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God created the real numbers

(www.ethanheilman.com)
136 points Bogdanp | 1 comments | 29 Aug 25 15:31 UTC | HN request time: 0.223s | source
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andrewla ◴[29 Aug 25 18:33 UTC] No.45067770[source]▶
I'm an enthusiastic Cantor skeptic, I lean very heavily constructivist to the point of almost being a finitist, but nonetheless I think the thesis of this article is basically correct.

Nature and the universe is all about continuous quantities; integral quantities and whole numbers represent an abstraction. At a micro level this is less true -- elementary particles specifically are a (mostly) discrete phenomenon, but representing the state even of a very simple system involves continuous quantities.

But the Cantor vision of the real numbers is just wrong and completely unphysical. The idea of arbitrary precision is intrinsically broken in physical reality. Instead I am off the opinion that computation is the relevant process in the physical universe, so approximations to continuous quantities are where the "Eternal Nature" line lies, and the abstraction of the continuum is just that -- an abstraction of the idea of having perfect knowledge of the state of anything in the universe.

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empath75 ◴[29 Aug 25 18:41 UTC] No.45067843[source]▶
> But the Cantor vision of the real numbers is just wrong and completely unphysical.

They're unphysical, and yet the very physical human mind can work with them just fine. They're a perfectly logical construction from perfectly reasonable axioms. There are lots of objects in math which aren't physically realizable. Plato would have said that those sorts of objects are more real than anything which actually exists in "reality".

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Eddy_Viscosity2 ◴[29 Aug 25 19:10 UTC] No.45068154[source]▶
The human mind can't work with a real number any more than it can infinity. We box them into concepts and then work with those. An actual raw real number is unfathomable.
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1. Agraillo ◴[30 Aug 25 07:27 UTC] No.45072640[source]▶
I felt also something like this before. Also integers seem pretty close to the reality around us. One of their functions is to symbolically represent the similarity of objects (there might be a better way to put it). Like, if you see 5 sheep in one group and 6 in another, after that point they’re no longer just distinct sheep with unique properties - the numbers act as symbols for the groups. Real numbers still can work in the brain, but they're most distant from the world around us, at least when it comes to going from visual to conceptual understanding.