We have defined dimension, as far as space is concerned, the wrong way. We may be able to crudely model our space using euclidean geometry, but the fact remains that in reality a length in any direction has its own meaning rather than being defined in terms of perpindicular axes, and yet still interacts with every other line.
If the math in question is well founded, it would be interesting to look at. It might give insight into how REAL space is constructed rather than how we pathetically try to model it with our math.