Cities are the crucible of civilization. They have been expanding, urbanization has been expanding, at an exponential rate in the last 200 years so that by the second part of this century, the planet will be completely dominated by cities. Cities are the origins of global warming, impact on the environment, health, pollution, disease, finance, economies, energy -- they're all problems that are confronted by having cities. That's where all these problems come from. And the tsunami of problems that we feel we're facing in terms of sustainability questions are actually a reflection of the exponential increase in urbanization across the planet.
都市是文明的大熔爐 它們持續擴大, 都市化持續的擴展, 兩百多年來隨指數率而爆增 以致後半世紀來臨前 地球將完全 被都市佔據。 都市是全球暖化形成的起因, 直接影響環境、 健康、污染、疾病、 財政、 經濟、能源 這些問題全是 因為都市的存在所遭遇到的 都市是這些問題形成的起源。 我們認為我們正面臨地震海嘯之困境 ──永續生存方面的問題── 實際則是一個 全球都市化 指數增長的反映。
Here's some numbers. Two hundred years ago, the United States was less than a few percent urbanized. It's now more than 82 percent. The planet has crossed the halfway mark a few years ago. China's building 300 new cities in the next 20 years. Now listen to this: Every week for the foreseeable future, until 2050, every week more than a million people are being added to our cities. This is going to affect everything. Everybody in this room, if you stay alive, is going to be affected by what's happening in cities in this extraordinary phenomenon. However, cities, despite having this negative aspect to them, are also the solution. Because cities are the vacuum cleaners and the magnets that have sucked up creative people, creating ideas, innovation, wealth and so on. So we have this kind of dual nature. And so there's an urgent need for a scientific theory of cities.
看看這些數據 兩百年以前,美國 都市化低於幾個百分比; 現在超過百分之八十二。 幾年前地球都市化已逾百分之五十, 中國將建造三百座新都市 在下個二十年。 現在聽聽這個: 可預見之未來的每一週, 一直至2050年 每週有超過百萬人口 增添到這個都市 這將會影響一切事物。 這演講廳的每個人──若你們仍然活著的話── 都會受都市裡 發生的事所影響 這是非比尋常的現象。 然而,都市本身 ──儘管有這不利的層面存在── 也還是解決的方法。 因為都市是吸塵器和磁鐵 已吸入了富有創造力的人群、 有創意的點子、創新、 資源等等。 所以有這種二元性存在。 因而迫切需要 都市科學理論。
Now these are my comrades in arms. This work has been done with an extraordinary group of people, and they've done all the work, and I'm the great bullshitter that tries to bring it all together.
這些是我戰友的名字 這項研究成果是與一群非凡的人共同完成的, 他們完成所有的研究工作, 而我是瞎掰天王 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. The 10 billion people on the planet in 2050 want to live in places like this, having things like this, doing things like this, with economies that are growing like this, not realizing that entropy produces things like this, this, this and this. And the question is: Is that what Edinburgh and London and New York are going to look like in 2050, or is it going to be this? That's the question. I must say, many of the indicators look like this is what it's going to look like, but let's talk about it.
問題來啦:這是我們都想要的, 到了2050年,地球上會有百億人口 想要住在像這樣的地方; 擁有像這樣的東西; 做這類的事情; 還有,經濟有如此的成長; 卻不了解「熵」 產生像這樣的東西, 這個、這個 和這個。 問題是 那是愛丁堡、倫敦和紐約 在2050年時的樣貌, 或者是會像這樣? 那是個問題。 我必須說,很多的指標 指向這個是它將來的樣貌, 那我們就來談談它。
So my provocative statement is that we desperately need a serious scientific theory of cities. And scientific theory means quantifiable -- relying on underlying generic principles that can be made into a predictive framework. That's the quest. Is that conceivable? Are there universal laws? So here's two questions that I have in my head when I think about this problem. The first is: Are cities part of biology? Is London a great big whale? Is Edinburgh a horse? Is Microsoft a great big anthill? What do we learn from that? We use them metaphorically -- the DNA of a company, the metabolism of a city, and so on -- is that just bullshit, metaphorical bullshit, or is there serious substance to it? And if that is the case, how come that it's very hard to kill a city? You could drop an atom bomb on a city, and 30 years later it's surviving. Very few cities fail. All companies die, all companies. And if you have a serious theory, you should be able to predict when Google is going to go bust.
