So, I have a feature on my website where every week people submit hypothetical questions for me to answer, and I try to answer them using math, science and comics.
我的網站上有一個功能, 在那裡人們每週可以向我發問, 一些假設性的問題。 而我會盡量以數學、科學 和漫畫的形式來回答。
So for example, one person asked, what would happen if you tried to hit a baseball pitched at 90 percent of the speed of light? So I did some calculations. Now, normally, when an object flies through the air, the air will flow around the object, but in this case, the ball would be going so fast that the air molecules wouldn't have time to move out of the way. The ball would smash right into and through them, and the collisions with these air molecules would knock away the nitrogen, carbon and hydrogen from the ball, fragmenting it off into tiny particles, and also triggering waves of thermonuclear fusion in the air around it. This would result in a flood of x-rays that would spread out in a bubble along with exotic particles, plasma inside, centered on the pitcher's mound, and that would move away from the pitcher's mound slightly faster than the ball. Now at this point, about 30 nanoseconds in, the home plate is far enough away that light hasn't had time to reach it, which means the batter still sees the pitcher about to throw and has no idea that anything is wrong. (Laughter) Now, after 70 nanoseconds, the ball will reach home plate, or at least the cloud of expanding plasma that used to be the ball, and it will engulf the bat and the batter and the plate and the catcher and the umpire and start disintegrating them all as it also starts to carry them backward through the backstop, which also starts to disintegrate. So if you were watching this whole thing from a hill, ideally, far away, what you'd see is a bright flash of light that would fade over a few seconds, followed by a blast wave spreading out, shredding trees and houses as it moves away from the stadium, and then eventually a mushroom cloud rising up over the ruined city. (Laughter)
例如,有人問: 如果你試圖擊中一個速度為高達 光速的90%的棒球,將會怎麼樣? 然後我做了計算, 通常情況下,當一個物體在空氣中飛行, 空氣將繞著此物環流。 但是對於這個案例, 棒球速度將會過快, 以至於空氣分子來不及讓道。 棒球將會碰撞空氣並穿透空氣分子, 然後這些與空氣分子的撞擊運動, 將會把氮、碳、氫 從棒球那擊退, 使球破裂成極小粒子, 同時也在空氣中引發熱核聚變的波。 這將導致 大量的X光線擴散開成一個大泡沫, 並伴隨著一些外來粒子, 泡沫裡面是等離子,集中在投球區。 然後這些X光線將 以比球稍快的速度遠離棒球。 此時,大約在 30 奈秒內, 本壘板遠到 光來不及去觸及它。 這意味著球棒打者仍能 看見投手即將拋球的動作, 並且沒想到事情不對勁。 (笑聲) 現在,70 奈秒之後, 這個棒球將會擊中本壘板, 亦或是那些球分離出的 擴散的等離子集合體, 它將吞沒球棒、打者、 本壘板、補手和裁判, 然後將它們全部分解, 同時棒球運載這些分解物 穿過擋球網,擋球網也被分解。 因此如果你從一座山上 觀察全過程 理想狀態下,要夠遠, 你看到的是一道閃光, 在數秒後消褪。 同時伴隨閃光的衝擊波會擴散 並撕毀樹和房子, 與此同時它遠離運動場, 最終一朵蘑菇雲 從這廢城中升起。
So the Major League Baseball rules are a little bit hazy, but — (Laughter) — under rule 6.02 and 5.09, I think that in this situation, the batter would be considered hit by pitch and would be eligible to take first base, if it still existed.
美國職業棒球大聯盟 對此的評分規則頗為模糊, (笑聲)但針對規則6.02和5.09, 我想在這種情況下, 打者將會被認為被球擊中, 並有資格上一壘, 如果壘包還存在的話。
So this is the kind of question I answer, and I get people writing in with a lot of other strange questions. I've had someone write and say, scientifically speaking, what is the best and fastest way to hide a body? Can you do this one soon? And I had someone write in, I've had people write in about, can you prove whether or not you can find love again after your heart's broken? And I've had people send in what are clearly homework questions they're trying to get me to do for them.
這些就是我常回答的問題。 我讓大家寫下的 各種千奇百怪的問題。 今天有人問我: 從科學的角度, 有沒有藏具屍體最佳最快的方法? 可以麻煩你盡快解答嗎? 也有人問, 有人寫, 你能否證明 當你傷心欲絕時,還能否重拾愛情? 還有人發給我 很明顯是作業題目, 希望我可以替他們效勞。
But one week, a couple months ago, I got a question that was actually about Google. If all digital data in the world were stored on punch cards, how big would Google's data warehouse be? Now, Google's pretty secretive about their operations, so no one really knows how much data Google has, and in fact, no one really knows how many data centers Google has, except people at Google itself. And I've tried, I've met them a few times, tried asking them, and they aren't revealing anything.
