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All the energies are negative because it is a bound system. I start up here with n equals one.
所有能量级都是负数，因为它是一个束缚系统,在这里我从n等于1讲起。
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but it's, it's like tough to get an A.
但是想得到A级的成绩，简直是太难了。
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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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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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We're going through a subprime crisis right now, which is a banking crisis as well.
我们现在正在经历一场次级债危机,它同时也是一场银行业危机
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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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So, flats are below, sharps take you up a half step.
降调是下降半音级,而升调是上升半个
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It's a good sign that this is logarithmic, and I'm going to come back in a second to why logs are a great thing.
为什么对数级复杂度是个好事情，让我们再来看一个算法,噢，抱歉是让我们再来看两个算法。
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All right. The question is, is there a point where it'll quit.
因为指数级函数真的很致命，好，问题是。
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It is certainly possible, for example, that a quadratic algorithm could run faster than a linear algorithm. It depends on what the input is, it depends on, you know, what the particular cases are. So it is not the case that, on every input, a linear algorithm is always going to be better than a quadratic algorithm.
一个二次平方级复杂度的算法,当然也是可能跑的比线性复杂度算法快的,这取决于，你知道的，输入以及特定的案例，因此并不是对于每个输入,线性复杂度就一定会,比二次平方级复杂度的算法的表现要好,只是通常来说是这样的。
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And as a consequence, it is log.
因此这是对数级复杂度的算法。
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I need a half step above G.
上面应该是个半音级
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What's a half step above D?
上升半音级是什么
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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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I got to go up just a half step there, I'm on E.
上升半音级到E
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Now we have what's called a VI chord and we're not moving directly to the IV chord; we're moving to another chord--here a VI chord, which happens to be a minor chord.
首先里面有VI级和弦，但没有直接进行到IV级和弦;,而是转向了另一个-这里是一个VI级和弦，它正好是一个小调和弦。
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He was a Yale graduate, class of 1914 and unfortunately I seem to have misplaced-- Well, I can generate a little bit of it here.
他是耶鲁1914级的毕业生,真不巧,我找不到乐谱了,好吧,我试着弹一段吧
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It has a constant.
它就是常数级复杂度。
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Melodies that are just running up and down a scale-- neighboring tones.
级进旋律是指在整个音阶的,相邻音符上跑动的旋律
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But it's just--F is just a half step away, so that's good.
也只是半音级的距离,很好
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What's a half step above G?
比G高半音级是什么
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