So the pain you're suffering now is actually instrumentally valuable, useful as a means, even though it's intrinsically bad.
所以你现在忍受的痛苦,是有利用价值的,作为手段是有用的,尽管痛苦本身是坏的。
That is, I think, essentially the difference between what we have been talking about so far, even though there have been a variety of outlooks, and what we are talking about now.
我想这就是形式主义者,和伊瑟尔的不同了,尽管大家对于我们这堂课有很多展望,对于我们现在的学习也有很多期待。
Now, Alsatians were French, even though many of them spoke German dialect.
阿尔萨斯人是法国人,虽然他们很多人说德国方言
Even though we started with a single vector, which is the position vector, we're now finding out that its derivative has to be a vector and the derivative of the derivative is also a vector.
即使我们从单个矢量出发,即位移矢量,我们现在也能得出它的导数是矢量,而且导数的导数也是一个矢量
So I'll now start to get into that habit, even though it's a bit of distracting detail, it's just consistent with the expectations that the compiler really has.
所以我现在将开始养成那个习惯,虽然这是一个有点分散注意力的细节,它只是与编译器,拥有的期望是并存的。
If it's going in a circle, you will say from now on, that it, indeed, has an acceleration, even though no one's stepping on the accelerator, of amount v^2 over R.
如果它在一个圆周上运动,你会说从现在起它其实有加速度,即使没有人去踩油门,加速度大小为 v^2 / R
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