What does a 4-Dimensional cube look like?

Day 286 / 365

I am currently reading the book “Flatland”, which is a fascinating novel about people who live in a two-dimensional world. The people in flatland don’t have the concept of up and down. And all they can see is just lines. The main protagonist encounters people in a 1-dimensional world “Lineland”, who can only just see points. He has a hard time trying to explain to them what a square is.

In the same way, you would have a hard time trying to explain what a cube is to the people of Flatland. It’s impossible for them to grasp it. But we being the residents of a three-dimensional world have no problem with it.

This makes me wonder, what things will be common in a 4-D world that is impossible for us to grasp? How would a 4-D Cube look like?

There is a name for a cube in 4 dimensions. It’s known as a tesseract. And with some practice, most people can imagine a tesseract. Think of it this way, if you take a square and project it to 1 dimension, you get a line. Similarly, if you take a cube and project it to 2 dimensions, you get a square. By following that line of reasoning, a tesseract would be something which when projected to a 3-D space gives you a cube.

If you see a movie on your TV, you know that all the objects in the movie are 3 dimensional, even though they are just pixels on a 2-D surface. In the same way, you can model 4-D objects in a 3-D space. This image from Wikipedia explains it much better —

This post is part of my 365 Day Project for 2019. Read about it here

Yesterday’s blog — Cryogenically Frozen People