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OK. What would you guess the order of growth here is? Yeah. Why? Good. Exactly. Right?
如果没听到答案的同学,答案是对数级的？
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you're looking for that first entry-level job that's going to help develop you the best that you can.
寻找的是能够最大程度地帮助自己发展的入门级工作。
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We started off talking about binary search, and I suggested that this was a log algorithm which it is, which is really kind of nice.
我告诉了你们这是一个对，数级的算法，这是很棒的,我们来一起看看这个算法到底做了什么。
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So will we be using the internet for video on-demand, will that be the killer app? Will millions of people wide watch this video right when they want to watch it?
所以我们会使用互联网实现随需视频么，那会成为杀手级应用么？会有数百万人,就在他们想看的时候看到视频么？
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This chart, very boring and uninteresting but useful to say there are very well defined rules as to when you're writing code, what operators, like what syntax should get evaluated first.
这个图表，看起来很烦，很无趣，但是它很有用,有非常明确的规定,譬如，当你写代码时，就会涉及操作符的优先级。
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And this is the energy level diagram for multi-electron atoms.
看一下能量级图表中,多电子原子的部分。
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We have the difference between conjunct music with the and disjunct music and that perhaps adds to the unsettled quality of the beethoven Fifth Symphony.
我们发现存在着不同,当级进混合着跳进时,也许正是这样的处理突出渲染了,贝多芬第五交响曲中的不安氛围
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The first is this, that emotions are basically mechanisms that set goals and priorities and we're going to talk a lot about in this class and the next class about universals.
首先，情感是基本机制,设定目标及事务优先级,我们将谈论很多关于宇宙的话题,在这堂课和下堂课。
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They often involve networks of reactions, not just one enzyme but a series of enzymes that serve to amplify each other.
这些反应通常包括一个反应网络,不只是一种酶,而是一系列的酶来进行级联放大
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Aaron Antonovsky Aaron Antonovsky, the third person I would consider the grandfather, brought in the idea of focusing on health.
还有，第三位祖父级人物，提出了关注健康的理念。
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And we can look at precisely why that is by looking at the equations for the energy levels for a hydrogen atom versus the multi-electron atom. So, for a hydrogen atom, and actually for any one electron atom at all, this is our energy or our binding energy.
而且我们可以精确地看看,为什么是这样的,通过看对于氢原子和,多电子原子能级的方程所以对于氢原子，事实上对于任何一个电子，这是我们的能量或者我们的结合能。
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Thank you. I mean, I know I sort of said it to you, but you're right. It's logarithmic, right?
但你们是正确的，是对数级的,它有这样的效率是因为他每次能把问题减半？
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Taught by a star who was a leader thinker in this area.
教授是该领域的,明星级领头思想家。
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OK. And then the exponentials, as you saw is when typically I reduce the problem of one size into two or more sub-problems of a smaller size.
好，然后说到指数级，正如你所见，典型的例子是,我讲一个问题分解成为,两个更小规模的子问题。
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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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OK. There's some constants in there, but this is order log b.
对数级的，这太重要了，接下来我要给你们看个例子。
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So you can see, even the quadratic ones can blow up in a hurry.
如你所见，甚至平方级复杂度的方法。
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Lowest energy to highest energy and it is a function of occupancy.
从最低能量到级最高能量级都是这样,而这是占据的函数。
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This case, I reduced the size of the problem in half.
这很好的表明了这是，对数级复杂度的问题，我马上就要解释。
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And if I'm running an exponential algorithm, any guesses?
杂度是指数级的呢？,有人猜猜么？
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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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Now downside of this, well, I've just now violated my preference for having main up top, maybe that's forgivable.
现在在后面，我违反了把main函数放在上面的优先级,可能那是可以宽恕的。
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It is a conservative system so all the energies are negative.
它是一个保守系统,所以所有的能量级都是负值。
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It's got that property of, it cuts things in half.
换个角度来思考下为什么是对数级的。
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This is what the energy level diagram looks like.
这就是能量级图表大致的模样。
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And possibly the most conjunct of all melodies in the history of music was the melody that we looked at very briefly in the first gathering, and that is Beethoven's famous Ode to Joy.
大概在音乐史上,最为级进的旋律,是我们第一堂课上撇过一眼的,贝多芬的《欢乐颂》
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You might want to say in the real world, if you go to a movie theater for this R-rated movie, "Are you 18 and over or are you with a parent?"
在现实世界中，你可能想说，如果你去电影院看R级电影，“你有18岁吗？,或者你跟随你的父母亲来的吗？“
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A log algorithm typically is one where you cut the size of the problem down by some multiplicative factor.
对数级复杂度的算法就是指,通过一系列常量级步数的操作,可以将问题的规模。
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First of all, as you can see by the trajectory here, it's very conjunct, right, all neighboring notes here.
首先,你可以通过这里的轨迹看到,这是明显的级进,全是相邻的音符
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There are some relative, the notion that the energy gap between n equals one and n equals two is greater than that for n equals two to n equals three. That is correctly represented.
还有很多与之相关的内容，比如说这个观点，第一能量级和第二能量级,之间的能量差要大于第二和第三能量级间的,能量差，而这已经被正确地表示出来了。
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