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The work that goes on at the Center for Educational Computing Innovations really falls into three Different intersecting areas.
教育主动性计算机研究中心,的研究工作主要可以归为,三个不同的领域。
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In week zero, when we tore the phonebook in half and half and half we were recursing through that problem.
当我们将电话簿划分为一半又一半的时候,其实就是利用递归在解决问题。
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I find it again in the Christian tradition, when we do the... in Lent, like "You're from dust and to dust you will return."
在基督教传统中我发现，大斋节的传统,如“尘归尘土归土“之类“
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I've been teaching this stuff for twenty years, and I tend to find two basic kinds of students who shop my classes for the New Testament Introduction course.
这门课我上了20年，发现所有参加新约导论的学生,大致可归为两类。
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So, they call in the Spartans, and the Spartans say, "Okay, we'll decide," And they decide that it belongs to Athens.
于是他们找来了斯巴达人,斯巴达人说,"好的,我们来决断",于是他们决定,该归雅典所有
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Well, the infinity mechanism, and many of you will be familiar with this from mathematics or computer science, is recursion.
这种无限机制是递归的,你们许多人会在数学与计算机科学中,熟悉这个词
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Instead of having a central bank we decided that there would be a list of banks called the National Banks.
与拥有一个中央银行不同的是,我们决定将很多银行归到,国家银行的行列中。
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What's the point of this? Again, now that I can think about things recursively, I can similarly break things down into simpler versions of the same problem. It could be one version.
这些的意思是什么呢？再一次我想说,我既然能够以递归的方式思考了,那么我就可以简单地把问题,转化为更简单的同类问题。
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The second half of verse 5 and 6 gives the reward: God is conferring on the Israelites this elevated status ; of royalty, of priesthood; "You'll be to me a kingdom of priests, and a holy nation."
诗5余下的部分和诗6，说明了遵守的奖赏：,上帝将会使犹太人的地位提升,忠诚的，祭司的国家;,“你们要归我作祭司的国度，为圣洁的国家“
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Now that's pretty far fetched and not many people would say that a pop tart should be a controlled substance and regulated by government, but there are some very interesting chemical properties associated with foods like this that trigger things going on in the brain that affect us in a very big way.
这多少有点牵强,而且也没有很多人会认为,这种果酱馅饼应归为管制品,并受到政府监管,但有趣的是这种食品,确实有一些特别的化学特性,它会作用于大脑并会对我们产生大的影响
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re now, gong to try to fix those mistakes and work with other nations to put ourselves back on track.
但是，现在我们想要改正这些错误，But，，we’,想和其他国家合作,让自己重归正道。
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This sentence expands to a noun followed by a verb followed by a sentence and there you get recursion.
这个句子就扩展成了,一个名词,后跟一个动词,再接刚才的句子,这样就变成了递归
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And I'm going to show you an example in a 1 second, just to drive this home, but notice the characteristics. In the first two cases, the problem reduced by 1 at each step.
在前面两个例子里,每一部问题的规模缩小了,不管是迭代的还是递归的，这表明这个问题的复杂性可能是线性的。
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Indeed, all the earth is Mine, but you shall be to Me a kingdom of priests and a holy nation.' These are the words that you shall speak to the children of Israel."
因为全地球都是我的,你们要归我作祭司的国度，为圣洁的国家’,这些话你要告诉犹太人“
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- So this is where recursion gets a little trippy-- certainly initially, and that you have to kind of keep diving deeper, deeper, deeper into the problem.
在这儿就会觉得递归有点迷糊了-,起初，你必须一层一层地,深入到问题中。
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So then you have Xenophon writing his Anabasis, The March Back, telling the story of how those 1,500-- those 10,000 Greeks rather got back home.
所以当色诺芬书写《远征记》时,讲述这一千五百,哦,是一万希腊人凯旋而归的故事
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Because the algorithm I proposed is going to leverage this idea of recursion which recall was just a piece of jargon we tossed out at the last-- at the end of last week's lecture, last time's lecture recursion really in this context refers to the act of a function calling it's self.
因为我提出的这种算法使用了,递归的思想，这是上周课程的最后,所提出的一个术语，上次的课程中，递归是指,函数的自我调用。
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And the reason I want to show you this is to notice that the recursion can be doubled.
如果我来写斐波那契数列你可以看看这儿,原因是我想让你看看这部分的递归可以翻倍。
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All right, this is what's called a recurrence relation, there are actually cool ways to solve them. We can kind of eyeball it.
好，这就是所谓的递归关系,也就是解决问题的相当好的办法,我们可以来看看。
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But I want to stress again, as long as I do the base case right and my inductive or recursive step reduces it to a smaller version of the same problem, the code will in fact converge and give me out an answer.
就开心的去做吧,但是我想再次强调,只要基础事件处理正确而我的递归,或递推步骤能把它简化为更简单的同类问题,那么这段代码就可以收敛。
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We're going to see variations of this, we're going to see a variation of it called recursion, a little later on, but for now we're just going to talk about how do we do iterations.
我们稍后会去，看它的变量,它的所谓的递归数的变量，但是现在我得先讲讲,怎么来实现迭代。
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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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That means Goodbody & Company owns the shares and you just have a contractual relationship with Goodbody that, in principle, some of those shares are yours.
也就是说持有股票的是古德巴迪,你只不过与其有着合同关系,原则上,部分股票归你所有
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All right, any questions about that. Yeah?
递归调用来解决其他问题？
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How many of you have heard the term used before? How may have you heard the term used before in terms of programming languages? Great. For the rest you, don't sweat it. This is a highfalutin term that computer scientists use to try and make them look like they're smarter than they really are.
这里就要引入递归的概念了,你们中有多少人以前听过这个词？,你们中有多少人在编程语言中,用过这个词？,很好，剩下的同学也不要担心,这是电脑科学家们用来让自己,显得更聪明的夸张词汇。
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It's actually a wonderful recursive definition.
这就是一个绝妙的递归定义。
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Because in your mind you're putting tickets and cash in different mental accounts, the mental account "Tickets" generates an emotional feeling and it changes my action-- that I lost in that account.
因为在你的心里,你会把票和现金,归为两个不同的心理账户，票的那个账户“,产生了一种感性的情绪,这种情绪改变了我的行为-,让我觉得迷惑。
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And the election was entirely God's initiative and is no cause for Israel to boast. So Deuteronomy 7, verses 6-8 read: For you are a people consecrated to the Lord your God: of all the peoples on earth the Lord your God chose you to be His treasured people.
而选择也完全是上帝自愿的,不该是以色列吹嘘的原因，《申命记》第7章6-8节：,因为你归耶和华你身为圣洁的民：,从地上的万民中拣选你,耶和华选你作自己的子民。
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Wonderful recursive definition.
很漂亮的递归定义。
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