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這是一張出自藝術家Michael Najjar手中的照片,以他去阿根廷拍攝照片這方面來說,它是真實的;但它也是虛構的,在拍攝後還進行了許多後製工作。事實上他所做的是依據道瓊指數的趨勢,以數位化方式重新塑造山的輪廓,所以你們看到的懸崖,山谷旁的高大懸崖,代表2008年的金融危機。這張照片拍攝的時間是景氣深陷在谷底的時候,我不知道我們現在位於何處,這是類似香港恆生指數的地形,我不知道為什麼會這樣。
這是藝術,也是一種隱喻,但我認為重點是關於這個齒狀曲線的隱喻。藉著這個齒狀曲線,我今天想提出的是,重新思考一些關於當代數學的角色,不僅是金融數學,而是一般數學。某些我們從這個世界擷取、源於這個世界的東西,已轉變成一種真正開始形塑世界的東西,對我們周遭和我們內心世界來說皆是如此,特別是演算法。基本上這是電腦用來做決定的數學,因為一遍又一遍地重複演算它們,獲得了辨別事實的能力;它們是固定、僵化的運算,最後成為真實的結果。
我總是不斷地思考這一點;幾年前,在跨大西洋的航班上,因為我正好坐在一位年齡跟我差不多的匈牙利物理學家旁邊,我們談論冷戰時期匈牙利物理學家的生活情形。我說,「那麼,你們當時都做些什麼?」
他說,「我們大多是在破解隱形技術。」
我說,「這工作不錯,很有趣,請問是怎麼進行的?」要明白這一點,必須稍微瞭解隱形技術的原理,所以-這是過於簡化的解釋,但基本上,這不是說你可以駕著156噸的鋼鐵在天空飛行而躲過雷達偵測,它不會就這麼消失無蹤;但如果你有辦法讓這個龐然大物轉變成一百萬個小物體,就像一群群的鳥一樣,當雷達追蹤它時,必須能看到天空中的每一群鳥,對雷達來說,這實在是非常艱難的工作。
他說,「是啊,但這是對雷達來說。因此我們不使用雷達,我們建造一個偵測電波及電子通訊訊號的黑盒子,每當我們看到一群帶有電子訊號的鳥時,就認為可能跟美國人有關。」
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以下為系統擷取之英文原文
This is a photograph by the artist Michael Najjar, and it's real, in the sense that he went there to Argentina to take the photo. But it's also a fiction. There's a lot of work that went into it after that. And what he's done is he's actually reshaped, digitally, all of the contours of the mountains to follow the vicissitudes of the Dow Jones index. So what you see, that precipice, that high precipice with the valley, is the 2008 financial crisis. The photo was made when we were deep in the valley over there. I don't know where we are now. This is the Hang Seng index for Hong Kong. And similar topography. I wonder why.
And this is art. This is metaphor. But I think the point is that this is metaphor with teeth. And it's with those teeth that I want to propose today that we rethink a little bit about the role of contemporary math -- not just financial math, but math in general. That its transition from being something that we extract and derive from the world to something that actually starts to shape it -- the world around us and the world inside us. And it's specifically algorithms, which are basically the math that computers use to decide stuff. They acquire the sensibility of truth, because they repeat over and over again. And they ossify and calcify, and they become real.
And I was thinking about this, of all places, on a transatlantic flight a couple of years ago, because I happened to be seated next to a Hungarian physicist about my age and we were talking about what life was like during the Cold War for physicists in Hungary. And I said, "So what were you doing?"
And he said, "Well we were mostly breaking stealth."
And I said, "That's a good job. That's interesting. How does that work?" And to understand that, you have to understand a little bit about how stealth works. And so -- this is an over-simplification -- but basically, it's not like you can just pass a radar signal right through 156 tons of steel in the sky. It's not just going to disappear. But if you can take this big, massive thing, and you could turn it into a million little things -- something like a flock of birds -- well then the radar that's looking for that has to be able to see every flock of birds in the sky. And if you're a radar, that's a really bad job.
And he said, "Yeah." He said, "But that's if you're a radar. So we didn't use a radar; we built a black box that was looking for electrical signals, electronic communication. And whenever we saw a flock of birds that had electronic communication, we thought probably has something to do with the Americans."
