I'll give you his direct line number.

我给你他的直线电话。

We need to take the number one line.

我们要坐一号线。

It flew through the bus line number, then on out the front of the white house, that, hopefully, you find comfort downtown.

这种现象能透过公交来到白宫面前，然后希望你们能从中寻求一些安慰。

If I have a bunch of numbers-- and I'll draw a number line, here.

如果我有一堆数字——我会在这里画一条数字线。

Notice that I've set up relative line numbering on the left.

请注意，我已在左侧设置了相对行编号。

If I draw a number line here-- let's say I have a bunch of numbers in my population.

如果我在这里画一条数字线——假设我的人口中有一堆数字。

You can only have a finite number of values, while the normal distribution is defined over the entire real number line.

您只能拥有有限数量的值，而正态分布是在整个实数线上定义的。

One dimensional space is really just the number line, so transformation like this takes into de vectors and spits out numbers.

一维空间实际上就是数轴 所以像这样的变换会得到向量 然后得到数字。

So, wherever my cursor is, it shows the current line number, but everywhere else, it's just the offset from where I am.

因此，无论我的光标在哪里，它都会显示当前的行号，但在其他地方，它只是与我所在位置的偏移量。

And finally, positive direction is always to the right, so if you see a number line, then a larger number will always be to the right of a smaller number.

最后，正方向总是向右，所以如果你看到一个数轴，那么一个较大的数总是在一个较小的数的右边。

Just to be clear, even though I've embedded the number line into d space like this, the outputs of the function are numbers, not two de vectors.

明确一点 即使我像这样将数轴嵌入到d空间中 函数的输出是数字 而不是两个de向量。

But before getting into that, I need to spend some time talking about linear transformations from multiple dimensions to one dimension, which is just the number line.

但在这之前 我需要花点时间讨论从多维到一维的线性变换 也就是数轴。

[Mike] To help us scratch the surface, our production team, along with the help of Texan locals, have lined up a number of challenges to help us immerse ourselves in this truly epic state.

为了让我们深入了解，我们的制作团队，在德克萨斯州当地人的帮助下，安排了一系列的挑战来帮助我们沉浸在这个真正的史诗般的州。

The lesson here is that any time you have one of these linear transformations whose output space is the number line, no matter how it was defined, there's going to be some unique vector V corresponding to that transformation.

这里的经验是 任何时候你有一个这样的线性变换它的输出空间是数轴 不管它是怎么定义的 都会有某个唯一的向量V对应于这个变换。