但在幾個月前的某個星期, 有人問了我一個關於谷歌的問題, 如果把世界上所有數據保存在穿孔卡片上, 那麼谷歌的數據庫要多大才足夠? 然而谷歌對自身運營情況十分保密, 無人曉得谷歌數據有多少。 實際上,沒人真正清楚谷歌擁有多少數據中心, 除了谷歌內部人員外。 我嘗試過去瞭解並與他們碰過幾次面, 可他們守口如瓶。
So I decided to try to figure this out myself. There are a few things that I looked at here. I started with money. Google has to reveal how much they spend, in general, and that lets you put some caps on how many data centers could they be building, because a big data center costs a certain amount of money. And you can also then put a cap on how much of the world hard drive market are they taking up, which turns out, it's pretty sizable. I read a calculation at one point, I think Google has a drive failure about every minute or two, and they just throw out the hard drive and swap in a new one. So they go through a huge number of them. And so by looking at money, you can get an idea of how many of these centers they have. You can also look at power. You can look at how much electricity they need, because you need a certain amount of electricity to run the servers, and Google is more efficient than most, but they still have some basic requirements, and that lets you put a limit on the number of servers that they have. You can also look at square footage and see of the data centers that you know, how big are they? How much room is that? How many server racks could you fit in there? And for some data centers, you might get two of these pieces of information. You know how much they spent, and they also, say, because they had to contract with the local government to get the power provided, you might know what they made a deal to buy, so you know how much power it takes. Then you can look at the ratios of those numbers, and figure out for a data center where you don't have that information, you can figure out, but maybe you only have one of those, you know the square footage, then you could figure out well, maybe the power is proportional. And you can do this same thing with a lot of different quantities, you know, with guesses about the total amount of storage, the number of servers, the number of drives per server, and in each case using what you know to come up with a model that narrows down your guesses for the things that you don't know. It's sort of circling around the number you're trying to get. And this is a lot of fun. The math is not all that advanced, and really it's like nothing more than solving a sudoku puzzle.
因此我決定自尋答案。 有注意到幾個方面, 先從資金說起, 谷歌必須得公開它們的開支狀況, 那麼,這就能夠限制 它們可建的數據中心的數量, 因為一個大型數據中心花費相當多。 這同樣也可以限制 他們佔世界硬碟市場的份量。 這數額也是相當可觀的。 我曾經看到過一個估算,我認為谷歌 每一到兩秒會發生硬碟故障。 他們會立刻扔掉壞的硬碟, 並且換上新的。 所以這過程消耗了大量的硬碟。 我們再回到資金方面, 你可以大致瞭解 谷歌擁有多少數據中心, 你也可以觀察能源方面, 看看他們需要多少電量。 這是因為運行伺服器需要相當多的電力, 在這方面谷歌比眾多同行更高效。 然而他們還是遵循一些基本要求, 然後讓你對他們的伺服器數量設限。 你也可以從面積入手, 觀察你所知道的數據中心: 它們有多大? 容量是多少? 裡面可以容納多少伺服器支架? 對於一些數據中心, 你或許會獲取其中兩份訊息。 假設你知道他們的開支, 同樣地,因為他們必須和地方政府 簽訂協議來獲取能源。 你會大概知道他們交易的內容, 知道有多少能源被消耗。 接著,你可以看看這些數目的比率, 然後計算一個 你不熟識的數據中心。 這也能計算, 或許你只知道其中一個數據, 你知道面積, 就能知道或許能量是成比例的。 你可以運用各種不同數據 來進行相同運算。通過對總容量、 伺服器數目、每台伺服器的 硬碟數目的估算,在每一項中 用已知來擬建出一個模型, 縮小對未知對象的猜測範圍。 這有點像在這些數據裡循環, 樂趣十足。 數學計算並不是完全先進, 說實在這不過就像 做出一道數獨題目罷了。
So what I did, I went through all of this information, spent a day or two researching. And there are some things I didn't look at. You could always look at the Google recruitment messages that they post. That gives you an idea of where they have people. Sometimes, when people visit a data center, they'll take a cell-cam photo and post it, and they aren't supposed to, but you can learn things about their hardware that way. And in fact, you can just look at pizza delivery drivers. Turns out, they know where all the Google data centers are, at least the ones that have people in them.
我所做的只是瀏覽所有相關信息, 用一兩天的時間做調查。 還有,我未曾注意到這幾方面: 而你可多留意 谷歌發佈的徵才啟示。 由此可知他們在哪些地方需要員工。 當有人參觀某數據中心時, 他們會用手機拍照並公開照片。 雖然他們不應該這麼做, 但你可以由此得知硬碟的情況。 實際上,你僅需留意那些比薩餅速遞員, 他們其實知道 所有谷歌數據中心的具體位置, 最起碼是那些有人的數據中心。
But I came up with my estimate, which I felt pretty good about, that was about 10 exabytes of data across all of Google's operations, and then another maybe five exabytes or so of offline storage in tape drives, which it turns out Google is about the world's largest consumer of.