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我說:「是啊,很不錯,所以你們有效的擊敗了60年來的航空研究。你們下一幕是什麼?你長大後做些什麼?」他說,「嗯,金融服務。」我說:「哦。」因為這在最近的新聞中有報導。我說,「請問是怎麼進行的?」他說,「嗯,目前有2000位物理學家在華爾街工作,我是其中之一。」我說,「那華爾街的黑盒子是什麼呢?」
他說:「你問的問題很有趣,因為這事實上就叫做黑箱交易,有時也稱為algo trading,演算法交易。」演變出演算法交易的部分原因是,商業機構的交易者發生跟美國空軍相同的問題,就是他們打算轉移這些資產-無論是寶鹼、埃森哲顧問公司或任何其他公司,它們要在市場中轉移100萬筆資產,如果它們一次全部投入,就像玩撲克牌,一下子將籌碼全部丟出,等於把底牌全掀了,所以他們必須找出一種方法。他們使用演算法進行交易,把一筆大交易分成一百萬筆小交易,這麼做的神奇和可怕之處在於,你將一筆大交易分成一百萬筆小交易所使用的數學方法,也可用來尋找一百萬筆小交易的流向,將它們拼湊回去,而瞭解市場上所發生的實際情形。
因此,如果你需要對目前股市發生的情形有些概念,你可以想像其中有一堆基本上編寫為隱藏交易流向的演算法,以及一堆編寫為尋找交易流向並採取行動的演算法。這一切都很棒,很不錯,美國股市的70%,這個操作系統的70%,原本是你的養老金,你的房貸。
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And I said, "Yeah. That's good. So you've effectively negated 60 years of aeronautic research. What's your act two? What do you do when you grow up?" And he said, "Well, financial services." And I said, "Oh." Because those had been in the news lately. And I said, "How does that work?" And he said, "Well there's 2,000 physicists on Wall Street now, and I'm one of them." And I said, "What's the black box for Wall Street?"
And he said, "It's funny you ask that, because it's actually called black box trading. And it's also sometimes called algo trading, algorithmic trading." And algorithmic trading evolved in part because institutional traders have the same problems that the United State Air Force had, which is that they're moving these positions -- whether it's Proctor & Gamble or Accenture, whatever -- they're moving a million shares of something through the market. And if they do that all at once, it's like playing poker and going all in right away. You just tip your hand. And so they have to find a way -- and they use algorithms to do this -- to break up that big thing into a million little transactions. And the magic and the horror of that is that the same math that you use to break up the big thing into a million little things can be used to find a million little things and sew them back together and figure out what's actually happening in the market.
So if you need to have some image of what's happening in the stock market right now, what you can picture is a bunch of algorithms that are basically programmed to hide, and a bunch of algorithms that are programmed to go find them and act. And all of that's great, and it's fine. And that's 70 percent of the United States stock market, 70 percent of the operating system formerly known as your pension, your mortgage.
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什麼地方可能會出錯?出錯的地方是,一年前,整個股市資產在五分鐘內消失了百分之九,人們稱之為2:45的閃電崩盤。突然間,百分之九的股市資產消失了,至今仍無人能對究竟發生了什麼事做出結論,因為沒人下令,沒人希望發生這種事,沒人對事實上發生的事有任何控制權,他們有的只是一台放在面前,上面顯現數字的螢幕,只有一個寫著「停止」的紅色按鈕。
而這個東西是我們寫出的,我們寫出這些我們再也無法讀懂的東西,我們寫出了一些難以理解的東西,我們弄不清這個我們一手打造的世界究竟發生了什麼事。我們正開始尋找解決之道,有一間位於波士頓,叫Nanex的公司,他們利用數學和魔法,我不知道是什麼,得到所有的市場資料,他們有時確實能找出其中一些演算法,找到之後,他們將資料取出,然後像蝴蝶一樣釘在牆上。他們所做的,就像當我們面對大量不明白的資料時所做的一樣,他們給這些資料取名並加上故事。這是他們找出的其中一份資料,他們稱之為「刀」;這是「嘉年華會」;這是「波士頓洗牌者」;這是「微光」。
令人驚訝的是,當然,這不只是存在於股市的情形,到處都可以發現這類情形,只要你學會如何找出它們。你可以在這裡找到:這是一本關於蒼蠅的書,你可能在亞馬遜網站看過,你可能已經注意到這本書,因為當時它的標價是170萬美元,它已經絕版了-目前還是。(笑聲)如果你在170萬美元時購買,可能算撿到便宜了;幾個小時後,它已經漲到2360萬美元,外加運費和手續費。問題是:沒有人購買或出售任何東西,這是怎麼回事?你在亞馬遜網站看到的這個行為,正如在華爾街所看到的,你看到的這種行為,正是演算法發生衝突的證據。演算法未經人類監督,而陷入彼此的迴圈裡,沒有任何成人監護者說,「事實上,170萬相當貴。」
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And what could go wrong? What could go wrong is that a year ago, nine percent of the entire market just disappears in five minutes, and they called it the flash crash of 2:45. All of a sudden, nine percent just goes away, and nobody to this day can even agree on what happened, because nobody ordered it, nobody asked for it. Nobody had any control over what was actually happening. All they had was just a monitor in front of them that had the numbers on it and just a red button that said, "Stop."
