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So again, idea on the left, fairly straightforward, idea on the right, same but just looks a little different.
从一方面来看，其中蕴含的编程思想是相当简单的，但从另一方面来看，相同中又有那么一丝不同。
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It looks like we're cut off the screen a little bit here, but you can see I've just circled it there.
看起来我们屏幕的边缘部分有些没显示，但是大家可以看到我刚才把它圈出来了。
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If it were just a little bit different I could say, all right, I have a different approximation. But when it's this different, something is wrong. Right?
但是如果仅仅有点差异的话,我可以认为没什么大问题,我得到了一个不太一样的估算，但这确实有差异，出问题了对不对？
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Now, this looks a little scary at first, but this is actually just another statement of the obvious.
起初你可能会觉得这有点儿不可思议，但显而易见，其实还有，另一个声明。
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This is a little bit more of a technical lecture, but I find it just as interesting myself.
这部分比较偏向技术方面,但我自己觉得很有意思
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But before I leave this, let me just point out that this is a little bit more general than it might appear.
在我讲别的之前,我需要指出,这模型比它看起来更具有普遍性
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Not just a little bit better, but significantly better than your competition, because you are a latecomer.
不仅仅是好一点儿，而是好一大截儿，因为你是新来的。
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What this entails is just trying to stop controlling things, but I also mistake it a little bit because by stopping controlling things, you're going to control it more.
必须的是,试着放手不去控制事物，但这也是个悖论,因为想不控制事物，反而会加强控制。
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I mentioned a little bit that this membrane is not just lipid bilayer but there's also proteins that are inserted into the membrane.
我之前说过,这层膜不仅仅是一层脂质双分子层,而是有很多蛋白质嵌插在膜上的
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Okay. I had intended to give you just a little bit of a rhythmic quiz but let's just do one of these things.
好了,我想给你们,做一些小小的节奏测验,不过我们现在就做一个吧
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I'm going to do a few little quizzes today where we're just going to do a show of hands, but beyond that, the clicker will be helpful.
我今天会做几个小测验,让大家来投票表决,不过表决器的作用不止这么简单
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Why not just put our own orgasmitron hat on with a little-- not rat lever, but now human lever-- with the electrodes stimulating our own brains so that we get this intense burst of pleasure?
我们为何不带上电子高潮帽-,把老鼠杠杆变成人类杠杆-,用电极刺激我们的大脑,获得强烈的快感？
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So, we actually met somebody who knew her; and the school is now named after her; but, it's a wonderful, wonderful read, it's just great. My family got a little tired of this and said, "Do we have to--how many more of these places do we have to see in which this woman taught?"
我们碰见一个认识她的人,然后学校也是以她命名,不过那本书真的很好看,就是特别精彩,我家人有点受不了了,然后说"咱还得,到底还得,去多少个这种她教书的地方"
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It might look a little bit similar to a question we just saw, but hopefully you'll find that it is, in fact, not the same question.
它看起来和我们刚看过的一道题很像，但希望你们能发现，这不是同样的题。
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It's a little redundant, admittedly, but I include not the same function, but just its prototype, as I say in the comment here.
它确实是有点长的，但是我包含的不是同一个函数，而只是一个原型，就像我这里的注释所说的。
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I'm narrowing it down. It's getting a little silly but you know I'm going to really be persistent and just follow the rules here of binary search, rather than jumping to conclusions.
按照二分法的规则来做的,而不是直接得出某种结论,很明显这儿我的目的是什么？,显示这两个相同的东西。
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But here, I'm just being a little more pedantic, that's really what a string is.
但是这里，我刚有点迂腐的，那实际上就是字符串。
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But it would just give you a little bit of an idea of shape.
但这会给你们一点关于形状的概念。
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You could absolutely implement something more interesting and something even more animated like we saw on Wednesday or even earlier today, but it takes a little more than just a format string.
你绝对可以实施一些更有用的,和一些更愉快的东西，像我们周三或今天早些时候,看到的，但它不只是,格式化字符串。
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We're going to see variations of this, we're going to see a variation of it called recursion, a little later on, but for now we're just going to talk about how do we do iterations.
我们稍后会去，看它的变量,它的所谓的递归数的变量，但是现在我得先讲讲,怎么来实现迭代。
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Alright, so maybe a little underwhelming and we saw already what this program is going to do but let's just go through this process once before we start doing more interesting things and then we'll come back and at least give you a hint of what some of these syntactic details are doing.
好吧，这个程序也许太平庸了，让人印象不够深刻,我们也知道这个程序是干嘛的,在我们开始更有意思的事情之前,让我们再来讨论一下整个过程后再回来,这些语法细节到底是在做什么呢？,先给你们一点小小的提示。
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So there's a little worry going in about not just this example but about the course, about the whole theme of learning Game Theory.
所以不仅担心这个例子,也会担心这个课程,担心博弈论整个理论
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It looks a little cryptic but it actually just does what it says.
这看起来有点神秘，但是它就是这样做的。
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It just feels a little cleaner, but it's going to depend.
它让人感觉更清晰点，但也要看情况。
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I'm not going to get into in too much detail because we don't have the time, there are other places where you can read about it if you're interested, but I'll just give you a little information on this.
我不会讲太多的细节,时间不太够,如果你们感兴趣,很多资源可供参考,我会给你们点提示
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Well, you can use what's called an array which is kind of a list or a little satchel of that you might physically carry that you can put things in again and again, and with an array can you actually keep track of not just numbers but any kinds of things, other sprites or other pictures, or perhaps a little something like this.
你可以使用数组,它其实是个列表,或者说是个小包,你可以把东西一个个放到里面，通过数组你可以保存任何种类的变量,图片或者像，这个例子中的一些小变量，而不仅仅是数字。
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They might very well be storing the addresses of memory elsewhere, but we just needed them as sort of a cheat sheet, a little address card to know where the original values x and y were.
它们存储在内存的其他地方是可以的,但是我们需要一个备忘单,一个地址卡，来知道,原始的值x和y是什么。
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So just to reinforce this, I could run gcc math2.c but I'm getting a little tired of this a.out convention and recall that there's this utility called "make" that right now doesn't really improve much, other than give it a better name.
所以我强调这点，我可以运行“gcc，math2，c“,但是我不是很喜欢a，out这个默认的名字,想取消它，那么这里有个叫做“make“的命令“,这个命令现在没有很大的改进，只是把用来更改名字用的。
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