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

要从某种数字的层面来解读，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，大多数人不会把芥麦早餐用纤维量的顺序。

I now try to estimate it numerically.

我现在试着用数字来估计它。

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.

从数据来看，就算你很想得奖，得奖的机会微乎其微。同样就算你不想得奖，得奖的机会还是会微乎其微。

And so you do it numerically.

所以你用数字来做。

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

当你用纯数值的方法计算时 它是矩阵向量的乘法。

So this tends to be done numerically.

所以这往往是用数字来完成的。

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

他们甚至可以从数字上评估赢得领土争端的。

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

因此， 尽管这两艘船在数量上相同，但在质量上并不相同。

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

实际上 让我们看看矢量编辑在数值上是怎样的。

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

再说一次 从数字上来说 强调这一点可能有点傻。

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

从数值上讲 这意味着对给定的向量进行旋转和旋转。

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数值上对此进行检验， 就我的不完美结果而言， 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?

你不必因为用数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.

但是中位数是把我们的年龄起来，你知道的，按时间顺序或数字，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的数值运算 再一次 和二维情况很相似。

Geometrically, this matrix transforms our grid into jennifer's grid, but numerically it's translating a vector described in her language to our language.

何上 这个矩阵将我们的网格转换成jennifer的网格 但从数字上讲 它将用她的语言描述的向量转换成我们的语言。

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，但两艘船在数字上是相同的， 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.

20 世纪 70 年代，美国人口总共增加了 2320 万人，这是有记录以来十年内第三大增长。

Now, if you try to work through this numerically, like I did back then, it's horrible, just horrible, and un enlightening, for that matter.

现在 如果你试着用数字来解决这个问题 就像我当时做的那样 这很可怕 非常可怕 而且没有启发性。