And that's the thing, is that we're writing things, we're writing these things that we can no longer read. And we've rendered something illegible. And we've lost the sense of what's actually happening in this world that we've made. And we're starting to make our way. There's a company in Boston called Nanex, and they use math and magic and I don't know what, and they reach in to all the market data and they find, actually sometimes, some of these algorithms. And when they find them they pull them out and they pin them to the wall like butterflies. And they do what we've always done when confronted with huge amounts of data that we don't understand -- which is that they give them a name and a story. So this is one that they found, they called the Knife, the Carnival, the Boston Shuffler, Twilight.
And the gag is that, of course, these aren't just running through the market. You can find these kinds of things wherever you look, once you learn how to look for them. You can find it here: this book about flies that you may have been looking at on Amazon. You may have noticed it when its price stared at 1.7 million dollars. It's out of print -- still ... (Laughter) If you had bought it at 1.7, it would have been a bargain. A few hours later, it had gone up to 23.6 million dollars, plus shipping and handling. And the question is: Nobody was buying or selling anything; what was happening? And you see this behavior on Amazon as surely as you see it on Wall Street. And when you see this kind of behavior, what you see is the evidence of algorithms in conflict, algorithms locked in loops with each other, without any human oversight, without any adult supervision to say, "Actually, 1.7 million is plenty."
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發生在亞馬遜網站的情形也發生在Netflix(網路租片業者)。過去幾年來,Netflix用過幾種不同的演算法,它們從Cinematch開始,嘗試過一堆其他的演算法,有Dinosaur Planet、Gravity,它們現在使用的是Pragmatic Chaos。Pragmatic Chaos跟所有Netflix使用的演算法一樣,試圖做同樣的事情;它試圖捕捉你,捕捉你人類頭骨裡的想法,這樣它就可以建議你下一部可能想看的電影是什麼。這是個非常、非常困難的問題,但問題的困難之處,以及事實上我們並未將它做的十分完善,它無法避免Pragmatic Chaos造成的影響。Pragmatic Chaos就像Netflix所有的演算法一樣,結果是,有60%被租用的電影最後是由它決定的,所以一段以你的想法為根據的代碼,負責決定了60%的電影租用情形。
但如果你能在電影拍攝前對它做評估呢?那不是很方便嗎?好,幾個英國資訊科學家前進好萊塢,發展出一種故事演算法。這是一間名為Epagogix的公司,你可以將你的腳本放上去做運算,他們可以量化地告訴你這是一部預算為3000萬美元的電影,或2億美元的電影。重點是,這不是Google,也不是資訊,這不是金融統計資料,而是文化。你在這裡看到的,或你通常並不能真正看出的是,這是文化的物理學。如果這些演算法就像華爾街的演算法一樣,有一天就這麼崩盤,出岔子了,我們怎麼知道,會發生什麼情形?
這些演算法在你家也有,就在你家中;這是在你家客廳中互相競爭的兩種演算法,這是兩個不同的打掃機器人,對乾淨的定義有十分不同的看法,你可以看到,如果你將它們調慢,在機身上加上燈光,它們有點像你臥室中的秘密建築師。建築本身多少是依據演算法的最佳化結果,這個想法並非牽強,這相當真實,就發生在你身邊。
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And as with Amazon, so it is with Netflix. And so Netflix has gone through several different algorithms over the years. They started with Cinematch, and they've tried a bunch of others. There's Dinosaur Planet, there's Gravity. They're using Pragmatic Chaos now. Pragmatic Chaos is, like all of Netflix algorithms, trying to do the same thing. It's trying to get a grasp on you, on the firmware inside the human skull, so that it can recommend what movie you might want to watch next -- which is a very, very difficult problem. But the difficulty of the problem and the fact that we don't really quite have it down, it doesn't take away from the effects Pragmatic Chaos has. Pragmatic Chaos, like all Netflix algorithms, determines, in the end, 60 percent of what movies end up being rented. So one piece of code with one idea about you is responsible for 60 percent of those movies.
