a better theory and the ‘correct’ answer on dimensionality. The smart money
seems to be that we’re living in an 11-dimensional universe.
Hyperspace
Unlike higher physical dimensions, there is absolutely no problem with a
mathematical space of more than three dimensions. Mathematical space can be
any number of dimensions. Since the early 19th century mathematicians have
habitually used n variables in their work. George Green, a miller from
Nottingham who explored the mathematics of electricity, and pure
mathematicians A.L. Cauchy, Arthur Cayley and Hermann Grassmann, all
described their mathematics in terms of n-dimensional hyperspace. There
seemed no good reason to limit the mathematics and everything to be gained in
elegance and clarity.
The idea behind n dimensions is merely an extension of three-dimensional
coordinates (x, y, z) to an unspecified number of variables. A circle in two
dimensions has an equation x^2 + y^2 = 1, a sphere in three dimensions has an
equation x^2 + y^2 + z^2 = 1, so why not a hypersphere in four dimensions with
equation x^2 + y^2 + z^2 + w^2 = 1.