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Let's begin with a kind of warm-up sheet which we can anchor in these little drawings I've made.
让我们先来热一下身,看一下我在黑板上画的图。
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So, just looking at putting in the electrons, filling up the energy diagram here, we should be able to see a little bit why this is happening.
那么，仅仅通过观察这些电子的位置，在能级图上如何填充，我们应该就可以看出一点端倪。
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Where on the picture, let me do a bit more cold calling here, where on the picture maximizes total industry profits?
我随便找个同学来回答一下,在图上哪一点实现了行业最大利润
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I showed you this in this picture here and those levels of control can be at the level of transcription.
我把这些都给你们显示在这张图上,调控可以在转录的水平下进行
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One, two, three, four, so on each level of the picture I'm drawing, I've seem only to be looking at each number once.
，2，3，4，可见，在我画的,这幅图的每一层上，对每个数字,都只会用到一次。
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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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What's really weird— One really weird finding about these lobes is that they include topological maps.
奇怪的是,关于这些脑叶,有一个奇怪的研究发现,那就是,在它们上都存在着地理定位图
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All right, so let's go again what our paths are.
现在来在图上看看这两条路径。
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You pull out your clicker, you do it, and then we'll get a nice little pie chart or a bar chart on the computer of your responses.
你们就拿出表决器,按一下,我们就能在电脑上得到一张饼状统计图,或者柱状统计图,代表你们的答案
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So I've put this very handy little chart on the board for you listing codes on one side. And you'll see the kinds of things that are punished you pay a certain amount of money to compensate for the death.
我在黑板上画了这个图，一边列出了,这些法典，你可以看到一些被处以,你可以付一定数额的钱作为对死者的赔偿。
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At any point on the graph you can take the derivative, which will be tangent to the curve at each point, and its numerical value will be what you can call the instantaneous velocity of that point and you can take the derivative over the derivative and call it the acceleration.
在图上的任意一点,你可以进行求导,得到曲线上每一点的切线斜率,所得到的数值,即为该点处的瞬时速度,然后你再求一次导,得出它的加速度
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So what we should expect to see is one radial node, and that is what we see here 3s in the probability density plot.
个节点,这就是我们，在这概率密度图上所看到的,如果我们考虑。
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- Is it a character of eight bytes -- sorry -- eight bits, eight bits, eight bits, and I've done the same picture on the board.
它是一个8字节的字符--对不起-,8位，8位，8位，我在黑板上画了个一样的图。
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And let's start by considering my payoffs on this picture, just to help myself a bit, let me put some points in here.
我们从在图上表示预期收益开始,稍微等我一下,我先标注出来几个点
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So, what this lets us do now is directly compare, for example, the strength of a bond in terms of a hydrogen atom and hydrogen molecule, compared to any kind of molecule that we want to graph on top of it.
因此，这让我们现在可以做到直接进行比较，比如，将一个氢原子，和一个氢分子的键的强度，与任何其它类型的分子进行比较,我们只需要把它的曲线也画在这幅图上。
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The budget constraint is a straight line through this point with a slope of .
这个预算限制在这幅图上是一条,是一条经过该点并以为斜率的直线
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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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They include maps of your body.
在它们上都存在身体的定位图
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If you put the electrodes in the right position and you measure in the right way you can detect the electrical activity of the heart and record it on a strip recorder like this one shown here, or display it on a computer.
如果将电极放置正确,并采用正确的方式检测,就能检测到心脏的电活动,并将它记录在像这样的长图记录仪上,或者显示在电脑上
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So again, if we think of a graph of the wave function, we had the wave function is at its highest amplitude when it's lined up with the nucleus, and then as we got further away from the nucleus, the amplitude of the wave function ends up tapering off until it never hits zero exactly, but it goes down very low.
同样，如果我们想象一幅波函数的图，波函数在原子核的位置上,有着最高的振幅，随着与原子核距离变远，波函数振幅逐渐变小直到,它永远不会到零，但它会变得很小。
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So this is a little bit trickier to look at and see what it means, but essentially we have two hybrid orbitals, which are shown in blue here, and then we have one p orbital that's left alone that's going up and down on the page.
看这个图肯能会觉得比较诡异，但本质上，骂我们有两个杂化轨道，这里用蓝色表示，还有剩下一个p轨道,在图中上下方向上。
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So you know your cycle, you know, you could have a whole complicated sequence on a p v diagram of steps going back.
因此，对某一的循环过程，可以在pV图上画出,一系列很复杂的小步骤。
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So on the p-V diagram, then, V1 V2 p1 p2 there's a V1 here a V2 here, a p1 here a p2 here.
在p-V图上，这是。
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Path number 1 I'm going straight up in the V-T diagram.
路径1在T-V图上,竖直向上。
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On each level in the picture, I'm touching each number once, alright.
在这幅图的每一层上，我只会移动每个数字一次。
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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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Well, the monopoly quantity was a - c over 2b and the competitive quantity was a - c over b, just to remind you of those, they're on our picture.
垄断产量是/2b,完全竞争产量是/b,提示大家一下,这几点都在图上呢
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It looks like we hit zero, but we actually don't remember that we never go all the way to zero, so there's these little points if we were to look really carefully at an accurate probability density plot, And then, for example, how many nodes do we have in the 3 s orbital?
但其实没有，记住，我们永远不会到零,如果我们，在概率密度图上,非常细致的看这些点的话,它永远不会到零，在3s轨道里，有多少个点呢？，2个，正确？
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Problem is here, that Player II has a continuum of strategies and trying to draw all possible probabilities over an infinite number of objects on the board is more than my drawing can do. Too hard.
现在问题是,参与人II的策略是连续的,想要把无限可能性的概率,做成图都画在黑板上,是不可能的了
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