Geoffrey West: The surprising math of cities and corporations

譯者: Resa CC 審譯者: Phoebe Yu

Cities are the crucible of civilization.

都市是文明的大熔爐

They have been expanding,

它們持續擴大,

urbanization has been expanding,

都市化持續的擴展,

at an exponential rate in the last 200 years

兩百多年來隨指數率而爆增

so that by the second part of this century,

以致後半世紀來臨前

the planet will be completely dominated

地球將完全

by cities.

被都市佔據。

Cities are the origins of global warming,

都市是全球暖化形成的起因,

impact on the environment,

直接影響環境、

health, pollution, disease,

健康、污染、疾病、

finance,

財政、

economies, energy --

經濟、能源

they're all problems

這些問題全是

that are confronted by having cities.

因為都市的存在所遭遇到的

That's where all these problems come from.

都市是這些問題形成的起源。

And the tsunami of problems that we feel we're facing

我們認為我們正面臨地震海嘯之困境

in terms of sustainability questions

──永續生存方面的問題──

are actually a reflection

實際則是一個

of the exponential increase

全球都市化

in urbanization across the planet.

指數增長的反映。

Here's some numbers.

看看這些數據

Two hundred years ago, the United States

兩百年以前,美國

was less than a few percent urbanized.

都市化低於幾個百分比；

It's now more than 82 percent.

現在超過百分之八十二。

The planet has crossed the halfway mark a few years ago.

幾年前地球都市化已逾百分之五十,

China's building 300 new cities

中國將建造三百座新都市

in the next 20 years.

在下個二十年。

Now listen to this:

現在聽聽這個:

Every week for the foreseeable future,

可預見之未來的每一週,

until 2050,

一直至2050年

every week more than a million people

每週有超過百萬人口

are being added to our cities.

增添到這個都市

This is going to affect everything.

這將會影響一切事物。

Everybody in this room, if you stay alive,

這演講廳的每個人──若你們仍然活著的話──

is going to be affected

都會受都市裡

by what's happening in cities

發生的事所影響

in this extraordinary phenomenon.

這是非比尋常的現象。

However, cities,

然而,都市本身

despite having this negative aspect to them,

──儘管有這不利的層面存在──

are also the solution.

也還是解決的方法。

Because cities are the vacuum cleaners and the magnets

因為都市是吸塵器和磁鐵

that have sucked up creative people,

已吸入了富有創造力的人群、

creating ideas, innovation,

有創意的點子、創新、

wealth and so on.

資源等等。

So we have this kind of dual nature.

所以有這種二元性存在。

And so there's an urgent need

因而迫切需要

for a scientific theory of cities.

都市科學理論。

Now these are my comrades in arms.

這些是我戰友的名字

This work has been done with an extraordinary group of people,

這項研究成果是與一群非凡的人共同完成的,

and they've done all the work,

他們完成所有的研究工作,

and I'm the great bullshitter

而我是瞎掰天王

that tries to bring it all together.

試著將研究發現牽扯在一塊。

(Laughter)

(笑笑)

So here's the problem: This is what we all want.

問題來啦:這是我們都想要的,

The 10 billion people on the planet in 2050

到了2050年,地球上會有百億人口

want to live in places like this,

想要住在像這樣的地方；

having things like this,

擁有像這樣的東西；

doing things like this,

做這類的事情；

with economies that are growing like this,

還有,經濟有如此的成長；

not realizing that entropy

卻不了解「熵」

produces things like this,

產生像這樣的東西,

this, this

這個、這個

and this.

和這個。

And the question is:

問題是

Is that what Edinburgh and London and New York

那是愛丁堡、倫敦和紐約

are going to look like in 2050,

在2050年時的樣貌,

or is it going to be this?

或者是會像這樣?

That's the question.

那是個問題。

I must say, many of the indicators

我必須說,很多的指標

look like this is what it's going to look like,

指向這個是它將來的樣貌,

but let's talk about it.

