[novia]

Take the approximate number of subatomic particles in the universe, call it Ω. Define the largest number as Ω² and the smallest number as -Ω², and define the number of decimal numbers between each integer number as Ω², evenly spaced. That should be more than enough numbers. Redefine Ω with each new discovery in physics.

If this seems too conservative to you, like if for some reason you want to talk about the volume of the universe in terms of the width of an up-quark or whatever, feel free to tack on some modifier to my proposed number system.

[vlovich123]

I want to count the number of possible permutations of the particles. We’ve now got a “larger” number than Ω will ever be able to represent by definition (even Ω² is minuscule by comparison).

[novia]

yeah that seems fine. there's like no good reason to do that. are you trying to simulate reality or something?

but my point still stands, choose whichever calculation you think is important to be able to do with Ω, defined as f(Ω), square it for good measure, and set that as the max, the min, and the number of numbers in between each integer.

The total number of possible numbers will be ~2*f(Ω)⁴ which should be more than enough numbers :)

[vlovich123]

AES256 already has more possible keys than exist atoms in the visible universe and that’s a pretty mundane thing. If you wanted to store all those keys, that’s even large. # of atoms in the universe turns into a very small very quickly when talking about permutations and permutations come up all the time (mathematical simulations, probability computations, etc).

I really don’t understand what point you’re trying to make saying “pick the largest possible number relevant” as that number varies. Also, that’s just the rational numbers. There’s plenty of digits of precision needed for trajectories over galactic distances and the more precision you try to give irrational numbers, the larger your magical “largest number” needs to grow again.

Also, we don’t know how big the “non observable universe” is and it’s beyond the scope of science. It very well could be an infinite number of atoms and then what?

[jcgrillo]

> It very well could be an infinite number of atoms and then what?

Where I get stuck with this is how might we measure that? Continuous measurements and infinite measurements are not something we can make. We fit continuous theories to discrete measurements--and the good ones fit really well!--but until we can measure it how can we actually know? I concluded we just can't, and we have to be OK with that.

[computably]

> We fit continuous theories to discrete measurements--and the good ones fit really well!--but until we can measure it how can we actually know?

Well, physicists came up with quantum mechanics because they found a way to distinguish a genuinely discrete phenomenon.

Understanding the physical universe overlaps with a subset of math. It shouldn't constrain the abstract tools which may or may not one day be useful for that understanding.

[jcgrillo]

I agree that continuity (and therefore infinity) are really useful tools. But it may also be useful to develop mathematical formalism that hews more closely to that which we can actually observe. Or not! But if nobody investigates we'll never know.

[random3]

Since we don’t know the number of atoms, we’d need to let omega be a function, then deal with all the edge cases, rename omega with ∞ and..

[vlovich123]

Yeah I can’t tell if op is trolling or really thinks they can just define a rational number big enough to not need infinity as a concept.

[euroderf]

At the bottom end we have the Planck length. How many cubic Planck lengths in the visible universe ? Anyone ? To paraphrase Bill Gates (allegedly), "(PlanckLengths/widthOfUniverse)*3 ought to be enough for anybody."

[something765478]

This system breaks down when you start looking at permutations; there are Ω! ways to arrange your subatomic particles, and that's just in 1 dimension.

[kbelder]

Sure. And then you can do permutations OF the permutations, until the end of the universe, and the unthinkably large result still firmly remains in the world of finite numbers.