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So I think that is one of those place where nature and the notion of God come together.
我想应该有一个点,自然和上帝这两个概念在这点汇合。
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So if I take p times V to the gamma, anywhere on the path, it's going to be equal to the same relation This is going to be true for any point on the path.
结果都，将等于，初态点的,只要在这条路径上。
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Now, suppose in fact these weren't x and y glued together, these were radius and angle glued together.
我实际也说过了,我在这里操作的是，和这两个点。
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So putting that all together, I know that it must go through here again, and once again, i get a straight line.
把这些点连在一起,我知道它一定会经过这一点,这次我们又画出了一条直线
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Such a person might pick a point up here and that would be a portfolio with--a leveraged portfolio.
那样的人可能会在这里选一个点来投资,那就是一个有。。。这是个杠杆投资组合。
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What they also did around the year one thousand was to identify-- to label--these particular spots--spaces and lines.
在公元一千年左右,他们还制定了规范,来标记这每一个点,间和线
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No, I don't get freedom; I'm told I have to be here at 11:00 Monday, Wednesday,and Friday.
不，我也不能自主选择啊;,我被告知要在周一周三和周五，的11点到这来。
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And then, I had all these dots moving around this beautiful picture of this map, which represented downtown St. Louis and then later represented New York City, which I was amazed by.
接着我让这些点在这张,漂亮的地图上动来动去，让它们展现出圣路易斯市中心的景象,之后表示出了纽约城，这让我很惊奇。
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The other thing that we looked at, which I want to stress again and I'll stress it as many times as I can fit it into lecture, because this is something that confuses students when they're trying to identify, for example, different nodes or areas of no probability.
另外一个我们要考虑的事情，我想再强调一次,而且我以后会在课上强调很多次，因为它很容易让人混淆,这就是当你们在确认，节点或者零概率点时候。
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Knowing what iambic pentameter is, is not a gift of birth, but rather something that comes through a little bit of practice, which means we have to work at it a little bit.
没有谁是生来就知道抑扬五音步格诗，是需要努力才能知道的，这说明我们必须在这个上面花点功夫。
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You have to know where the vowels are supposed to go, and that makes it harder to learn how to read, but when you have the vowel sounds it's easier and the Greeks made that contribution.
你必须知道这些元音都应该加在哪,这使的学习阅读变得更加困难,但是如果填入元音,那么就会简单点,而希腊人在这方面做出了贡献
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These junctions, these red dots here are actually made up of proteins, some are synthesized by one cell, some are synthesized by each other, and they lock together to form a very tight barrier, to form a tight junction between the two cells.
这些红点表示细胞连接,实际上是由蛋白质构成的,有些是由一个细胞单独生成的,有些是由两个细胞共同生成,使这两个细胞紧锁在一起形成紧密的屏障,并在两细胞间形成紧密连接
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So Jordan, playing the role of human is going to type or write something down on this piece of paper, GetInt hand it back to, get int.
所以Jordan，担任人类的角色，键入,或者在这张纸上写下点东西，把它传给。
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And in the Apology, the speech between Socrates and the laws that form, as it were the kind of central action of the dialogue, Anytus presents the case that Meletus and Anytus should have made against him.
则在《自辩篇》中,苏格拉底与城邦的法律，这几乎是语录的中心诉讼点，呈现的便是，Meletus及,应拿来对付他的论点。
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The second problem is, 1 suppose actually I had p 1 and p 2 were in polar form, and I ran add points on them.
第二个点也就是，半径为3角度为1,也就是差不多在这，那么什么点，对不起。
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So the next little piece of code I've written here, just move down to it slightly.
好，我可能想做的一件事情是,这两个点是不是同一个点呢？,因此我在下面写的。
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So for each person, there is a point representing my income today and my income next period.
所以每个人,在这图上都有一个点表示目前收入和,下一个时间段的收入
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Second thing, we started talking about the periodic table and I believe that it's a hallmark of any educated person in the 21st century who is technically literate to know the periodic table by heart.
第二点，我们之前讨论过元素周期表,我相信这是个标志性的特征,对于那些在21世纪里,用心去学习,元素周期表的人来说。
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So I said that we want to be talking about valence electrons here, so that means if we're talking about, for example, the octet rule for an f f molecule where we have two fluorine atoms, we need to write the valence electrons as dots around them.
我说过我们在这要讨论的是价电子，这就意味着，如果我们要讨论，比如，关于两个氟原子组成的分子的八隅体规则,我们首先需要把价电子画成围绕在它们周围的点。
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I want to do this carefully and slowly, and before I even start, let me point out in passing that calculus is not going to help us here.
我要慢点仔细讲这部分,在我开始之前,我需要说明微积分,在这里是用不着的
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- Now that's a slight lie-- or actually in these days of political debates, a slight misspeaking, a wonderful word-- -- it is technically correct. It is enough to allow us to write any program, but it's not enough to allow us to easily write any program.
现在还有点说谎的感觉,或者在这些强调政治辩论的日子中，可以说成是有些词不达意-,这是一个绝妙的形容词,在语义上是完全正确的，用这种语言我们可以编写任何程序,但是不能轻松地编写程序。
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So let's think about a particular consumer, so suppose this consumer is here, at point Y say.
让我们来考察一个特定的消费者,假设这个消费者在这,在Y点
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So, if you can't immediately know, and you don't all have periodic tables in front of you, so that's fine, but if you have a periodic table in front of you, you need to be able to count valence electrons, so work on that if it doesn't come naturally to you in terms of figuring that out.
如果你不能马上想到，而且你手上没有周期表，那还好，但如果你面前有一张周期表，那你就得具备从中查出价电子个数的能力，如果你不能自然而然地想到,请在这方面多下点功夫。
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That's a choice, and that choice turns out to be very interesting and really important, because if you connect these two points together, you get a straight line that has to intercept the x-axis at some point.
在这一选择下,我们会发现一件非常有趣，而且极其重要的事,当你把这两点用直线连接起来，你会发现这条直线,将与x轴在某点相交。
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In the real world, it's often not desirable to say that I have a point here, and a point here, therefore the next point will surely be here.
在现实生活中，说这个点在这,那个点在那，所以下一个点在这儿，这种话往往是没有用的。
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That means that you want to pick, ultimately, a point on this-- this line is tangent to the efficient portfolio frontier with all the other assets in it.
那意味着你会最终会在这上面选一个点-,这条直线是与有效边界相切的,后者包含了所有的资产组合。
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Once it passes 2000, then it seems completely natural; that's anchoring.
而在2000年之后,突破万点便极有可能,这就是锚定效应
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If we think about the drinks industry more generally here, rather than just beer, this would be Guinness, this would be Poland Spring, This is water and everything else would be in between here.
如果我们把啤酒业想得更普遍点,不仅仅只有啤酒,这可能是吉尼斯,这可能是波兰泉水,这是水而其他的产品分布在中间
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So in hydrogen atom a, I'll depict that here where the nucleus is this dot, and then the circle is what I'm depicting as the wave function.
在氢原子A里，我在这里把原子核画成一个点，这圆就是波函数。
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Yeah. Suppose I choose it right down there I guess 0. Well, the tangent there will not even have an x intercept. So I'm really going to be dead in the water.
好，如果我选猜想数为0，好吧,这个点的切线甚至和x轴都没交点,所以在这儿这一原则,真的不起作用了。
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