So foremen brought in high scalers who descended the cliffs on ropes, removing rubble with jackhammers and dynamite.

所以工头找来了攀登者，用绳索从悬崖垂降下去，用轻型凿岩机及炸药来清除碎石。

And you know, the scaler effects are huge.

你知道，缩放效应是巨大的。

So it's common to use the word scaler pretty much interchangeably with the word number.

scaler这个词和number这个词通常可以互换使用。

" The scalers of the Alps and conquerors of Venice" now looked across the sea for new scenes of adventure.

“阿尔卑斯山的攀爬者和威尼斯的征服者”现在跨海寻找新的冒险场景。

I want you to think about each coordinate as a scaler, meaning think about how each one stretches or squishes.

我想让你们把每个坐标看作一个标量 也就是说 想想每个坐标是如何拉伸或挤压的。

Which two dimensional vectors can you reach by altering the choices of scalers?

通过改变标量的选择可以得到哪些二维向量？

And whenever you catch a number like two or one, 3rd or negative 1.8 acting like this, scaling some vector, you call it a scaler.

当你捕捉到像2或1 3或-1 8这样的数 缩放某个向量 你称它为标量。

Now, the more linear, algebra oriented way to describe coordinates is to think of each of these numbers as a scaler, a thing that stretches or squishes vectors.

现在 更线性的 代数化的描述坐标的方法是把每一个数字看作一个标量 一个拉伸或压缩向量的东西。

So in the conception of vectors as lists of numbers, multiplying a given vector by a scaler means multiplying each one of those components by that scaler.

所以在向量作为一串数字的概念中 一个给定向量乘以一个标量意味着每一个分量都乘以这个标量。

Now, if you let both scalers range freely and consider every possible vector that you can get, there are two things that can happen for most pairs of vectors.

现在 如果你让两个标量自由变换考虑你能得到的每一个可能的向量 对于大多数向量对 有两种情况可能发生。

You can kind of imagine turning two different knobs to change the two scalers, defining the linear combination, adding the scaled vectors, and following the tip of the resulting vector.

你可以想象一下 转动两个不同的旋钮来改变两个标量 定义线性组合 将缩放的向量相加 然后沿着得到的向量的尖端移动。

What this means basically is that when you think about coordinates as scalers, the basis factors are what those scalers actually, you know, scale.

这基本上意味着 当你把坐标看作标量时 基因子就是这些标量所占的比例。

You'll choose three different scalers, scale each of those vectors, and then add them all together, and again, the span of these vectors is the set of all possible linear combination.

你会选择三个不同的标量 缩放每一个向量 然后把它们加在一起 同样 这些向量张成的空间是所有可能的线性组合的集合。

Take a moment to think about all the different vectors that you can get by choosing two scalers, using each one to scale one of the vectors, than adding together, what you get.

花点时间想想所有不同的向量你可以通过选择两个标量 用每个标量缩放其中一个向量 而不是相加 得到什么。

Another way to think about it is that you're making full use of the three freely changing scalers that you have at your own disposal to access the full three dimensions of space.

另一种思考方法是你充分利用了这三个自由变换的标量你可以随意使用它们来访问空间的全部三维空间。

Now think of the ex coordinate of our rector as a scaler that scales eye hat, stretching it by a factor of three, and the y coordinate, as a scaler that scales j hat, flipping it and stretching it by a factor of two.

现在把我们的rector的前坐标想象成一个缩放eyehat的标量 将其拉伸到原来的3倍 而y坐标 作为缩放jhat的标量 将其翻转并拉伸到原来的2倍。