Hello fellow meat sacks,
I am of the personal belief that thought games and the like have gone out of practice with each generation.
We don't really have a lot of people doing recreational mathematics these days, which I think is a shame.
Because of this, I like to introduce people to thought games.
Today I'd like to discuss a very engaging and completely worthless thought game...
Picturing a hypercube.
Okay, so a 2 dimensional square is a square. 4 lines with 4 right angles.
Add another dimension by drawing equally long lines at 90 degree angles "up" from the square.
So how do you add a 4th dimension? Well, you add more lines at 90 degree angles of equal length along the 4th dimension.
That's probably where the image breaks down in your head, as we have no actual example of a 4th dimensional object to use as a starting point.
We can see the "shadow" of a hypercube though, much like you can draw a cube on a two dimensional piece of paper using false depth.
The 3 dimensional shadow of a hypercube looks like this
Anyway, the purpose of the thought game is to picture a 4 dimensional object. You're basically trying to force your brain to imagine a completely new image, something impossible for you to visually perceive.
By now, I can "sort of" imagine it. At least pieces of it. I can't exactly wrap my mind around the whole picture, but I can kind of picture the "corner" of a tesseract.
Once you're through with this, try a hyper-sphere :)
Ah yes, the tesseract. I've always wanted to make a dungeon of one.