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

要从某种数字的层面解读，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排列。

I now try to estimate it numerically.

我现试着用数字估计它。

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.

从数据看，算你很想得奖，得奖的机会微乎其微。算你不想得奖，得奖的机会还是会微乎其微。

And so you do it numerically.

因此，你会采用数值方法处理。

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几率。

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

因此， 尽管这两数量上相，但质量上并不相。

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

登山者们与数量和技术上占优势的敌人展开了激烈的游击战。

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。

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。

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数值上对此进行检验， 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?

因此，你选择用数值方法处理， 这并不需要感到不安， 因为你会想，“我怎么才能求这个积分呢？ ” 实际上，有现成的函数可以用计算， 甚至还能进行近似求解。

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排列起，你知道的，按时间顺序或数字排列，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的数值运算 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.

但他们音乐领域的真正发现是, 音符之间的音乐间隔可以用数字表示。

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

再说一次 从数字上说 强调这一点可能有点傻。

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

实际上 让我们看看矢量编辑数值上是怎的。

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之处，但两数字上是相的， 意思是一，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.

总的说，美国人口1970年代增加了2320万人——单一十年中记录的第三大增长。

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