Something that looks at the problem numerically, and not theoretically.

要从某种字层面来解读，而不是理论。

Hard as it may be for you to believe, most people don't sort their breakfast cereal numerically by fiber content.

也许你很难相信，大多人不会把芥麦早餐纤维排列。

I now try to estimate it numerically.

我现在试着字来估计它。

It's very difficult，numerically，to win a prize if you want to.Even if you don't want to, it's very difficult numerically.

从据来看，就算你很想得奖，得奖机会微乎其微。同样就算你不想得奖，得奖机会还是会微乎其微。

And so you do it numerically.

所以你字来做。

So this tends to be done numerically.

所以这往往是字来完成。

They can even numerically assess the  odds of winning a territorial dispute.

他们甚至可以从字上评估赢得领土争端几率。

So, though the two ships are numerically identical, they are not qualitatively identical.

因此， 尽管这两艘船在上相同，但在质上并不相同。

The mountaineers waged spirited guerilla warfare against the numerically and technologically superior enemy.

登山者们和技术上占优势敌人展开了激烈游击战。

This is numerically speaking, what it means to apply a rotation then a sheer to a given vector.

从值上讲 这意味着对给定向进行旋转和旋转。

When you do this calculation purely numerically, its matrix vector multiplication.

当你纯值方法计算时 它是矩阵向乘法。

I have endeavoured to test this numerically by averages, and, as far as my imperfect results go, they confirm the view.

我已努力通过平均值在值上对此进行检验， 就我不完美结果而言， 它们证实了这一观点。

You don't have to feel bad about doing it numerically, because you're like, oh, how do I take the integral of this?

你不必因为字来做这件事而感到难过， 因为你会想，哦，我该如何计算这个积分？

But a median is taking our ages and lining it up, you know, chronologically or numerically and taking the middle age.

但是中位是把我们年龄排列起来，你知道，按时间或字排列，然后是中年。

Easier to think about rotations performing This matrix multiplication numerically is, once again, pretty similar to the two dimensional case.

更容易考虑旋转执行这个矩阵乘法值运算 再一次 和二维情况很相似。

But their true discovery in the field of music was that the musical intervals between the notes could be expressed numerically.

但他们在音乐领域真正发现是, 音符之间音乐间隔可以字表示。

Again, numerically, this might feel like a silly point to emphasize.

再说一次 从字上来说 强调这一点可能有点傻。

In fact, let's see how vector edition looks numerically.

实际上 让我们看看矢编辑在值上是怎样。

Though they have absolutely no parts in common, the two ships are numerically identical, meaning one and the same, so A equals B.

尽管它们完全没有共同之处，但两艘船在字上是相同， 意思是同一艘船，所以 A 等于 B。

Altogether, the US population rose in the 1970s by 23.2 million people -- numerically the third-largest growth ever recorded in a single decade.

总来说，美国人口在1970年代增加了2320万人——在单一十年中记录第三大增长。