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And so, I need to cheat a little bit on the drawing and make sure that this minimum occurs right here.
所以，我需要在画时作点弊,以确保最小值出现在这儿。
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you know, just for a little exercise, because I'm sitting in a cab 4 or 5 days a week.
做点运动，因为我一周四、五天都是在驾驶室里坐着。
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And maybe at 4 p.m., I watch the news and I'll have this little chat with my family about Sharon and elections.
可能在4点时，我会看新闻,与我的家人交谈,谈论沙龙以及选举。
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Square root of 16, and my plot basically shows it crosses at 4 and-- well, I think that's minus 4.
我的图清楚的显示这个函数,在4和-4两个点和x轴交合。
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They're plainly interrelated in a variety of ways, but it's more to the question of determinism I want to return today.
在很多方面他们都相互联系，但是今天我要多谈点有关决定论的问题。
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I've never seen anyone like them.' 'I found them in the West.'" So, there is that sense of the West as a source, and what he's going to do is take them back East.
我从未见过像他们一样的人’,’我在西部遇到他们的’“,对新西部的感觉成了一个源点，而他正想要把这群人带回东部。
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And let's start by considering my payoffs on this picture, just to help myself a bit, let me put some points in here.
我们从在图上表示预期收益开始,稍微等我一下,我先标注出来几个点
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And then, I had all these dots moving around this beautiful picture of this map, which represented downtown St. Louis and then later represented New York City, which I was amazed by.
接着我让这些点在这张,漂亮的地图上动来动去，让它们展现出圣路易斯市中心的景象,之后表示出了纽约城，这让我很惊奇。
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The other thing that we looked at, which I want to stress again and I'll stress it as many times as I can fit it into lecture, because this is something that confuses students when they're trying to identify, for example, different nodes or areas of no probability.
另外一个我们要考虑的事情，我想再强调一次,而且我以后会在课上强调很多次，因为它很容易让人混淆,这就是当你们在确认，节点或者零概率点时候。
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That will again be a Friday but it will be at nine o'clock and he will be here so I think that will be a lot of fun also.
那天会是一个星期五,但是会在9点开始并且他会来到这里,所以我认为届时会非常有趣。
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My soul got destroyed, let's suppose, 3:00 a.m. Sunday morning.
我的灵魂假设被毁了，在星期天凌晨3点。
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If I look at different points in my container during that path, I'm going to have to use a different value of pressure or different value of temperature That's not an equilibrium state, and that process turns out then to be an irreversible process.
如果我要研究在路径中容器里的,不同的点，我就得在容器里不同的点上使用,不同的压强值,或不同的温度值,实际上这不是个平衡态，这个过程是,不可逆过程。
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I want to end though on a positive note.
在课程结束前我想说点正面的知识。
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Couple of things. One, all my favorite activities that I love doing are available here.
好几点呢。第一，我可以在这里做我最喜欢的活动。
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I don't always do that but I'd like to, ; and I can if you come at 11:30. Bring your books; I'm going to be talking about the texts and I hope you'll have them open.
当然我并不是经常这样，但我还是会尽力，你们需要在11点30分到，带上自己的书;,我会做一些关于课文的讲解,我希望由你们来开始讲。
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It helped me in my mind sort of take that step that I was otherwise just a little too hesitant to take in my freshman year.
当初这让我下定决心,虽然当时我还有点犹豫不决,那是在我上大一的时候。
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You can pick a point and say, "I'm at the point ."
你可以选一个点,然后说,"我在,点处"
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So I think that is one of those place where nature and the notion of God come together.
我想应该有一个点,自然和上帝这两个概念在这点汇合。
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And the second point is of radius 3 and angle 1, which is up about there.
半径为2然后角度为1的一个点,也就是差不多在这儿，我认为为了确保我做的是。
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I don't know if you know how a spark plug works, but for the electrical current to fly into operation in a spark plug, the two points of contact have to be gapped.
我不知道你们是否知道,火花塞是怎样工作的，在电流通入火花塞中使它运转之前，两个接触点之间需要有空隙。
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And we can just extrapolate in a straight line We before saw some examples where I had an algorithm to generate points, and we fit a curve to it, used the curve to predict future points and discovered it was nowhere close.
我们可以干脆用一条直线来描述它,我们之前看到在一些例子中,我用一个算法去生成一些点，然后用一条曲线对它进行拟合，然后用这条曲线来预测未来的点,最后却发现结果完全不对。
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p1 But if I say, are p 1 and p 2 the same point, it says yes.
和p2是不是同一个点，It，says，no。,返回的结果是肯定的，在这里我有个要强调的点，这个例子里发生的是。
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So let's actually, you might want to be a little bit gentle in your own notebook, but on my board let's get rid of all these strategies that are never a best response.
所以我们干脆点,在笔记本上,你们动作轻点,我直接在划掉这些非最佳对策的策略
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bug If you find a bug, it probably means there bug are more of them. So you ought to be bug a little bit careful. The story I've heard told is you're at somebody's house for dinner, and you're sitting at the dining room table, then you hear a .
对不对？你得修复这个,如果你发现了一个,可能就意味着还有更多的,因此你应该小心点，我听说的一个故事，是当你在别人家吃饭的时候，你坐在餐桌上呢，然后听到了邦的一声响。
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I have a way to account for that, but it's going to take to the end of my argument to do that, so I'm going to argue that that's significant, but I'm not going to talk about why it's significant yet.
我对那有自己的理解，但是我在最后才会告诉你们，我要跟你们说，那点的意义是非常重大的，但我现在还不能谈论它的重大意义。
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Now, suppose in fact these weren't x and y glued together, these were radius and angle glued together.
我实际也说过了,我在这里操作的是，和这两个点。
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So putting that all together, I know that it must go through here again, and once again, i get a straight line.
把这些点连在一起,我知道它一定会经过这一点,这次我们又画出了一条直线
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In binary search-- ah, there's that wonderful phrase, this is called a version of binary search just like you saw bin-- or bi-section methods, - when we were doing numerical things- in binary search, I need to keep track of the starting point and the ending point of the list I'm looking at.
就是当我们处理数字的时候，所称的二分检索，在二分法搜索中,我需要记录区间的开始点和尾点，初始化的时候就是-,问题输入的开始点和尾点，当我开始做测试的时候,我想要做的就是去取中值点。
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So this first little piece of code right here says, ok you give me 2 points, I'll create another 1 of these lists and I'll simply take the x, sorry I shouldn't say x, I'm going to assume it's the x, the x-values are the two points, add them together, just right there, the y-values, add them together and return that list.
好，为了来认识到这一点,让我们来看一个简单的小例子，在你们的课堂手册上，你可以看到我写了一个小程序,它假设我得到了，这些点中的一些，我想对它们做一些操作，例如我想把它们加到一起，那么这里的第一小片，代码的意思是，好给我两个点，我会再创建一个数组。
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Remember last time, I said that there's different kinds of complexity in our code, and I suggested for simple branching programs, the amount of time it takes to run that program is, in essence, bounded by the number of instructions, because you only execute each instruction at most once.
但是这里有个很重要的点,记得上节课，我提过在我们的代码中，有不同种类的复杂度，而且我还说了对于简单的分支程序,运行这种程序需要的总体时间,大体上，是和指令的数目相关的,因为每个指令只会被执行最多一次。
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