What can we gain by losing infinity? • Hacker News Board

Re: What can we gain by losing infinity?

#31

Post by magicalhippo » Thu, Apr 30, 2026, 2:42 AM UTC

jcgrillo wrote: post #3

In school I developed a strong hunch that continuity and infinity are "convenient delusions" we have that allow us to process the otherwise horrific complexity of the world. Experiencing time, sound, or visual motion as continuous, rather than discrete signal inputs is so much simpler . Similarly, the mathematical tricks and shortcuts we can use on well behaved continuous functions are both "unreasonably effective" a…

All math is made up. We've specifically made up math in a way which is useful to us.

You can make up math using different rules[1][2], and get different possibilities.

[1]: https://en.wikipedia.org/wiki/Non-standard_model_of_arithmet...

[2]: https://en.wikipedia.org/wiki/Internal_set_theory

Re: What can we gain by losing infinity?

#32

Post by analog31 » Thu, Apr 30, 2026, 2:50 AM UTC

jcgrillo wrote: post #3

In school I developed a strong hunch that continuity and infinity are "convenient delusions" we have that allow us to process the otherwise horrific complexity of the world. Experiencing time, sound, or visual motion as continuous, rather than discrete signal inputs is so much simpler . Similarly, the mathematical tricks and shortcuts we can use on well behaved continuous functions are both "unreasonably effective" a…

"All models are wrong but some are useful." -- George Box

Re: What can we gain by losing infinity?

#33

Post by vlovich123 » Thu, Apr 30, 2026, 3:16 AM UTC

novia wrote: post #24

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 o…

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).

Re: What can we gain by losing infinity?

#34

Post by svnt » Thu, Apr 30, 2026, 3:57 AM UTC

Animats wrote: post #29

bmenrigh wrote: post #8

The article doesn’t really tell us what is gained by rejecting infinity. And in general, why not also reject zero, negative numbers, irrational numbers, complex numbers, uncomputable numbers, etc.? Seems like an article about quacks that can’t even agree on what the bounds and rules of their quackery are.

> The article doesn’t really tell us what is gained by rejecting infinity. Decidability. The issues around undecidability all involve the lack of an upper bound. In a finite deterministic space, everything is decidable, although some things may be too costly computationally to decide. There are several ways to go for decidability. The brute force way is computer arithmetic - there is no number larger than 2^64-1. Tha…

> Looked at in this light, infinity is a labor-saving device to eliminate special cases, at a potential cost in soundness.

Or it is something that clearly conceptually exists, and makes simplistic reductionist viewpoints impossible to prove, which frustrates those who attempt to extend them into twisted metaphysical conjectures.

Re: What can we gain by losing infinity?

#35

Post by novia » Thu, Apr 30, 2026, 4:22 AM UTC

vlovich123 wrote: post #33

novia wrote: post #24

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 o…

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).

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 :)

Re: What can we gain by losing infinity?

#36

Post by vlovich123 » Thu, Apr 30, 2026, 4:49 AM UTC

novia wrote: post #35

vlovich123 wrote: post #33

Earlier quoted context omitted.

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).

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…

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?

Re: What can we gain by losing infinity?

#37

Post by random3 » Thu, Apr 30, 2026, 5:01 AM UTC

vlovich123 wrote: post #36

novia wrote: post #35

Earlier quoted context omitted.

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…

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 m…

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..

Re: What can we gain by losing infinity?

#38

Post by alex_young » Thu, Apr 30, 2026, 5:08 AM UTC

marcus_holmes wrote: post #30

alex_young wrote: post #22

And no discussion of Zeno? Pish. The idea that nothing is demonstrative of infinity is clearly incorrect. Take the screen you're reading this on. One pixel is composed of a bunch of different atoms, and once you get down to one of them, that atom subdivides into a bunch of subatomic particles, some of which even have mass. Let's take one of those for argument's sake. Split that, and you get some quarks. Now let's ima…

I think you missed the point. So, firstly, you have split the particle 5 times. That's not infinite times. You can split it more, so that would be 6 times. And more. Even if you could split it 1000 times, that's not infinity. The standard argument for infinity is that "you can always add 1 to any number, so there must be an infinity of them", and the refutation is that no matter how many times you add 1 to a number,…

Time has nothing to do with it. There are an infinite number of ways to divide anything. You don’t need time to prove that. Whatever number you think of you can divide by a larger number.

Re: What can we gain by losing infinity?

#39

Post by vlovich123 » Thu, Apr 30, 2026, 5:20 AM UTC

random3 wrote: post #37

vlovich123 wrote: post #36

Earlier quoted context omitted.

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 m…

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..

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.

Re: What can we gain by losing infinity?

#40

Post by rdevilla » Thu, Apr 30, 2026, 5:29 AM UTC

jcgrillo wrote: post #3

In school I developed a strong hunch that continuity and infinity are "convenient delusions" we have that allow us to process the otherwise horrific complexity of the world. Experiencing time, sound, or visual motion as continuous, rather than discrete signal inputs is so much simpler . Similarly, the mathematical tricks and shortcuts we can use on well behaved continuous functions are both "unreasonably effective" a…

> Experiencing time, sound, or visual motion as continuous, rather than discrete signal inputs is so much simpler.

Some practice with Mahasi Sayadaw style "noting" can train you into seeing your phenomenological experience as a stream of point-events between which we weave the illusion of continuity.