Dec 1, 2019, 8:51 AM
At present, aside from testimony and reciprocity I think I understand this problem (mathematical foundations) better than anyone else, for reasons I’m still … exasperated by.
Math is a language. It consists of one dimension: positional names. Positional names consist of one constant relation: position (ordinality). Names are unique. Positional names are unique. Positions are scale independent. Positional names can be assigned to any referent in any dimension. We can assign names to any set of dimensions, just as we assign names to any set of referents within it, and as such we can used dimensional order or name, and position order or name, to describe ANY CONSTANT RELATIONS at any scale or combination of scales relative to the observer, and we can scale this technique of dimensional and positional names to any comprehensible scale.
So it’s not that math is unreasonably useful, it’s that it’s fucking OBVIOUSLY useful in describing the natural world, because like the natural world mathematics is SIMPLE (consisting of constant relations). However, like anything else, we learn it’s constitution by it’s failure. And mathematics is terrible at inconstant relations (economics, sentience), and at that point of failure we must move from positional (linear) language (averages) to operations language (discrete operations).
So for example, as far as I know, the reason that physics is frozen is Einstein published before Hilbert solved the underlying problem by Einstein NOT solving the problem of the underlying structure, by the presumption that the wave (calculus) was the primitive, rather than the operations that averaged into the wave – demonstrating that Einstein like many mathematicians understood the application of the language of mathematics without understanding it’s construction relative to ALL languages.
In fact, if I had my druthers, I would have people learn the abacus, the gear, the computer, and the shape to learn mathematics, not just memorization by wrote repetition.
Welcome to continue this but it’s not possible that I’m wrong.
Foundations of language of which mathematics is the simplest because it consists of only one property, and our brains evolved to grasp the world as spaces first by very similar (geometric) means, an understanding of which usually awes the audience.