But what if you could rate those movies before they get made? Wouldn't that be handy? Well, a few data scientists from the U.K. are in Hollywood, and they have story algorithms -- a company called Epagogix. And you can run your script through there, and they can tell you, quantifiably, that that's a 30 million dollar movie or a 200 million dollar movie. And the thing is is that this isn't Google. This isn't information. These aren't financial stats; this is culture. And what you see here, or what you don't really see normally, is that these are the physics of culture. And if these algorithms, like the algorithms on Wall Street, just crashed one day and went awry, how would we know, what would it look like?
And they're in your house. They're in your house. These are two algorithms competing for your living room. These are two different cleaning robots that have very different ideas about what clean means. And you can see it if you slow it down and attach lights to them. And they're sort of like secret architects in your bedroom. And the idea that architecture itself is somehow subject to algorithmic optimization is not far-fetched. It's super-real and it's happening around you.
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最能感受到這件事的情況就是當你在一個密閉的金屬盒中時。一種新型電梯,所謂目的地控制電梯;進電梯之前,你必須先按下要去的樓層,它使用所謂的裝箱演算法,因此,它不會隨意讓每個人進入任何他們想搭的電梯。每個想去十樓的人都得搭二號電梯,每個想去三樓的人都得搭五號電梯。這麼做產生的問題是,人們嚇壞了,驚慌不已,你們知道為什麼吧?你們知道為什麼。因為這部電梯缺少一些重要的裝置,如按鈕。(笑聲)就是那些人們都會使用的東西。電梯裡只有顯示上升或下降的數字,以及寫著「停止」的紅色按鈕。這正是我們想要設計的,這正是我們為這種機器語言所做的設計。你能將它應用到什麼程度?你能將它延伸到什麼程度?可以延伸到相當極端的程度。
讓我們回頭來談華爾街。因為華爾街的演算法有賴於一個勝於一切的特質,那就是速度。它們以毫秒和微秒的速度運行,舉個例子讓你們對微秒有些概念:只是按一下滑鼠,所花的時間就等於50萬微秒。但如果你是一個華爾街演算法,只要落後5微秒,就會成為失敗者。因此,如果你是一個演算法,你會想找個像我在法蘭克福遇到的建築師,他清空了一棟摩天大樓,扔了所有家具,及所有供人使用的基礎設施,只在地板上鋪好鋼板,準備讓伺服器層層堆疊上去,這樣演算法就可以接近網路。
你會認為網路是一種分佈式系統,當然,確實如此,但它是由某處分佈出來的,這就是它在紐約的分佈來源:位於哈德遜街的Carrier Hotel,這是網路進入城市的真正傳輸路線。實際情況是,你離它越遠,在每次傳輸中就會落後幾微秒。這些在華爾街的企業,Marco Polo和Cherokee Nation,比這些傢伙(微光、嘉年華會、波士頓洗牌者演算法)落後八微秒,因為它們已經駐進Carrier Hotel周圍被清空的空建築物。這種情形會一再發生,我們會繼續將建築物清空,因為在一吋吋距離及分分毫毫的金錢競爭之下,沒有人能像「波士頓洗牌者」演算法那樣,從這些空間中擠出收益。
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You feel it most when you're in a sealed metal box, a new-style elevator, they're called destination control elevators. These are the ones where you have to press what floor you're going to go to before you get in the elevator. And it uses what's called a bin packing algorithm. So none of this mishegas of letting everybody go into whatever car they want. Everybody who wants to go to the 10th floor goes into car two, and everybody who wants to go to the third floor goes into car five. And the problem with that is that people freak out. People panic. And you see why. You see why. It's because the elevator is missing some important instrumentation, like the buttons. (Laughter) Like the things that people use. All it has is just the number that moves up or down and that red button that says, "Stop." And this is what we're designing for. We're designing for this machine dialect. And how far can you take that? How far can you take it? You can take it really, really far.
So let me take it back to Wall Street. Because the algorithms of Wall Street are dependent on one quality above all else, which is speed. And they operate on milliseconds and microseconds. And just to give you a sense of what microseconds are, it takes you 500,000 microseconds just to click a mouse. But if you're a Wall Street algorithm and you're five microseconds behind, you're a loser. So if you were an algorithm, you'd look for an architect like the one that I met in Frankfurt who was hollowing out a skyscraper -- throwing out all the furniture, all the infrastructure for human use, and just running steel on the floors to get ready for the stacks of servers to go in -- all so an algorithm could get close to the Internet.
