Previously, previously, previously.
I wonder if a person can start to develop an intuition for 4-D space by playing with something like this? Or by playing with the real-world equivalent (which doesn't exist)?
It would probably help to have a VR version of this, so that instead a 3D environment projected onto a 2D screen, you can have a 3D environment you can see depth in and move around in.
Of course, we don't see 3D, either, we see a pair of 2D projections on our retinas. That 2D character in the example? Can only see a 1D projection.
Years ago I had a screen saver of a hypercube rotating regularly along the fourth axis (in addition to slowly tumbling along the first three). It took a lot of staring, but the regularity of the motion did give a weird intuitive sense of the entirety of the shape.
That question forms the basis of a classic SF short story called "Mimsy Were The Borogoves" by Lewis Padgett which you can find in a lot of anthologies and which made it to the screen in seriously mangled form as "The Last Mimzy"
I will check those out, thanks.
I need more of this! I can understand the concept but I can't predict how the items will interact like I could with the 3D example. It(I) need[s] an example with layered slices showing how the object moves through 4d space.