Some people asked me, if they bought the earlier version of the text, you can find the translation to the earlier version of the text on these question numbers.

有人问我，如果他们买了这本书的早期版本，你们找到这本书早期版本的翻译,关于这些问题的数字。

麻省理工公开课 - 固态化学导论课程节选

Let's look at the numbers here. We had 15, 20, then this one, up to 20, 25 and so on.

看看这些数字,15%,20%,还有20%,25% 等等

耶鲁公开课 - 博弈论课程节选

and if the bits represent one here, 1 those exact same bits are going to represent one here.

如果这个二进制数字在这里表示，这些相同的二进制也将表示。

哈佛公开课 - 计算机科学课程节选

Twenty-eight percent-- only 28% are eating the recommended amount of vegetables, so this is a pretty discouraging number.

8%,只有28%的人蔬菜摄入达标,这些数字可真叫人泄气

耶鲁公开课 - 关于食物的心理学、生物学和政治学课程节选

What he did was coined this. But he found that by taking the reciprocal of the wavelengths, you have four numbers, he took the reciprocals of those wavelengths and found that they fit a numerical sequence.

这些都是由他所做的一切得来的,但是他发现通过取波长的倒数，你有四个数字，他取了这些波长的倒数,发现它们构成了一个数列。

麻省理工公开课 - 固态化学导论课程节选

Both of us have probably programmed in more than those number of languages, at least programmed that many, since we taught in those languages.

我们俩大概都用过,多于那个数字的语言编过程，自从我们开始教这些语言开始，至少有那么多种吧。

麻省理工公开课 - 计算机科学及编程导论课程节选

We have to add it all up so it's not just numbers, three against one; it's also all of those people at home.

得把这些加起来考虑,所以就不只是这个数字，三比一;,还要加上这三人的家人。

耶鲁公开课 - 公正课程节选

If I were to rip these pieces of paper, I wouldn't be destroying the number two.

要是我把这些纸撕碎,数字2并没有被我给损毁了

耶鲁公开课 - 死亡课程节选

So let's just plug in these numbers here.

让我们把这些数字代入进去。

麻省理工公开课 - 化学原理课程节选

Now, we know how the numbers come in.

现在我们知道这些数字是如何得到的了

耶鲁公开课 - 基础物理课程节选

This is incredibly important because,when you look at this number that we started out with,saying the benchmark was 9.9 but net of fees the managers on average only lost thirty basis points--or .3% -you'd say,well that's a game I don't mind playing.

这极其重要,因为当你看这些数字时,刚才说过基准收益是9.9%,但是主动管理型基金经理人的平均净利润,只落后了30个基点或者说0.3%,你可能会说这个游戏,我不介意玩一玩

耶鲁公开课 - 金融市场课程节选

Seventy-nine. In fact, if you add up each of these numbers, 9 you should get the decimal number 79 79 from this binary number here.

9，事实上，如果你把这些数字累加，你应该能从这些二进制中9,得到十进制数。

哈佛公开课 - 计算机科学课程节选

And some of you will perhaps recognize these numbers, but that's not really relevant for now.

有些人可能事先见过这些数字,但是现在这都无关紧要

耶鲁公开课 - 博弈论课程节选

So let's take those ideas and go back to the numbers game from last time.

那么我们带着这些方法,回到上次的数字游戏中

耶鲁公开课 - 博弈论课程节选

Is it government's responsibility to correct this or do people just need to buck up and change their lives in a way that turns these numbers around?

纠正这些行为是政府的责任,还是只需人们行动起来,改变自己的生活方式,来挽回这些数字代表的趋势

耶鲁公开课 - 关于食物的心理学、生物学和政治学课程节选

The bad news is I hate this number. Look it.

我讨厌这些数字，看看。

麻省理工公开课 - 固态化学导论课程节选

And he is playing with those numbers.

他也一直在和这些数字打交道。

麻省理工公开课 - 固态化学导论课程节选

So, using the terminology of chemists, which is a good thing to do, because in this course we are all chemists, we want to make sure that we're not using just the physical description of the numbers, but that we can correlate it to 1 0 0 what we understand as orbitals, and instead of 1, 0, 0, 1s we call this the 1 s orbital.

我们最好学会，利用这些化学术语，因为我们这课,就是关于化学的，我们,不仅要知道，这些数字,的物理描述，还要能把它,和我们知道的轨道联系起来，我们叫它。

麻省理工公开课 - 化学原理课程节选

So, what's the idea? If I know what my hash function does, it maps, in this case characters into a range zero to 256, which is zero to 255, I create a list that long, and I simply mark things.

我知道我的哈希函数做什么,在这个例子中，它将字母，映射成0到255的256个数字，我创建了一个这么长的列表，并且我只是简单的标志这些东西。

麻省理工公开课 - 计算机科学及编程导论课程节选

So you can't do this, because you're going to lose track of the numbers if you do that.

你不能这样做，因为你那样做，你将会和,这些数字失去联系。

哈佛公开课 - 计算机科学课程节选

I'm out of numbers here, so now I can blindly write down the rest of these numbers.

这儿再没有数字了，所以我可以直接,将剩下的这些数字写下来。

哈佛公开课 - 计算机科学课程节选

So, how do you go from just numbers, zeros and ones to actually useful information?

那么，你该怎样由这些数字0和,1来表述有用信息？

哈佛公开课 - 计算机科学课程节选

And again, how many numbers have I touched physically this time?

这次我真正用了这些数字几次？

哈佛公开课 - 计算机科学课程节选

Assuming these numbers are true, what jumps out at you from this picture?

假设这些数字都是真实准确的,你能从这张图中看出什么

耶鲁公开课 - 博弈论课程节选

Well the first idea is that these numbers represent utiles or utilities.

首先这些数字代表了效用或者说功利

耶鲁公开课 - 博弈论课程节选

So that's how you get a sense of these numbers.

这样你对这些数字就有个概念

耶鲁公开课 - 关于食物的心理学、生物学和政治学课程节选

The algebra is, of course, very trivial here.

这些数字本身当然是平凡无奇

耶鲁公开课 - 基础物理课程节选

So the strategy choices, we're not going to do it in hours, let's just normalize and regard these choices as living in 0 to 4, and you can choose any number of hours between 0 and 4.

我们用小时数来表示策略吧,用0到4的数字来标记这些策略,你可以从0到4中任选工作的小时数

耶鲁公开课 - 博弈论课程节选

But there's an important thing going on here, if I in fact wanted to combine those into a string I should have told the machine to do that, and I can do that, by explicitly saying, take that, which is a number, then add it to that string.

但是这里有个很重要的事情，实际上想要把这些加到一个字符串里面去,我应该告诉计算机去做这个，我应该这么做，通过明确的输入，也就是把这个对象，一个数字，然后把它加到一个字符串里面去。

麻省理工公开课 - 计算机科学及编程导论课程节选

So things are not... I haven't given you the numbers for the middle but... So you can see that whoever it was who said, you're slightly better off, you score with slightly higher probabilities when you kick to your natural side is exactly right.

所以事情不像是……,我虽然没有给出中路的概率,但是,我们先不管这些数字到底是谁总结的,我们发现我们走运了,当你从自然方向攻门的时候,你进球的概率会稍微提高

耶鲁公开课 - 博弈论课程节选