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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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but we need a sense of growth, not just spending to keep us out of depression essentially
但是我们需要有增长意识，不能只是通过花钱来让我们免于陷入危机。
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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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And what are some of the obstacles to sustain high growth? Some questions are... we are going to look at today.
又有哪些因素可能阻碍其经济的,高速增长？今天我们会。,讨论相关的问题。
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This is essentially a reboot of something we put together a few years ago but the thing had grown in size, this particular app.
这从本质上来说是,重新启动前几年我们组装的一个东西,但它的大小已有所增长，尤其是应用程序。
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If the rate of growth had sustained, that's what the population would've been.
假如高增长率持续的话,我们现在得有多少人口啊
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Because we underestimate the growth of exponential function.
因为我们低估了指数函数的增长。
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And you went ahead and worked with the Listening Exercises nine through eleven to engage the musical instruments a bit in those particular exercises, and we have performers here today that are going to, as you can see, demonstrate some of these instruments for us.
你们先前做过,听力练习九至十一题,在这些练习中,你们增长了对乐器的一些认识,今天我们请来了表演者,你们将看到,他们稍候,将为我们在这里演示一些乐器
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Usually what I want to talk about is what's the smallest size class in which this function grows? With all of that, what that says b is that this we would write is order b.
通常我们想要的是,方法增长时最贴切的描述,也就是说，在这个问题上,算法关于。
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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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If the rate of population growth of the United States between 1820 and 1850 had sustained over time, we'd have today approximately one and a half billion people in the United States.
如果在1820至1850年间,美国人口增长率保持下去的话,今天我们的美国,就会拥有近十五亿人口
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So you can see, and this is an important thing we look at, is that as we look at growth, it didn't look like it mattered a lot with 6.
现在你可以明白，我们在做的是一件很重要的工作，那就是当我们看到增长的时候，参数为6的时候倒是没什么关系。
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But effectively it is, as we saw before, exponential.
但是实际上正如我们之前看到的，它是指数增长的。
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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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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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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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And what we want to do then, is we want to basically come up with, how do we characterize the growth-- God bless you-- of this problem in terms of this Quadra-- sorry, terms of this exponential growth.
现在我们想要做的就是,我们怎么来量化增长率呢？,在这个问题中也,就是框架-对不起是，输入指数的增长。
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Let's suppose n is 1000, and we're running at nanosecond speed.
假入我们一秒钟运算十亿次，我们已经看过了对数级，线性增长的。
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I could get a really big upper bound, this thing grows exponentially.
那么我可以得出一个相当大的上界，我们可以给一个指数级增长的上限。
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We don't like exponential algorithms, or at least you shouldn't like them, because they blow up quickly. And we saw some examples of that. And unfortunately, some problems are inherently exponential, you're sort of stuck with that, and then you just have to try be as clever as you can.
我们并不喜欢指数算法，至少你不应该喜欢，因为他们会,爆炸式的增长，我们将看到,这样的例子，不幸的是，一些问题先天是指数型的，你会被它们稍稍的卡住,然后你就得尽可能的发挥你聪明才智了。
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