As the simplest theory, my default position is the universe is computable and that everything in the universe is computable. Note that they are not the same thing.
Some intuition:
1. If the universe contains an uncomputable thing, then you could utilize this to build a super turing complete computer. This would only make CS more interesting.
2. If the universe extends beyond the observable universe, and it's infinite, and on some level it exists, and there is some way that we know it all moves forward (not necessarily time, as it's uneven), but that's an infinite amount of information, which can never be stepped forward at once (so it's not computable). The paper itself touches on this, requiring time not to break down. Though it may be the case, the universe does not "step" infinitely much information.
One quick side, this paper uses a proof with model theory. I stumbled upon this subfield of mathematics a few weeks ago, and I deeply regret not learning about it during my time studying formal systems/type theory. If you're interested in CS or math, make sure you know the compactness theorem.
Do you mean like ghosts or like quantum randomness and Heisenberg's uncertainty principle?
We cannot compute exactly what happens because we don't know what it is, and there's randomness. Superdeterminism is a common cop out to this. However, when I am talking about whether something is computable, I mean whether that interaction produces a result that is more complicated than a turing complete computer can produce. If it's random, it can't be predicted. So perhaps a more precise statement would be, my default assumption is that "similar" enough realities or sequences of events can be computed, given access to randomness, where "similar" is defined by an ability to distinguish this similulation from reality by any means.
The last digit of pi doesn't exist since it's irrational. Chaitan's constant, later busy beaver numbers, or any number of functions may be uncomputable, but since they are uncomputable, I'd be assuming that their realizations don't exist. Sure, we can talk about the concept, and they have a meaning in the formal system, but that's precisely what I'm saying: they don't exist in this world. They only exist as an idea.
Say for instance that you could arrange quarks in some way, and out pops, from the fabric of the universe, a way to find the next busy beaver numbers. Well, we'd be really feeling sorry then, not least because "computable" would turn out to be a misnomer in the formalism, and we'd have to call this clever party trick "mega"-computable. We'd have discovered something that exists beyond turing machines, we'd have discovered, say, a "Turing Oracle". Then, we'd be able to "mega"-compute these constants. Another reason we'd really feel sorry is because it would break all our crypto.
However, that's different than the "idea of Chaitan's constant" existing. That is, the idea exists, but we can't compute the actual constant itself, we only have a metaphor for it.
Some intuition:
1. If the universe contains an uncomputable thing, then you could utilize this to build a super turing complete computer. This would only make CS more interesting.
2. If the universe extends beyond the observable universe, and it's infinite, and on some level it exists, and there is some way that we know it all moves forward (not necessarily time, as it's uneven), but that's an infinite amount of information, which can never be stepped forward at once (so it's not computable). The paper itself touches on this, requiring time not to break down. Though it may be the case, the universe does not "step" infinitely much information.
One quick side, this paper uses a proof with model theory. I stumbled upon this subfield of mathematics a few weeks ago, and I deeply regret not learning about it during my time studying formal systems/type theory. If you're interested in CS or math, make sure you know the compactness theorem.
Paper direct:
https://jhap.du.ac.ir/article_488.html
I enjoyed some commentary here:
https://www.reddit.com/r/badmathematics/comments/1om3u47/pub...
See also:
https://en.wikipedia.org/wiki/Mathematical_universe_hypothes...