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cousin_it comments on Supernatural Math - Less Wrong
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Thanks! I stand 50% corrected. Yes, we keep those models that work. But math seems an unreasonably effective model even after accounting for the selection effect. Why did conic sections turn out useful for describing planetary orbits 2000 years later, and why did Hilbert spaces turn out useful for quantum mechanics 10 years later?
That misses the point. Conic sections are useless for how many things? Likewise for Hilbert spaces. Likewise for all of mathematics. A mathematical construct is useful for the things it is useful for, and useless for everything else.
Mathematics isn't a model. (Well, it is, but not in the sense that you mean it.) It's what we use to build models out of, what makes them possible.
If a branch of mathematics exists, and someone finds a way to use it to describe a set of relationships they find in the world, we call that branch 'useful'. If its behavior doesn't match the relationships we're interested in studying, we ignore it. And if it was needed, but doesn't exist yet, we never realize it.
Do you have a citation for this analysis, or did you make it up? (or non-excluded middle)
Thanks, I stand 100% corrected.