people submit hypothetical questions

我的網站上有一個功能，

for me to answer,

在那裡人們每週可以向我發問，

and I try to answer them using math, science

一些假設性的問題。

and comics.

而我會盡量以數學、科學

So for example, one person asked,

和漫畫的形式來回答。

what would happen if you tried to hit a baseball

例如，有人問：

pitched at 90 percent of the speed of light?

如果你試圖擊中一個速度為高達

So I did some calculations.

光速的90%的棒球，將會怎麼樣？

Now, normally, when an object flies through the air,

然後我做了計算，

the air will flow around the object,

通常情況下，當一個物體在空氣中飛行，

but in this case, the ball would be going so fast

空氣將繞著此物環流。

that the air molecules wouldn't have time

但是對於這個案例，

to move out of the way.

棒球速度將會過快，

The ball would smash right into and through them,

以至於空氣分子來不及讓道。

and the collisions with these air molecules

棒球將會碰撞空氣並穿透空氣分子，

would knock away the nitrogen,

然後這些與空氣分子的撞擊運動，

carbon and hydrogen from the ball,

將會把氮、碳、氫

fragmenting it off into tiny particles,

從棒球那擊退，

and also triggering waves of thermonuclear fusion

使球破裂成極小粒子，

in the air around it.

同時也在空氣中引發熱核聚變的波。

This would result in a flood of x-rays

這將導致

that would spread out in a bubble

大量的X光線擴散開成一個大泡沫，

along with exotic particles,

並伴隨著一些外來粒子，

plasma inside, centered on the pitcher's mound,

泡沫裡面是等離子，集中在投球區。

and that would move away from the pitcher's mound

然後這些X光線將

slightly faster than the ball.

以比球稍快的速度遠離棒球。

Now at this point, about 30 nanoseconds in,

此時，大約在 30 奈秒內，

the home plate is far enough away

本壘板遠到

that light hasn't had time to reach it,

光來不及去觸及它。

which means the batter

這意味著球棒打者仍能

still sees the pitcher about to throw

看見投手即將拋球的動作，

and has no idea that anything is wrong.

並且沒想到事情不對勁。

(Laughter)

（笑聲）

Now, after 70 nanoseconds,

現在，70 奈秒之後，

the ball will reach home plate,

這個棒球將會擊中本壘板，

or at least the cloud of expanding plasma

亦或是那些球分離出的

that used to be the ball,

擴散的等離子集合體，

and it will engulf the bat and the batter

它將吞沒球棒、打者、

and the plate and the catcher and the umpire

本壘板、補手和裁判，

and start disintegrating them all

然後將它們全部分解，

as it also starts to carry them backward

同時棒球運載這些分解物

through the backstop, which also starts to disintegrate.

穿過擋球網，擋球網也被分解。

So if you were watching this whole thing

因此如果你從一座山上

from a hill,

觀察全過程

ideally, far away,

理想狀態下，要夠遠，

what you'd see is a bright flash of light

你看到的是一道閃光，

that would fade over a few seconds,

在數秒後消褪。

followed by a blast wave spreading out,

同時伴隨閃光的衝擊波會擴散

shredding trees and houses

並撕毀樹和房子，

as it moves away from the stadium,

與此同時它遠離運動場，

and then eventually a mushroom cloud

最終一朵蘑菇雲

rising up over the ruined city. (Laughter)

從這廢城中升起。

So the Major League Baseball rules

美國職業棒球大聯盟

are a little bit hazy,

對此的評分規則頗為模糊，

but — (Laughter) — under rule 6.02 and 5.09,

（笑聲）但針對規則6.02和5.09，

I think that in this situation,

我想在這種情況下，

the batter would be considered hit by pitch

打者將會被認為被球擊中，

and would be eligible to take first base,

並有資格上一壘，

if it still existed.

如果壘包還存在的話。

So this is the kind of question I answer,

這些就是我常回答的問題。

and I get people writing in with

我讓大家寫下的

a lot of other strange questions.

各種千奇百怪的問題。

I've had someone write and say,

今天有人問我：

scientifically speaking, what is the best

從科學的角度，

and fastest way to hide a body?

有沒有藏具屍體最佳最快的方法？

Can you do this one soon?

可以麻煩你盡快解答嗎？

And I had someone write in,

也有人問，

I've had people write in about,

有人寫，

can you prove whether or not you can find love again

你能否證明

after your heart's broken?

當你傷心欲絕時，還能否重拾愛情？

And I've had people send in

還有人發給我

what are clearly homework questions

很明顯是作業題目，

they're trying to get me to do for them.

希望我可以替他們效勞。

But one week, a couple months ago,

但在幾個月前的某個星期，

I got a question that was actually about Google.

有人問了我一個關於谷歌的問題，

If all digital data in the world were stored on punch cards,

如果把世界上所有數據保存在穿孔卡片上，

how big would Google's data warehouse be?

那麼谷歌的數據庫要多大才足夠？

Now, Google's pretty secretive about their operations,

然而谷歌對自身運營情況十分保密，

so no one really knows how much data Google has,

無人曉得谷歌數據有多少。

and in fact, no one really knows how many data centers Google has,

實際上，沒人真正清楚谷歌擁有多少數據中心，

except people at Google itself.