那我們就來談談它。

So my provocative statement

我的挑戰論點是

is that we desperately need a serious scientific theory of cities.

我們極需要一個嚴謹的都市科學理論。

And scientific theory means quantifiable --

而科學理論是指可計量的──

relying on underlying generic principles

依據根本的通則,

that can be made into a predictive framework.

能導出可預測的架構。

That's the quest.

那得經過長期的探索。

Is that conceivable?

那可信嗎?

Are there universal laws?

有普遍法則嗎?

So here's two questions

所以,有兩個問題:

that I have in my head when I think about this problem.

在思考這個問題時,我想到的。

The first is:

第一個是:

Are cities part of biology?

都市是生物的一部分嗎?

Is London a great big whale?

倫敦是條巨鯨?

Is Edinburgh a horse?

愛丁堡是匹馬嗎?

Is Microsoft a great big anthill?

微軟是一個超大的蟻丘嗎?

What do we learn from that?

我們從那學到什麼?

We use them metaphorically --

我們將其暗喻化

the DNA of a company, the metabolism of a city, and so on --

──公司的DNA、一座都市的新陳代謝等等──

is that just bullshit, metaphorical bullshit,

那只是胡扯嗎?隱喻法的爛用嗎?

or is there serious substance to it?

或有重要的含義嗎?

And if that is the case,

若真是這樣,

how come that it's very hard to kill a city?

殺死一個都市怎麼那麼難?

You could drop an atom bomb on a city,

你可以在都市丟顆原子彈,

and 30 years later it's surviving.

三十年後它仍然存在

Very few cities fail.

幾乎沒有都市會消失；

All companies die, all companies.

所有的企業會死亡......,所有企業。

And if you have a serious theory, you should be able to predict

而且若你有嚴謹的理論,你該可以預測

when Google is going to go bust.

何時Google要倒閉。

So is that just another version

那麼,「都市」只是「叢林」的另一個

of this?

說法囉?

Well we understand this very well.

我們對這點有相當的研究。

That is, you ask any generic question about this --

也就是,你提出任何一般性的問題,如:

how many trees of a given size,

特定大小的樹有多少,

how many branches of a given size does a tree have,

一棵樹有多少特定大小的樹枝,

how many leaves,

有多少葉子,

what is the energy flowing through each branch,

遍佈每枝樹枝的能量是什麼,

what is the size of the canopy,

天篷有多大

what is its growth, what is its mortality?

它的成長特性?何時死亡?

We have a mathematical framework

我們有一個數學架構,

based on generic universal principles

是基於一般普遍原則而導出的

that can answer those questions.

能夠回答那樣的問題。

And the idea is can we do the same for this?

而構想是我們能為都市/企業做同樣的事嗎？

So the route in is recognizing

所以,解答的路徑是認清

one of the most extraordinary things about life,

與生命有關的最非凡的事物之一是

is that it is scalable,

它是可縮放的,

it works over an extraordinary range.

它運作範圍相當驚人

This is just a tiny range actually:

事實上,這只是一個極小的範圍,

It's us mammals;

我們人類是哺乳動物

we're one of these.

我們是哺乳動物之一

The same principles, the same dynamics,

相同的原則、相同的生物動力學、

the same organization is at work

相同的系統,產生特殊作用在

in all of these, including us,

所有這些生物體,包括我們在內,

and it can scale over a range of 100 million in size.

而且,它縮放含蓋大小範圍超過一億萬。

And that is one of the main reasons

再說,那是主要理由之一

life is so resilient and robust --

生命是多麼地有韌性和堅實

scalability.

縮放自如。

We're going to discuss that in a moment more.

再一會兒,我們會再多加討論這部分。

But you know, at a local level,

但你知道,以局部的角度而論,

you scale; everybody in this room is scaled.

你縮放,在這房內的每個人隨著縮放。

That's called growth.

那就是所謂的成長。

Here's how you grew.

