Quote Originally Posted by mojo
Hmm... Can a 2D surface contain an n-dimensional volume?
I have no idea, but it seems to me string theory proposes this to be the case. Well, it proposes a 3D volume can contain a 4th dimensional extravolume (I just made that word up). If gravity propagates through a fourth dimension, and that dimension is infinite, then gravity would obey the inverse cube law. Clearly that isn't the case. It is either precisely inverse square (and therefore 3 dimensions) or it is very close to inverse square (three infinite dimensions and one or more closed dimensions). If it's somehow lower than inverse square (<3D) that would make absolutely no sense and conservation of energy is already being violated.

If I were to wildly speculate like a stoner, I'd be inclined to believe that any extra dimensions are complex in nature. I can't wrap my head around complex numbers and how they relate to the real world, but I also have ultimate faith in the absolute truth of mathematics. Discovering i was a seismic moment in maths, it solved so many equations that many assumed were unsolvable.

The reason I think complex numbers are at play here is because the complex plane is very circular in nature. If you iterate multiplications of i you go round in a mathematical circle.

i*i = -1
-1*i = -i
-i * i = 1
1*i = i

I think Schrödinger himself was shocked that i emerged in the wave function. Or was it Heisenberg? One of them two. It was shocking for them to see what they believed was a mathematical curiosity emerging in the physical universe. It's basically proof that i is very much a real number.