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...
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.