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That essay is a significant source of belief in the myth of inherent mathematical truth, but it has flaws and is far from proof. It focuses on cherry-picked phe

That essay is a significant source of belief in the myth of inherent mathematical truth, but it has flaws and is far from proof. It focuses on cherry-picked phenomena that are easily represented by simple math, but ignores those where math struggles or appears to be inherently incapable. Most importantly, the leap that if a medium can be used to create accurate representations, it must contain inherent, unquestioning truth about that represented phenomena, is just hogwash. Michelangelo could sculpt masterful representations of the human form, but the beauty and accuracy of the representation are the products of a skilled master, not the inherent humanness of marble.

BeetleB 8y ago
>That essay is a significant source of belief in the myth of inherent mathematical truth, but it has flaws and is far from proof. I don't know where this characterization of "proof" comes from. It is merely an essay, and not intended as anything other than one. When I read it years ago, I did not get the sense that Wigner was asserting inherent mathematical truth. >It focuses on cherry-picked phenomena that are easily represented by simple math, but ignores those where math struggles or appears to be inherently incapable. Does he assert anywhere that any phenomenon will yield easily to mathematics? I don't think so. I think his point is that there's no good reason that even the phenomena that are well explained by mathematics should yield so easily to it. It's not "All of nature is surprisingly mathematical." It's "I see no good reason that a lot of phenomena is mathematical." I'm too lazy to reread the essay, so I may be remembering it wrong.
jrochkind1 8y ago
I don't think the essay is any kind of "proof", but I think you are under-appreciating the mysteriousness it speaks of. It's not just the medium _can_ be used to create accurate representations, by a skilled master. It's that mathematical concepts created with no regard for the natural world but purely on their formal elegance, turn out, years later, to be an elegant way to describe and predict natural phenomena. I don't think it "proves" anything, it's just... mysterious. The mystery doesn't go away if we insist that math is just an arbitrary human invented formal system. There's no a priori reason it should work to describe and predict the natural world at all, is there? We could invent other arbitrary formal systems based on completely different axioms and rules that _weren't_ useful to describe and predict the natural world at all, could't we? I think?
- protonfish 8y ago
  I guess I just don't see any mystery. We've used a language of symbols to communicate and think about the world around us since language first evolved. That fact that it works well should come as no surprise to anyone. Especially since we use a language of symbols to discuss the language of symbols so things that don't fit neatly into that system are inherently undiscussable.

BeetleB 8y ago

>That essay is a significant source of belief in the myth of inherent mathematical truth, but it has flaws and is far from proof. I don't know where this characterization of "proof" comes from. It is merely an essay, and not intended as anything other than one. When I read it years ago, I did not get the sense that Wigner was asserting inherent mathematical truth. >It focuses on cherry-picked phenomena that are easily represented by simple math, but ignores those where math struggles or appears to be inherently incapable. Does he assert anywhere that any phenomenon will yield easily to mathematics? I don't think so. I think his point is that there's no good reason that even the phenomena that are well explained by mathematics should yield so easily to it. It's not "All of nature is surprisingly mathematical." It's "I see no good reason that a lot of phenomena is mathematical." I'm too lazy to reread the essay, so I may be remembering it wrong.

jrochkind1 8y ago

I don't think the essay is any kind of "proof", but I think you are under-appreciating the mysteriousness it speaks of. It's not just the medium _can_ be used to create accurate representations, by a skilled master. It's that mathematical concepts created with no regard for the natural world but purely on their formal elegance, turn out, years later, to be an elegant way to describe and predict natural phenomena. I don't think it "proves" anything, it's just... mysterious. The mystery doesn't go away if we insist that math is just an arbitrary human invented formal system. There's no a priori reason it should work to describe and predict the natural world at all, is there? We could invent other arbitrary formal systems based on completely different axioms and rules that _weren't_ useful to describe and predict the natural world at all, could't we? I think?

protonfish 8y ago
I guess I just don't see any mystery. We've used a language of symbols to communicate and think about the world around us since language first evolved. That fact that it works well should come as no surprise to anyone. Especially since we use a language of symbols to discuss the language of symbols so things that don't fit neatly into that system are inherently undiscussable.