This gambit occurs in hindsight, yet here I can present it with foresight.
To what degree does a basis for physics imply pure mathematics?
I believe that this statement is acceptable and that it exposes a flaw in modern theoretical physics, for their basis is done empirically. They readily bow to the mathematics of the real number, and since space exhibits a three dimensional nature they
happily go to RxRxR as a sensible workspace of, let's say, a first physical form. Yet the three was plucked from thin air and is a matter of empirical correspondence, and so we see a bleak theoretical claim here for all theory that works from such a
basis, which is modern physics. While most of us will admit that the experimental physicists have the upper hand, few will admit that it started way back here.

To explain that all of theory is empirical is to explain that we lack a clean theory. To expose the problem as a lacking in mathematics is where I care to shine the light. This notion of 'basis' and what exactly it means... does the ideal mathematics
then provide emergent spacetime without any physics? In effect these are the details which make a basis, or at least which give a basis correspondence.

To claim that you will require three copies of your basis for your basis, and never have any theory for the three, or four for that matter... and to claim that identical copies are effective: now here I am attacking the Cartesian product and it would
seem impossible to do so, yet from this theoretical stance it can be done. Still, this is not the start of the journey that I would take you on on this thread. It is more a stop along the way.

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