I've always thought that "density at the edges" would have interesting implications for moment of inertia. Euler's column formula depends on moment of inertia so that would seem to imply a "Flatland-but-in-11D-instead-of-2D" would have significant mechanical engineering problems compared to our 3-D world.
I think macro-scale higher dimensions as a hard sci fi topic would also have weird aerodynamic and heat exchanger effects. How would the ratio of radiative cooling to convective cooling vary if the world had 10,11,100,100000000 dimensions instead of 3?
Intuitively if we had 4 dimensions of space I think automotive-type radiators could be quite a bit smaller for a given heat exchange?
I think macro-scale higher dimensions as a hard sci fi topic would also have weird aerodynamic and heat exchanger effects. How would the ratio of radiative cooling to convective cooling vary if the world had 10,11,100,100000000 dimensions instead of 3?
Intuitively if we had 4 dimensions of space I think automotive-type radiators could be quite a bit smaller for a given heat exchange?