How Many Dimensions Are There? Is Math Easier to Grasp with Real World Examples?

It seems maths are more easily understood when grounded in real structures, such as: "If we have one apple, add another, and how many apples do we have?" On the other hand, math tends to train us to overlook much of nature, going so far as to assert what fairly reasonable standards might judge falsehoods. We accept the dubious western assumption that apples are separate, however no apple has ever been measured to constitute exactly 1 standard apple...and we ignore the imprecision required for our most simple math concepts.

1 + 1 = 2 may be our first equation pedagogically, but it comes with a slew of logical and practical problems we may be well advised to keep in mind. Identifying one item, obtaining it, doing the same with another item, combining them into a set, and then counting to obtain a result is much more than "2" things. Even simple maths ignore time, existence over time.

There is a more significant reason for skepticism regarding mainstream dimensional models of fundamental physics as they posit integer-based dimensions: this assumes the fundamental structures of the universe (even in other multiverses) correspond to the way some insignificant hominid counts fingers, toes, and the fruits it loves to eat. That coincidence seems less likely than an Earth-centered universe.

It also runs counter to all available physical evidence. As Mandelbrot pointed out: we never observe anything of integer dimension. No Euclidean lines, planes, or solids have ever been observed.

On the other hand, current assumptions are of exactly the kind we should expect a species like ours to make: one based on observer-centric bias. Such a biases are completely natural for us, and we have always had them.

Geocentrism provides the classic example, while the history of revolutionary progress in science shows that identification and reinterpretation of such assumptions has proven a common factor in resolving pernicious questions. It could well be that some fractal octonian offers better value for the dimensional discussion the question above is posted to.