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STUDENT: Right, we're going to do that in a second, but the answer is Fibonacci numbers, we define the first two.
学生：听不见：,我们马上会试一试，但是答案是斐波那契数列，我们可以定义下最初的两个数。
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Before eating the last slice, you could check with your friends to make sure it's alright for you to delve in.
在伸手拿最后那片披萨前，你可以跟你的朋友确认下，你吃完最后一片有没有关系。
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What place can it occupy in each type of discourse, what functions can it assume, and by obeying what rules?"
它可以在每种话语中占据什么样的位置，它在遵循什么原则的情况下可以有什么样的功能？“
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Adiabatic can be either reversible or not, and we're going to do that probably next time or two times.
绝热过程可以是可逆的，也可以不是，我们可能会在下一次或下下次课上,研究这个问题。
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I won't be able to show you what a market does unless I have stocks, but I can look at what an individual stock does without having a market.
我不会在没有股票的时候,就给你讲股市应该是怎么样的，但是我可以在没有股市的情况下,先去看单独的股票。
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When the date came, you would cut the coupon off and go to the bank and get your interest payment.
到息日到了以后，你就可以剪下这张息票拿到银行,去兑换利息。
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As I say, the syllabuses should be accessible on the Classsv2 server; however, I've had problems with that in the past and you should please let me know if it's not.
你们可以在2号课程服务器上下载大纲;,不过我曾经下载不了,如果现在还不能下的话，一定要告诉我。
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Since we're talking about wave functions, since we're talking about the properties of waves, we don't only have constructive interference, we can also imagine a case where we would have destructive interference.
因为我们讨论的是波函数，因为我们讨论的是波的性质，我们不仅有相长干涉，我们也可以想象在,某种情况下会有相消干涉。
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Realize that there's this wonderful mechanism in place that allows you to put your toe in the water for several weeks no less and then get a sense, and then decide whether or not this is something for you.
要知道这种好的评分体制哈佛也有,在这种机制下你可以先试听几周,熟悉这一机制，然后再决定这是否适合你。
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But you can grow it in cultured cells, and the advantages of that are that you can do this under very reproducible conditions.
而且采用细胞培养疫苗,这种方法的优点是,你可以在同样条件下进行再培养
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Now, you know, take your hands and kind of do that and you can get a sense of how small that really might be.
你们可以用自己的手指比划下,感觉下三英寸有多小
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You can poison them, you can strangle them, you can shoot them in the heart.
你可以下毒或是勒死他们,你可以朝他心脏开一枪
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It can be challenged on normal... Yeah, open to challenge. -Right.
一般情况下人们可以挑战。,对，人们可以挑战其中的观点，-是的。
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The church shouldn't be under the control of the bishops -this is Milton's argument -or prelates, a common seventeenth-century word for bishops, but the church should be led by preachers: men who were chosen by their congregations to preach.
弥尔顿认为,教会不应该在主教的完全掌控之下,或者这里可以用17世纪指称主教的常用词，高级教士，反而教会应当在布道者的领导下：,在那些被教堂会众所选出布道的人的领导下。
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Because at the whim of the king, or for that matter, of the parliament, we can name you or you to give up your property or to give up your life.
因为这样的话，国王就可以随心所欲，在这种情况下，就是国会可以随心所欲，让你们中的任何人放弃财产，或放弃生命。
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What would you do if you had this power, the power of this magic ring, where you could commit any crime, indulge any vice, commit any outrage and be sure you could always get away with it?
你们如果也拥有这般神力，透过来自神奇戒指的魔力，将可以违犯任何罪行，放纵自己，干下任何不道德的行为或暴行,也不用担心,因为永远可以藉由神力遁逃？
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We could just collect a bunch of data. For a material .What's the volume it occupies at some pressure and temperature?
对一种物质我们可以得到一系列测量数据,在给定的温度和气压下,它的体积是什么？
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Whereas under these conditions, these quantities, if you look at free energy change, for example at constant temperature and pressure, H you can still calculate H.
但是，在这些条件下，这些物理量，如果我们考察自由能的变化,例如在恒定的温度和压强下，我们仍然可以计算。
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As we said, Newtonian mechanics does work in most cases, it does work when we're discussing things that we can see, it does work even on things that are too small to measure.
在大部分情况下都适用,对我们可以看到的东西,它都能适用，甚至对一些小到,无法测量的东西它也可以适用。
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You can still calculate the heat that's released. This is what will tell you under some particular conditions what will actually happen. Where will you end up.
你仍然可以计算放热,在特定条件这些下这些物理量,能告诉我们将会发生的事情。
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In an ideal world, where you can borrow and lend freely, an individual could choose consumption along any point on this line.
在理想情况下,你可以随意借贷,每个人都可以将这条线上任意一点,作为自己的消费额
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Cause when you can actually manipulate a computer's memory at this low level, you can steal people's passwords, you can steal their data if you know how that memory is laid out.
因为即使是在这么低的权限下,你也能熟练控制电脑的存储器,你就可以窃取别人的秘密，如果知道相应数据位于哪里的话,你也能窃取别人的数据。
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So in a moment you're going to go ahead and hit the spacebar and then as things fall from the screen when they line up with the left arrow, hit the left arrow with a different arrow, hit that arrow and see how good a score you can get.
一会儿你走到前面，敲一下空格键,当屏幕上面的东西从左边往下掉的时候,你就敲一下键盘上的左键,是哪个方向，敲对应的方向键就可以了,我们来看看你能得多少分。
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V So this nR over V. And then, using the relation again, T we can just write this as p over T.
恒定温度下的dp/dT等于nR除以，再次利用状态方程，可以把它写成p除以。
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That is, it's easy to write down straight away that dG with respect to temperature at constant pressure S is minus S.
这就是说，可以很简单的写出dG在,恒定压强下对温度的偏导数,是负。
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And you can imagine this gets complex and there's lots of interesting things to do to look to the real form, but those are the things that you should see.
可以想象下这样下去问题会变的复杂起来,而且当面对真实情况的时候,会有很多有趣的事情发生，但是这些东西你都应该明白的。
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Once you've got them together, then you can compute the efficient portfolio frontier without the riskless asset.
当你明确了这些参数后，就可以算出没有无风险资产情况下的,有效边界了。
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By the way, when we turn in concept sheets each week you'll have the option of turning them in either on Monday or on the Wednesday of that week, whenever you choose to do it is fine.
顺便说下,当我们每周收观点报告时,你们可以在当周周一,或者那周三上交,无论你选哪一天都是可以的
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So, for example, if we look at sodium channels, and sodium channels are some of the particularly prevalent ones when we're talking about neurons, if you think about the cell membrane, and this little green cartoon is me trying to show a sodium channel here, and in this case, you can see that it's closed, such that no ions are getting through.
比如，让我们来看一下钠离子通道，钠离子通道是我们会经常遇到的几个之一,在讨论神经元的时候，如果大家想想细胞膜，而这个绿色的小示意图就是我用来表示,钠离子通道的，在这种情况下，大家可以看到它是关闭的，因此没有离子可以通过。
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So, these are two different definitions of how to think about atomic radius, but really what you find when these are measured is they come up with almost the identical values, so there are tables, you can look up of atomic radii and see these values, and you can trust them that, they work for both this definition and for this definition here, in most cases.
这就是,关于原子半径的两种不同的定义，但实际上你会发现按照这两种方法,测量出的值是相等的，因此有很多关于原子半径的表格，你可以通过查阅它找到这些值，你可以相信这些值，它们对于这两种定义都是适用的，在大多数情况下。
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