Photocopiers print in two dimensions. Now,imagine how this would work for three dimensions.

VOA: special.2010.10.29

When I think about the two dimensions I'd like to explore first, I'd like to let you think about for a while the purpose of education.

在想两种形式的教育时,我要先进行探究，我希望你们先思考一下,教育的目的。

麻省理工公开课 - 媒体、教育、市场课程节选

Then next week we'll do more complicated problems that involve motion in higher dimensions, how to go to two dimensions or three dimensions.

下周我们将会处理更复杂的问题,包括更高维数的物体运动,如何处理二维以及三维运动

耶鲁公开课 - 基础物理课程节选

Think about dimensions of painting or architecture perhaps but what are the two dimensions of music?

想想绘画或者建筑的维度,那么音乐的两个维度又是什么呢

耶鲁公开课 - 聆听音乐课程节选

First, I'd like to explore two dimensions of education and I'm thinking not only in terms of classroom education which you are familiar with but also the distance education which is so prominent in the development today.

首先，我想探究两个维度的教育,其中一个角度是,你们熟悉的课堂教育,另一个角度是远程教育,现在它的发展十分显著。

麻省理工公开课 - 媒体、教育、市场课程节选

These other two, primaries and higher dimensions, they're both great points.

另外两个约束条件,初选和多维度,这二者都是很有现实意义的

耶鲁公开课 - 博弈论课程节选

If you live in two dimensions or more, you've got to use vectors to describe most things.

如果你要考虑二维或二维以上的问题,大多数情况下需要用矢量来描述

耶鲁公开课 - 基础物理课程节选

So, when you go to two dimensions, you need a pair of numbers.

因此在二维空间里,你需要一对数字来描述

耶鲁公开课 - 基础物理课程节选

What are the two dimensions of music?

音乐的两个维度是什么

耶鲁公开课 - 聆听音乐课程节选

That's the problem in two dimensions.

那是二维中的问题

耶鲁公开课 - 基础物理课程节选

Time. Okay, pitch and time and pitch and duration, excellent, so those are the two dimensions of music and well, indeed we could even call them the axes of music because we tend to think of pitch on a vertical axis.

时间,音高和时间,或者是音高和时值,非常好,它们是音乐的两个维度,其实我们可以称呼它们为音乐的两轴,因为我们趋向于将音高放在竖轴上来考虑

耶鲁公开课 - 聆听音乐课程节选

Well,if you go back to the formation of musical notation from the ninth through the twelfth centuries we see that very early on these two dimensions of music the two axes of music that we talked about before pitch vertically and duration horizontally, are in place and we have these spots in this grid.

回顾一下从公元九世纪至二十世纪,音乐记谱法的历史形成过程,我们可以看出,音乐的两个维度,就是我们之前提到的音乐的两个轴,纵轴是音高,横轴是时值,在早期已经存在了,我们在这样的网格上用点记录

耶鲁公开课 - 聆听音乐课程节选

In fact, I'm going to use only two dimensions for most of the time because the difference between one dimension and two is very great.

实际上,大多数时候我只考虑二维的情况,因为一维和二维的差别很大

耶鲁公开课 - 基础物理课程节选

I picked for it two dimensions as the standard way to explain it.

我选取二维的情形作为标准模型来讨论

耶鲁公开课 - 基础物理课程节选

But this is the way to do it in two dimensions.

但这也是在二维空间里的方法

耶鲁公开课 - 基础物理课程节选