I'm not quite sure,because we have to turn to a metaphysical question that we've touched upon before,namely,can souls split?
我不太确定,因为要先提出一个以前说过的,形而上学的问题,就是,灵魂可以分裂么?
You said that you used to live in Alaska.
你说过你以前住在阿拉斯加。
I mean, you may not understand it with algebra before but some of these sorts of pictures have you seen before?
我是说可能代数部分你没看懂,但你们以前见过类似的图像吧
Bisection methods were known to the ancient Greeks, and it is believed by many, even to the Babylonians.
二分法由古希腊人所发明,我以前也说过,一直到17世纪二分法都被。
So it's not just a question of the past, as I say and as I've said before.
正如我以前说过的,它不只是过去的问题。
I don't recall having shared my love of pizza with you before, but there it is--two favorite things I love--love pizza, delicious, love chocolate, delicious.
我不记得我以前跟你说过我对比萨饼的喜爱,但事实就是--我最喜欢的两种食物,喜欢比萨饼,好吃,喜欢巧克力,好吃。
It's all over the place, and as soon as I start to play it, at least once we get in to it, you'll say, "Oh, yeah, i've heard that."
我们经常会听到它,只要我一开始放,至少当我们听到主要部分,你们会说,原来这样啊,我以前听过
It used to be the case that-- well I mean my guess is that very few of you probably go through a day without interacting with a water bottle at some point.
以前的情况是,我是说,我猜在座很少有人经历过,一整天不带水壶的日子
You have done it before, but when you say, "I know calculus, " Sometimes it means you know it, sometimes it means you know of some fellow who does or you met somebody who knows.
你们以前学过,但当你们说,"我懂微积分",有时这表明你们懂,有时表示你知道谁懂,或者你遇到了懂这个的人
Now. You might look at that and say, well that's just a lot like what we had over here Right? We had some additive constant plus a simpler version of the same problem reduced in size by 1.
现在你可能会看着这个说,这很像我们以前做过的,对不对?我们用一些附加的常量,加上问题的另外一个规模缩小了1的,简化版本来代替这个问题本身。
We said before that in Western music we have musical notation.
我们以前说过,在西方的音乐里有音乐记谱法
Okay. So that's the basic distinction and, as I say, as far as I can see it's irreconcilable so it leaves us with a choice that really does have to be made, and it's a choice which looms over a course in literary theory and coming to understand the tradition of literary theory.
这就是二者基本的不同之处,我以前说过,只要二者不能兼容,我们就不得不从中选择一个,这个选择将会一直出现在文学理论课,和理解文学理论传统的过程中。
We've talked about some of these already, having to do with the nature of the harmony-- that pop music tends to have simpler harmonies, and that those harmonies tend to be more repetitious, that they tend to have harmonies that have chords in root position.
我们以前说过,这个问题与和声的性质有关-,流行乐通常用较为简单的和声,流行乐通常用较为简单的和声,流行乐手也大多喜欢用原位和弦。
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