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Where on the picture, let me do a bit more cold calling here, where on the picture maximizes total industry profits?
我随便找个同学来回答一下,在图上哪一点实现了行业最大利润
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Maybe I should make a bigger-- let me do it here, I can fit it in here I think.
也许我该弄个更大的...,要不我画在这儿吧
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Now let me do it a second time to show you that -- I'm saying this poorly.
还不至于如此呢,现在让我再做一次给你们看。
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Just to make sure you've understood this, let me do an example on the board.
为了让大家都听明白,我来举个例子
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I have yet to show you the solution to a wave function for the hydrogen atom, so let me do that here, and then we'll build back up to probability densities, and it turns out that if we're talking about any wave function, we can actually break it up into two components, which are called the radial wave function and angular wave function.
我还没有给你们看过,氢原子波函数的解，让我现在给你们看一下，然后再来说,概率密度，实际上,对于任何一个波函数来说，我们可以把它,分解为两部分，分别叫做径向波函数,和角向波函数。
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long l So let me try this, long l, and then let me do a little Copy Paste here and say a long is actually the size of l. So let me quit that program; recompile.
让我们来试一下，然后我在这里复制粘贴一下,这里long的大小实际上是l的大小，所以让我退出,那个程序，重新编译。
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I hope you enjoy using Star Festival and do let me know the questions that you are trying to answer.
事情，我希望你使用“七夕“愉快并让我了解,你想找出答案的那些问题。
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Having said that, let's assume that we do have the slower tempo here, one--Let me play a little bit at the piano.
说完这些,假设我们运用较慢的速度,一,我还是在钢琴上弹一下
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It doesn't really-- well, let me just say what the polis claims to do here in Homer.
这并不算...,我还是说说在荷马时代,城邦是如何阐明法律的
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But let me just ask you in the brown shirt, just curious, why do you think ? he is innocent and should be acquitted?
我想请问穿褐色上衣的同学，出于好奇,为何你认为他是无辜且应无罪开释？
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There's a perfectly good reason why I let them do all those things to me.
我一定有很充分的理由,让他们这样来折磨我。
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I guess it's not macho enough, John, to just, you know, you know, go off and do things by hand, you ought to just run them, but it's a valuable tool to get into, so let me do that here.
我认为这不太男人了，John，你知道的，他们仅仅是认为比起用手做来,更应该直接去运行程序，但是这确实是调试代码的非常有价值的工具，让我在这里给大家演示下吧。
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And if I'm already in this habit, let my software, let my computer do that thinking for me and bubble up to the top of my attention what I should address first.
如果我已经有这样的习惯，让我的软件，或者电脑为我考虑这些事情，自动的把这,些邮件放到的最醒目的地方---最上面。
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So let's do a quick clicker question, and you tell me how many valence electrons does fluorine have? Remember, valence electrons are different from core, they're only the outer-most electrons in the outer-most shell.
那么让我们来做一个小选择题，请大家来告诉我,氟有多少个价电子，要记得，价电子与芯电子不同，它们是在最外壳层的最靠外面的电子。
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So let me just tell what we are going to do next.
接下来谈谈后面怎么做。
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So now let me just do some grade school substitution.
接下来做一些简单的代换。
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Okay, so let me do that and you'll see what I mean.
我来做个示范,你就明白我的意思了
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So let me write that down, it's how much memory do I need to complete a computation.
让我把它写下来,当我计算的时候。
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So even within this framework of, given a description of a computation as a set of steps, in the idea that I could build a circuit to do it, let me suggest for you what would be a wonderful circuit to build.
所以即使需要在将计算描述，当成一系列步骤中的一步,这个框架之内,我也完全可以建立一个线路,来完成那个想法，让我为你们假设能建造起,一个多么棒的线路吧。
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I'm the sort of person who will let people do those things to me.
我就是那种愿意让别人折磨我的人。
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How could we do better? Let me set the stage.
我们怎样能做的更好？
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We'll come back and discuss it more in a second, but before I do, let me mention that the same model, exactly the same idea, has an application in Economics.
我们一会再深入导论这个问题,在此之前,我再来列举一个模型,是经济学里面一个完全类似的模型
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- And we could never do this-- and one could never do this experiment today but let me go through it with you and you'll apologize for its--some of its qualities.
我们不能再-,这种实验，如今再不能做了,我给你们从头至尾讲一下,因为实验中性别歧视的原因，我再次道歉。
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Here's what I do. I change-- oops! Let me do that this way-- I change last to here, and keep first there, and I throw away all of that. All right?
接下来，我来改过来,此时这里是last，first位置没变,把这些都擦掉，好？
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So I guess I should go back, and let me do this correctly this way. Again, I can look at test, test and I guess test now if I want to get the element out-- angle bracket or square bracket?
但是这不是我想要的对不对？,我认为我该回到这里，让我改正这个错误，好，那么我还是对元组,那么现在我想从test中取出元素来？
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What in the world does that have to do with my divisor example? Well, actually, before I do that let me in fact fill in a piece here.
那么这到底跟我的除数的例子有什么关系呢？,好，实际上，在我讲之前请我先来补充一点，大家还记得我说过,我们可以概念上认为。
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All right. I want to do one more extended example here., because we've got another piece to do, but I want to capture this, because it's important, so let me again try and say it the following way.
很好的问题，谢谢你,我还要带大家去看一个延伸的例子,尽管我们还有别的事情要去做，但是我还是想提提这一点，因为这很重要。
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Let me ask you if you have questions about the course in general and do you have questions of me at this point?
我来问问大家,你们对这门课程有何疑问,或者对我有何疑问呢
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And then I could do things like again, say, okay having done, that let me just run it here, run that, so I've now got polar point 1, and polar point 2.
然后给它们赋值半径和角度，然后我可以进行刚才的操作，也就是说，对刚才的笛卡尔坐标进行的操作，让我们来运行下它吧，运行下，现在我有一个极坐标点。
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Let me write a function, in fact the literal thing I would do is to say, identify the things that change, give each of them a variable name because I want to refer to them, and then write a function that captures the rest of that computation just with those variable names inside.
让我来写个方法,实际上我的意思是，辨别出变化的东西,然后给它们逐个命名以区分,然后写一个用来计算,这些变量的,包括计算过程的方法。
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