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"This problem is a very special problem and you cannot draw general conclusions from this about Japanese manufacturers as a whole."
VOA: standard.2010.02.15
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This is an example of a problem called Towers of Hanoi. Anybody heard about this problem?
有人听说过么？,几个尝试性的举手？
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Not so easy to see. All right, but this is actually a great one of those educational moments. This is a great example to think recursively. If I wanted to think about this problem recursively- what do I mean by thinking recursively?
看不太出来，好，但实际上是一个有教育意义的时刻,这是一个很好的关于递归的例子,如果我用递归的思想,去考虑这个问题-,我该怎么用递归去解决这个问题呢？
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"This is about every family, every business and every taxpayer who continues to shoulder the burden of a problem that Washington has failed to solve for decades.
VOA: standard.2009.07.23
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Another way into this problem: let's look at the comments that Dr. Johnson made about Milton's Lycidas in the eighteenth century.
看这个问题的另一个角度：让我们看看,约翰逊博士在18世纪队弥尔顿的《利西达斯》所做的评论。
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Or, maybe speaking about the answer to the questions on the Problem Set NO.4 will help you to think this through.
习题册上第四题的答案,也许会对你们有所帮助
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At the end of the day this is all about equipping you with skills and knowledge and understanding with which to take a problem, take a large data set maybe and actually produce something useful-- produce a project that is of interest to you.
下午放学后,就用学到的技能，知识和理解力来,解决问题，或者处理超大数据集,或制造一些有用的东西-,例如发起一个你们感兴趣的项目。
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So, remember we solved this problem earlier in the class, but we were talking about orbitals.
记得吗我们之前的那个问题，我们讨论的是轨道。
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Secondly, the real problem here is Locke has this view about consent and natural rights.
其次，真正的问题是,洛克对同意和自然权利有这样的看法。
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It puts together the experience with tobacco and the experience with diet, to talk about how countries might see this problem coming and doing something about it.
它把发生在香烟和饮食上的,事情放在一起进行对比,讲述了国家是如何发现问题,并做一些事情来解决问题
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And I think--This strategy is one I'm very enthusiastic about but there still remains what's sometimes called the "Hard Problem of Consciousness" and this involves subjective experience.
这是我所热衷的策略,但却依然存在着,所谓的"意识难题",而这牵涉到个体的主观感受
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If this was a class in which we were going to worry about the general problem of identity across time, this would be a problem we'd have to directly face.
如果我们要讨论的是,贯穿时间的,质的总的问题，我们就需要,直面这个问题。
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One other very important thing to understand about this defensive problem and this is one of the debatable issues between the old guard and the traditional interpretation; I'm still giving you the traditional view.
对于防御的问题还有另外一个很重要的因素,这也是老顽固们对传统观点,争论的一个话题,我还是采用传统观点的说法
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So David, you're about to go, you realize you've got this coordination problem, so you phone Nina up and you can say whatever you like, so what would you say to Nina?
大卫你来吧,你觉得最好事先能联系稳妥,所以你就给妮娜打了个电话,你会对她说点什么呢
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The fascinating part about this layer is that it solves the problem for phospholipids about how to exist in water when half of you wants to be in oil, and that the water soluble part of the top leaflet here, of the top points up into the water, and the fatty acid chains point down.
这层膜的迷人之处在于,它解决了磷脂,如何存在于水中和油脂中的问题,水溶性的顶端部分,向上插入水中,而脂肪链则指向下
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We'll talk more about this later, but it often happens that when you change your program to solve one problem you break it, and things that used to work don't work.
我们以后会更多的去讨论者一点，但是经常发生的情况是当你因为,一个问题修改你的程序的时候,你修改了程序,但原来没问题的模块。
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Now this will become a problem obviously when we talk about Judaism, because Jews--the Greek rulers, were trying to do the same thing with Jewish gods and Jewish figures, as they had elsewhere.
显然，这种方法用在犹太教会产生问题，因为犹太人。。。希腊统治者试图用，同样的方法，处理犹太神。
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So when you're trying to think about is this a problem that I can solve with dynamic programming, these are the two questions you ask.
所以当你想知道能否,用动态编程来解决这个问题时,你可以问自己两个问题。
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What we really want to worry about is, as the size of the problem gets larger, how does this thing grow? How does the cost go up?
随着问题规模的变大，解决问题花费的代价是怎么增长的,因此我们将会主要地讲讲？
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So this is very similar, this is a kind of recursive thinking we talked about earlier, where we take our problem and we make it smaller we solve a smaller problem, et cetera.
我们则跳过比猜想数小的那个区间,然后我们重复这一过程,跟之前我们讲过的，递归思想非常类似,我们解决问题的时候,先把问题一步步变小，然后解决小问题。
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This is what I want you to think about on the Problem Set.
这也是习题册上的一道思考题
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A second problem is what I was talking about immediately before this is some of our data are misleading so we get a lot of the information about the world from the media.
刻板印象的另一个问题是,我刚才就讲了,我们接收到的有些信息是误导人的,我们能接收到这个世界很多信息,从媒体上接收到。
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So how would we go about solving this problem if I told you not only was there a maximum weight, but there was a maximum volume. Well, we want to go back and attack it exactly the way we attacked it the first time, which was write some mathematical formulas.
有些时候两个都重要,所以如果我告诉你这里不仅有,最大重量还有最大容量，我们应该怎么解决这个问题呢？,好了，我们想回过来然后,和第一次一样看看这个问题。
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And in particular, if I think about that problem - actually I want to do this- if I think about that problem, I'm going to write a little piece of pseudo code.
关于这个问题尤其要注意的是,实际上当我考虑这个-,问题的时候我想这么做，我会去写一点伪代码。
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The second problem set is about this model.
第二次练习作业就是关于这个模型的。
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I wanted to say one more thing because I realize that you have to-- your first problem set will cover this-- is to talk about the concept that applies probability theory to Economics.
我还想提一点,因为我意识到...,你们的练习题中会涉及到这个,概率论在经济学中的,应用的问题
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That gets us to the smart thief. Why is this thief smart? Because she took 600. And she learned 600 that in fact there is a good way to solve this problem. And that's what we're going to talk about next. And that's something called dynamic programming.
现在我们要当聪明的贼,这个贼为什么聪明呢？,因为它选择了,它知道这事实上是解决这个问题的好方法,这就是我们接下来要讲的,也就是动态编程。
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That's the question we're going to try and address. If we can do this, this is good, because first of all, it removes any questions about what machine I'm running on, it's talking about fundamentally, how hard is this problem, and the second thing is, it is going to do it specifically in terms of the input. Which is one of the things that I was worried about.
这是一个我们接下来要去,尝试和解决的问题，如果我们能做到的话会很不错，因为首先，它解决了结果可能和我,运行的计算机有关系的问题，因为这从根本了告诉了，我们这个问题的复杂度，第二件事情,就是这种方法可以依据输入的大小来计算,而这正是我最担心的地方。
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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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