我的挑戰論點是 我們極需要一個嚴謹的都市科學理論。 而科學理論是指可計量的── 依據根本的通則, 能導出可預測的架構。 那得經過長期的探索。 那可信嗎? 有普遍法則嗎? 所以,有兩個問題: 在思考這個問題時,我想到的。 第一個是: 都市是生物的一部分嗎? 倫敦是條巨鯨? 愛丁堡是匹馬嗎? 微軟是一個超大的蟻丘嗎? 我們從那學到什麼? 我們將其暗喻化 ──公司的DNA、一座都市的新陳代謝等等── 那只是胡扯嗎?隱喻法的爛用嗎? 或有重要的含義嗎? 若真是這樣, 殺死一個都市怎麼那麼難? 你可以在都市丟顆原子彈, 三十年後它仍然存在 幾乎沒有都市會消失; 所有的企業會死亡......,所有企業。 而且若你有嚴謹的理論,你該可以預測 何時Google要倒閉。
So is that just another version of this? Well we understand this very well. That is, you ask any generic question about this -- how many trees of a given size, how many branches of a given size does a tree have, how many leaves, what is the energy flowing through each branch, what is the size of the canopy, what is its growth, what is its mortality? We have a mathematical framework based on generic universal principles that can answer those questions. And the idea is can we do the same for this? So the route in is recognizing one of the most extraordinary things about life, is that it is scalable, it works over an extraordinary range. This is just a tiny range actually: It's us mammals; we're one of these. The same principles, the same dynamics, the same organization is at work in all of these, including us, and it can scale over a range of 100 million in size. And that is one of the main reasons life is so resilient and robust -- scalability. We're going to discuss that in a moment more.
那麼,「都市」只是「叢林」的另一個 說法囉? 我們對這點有相當的研究。 也就是,你提出任何一般性的問題,如: 特定大小的樹有多少, 一棵樹有多少特定大小的樹枝, 有多少葉子, 遍佈每枝樹枝的能量是什麼, 天篷有多大 它的成長特性?何時死亡? 我們有一個數學架構, 是基於一般普遍原則而導出的 能夠回答那樣的問題。 而構想是我們能為都市/企業做同樣的事嗎? 所以,解答的路徑是認清 與生命有關的最非凡的事物之一是 它是可縮放的, 它運作範圍相當驚人 事實上,這只是一個極小的範圍, 我們人類是哺乳動物 我們是哺乳動物之一 相同的原則、相同的生物動力學、 相同的系統,產生特殊作用在 所有這些生物體,包括我們在內, 而且,它縮放含蓋大小範圍超過一億萬。 再說,那是主要理由之一 生命是多麼地有韌性和堅實 縮放自如。 再一會兒,我們會再多加討論這部分。
But you know, at a local level, you scale; everybody in this room is scaled. That's called growth. Here's how you grew. Rat, that's a rat -- could have been you. We're all pretty much the same. And you see, you're very familiar with this. You grow very quickly and then you stop. And that line there is a prediction from the same theory, based on the same principles, that describes that forest. And here it is for the growth of a rat, and those points on there are data points. This is just the weight versus the age. And you see, it stops growing. Very, very good for biology -- also one of the reasons for its great resilience. Very, very bad for economies and companies and cities in our present paradigm. This is what we believe. This is what our whole economy is thrusting upon us, particularly illustrated in that left-hand corner: hockey sticks. This is a bunch of software companies -- and what it is is their revenue versus their age -- all zooming away, and everybody making millions and billions of dollars.