這是你們成長的情形。

Rat, that's a rat -- could have been you.

老鼠,那是隻老鼠,可能本來是你,

We're all pretty much the same.

我們有相當多雷同的地方。

And you see, you're very familiar with this.

而且你們看,你們對這個非常熟悉,

You grow very quickly and then you stop.

你長得非常快,然後停了下來。

And that line there

那條曲線

is a prediction from the same theory,

是來自相同理論的一個預測,

based on the same principles,

基於相同的原則,

that describes that forest.

此原則也用來敍述(前述)那座森林。

And here it is for the growth of a rat,

而在這兒,是用來敍述一隻老鼠的成長

and those points on there are data points.

那些點點是數據點。

This is just the weight versus the age.

此圖是重量對上年紀

And you see, it stops growing.

你看,線條停止發展

Very, very good for biology --

對生物而言是非常合適的

also one of the reasons for its great resilience.

──也是作為它極佳韌性的解釋之一──

Very, very bad

但卻非常非常不利,

for economies and companies and cities

對經濟、企業、都市而言;

in our present paradigm.

這是從我們目前的範例看來,

This is what we believe.

這是我們所認為的。

This is what our whole economy

這是我們整體的經濟制度

is thrusting upon us,

強加諸在我們身上的......,

particularly illustrated in that left-hand corner:

具體地顯示在左邊角落:

hockey sticks.

曲棍球棒。

This is a bunch of software companies --

這是一堆的軟體公司

and what it is is their revenue versus their age --

──收入對上經營年資──

all zooming away,

急遽上升

and everybody making millions and billions of dollars.

而且每個人都賺好幾百萬和好幾十億的美元

Okay, so how do we understand this?

Okay,那麼我們如何了解其內含?

So let's first talk about biology.

讓我們先談談生態學。

This is explicitly showing you

這張圖清楚的顯示

how things scale,

事物縮放的情形。

and this is a truly remarkable graph.

這是一張非常值得注意的圖表。

What is plotted here is metabolic rate --

這張圖標繪的是新陳代謝率

how much energy you need per day to stay alive --

你每天需要多少能量以維持生存

versus your weight, your mass,

對上你的體重,你的質量

for all of us bunch of organisms.

通用於我們這群有機體

And it's plotted in this funny way by going up by factors of 10,

這張圖是以好玩的方式繪製──以十倍等系數增加,

otherwise you couldn't get everything on the graph.

否則無法把所有的東西放進圖表上。

And what you see if you plot it

而且你看到的是──若你以

in this slightly curious way

略為奇怪的方式來繪製它──

is that everybody lies on the same line.

每個人都在相同的線上。

Despite the fact that this is the most complex and diverse system

儘管事實是,這是在宇宙中最複雜又

in the universe,

多樣化的系統,

there's an extraordinary simplicity

有個極其簡單易懂的事物

being expressed by this.

藉由這個系統傳遞。

It's particularly astonishing

尤其驚人是,

because each one of these organisms,

由於各個有機體、

each subsystem, each cell type, each gene,

各別次系統、各別細胞種類、各別基因

has evolved in its own unique environmental niche

在自己獨特的環境利基中,已逐漸演化

with its own unique history.

且有自己獨一無二的歷史。

And yet, despite all of that Darwinian evolution

然而,儘管達爾文進化論和

and natural selection,

自然淘汰存在,

they've been constrained to lie on a line.

他們已受限於立足在同一條線。

Something else is going on.

有某個重要的東西正在運作。

Before I talk about that,

在談論那以前,

I've written down at the bottom there

我已在下方寫下

the slope of this curve, this straight line.

這條曲線的斜率,這條直線。

It's three-quarters, roughly,

約略為3/4(又四分之三)

which is less than one -- and we call that sublinear.

小於1,我們稱那「次線性」。

And here's the point of that.

那有個重點

It says that, if it were linear,

就是說:若它是「線性」的

the steepest slope,

最陡的斜度,

then doubling the size

那麼加倍放大其尺寸

you would require double the amount of energy.

