The set of trajectories created by assuming all possible sets of laws would be the set of all possible universes, at least one of which contains us (only one if our universe is deterministic, so the world line does not branch).
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The transition function correlates adjacent universe states by explaining how information travels across locations in the individual states. The arrow of time is given by increasing entropy, i.e. the degree of distributedness of the starting state information across locations.
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The hypothetical "big bang state" is a state in which information is perfectly aligned with location, i.e. different locations don't hold correlated information. There is no time before the big bang, moving away from it in any direction means moving forward in time.
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A pure big bang state seems incompatible with a deterministic universe, because when we trace the evolution of the universe backwards into it, we cannot recover our trajectory. The universe either does not hold such a state, or it is continuous, or it is indeterministic.
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I don't know about the universe, but every finitely resolved set of observations can be modeled by a finite set of bits. Conversely, infinity seems to be a symbol without referent, because I cannot construct it, and neither can I point at it.
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How does this differ from Wolfram's view of the universe as computation? I haven't looked into it, but I always assumed he was doing something along these lines. Is he doing something entirely different?
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His ideas operate in the same space, yes.
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Now I am wondering if the universe can be expressed as a formal language...
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I think that all our observations and thoughts can, and it cannot be shown that the universe cannot.
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