4D Toys: a box of four-dimensional toys
This is so cool, but its driving me crazy. I was wondering if someone could provide me with more resources that help intuit about 4d space. For example, in Miegekure, he walks through the 4th dimension to get to the other side of the wall, but thats assuming that no part of the wall extends into the forth dimension (aside from rubble). What would happen if he switched back to the normal 3 dimensions in the middle of the wall. In miegekure everything is kind of discretized (grassy area to desert area), but in reality that would be continuous. What would that actually look like, for example, the area right next to the wall? How would this work at a subatomic level, would electrons be traveling in and out of the 4th dimension? Could this explain things like action at a distance or black holes? How does the explain shared surfaces in the 4th dimension? I can&#x27;t even answer a basic question like, if I were sitting in an easy chair and started looking down the 4th dimension what would happen. Since it has to share one cross section of the easy chair would it have to be simply a fatter or skinnier easy chair? But that is true for any cross section of the chair correct? The easy chair is the 3d cross section of the 4d object then what (would&#x2F;could) the 3d cross section exchanging one of our spatial dimensions for the hidden one look like? How does gravity work in those 3 dimensions (2 of our spatial dimensions + 1 of the hidden dimension). Supposing the world was like this, wouldn&#x27;t it be obvious if any object was extending into the 4th dimension thus we can stand to reason our world must be strictly 3 dimensional? If there were 4 dimensions since we can&#x27;t see or interact with it, does it stand to reason that the spatial extent of any object doesn&#x27;t extend into the 4th dimension?
For example, since the three dimensional projection of a hypersphere changes diameter, does that mean the 4d dimensional analogues of earth are just different size earths?
I also notice that in one of the miegekure videos the windmill in the new 3d space is like a cross section of the windmill but extending for a distance, Im guessing this is a product of the way the 4th dimension is discretized but Im wondering, what would that really look like if the game weren&#x27;t made that way?