Not all things are possible, only potentially possible ones.
If you take all the numbers between zero and one, you will find an endless supply of distinct numbers but none of them are 3.
If so, this has interesting implications for the cause of the baryon asymmetry problem.
Either the baryon number started non-zero and was conserved; or non-conservation of baryon number (protons vs antiprotons etc) have to be paired with equivalent non-conservation of lepton number (electrons vs positrons etc); or it can happen without simultaneously balancing the lepton number, and charge isn't conserved.
Unfortunately (for me) those implications are above my level. I can't usefully converse with an LLM about it, as this isn't a domain I know well enough to detect if it's making stuff up.
Aren't you really just talking about the level of abstraction being applied? If there are infinite possibilities between zero and one, then it's just our way of relating to it that imposes the perception of a limitation.
No. You might be reading into it a little bit too much.
My point was that finding three needs to be possible for you to find it. If you are looking on the interval 0-1, it is not possible. As other comments have kinda of suggested, you could map every integer to a real and find "three" but if you are going to do that, why not just look on an interval that actually contains the number?
It's unclear to me at least what you mean here. In term of what is logically possible, if we take for granted that all integer numbers and more are mappable from a subset of this interval, then we do have this number.
Now, on logistical level, the mapping procedure is not free, it does have a physical/energetic/mental cost to handle it, and a more trivial representation of integer has a lower cost on this regard.
But the simpler integer representation can represent less many situations. If all one need to deal with in a certain frame is covered by a simpler shipper representation, from an economical perspective it can be argued it worth the risk of hitting a point where the representation will be insufficient as the situation evolved with cases it can't handle.
My impression is that your underlying premises are conflating all of this distinguishable aspects. But of course my impression is limited by my own narrow representation of the world, no matter how open and curious I can be about learning from experiences it makes me go through.
I think you are overthinking it too. The task was to find three, not something that is equivalent to three. However you choose to represent it, it wouldn't be hard to come up with a different "three" that you won’t find within that representation. If you are changing the representation, why wouldn't you just change the interval that you are searching?
Experimental physics takes it one step back: it's all about setting bounds on what is potentially possible. A model of the universe might say that the numbers are between zero and one, but there's some other model that says there could be 3s.
Note that this epistemic uncertainty is not the same thing that the article is focused on. The article is mostly about one specific model, which itself has some randomness baked on.
I love this podcast. The solo or very physics focused episodes go over my head sometimes but they're always a fun listen. I enjoyed "Jody Azzouni on What Is and Isn't Real" where they (among other things) argue about what it means for a thing to be "real"/"exist", and extend that to mathematical concepts, fictional characters etc.
Surprising that he could have that intuition in 1935, before the Unruh effect was known of, before AQFT was invented, and really before most of QFT was formulated.
You’ve probably been reading a lot of physicists that believe in the Many Worlds view. Nature did a poll of physicists last year[1] and it’s still only the third most popular interpretation, behind the Copenhagen Interpretation and information-based interpretations like QBism.
Yes! But at some level, doesn’t it kind of get blurred?
That is, we are trying to come up with rules describing the underlying rules, right? The world isn’t made of stuff, it’s made of rules, right? Or math? Just not the same notation, at least.
Help! I feel like I’m falling off a metaphysical cliff!
Given infinite time, is it possible to randomly draw a rational (instead of an irrational) from the interval [0, 1]? And if so, is it possible infinite times?
In this case it does. Describe any effective measure to pick a random sample from the interval and you will have cheated into choosing from the computable reals instead (of which there is a countable amount)
I don't think that's correct. You're describing a limitation of our physical computing devices (or perhaps physical reality itself) as opposed to a theoretical flaw. At least as far as I can tell.
Either the baryon number started non-zero and was conserved; or non-conservation of baryon number (protons vs antiprotons etc) have to be paired with equivalent non-conservation of lepton number (electrons vs positrons etc); or it can happen without simultaneously balancing the lepton number, and charge isn't conserved.
Unfortunately (for me) those implications are above my level. I can't usefully converse with an LLM about it, as this isn't a domain I know well enough to detect if it's making stuff up.
Now, on logistical level, the mapping procedure is not free, it does have a physical/energetic/mental cost to handle it, and a more trivial representation of integer has a lower cost on this regard.
But the simpler integer representation can represent less many situations. If all one need to deal with in a certain frame is covered by a simpler shipper representation, from an economical perspective it can be argued it worth the risk of hitting a point where the representation will be insufficient as the situation evolved with cases it can't handle.
My impression is that your underlying premises are conflating all of this distinguishable aspects. But of course my impression is limited by my own narrow representation of the world, no matter how open and curious I can be about learning from experiences it makes me go through.
on edit: maybe should say infinite set instead of infinite sequence.
What leads you to claim that you can't encode infinite information given an infinite set to work with?
Infinity is an abstraction that simplifies a lot of maths, it isn't real though.
Experimental physics takes it one step back: it's all about setting bounds on what is potentially possible. A model of the universe might say that the numbers are between zero and one, but there's some other model that says there could be 3s.
Note that this epistemic uncertainty is not the same thing that the article is focused on. The article is mostly about one specific model, which itself has some randomness baked on.
I particularly like the one with David Wallace.
Subtle difference, but energy conservation for example has to be adhered to.
But then again, he was John von Neumann.
[1] https://gizmodo.com/app/uploads/2025/07/favored-explanations...
That is, we are trying to come up with rules describing the underlying rules, right? The world isn’t made of stuff, it’s made of rules, right? Or math? Just not the same notation, at least.
Help! I feel like I’m falling off a metaphysical cliff!
-- David Hilbert.
Disclaimer: total armchair philosophy.