你會需要加倍的能量。

But it's sublinear, and what that translates into

但它是「次線性」, 也就是說:

is that, if you double the size of the organism,

若你加大有機體的尺寸

you actually only need 75 percent more energy.

你其實只需要多百分之七十五的能量。

So a wonderful thing about all of biology

因此,有關生態學的一件奇妙的事是

is that it expresses an extraordinary economy of scale.

它揭露一個不尋常的規模經濟

The bigger you are systematically,

你有系統地變得越大

according to very well-defined rules,

──根據非常明確定義的規則──

less energy per capita.

每個人需要的能量越少。

Now any physiological variable you can think of,

現在你能想到的任何物理變數；

any life history event you can think of,

你能想到的任何生活史事件,

if you plot it this way, looks like this.

如果以這個方式繪製它,會像這樣。

There is an extraordinary regularity.

有個驚奇的規律性。

So you tell me the size of a mammal,

這麼說吧!你告我哺乳動物的大小,

I can tell you at the 90 percent level everything about it

我能告訴你百分之九十與其相關的事,

in terms of its physiology, life history, etc.

它的生理機能、生活史等等。

And the reason for this is because of networks.

而之所以能如此,是因為「脈絡」

All of life is controlled by networks --

所有的生命受制於脈絡──

from the intracellular through the multicellular

從細胞內到多細胞

through the ecosystem level.

到生態系統層面。

And you're very familiar with these networks.

而且你們對這些脈絡非常熟悉。

That's a little thing that lives inside an elephant.

那是存在大象內的一個小東西。

And here's the summary of what I'm saying.

接著,這是我所談之事的摘要,

If you take those networks,

若你利用這些脈絡,

this idea of networks,

脈絡這個點子

and you apply universal principles,

並運用普遍原則

mathematizable, universal principles,

──數學的普遍原則:

all of these scalings

所有這些呈線性變換縮放

and all of these constraints follow,

及所有這些約束跟著仿效

including the description of the forest,

包括森林的描繪、

the description of your circulatory system,

你們循環系統的描繪、

the description within cells.

細胞內的描繪。

One of the things I did not stress in that introduction

有件事我沒有在開頭介紹時強調的是

was that, systematically, the pace of life

生命的節奏有系統地減緩,

decreases as you get bigger.

當你變得越大。

Heart rates are slower; you live longer;

心跳率越慢,你活得越久；

diffusion of oxygen and resources

氧氣和資源

across membranes is slower, etc.

在整個黏膜擴散得越慢等等。

The question is: Is any of this true

問題是:對都市和企業而言

for cities and companies?

這是真的嗎?

So is London a scaled up Birmingham,

那麼倫敦是一個放大的伯明罕

which is a scaled up Brighton, etc., etc.?

伯明罕是一個放大的布萊頓......等等?

Is New York a scaled up San Francisco,

紐約是一個放大的舊金山?

which is a scaled up Santa Fe?

舊金山是放大的聖塔菲(Santa Fe)嗎?

Don't know. We will discuss that.

不曉得,我們會討論到那點。

But they are networks,

但它們是脈絡。

and the most important network of cities

而最重要的都市脈絡

is you.

是你。

Cities are just a physical manifestation

都市只是個物理的明顯跡象──

of your interactions,

你們的交流、

our interactions,

我們的交流、

and the clustering and grouping of individuals.

及許多個體結群和聚集的產物。

Here's just a symbolic picture of that.

這只是一幅象徵脈絡的圖。

And here's scaling of cities.

而這是都市的縮放

This shows that in this very simple example,

這張圖以非常簡單的例子來說明脈絡

which happens to be a mundane example

而且恰好是個平凡的例子

of number of petrol stations

──加油站的數字

as a function of size --

為隨規模大小變化的因素

plotted in the same way as the biology --

──如標繪生態學一般繪製──

you see exactly the same kind of thing.

