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.
這是張相片 由藝術家Michael Najjar 拍攝的 這張相片是真的 也就是說,他親自到阿根廷,那座山的所在處 拍攝這張照片。 但也可以說,這是張虛構的相片。這張相片的完作花了很多功夫。 他對相片動了些手腳: 數位化重整 整片山脈的形體輪廓, 使其隨道瓊指數曲線變化。 你所看到的 那個峭壁, 那個有處凹陷的高聳峭壁 代表2008年的金融危機。 拍攝這張相片時 我們的金融情勢正處於低谷, 不曉得我們現在處於何種形勢。 這是恆生指數, 香港股市價格的重要指標。 (兩張相片)地形相似, 我想知道為什麼
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.
這是藝術;這是種象徵。 但我認為重點是 這個象徵有“牙齒”。 就是因為這些“牙齒”,我今天提議 我們稍微重新思考 當代數學的角色; 不只金融數學,還有普通數學。 「它」的演變: 從我們鑽研這個世界,抽絲撥繭而取得的發現 到實際開始形成「它」的重要發現, 這含括我們的外在世界和我們內在的世界。 說明確些,它是演算法, 基本上,是種數學─ ─電腦用來測定東西的數學。 演算法掌握高度精確的計量, 因為它們一而再,再而三的重覆著; 然後漸漸成型,發展出基本架構 然後它們變得實際且可靠。
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?"
我當時正在思考這點, 真是太湊巧了! 就在幾年前,橫越大西洋的班機上, 因為我的座位碰巧 在一位年紀與我相仿的匈牙利物理學家隔壁 我們談論關於 匈牙利冷戰期間 物理學家的生活情況。 我說:「你那時在做什麼?」
And he said, "Well we were mostly breaking stealth."
他說:「嗯,我們大多在打擊祕密行動。」
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.
「那是個好工作,有趣吧, 那是怎麼運作的?」 要了解那之前 你必須稍稍了解祕密行動的運作。 這是個超簡單化的例子, 基本上,它不像是 你可以藉由156噸在天空飛的鋼鐵 傳送雷達信號。 飛機不會消失不見。 但若你能將這個龐大、具規模的東西 變成 百萬個小玩意 ─像鳥群一樣的東西─ 那麼雷達偵測到那一群群的小東西 必定會看到 在空中有“一群群的鳥” 若你是一個雷達,事情可就糟了。
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.'"
他說:「對,但那是,如果你是個雷達。 所以我們不用雷達, 我們建造一個黑箱子,用它搜尋電波, 電子通訊。 任何時候,我們發現帶有電子通訊的鳥群, 我們會認為這很可能跟美國人有關。」
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?"
我接著說:「是啊, 真行, 你們成功地消磨了 60年的航空學研究心血。 你接著要做什麼? 當你長大成人以後,你從事什麼工作?」 他回答: 「嗯,金融服務業。」 我驚呼:「喔!」 那一陣子相關報導一直在新聞出現。 我問:「進行的如何?」 他說:「現有2,000名物理學家在華爾街(美國金融中心), 我是他們其中一人。」 我接著問:「華爾街用的『黑箱』是什麼?」
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 States 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.
他回說:「你這樣問很好笑, 事實上,人們會稱它為『黑箱交易』 有時也稱為 「演算法交易」(algorithmic trading 或algo trading) 「演算法交易」的演進發展,有部分是因為 某些機構交易人遇到相同的問題; 而那問題美國空軍也同樣遭遇到, 他們都在「移動這些位置」── 不論是寶僑(Proctor&Gamble)或埃森哲(Accenture:管理顧問、技術服務公司) 他們都在移動一百萬股的東西, 透過市場交易而進行。 如果他們一次就挪動全部, 就像玩撲克牌,把剩下的所有籌碼一次全部壓上, 你只會過早洩露底餡; 所以他們必須找到方法 ─他們用演算法,有系統的操作─ 將龐然大數化整為零 成為百萬個小交易。 恐怖的是這個魔術正是 「相同的數學」 ─用來瓦解龐然巨物 變成百萬個小東西─ 可以用來計算出百萬個零星單位 又將他們統整在一起 並推算出實際在市場上發生的事情。
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.
如果你立即需要 一些股市交易的樣貌, 你可以構想到的是,成串的運算法 基本上被設計為隱藏不顯示 和成串的運算法被設計為可搜尋並執行。 整個設計的真是太棒了,又精確。 那是百分之七十的 美國股票市場, 這個百分之七十的營運系統 之前堪稱為某些人的“退休金” 某人的“抵押借款”。
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."
