So, no matter how you say it, this is always zero. So, in a way, this reinforces our intuition that del, even though it's not at all an actual vector sometimes can be manipulated in the same way.

因此，无论你怎么描述它，它总是0，那么在某种程度上，这加强了我们的直觉，即▽有时也可以用同样的方式计算,即使它并不是真正的向量。

youdao

Now guys, even though you are great, she still might say no.

男士们，即使你们是很棒的，她还是有可能会说不。

youdao

Well, that's at least an improvement, because then we say, look, while you're asleep, even though there's no P-functioning going on, the lack of P-functioning is temporary, so you're still alive.

这至少算是个改进，因为我们能说，看，你睡着了，即便没有任何人格功能性发生，人格功能性的缺少是暂时的，就说明你还活着。

耶鲁公开课 - 死亡课程节选

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

耶鲁公开课 - 基础物理课程节选