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.
我的网站有个功能 每周人们提出他们的假设问题 让我解答 我试图用数学 科学还有 漫画方式来回答这些问题
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)
比如 有人问道 如果你试着击打一个 以90%的光速投出的棒球会怎么样? 于是我做了一些计算 通常来说 当一个物体在空中飞过 空气会环绕在物体周围 但在这个例子里 球飞得太快了 所以空气分子来不及 避开物体 球体会直接撞击并穿过它们 和空气分子的这种相撞 会将球体上的氮原子 碳原子和氢原子击走 把棒球变成极小的粒子 而且会激发球体周围空气 发生热核聚变波 那会导致大量X射线 随着外来粒子 变成一个气泡扩散开 里面是等离子体 聚集在投手区 这些射线将会以比球还稍微快的速度 远离投手区 这些事大约发生在30纳秒 本垒就离得太远 光还没有来得及接触它 这就意味着棒球击手 仍然看见投球手准备抛球 还不知道事情很不对劲 (笑声) 现在 在70纳秒以后 球会达到本垒 或至少是 曾经是球的等离子体 会把球棒 棒球击手 本垒 捕球手以及裁判吞没 然后他们开始全部分解 同时球会承载着这些分解物 穿过挡球网 它同时也在开始分解 那么当你从山坡上 观看这整个过程时 最好是离得远远的 你会看见一道明亮的闪光 几秒钟钟后消失了 接着是一片冲击波扩散出来 粉碎了树木和房屋 当它从球场离开的时候 最终是一片蘑菇云 在一片毁坏的城市上空升起(笑声)
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.
所以 棒球联盟的规则 有点儿模糊 但是针对规则6.02 和5.09 我认为在这个情形下 棒球击手会认为是被投球手击中了 会有资格上一垒 如果它依然存在的话
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.
这就是我常回答的问题 我收到了大家留下的 很多稀奇古怪的问题 有某人问我 从科学角度 隐藏一具尸体 最佳最快办法是什么? 你能快点解答这个问题吗? 还有人写道 以前也有人这样问 你能否能证明心碎以后 还能再次找到爱情? 我还有人发信问 很明显是家庭作业的问题 他们希望我能帮忙
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.
但几个月以前的某一周 我收到一个关于谷歌的问题 如果世界上所有的电子数据都储存在打孔卡上 那么谷歌的仓库会有多大? 现在 谷歌对他们的运营十分保密 所以没人知道谷歌到底有多少数据 实际上 没人真正知道谷歌有多少数据中心 除了谷歌自己的人以外 我也试图弄清楚 我跟他们碰过几次头 想问他们 他们却不透露任何消息
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.
于是我决定自己来搞清楚 我注意到几件事 我先从资金开始 谷歌透露了他们的总支出 那就可以估计 他们可以建立多少个数据中心 因为大的中心需要一定数额的预算 你也可以在他们 占世界硬件市场得份额上押宝 结果是份额相当大 我曾看到过一个估算 我认为谷歌大约每一两分 有一个驱动器失败 而且他们只是把硬盘驱动丢掉 更换一个新的 所以他们消耗了大量硬盘驱动器 因此通过支出 你可以得知他们到底有多少个中心 你也可以观察用电量 看他们需要用多少电 因为需要一定的电力来维持服务器 当然谷歌比大部分的公司更有效率 他们还是有基本的需求量 那可以让你得知他们 服务器数量的底线 你还可以看已知的 数据中心面积 有多大? 有多少房间? 里面可以放多少个服务器? 对于一些数据中心 你也许可以得到这些信息中的两个 你知道他们的开销 同样 因为他们必须同 所在地的政府签约 来得到能源供应 你会知道他们交易的内容 从而得知消耗了多少能源 你可以查看这些数字的比值 然后计算一个 没有这些信息的数据中心 你可以弄清楚 也许你只有这些条件中的一个 你知道面积 那么你就可以推出 电力也许是按比例的 你可以用不同的数据进行同样的运算 通过总储存库数量 服务器的数量 每个服务器所需要的驱动器数量 在每一项上用已知数据 建出一个模型 缩小对未知对象的猜测范围 有些像在你想得知的数据中循环 十分有趣 这个数学计算并不很高级 是真的不比 解决数独更难
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 就是用了所有这些信息 花了一两天的时间来调查 有一些事情我未曾注意 你可以上谷歌 看他们贴出的招人信息 你可以得知他们从何处发掘人才 有时当人们去访问数据中心 他们会用手机拍照 然后贴出来 虽然他们不该这么做 但是你可以由此了解硬件情况 事实上 你还可以留意送皮萨的送餐员 他们其实知道谷歌所有数据中心的位置 至少是有人工作的数据中心
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.
但是我有一个让我感觉 不错的估测 就是覆盖整个谷歌的操作系统的 差不多10EB的数据量 另外还有5EB的离线数据 保存在磁带驱动器里 这印证了谷歌是 世界上最大的消费者
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.
我推断出来的这个估测 这是惊人的数据量 这比世界上任何其它的机构 都大得多 据我们目前所知的。 同时有几个竞争对手 尤其是众所周知的美国国家安全局 用同样一些方法 我们可以观察安全局的数据中心 虽然我们我们不清楚哪里的情况 但很清楚他们的操作系统 谷歌的大小不同
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.
统计起来我想出了 另一个我们可以回答的问题 这些需要多少打孔卡? 一个打孔卡大约能写下 80个字母 一个盒子大约可以装下2000张卡片 然后你把它们放到 比如 我的家乡新英格兰 大概会以将近 5千米的深度覆盖整个地区 这大约是上一个冰河时期 冰川厚度的三倍 那大约是两万年前
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.
这并不切实际 但是我想 这是我能推断出来的最好的答案 于是我把它在网站上贴了出来 我并没有期望得到谷歌回应 因为他们那么神秘 他们不会回答我的任何问题 所以我只是贴出来顺便说 我猜我们永远不会知道
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)
但是过了一阵 几星期以后 我从谷歌得到一个信息 嗨 这儿有一封给你的信 我拿到后打开一看 是打孔卡(笑声) 谷歌出产的打孔卡 在这个打孔卡上有很多孔 我说 谢谢 谢谢啊 后来怎么样了呢? 我用软件开始阅读打孔卡 并且扫描他们 结果 这是一个谜语 有一堆密码 我得到一些朋友的帮助 我们解破了密码 而里面是另一个密码 有一些方程 然后我们解决了这些方程 最后显出了从谷歌发来的信息 是他们对我文章的官方回复: “不予评置“ (笑声)(鼓掌)
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.
我喜欢计算这类奇怪的东西 并不是因为我就喜欢做数学 我做很多演算 但我不因为数学和喜欢数学 我喜欢的是它让你利用 一些已知的东西 只是在纸上将一些符号移来移去 就可以发现一些未知的东西 这令人惊奇 我有很多愚蠢的问题 我喜欢数学给予了 我能解决它们的力量
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)
但有时行不通 这是我从一个读者那里得到的一个问题 一个匿名的读者 主题只是写了“紧急” 邮件内容如下: “如果人们有轮子而且能够飞 我们怎样把他们和飞机区分开来?” 紧急(笑声)
And I think there are some questions that math just cannot answer. Thank you. (Applause)
我认为有些问题 是数学不能回答的 谢谢 (鼓掌)