然而我想到了一個讓我 興奮不已的一個估測: 那是關於覆蓋整個 谷歌操作系統的10 EB的數據量, 另外大約五個EB的離線數據 被保存在磁帶伺服器裡。 這印證了谷歌 是世界上最大的消耗者。
So I came up with this estimate, and this is a staggering amount of data. It's quite a bit more than any other organization in the world has, as far as we know. There's a couple of other contenders, especially everyone always thinks of the NSA. But using some of these same methods, we can look at the NSA's data centers, and figure out, you know, we don't know what's going on there, but it's pretty clear that their operation is not the size of Google's.
所以我想出了這個估測, 這一數值也是大到相當驚人。 這超過了世界上其他任何一個機構, 就目前已知的來說。 同時總會有些其他競爭對手, 尤其是眾所周知的美國國家安全局, 但運用以上某些相同的方法, 我們可以觀察到國家安全局的數據中心。 雖然我們並不知道那裡的具體情況, 但很清楚的是, 它們的操作系統大小和谷歌的不同。
Adding all of this up, I came up with the other thing that we can answer, which is, how many punch cards would this take? And so a punch card can hold about 80 characters, and you can fit about 2,000 or so cards into a box, and you put them in, say, my home region of New England, it would cover the entire region up to a depth of a little less than five kilometers, which is about three times deeper than the glaciers during the last ice age about 20,000 years ago.
統計起來, 我想出了一個我們可以回答的問題, 那就是,這將需要張多少穿孔卡片? 一張穿孔卡片可以 容納約80個字母。 接著,一個盒子 能被大約2000張卡片裝滿。 我們打個比方, 這些卡片可覆蓋我家鄉 新英格蘭地區的全部面積, 覆蓋深度稍稍低於5000米。 這差不多是上一個冰河時期 冰川深度的三倍。 這大約在兩萬多年前。
So this is impractical, but I think that's about the best answer I could come up with. And I posted it on my website. I wrote it up. And I didn't expect to get an answer from Google, because of course they've been so secretive, they didn't answer of my questions, and so I just put it up and said, well, I guess we'll never know.
即使這想法不切實際, 但這是我所能想到的最佳答案。 我在我官網上發佈並寫出過程, 然而我沒預料到能得到谷歌的回覆。 當然他們一直保密有加, 所以並沒有直接回答我的問題, 我只是順便說說: 我們永遠都不會知道答案。
But then a little while later I got a message, a couple weeks later, from Google, saying, hey, someone here has an envelope for you. So I go and get it, open it up, and it's punch cards. (Laughter) Google-branded punch cards. And on these punch cards, there are a bunch of holes, and I said, thank you, thank you, okay, so what's on here? So I get some software and start reading it, and scan them, and it turns out it's a puzzle. There's a bunch of code, and I get some friends to help, and we crack the code, and then inside that is another code, and then there are some equations, and then we solve those equations, and then finally out pops a message from Google which is their official answer to my article, and it said, "No comment." (Laughter) (Applause)
但是過了一會兒, 也就是幾周前,我收到谷歌的訊息。 我被告知我有封來信。 我拿來打開一看, 裡面全是穿孔卡片。(笑聲) 谷歌牌的穿孔卡片。 卡片上有很多孔。 我還是表示感謝。 好,究竟上面有什麼? 我藉助一些軟體, 開始讀它,並掃描。 結果發現,這是個字謎。 裡面有一堆編碼。 在友人相助下, 我們破解了一個編碼後, 裡面藏著新編碼。 還有一些方程式。 我們算出了這些算式後, 谷歌那邊發來了一條訊息, 也是他們對我文章 作出的官方答案,那即是: 不予置評。 (笑聲)(掌聲)
And I love calculating these kinds of things, and it's not that I love doing the math. I do a lot of math, but I don't really like math for its own sake. What I love is that it lets you take some things that you know, and just by moving symbols around on a piece of paper, find out something that you didn't know that's very surprising. And I have a lot of stupid questions, and I love that math gives the power to answer them sometimes.
我熱愛計算各式奇異的東西。 這不只是因為我喜歡數學。 是的,我常做很多演算, 但我並不針對喜歡數學本身。 我真正喜歡的是數學 能讓你運用你已知的, 在紙上將字符移來移去 來解讀未知。 這非常令人驚奇。 我常有很多笨問題, 我欣賞數學能輔助我 去解決這些問題。
And sometimes not. This is a question I got from a reader, an anonymous reader, and the subject line just said, "Urgent," and this was the entire email: "If people had wheels and could fly, how would we differentiate them from airplanes?" Urgent. (Laughter)
但也不是時時都行得通。 下面是一個讀者給我的問題, 一個匿名讀者, 標題寫了「緊急」一詞。 郵件內容如下: 如果人們有輪子而且有飛行能力, 我們將如何區分這些人和飛機呢? 這是個緊急問題。
And I think there are some questions that math just cannot answer. Thank you. (Applause)
(笑聲)我覺得有對某些問題, 數學無能為力的。 謝謝。 (掌聲)