But because you only have a finite number of bits, the takeaway for today is that there's only so much precision.
因为只有有限个比特,今天的重点就是,它就这么点精度。
When Alexander gets to Persia, or let's say when he gets to Egypt, he knows that there is this god Isis, this female god Isis, that's very important.
亚历山大抵达波斯时,这么说吧,他来到埃及后,发现当地有个叫艾西斯的神,这位艾西斯女神地位非常崇高。
Nobody knows, but there's a theory which won't answer your question but will put it into a broader context.
没有人知道答案,但有这么个理论,它无法回答你的问题,但却能让你从更宽广的视角来看这个问题
It's not so simple, and so let's see how, let's take an example.
就没这么简单了,让我们看看,这里有个例子。
In the case of a recursive exponentiator, I'm going to do the following trick.
在这个迭代求乘方的例子里面,我会用这么个小把戏。
So, for example, to give an example that Plato actually gives in the dialogue, we are all awake now, but previously we were asleep.
举例来说吧,柏拉图在对话中举过这么个例子,我们现在都清醒着,但之前我们都在熟睡
And of course, that's what the overwhelming portion of the investment community did in the 1930s, and in the 1940s, and in the 1950s.
当然,绝大部分投资机构,在上个世纪30年代,以及40和50年代就是这么做的
You have a freewill offering--just because someone wants to do this, a freewill offering. And you have a vow offering that would be offered on the successful completion of a vow, for example. And these sacrifices are all entirely optional.
自由祭品--只因为有人想这么干,自由祭品,还有一个誓言祭品,举个例子,一个誓言如果成功达成,便会供奉祭品,这些祭品都是可选择的。
I never met anybody who seemed more like an author than this person, and yet he's raising the question whether there is any such thing, or in any case, the question how difficult it is to decide what it is if there is.
我从来没有遇见过比他看起来更像作家的人,现在他提出了一个问题,问无论如何,如果有这么个东西的话那么决定它是什么有多难。
Before that, he was a child prodigy She was a music teacher, and probably a concert pianist. But I don't think she had a great career.
在这之前,他是一个神童,她是一个音乐教师,也可能,是一个音乐会钢琴家,但我不认为,她有个这么好的职业。
Well, we have this idea of a seven-note major and seven-note minor.
那个,我们有这么个概念,七音符大调和七音符小调
And we're actually going to get a little bit deeper in our clicker questions here, since when you do your problem-set it won't be quite this straight forward that you'll be answering this kind of question, but actually you'll be thinking about how many different orbitals can have certain state functions or certain orbital names.
事实上我们要讲的,比这个问题还要深一些,因为当你们做习题集的时候,你们不会遇到这么明显的问题,而是要考虑有多少个轨道,有某种特定的态函数,或者特定的轨道名字。
Right, that's what happened in the actual case. - Right.
对,就是这么个情况,-对。
And it's not a la-di-dah thing where--I'll tell you, once there was a student in there who had really fantastic French and I said, "Why is your French so good?"
其实也不是那么严格要求的,我给你们讲,以前有个学生法语特好,我就问他你法语怎么这么好啊
This is the most recent version of this that--and we'll talk about whether this graphic makes sense to people, whether it's the kind of information people can access, and make use of, whether people even pay attention to it or know about it.
这是最近的修订版本,我们来讨论一下,这个图是不是够简单明了,提供的是不是人们可获取和利用的信息呢,甚至人们没有注意或者知道有这么个图表
And to do that, in this it says, if I have a value, I want to keep it around, to do that, I can do things like this.
为了达到这个目的,在这里面是这么说的,如果我有个值,想把它保存起来,我可以这么做。
I've gotten pretty far in my life, and as far as I can tell I've never, ever, ever had to remember the capitals of the 50 states.
都这么多年了,我还记得我从来没有,需要住50个州的首府的时候。
I tried to find it on Google really quick and nothing came up, but I think there is this idea of how you organize a tapestry in that fashion.
我试图在谷歌上查找但是没有结果,但是我想有这么个想法,就是怎么用那种方式编织挂毯
So, what's the idea? If I know what my hash function does, it maps, in this case characters into a range zero to 256, which is zero to 255, I create a list that long, and I simply mark things.
我知道我的哈希函数做什么,在这个例子中,它将字母,映射成0到255的256个数字,我创建了一个这么长的列表,并且我只是简单的标志这些东西。
Once there was a story on grade inflation that the Yale Daily News began by saying, " As Shelly Kagan So I know I've got at least the reputation of being a hard grader.
一旦有关于成绩膨胀的故事,耶鲁日间新闻会从下面这句话开始“,薛立·卡刚,这至少让我知道了,我有严厉这么个名声。
We could imagine a person dying and then reemerging in another body.
我们可以想象,有这么个一个人,死了,然后出现在另一个身体里
So use whatever you can get out of me for the rest of way don't be deterred don't be flawed " because "Oh, he's produced so much", no I'm such an old man,too.
可以使用任何你们可以从我这里得到的东西,在剩下的道路中,不要受阻,不要觉得有缺陷,不要想着“哦,他有这么多成果,我也只是个老头。
So over here,we've got something that's going to think to itself, I'm Shelly Kagan.I'm in horrible pain.
所以这边有个东西心里这么想,我是Shelly,Kagan,我现在很痛苦。
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