你看到的確實是同類東西

There is a scaling.

這是縮放圖

That is that the number of petrol stations in the city

這是都市裡加油站的數量

is now given to you

現在提供給你,

when you tell me its size.

若你告訴我都市的大小。

The slope of that is less than linear.

其斜率小於線性。

There is an economy of scale.

有一個規模經濟。

Less petrol stations per capita the bigger you are -- not surprising.

每個人分到的加油站越少,都市規模就越大──沒什麼好驚訝的。

But here's what's surprising.

但令人驚訝的是

It scales in the same way everywhere.

這種縮放方式在處處皆相同

This is just European countries,

這只是歐洲國家

but you do it in Japan or China or Colombia,

但在日本、中國、歌倫比亞作測試

always the same

結論總是相同:

with the same kind of economy of scale

同類的規模經濟

to the same degree.

達到相同的等級。

And any infrastructure you look at --

你看到的任何公共建設,

whether it's the length of roads, length of electrical lines --

無論是路的長度、電線長度

anything you look at

任何你所看到的

has the same economy of scale scaling in the same way.

有相同的規模經濟,以同種方式縮放。

It's an integrated system

這已經是成型的協調系統

that has evolved despite all the planning and so on.

儘管是用各種的規劃設計安排等等,

But even more surprising

但更令人驚訝的是

is if you look at socio-economic quantities,

若你詳看社會經濟量

quantities that have no analog in biology,

──生態學不存在這種量──

that have evolved when we started forming communities

在我們開始形成社群時,便已逐步演進

eight to 10,000 years ago.

從八千年前至一萬年以前

The top one is wages as a function of size

上面那是薪資作為隨大小變化的因素

plotted in the same way.

以相同方式標繪,

And the bottom one is you lot --

橫軸標示你們這群人

super-creatives plotted in the same way.

緃軸標示超創造力的分佈圖,以相同方式繪製

And what you see

你所看到的是

is a scaling phenomenon.

一個縮放現象。

But most important in this,

但這張圖最要的是

the exponent, the analog to that three-quarters

指數──0.75(3/4)新陳代謝率的

for the metabolic rate,

類似物──

is bigger than one -- it's about 1.15 to 1.2.

是大於1,約1.15到1.2

Here it is,

重點來了

which says that the bigger you are

就是說,人口越大

the more you have per capita, unlike biology --

每座都市擁有的越多,不像生態學。

higher wages, more super-creative people per capita as you get bigger,

當人口變得越大,每座都市的超級創造者越多

more patents per capita, more crime per capita.

每個都市的專利更多、犯罪更多。

And we've looked at everything:

我們已檢視過每個項目:

more AIDS cases, flu, etc.

AIDS 病例、流感......等等

And here, they're all plotted together.

看!他們全被繪製在一塊兒。

Just to show you what we plotted,

只是讓你們看看我們繪製的東西

here is income, GDP --

收入、GDP

GDP of the city --

都市的GDP

crime and patents all on one graph.

犯罪和專利都在一份圖表

And you can see, they all follow the same line.

你可以看到,它們全隨著同一條線。

And here's the statement.

作個說明,

If you double the size of a city from 100,000 to 200,000,

若你將都市由十萬放大兩倍至二十萬、

from a million to two million, 10 to 20 million,

一百萬至二百萬、一千萬至二千萬

it doesn't matter,

都無所謂。

then systematically

然後,有系統地

you get a 15 percent increase

得到百分之十五的增加,

in wages, wealth, number of AIDS cases,

如:薪資、資源、愛滋病案例、

number of police,

、警察人數

anything you can think of.

任何你可以想得到的事物都會增加。

It goes up by 15 percent,

上漲了百分十五。

and you have a 15 percent savings

你就有一個百分之十五的存款

on the infrastructure.

在公共建設。

This, no doubt, is the reason

無庸置疑,這是為何

why a million people a week are gathering in cities.

