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What do you think? Even with these glasses on, I can see no hands up, any suggestions? Somebody help me out.
戴着眼镜我也能看出来没人举手，有想法么？大家来帮帮我吧，你们对这个算法的增长率是怎么认为的？
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And so when we say something is exponential, we're talking about in terms of the number of bits required to represent it.
所以当我们说某些东西，是指数增长的我们指的,就是代表它的比特数。
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It can be honed but those are some of the skills for a consumer internet company and one that is growing this quickly that is just essential.
是可以通过磨练而得的,但是对于增长如此迅速的,客户导向型互联网公司来说,有一些技能是不可习得的。
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And we might be attracted to the thought that the value of life is increased by its very preciousness.
我们可能会被这种想法所吸引,那就是生命的价值是因为它的珍贵而增长的。
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.. You mentioned earlier that you doubt... you have questions about whether this high rate of growth is sustainable?
您之前提到过您怀疑。,您质疑印度经济的高增长率,能否保持下去？
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This is an example of an exponential growth process and you're familiar with processes like these.
这是一个指数增长的过程,你们应该都很熟悉的
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And the company grew 80%per year for the first eight years compounded, and 60 % per year for the six years after that, which adds up to tens of billions real quick, as you know.
公司保持百分之八十的年增长,持续了八年，这之后的六年，每年增长百分之六十，正如你们所知，在很短的,一段时间内赚了数百亿。
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Implicit declaration of function increment.
函数增长的隐式说明。
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Aristotle, who was increasingly being embraced by civic republicans in England of his time had been brought up, according to Hobbes, on Aristotle's teaching that man is by nature a political animal.
在霍布斯成长的年代里,亚里士多德受到英国共和派,日益增长的拥护，在霍布斯看来，亚里士多德教导人们,人类本性上是政治性的动物。
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That's the harmonic series that's on that, and what the valves do is they shorten and lengthen that vibrating column of air very much like the cello string on the fingerboard.
这就是圆号上的泛音列,活瓣的作用是增长或减短,空气柱的高度,很像大提琴指板上的弦
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If we want to know the possibilities for spiritual growth, value growth or moral development in human being, then I maintain that we can learn most by studying our most moral,ethical,or saintly people.
如果想知道心灵成长的可能性，人类价值增长或道德发展的可能性，那我认为，我们可以研究,最道德或圣洁的人。
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They go up at rates squared.
它们以平方的速度增长
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It's a little bit of a digression, but one of the things that I've witnessed over the past twenty years is that the leakage of the -the leakage from the system in terms of the returns that go to the owners of capital -leakage has increased enormously.
讲一点稍稍离题的内容,我发现,过去的二十年中,这种损耗,这种减损资本所有者收益所得的,系统性损耗,有相当巨大的增长
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Because we've now put in a bias suggesting that it should go up. Oops. It wouldn't have hurt it.
因为我们现在加入了一个,说明股市会增长的偏向值。
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So I haven't done magic, I've given you a really fast way to solve a knapsack problem, but it's still exponential deep down in its heart, in something.
所以我并没有施魔法，我已经告诉了你,一种快速解决背包问题的方法了,但是某些方面它的核心仍然是指数增长的。
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Now. Two other things, before we do this last example. One is, I'll remind you, what we're interested in is asymptotic growth.
好，我们看最后的例子之前还有两件事情,第一是，我要提醒大家，我们感兴趣的是渐进的增长率。
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What we really want to worry about is, as the size of the problem gets larger, how does this thing grow? How does the cost go up?
随着问题规模的变大，解决问题花费的代价是怎么增长的,因此我们将会主要地讲讲？
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OK. At this point, if we stop, you'll think all algorithms are linear. This is really boring.
可能我们就认为所有的解决这个问题的，算法都是线性增长的了，真很没意思,但是他们真不是对不对？
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I want to talk about efficiency, and we're going to, or at least I'm going to, at times also refer to this as orders of growth, for reasons that you'll see over the next few minutes.
为什么是很有价值的，我想要讨论下效率，我们将会，或者至少我将会不时的，提到有序的增长,原因你们很快就会明白的。
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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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And you really, wherever possible, want to avoid that exponential algorithm, because that's really deadly. Yes.
比你的电脑的性能增长的快多了，并且大家无论何时，都要避免去用指数级的函数。
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All right. Nonetheless, even with this change, what's the order growth for bubble sort?
好的，不管怎么样，尽管这发生了，冒泡排序的增长率是多少呢？
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If it was, how much bigger does this get as I make the problem bigger?
解决方法耗费的时间会增长多少？,这实际意味着？
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India's economy was growing at close to 3 to 4% 4% from about 1950s to 1980s.
从20世纪50年代到80年代,印度经济的增长速度%,大概是3%到。
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OK. Now I want to know what's the order of growth here?
那我想知道,这个解决方法的增长率是多少呢？
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Because nutrition is going to be one of the big problems of your generation; how to have enough nutritious food for the population as it grows.
因为营养,对你们这一代人是个大问题,怎样才能确保食物的质和量,能够满足日益增长人口的需求
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Now. What's the order of growth here?
这里的增长率是多少，复杂度呢？
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One of the interesting properties of cells that are in exponential growth is that the time to increase the cell number by a factor of 2 is always the same.
细胞有一个有趣的性质,那就是在指数增长阶段,细胞增长的速度,永远是以二为底数来增长的
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As much as we know about tobacco in the United States and the fact that there are only half the number of people smoking than used to be the case, it's still expected to rise by 45% worldwide By 2030 the deaths attributed to smoking will increase from four to ten million.
就我所知美国的烟民情况,在美国吸烟的人数,只有过去的一半,在世界范围内仍有预计45%的增长,到2030年,死于吸烟的人数,将由四百万增长至一亿
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