←back to thread

God created the real numbers

(www.ethanheilman.com)
136 points Bogdanp | 3 comments | 29 Aug 25 15:31 UTC | HN request time: 0.782s | source
Show context
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.

replies(10): >>45067843 #>>45068041 #>>45068086 #>>45068269 #>>45068318 #>>45068389 #>>45069577 #>>45070658 #>>45071417 #>>45075257 #
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".

replies(4): >>45068027 #>>45068111 #>>45068154 #>>45068255 #
1. shkkmo ◴[29 Aug 25 19:06 UTC] No.45068111[source]▶
> They're unphysical, and yet the very physical human mind can work with them just fine.

Can it? We can only work with things we can name and the real numbers we can name are an infinitesimal fraction of the real numbers. (The nameable reals and sets of reals have the same cardinality as integers while the rest are a higher cardinality.)

replies(1): >>45068604 #
2. SabrinaJewson ◴[29 Aug 25 19:50 UTC] No.45068604[source]▶
We can work with unnameable things very easily. Take, for instance, every known theorem that quantifies over all real numbers. If you try to argue that proving theorems about these real numbers does not constitute “working with” them, it seems you have chosen a rather deficient definition of “working with” that does not match with how that phrase is used in the real world.
replies(1): >>45069106 #
3. shkkmo ◴[29 Aug 25 20:36 UTC] No.45069106[source]▶
I would argue that all of those theorems work with nameable sets of real numbers but not with any unnamable real numbers themselves.