Maybe it's some evidence, some artifact of a higher dimension that we can't consciously perceive.

也许是一些证据，一些更高维度的文明，只是我们目前还不能感知。

So a Wormhole bends space like this, so you can take a shortcut through a higher dimension.

虫洞可以把空间像这样折叠起来，于是你可以从更高的维度抄近路。

But if we imagine sliding Mister Triangle into the mirror, there's no way he can cover his mirror image without us rotating him in a higher dimension.

但是如果我们想象三角形先生滑入镜子，如果我们不把他旋转到更高的维度，他不可能遮住他的镜像。

As with transformations in higher dimensions, like the ones I talked about in chapter three.

就像高维变换一样 就像我在第三章讲的那样。

This idea also makes sense in higher dimensions, when the number of equations equals the number of unknowns.

当方程的数量等于未知数的数量时 这个想法在高维也有意义。

Now consider a vertical plane representing a for us inaccessible higher dimension that intersects with the horizontal plane and in doing so, places the random points on a curve that does reveal a meaningful connection.

现在想象一个垂直面，代表我们无法触及的更高次元，让它与水平面相交，这样，那些随机的点会由曲线连结而展现出意义。

But more importantly than that, once you get all the core ideas in two dimensions, they carry over pretty shamelessly to higher dimensions.

但更重要的是 一旦你在二维空间中掌握了所有的核心思想 它们就会毫不羞耻地转移到更高的维度。