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So that can be unsettling when we think of this as happening at a certain contemporaneous moment in the history of thought.
如果把这个问题放在思想史的特定时期来想,它可能是难以解决的。
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It's going to lead to a lot of interesting things. It's also going to create a really huge problem for monotheistic thought they're going to struggle with for centuries and actually still do struggle with today.
并会引发一系列的有趣事件，它也将给一神论思想,带来一个相当大的问题，这个问题,他们纠结了好几个世纪，直到现在依然存在。
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So this is very similar, this is a kind of recursive thinking we talked about earlier, where we take our problem and we make it smaller we solve a smaller problem, et cetera.
我们则跳过比猜想数小的那个区间,然后我们重复这一过程,跟之前我们讲过的，递归思想非常类似,我们解决问题的时候,先把问题一步步变小，然后解决小问题。
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But can I borrow that idea of taking a problem and dividing it into something smaller.
但是我可以借鉴解决这个问题的思想并将其划分为,更小的问题。
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Milton is inheriting here an enormously rich tradition of thought on this subject.
弥尔顿在这个问题上正是遗传了,这些传统思想。
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Exposure to the things that participate in the forms may nudge our minds or our souls in such a way that at that point.
接触到一些有关形式的问题,使我们的思想或者灵魂,在某一点开始考虑这个问题。
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All right. Let's hope we can free our minds of these matters now and turn to something a little more substantive, which is the question--before we plunge in to Gadamer really: what is hermeneutics?
现在让我们把思想从这些事物中解放出来,转向更实质性的问题，在我们探讨伽达默尔之前：,曾提出这样一个问题：诠释学是什么？
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Which questions and which thinkers ? should one pick up for oneself?
哪些问题和哪些思想家,是必需认识的呢？
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Another Florentine, Machiavelli, moved further in the same direction.
另一位来自佛罗伦萨的思想家马基雅弗利,更加深入的研究了这个问题
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How it is to enter into the creation of films and what are the schools of thoughts that have origined by emphasizing one or the other so that immediately we'll be get into the question that you are already sensative to I'm sure.
怎样走进电影创作,电影创作有哪些相伴相生的,思想流派,我们很快就会,探讨这个问题,你已经对此有所感悟。
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OK. So, what do I want you to take away from this? This idea of binary search is going to be a really powerful tool. And it has this property again, of chopping things into pieces.
从这里学到些什么？二分查找的思想,是一个非常有用的工具,我重复一遍，把问题拆成几部分来解决,那事实上，这里的增长率是多少？
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It's probably among the most useful ideas there is for solving complicated problems.
这大概是解决复杂问题,最有用的思想之一。
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All right. So it's fun, and I got a little bit of applause out of it, which is always nice for me, but I also showed you how to think about it recursively.
好，挺有趣的，我也得到了一点掌声，这让我挺高兴的，但是我想让大家明白,怎么用迭代的思想来解决这个问题。
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This is a problem that we will see considerably later in the term that vexes a very important political thinker by the name of Hobbes about whether an individual can somehow put their own sense of conscience or moral integrity even above the law.
这是个我们,稍后会仔细探讨的问题,也是让这位重要政治思想家,贺伯斯大力争论的问题,他质疑个人,是否可以将其自身的道义感,或道德正直置于法律之上。
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Well, realize one of the themes in this course and really one of the themes in programming and solving any problem with a machine is going to be really to just take small bites one at a time out of these problems until the end result ultimately is that you've actually bitten off a fairly large fairly interesting problem and in the aggregate, you've actually implemented something pretty sophisticated.
好吧，让我们先想一下这件事带给我们的主题,编程和解决问题的思想,一台机器最开始只会一步一个脚印,沿着要解决的问题向前迈进,直到最终的结果出来,最后你会发现，你已经解决了一个相当大,相当有趣的问题，而这个问题在最初看起来确是相当复杂的。
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Not so easy to see. All right, but this is actually a great one of those educational moments. This is a great example to think recursively. If I wanted to think about this problem recursively- what do I mean by thinking recursively?
看不太出来，好，但实际上是一个有教育意义的时刻,这是一个很好的关于递归的例子,如果我用递归的思想,去考虑这个问题-,我该怎么用递归去解决这个问题呢？
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I spotted an error here, I could have spotted it by running it on different test sets, and using prints things, another way of doing it, but this idea of at least simulating it on simple examples lets you check a couple of important questions.
操作么？我在这里发现了一个错误,我也可以通过运行不同的测试集，或者运用print声明来发现这个错误，但是至少应该用简单的例子来手工模拟下,代码的思想可以让你,对一些很重要的问题进行检验。
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