And you think of the Internet as this kind of distributed system. And of course, it is, but it's distributed from places. In New York, this is where it's distributed from: the Carrier Hotel located on Hudson Street. And this is really where the wires come right up into the city. And the reality is that the farther away you are from that, you're a few microseconds behind every time. These guys down on Wall Street, Marco Polo and Cherokee Nation, they're eight microseconds behind all these these guys going into the empty buildings being hollowed out up around the Carrier Hotel. And that's going to keep happening. We're going to keep hollowing them out, because you, inch for inch and pound for pound and dollar for dollar, none of you could squeeze revenue out of that space like the Boston Shuffler could.
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但如果你拉遠來看,將視野拉遠,會看到在紐約市和芝加哥之間,有一條825英哩長的電纜溝,這是近幾年由一間名為Spread Networks的公司建造,鋪設於這兩個城市之間的光纖電纜,只為了能用比你點擊一次滑鼠快37倍的速度傳輸一個訊號,只為了這些演算法,只為了「嘉年華會」和「刀」這些演算法。仔細思考一下,我們用炸藥和切石鋸鑿穿美國大陸,使一個演算法完成交易的時間能快個3微秒,只為了一個永遠沒人能懂的通訊架構,這是一種領土擴張政策,永遠在尋找新疆界。
不幸的是,我們天生就適合做這種工作。這只是理論上的圖形,這是一些麻省理工學院的數學家做的,事實上,他們所說的大部份我都不是真的很瞭解,其中涉及了光錐和量子纏結,我都不太明白,但我看的懂這張地圖。這張地圖表達的是,如果你想在圖上紅點之處的市場賺錢,就是人群和城市集中之處,就必須將伺服器裝在圖中藍點之處,以達到最佳效率。你可能已經注意到與這些藍點有關的情形,其中很多是在海洋當中,所以這就是我們將要做的事。我們將建造氣泡或平台之類的東西,我們事實上打算分開海洋,憑空變出錢來,因為這是一個光明的未來,如果你是一個演算法的話。
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But if you zoom out, if you zoom out, you would see an 825 mile trench between New York City and Chicago that's been built over the last few years by a company called Spread Networks. This is a fiber optic cable that was laid between those two cities to just be able to traffic one signal 37 times faster than you can click a mouse -- just for these algorithms, just for the Carnival and the Knife. And when you think about this, that we're running through the United States with dynamite and rock saws so that an algorithm can close the deal three microseconds faster, all for a communications framework that no human will ever know, that's a kind of manifest destiny and will always look for a new frontier.
Unfortunately, we have our work cut out for us. This is just theoretical. This is some mathematicians at MIT. And the truth is I don't really understand a lot of what they're talking about. It involves light cones and quantum entanglement, and I don't really understand any of that. But I can read this map. And what this map says is that, if you're trying to make money on the markets where the red dots are, that's where people are, where the cities are, you're going to have to put the servers where the blue dots are to do that most effectively. And the thing that you might have noticed about those blue dots is that a lot of them are in the middle of the ocean. So that's what we'll do, we'll build bubbles or something, or platforms. we'll actually part the water to pull money out of the air, because it's a bright future if you're an algorithm.
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事實上,有趣的不是金錢本身,而是金錢產生的驅動力。我們事實上藉由這種演算法效率,改造了地球本身的環境,想通了這一點,回頭來看Michael Najjar拍攝的照片,就會瞭解,這不是隱喻,而是預言。這預示了我們正創造出的數學,對整個地球造成驚天動地的全面影響。過去地景的形成總是源於這種大自然與人類之間奇怪而不自然的合作關係,但這是第三種共同演化的力量:演算法。「波士頓洗牌者」、「嘉年華會」,我們必須以自然的觀點去瞭解它們,以某方面來說,它們確實屬於自然。
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And it's not the money that's so interesting actually. It's what the money motivates. That we're actually terraforming the Earth itself with this kind of algorithmic efficiency. And in that light, you go back and you look at Michael Najjar's photographs, and you realize that they're not metaphor, they're prophecy. They're prophecy for the kind of seismic, terrestrial effects of the math that we're making. And the landscape was always made by this sort of weird, uneasy collaboration between nature and man. But now there's this third co-evolutionary force: algorithms -- the Boston Shuffler, the Carnival. And we will have to understand those as nature. And in a way, they are.
Thank you.