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So if you need more--bigger numbers, you just have a 16's column and a 32's column, and so forth.
所以，你需要有一个更大的数字，就采用16位，32位等等。
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And then that one's got an 18 on it, so I had it for like two years now.
然后那个上面有一个数字18，所以我拥有它两年了。
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And in the--from 1989 to 2006 there was a pretty significant decline, but even in 1989 the numbers weren't very high.
我们看到,从1989到,2006年有个很明显的下降,但是即使是在1989年这个数字也不高
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So a bit of uninteresting math, a bit of focus on sizes of types, but any questions on syntax or concepts thus far before we now put this to the test?
一些比较无趣的数字，一些关于类型的大小,在我们现在进行试验之前,你们对这其中的语法或概念有什么问题吗？
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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。
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Another way to say that it's going to be less, so you don't get confused with that the fact this is in the numerator here, there is that negative sign so it's less energy but it's a bigger negative number that gives us that less energy there.
另一个方式去说它将会变得很低实用，你们不用在这里的计算器的事实感到迷惑,这里有一个负号实用，它是更少的能量,但它是一个更大的数字,这里了它给了我们更少的能量。
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All of you, at the end last time, wrote down this number and handed them in so we had one number, one strategy choice for each person in the class.
上节课大家都交上来了一个数字,所以每个人都有对应的数字,这就是每个人都有一个策略
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We are able to talk about the fact that two plus one equals three, but it's not as though we ever come across numbers-- number three itself--anywhere in the empirical world.
我们可与去探讨,二加一等于三的这个事实,但是我们不可能有一天真的碰到数字,在现实世界中碰到个叫"数字三"的东西
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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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The Swedish army was 110,000 people, soldiers. That's an awful lot.
瑞典有十一万军队 数字多得惊人
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So, the bid price is the--they don't do it in terms of price, they do it in terms of discount so the bid discount rate- there would be two numbers for each.
出价,往往不以报价的形式出现,而是以折扣率,出价的折扣率,有两个相关的数字
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And like the first one, I think that one's got a 16 on it, all right?
就像第一个，我想那个上面有一个数字16，对吗？
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Fast forward mid-semester when we talk about cryptography and scrambling information, we need the ability to express ourselves in words, not just numbers, and we have that already.
回想一下期中的时候，我们讨论过密码学,和一些不规则信息,我们需要话语来表达自己，而不是数字，其实我们已经有了。
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So that's how you get a sense of these numbers.
这样你对这些数字就有个概念
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If a person has the basic concept down, regardless of numerical errors, if the person has the basic concept down, he or she must get at least five out of ten.
如果一个人有一些基本的概念，不管一些数字上的错误，如果他有基本的概念，至少都能够得到一半的分。
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> Wow 210 and 233 and the total 550 that the teaching fellows got was 550 give or take so a little take maybe, but let's call it a success.
10和233，但,老师给的数字是,有一点小出入，但我们就算是成功了。
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Given the number of people in the room there may be multiple winners, I accept that possibility.
教室里每个人都写个数字,确实有可能出现多个赢家
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We got an easy one. Let's just for the heck of it I should have found some better examples before I tried this. No mutant spiders here.
我们有了个简单的数字,让我们以防万一,我应该在尝试这个之前找几个更好的例子。
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I have to have a whole number of wavelengths to get around the circumference.
我必须要有个关于波长的总体数字,测量周长。
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But for numbers, for example, we can have a variety of types.
可是对于比如数字，我们有很多种类型。
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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。
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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 think one of the classic ones for strings is called the Rabin-Karp algorithm. And it's simply the same idea that you have a mapping from your import into a set of integers.
我认为字符串哈希,最经典的是Rabin-Karp算法,它只是简单的相同概念,你有一个映射关系将你的输入映射成一组数字。
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You'll notice I have the string with the number 1 MIT a string with MIT, and then it just a plain old number, not a string, again it didn't quite give me 3.3 for reasons we've talked before, a and now it in the list a.
你们可以看到这儿有个以字符串1,形式显示的数字1，1个字符串,还有一个非字符串形式的平常数字,结果并不是3。3，原因之前我们，已经讨论过了，还有一个在list中的。
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Well it turns out a bunch of years ago people just decided that if we have the ability to express numbers and we actually care about expressing letters of the alphabet, well we just need some kind of mapping between one and the other, ASCII and so thus was born what's generally called the ASCII.
结果证实，数年前,人们觉得如果我们,有数字表达能力,而我们真正在乎其实是字符的表达，那么我们就需要数字和字符的某种对应关系，于是就有了俗称的。
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This is a game where you get a little plastic device, it's got 15 plastic numbers on it and one hole in this little plastic board and you can move those numbers up, down, left to right, and the goal is to take what's a random assortment of tiles and arrange them in numeric order and that's one of these little things you can play sort of absentmindedly.
在这个游戏中，你会拿到一个可塑的装置，上面有15个数字和一个孔,你可以将数字上下移动，左右移动，目标就是,拿到一个随机的组合后,将其按数字顺序排列,这个你可以随便玩玩。
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It's a secret number so that if Julius Caesar scrambled his message with the key 13, well, then the recipient had better know what that number is or realistically, -- and this is why it's kind of hard to buy -- into some of these age old algorithms, -- what would an alternative approach be to figuring out Julius Caesar's messages to his generals if he didn't know that secret number was 13?
它是一个机密的数字，以至于,如果凯撒大帝使用密钥13加密了它的消息，然后接收者最好知道那个数字是什么,实际上--这就是为什么很难,破解这些古老的算法-,有什么变换方法使凯撒大帝的将军,可以解密凯撒大帝的消息，如果他不知道,那个机密数字是13呢？
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So unlike an int, this is the type of number that can have numbers after a decimal place.
所以，不同于int，这个类型的数字,可以有小数位。
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I've got each person's name and I've got a number from each person: a strategy from each person.
我有你们每个人的名字和所选数字,即每个人的策略
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But you don't know that there is an easy one for you down at number four 4 if you haven't bothered to look at number four.
但是你不知道,在数字4的时候会有一个简单的题目,如果你没有尝试去看数字。
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