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And I think this is perhaps the whole one area in which we treat animals better than we treat humans.
只有在这一点上，我们对待动物的方式,要比对待人的方式人道得多。
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Yeah, that's the bad thing about Columbia, I guess, it's like, here in New York,
我猜这是上哥伦比亚大学不好的一点，虽然是在纽约，
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In that respect, it has a kind of priority over the hells or the underworlds of Homer and Virgil.
在这一点上，它优胜于荷马与维吉尔笔下描绘的,那些地狱或阴间。
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That's got the lowest possible standard deviation of expected return and that's 25% stocks and 75% bonds with this sample period.
这个组合预期回报的标准差最小,在这一点上，投资组合,由25%的股票和75%的债券构成。
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And Rutherford, who I have already described to you as being a little bit colorful in his language, backed up Bohr on this.
而卢瑟福，就是以前我跟你们提过的那个,语言丰富生动的人，在这一点上证实了波尔的理论。
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I could have that path be very slow and steady, so that at every point along the way, my gas is an equilibrium.
我可以很慢，很稳定地经过这条路径，因此在这条路径上的任意一点，气体都处于平衡态。
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Some people find that a psychologically difficult thing to accept, but I've believed that pretty much all my life, so I'm quite comfortable with it.
有些人会觉得心理上,很难接受这一点，但在我的人生中，我一直相信这一点，我也坦然接受这一点。
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Well,maybe what the soul theorist would have to do at this point is accept the--da-ta-da--the no branching rule.
在这一点上也许灵魂理论者必须,也接受无分支规则。
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You should not, at this point be worrying about those things.
在这一点上你,不应该为此担心。
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At the same time that he is this great thing almost like a god, he is also not a god in the most crucial way possible.
他几乎像神一样伟大,但与此同时,在这可能是最关键的一点上,他又不是神
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That's right; where can I see that one on the picture though?
好了,那这一点在图上怎么表示呢
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And I can point you to some of these pages. This is on 189.
我能够在这几页里给你们指出这一点，在189页上。
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So you pick a better material like iron and steel, that makes a better bridge, we know that now because we have experience with bridges, but still your bridge might fail.
你选择了钢铁作为材料,来造了一座更好的桥,我们现在能够明晰这一点,是因为在造桥这件事上我们现在很有经验,但即使是我们现在造的桥也仍然会倒塌
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And I realize I'm moving over this very quickly, ? but is Thrasymachus wrong to believe that?
我知道我在这一点上推得很快，但，Thrasymachus，那么相信真的错了吗？
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That's an idea that struck people intuitively at various times in history, but they didn't know how to do these calculations.
在历史上,人们很多次,直觉地感知到了这一点,但是他们不知道怎么去计算
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In order to explain it-- I had to write down the binomial distribution to explain it properly.
要解释这一点,我要先在黑板上写一个二项分布,以便于解释清楚这个问题
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Where can I see it on this picture?
在图上怎么表示这一点呢
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Well, you could short in the stock market, you could short $.50 worth of stocks and buy $1.50 worth of bonds and that would put you down here.
你可做空股票，卖空价值0。5美元的股票,购买价值1。5美元的债券,这样就落在这一点上。
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You could argue, well, x is in some sense inherently a method, but it's not nearly as clean as what I would like.
你可以争论这一点，好，x在某种意义上，页是一个方法,但是它可能并没有。
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Well, he's a good friend of mine, but I think he may be overstating it a little bit; we have some disagreements.
当然他是我一个很好的朋友,但我觉得他在这一点上有点言过其实,我们在这点上意见不合
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Once you hear that description, it's easy to write the code, in fact. This is a place where the recursive version of it is much easier to think about than the iterative one.
实际上一旦你听到了大致描述,就能很轻松的写出代码来,在这一点上应用递归来解决问题,比用迭代要容易理解多了。
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Now, at this point I have to just confess, as I've confessed at other times before, the three is a claim about empirical science.
在这一点上我必须承认,像我之前承认过的那样,前提三是关于实证科学的
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One thing that I wanted to emphasize in this course, or try to emphasize, is that part of finance is actually philanthropy.
在这堂课上我还要重点强调一点,或者说是试图强调,金融中的一部分,慈善事业
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That would be the bold claim to make at this point.
这就是在这一点上能做出的大胆的观点。
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