←back to thread

God created the real numbers

(www.ethanheilman.com)
136 points Bogdanp | 2 comments | 29 Aug 25 15:31 UTC | HN request time: 0.41s | 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 #
NoahZuniga ◴[29 Aug 25 19:33 UTC] No.45068389[source]▶
You know it wouldn't be possible for us to tell the difference between a rational universe (one where all quantities are rational numbers) and a real universe (one where you can have irrational quantities).

The standard construction for the real numbers is to start with the rationals and "fill in all the holes". So why even bother with filling in the holes and instead just declare God created the rationals?

replies(8): >>45068658 #>>45068743 #>>45068954 #>>45068991 #>>45070837 #>>45070881 #>>45071862 #>>45073728 #
IAmBroom ◴[29 Aug 25 19:56 UTC] No.45068658[source]▶
> You know it wouldn't be possible for us to tell the difference between a rational universe (one where all quantities are rational numbers) and a real universe (one where you can have irrational quantities).

Citation needed.

Especially since there are well-established math proofs of irrational numbers.

replies(2): >>45068714 #>>45070603 #
NoahZuniga ◴[29 Aug 25 20:00 UTC] No.45068714[source]▶
The argument is essentially that you can only measure things to finite precision. And for any measurement you've made at this finite precision, there exist both infinitely rational and irrational numbers. So it's impossible to rule out that the actual value you measured is one of those infinitely many rational numbers.
replies(2): >>45069122 #>>45075148 #
1. BobaFloutist ◴[30 Aug 25 14:51 UTC] No.45075148[source]▶
If I'm carrying a single apple, I can measure the number of apples I'm carrying to infinite precision. I'm carrying 1.000... apples.
replies(1): >>45075557 #
2. griffzhowl ◴[30 Aug 25 15:39 UTC] No.45075557[source]▶
You're implicitly assuming your conclusion by calling it a "single" apple, which means exactly one. "Apple" is an imprecise concept, but they're often sufficiently similar that we can neglect the differences between them and count them as if they're identical objects, but this is a simplification we impose for practical purposes.

Even for elementary particles, we can't be sure that all electrons, say, are exactly alike. They appear to be, and so we have no reason yet to treat them differently, but because of the imprecision of our measurements it could be that they have minutely different masses or charges. I'm not saying that's plausible, only that we don't know with certainty