (Part I),

Vol 122, No 2, May 1965, pp 58-62 (Part II)

Also published in :

Design, No 206, February 1966, pp46-55

Ekistics, Vol 23, pp 344 - 348, June 1967

Bell, G & Tyrwhitt, J(eds) Human Identity in the Urban Environment,

Harmondsworth, UK, Penguin Books, 1972

This version taken from:

Thackara, J. (ed.) (1988), Design After Modernism: Beyond the Object,

Thames and Hudson, London, pp. 67-84.

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