What in the world does that have to do with my divisor example? Well, actually, before I do that let me in fact fill in a piece here.
那么这到底跟我的除数的例子有什么关系呢?,好,实际上,在我讲之前请我先来补充一点,大家还记得我说过,我们可以概念上认为。
I got from a person that I worked with for two and a half years before coming here.
我在来这儿之前和他一起工作了两年半的时间。
OK. You can see that thing is cutting down the problem in half each time, which is good, but there's one more thing I need to deal with.
这很棒,但是我们还需要处理另外一件事情,让我们仔细来看看,我在开始做之前一直在说,应该先试验试验。
We're actually going to do one more clicker question to get started with today, and as we do, I'll explain something we're going to be trying today, which is a little bit of a friendly competition in terms of answering the clicker questions correctly.
我们将在开始讲授今天的课程之前,再多做一个选择题,我先来说明一下做这件事的原因,这实际上是一个,回答选择题的小比赛。
Well before I say that, I should say I'm not going to change it, you are.
在我说出来之前,我需要说明 不是由我来改变它,而是由你们来做
I mentioned religion and so we should take a look first at the gods.
我之前讲到宗教,因此就先来看看这些神明
I think I might want to take it down before he comes.
但在他来之前我得把这篇文章撤掉
So, in all of this, what he does is he makes, to use an expression that I've already used before in the context of absolutism, he makes the Boyars, while he's building his navy and expanding Russia, he makes the Boyar junior partners in absolutism.
所以,通过所有的这些事情,用我之前用过的一个词来形容,他使得波维尔们,当他在建海军和扩张领土时,他使得波维尔贵族臣服在他的绝对权威之下
Can't my mind take off from there and push straight ahead to the idea of the perfectly straight, even if I never have encountered it before?
即使我之前没有直接碰到过,难道我的心灵不能借此来推断出,完美的直线是什么样子的吗
I just need to clean the dishes, before I come over.
在我来之前,我还得把盘子刷了。
Yet once more, O ye Laurels, and once more Ye Myrtles brown, with Ivy never sere, I come to pluck your Berries harsh and crude, And with forc'd fingers rude, Shatter your leaves before the mellowing year.
我再一次来,月桂树啊,棕色的番石榴和常青藤的绿叶啊,在成熟之前,来强摘你们的果子,我不得已伸出我这粗鲁的手指,来震落你们这些嫩黄的叶子。
Nature is a meaningless concept just like the lack of meaning within nature, where there's no culture until culture comes along and says, "Oh, not so much there is nature, but I'm terribly unhappy because before I came along, there was nature." Right?
自然是个没有意义的概念,正如自然之中意义的缺乏,自然中原本没有文明,直到文明走过来说,“哦,自然的存在并不算什么,我很不高兴的是因为,我来之前,这里就有自然了“,是吧?
Well, what she found was that life insurance salespeople were going to families and trying to sell them on life insurance by explaining the concept and they would say something like I did.
这是因为她发现当时的保险推销员,总是来到客户家中,并且希望通过介绍各种概念来推销保险,他们会说一些类似我之前讲过的东西
Claire Elise is going to get her own vote plus 1, 2, 3, 4, 5, 6, 7, 8, 8 votes and Beatrice is getting 1, 2, 3, 4, 5, 6, 7, how did I end up with eight, I thought I had an odd number. 1, 2, 3, 4, 5, 6, 7 there must have been an odd number before.
克莱尔·伊莉斯将获得自己的选票加上,12345678 8张选票,而比阿特丽斯获得1234567,我怎么数出8个来的,我想应该是个奇数,1234567,之前也应该是个奇数
And we can just extrapolate in a straight line We before saw some examples where I had an algorithm to generate points, and we fit a curve to it, used the curve to predict future points and discovered it was nowhere close.
我们可以干脆用一条直线来描述它,我们之前看到在一些例子中,我用一个算法去生成一些点,然后用一条曲线对它进行拟合,然后用这条曲线来预测未来的点,最后却发现结果完全不对。
So let's start somewhere; what we're going to do is we'll refer back to this other picture, which is why I left it here.
就从这里开始着手吧,我们先来参考一下之前的图像,所以我之前没有擦掉它
Now, D here stands for debt; a minute ago I was using Div to stand for dividends.
这里D代表着债务,之前我曾用Div来代表股利
We'll come back and discuss it more in a second, but before I do, let me mention that the same model, exactly the same idea, has an application in Economics.
我们一会再深入导论这个问题,在此之前,我再来列举一个模型,是经济学里面一个完全类似的模型
So before we leave it, I've been making a point in this class of coming back to reality from time to time, so this is a very simple model of the soccer game in reality.
在我们结束讨论之前,我来强调一下,我们应该回到现实中,这是一个很简单的足球模型
We don't have adequate reason to conclude that it's something that existed before I was put together, it's something that will be recycled and continue to exist after I fall apart, after my body decomposes, after I'm separated from my body, or what have you.
我们并没有充分的理由来断定,灵魂是在我被组装起来之前就存在了,它会被循环利用,并且在我解体后依然存在,我的身体分解了之后,在灵魂与肉体分离之后,或者其他说法
So just rewriting, Player i's strategy, same thing, ?i is a best response.
我来写一下,参与人i的策略,和之前一样,?i是最佳对策
I remember--before I taught here I used to teach at the University of Illinois at Chicago.
我记得,在我来这教书之前,我在芝加哥的伊利诺伊大学教书。
For most people, that's a difficult concept and-- I think I may have mentioned some of this before, but let me give this history.
这个概念对大多数人来说有些难,我记得我之前提及过其中一些,但还是让我来讲述一下它的历史
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