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God created the real numbers

(www.ethanheilman.com)
136 points Bogdanp | 8 comments | 29 Aug 25 15:31 UTC | HN request time: 0.001s | source | bottom
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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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chasd00 ◴[29 Aug 25 19:20 UTC] No.45068269[source]▶
> The idea of arbitrary precision is intrinsically broken in physical reality.

you said a lot and i probably don't understand but doesn't pi contradict this? pi definitely exists in physical reality, wherever there is a circle, and seems to be have a never ending supply of decimal points.

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Dylan16807 ◴[29 Aug 25 19:47 UTC] No.45068570[source]▶
Can you name a physical thing that is a circle even to the baseline precision level of a 64 bit float?
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1. IAmBroom ◴[29 Aug 25 19:57 UTC] No.45068682[source]▶
A black hole.
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2. andrewla ◴[29 Aug 25 20:25 UTC] No.45068985[source]▶
A non-rotating black hole. Or a rotating black hole with zero charge. Or a rotating black hole with non-zero charge no external magnetic fields. Or a rotating black hole with non-zero charge with non-time-varying external magnetic fields. Or a wart on a frog on a bump on the log on a hole on the bottom of the sea.
3. tromp ◴[29 Aug 25 20:34 UTC] No.45069088[source]▶
A black hole is no more a perfect sphere than a sun is. Would gravity from the nearest other black hole not have a deforming effect of at least 2^-64 ?
4. Kranar ◴[29 Aug 25 22:14 UTC] No.45070028[source]▶
There is no black hole that is a perfect sphere. That would, at a minimum, require a body with absolutely no angular momentum which isn't in anyway feasible.

Any rotating/spinning black hole will no longer be a perfect sphere.

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5. gpm ◴[29 Aug 25 22:35 UTC] No.45070182[source]▶
Yeah but if you look down the axis of rotation you will have a perfect (to many decimal places anyways) circle... which was the demand.
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6. Dylan16807 ◴[30 Aug 25 05:58 UTC] No.45072227{3}[source]▶
That might be right.

But even then, the biggest black hole we think is possible measured down to the planck length gives you a number with 50 digits. And the entire observable universe measured in planck lengths is about 60 digits.

So how are you going to get a physical pi of even a hundred digits on the path toward arbitrary precision?

7. andrewla ◴[02 Sep 25 18:49 UTC] No.45107383{3}[source]▶
> to many decimal places anyway

> > The idea of arbitrary precision is intrinsically broken in physical reality.

There is no contradiction here.

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8. gpm ◴[02 Sep 25 20:46 UTC] No.45108810{4}[source]▶
Yeah I was just responding to the 64bit float thing, people overestimate floats.