I've been wondering what spaces with an extra physical dimension would look like. That is, instead of our 3+1D space it would be a 4+1D space. In general, it can't be done. There is too much information for a human brain to handle. But some special cases can work. The main one I thought of was a 4D road race. Now in our world a Formula One road race is mainly a 2D phenomenon. The track is more or less flat, so all that matters is forward-back and left-right. The up-down dimension could be reused. The way this would be done is to not show the up-down dimension at all, and instead use that for the new, novel, extra dimension. The road then would like like a curved rod instead of a strip. That curved rod can wind around in all three dimensions, so it can curve as freely up and down as it does left and right, or any combination of these two directions. The road would appear on the screen as a circle extending off into the distance, turning and twisting as it will. The driver has to be careful not to exceed the the friction of the road and skid off of it. Has this already been done? The sky wouldn't be usually be visible, instead the round road would be surrounded all 360 degrees by buildings, trees, or whatever. The 4th dimension up-down dimension couldn't be seen directly but could be encoded topographically. Off-road 4D is much harder. The trouble is that a human can see only 3D slices of the 4D world, and has to construct the 4D world from that, then find an optimal path through this 4D world constructed in the imagination. It would be even more difficult that constructing a 3D world from 2D slices. Imagine a game where you could only see only a few one-pixel-wide vertical and a horizontal slits. It wouldn't be easy, but at least we know how to imagine a 3D world.