On 01/25/2014 04:14 PM, Phil wrote: > Hi, > > I was playing a video game (Skyrim) which involves traveling through > tunnels and dungeons. Some are complicated -- the tunnels go up, down, > circle around and go under themselves. > > So I felt sorry for Flatlanders. They can get the side-to-side and the > near-and-far, but they can't comprehend up or down. A very limiting > experience. > > So then I wondered if 4D-people feel sorry for us. But they probably > shouldn't. It just seems that the shift from 3D to 4D is not that > overwhelming, whereas going from 2D to 3D is. (e.g. there is nothing > like the 4-color map theorem in 3D). > > I'm not sure if this sort of thing has been quantified (other than the > obvious, that 2->3 is a 50% increase whereas 3->4 is a 33% increase). >
I seem to remember that for a 4D world, with gravity falling-off under a inverse-cube law, instead of inverse-square, but keeping F = ma, the non-circular orbits of a test-mass around the "sun" would be very different from ellipses/conic in character.
For example, they might be non-periodic; I forget the details.