會有什麼錯呢? 事情出了差池: 一年前 整體股市的百分之九突然消失了五分鐘, 人們稱之為『瞬間當機2:45』 突然, 百分之九就這樣不見了, 直到今天,仍沒有人 對發生的事取得一致的意見, 因為沒人“下令”當機;沒人自找麻煩。 大家對實際正在發生的事情束手無策 他們只有 盯著面前的電腦螢幕, 電腦螢幕上的數字, 和一顆紅色按紐 上面寫著: 『停止』
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 into 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.
事情就是這樣, 我們正在編寫的「東西」, 我們正在編寫這些連自己都看不懂的東西。 我們已經對「某種東西」投降了, 某種「難以辨識」的東西。 而且我們失去了 對實際正發生之事的判別力 就在我們自己創造的這個世界中, 況且我們正開始邁向成功。 在波士頓有間公司叫Nanex(該公司開發市場數據供給系統), 他們用數學和魔法 和我不知道的什麼來的 他們深入研究市場數據資料 他們確實發現值得重視的東西:某些演算法 當他們發現這些演算程序,便把它們擷取出來 並將它們像蝴蝶一樣釘在牆上。 他們做大家總是會做的事情, 當面臨龐大又不懂的數據資料時, 為其命名 和揑造故事。 這是他們的發現: 他們稱為『刀』 『嘉年華會』(Carnival) 『波士頓通勤者』(Boston Shuffler ) 『暮光』
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 started 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."
好玩的是 當然,這些不光是存在於金融市場; 你能在任何你看得到的地方,發現這些東西, 一旦你明白如何找尋到它們(演算法)。 從這兒你可以發現:這是本關於蒼蠅的書, 你可能已在亞馬遜看到這本書; 你可能已經注意到 它的價格從一百七十萬元起價時, 這本書是絶版的......仍然絶版中。 (笑笑) 如果能以一百七十萬的價格買下它是很划算的 稍後幾小時,它飆漲至 兩千三百六十萬元, 包含運費和手續費。 問題是: 這並無產生任何買賣行為;發生了什麼事? 你在亞馬遜見到這樣的行為, 確實跟你在華爾街看到的一般。 當你見到這種行為: 你所看到的顯然正是 矛盾的演算程序, 演算程序被彼此套住,卡在電腦程式回路中; 沒有任何“人類監管” 沒有任何“成人監護” 來告訴你,“其實,一百七十萬已經夠多了!”
(Laughter)
(笑笑)
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.
如同亞馬遜,Netflix(美國公司,經營線上串流影片)也一樣。 多年來, Netflix採用過 好幾個不同的演算程序。 他們從Cinematch(推薦系統軟體)開始,也試了一連串其他的軟體。 有Dinosaur Planet團隊、Gravity團隊各別研發的推薦系統。 他們現在使用 Pragmatic Chaos研發的系統。 像所有Netflix的運算系統, Pragmatic Chaos研發的推薦系統,試圖做相同的事。 它試著去掌控你們, 控制人類頭顱內的思考邏輯, 以便它能推薦你 下次你也許想看的電影─ ─這是非常高難度的難題。 但問題和事實的艱難度 ─我們不是真的掌握問題的事實─ 並沒減損 Pragmatic Chaos的影嚮。 Pragmatic Chaos,如同所有Netflix運算系統, 至終裁定 百分之六十的 哪些電影最後會被租借。 所以一片程式編碼 ─紀錄著你們看片的喜好─ 得為百分之六十的電影負責。
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?
但倘若你能評估這些電影, 在電影製作前作預測呢? 那不就簡便多了? 嗯,在好萊塢,一些來自英國的數據科學家 擁有故事情節演算程式系統── 一間公司叫Epagogix(英國一家預測劇本未來票房好壞的公司) 你可以拿劇本請這間公司幫你預測; 他們會提供你數據: 那是一部可賣三千萬的電影 或是一部兩億的賣座電影。 事情是......這不是Google; 這不是情報資料; 這些不是金融統計;這是文化。 你們在這裡見到的, 或者說,實際上,你通常不會察覺的 是物理文化 而且若這些演算系統 像華爾街的演算系統 某天突然當機,出岔子了 我們如何會知道..... 那會如何?
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.
再者,它們就在你的房子內,它們就在你的房子內 兩個演算系統在競爭你的客廳。 兩個不同的清潔機器人 對乾淨的定義有不同的概念。 而且你能從中看到演算程序, 如果讓它慢下來,為它們裝上LCD燈的話,你們就能見識到。 而且他們有點像在你卧房內的袐密建築師。 況且建築學本身的概念 從某種角度而言,是基於演算法的最佳化 一點也不牽強喔, 超真實而且就在存在你週遭。
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.
