TED演讲之2.0版城市:城市与企业中的奇妙数学(3)
Before I talk about that,
谈到这之前
I've written down at the bottom there
我在底下标出了
the slope of this curve, this straight line.
这条曲线的斜率，即这条直线
It's three-quarters, roughly,
大约为3比4
which is less than one — and we call that sublinear.
小于1,呈“次线性”
And here's the point of that.
这里有一点值得注意
It says that, if it were linear,
当最大斜率
the steepest slope,
呈线性
then doubling the size
那么当体型翻倍
you would require double the amount of energy.
所需能量也随之翻倍
But it's sublinear, and what that translates into
而若呈次线性，情况则是
is that, if you double the size of the organism,
当生物的体型翻倍
you actually only need 75 percent more energy.
它实际只需增加75%的能量
So a wonderful thing about all of biology
生物的奇妙之处就在于
is that it expresses an extraordinary economy of scale.
它巧妙地展现了经济的伸展能力
The bigger you are systematically,
根据准确定义的规律
according to very well-defined rules,
一个系统越大
less energy per capita.
其所需的平均能力越少
Now any physiological variable you can think of,
你能够想到的任何变量
any life history event you can think of,
任何历史事件
if you plot it this way, looks like this.
只要你照着这样制表，都会得到相似的图形
There is an extraordinary regularity.
其一致性非常惊人
So you tell me the size of a mammal,
只要你说出一种哺乳动物的体型
I can tell you at the 90 percent level everything about it
我就能告诉你关于其生理和生命周期等情况
in terms of its physiology, life history, etc.
正确率90%
And the reason for this is because of networks.
原因就在于网络
All of life is controlled by networks —
所有生命都由网络所控制
from the intracellular through the multicellular
不论是单细胞还是多细胞生物
through the ecosystem level.
整个生态系统都是如此
And you're very familiar with these networks.
你对这些网络并不陌生
That's a little thing that lives inside an elephant.
这是生长在大象体内的一种小生物
And here's the summary of what I'm saying.
这是我讲话内容的总结
If you take those networks,
你有了这些网络
this idea of networks,
网络的概念
and you apply universal principles,
再用上普遍原理
mathematizable, universal principles,
数学化的普遍原理
all of these scalings
所有规模增长
and all of these constraints follow,
所有限制因素
including the description of the forest,
包括森林的情况
the description of your circulatory system,
你循环系统的情况
the description within cells.
细胞内部情况等
One of the things I did not stress in that introduction
我在介绍中没有提及的一点是
was that, systematically, the pace of life
生长的节奏会随着你体型的增大
decreases as you get bigger.
而系统性地减缓
Heart rates are slower; you live longer;
心率会减缓，你活得更久
diffusion of oxygen and resources
通过细胞膜的氧气
across membranes is slower, etc.
和物质的流动减缓
The question is: Is any of this true
问题是，这是否
for cities and companies?
也适用于城市和企业
So is London a scaled up Birmingham,
伦敦是否是长大了的伯明翰
which is a scaled up Brighton, etc., etc.?
而伯明翰是否是长大了的布莱顿，等等
Is New York a scaled up San Francisco,
纽约是否是长大了的旧金山
which is a scaled up Santa Fe?
而旧金山是否是长大了的圣达菲
Don't know. We will discuss that.
不知道，我们稍候再讨论
But they are networks,
但它们都是网络
and the most important network of cities
而城市最重要的网络
is you.
就是你
Cities are just a physical manifestation
城市只是
of your interactions,
你我社会活动
our interactions,
以及个体相互聚拢集合的
and the clustering and grouping of individuals.
物质表现
Here's just a symbolic picture of that.
这只是一张简易图表
And here's scaling of cities.
这是城市规模的扩大
This shows that in this very simple example,
这幅图显示出了一个非常简单的例子
which happens to be a mundane example
这例子很寻常
of number of petrol stations
加油站的数量
as a function of size —
作为规模
plotted in the same way as the biology —
按照同于生物的方法制表
you see exactly the same kind of thing.
你能够观察到一模一样的结果
There is a scaling.
上面显示了增长的趋势
That is that the number of petrol stations in the city
你告诉我城市的规模
is now given to you
我就能够说出
when you tell me its size.
这座城市有多少个加油站
The slope of that is less than linear.
斜率呈次线性
There is an economy of scale.
这是规模经济
Less petrol stations per capita the bigger you are — not surprising.
城市越大，人均加油站数量就越小，并不稀奇
But here's what's surprising.
稀奇的在这里
It scales in the same way everywhere.
增长的规律在哪里都适用
This is just European countries,
这反映的只是欧洲国家的情况
but you do it in Japan or China or Colombia,
但如果你用同样的方法观察日本，中国或哥伦比亚
always the same
结果都是一样的
with the same kind of economy of scale
同样的规模经济
to the same degree.
同样的水平
And any infrastructure you look at —
而且，你看到的所有基础设施
whether it's the length of roads, length of electrical lines —
不论是道路还是电线的长度
anything you look at
不论是什么
has the same economy of scale scaling in the same way.
都存在增长模式相同的规模经济
It's an integrated system
这个综合体系
that has evolved despite all the planning and so on.
不停演进，无论如何规划都是如此
But even more surprising
而当你看到
is if you look at socio-economic quantities,
社会经济数量
quantities that have no analog in biology,
即八千到一万年前
that have evolved when we started forming communities
我们开始建立社区时的社会经济数量
eight to 10,000 years ago.
你们会感到更加意外
The top one is wages as a function of size
上图以工资作为规模参数
plotted in the same way.
同理制表
And the bottom one is you lot —
而下面的是“你”
super-creatives plotted in the same way.
也就是超级智能人，同理制表
And what you see
上面显示出
is a scaling phenomenon.
一个规模增长的现象
But most important in this,
但图上最重要的是
the exponent, the analog to that three-quarters
新陈代谢率的幂
for the metabolic rate,
近似于三分之四
is bigger than one — it's about 1.15 to 1.2.
大于1,大约在1.15和1.2之间
Here it is,
意思是
which says that the bigger you are
规模越大
the more you have per capita, unlike biology —
人均数就越多，与生物学的情况相反
higher wages, more super-creative people per capita as you get bigger,
工资越高，就有越多的超级智能人出现
more patents per capita, more crime per capita.
人均专利和犯罪率越高
And we've looked at everything:
我们研究了所有事物
more AIDS cases, flu, etc.
艾滋病病例，流感等等
And here, they're all plotted together.
把这些都放在一起制成表
Just to show you what we plotted,
让你们看到
here is income, GDP —
我们把收入 GDP
GDP of the city —
城市的GDP
crime and patents all on one graph.
犯罪和专利都放在一张图上
And you can see, they all follow the same line.
你们可以看到
And here's the statement.
下面是图的表述
If you double the size of a city from 100,000 to 200,000,
如果一个城市的规模从10万增长至20万
from a million to two million, 10 to 20 million,
从一百万到两百万，从一千万到两千万
it doesn't matter,
都一样
then systematically
在这个城市中
you get a 15 percent increase
工资，财富，艾滋病病例
in wages, wealth, number of AIDS cases,
警察人数
number of police,
任何你能想到的事物
anything you can think of.
都会系统地增加15%
演讲简介：
物理学家Geoffrey West发现，简单的数学定律治理着城市的各种属性－－财富，犯罪率，步行速度以及城市的其它方方面面都可由一个数字推算出来：即城市的人口。他通过展示其中的原理，阐述生物与企业拥有的相似定律，让这场TED全球演讲颠覆了人们思想。
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