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So it's a complex issue, and I should leave it having said this much, at least for the moment.
因此它是一个很复杂的问题，而我就讲到这里，至少暂时这样。
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We'll get into some spots where it gets a little trickier, a little bit more complicated later in class.
我们接下来在课堂上,会做一些更棘手，更复杂的问题。
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It's a problem, as you'll see, designed to give you some practice at dealing with some of the, dare I say, more theoretical concepts we've covered in class.
这种问题会让你在处理我们,课堂上并没有讲到的更多,理论概念这方面上有更多实践,这种问题就像算法复杂度一样。
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Here's where three great figures there are others but these are considered the seminal figures begin to raise questions which complicate the whole issue of consciousness.
看一下这三个伟大的人物,当然了还有其他的人物，但这三位影响最为深远,这三个人物开始提出了一些问题,这些问题使整个意识的问题复杂化了。
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That's really a complex systems problem, the kind of problems that engineers are very good at dealing with.
这真是复杂的系统性问题,解决这类问题,恰恰是生物医学工程的拿手好戏
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So, the issues are complicated as to what sort of generalizations we're--are reasonable to make and what aren't.
所以什么情况可以用刻板印象，什么不可以,问题就变得复杂了。
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I'm going to start with the simplest example and slowly add on bells and whistles and make it more and more complicated.
我会从最简单的例子开始,逐渐增加难度,让问题越来越复杂
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Now let's take just one somewhat more complicated case.
现在考虑一个,更加复杂的问题。
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In fact, linguists often argue about this subject, and it's a complicated one.
实际上，语言学家经常在这个问题上有争议，这是很复杂的一个东西。
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Unless there are some tax effects, which might matter-- and taxes always complicate things--but disregarding tax effects, it doesn't matter which you do.
除非这里涉及到税负,可能会影响...,税款常常把问题变得复杂,但不考虑税的话,什么时候买是没区别的
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Normally the errors don't look this complicated but they still look fairly arcane.
一般来说，问题都不会很复杂,但是还是看起来有点神秘，不是吗？
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And like all the other topics we've talked about in this class, it's a complicated subject, about which one could spend a great deal of time.
和课堂中涉及的所有话题一样，这是个复杂的问题，需要很长时间才能搞清楚。
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So before we leave coordination games, I want to look at another one, a little bit more complicated one perhaps, that we mentioned briefly last time.
在我们结束讲解协调博弈前,我们再来看一个,稍微复杂点的问题,上一讲我简单提到过的
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But there is yet a complication to this problem.
但这问题还要复杂。
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But then also a little bit about your history, where you come from, some of your experiences which have helped you or informed your opinions on this very difficult issue that the entire world really is spending a lot of time trying to work on.
然后再谈谈你们各自的经历，你们从何而来，谈一些你们自己的经历,一些帮助过你们，或形成了你们,就这个复杂问题的观点,这个全世界都在投入大量时间试图解决的问题。
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Again, you get a sense of how complicated this is.
你们体会到这个问题有多复杂了吗
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So in fact, over the next thirty or forty minutes we're going to show you a set of examples of sort of canonical algorithms, and the different classes of complexity.
在接下来的三四十分钟里面,我们将要讲一系列的,权威算法，以及不同种类的复杂度问题。
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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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In large part because our government has confused us about it, but it's a confusing question to know.
虽说很大程度上,是政府把这个问题变得复杂,但这个问题本身确实值得商榷
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We can already use that in terms of single ions to think about a really complex biological issue, which is to talk about ion channels.
我们已经能够仅仅凭借这个关于单个离子的原理,来讨论一个非常复杂的生物问题了，我们要讨论的就是离子通道。
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So, let's write this one electron orbital approximation for berylium, that sounds like a pretty complicated question, but hopefully we know that it's not at all, 1s22s2 it's just 1 s 2, and then 2 s 2.
所以让我们写出,铍的单电子轨道近似，那听起来像是一个更为复杂的问题，但是希望我们知道它一点都不是，它仅仅是。
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Ah, n times, because for each value of i, I'm going to do that m thing, n*m so that is, close to what you said, right?
因此这就和你说的差不多了对不对？,这个问题的复杂度为，让我写下来，是-对不对，是？
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It's probably among the most useful ideas there is for solving complicated problems.
这大概是解决复杂问题,最有用的思想之一。
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When you do something complicated you save the answers and then you go get it later.
当你计算一些复杂问题时,你保存答案，然后再次查询利用。
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That's, there are whole courses on that, there's some great courses here on that, it takes some mathematical sophistication, we're going to push that off a little bit.
有一些课程是专门讲这个的，那些课一般都涉及，一些复杂的数学问题，我们只是简单的讲一些基础知识。
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But I want you to take away from this how we reason about the complexity of these algorithms. And I'll remind you, we said we're going to mostly talk about time.
但是我想你们理解我们,是怎么推出这些问题的复杂度的,提醒大家，我说过了我们主要讨论时间问题。
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That's a really complicated question that we have gotten very confused about.
这也依然是一个复杂的问题,人们现在对此十分困惑
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Now, as I said last time, the subject of free will--or free will, determinism, causation and responsibility, this cluster of problems-- is an extremely difficult and complicated physical problem.
正如我上次所说的,自由意志这个主题 或者说自由意志,决定论,因果论,责任,这一堆问题,是极端困难和复杂的物理问题
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That's a complicated thing that accountants figure out and accountants find it difficult to define the earnings of a company, but they do something and they come up with a number.
会计们会计算这个复杂的问题,他们还会发现公司收益很难定义,但是他们会想办法,得出一个数字
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