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Does anyone know the history of what Fibonacci was trying to do? Sorry, let me re-ask that. Fibonacci.
创始人是斐波纳契,有人知道斐波纳契想要干什么吗？抱歉，让我再问一次。
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All right. Now in giving the example, I've gotten a little bit ahead of myself, so let me reprise a bit.
好，刚刚讲例子，可能讲得有点快，所以我再重复一下。
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On the 30th day, I will give you another 1000 dollars-- you'll have a total of 30000 dollars from me.
在第30天，我再给你一千美元-,你将从我这里一共得到三万美元。
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I produce any quantity at all in addition to what's out there already, what's going to happen to the price?
如果我再额外生产一些产品,会对产品价格产生什么影响
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And then I take as many raisins as will fit in and I leave. Right? I hope almost every one of you could figure out that was the right strategy.
然后我再尽量装葡萄干,最后我离开，对吧？,我希望你们每个人都发现了这是最优策略。
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So I've got, this piston here is compressed, and I slowly, slowly increase the volume, drop the temperature.
这样，这个活塞就被压缩了，然后我再很慢很慢地增加它的体积，降低温度。
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But, you know, this undergraduate's very eager to do it, let's let him have a try.
就不值得我再花时间,寻找是否有粒子。
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What we call this is the--I want to emphasize it, I'll write this again--the equity premium puzzle.
我们称之为...我想强调一下,我再写一次,股权溢价之谜
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Let me talk a little bit about technology because that's also a big part of it.
我再谈谈技术方面吧,因为技术也是很重要的部分。
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Okay. That's another example. And the last one I'll give you is on 55.
好的，我再给出最后一个例子，在第55页。
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I then insist, okay, swap, and then I print out their values again.
我再强调，好的，交换好了，然后我再打印出,它们的值。
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Now here's piece two: All right. So here's one if--I'm going to play it again.
接下来是曲目二,好的,曲目一,我再弹一遍
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Let me just give you a couple examples of what one can mean here.
让我再给你们举几个很有说服力的例子
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Let me try it again, here we go .
我再试试,好了
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Then, I bring the elephant and I pull the spring by the same amount and I find the acceleration of the elephant and the denominator is obviously the mass of the elephant.
然后我再找来大象,用相同的力去拉弹簧,大象就具有了加速度,很明显,分母就是大象的质量
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Let me just warn you couple more times.
我再提醒大家一下。
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I might just say a little bit more.
我再来多言几句
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So, again, I want to stress you have the option of staying anonymous in this class, but you also have the option of seeking out and making some sort of contact with us.
那么,我再强调一遍,你们可以选择在这门课上默默无闻,但是你们也可以选择站出来,跟我们多多接触
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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
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OK, says it says enter a float. I give it something that can be converted into a float, it says fine. I'm going to go back and run it again though. If I run it again, it says enter a float.
好了，看到他说输入一个浮点数,我输入它可以转换为浮点数的值,那没问题，我回过来再运行一遍,如果我再运行一遍。
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I just kept sub-dividing down until I got really easy problems, and then I combine them back.
我不断的进行子分解,直到得到简单的问题，然后我再把它们合并回去。
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Let me give you one other anecdote that I can't resist. This is the kind of thing you can use at cocktail parties to impress your friends from Harvard. OK.
让我再告诉一个秘密吧,这事儿在鸡尾酒会上,你能用来唬唬,哈佛的那帮人，好。
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Except, before I return the value, I save it.
除了我再返回之前,还保留了这个值意外。
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So close. Let me tweak a little bit.
差不多是的，我再补充一点。
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And let me describe it a little bit.
我再详细描述一下这个过程吧。
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So just to repeat the argument that we just heard.
我再重复一遍,他刚才说
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Can anyone tell me? Let's cold call somebody again.
谁来说,我再随便找一个人吧
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In this case, it's cutting up from the bottom end, which makes sense because the thing I'm looking for is always bigger than the midpoint and then, I don't know, let's pick something in between. Somebody want-- ah, I keep doing that-- somebody like to give me a number?
排除元素，这是讲得通的，因为我总是找比中点大的元素,那让我们挑一个同,中点之间的元素吧,我再来试试，谁给我个数字吧,我知道你们想给我些其他东西？
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In the numbers game, you'all, were the players.
我再强调下,你们都是参与人
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That's the general idea.
让我再说明一下，那是一个一般性的思路。
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