h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Great article! I remember reading about tesseracts years ago in a role-playing games magazine (might have been White Dwarf back in the good old days)- an article about using tesseracts in scenarios. The characters somehow get trapped in one, have to figure out what's going on and how to escape. Hours of fun as they slowly go nuts thinking in four dimensions.

So what happens if you put eight tesseracts together into an even bigger cube? Or would it need to be sixty four? My brain hurts...

*just has to answer, hey, I'm a mathematician*

You would need to put ten tesseracts (or 4-cubes) together to make the 5-cube; the n-cube is made from 2n (n-1)-cubes, e.g. six squares make the normal cube. Each tesseract would be connected 6 neighbouring tesseracts, one by each of its constituent cubes.

I thought the article might do better to mention the usual projection of a cube onto a plane (one square inside another, with sides parallel and each corner of the inner square joined by a line to the nearest corner of the outer square) to explain the projection of the tesseract into 3-space, but other than that, it's very good.

I was thinking about a 5-dimensional cube, and I realized something interesting.

I thought - "How could one translate a 5-cube into a 3-d object? I discovered an interesting pattern. Think of a one-dimensional creature moving along the edges of a cube. It would come to an intersection. What would it do then? It has never encountered an intersection before. Similarly, but a little more dificult to understand, a two dimensional creature moving on the surface of the cubes making up the tesseract would come to an intersection.

Assuming Einstein was right and the fourth dimension is time, through which we travel in one direction. What if we encountered an intersection? Alternate timelines?

Well, I've seen a 2-d computer model of a tesseract before (line drawing, naturally, or it'd be a bit boring), so it's probably possible. What it would look like I don't know.