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And in fact, it lies at the heart of a lot of useful computational techniques where we save results.
实际上，它也是很多保存结果的,计算技巧的核心。
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And that's what led us to a number of results to determine what quantities we even need to be looking at.
这就要求我们考察一系列结果,然后决定到底需要计算什么物理量,来找出。
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PROFESSOR: All right. Good. So we can fully believe what our calculations were now, which is a nice thing to do.
教授：好了，我们现在可以,完全相信我们的计算结果了，多么美妙的一件事。
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Literally, return the control from this function, and take the value of the next expression, and return that as the value of the whole computation.
正如字面意义上说的，从这个函数返回，然后取得下一个表达式的值,并把这个值作为整个计算的结果返回。
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That means--his calculations are very different than the ones I have because he has a much longer sample period.
那表明。。。他的计算结果与我的大相径庭,因为它数据的取样跨度比我的长多了。
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The mind reflects the workings of the brain just like computation reflects the working of a computer.
心理反映了大脑的活动,就像运算结果反映了计算机的运行一样
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You could use a calculator or any number of other tools but we'll get there.
我们可以用一个计算器或,其他的运算工具来计算那个结果。
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You can do that, but we like to get the answer the way this gentleman described it, because we like to get an answer more readily than by doing the mundane work.
你可以那样做,但是我们喜欢,用这位同学所说的方法来得到结果,因为我们喜欢更简洁地获得结果,而不是通过繁琐的计算
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On the other hand, if the balance from here on out would've been negative, then it's good for me that I died now instead of being kept alive with a life not worth living.
另一方面，如果从现在开始计算其结果是负数，那么我现在死去就是好事,因为我不用不值地活着。
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It turns out after you do all the math, H it turns out to be delta H equals zero.
要等你做完所有的计算之后，才能知道结果，结果证明Δ
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Because it says, your program will still give you a value, but it may not be what you intended, and you can't always tell, and that may propagate it's way down through a whole bunch of other computations before it causes some catastrophic failure.
因为这意味着，你的程序依然会返回一个值，但是这个值可能不是你想要的，你可能还分辨不出来，而且这种情况会传播,结果会沿着正果计算过程传播下去,直到产生一个灾难性的错误。
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So it turns out that he could have picked anything to explain this, and hopefully done out the calculation, and we'll do this ourselves.
结果是他可能用任何事情,来解释这个说法，有希望完成这个计算，而且我们将自己做这件事。
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It says, well I'm going to print out first and last just so you can see it, and then I say, gee 2 if last minus first is less than 2, that is, if there's no more than two elements left in the list, then I can just check those two elements and return the answer.
然后它计算了尾点和开始点的差,如果小于2的话,也就是说数组中的元素小于等于，我对这两个元素进行比较,然后返回结果就可以了，否则的话，我们就去寻找中值点，注意它是怎么实现的,首先这个指向一个列表的开头。
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As of then, I calculated the value of their oil in the North Sea and that's what I got-- it's worth about 3.5 billion Norwegian Kroner.
我计算了当时他们拥有的北海石油的价值,这是我的计算结果-,它价值35亿挪威克朗。
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That is the final aspect of the efficient portfolio calculations.
那是计算有效资产组合所得到的最终结果。
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It was as if, when we went through this search tree, we never remembered what we got at the bottom, and we just re-computed things over and over.
如果当我们遍历完这棵树，我们不可能，记得我们在最下面得到什么结果,我们只是不断地重复计算，所以这让。
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Now remember, we went through before how it's a state function but to calculate it, you'd need to find a reversible path, along which you can figure this out.
请记住，我们不需要知道它是怎样的一个态函数,只计算就可以了，你需要找到一条可逆路径，沿着这条路径就能算得这个结果。
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When you do these calculations, which I just did for insurance-- I was talking about insurance companies-- assuming that risks are independent, everything's independent and we've got it all figured out.
当你试图去,做保险相关计算时,我指的是保险公司...,假定风险是独立的,事件都是独立的,可以算出一个结果
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Secondly, as we go to the more advanced part of the course, we'll take a result from this part of the blackboard, stick it into the second part and keep manipulating, so if I screwed up in the beginning and you guys keep quiet, we'll have to do the whole thing again.
其次,随着我们课程的深入,我们需要把黑板这边的计算结果,抄到黑板的那边,不停地这么做,如果我一开始就写错了,而你们又不出声,我们就得全部重新来过
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So if we look at what we've got here, we've got something rather peculiar, right? What's peculiar about what this computer is now printing for us?
那么如果我们看看，现在我们得到的，结果的话，结果相当奇怪,对不对？计算机现在显示的结果？
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We found an equity premium-- or actually Jeremy Siegel's book gave an equity premium of 4% a year.
我们发现了股权溢价的存在,根据杰里米·西格尔所计算得出的结果,股权溢价大约为每年4%
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Well, you'll know when it crashes, that doesn't help you very much, but you can't always tell whether something's stuck in an infinite loop or whether it's simply taking a long time to compute.
好，你将学到它在什么时候会崩溃，这对你帮助并不大，但是你不能辨别出到底是在一个循环中,有什么东西卡住了呢,还是程序需要很长的时间来计算一个结果呢。
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It's using its set of rules to deduce the value and print them back out.
计算器用自己的规则,去计算出结果来并返回。
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For him, the optimal portfolio should be very heavily into stocks.
以他的计算结果，最佳投资组合应该是大量投资股票。
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Second thing we've got to worry about is, what's a basic step? All right, if I bury a whole lot of computation inside of something, I can say, wow, this program, you know, runs in one step. Unfortunately, that one step calls the Oracle at Delphi and gets an answer back. Maybe not quite what you want.
我们需要担心的第二件事情就是，什么该作为一个基本的步骤呢？,如果我把一大堆的计算过程放到里面，我可以说，噢，这个程序你知道的，一步就完成了，不幸的是,这一步可能要靠预言家才能得到答案,这可能跟你想要的结果不太相同吧。
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They might say my sample period was off, ... but that's what the theory-- ... using my data for the sample period that I computed-- the expected returns and co-variances says one should do.
他们可能说我的采样周期是有问题的，不过我的结果都是靠理论-,我采用自己收集的数据计算出-,预期收益和协方差可以用来指导我们的投资行为。
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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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It turns out that in a lot of languages, C included, you the programmer knowing a bit about how the computer works and the language works, can exercise more fine-grained control.
结果在包括C语言的很多语言当中，你作为一个程序员懂得了一些计算机的工作方式,和语言的处理方式，可以更精确地控制运用它。
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Because in doing that, Python would then have a value that it could pass on into some other part of a computation, and if it wasn't what I wanted, I might be a long ways downstream in the computation before I actually hit some result that makes no sense.
因为如果这样做的话，Python会将,输入的值传递到下面的,一些运算中去，如果这个值的类型不是我想要的，我可能会在得到,一个毫无意义的结果之前,经历一个很长时间的,计算过程。
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And it turns out that if we have a, for example, for s, a very large z effective or larger z effective than for 2 p, and we plug in a large value here in the numerator, that means we're going to end up with a very large negative number.
结果是如果我们有一个，举例来说对于s一个很大的有效电荷量或者,比2p大的有效电荷量，并且我们将一个较大的值代入计算器，那意味着我们最后会得到,一个非常大的负数。
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