但你知道,以局部的角度而論, 你縮放,在這房內的每個人隨著縮放。 那就是所謂的成長。 這是你們成長的情形。 老鼠,那是隻老鼠,可能本來是你, 我們有相當多雷同的地方。 而且你們看,你們對這個非常熟悉, 你長得非常快,然後停了下來。 那條曲線 是來自相同理論的一個預測, 基於相同的原則, 此原則也用來敍述(前述)那座森林。 而在這兒,是用來敍述一隻老鼠的成長 那些點點是數據點。 此圖是重量對上年紀 你看,線條停止發展 對生物而言是非常合適的 ──也是作為它極佳韌性的解釋之一── 但卻非常非常不利, 對經濟、企業、都市而言; 這是從我們目前的範例看來, 這是我們所認為的。 這是我們整體的經濟制度 強加諸在我們身上的......, 具體地顯示在左邊角落: 曲棍球棒。 這是一堆的軟體公司 ──收入對上經營年資── 急遽上升 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? So let's first talk about biology. This is explicitly showing you how things scale, and this is a truly remarkable graph. What is plotted here is metabolic rate -- how much energy you need per day to stay alive -- versus your weight, your mass, for all of us bunch of organisms. And it's plotted in this funny way by going up by factors of 10, otherwise you couldn't get everything on the graph. And what you see if you plot it in this slightly curious way is that everybody lies on the same line. Despite the fact that this is the most complex and diverse system in the universe, there's an extraordinary simplicity being expressed by this. It's particularly astonishing because each one of these organisms, each subsystem, each cell type, each gene, has evolved in its own unique environmental niche with its own unique history. And yet, despite all of that Darwinian evolution and natural selection, they've been constrained to lie on a line.
Okay,那麼我們如何了解其內含? 讓我們先談談生態學。 這張圖清楚的顯示 事物縮放的情形。 這是一張非常值得注意的圖表。 這張圖標繪的是新陳代謝率 你每天需要多少能量以維持生存 對上你的體重,你的質量 通用於我們這群有機體 這張圖是以好玩的方式繪製──以十倍等系數增加, 否則無法把所有的東西放進圖表上。 而且你看到的是──若你以 略為奇怪的方式來繪製它── 每個人都在相同的線上。 儘管事實是,這是在宇宙中最複雜又 多樣化的系統, 有個極其簡單易懂的事物 藉由這個系統傳遞。 尤其驚人是, 由於各個有機體、 各別次系統、各別細胞種類、各別基因 在自己獨特的環境利基中,已逐漸演化 且有自己獨一無二的歷史。 然而,儘管達爾文進化論和 自然淘汰存在, 他們已受限於立足在同一條線。
Something else is going on. Before I talk about that, I've written down at the bottom there the slope of this curve, this straight line. It's three-quarters, roughly, which is less than one -- and we call that sublinear. And here's the point of that. It says that, if it were linear, the steepest slope, then doubling the size you would require double the amount of energy. But it's sublinear, and what that translates into is that, if you double the size of the organism, you actually only need 75 percent more energy. So a wonderful thing about all of biology is that it expresses an extraordinary economy of scale. The bigger you are systematically, according to very well-defined rules, less energy per capita. Now any physiological variable you can think of, any life history event you can think of, if you plot it this way, looks like this. There is an extraordinary regularity. So you tell me the size of a mammal, I can tell you at the 90 percent level everything about it in terms of its physiology, life history, etc.
有某個重要的東西正在運作。 在談論那以前, 我已在下方寫下 這條曲線的斜率,這條直線。 約略為3/4(又四分之三) 小於1,我們稱那「次線性」。 那有個重點 就是說:若它是「線性」的 最陡的斜度, 那麼加倍放大其尺寸 你會需要加倍的能量。 但它是「次線性」, 也就是說: 若你加大有機體的尺寸 你其實只需要多百分之七十五的能量。 因此,有關生態學的一件奇妙的事是 它揭露一個不尋常的規模經濟 你有系統地變得越大 ──根據非常明確定義的規則── 每個人需要的能量越少。 現在你能想到的任何物理變數; 你能想到的任何生活史事件, 如果以這個方式繪製它,會像這樣。 有個驚奇的規律性。 這麼說吧!你告我哺乳動物的大小, 我能告訴你百分之九十與其相關的事, 它的生理機能、生活史等等。
And the reason for this is because of networks. All of life is controlled by networks -- from the intracellular through the multicellular through the ecosystem level. And you're very familiar with these networks. That's a little thing that lives inside an elephant. And here's the summary of what I'm saying. If you take those networks, this idea of networks, and you apply universal principles, mathematizable, universal principles, all of these scalings and all of these constraints follow, including the description of the forest, the description of your circulatory system, the description within cells. One of the things I did not stress in that introduction was that, systematically, the pace of life decreases as you get bigger. Heart rates are slower; you live longer; diffusion of oxygen and resources across membranes is slower, etc.
