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With the computer today, you can, for the most part, not represent every possible number that mankind can think of.
在当今世界，大多数情况下，并不是要把每个数字,都精确表示出来。
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To do that, we need to describe: not only, what are the primitives, but how do we capture things legally in that language, and interact with the computer?
为了达到这个目的，我们需要描述：,包括程序基本的东西，以及怎么在这种语言中，做我们想做的事情并和计算机交互？
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Sometimes you can mess with the computer, for better or for worse.
其实你也可以恶搞一下电脑，好也罢坏也罢，都行。
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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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You get things in the energy of the room with so many students so you wouldn't just get from your computer.
和大家一起，在课堂的气氛中学习,而不是仅仅对着电脑。
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Construction is a combination of workmanship and choice of materials. Take this computer, if I pull the silicon out, I replace it with gallium arsenide, leave everything else the same.
构造则是技巧和材料的选择,的结合，拿这个电脑为例，如果我将硅取出，替换成砷化镓，其他东西不变。
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It's the various programs you run on your computer along with the various data files that you have saved on your hard drive,and so forth.
是你自身这个电脑中运行的各种程序,硬盘存有的各种数据和文件，类似种种。
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It used to be case that trained people like dieticians would have to sit down and go through one by one by one and do nutrient analysis, but of course the computer helps with that.
过去那些受过专业训练的人,如营养师,不得不坐下来,一项一项仔细查看,并做营养分析,当然,现在有电脑协助来做这些
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I'm really just messing around with the computer.
我真的是被计算机弄混乱了。
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But really, the computer's just so fast I'm drawing the same string with just a slightly different number again and again after going to sleep one second at a time.
但是真实地，这个计算机到现在为止,我一次又一次用稍微不同的数字,绘画了相同的字符串,在睡眠1秒钟之后。
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Which are actually things that take in a value and ask the computer to do something with it.
这其实也就是让计算机,对某个值进行某种操作。
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You can touch almost any part of memory in the computer systems that you want with your program, but do you want to?
通过你的程序，你可以触及到计算机系统,内存的任意部分，但是那是你想要的吗？
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So with the problems, that is where you really will get your hands dirty and truly immerse yourself in this world of computer science and programming.
带着这些问题，你就能深入研究,这真的可以使你沉浸到计算机科学,和编程世界中。
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- Your lecture -- I don't normally do this with your emails -- but your lecture the other day reminded me of this scene from The Computer Wore Tennis Shoes.
你的演讲--我通常不喜欢发邮件-,但是你几天前的演讲使我想起,“电脑穿网球鞋“的画面。
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The paradox then is how do you create such a fast computer with such slow stuff?
那么这里的悖论就是,你是如何用传输如此缓慢的材料,制造出反应如此迅速的计算机的
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I've added the ability to have more complex data structures here. But I dropped a hint in the first lecture about what you could computer with things. In fact if you think for a second about that list, you could ask what can I compute with just that set of constructs?
我添加了使用更复杂的数据结构的能力,但是我在第一节课给大家了了一个,关于你可以用什么来做计算的暗示,实际上如果你思考,这个列表一会儿的话,你会问我可以用？
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