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Gas phase single atom. So we don't have to deal with work function or any kind of energies associated with some condensed form of matter.
气相的单原子，所以我们不需要再,处理功函数的问题,以及和凝聚态相关的能量问题。
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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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Then next week we'll do more complicated problems that involve motion in higher dimensions, how to go to two dimensions or three dimensions.
下周我们将会处理更复杂的问题,包括更高维数的物体运动,如何处理二维以及三维运动
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The one problem that we run into is as we go to more and more atoms on the table, as we add on electrons, the Schrodinger equation is going to get more complicated.
我们将会遇到的一个问题,是当我们处理周期表中越来越多的原子时，当我们增加了电子，薛定谔方程,变得愈加复杂。
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In other words, we need criteria for equilibrium under more general conditions than the ones that we've dealt with so far, than the one set of conditions that we've dealt with so far, which is isolated system.
换句话说,相比我们目前为止,考虑和处理的问题，我们需要更一般条件下平衡的判据,我们目前，只考虑了孤立系统。
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There's ancient evidence, there's an ancient source for that, that says that's what happened and that's one of the things that we have to deal with.
这里有古老的证据,有一份古代的资料表明,事情就是这样发生的,这也是我们要处理的问题之一
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Next we will deal with what's the--arguably-- the single most important thing when we listen to any piece of music and that is its musical form.
接下来我们要处理一个有争议的问题,音乐作品中的最重要的部分是什么,那就是曲式
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We weren't going to be in a position to see that until we went through all the stuff we've been going over for the last couple of weeks.
我们处理了过去几周研究过的问题,才能搞清这个。
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So as you can see, as we escalate the problem difficulty, the difference between the good method and the not quite as good method gets bigger and bigger and bigger.
如你所见，当我们处理更复杂的,问题的时候，优良的算法,和并不那么好的算法之间的,差异会变的越来越大，这一点很重要。
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But what we-- what we do want to do, is to give you some intuition about how to approach questions of efficiency.
但是我们想要你们产生，对于处理效率问题的一些直觉,你应该会意识到为什么。
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And so frequently what we try and do is, we take a new problem and map it onto an old problem so that we can use an old solution.
我们经常做的一件事就是，我们处理一个新问题时,把它归结为一个老问题,以便我们能采取老的解决方式。
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For a couple of reasons. In some ways, this would be nicer, do expected cases, it's going to tell you on average how much you expect to take, but it tends to be hard to compute, because to compute that, you have to know a distribution on input.
关注最快的情况，在某种意义上来说，因为一些原因这样想挺不错的，当我们处理一个给定的问题,计算平均时间的时候,是很难计算的，因为你并不知道输入的分布情况,这些输入会是怎么样的呢？
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The problem we want to do today, a whole family of problems, looks like this.
我们今天要处理的问题,是一系列像这样的问题
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The problem comes when instead we're dealing with ions.
当我们处理离子的时候,问题出现了。
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And then we're going to turn to the question of efficiency. How do we measure efficiency of algorithms? Which is going to be a really important thing that we want to deal with, and we'll start it today, it's undoubtedly going to take us a couple more lectures to finish it off.
然后我们会回头继续讨论效率问题,我们如何计算算法的效率？,我们处理这些问题的时候,最重要的事情是什么？,我们今天要去讨论这个问题，毫无疑问我们要用,挺多节课来学习这个。
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Well the problem is that the problems grow faster than the computers speed up.
问题就在于我们要处理的问题的复杂度,比计算机提速还要快。
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Well, it's interesting, I think, to compare the Greek way of dealing with this human problem that we all have, the problem of death. How do we deal with the fact that we will die?
我觉得,这是一件很有意思的事,拿希腊人的方式来对照,如何处理死亡这个人人面临的问题,我们应该如何面对,我们将会死去这一事实
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More fundamentally, I want to get back to what I think of as the main theme of 6.00, which is taking a problem and finding some way to formulate the problem so that we can use computing to help us get an answer.
花一些时间来讲,更重要的是我想，回到我认为的6。00的重点,即处理问题并公式化问题,从而使我们能够靠电脑得出答案。
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