而之所以能如此,是因為「脈絡」 所有的生命受制於脈絡── 從細胞內到多細胞 到生態系統層面。 而且你們對這些脈絡非常熟悉。 那是存在大象內的一個小東西。 接著,這是我所談之事的摘要, 若你利用這些脈絡, 脈絡這個點子 並運用普遍原則 ──數學的普遍原則: 所有這些呈線性變換縮放 及所有這些約束跟著仿效 包括森林的描繪、 你們循環系統的描繪、 細胞內的描繪。 有件事我沒有在開頭介紹時強調的是 生命的節奏有系統地減緩, 當你變得越大。 心跳率越慢,你活得越久; 氧氣和資源 在整個黏膜擴散得越慢等等。
The question is: Is any of this true for cities and companies? So is London a scaled up Birmingham, which is a scaled up Brighton, etc., etc.? Is New York a scaled up San Francisco, which is a scaled up Santa Fe? Don't know. We will discuss that. But they are networks, and the most important network of cities is you. Cities are just a physical manifestation of your interactions, our interactions, and the clustering and grouping of individuals. Here's just a symbolic picture of that. And here's scaling of cities. This shows that in this very simple example, which happens to be a mundane example of number of petrol stations as a function of size -- plotted in the same way as the biology -- you see exactly the same kind of thing.
問題是:對都市和企業而言 這是真的嗎? 那麼倫敦是一個放大的伯明罕 伯明罕是一個放大的布萊頓......等等? 紐約是一個放大的舊金山? 舊金山是放大的聖塔菲(Santa Fe)嗎? 不曉得,我們會討論到那點。 但它們是脈絡。 而最重要的都市脈絡 是你。 都市只是個物理的明顯跡象── 你們的交流、 我們的交流、 及許多個體結群和聚集的產物。 這只是一幅象徵脈絡的圖。 而這是都市的縮放 這張圖以非常簡單的例子來說明脈絡 而且恰好是個平凡的例子 ──加油站的數字 為隨規模大小變化的因素 ──如標繪生態學一般繪製── 你看到的確實是同類東西
There is a scaling. That is that the number of petrol stations in the city is now given to you when you tell me its size. The slope of that is less than linear. There is an economy of scale. Less petrol stations per capita the bigger you are -- not surprising. But here's what's surprising. It scales in the same way everywhere. This is just European countries, but you do it in Japan or China or Colombia, always the same with the same kind of economy of scale to the same degree. And any infrastructure you look at -- whether it's the length of roads, length of electrical lines -- anything you look at has the same economy of scale scaling in the same way. It's an integrated system that has evolved despite all the planning and so on. But even more surprising is if you look at socio-economic quantities, quantities that have no analog in biology, that have evolved when we started forming communities eight to 10,000 years ago. The top one is wages as a function of size plotted in the same way. And the bottom one is you lot -- super-creatives plotted in the same way. And what you see is a scaling phenomenon. But most important in this, the exponent, the analog to that three-quarters for the metabolic rate, is bigger than one -- it's about 1.15 to 1.2. Here it is, which says that the bigger you are the more you have per capita, unlike biology -- higher wages, more super-creative people per capita as you get bigger, more patents per capita, more crime per capita.
這是縮放圖 這是都市裡加油站的數量 現在提供給你, 若你告訴我都市的大小。 其斜率小於線性。 有一個規模經濟。 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。 但令人驚訝的是 這種縮放方式在處處皆相同 這只是歐洲國家 但在日本、中國、歌倫比亞作測試 結論總是相同: 同類的規模經濟 達到相同的等級。 你看到的任何公共建設, 無論是路的長度、電線長度 任何你所看到的 有相同的規模經濟,以同種方式縮放。 這已經是成型的協調系統 儘管是用各種的規劃設計安排等等, 但更令人驚訝的是 若你詳看社會經濟量 ──生態學不存在這種量── 在我們開始形成社群時,便已逐步演進 從八千年前至一萬年以前 上面那是薪資作為隨大小變化的因素 以相同方式標繪, 橫軸標示你們這群人 緃軸標示超創造力的分佈圖,以相同方式繪製 你所看到的是 一個縮放現象。 但這張圖最要的是 指數──0.75(3/4)新陳代謝率的 類似物── 是大於1,約1.15到1.2 重點來了 就是說,人口越大 每座都市擁有的越多,不像生態學。 當人口變得越大,每座都市的超級創造者越多 每個都市的專利更多、犯罪更多。
And we've looked at everything: more AIDS cases, flu, etc. And here, they're all plotted together. Just to show you what we plotted, here is income, GDP -- GDP of the city -- crime and patents all on one graph. And you can see, they all follow the same line. And here's the statement. If you double the size of a city from 100,000 to 200,000, from a million to two million, 10 to 20 million, it doesn't matter, then systematically you get a 15 percent increase in wages, wealth, number of AIDS cases, number of police, anything you can think of. It goes up by 15 percent, and you have a 15 percent savings on the infrastructure. This, no doubt, is the reason why a million people a week are gathering in cities. Because they think that all those wonderful things -- like creative people, wealth, income -- is what attracts them, forgetting about the ugly and the bad.
