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God created the real numbers

(www.ethanheilman.com)
136 points Bogdanp | 3 comments | 29 Aug 25 15:31 UTC | HN request time: 0.956s | 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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1. tialaramex ◴[29 Aug 25 19:19 UTC] No.45068255[source]▶
> They're unphysical, and yet the very physical human mind can work with them just fine

Nah, you're likely thinking of the rationals, which are basically just two integers in a halloween costume. Ooh a third, big deal. The overwhelming majority of the reals are completely batshit and you're not working with them "just fine" except in some very hand wavy sense.

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2. ysofunny ◴[29 Aug 25 22:27 UTC] No.45070110[source]▶
the rationals are 3 naturals with in a "2,1" structure.

the first 2 naturals form an integer.

that integer and a 3rd natural constitute a real (but this 3rd natural best be bigger than zero, else we're in trouble)

what I choose to focus after observing the "unphysical" nature of numbers. is the sense of natural opposition (bordering on alternation) between "mathematical true" and "physical true". both are claiming to be really real Reality.

in the mathematical realm, finite things are "impossible", they become "zero", negible in the presence of infinities. it's impossible for the primes to be finite (by contradiction). it's impossible for things (numbers or functions of mathematical objects) to be finite.

but in the physical reality, it's the "infinite things" which become impossible.

the "decimal point" (i.e. scientific notation i.e. positional numeral systems) is truly THE wonder of the world. for some reason I want something better than such a system... so I'm still learning about categories

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3. tialaramex ◴[29 Aug 25 23:16 UTC] No.45070473[source]▶
Huh?