The Structure of the Universe
We say that space is three-dimensional. But in the world of Mathematics, though, we are not limited by physical constraints!! We might have four, five, or six geometric dimensions, or even infinitely many!!!

Let's go back to two-space. Thos might be a plane or the surface of a smooth objects. Suppose we have little cretures on this two-dimensional surface. Their movements are limited compared to what we are used to.

Imagine one of these two-dimensional creatures, imprisoned inside a square. He cannot get out. But it is easy for us to think of a way to get him out: reach in, grab him, yank him off the two-dimensional surface that is his universe, and plop him out down outside the square! So easy for us, but impossible for him, or anyone else in his universe.

We can extend this idea to our own universe. Suppose somebody is locked in a cubicle that cannot be broken open. There is no escape unless the walls are breached. But a four-dimensional being, looking at this poor three-space person, could quite easily grab him and pull him ouot without the walls of the cubicle even being touched. We cannot envision how this could be done, but mathematically it could be, if we allow four dimensions to exist. More on this in Flatland.

There is another way a person could escape from the cubicle, and the method is easy for us to imagine. Figure it out!!