I think you could approximate a 4d projection onto a 3d display, much like we approximate a 3d projection onto a 2d display. So perhaps one could enjoy a fun and intuitive game of 4d doom if you have an appropriately fancy volumetric display. Pity they're so rare/expensive.

Feels like in 3D you can move continuously and build intuition.

But in 4D there isn’t really an equivalent control, so it ends up feeling more like toggling something you don’t fully understand.

Could transparency help?

Ordinarily, a 3D scene rendered in 2D only allows you to see a cone from your eye up to the first surface the ray encounters, thus defining the 2D projection which you see.

But you can make the surfaces transparent so the ray continues, and each additional surface adds a bit to the final pixel. This can look like a mess if you stand still but if you wiggle your movement left and right (or any other direction), your brain suddenly manages to process it into the full 3D structure.

Can something like this be done in 4D?