我們已檢視過每個項目: AIDS 病例、流感......等等 看!他們全被繪製在一塊兒。 只是讓你們看看我們繪製的東西 收入、GDP 都市的GDP 犯罪和專利都在一份圖表 你可以看到,它們全隨著同一條線。 作個說明, 若你將都市由十萬放大兩倍至二十萬、 一百萬至二百萬、一千萬至二千萬 都無所謂。 然後,有系統地 得到百分之十五的增加, 如:薪資、資源、愛滋病案例、 、警察人數 任何你可以想得到的事物都會增加。 上漲了百分十五。 你就有一個百分之十五的存款 在公共建設。 無庸置疑,這是為何 一週有一百萬人湧入都市的理由。 因為他們認為所有這些美妙的事物 如:有創造力的人、資源、收入......等, 引人入勝, 而忘了醜陃和邪惡的一面
What is the reason for this? Well I don't have time to tell you about all the mathematics, but underlying this is the social networks, because this is a universal phenomenon. This 15 percent rule is true no matter where you are on the planet -- Japan, Chile, Portugal, Scotland, doesn't matter. Always, all the data shows it's the same, despite the fact that these cities have evolved independently. Something universal is going on. The universality, to repeat, is us -- that we are the city. And it is our interactions and the clustering of those interactions. So there it is, I've said it again. So if it is those networks and their mathematical structure, unlike biology, which had sublinear scaling, economies of scale, you had the slowing of the pace of life as you get bigger. If it's social networks with super-linear scaling -- more per capita -- then the theory says that you increase the pace of life. The bigger you are, life gets faster. On the left is the heart rate showing biology. On the right is the speed of walking in a bunch of European cities, showing that increase.
怎麼會忘了這一面呢? 我沒有足夠的時間告訴你所有的這些數學 根本而言,這是社會脈絡, 因為這是普遍現象。 這百分之十五的估算 是真的 不論在地球的那裡 日本、智利、 葡萄牙、蘇格蘭等都不打緊 所有的數據資料總是顯示相同的結果, 儘管事實是,這些都市一直是獨立演化發展。 某個萬能的東西正在運行、 重申!普遍性即是我們, 我們是都市。 而且都市是我們之間的交流及那些交流的群集。 又來了,我已再度提到它 若它是這些脈絡及此等脈絡的數學結構; 不像生態學有「次現性縮放」、 規模經濟、 生命節奏減緩 當你變得較大時。 若都市有「超線性縮放」的社會脈絡 ──更多人口── 那麼該理論指示 生活的節奏加快。 人口越大,生活步調就變得越快。 左圖顯示生物之心跳率 右圖則是走路的速度 地點是在歐洲都市, 顯示走路速度增快。
Lastly, I want to talk about growth. This is what we had in biology, just to repeat. Economies of scale gave rise to this sigmoidal behavior. You grow fast and then stop -- part of our resilience. That would be bad for economies and cities. And indeed, one of the wonderful things about the theory is that if you have super-linear scaling from wealth creation and innovation, then indeed you get, from the same theory, a beautiful rising exponential curve -- lovely. And in fact, if you compare it to data, it fits very well with the development of cities and economies. But it has a terrible catch, and the catch is that this system is destined to collapse. And it's destined to collapse for many reasons -- kind of Malthusian reasons -- that you run out of resources. And how do you avoid that? Well we've done it before.
