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But really, the computer's just so fast I'm drawing the same string with just a slightly different number again and again after going to sleep one second at a time.
但是真实地，这个计算机到现在为止,我一次又一次用稍微不同的数字,绘画了相同的字符串,在睡眠1秒钟之后。
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I used to be a campus tour guide, and what I'd say is, you know, everyone uses a number.
我以前是校园的导游，我要说的是，每个人都用数字。
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But we know already from week zero that computers ultimately represent all information with numbers, and if they want to represent letters inside memory, well what do they do or what do they use?
但是自从上周我们已经知道,计算机最终是用数字来表示所有的,信息，如果它们要描绘,在内存中的字母，它们该怎么做，用什么方式呢？
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It says, with six primitives, I can rule the world. With six primitives, I can program anything.
它说，用六个基本类型，我可以规定整个世界，用六个数字，我可以编写任何程序。
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Instead, right off the bat you have some stupid number and you are dragging that through the calculations.
相反，在交卷时，你得到一些愚蠢的数字,并且你还把它用在整个计算中。
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That's going to presumably be given--mathematically if we gave it a number, we'd slap a zero on that.
如果用数学解释,给它一个数字，给它一个零。
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We were talking about the subdivision of that pulse, the organizing of that pulse into meters, and that we had this capacity to indicate what the meter was by these numbers: two-four, and three-four for duple and triple meter.
我们还讲到律动的进一步划分,将律动组织成拍子,与此同时我们能够用一些数字,来表示不同的拍子,比如,用二四拍和三四拍表示二拍子和三拍子
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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
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But Ian Hacking, being a good historian, thought that someone must have had some concept of probability going before even if they didn't quote it as a number the way-- it must have been in their head or in their idea.
但是这位优秀的历史学家伊恩·哈金认为,一定有人在更早时候就用过概率这个概念,即便他们没有用数字来表述,但他们一定有过类似的想法
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I noticed that lots of students here use numbers when they refer to their courses, classes or buildings.
我发现这儿的学生用数字来描述他们的课程和建筑。
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And that was only possible because, besides using the sea, the shipping lanes for travel, which was much faster than overland travel, the Romans maintained roads.
之所以能达到这个数字，原因之一是走海路，用海洋航路运输，比陆路快得多，另一个原因就是修路。
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So multiplying a vector by a number means stretch it by that factor.
所以用数字乘以矢量,就相当于将它伸长了相应的倍数
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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。
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And again, how many numbers have I touched physically this time?
这次我真正用了这些数字几次？
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So what we're going to do is we're going to look at some numbers that are approximately the probabilities of scoring when you kick the penalty kick in different directions.
接下来,我们来用数字表示,在不同角度踢点球射门,能够得分的概率
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That means starting at the first one, I'm going to do something to it. And what am I'm going to do? I'm going to take that character, convert it back into an integer, and add it into some digits. And I've done a little short hand here, which is I should have said some digits is equal to some digits plus this.
这意味着从第一个字符开始，我要对他们进行一些操作,我要去做什么呢？我要取得这个字符，然后把它转换为整数,然后加到某些数上面去,我在这里用了一些缩写,我本来应该写一个数字等于这个数字。
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All right, so here once again is our same matrix with me and my pair, choosing actions Alpha and Beta, but this time I'm going to put numbers in here.
我们首先讨论我和我对手,选择α或β的矩阵,不过这次我们用数字来表述
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Pick any two perpendicular directions Then the same entity, the same arrow which has an existence of its own, independent of axis, can be described by you and me using different numbers.
选取两个互相垂直的方向,这样同样的物体,同一矢量,并且是独立于坐标轴而存在的,可以被你和我用不同的数字来描述
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Do you realize that this is a pair of simultaneous equations in which you can solve for these two unknowns, if you like, in terms of these two knowns and these coefficients, which are like these numbers, 3, 2, 4, and 6?
你们是否发现这其实就是一个方程组,你可以用它来解出这两个未知量,你愿意的话,可以用这两个已知量,和这些系数,比如这些数字,3,2,4和6
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And, that gives you a number for the fluorine, minus 0.29. Now, if you do the same for the hydrogen, you'll come up with the same number.
然后给出F的数字，负的0。29，如果同样的用H来计算，你会得到一样的答案。
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Yeah. So pretty much everything is numbers in terms of classes and courses.
所以，几乎所有的事情，包括课程，都是用数字表示的。
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In which I said, you know, I didn't like the fact that things like plus are overloaded, because you can use plus to add strings, you can use plus to add numbers, you can use plus to add floats.
那个玩笑是这样的，你们懂得，我并不喜欢,加法被重载这样的事情，但是你可以用加法，来对字符串进行合并，你可以用加法来加数字。
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And it boils down to modifying the format string with just a simple number.
它归结于是用一个简单的数字来,修改字符串的格式。
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You can either think of it as an arrow and imagine the arrow, or you can reduce it to a pair of numbers, x and y.
你既可以用有向线段来表示,也可以用一组数字来表示,x 和 y
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So, for the most part any time we talk about or draw pointers an arrow suffices, which really 71 in there is a number like 71, which is the literal byte that the F is actually in in RAM, but frankly who cares?
所以，每次我们讨论,或者用箭头表示指针,在指针里面有一个数字，如,那是F在RAM中的字节，但是谁在乎它呢？
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This might look a little cryptic at first, but it turns there is some very obvious patterns here, for instance. According to this chart, if you want to represent the letter A A in the so called ASCII system, what number do you actually use to do so?
起初，它看起来有点神秘，但你会发现它有一些明显的对应模式，这里就有例子，根据图表，在所谓的ASCII系统中,你想表示字母，你该用哪些数字呢？
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