除了谷歌內部人員外。

And I've tried, I've met them a few times,

我嘗試過去瞭解並與他們碰過幾次面，

tried asking them, and they aren't revealing anything.

可他們守口如瓶。

So I decided to try to figure this out myself.

因此我決定自尋答案。

There are a few things that I looked at here.

有注意到幾個方面，

I started with money.

先從資金說起，

Google has to reveal how much they spend,

谷歌必須得公開它們的開支狀況，

in general, and that lets you put some caps

那麼，這就能夠限制

on how many data centers could they be building,

它們可建的數據中心的數量，

because a big data center costs a certain amount of money.

因為一個大型數據中心花費相當多。

And you can also then put a cap on

這同樣也可以限制

how much of the world hard drive market are they taking up,

他們佔世界硬碟市場的份量。

which turns out, it's pretty sizable.

這數額也是相當可觀的。

I read a calculation at one point,

我曾經看到過一個估算，我認為谷歌

I think Google has a drive failure

每一到兩秒會發生硬碟故障。

about every minute or two,

他們會立刻扔掉壞的硬碟，

and they just throw out the hard drive

並且換上新的。

and swap in a new one.

所以這過程消耗了大量的硬碟。

So they go through a huge number of them.

我們再回到資金方面，

And so by looking at money,

你可以大致瞭解

you can get an idea of how many of these centers they have.

谷歌擁有多少數據中心，

You can also look at power.

你也可以觀察能源方面，

You can look at how much electricity they need,

看看他們需要多少電量。

because you need a certain amount of electricity to run the servers,

這是因為運行伺服器需要相當多的電力，

and Google is more efficient than most,

在這方面谷歌比眾多同行更高效。

but they still have some basic requirements,

然而他們還是遵循一些基本要求，

and that lets you put a limit

然後讓你對他們的伺服器數量設限。

on the number of servers that they have.

你也可以從面積入手，

You can also look at square footage and see

觀察你所知道的數據中心：

of the data centers that you know,

它們有多大？

how big are they?

容量是多少？

How much room is that?

裡面可以容納多少伺服器支架？

How many server racks could you fit in there?

對於一些數據中心，

And for some data centers,

你或許會獲取其中兩份訊息。

you might get two of these pieces of information.

假設你知道他們的開支，

You know how much they spent,

同樣地，因為他們必須和地方政府

and they also, say, because they had to contract

簽訂協議來獲取能源。

with the local government

你會大概知道他們交易的內容，

to get the power provided,

知道有多少能源被消耗。

you might know what they made a deal to buy,

接著，你可以看看這些數目的比率，

so you know how much power it takes.

然後計算一個

Then you can look at the ratios of those numbers,

你不熟識的數據中心。

and figure out for a data center

這也能計算，

where you don't have that information,

或許你只知道其中一個數據，

you can figure out,

你知道面積，

but maybe you only have one of those,

就能知道或許能量是成比例的。

you know the square footage, then you could figure out

你可以運用各種不同數據

well, maybe the power is proportional.

來進行相同運算。通過對總容量、

And you can do this same thing with a lot of different quantities,

伺服器數目、每台伺服器的

you know, with guesses about the total amount of storage,

硬碟數目的估算，在每一項中

the number of servers, the number of drives per server,

用已知來擬建出一個模型，

and in each case using what you know

縮小對未知對象的猜測範圍。

to come up with a model that narrows down

這有點像在這些數據裡循環，

your guesses for the things that you don't know.

樂趣十足。

It's sort of circling around the number you're trying to get.

數學計算並不是完全先進，

And this is a lot of fun.

說實在這不過就像

The math is not all that advanced,

做出一道數獨題目罷了。

and really it's like nothing more than

我所做的只是瀏覽所有相關信息，

solving a sudoku puzzle.

用一兩天的時間做調查。

So what I did, I went through all of this information,

還有，我未曾注意到這幾方面：

spent a day or two researching.

而你可多留意

And there are some things I didn't look at.

谷歌發佈的徵才啟示。

You could always look at the Google

由此可知他們在哪些地方需要員工。

recruitment messages that they post.

當有人參觀某數據中心時，

That gives you an idea of where they have people.

他們會用手機拍照並公開照片。

Sometimes, when people visit a data center,

雖然他們不應該這麼做，

they'll take a cell-cam photo and post it,

但你可以由此得知硬碟的情況。

and they aren't supposed to,

實際上，你僅需留意那些比薩餅速遞員，

but you can learn things about their hardware that way.

他們其實知道 所有谷歌數據中心的具體位置，

And in fact, you can just look at pizza delivery drivers.

最起碼是那些有人的數據中心。

Turns out, they know where all the Google data centers are,

然而我想到了一個讓我

at least the ones that have people in them.

興奮不已的一個估測：

But I came up with my estimate,

那是關於覆蓋整個

which I felt pretty good about,

谷歌操作系統的10 EB的數據量，

that was about 10 exabytes of data

另外大約五個EB的離線數據

across all of Google's operations,

被保存在磁帶伺服器裡。

and then another maybe five exabytes or so

這印證了谷歌

of offline storage in tape drives,

是世界上最大的消耗者。

which it turns out Google is

所以我想出了這個估測，

about the world's largest consumer of.

