[bheadmaster]

> Rather, math's power stems from the fact that it emphatically does not expect or require the symbols to have any connection to real world observations.

What exactly do you mean by "power" here, if not the ability to predict real-world phenomena? In absence of it, what exactly would make it anything more than an exotic artform?

[fenomas]

I meant the fact that math works at all, as a symbolic framework with consistency and the power to prove some statements and disprove others, etc. Math only has those features because it examines symbols abstractly regardless of any connection to the real world.

Like, consider: parabolas were pretty fully described by the ancient Greeks, purely as a symbolic abstraction. It was only 1500+ years later that anyone realized that they could also predict the motion of cannonballs and planets. But that discovery was completely orthogonal to the math - e.g. symbolic statements about parabolas didn't get any truer just because they now also described real-world phenomena. (And likewise when we later discovered that planetary motion isn't quite parabolic after all, that didn't affect our understanding of parabolas either.)

That's all I was saying here - that the "esoteric artform" part of math where one abstractly examines symbols is the essence of the thing, and the "predict real-world phenomena" aspect is a side effect that sometimes happens and sometimes doesn't.

[bheadmaster]

True, but what I'm pointing out is - imagine parabolas never predicted movement of anything, or imagine that math itself never had any prediction power in the real world. The self-consistency and the aestethics and the ability to prove statement inside itself would all be just a bunch of symbolic games, much like poetry or crossword puzzles.

You may argue that that, in itself, is powerful, in which case fair enough. But that "power" would be comparable to that of poetry or painting, which, in my opinion, does a disservice to the true power that mathematics holds. Mathematics is much more powerful than poetry and painting, because poetry never helped us build nuclear reactors.