Consider a set of number in a base 10 system. Are the numbers mutually exclusive? When you consider 0-9 are you either at 0 or at 1 or at 9, etc? On the number line you are not simultaneously at 2 and 8. You are either at one or the other. So if you consider the universe of numeric bases, even fractional or irrational bases if they are possible, aren’t you considering a set of the possible dimensionalities of your own universe. If you pick the right basis wouldn’t you see that reflected in your own universe? Wouldn’t math work out the same. So we have a kind of orthogonality along the number line. Now consider a decimal point and the numbers after the decimal point. If we limit things to one number before the decimal point and one afterward, then don’t we have a universe of a hundred objects that are in some sense orthogonal? So we would have 100 observable aspects of the universe and no more. Anything else would be resolvable to that 100. Everything beyond 100 observable characteristics is either an illusion or is some combination of that fix set of basis objects.
No let us posit a different universe. One in which you could be not only at 2 and 8 at the same time but and any number of numbers at the same time. One way of think about this is that there are many universes but they are each of them infinitesimally small. It is difficult to know where to go with this one but one way is to say that fixed or limited number of dimensions is an illusion. Actually there are an infinite number of dimensions and every point in space represents a universe. We stride between worlds, universes and dimensions with every step.
Some savants say that they can see or sense numbers and that certain problems, questions, answers and solutions have special shapes that makes them easy to see even if those of using conventional mathematics could not solve the problems as quickly. It would be interesting if this eventually proved to be correct. If the number line is actually a surface or a field of shapes, or even a field of locks and keys and if only we knew the color scheme or the morphology, then we two could solve difficult or arcane problems easily. Just by chosing the right basis for instance. Maybe each problem requires a different basis for the easiest solution.