這一數值也是大到相當驚人。

So I came up with this estimate, and this is

這超過了世界上其他任何一個機構，

a staggering amount of data.

就目前已知的來說。

It's quite a bit more than any other organization

同時總會有些其他競爭對手，

in the world has, as far as we know.

尤其是眾所周知的美國國家安全局，

There's a couple of other contenders,

但運用以上某些相同的方法，

especially everyone always thinks of the NSA.

我們可以觀察到國家安全局的數據中心。

But using some of these same methods,

雖然我們並不知道那裡的具體情況，

we can look at the NSA's data centers,

但很清楚的是， 它們的操作系統大小和谷歌的不同。

and figure out, you know, we don't know what's going on there,

統計起來，

but it's pretty clear that their operation

我想出了一個我們可以回答的問題，

is not the size of Google's.

那就是，這將需要張多少穿孔卡片？

Adding all of this up, I came up with

一張穿孔卡片可以

the other thing that we can answer, which is,

容納約80個字母。

how many punch cards would this take?

接著，一個盒子 能被大約2000張卡片裝滿。

And so a punch card can hold

我們打個比方，

about 80 characters,

這些卡片可覆蓋我家鄉

and you can fit about 2,000 or so cards into a box,

新英格蘭地區的全部面積，

and you put them in, say,

覆蓋深度稍稍低於5000米。

my home region of New England,

這差不多是上一個冰河時期 冰川深度的三倍。

it would cover the entire region

這大約在兩萬多年前。

up to a depth of a little less than five kilometers,

即使這想法不切實際，

which is about three times deeper

但這是我所能想到的最佳答案。

than the glaciers during the last ice age

我在我官網上發佈並寫出過程，

about 20,000 years ago.

然而我沒預料到能得到谷歌的回覆。

So this is impractical, but I think

當然他們一直保密有加，

that's about the best answer I could come up with.

所以並沒有直接回答我的問題，

And I posted it on my website. I wrote it up.

我只是順便說說：

And I didn't expect to get an answer from Google,

我們永遠都不會知道答案。

because of course they've been so secretive,

但是過了一會兒，

they didn't answer of my questions,

也就是幾周前，我收到谷歌的訊息。

and so I just put it up and said,

我被告知我有封來信。

well, I guess we'll never know.

我拿來打開一看，

But then a little while later

裡面全是穿孔卡片。（笑聲）

I got a message, a couple weeks later, from Google,

谷歌牌的穿孔卡片。

saying, hey, someone here has an envelope for you.

卡片上有很多孔。

So I go and get it, open it up,

我還是表示感謝。

and it's punch cards. (Laughter)

好，究竟上面有什麼？

Google-branded punch cards.

我藉助一些軟體，

And on these punch cards, there are a bunch of holes,

開始讀它，並掃描。

and I said, thank you, thank you,

結果發現，這是個字謎。

okay, so what's on here?

裡面有一堆編碼。

So I get some software and start reading it,

在友人相助下，

and scan them, and it turns out

我們破解了一個編碼後， 裡面藏著新編碼。

it's a puzzle.

還有一些方程式。

There's a bunch of code,

我們算出了這些算式後，

and I get some friends to help,

谷歌那邊發來了一條訊息，

and we crack the code, and then inside that is another code,

也是他們對我文章

and then there are some equations,

作出的官方答案，那即是：

and then we solve those equations,

不予置評。

and then finally out pops a message from Google

（笑聲）（掌聲）

which is their official answer to my article,

我熱愛計算各式奇異的東西。

and it said, "No comment."

這不只是因為我喜歡數學。

(Laughter) (Applause)

是的，我常做很多演算，

And I love calculating these kinds of things,

但我並不針對喜歡數學本身。

and it's not that I love doing the math.

我真正喜歡的是數學

I do a lot of math,

能讓你運用你已知的，

but I don't really like math for its own sake.

在紙上將字符移來移去

What I love is that it lets you take

來解讀未知。

some things that you know,

這非常令人驚奇。

and just by moving symbols around on a piece of paper,

我常有很多笨問題，

find out something that you didn't know

我欣賞數學能輔助我

that's very surprising.

去解決這些問題。

And I have a lot of stupid questions,

但也不是時時都行得通。

and I love that math gives the power

下面是一個讀者給我的問題，

to answer them sometimes.

一個匿名讀者，

And sometimes not.

標題寫了「緊急」一詞。

This is a question I got from a reader,

郵件內容如下：

an anonymous reader,

如果人們有輪子而且有飛行能力，

and the subject line just said, "Urgent,"

我們將如何區分這些人和飛機呢？

and this was the entire email:

這是個緊急問題。

"If people had wheels and could fly,

（笑聲）我覺得有對某些問題，

how would we differentiate them from airplanes?"

數學無能為力的。

Urgent. (Laughter)

謝謝。

And I think there are some questions

（掌聲）

that math just cannot answer.

Thank you.

(Applause)