最後,我要談談成長。 這是生物界所有的特性,只是重申! 規模經濟 產生這個「S型函數」作用下的行為。 快速成長,然後停止─ ─那是生物韌性的一部分。 那對經濟和都市不利。 而且的確,有關這個理論的奇妙之處之一是 若由資源的創造和創新得到 「超線性縮放」 出自相同的理論,你甚至得到 一個漂亮的上升指數曲線──好極了。 而且事實上,如果拿它和數據資料比照 完全吻合, 與都市和經濟的發展相符。 但這有一個嚴重的隱患。 這個隱患是 該系統遲早崩潰 有好幾個理由註定它會瓦解── 有幾分數學原因──資源耗盡。 你如何避免耗盡資源?嗯,我們之前就已這麼做了
What we do is, as we grow and we approach the collapse, a major innovation takes place and we start over again, and we start over again as we approach the next one, and so on. So there's this continuous cycle of innovation that is necessary in order to sustain growth and avoid collapse. The catch, however, to this is that you have to innovate faster and faster and faster. So the image is that we're not only on a treadmill that's going faster, but we have to change the treadmill faster and faster. We have to accelerate on a continuous basis. And the question is: Can we, as socio-economic beings, avoid a heart attack?
我們怎麼做呢? 隨著發展,我們越接近衰敗。 一個重要的創新發生 我們就又重新開始。 當我們接近下一個威脅,我們又重新開始, 一直循環下去 所以,有創新的連續循環 是必需的 以便維持發展和避免突然垮掉。 然而,解套的方法是 你必須革新 加快、加速、再加速度 因此,構想的樣貌是 我們不只在運轉非常快速的跑步機上 而且我們還要超快速地改造這台跑步機; 我們必須以連續的形式加速。 而且問題是:身為社會經濟的生物, 我們能避免心臟病嗎?
So lastly, I'm going to finish up in this last minute or two asking about companies. See companies, they scale. The top one, in fact, is Walmart on the right. It's the same plot. This happens to be income and assets versus the size of the company as denoted by its number of employees. We could use sales, anything you like. There it is: after some little fluctuations at the beginning, when companies are innovating, they scale beautifully. And we've looked at 23,000 companies in the United States, may I say. And I'm only showing you a little bit of this.
那麼,最後我要在這最後一、兩分鐘內結束 來探討企業。 看這些企業,他們向上攀升 事實上,上面這條線是描繪沃爾瑪的現況 有相同的標繪。 橫軸是收入和資產 對上公司規模大小,以員工數代表。 我們能用銷售或任何你喜歡的事物替換。 是這樣子的:一開始在些許微乎其微的波動後 ──正值企業創新時期── 它們向上美妙地攀升。 我們檢視過兩萬三千家企業, 在美國的企業,可以這麼說吧。 我讓你們看到只是其中一小部分
What is astonishing about companies is that they scale sublinearly like biology, indicating that they're dominated, not by super-linear innovation and ideas; they become dominated by economies of scale. In that interpretation, by bureaucracy and administration, and they do it beautifully, may I say. So if you tell me the size of some company, some small company, I could have predicted the size of Walmart. If it has this sublinear scaling, the theory says we should have sigmoidal growth. There's Walmart. Doesn't look very sigmoidal. That's what we like, hockey sticks. But you notice, I've cheated, because I've only gone up to '94. Let's go up to 2008. That red line is from the theory. So if I'd have done this in 1994, I could have predicted what Walmart would be now. And then this is repeated across the entire spectrum of companies. There they are. That's 23,000 companies. They all start looking like hockey sticks, they all bend over, and they all die like you and me.
有關這些企業的驚人發現是, 它們呈「次線性」地向上攀升, ──像生態的規律一般── 表示它們受支配 ──非受超線性的 創新和概念所控制── 它們開始變得受 經濟規模所支配。 官僚制度和監管 可解釋那點。 而且它們運作地極棒,可以這麼說吧。 所以若你告訴我某公司的規模大小、某間小公司 我早可以預測沃爾瑪的規模大小。 若它存有「次線性縮放」, 這個理論指示 我們應會有呈「S型函數的發展」。 這條是沃爾瑪,看來非常不「S型函數曲線」。 那是我們喜歡的曲棍球棒 但注意看,我在哄騙你們 因為這條線只顯示到1994年, 咱們來看看繪製到2008年的圖表。 那紅線是依理論產生的 那麼,若我在1994完成這張圖 我早可以預測沃爾瑪現在的狀況。 然後這數學架構重覆應用 橫跨所有領域的眾多企業。 它們都在這兒。那兩萬三千間公司 它們全開始長得像曲棍球棒, 它們均呈現向下彎曲, 它們就像你我一樣生命終會消失。
Thank you.
謝謝大家
(Applause)
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