I very strongly do. I think the universe runs on math. I think there exist one or more sets of statements that can the universe in its entirety. I can’t actually imagine the alternative, actually.
What if it requires an infinite set of statements to specify? Consider the hypothetical of a universe where there are no elementary particles but each stage is made up of something still simpler. Or consider something like the Standard Model but where the constants are non-computable. Would either of these fit what you are talking about?
Yes, that would fit in what I am talking about. I have a bad habit of constantly editing posts as I write, so you might have seen my post before I wrote this part.
I don’t necessarily think we can find such a set of axioms. mind you. I can’t guarantee that there are a finite number of statements required, or that the human mind is necessarily is capable of producing/comprehending said statements, or even that any mind stuck within the constraints of the universe itself is capable. (I suppose you can take issue with the use of the word “describable” at this point). But I do think the statements exist, in some platonic sense, and that if we buy into logic we can at least know that they exist even if we can’t know them directly. (In the same sense that we can often know whether or not a solution exists even if it’s impossible to find)
Such a universe wouldn’t even necessarily be “complicated”. A single infinite random binary string requires an infinitely long statement to fully describe (but we can at least partially pin it down by finitely describing a multiverse of random binary strings)
Yes, thank you, I don’t think that was there when I read it. I’m not sure then that the statement that universe runs on math at that point has any degree of meaning.
It seems self evident once you get it, but it’s not obvious.
In the general population you get these people who say “well, if it’s all just atoms, whats the point”? They don’t realize that everything has to run on logic regardless of whether the underlying phenomenon is atoms or souls or whatever. (Or at least, they don’t agree. I shouldn’t say “realize” because the whole thing rests on circular arguments.)
It also provides sort of ontological grounding onto which further rigor can be built. It’s nice to know what we mean when we say we are looking for “truth”.
What if it requires an infinite set of statements to specify? Consider the hypothetical of a universe where there are no elementary particles but each stage is made up of something still simpler. Or consider something like the Standard Model but where the constants are non-computable. Would either of these fit what you are talking about?
Yes, that would fit in what I am talking about. I have a bad habit of constantly editing posts as I write, so you might have seen my post before I wrote this part.
Such a universe wouldn’t even necessarily be “complicated”. A single infinite random binary string requires an infinitely long statement to fully describe (but we can at least partially pin it down by finitely describing a multiverse of random binary strings)
Yes, thank you, I don’t think that was there when I read it. I’m not sure then that the statement that universe runs on math at that point has any degree of meaning.
It seems self evident once you get it, but it’s not obvious.
In the general population you get these people who say “well, if it’s all just atoms, whats the point”? They don’t realize that everything has to run on logic regardless of whether the underlying phenomenon is atoms or souls or whatever. (Or at least, they don’t agree. I shouldn’t say “realize” because the whole thing rests on circular arguments.)
It also provides sort of ontological grounding onto which further rigor can be built. It’s nice to know what we mean when we say we are looking for “truth”.