Math + Physics + Probably a dose of philosophy

Rej

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Apr 5, 2021
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I honestly didn't know where to turn with this question but I thought I would start with mathematicians and see how I fair and go from there.

Not too uncommonly you will come across the phrase in physics, "The unreasonable effectiveness of mathematics", and it obviously comes back to just how well mathematics works for physics and along with experiment/observation you could probably call it one of the two main pillars of our understanding of nature on the most fundamental level (physics).

I'm sure there are other things I could use as reason for concern but π and circles were the first thing that came to my mind. Calculus perhaps since it's essentially a method of approximation? The fact that when we compute we have to do so for discrete moments in time when as far as we can measure and our best theories say, time (and space) are not discrete so we can only approximate when we compute... especially when those pesky irrational numbers show themselves... smarter people than me I'm sure would have many more items to add.

It disturbs me (not Earth shattering stuff but certainly enough to be a concern and more than idle curiosity) that people think that way (that mathematics is that perfect) because take one of the most humble of shapes other than a line, a circle. We can't calculate the circumference from the diameter in any way other than an approximation since π is not something we can know perfectly and as I understand it the circle is a special case of ellipses which is what most if not all orbits are and so it snowballs because π is everywhere in physics.

Now couple that with a not so well known trait of human psychology which is when a person uses a tool enough, say a hammer (or a car if you want something more familiar), with often use and it being important enough to us we subconsciously make that tool an extension of ourselves and it makes me wonder if this phrase is just physicists "becoming one with the tool of their trade" and being that mathematics is entirely mental I would be willing to suppose that this effect with physical tools could have a multiplied/added/"whatever algorithm works for you" effect on them.

So I guess my question is to you gals and guys, as mathematicians do you think mathematics is seriously unreasonably aligned with how nature works?

BTW, something I didn't mention because I know almost nothing about it, if not actually nothing, but it seems that mathematics has been invented in different "flavors" (for want of a better term) by some mathematicians for various reasons and those different systems may not reflect nature at all and that makes me wonder if physicists were just cherry picking what they used rather than looking at the bigger picture. I wish I could elaborate on this but it's vague notion from past research so if I'm completely off base on this one then just ignore this comment.

Anyway, anyone who cares to chime in I really really welcome your thoughts because I have more questions in my mind about this than conclusion as you probably gathered.
 
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