Good point! My intuition was that the Berkenstein bound (https://en.wikipedia.org/wiki/Bekenstein_bound) limits the amount of information in a volume. (Or more precisely the information surrounded by an area.)
Therefore the number of states in a finite volume is also finite.
I must add: since writing this comment, a man called george pointed out to me that, when modeling the universe as a computation one must take care, to not accidentally derive ontological claims from it.
So today I would have a more ‘whatever-works-works’-attitude; UTMs, DFAs both just models, neither likely to be ontologically true.
Good point! My intuition was that the Berkenstein bound (https://en.wikipedia.org/wiki/Bekenstein_bound) limits the amount of information in a volume. (Or more precisely the information surrounded by an area.) Therefore the number of states in a finite volume is also finite.
I must add: since writing this comment, a man called george pointed out to me that, when modeling the universe as a computation one must take care, to not accidentally derive ontological claims from it.
So today I would have a more ‘whatever-works-works’-attitude; UTMs, DFAs both just models, neither likely to be ontologically true.