Eli5 What exactly is a tesseract?

Question

Please explain like I’m actually 5. I’m scientifically illiterate.

In: 172

Answer 1

Imagine moving your pen on a piece of paper. That paper is 2D. What happens if you stop moving your pen up or down and only allow left and right movements? You get a line (1D).

What happens when you restrict left and right movements too? You get a point (0D).

Mathematically, moving left and right is done by changing the x coordinate. Moving up and down is done by changing the y coordinate. Freezing one coordinate moves you down a dimension. It works in 3D too: if you freeze the third coordinate while traversing a cube, you get a plane.

So now, you could just say “Well what if we had 4 coordinates?”. Geometrically, there is no way to fit a fourth axis. But coordinates really are just bundles of numbers so why not have 4 instead of 3 numbers? If we apply the coordinate freezing trick here and freeze the fourth coordinate, we lose a dimension and get a cube. Some people say that a 3D cube is the shadow of a 4D cube and this is what they mean. Its in the same way that a 2D plane is the shadow of a 3D cube: you get the shadow by removing a dimension, and you remove the dimension by freezing a coordinate.

So what we can say is: you can think of 4D points as a bundle of 4 numbers. That fourth axis doesnt really fit into our coordinate system, its abstract. But by freezing movement along that axis, you move down a dimension and get a 3D slice of the 4D object. In this case, the slice of a tesseract is a 3D cube.