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Okay so exchange numbers; okay good half of that problem is gone now we have just these two left.
好，交换数字,好，问题解决一半了,只剩你们两个了。
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And Milton uses the language of these two parables to get at this problem that has resonances in every conceivable sphere.
弥尔顿用这两则寓言来解释,可以想象出的与此有共鸣的问题。
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There are two aspects of it. Thus far, the problem sets have mostly focused on function.
关于这个问题有两个方面，迄今，问题集只关注了方法。
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To attend these lectures in sections-- more on that in a moment; to submit 9 problem sets, take two quizzes and ultimately design a final project.
每节课都要来参加-,这个一会儿再解释，做完九套习题，参加两次测验，最后设计好期末的大作业。
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Now, in practice, this is not the only problem facing two firms who are trying to produce the monopoly output.
实际上 这并非两个想维持垄断产量的,企业需要面对的唯一问题
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Then the problem was that the price relative price of those two was not really fixed by the government.
然后，问题就在于价格,这两种货币的相对价格,没有被政府统。
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Two or one! It was, in other words, about the problem of incest, the problem of the over-determination of blood relations and the under-determination of blood relations.
二或一，换句话说，是乱伦问题，是血缘的超定,和不充分决定的问题。
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But what I needed to do this problem was to find these two unknowns.
但我解决这道题需要找到这两个未知量
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The problem is we can't add these two together.
这个问题是我们不能把他们直接相加。
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So, just, if you can take what I'm saying for a moment right now that in fact this should collapse in this very small time frame, we have to see that there's a problem with one of these two things, either the Coulomb force law or Newtonian mechanics. So, what do you guys think is probably the issue here?
所以如果你们考虑我,开始说的这个塌缩应该,发生在很短的时间里，那么这两者之一就有问题,要么是库伦定律,要么是牛顿力学,你们觉得应该是哪个的问题？
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This solves a major problem which I'm going to talk about just at the beginning of class here in a slide or two, is how to get DNA into cells?
这解决了我要讲到的一个主要问题,就是在这节开始的一两张幻灯片中要讲的,怎样将DNA导入细胞的问题
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Long before Milton had begun to tackle the problem, Christians had for centuries, for millennia, puzzled over the logical inconsistency between these two concepts.
早在弥尔顿应对这个问题之前，基督教徒们就已经花了成百上千年，为这两个概念之间逻辑上的前后矛盾感到困惑。
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We're reproducing the problem that the two brothers were rehearsing in their debate.
问题再次出现,两兄弟再次详述了他们的争论。
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Linear algorithms tend to be things where, at one pass-through, you reduce the problem by a constant amount by one. If you reduce it by two, 1 it's going to be the same thing.
有问题么？,线性复杂度的算法，当进行了一个,常量级步数的操作的时候，将问题的规模缩小了一个。
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OK. And then the exponentials, as you saw is when typically I reduce the problem of one size into two or more sub-problems of a smaller size.
好，然后说到指数级，正如你所见，典型的例子是,我讲一个问题分解成为,两个更小规模的子问题。
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What I though I'd do is just tease you with some visuals if you haven't gotten to the point of playing with the staff solution so the themes of problem set 3 are two-fold.
如果你们还没达到使用解决方案的程度,那现在我能做的就是用一些图形为你们梳理一下,习题集3的主题,是两方面的。
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That's the problem in two dimensions.
那是二维中的问题
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And I'm going to show you an example in a 1 second, just to drive this home, but notice the characteristics. In the first two cases, the problem reduced by 1 at each step.
在前面两个例子里,每一部问题的规模缩小了,不管是迭代的还是递归的，这表明这个问题的复杂性可能是线性的。
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