一週有一百萬人湧入都市的理由。

Because they think that all those wonderful things --

因為他們認為所有這些美妙的事物

like creative people, wealth, income --

如:有創造力的人、資源、收入......等,

is what attracts them,

引人入勝,

forgetting about the ugly and the bad.

而忘了醜陃和邪惡的一面

What is the reason for this?

怎麼會忘了這一面呢?

Well I don't have time to tell you about all the mathematics,

我沒有足夠的時間告訴你所有的這些數學

but underlying this is the social networks,

根本而言,這是社會脈絡,

because this is a universal phenomenon.

因為這是普遍現象。

This 15 percent rule

這百分之十五的估算

is true

是真的

no matter where you are on the planet --

不論在地球的那裡

Japan, Chile,

日本、智利、

Portugal, Scotland, doesn't matter.

葡萄牙、蘇格蘭等都不打緊

Always, all the data shows it's the same,

所有的數據資料總是顯示相同的結果,

despite the fact that these cities have evolved independently.

儘管事實是,這些都市一直是獨立演化發展。

Something universal is going on.

某個萬能的東西正在運行、

The universality, to repeat, is us --

重申!普遍性即是我們,

that we are the city.

我們是都市。

And it is our interactions and the clustering of those interactions.

而且都市是我們之間的交流及那些交流的群集。

So there it is, I've said it again.

又來了,我已再度提到它

So if it is those networks and their mathematical structure,

若它是這些脈絡及此等脈絡的數學結構;

unlike biology, which had sublinear scaling,

不像生態學有「次現性縮放」、

economies of scale,

規模經濟、

you had the slowing of the pace of life

生命節奏減緩

as you get bigger.

當你變得較大時。

If it's social networks with super-linear scaling --

若都市有「超線性縮放」的社會脈絡

more per capita --

──更多人口──

then the theory says

那麼該理論指示

that you increase the pace of life.

生活的節奏加快。

The bigger you are, life gets faster.

人口越大,生活步調就變得越快。

On the left is the heart rate showing biology.

左圖顯示生物之心跳率

On the right is the speed of walking

右圖則是走路的速度

in a bunch of European cities,

地點是在歐洲都市,

showing that increase.

顯示走路速度增快。

Lastly, I want to talk about growth.

最後,我要談談成長。

This is what we had in biology, just to repeat.

這是生物界所有的特性,只是重申!

Economies of scale

規模經濟

gave rise to this sigmoidal behavior.

產生這個「S型函數」作用下的行為。

You grow fast and then stop --

快速成長,然後停止─

part of our resilience.

─那是生物韌性的一部分。

That would be bad for economies and cities.

那對經濟和都市不利。

And indeed, one of the wonderful things about the theory

而且的確,有關這個理論的奇妙之處之一是

is that if you have super-linear scaling

若由資源的創造和創新得到

from wealth creation and innovation,

「超線性縮放」

then indeed you get, from the same theory,

出自相同的理論,你甚至得到

a beautiful rising exponential curve -- lovely.

一個漂亮的上升指數曲線──好極了。

And in fact, if you compare it to data,

而且事實上,如果拿它和數據資料比照

it fits very well

完全吻合,

with the development of cities and economies.

與都市和經濟的發展相符。

But it has a terrible catch,

但這有一個嚴重的隱患。

and the catch

這個隱患是

is that this system is destined to collapse.

該系統遲早崩潰

And it's destined to collapse for many reasons --

有好幾個理由註定它會瓦解──

kind of Malthusian reasons -- that you run out of resources.

有幾分數學原因──資源耗盡。

And how do you avoid that? Well we've done it before.

你如何避免耗盡資源?嗯,我們之前就已這麼做了

What we do is,

我們怎麼做呢?

as we grow and we approach the collapse,

隨著發展,我們越接近衰敗。

a major innovation takes place

一個重要的創新發生

and we start over again,

我們就又重新開始。

and we start over again as we approach the next one, and so on.

