Why We Cannot Comprehend Past the 3rd Dimension

First off, I am not talking about time as the 4th dimension. I am talking about geometrical dimensions.

Trying to picture what the 4th dimension would look like is very tricky, but one (if not the main) reason we cannot comprehend it is the same reason that a 2D person comprehend the 3rd dimension.

One way to think of it is if a stick person was a living thing. If you were to talk to him, he would never be able to see you. Why? Simply because he cannot look what we call "up"

When he looks up, he his merely turning his head on the page. He cannot see you unless you were to touch the page that he was on.

It would be similar if he was to make a safe that had a really strong lock. While none of his friends would be able to open it, you could see everything inside and would have no trouble taking anything (assuming you wanted a 2D good) but they would be baffled by it. No matter how hard they tried, they would have no way of preventing you from getting into the safe, since they have no way to block the "upward" dimension.

My Awesome Drawing

If a being was in the 4th dimension, they would be able to hide from us if they wanted to for the same reason we can hide from a stick person so easily. So if they wished to show themselves, we could see them, otherwise they could disappear and reappear somewhere else and we wouldn't be able to see why.

This was all inspired by the story Flatland that one of my professors told me about, and I decided to look into it. Here is a link to the story I looked at (I don't know if there is another version) but it came out many years ago http://www.geom.uiuc.edu/~banchoff/Flatland/