Everybody is giving advice on how to imagine and intuit about integer dimensions beyond 3.
But what about fractional dimensions (not to be confused with fractal dimensions)? Any advice about reasoning about the geometry of lets say something 0.6309297535... dimensional? It seems so easy, I mean it is somewhere between 0 and 1 dimensions, both of which have trivial geometric interpretations.
Closest I could think of is doing augmentations into the next highest integer dimension. That would be similar to how we often use projections to lower integer dimensions to think about higher integer dimensions, but in reverse.
And yes, fractional dimensions do exist, just like fractional derivatives or fractional Fourier transform, etc.
Maybe not exactly what you are describing, but I recently did some layman research on "Strange Attractors" and chaos theory, which covers very similar topics. I cannot summarize here, but it's a neat rabbit hole to go down
But what about fractional dimensions (not to be confused with fractal dimensions)? Any advice about reasoning about the geometry of lets say something 0.6309297535... dimensional? It seems so easy, I mean it is somewhere between 0 and 1 dimensions, both of which have trivial geometric interpretations.
Closest I could think of is doing augmentations into the next highest integer dimension. That would be similar to how we often use projections to lower integer dimensions to think about higher integer dimensions, but in reverse.
And yes, fractional dimensions do exist, just like fractional derivatives or fractional Fourier transform, etc.