I don't want to come across as harsh because the idea is neat and I'm sure creating this helped the author through their own study/understanding of the subject. But if you want to learn it would be better to study a textbook written by a mathematician.
The preamble already contains multiple errors (conflation of general and special relativity, assertion that category theory formalizes the common diagram, assertion that mathematical reasoning underwrites thought itself, assertion physical models are unnecessary/curve fitting is all you need ...)
The intro reminds me that V.I. Arnold once accused his algebraist colleagues (quite unfairly), especially in France, were primarily driven by their inferiority complex with respect to the hard sciences. The book would be much better if it didn't begin in this manner. It's valid to study mathematics (or anything of beauty, anything indispensable) for its own sake, of course.
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