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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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When I say dirty, I am referring mostly to like a graffiti. There's a lot of graffiti on walls, on buildings.
我说的脏，主要指的是涂鸦。大楼墙上到处画满了乱七八糟的涂鸦。
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And I don't know why, but since time immemorial that is the way computer scientists have drawn trees.
叶子是在最下面的，我不知道为什么,但从记事以来他们就是这么画树的,这也许就是为什么我们。
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I wrote it down your notes, if you can put a big star next to it so you don't forget this.
我写在了你们的讲义里，如果你们在旁边画上一个,大星号就不会忘记了。
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Well, I'm going to get back, let's just draw a bigger square than usual that's roughly four times the size.
嗯，返回的是，我画一个更大的方形,大致上是4倍的大小。
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Now as I did last time, let me put in two axes to make the picture a little easier to draw.
和我上次做的一样,画两个纵轴来帮助我们作图
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Your young brother or sister, or my little children, can draw pictures of family members that barely look like family members.
你的弟弟妹妹或者我的小宝贝们,可以画一些看起来,仅仅有点像家庭成员的画
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I got this from Google Images, typing in "cute baby," getting rid of the porn and coming on to that.
这幅画我从谷歌图片找的，标题为可爱的孩子“,忘记色情，看着图片。
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OK, so this, what I've sketched here would be a constant pressure calorimeter. There's a reaction.
好，我画的就是一个恒压量热计,其中进行一个反应。
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In other words, I think of something and that thinking of something corresponds to a sound image that I have ready to hand for it.
现在，我们来想想,一个词和它所对应的声音形象,我已经画出来了。
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This is my humble drawing to indicate discrete sodium chlorine pairs.
我画的比较丑,想表示不连续的氯化钠对。
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I did it myself using my data, but it would always look more or less like this-- slightly different positions if people use different estimates.
这幅图是我根据自己的数据画出来的，有效边界的图形大致就是如此-,随着人们采用不同的估计值,其位置会发生微小的变化。
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What I want to leave you with is my picture, not a very elaborate picture, of what Biomedical Engineering is to me, and two parts of it.
我想给你们看我画的这张图,图虽然画得不太好,但包含了我对生物医学工程的理解,有两部分
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It was very, very basic and very simple.
我画了一张很基础很简单的地图。
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That is, until the great archaeological discoveries of the nineteenth and twentieth centuries, which unearthed for us the great civilizations of the Ancient Near East, of which I have drawn a remarkably life-like map ] here on the board: Mediterranean, I always start with the Mediterranean Ocean, the Nile River, the Tigris and the Euphrates.
直到十九至二十世纪,一些重大的考古发现，才让我们了解到,远古近东的文明,我已经在黑板上画了一幅,栩栩如生的地图了：,地中海，我总是从地中海讲起，尼罗河，底格里斯河，还有幼发拉底河。
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This was the Stieglitz picture, City of Ambition, I showed you last Wednesday.
这个是施蒂格利茨的画，叫“城市的野心“，我上周三给你们看过。
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2 7 And I'm not going to draw the rest of the tree for you here, because I drew it last time, and you don't need to see the whole tree.
从这儿我们得到了,我在这里不会剩下的树都画出来，因为我上次画过了。
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So, this, in fact, is my very schematic representation of a Geiger counter.
这是我给它画的示意图,你们有些人可能。
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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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The way I've got this drawn, the volume is going up in the process. It's an expansion.
像我画的图这样，这个过程中,体积是增加的，这是个膨胀。
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So if I had drawn that better it would look as if this was half of this distance, but I didn't draw it well.
如果我画得准确的话,这段应该是整段长度的一半,不过我没画好
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I think I might have missed slightly but it's more or less right.
我感觉我画的不是很直啊,大概大概吧
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Now there many ways I can connect these two points together. The simplest way is to draw a straight line. It's called the linear interpolation. My line is not so straight, right here. You could do a different kind of line.
最简单的办法是,像这样画一条直线,这叫线性插值,不过我的这条线画得不太直，你也可以用别的办法,比如一条抛物线。
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The way I've drawn it they're not the same at all.
我画的一看就不相等
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Did everyone understand how I constructed this picture?
大家都知道我怎么画的这个图了吗
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Everyone happy with how I drew that?
大家看懂我画的了吗
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Well one reason I want to go back is you'll notice I've been putting up these lines on the board and when we visited elections on the second day, we said that you could think of that line on the board, as being not just left wing, right wing politics but also some dimension of products.
原因之一是我想你们将注意到,我在黑板上画了一条线,当我学习第二天学习的选举时,我们讲过你们可以想象黑板上有条线,不仅是左派和右派的政治家,还可以是某种产品特性
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I have the skeletal structure written up there, I've written it twice and you'll see why in a minute.
我已经把它的骨架结构画在上面了，我画了两遍，等会你就会知道为什么。
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Maybe I should make a bigger-- let me do it here, I can fit it in here I think.
也许我该弄个更大的...,要不我画在这儿吧
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What I want to do is I want to draw a picture, a little bit like we did for the partnership game.
下面我来画出函数图像,这与合伙人博弈的有点像
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