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And yet if a computer can only count up to 2 billion or maybe 4 billion, I mean, what do you then do?
如果一台计算机只能够支持20亿,或者40亿，那我们该怎么办？
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What that's going to allow us to do is, if we say, OK I have a mixture of stuff, how does the free energy change?
我们能够说的是，如果我们有一份混合物，自由能怎么变化？
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Right, and just to get a sense of this, let's look at a simple little example, so on your hand-out, you'll see I've got a little piece of code that says assuming I've got one of these points, I want to do things with it, for example I might want to add them together.
这些数组中的一个，你怎么能够知道，它是哪种类型的呢？,你怎么知道它是以笛卡尔坐标,表示的还是以极坐标,形式表示的呢？,你没有可以用来区分的东西，你没有说明这种信息,聚集实际上的意义。
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So, let's see how some of this works, and hopefully your counterparts from 100 years ago would also be able to think about how this works, even if they don't have the quantum mechanics behind the individual electron configurations for atoms.
那么，下面让我们来看一下它是怎么用的，希望一百年前想你们一样的同学,也能够弄懂它为什么能用，尽管他们没有量子力学,不知道原子的电子排布。
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Well,I think one of the questions --the question is how can you successfully invest in a market where,I guess, people say you might catch a falling knife.
其中一个问题,提问是,怎么能够成功地,投资于一个,有所谓抄底行情的市场
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I leave it to my expert colleagues in History of the American West to decide exactly who came up with the term Manifest Destiny, who actually first used it.
我的同事是美国西部史专家,他也许能够,阐述清楚命运天定这个术语是怎么出现的,以及到底是谁第一个用它
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What I was going to say is that you could, at least theoretically, strike with your spear in a overhand manner or you could strike with it in an underhand manner, the only thing is I don't know how you do that underhand when you're in the middle of a phalanx.
我要说的是,士兵们能够,至少从理论上来说,可以自上而下地刺矛,也可以这样自下而上地刺矛,我不太清楚在方阵中,士兵们怎么能够自下而上地刺矛
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We can measure the heat capacity at constant volume, and now we have another term, and if we can figure out how to measure it, we'll have a complete form for this differential du which will enable us to calculate du for any process.
我们能够测量恒定体积下的热容，这里我们有另一项，如果能够知道怎么测量它，问我们就有了这个完整的微分式,就能够对任何过程计算。
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How do you ever get a hold of cash flow?
你怎么能够拿到现金流？
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