當我們接近下一個威脅,我們又重新開始, 一直循環下去

So there's this continuous cycle of innovation

所以,有創新的連續循環

that is necessary

是必需的

in order to sustain growth and avoid collapse.

以便維持發展和避免突然垮掉。

The catch, however, to this

然而,解套的方法是

is that you have to innovate

你必須革新

faster and faster and faster.

加快、加速、再加速度

So the image

因此,構想的樣貌是

is that we're not only on a treadmill that's going faster,

我們不只在運轉非常快速的跑步機上

but we have to change the treadmill faster and faster.

而且我們還要超快速地改造這台跑步機；

We have to accelerate on a continuous basis.

我們必須以連續的形式加速。

And the question is: Can we, as socio-economic beings,

而且問題是:身為社會經濟的生物,

avoid a heart attack?

我們能避免心臟病嗎?

So lastly, I'm going to finish up in this last minute or two

那麼,最後我要在這最後一、兩分鐘內結束

asking about companies.

來探討企業。

See companies, they scale.

看這些企業,他們向上攀升

The top one, in fact, is Walmart on the right.

事實上,上面這條線是描繪沃爾瑪的現況

It's the same plot.

有相同的標繪。

This happens to be income and assets

橫軸是收入和資產

versus the size of the company as denoted by its number of employees.

對上公司規模大小,以員工數代表。

We could use sales, anything you like.

我們能用銷售或任何你喜歡的事物替換。

There it is: after some little fluctuations at the beginning,

是這樣子的:一開始在些許微乎其微的波動後

when companies are innovating,

──正值企業創新時期──

they scale beautifully.

它們向上美妙地攀升。

And we've looked at 23,000 companies

我們檢視過兩萬三千家企業,

in the United States, may I say.

在美國的企業,可以這麼說吧。

And I'm only showing you a little bit of this.

我讓你們看到只是其中一小部分

What is astonishing about companies

有關這些企業的驚人發現是,

is that they scale sublinearly

它們呈「次線性」地向上攀升,

like biology,

──像生態的規律一般──

indicating that they're dominated,

表示它們受支配

not by super-linear

──非受超線性的

innovation and ideas;

創新和概念所控制──

they become dominated

它們開始變得受

by economies of scale.

經濟規模所支配。

In that interpretation,

官僚制度和監管

by bureaucracy and administration,

可解釋那點。

and they do it beautifully, may I say.

而且它們運作地極棒,可以這麼說吧。

So if you tell me the size of some company, some small company,

所以若你告訴我某公司的規模大小、某間小公司

I could have predicted the size of Walmart.

我早可以預測沃爾瑪的規模大小。

If it has this sublinear scaling,

若它存有「次線性縮放」,

the theory says

這個理論指示

we should have sigmoidal growth.

我們應會有呈「S型函數的發展」。

There's Walmart. Doesn't look very sigmoidal.

這條是沃爾瑪,看來非常不「S型函數曲線」。

That's what we like, hockey sticks.

那是我們喜歡的曲棍球棒

But you notice, I've cheated,

但注意看,我在哄騙你們

because I've only gone up to '94.

因為這條線只顯示到1994年,

Let's go up to 2008.

咱們來看看繪製到2008年的圖表。

That red line is from the theory.

那紅線是依理論產生的

So if I'd have done this in 1994,

那麼,若我在1994完成這張圖

I could have predicted what Walmart would be now.

我早可以預測沃爾瑪現在的狀況。

And then this is repeated

然後這數學架構重覆應用

across the entire spectrum of companies.

橫跨所有領域的眾多企業。

There they are. That's 23,000 companies.

它們都在這兒。那兩萬三千間公司

They all start looking like hockey sticks,

它們全開始長得像曲棍球棒,

they all bend over,

它們均呈現向下彎曲,

and they all die like you and me.

它們就像你我一樣生命終會消失。

Thank you.

謝謝大家

(Applause)

(掌聲)