你感受最深的時刻是, 當你在一個密閉的金屬箱子內 ─一臺新型的電梯─ 他們被稱為「終點控制電梯」。 這些是電梯,你可以按鈕到你要去的樓層 在你“進電梯前”按鈕。 它使用所謂的「裝著演算法的盒子」。 也就是說,這一點也不異常或瘋狂, 讓每個人選擇進入任何一台電梯。 要到十樓的人進入二號電梯; 要到三樓的人進入五號電梯。 問題是 人們嚇壞了 人們驚慌失措。 你看看為什麼......你看看為什麼...... 原因是: 電梯缺少了某些種要的儀表,譬如說「按鈕」 (笑笑) 人們會使用那個東西。 電梯內只顯示 上樓或下樓的數字 還有紅色的按鈕,寫著:『停止』 而這是我們正在設計的, 我們正在設計 這種「機器方言」。 你可以作到什麼樣程度?你可以利用它到何種境界? 你可以“搭乘它(演算法)”至無遠弗界。
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.
讓我們退回到華爾街, 因為華爾街的演算系統 仰賴某種性質更勝於一切 即「速度」。 他們以毫秒和微秒運作 讓你了解什麼是微秒, 你需要花五十萬微秒 去點擊滑鼠; 若你是華爾街的演算法 而你落後了五微秒, 你就是失敗者。 所以,倘若你是一個演算法, 你會找一個建築師,像我在法蘭克福市遇到的那位, 掏空摩天大樓, 扔掉所有傢俱、所有供人類使用的基礎建設, 只有鋼鐵舖地 準備好讓大批的伺服器入駐。 整個如此的演算程序 能使網路通路密切而有效率。
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 further 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 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.
再者,你們認為網路是種分散式系統。 當然,它是;可是,是從各個定點分散 在紐約,這裡是分佈的中心據點: 電信機房(Carrier Hotel) 座落在哈德森街(Hudson Street) 這裡的確是電纜貫穿整座城市的源頭。 事實是,離那裡越遠 每一次就落後數微秒。 在華爾街這一帶的“這些傢伙” Marco Polo和Cherokee Nation 他們落後八微秒, 落後所有“這些傢伙” 這些傢伙進入被掏空的建築物 而這些建築座落接近電信機房的周邊。 而且那將會持續發生 ─這些建築物將會持續被掏空─ 因為每一英寸 每一磅和每一(美)元 你們沒人能從那個空間距離強擠出收益 像『波士頓通勤者』那般。
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 we'll always look for a new frontier.
但如果縮小地圖 縮小地圖 你會看到825英里(1327.7公里)的溝渠 在紐約和芝加哥之間, 已建立有幾年了 由Spread Networks 經營。 這一道光纖電纜 被設置在兩城市間 只為一個信號的傳遞 能以37倍速快過點擊滑鼠─ ─只為了這些演算系統; 只為了『嘉年華會』和『刀』。 當你們想著這點時, 我們正以炸藥與岩石鋸貫穿、 損耗美國, 以便一個演算法能快速達成交易 ─以減少三微秒的速度─ 全都為了一個人類 將永不會明瞭的通訊機制 那是一種顯而易見的定數 且將永遠不斷地尋找未開拓的新領域。
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.
不幸的是,我們必須要完成這個任務。 這只是一個理論。 這是某些在麻省理工學院(MIT)的數學家製作的 事實上,我不真的都了解 他們在談論些什麼 它涉及光圓錐體和量子糾結 我不真的了解那是什麼 但我會讀這面地圖。 這面地圖指示 如果你試圖在有紅色點點的市場中賺錢 也就是在人們聚集的地方及市鎮重心, 你就必須將伺服器設置在藍色點點的地方 讓運作效率最大化。 你也許注意到那些藍色點點的分佈, 很多藍色點點在海的中央; 所以,我們要怎麼做:我們要建立透明圓外罩(bubbles意同泡泡)或什麼來的 或者很多平臺。 我們將能確實分開海水 將錢從空氣中抽取出, 未來是光明閃亮的 如果你自己就是一個演算法的話。
(Laughter)
(笑笑)
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.
然而,事實上,不是錢有趣 而是錢激發的東西引人入勝─ ─我們能確實地地球化(terraforming) 地球本身, 透過演算法具有的最佳效率(能)。 根據這點, 咱們回到前面, 看著Michael Najjar的相片 我們領悟到:他們不是象徵;他們是預言 他們預言了 數學之地震效應、陸地效應 即將發生在我們創造出來的數學世界中。 而且這風貌過去一直是由自然界和人之間 不可思議的協作及不易妥協而創作出來的, 是自然界和人之間的對話。 但現在有第三股共同演化勢力:演算系統 『波士頓通勤者』、『嘉年華會』 我們必須明白這些皆為自然。 在某種程度上,它們是!
Thank you.
謝謝大家
(Applause)
(掌聲熱烈)