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And empathy has different definitions but we can simply view it as the feeling that your pain matters to me.
移情有几个不同的定义,但用简单的话来说就是,我不会对你的痛苦无动于衷。
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but what works for me the best is to really step out of this sort of need to create
但是对我来说最有用的方法，就是要走出一种必需创造的意念
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Now, let me take a sidebar for about five minutes to talk about course administration, the administrivia things that we're going to do in the course, just so you know what the rules are.
现在，让我用大约五分钟的边角料时间,来说说本门课的基本信息,也就是我们需要在课上做的事儿，好让你们了解一下规则。
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And so it wasn't all that many years ago frankly that you know, certainly, people in this class were still using these things.
这跟多年前完全不一样，当时我们用的就是现在我手头的这种。
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Mine is to demonstrate over and over how little mathematics you need to get the job done.
我的方法就是,反复演算,用最少的数学来解决问题
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When I say "pigeon," I don't really seem to have any particular sense of an onomatopoetic word, but if I use the Latin, pipio, which means "to chirp," all of a sudden I say, "Oh, that's onomatopoetic."
当我说鸽子的时候,这个词并不能，反应它自身的意思，但是如果我用拉丁语说鸽子，也就是咕咕“,这就是拟声了“
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Which of the various futures that are open to me are likely to give me the better life, leave me better off, measured in terms of pleasure or pain?
也就是向我敞开的各种未来,哪种能给我更好的生活，让我更幸福，用快乐和痛苦来衡量？
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If I talk about it in general terms, they might not put it in that frame Really, an important example of framing is how we deal with money and indexation.
但如果我用简单的话来表述它，他们可能就无法往保险那想,心理框架的另一个重要例子就是,我们是如何处理货币和指数之间的关系。
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For example, you can't acquire a land that is common property, so people in terms of the American Indians, I feel like they already have civilizations themselves and they were using land in common.
比如，你不能掠夺公共财产，对于印第安人来说，我觉得他们已经有了自己的文明,他们用的就是公共土地。
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And this is what linguists do for a living so if you hear me talking about this and say, "I want to spend the next forty years of my life studying that," you should become a linguist.
这就是语言学家们研究的问题,如果你听了我的讲解然后说,"我想用我的余生来研究这些东西",那你该去做一个语言学家
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and they reply in German, "Yes, I'm French," that doesn't--language doesn't necessarily tell you how people feel about their identity. Some sage once said, I don't know who it was, but I love this expression, that a language is a dialect with a powerful army.
然后他们用德语回答,"我是法国人",不一定--语言不一定能代表,对自己的身份认同,有个哲人说过,我忘了是谁,但我特喜欢这句,说语言就是有强大军队撑腰的方言
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I mean, you know the wings go, and the air runs, and then the motor on the engine and it's a miracle how it gets up there and that is the way I used to explain the Greeks, because I had no better idea.
我的意思是,你知道机翼的作用,空气的流动,还有引擎上的发动机,飞机能飞起来,是个奇迹,我就是用这种方式来解释希腊历史的,因为我也没有更好的方法了
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Now this is fundamentally important, and as you know that means that it warrants the exalted distinction of being put up in colored chalk.
这个非常重要，我用彩色粉笔将它写出来就是为了区分,它与其他公式的区别并强调其重要性。
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Or, in my favorite unit, 19.80 electron volts.
或者用我最喜欢的单位，就是19。80电子伏特。
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So again, part of the point here is that things grow-- or to rephrase it, interesting things grow at an incredible rate.
好，这儿我要说的就是,事情的规模发展到，或者用另外的话说。
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That will lead me to use a technique I mentioned again last time, called memoization.
这就使得我要是,用我上次提过的一种技术，也就是默记法。
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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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I've explained my embarrassment about using terms that I really have no absolutely no idea of the meaning of except that I'm told what the meaning of them is in the books that I am reading, which are the same books that you're reading.
我已经解释过了，用这些我完全不知道什么意思的词,真的很尴尬，除非有人告诉我他们是什么意思,就像这本书里说的那样,而我读的这本书，也就是你们现在也在读的。
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And what it's saying semantically is, using that variable as my placeholder, have it walk through this collection, starting at the first thing, execute that code, then the next thing, execute that code, and so on.
它的语义意思就是，把这个变量应用为我的占位符，用它来遍历这个集合，从第一个元素开始，执行代码，然后下一个元素，再执行代码。
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Then, I bring the elephant and I pull the spring by the same amount and I find the acceleration of the elephant and the denominator is obviously the mass of the elephant.
然后我再找来大象,用相同的力去拉弹簧,大象就具有了加速度,很明显,分母就是大象的质量
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OK. The other piece I want to say about variable names is, once I have that choice of variable name, I can use it, but in fact there are a few things that I can't use in terms of variable names.
关于变量名字我还想说的,另外一点就是，一旦我对变量的名称可以选择，我可以用自己的方式命名，但是,有一些词汇是,不能用来命名变量的。
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Or, said a different way, what's going to happen when I run it?
或者，用不同说法来讲就是，当我运行它的时候会发生什么？
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OK. All right, let me show you one other tool that I want to use. Which is, I've written that piece of code, I ought to check it. Well, I could just run it, but another useful thing to do is, I'm, especially as I want to debug these things, is to simulate that code.
好，那么，让我给大家讲下,我想用的另外一个工具吧,也就是，我已经写好了这一块代码，我应该去检查检查,那么我可以去运行它,但是特别是当我想要调试代码的时候。
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And that's a wonderful thing to have because it gives you that modularity, that encapsulation that basically says, when I create a point, the only way I can get at the values, is by using one of the defined methods, in this case it could be Cartesian, Cartesian and get all the pieces of that.
这是很棒的一件事情,因为它让你有了，模块性以及封装性，这基本上也就是说，当我创建了一个点，我能够得到它的值的唯一的方式，就是用一个定义好的方法，在这个例子中也就是。
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And that's why I use double equals.
这就是我用双等号的原因。
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Computing square root. I'm going to capture it in a piece of code, I'm going to be able to refer to it by a name, and I'm going to suppress the details, meaning inside of that computation, you don't need to know what it does. You just need to know, if I give it the right kind of input, it'll give me back an input that satisfies the contract that I set up.
比如计算平方根,我会用一段代码来说明,我将给它命名,并且忽略细节,意思就是在这一段计算过程中,你不用知道它做了什么，你只需知道，如果我进行了正确的输入,它将会给我符合条件的输出。
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If I strike you in a vulnerable place with a stick that has a bronze butt on it, it could well kill you.
如果我用一根有铜质尾部的棍子,刺你的软肋的话,很可能就是一击必杀
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Well I'm going to suggest that what I did was I really traded space for time. It makes me sound like an astro physicist somehow right?
困难在哪里？我在这里是如何权衡的？,我在这里所做的就是用空间换时间,这让我听起来像一个天体物理学家，是不是？
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Just take a look: if this is 9, 5 divided by 9 is always going to be 0 point something, and if you thus have two integers and you're rounding down, which is what happens when you do integral math we're using this operator, I'm going to get zero times whatever.
稍微看一看：如果这是9，5除以9会得到,0点几，如果你用两个整型数,你舍去小数，这就是当你们,用整型数使用这个操作的所发生的事情，我将得到数值0乘以任何一个数字。
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