Are uncomputable numbers/things a problem for Wheeler's "it from bit"?

Question

I have some questions related to Wheeler's ideas of "It from bit" and "Law without law"

In summary, these both theories postulate that there was an initial universe with no laws from which laws of physics appeared from informational processes (It from bit)

1. In a book ("The Hidden Pattern" by Ben Goertzel) it is said "John Archibald Wheeler's (1988) idea of “law without law” and “it from bit” —which hypothesizes that the laws of our physical universe are in some sense optimal, so that if someone has an objective or physical world with unformed, indefinite laws, the laws will eventually settle into the optimal law configuration (being the laws of our universe)"

   • Assuming Wheeler was right and According to Wheeler's "it from bit" and "law without law", could the optimal laws have been different? If I understand these theories correctly, the initial universe did not have any laws/rules and the laws were created by the informational processes of "it from bit". Because of this, could these informational processes have created different rules/processes that would give as a result a different universe with different laws? I mean, could the initial lawless/ruleless-universe have evolved differently, giving as a result a different universe with different laws (not only our own set of laws)? Arbitrarily different?

2. Since the initial universe did not have any rules, could "it from bit" have created radically different truly fundamental laws and rules? Could it have created a different universe behaving even according to fundamentally different types of mathematics/logic? Could it have created a universe with fundamentally different computability/information theory? Could it have created a universe where uncomputable or even illogical/logically impossible/indescribable/nonexistent/impossible things could be computed? Since the initial universe would not have any rules, would it from bit be adjusted to computability and information theory? Or would computability/information theory not exist in the initial universe, and because of that, "it from bit" could do things outside of them (could do things forbidden by them)? Would the same happen with logic (Did the initial universe behave according to some type of mathematics/logic or they did not exist at the initial universe)?

3. If the above would be right and the universe could have behaved according to radically/fundamentally different laws/maths/logic, could "it from bit" processes have created a universe behaving according to paraconsistent logic ( https://en.wikipedia.org/wiki/Paraconsistent_logic) or a trivialism (a system where every statement/"thing" would be true and false at the same time: https://en.wikipedia.org/wiki/Trivialism, it could be called an illogical system)? (the consequences of both systems would be uncomputable, but if it from bit created computability and information theory, could they have created a different computability or information theory where they would be computable?) Or, since things in it from bit would derive their existence from solely informational processes, and since the definition of a trivialist/paraconsistent system is a computable definition (otherwise we could not define them), could an it from bit-informational process computing just the solely definition of these systems be enough for these systems to exist? In summary: Could "it from bit" make trivialist/paraconsistent systems exist in a universe?

4. If the above is right, wouldn't that mean that Wheeler's law without law and it from bit would be an unfalsifiable theory? (Since they could produce all types of universes/outcomes, even impossible/uncomputable/logically impossible/illogical ones.) Also, would they be a multiverse theory? (besides being capable of creating different versions of a given universe, could they create multiple universes at once?)

(I need answers from people that know well these theories. Although this is relate with philosophy, that's why I put this question here, I need answers mostly based on a scientific point of view not only/purely philosophical)

Answer 1

Bearing in mind that no consensus has been reached on most/all of the questions you pose here, I’ll take a shot anyway!

1 and 2: Different Laws, Yes / Arbitrarily Different Rules, No

I love Wheeler’s style and many of his ideas, but many of his ideas were never fleshed out. They really were more like questions then ideas. What if hypotheticals that were, I think, intended to provoke thought and inspire.

Yes in that the law without laws and it from bit would most likely allow for a great deal of ambiguity in the way the early universe would shake out. I, personally, don’t think the different possible laws would be arbitrarily different though. I forget which book it was, but the author was presenting analogy for symmetry breaking. There’s a dinner party and for each place setting there is a water glass placed exactly half way between them. The guests all sit and, for a time, it is equally likely that any one of them could reach for the glass on their left or their right, but as soon as any one of them does, the symmetry is broken and the choice is made for ALL of the guests. From that point onward, there is no question as to who’s water glass is who’s.

But, again personally, I don’t feel like different rules and different forces could be arbitrarily different. I’m a big believer in information theory (and the idea of “it from bit”) and I just cannot conceive of a universe where the fundamental rules of computation are different than they are in this one. Change the laws of physics, sure, but take away my NAND gate and we’re going to have a problem.

3: Paraconsistent, Maybe / Trivialism, No / Computable Uncomputability, No

I’m not sure what book it was, but this time the author was talking about human generations (mother, father, brother kind of stuff) and the idea of partially ordered sets. I think partially ordered sets are a good way, better than Paraconsistent logic, to introduce enough “wibbly wobbly” into a universe to grease the wheels of existence. Enough wobbly wobbly for Loop Quantum Gravity and the recent Quantum Eraser Experiments anyway.

You might be able to convince me that the logical rule set for possible universes can vary, but I would draw the line just after Paraconsistent logic and well before Trivialism. I’d also insist on the caveat that any possible logical rule set must at least allow NAND or NOR (preferably both). I just don’t see much of a possibility for NAND and NOR existing under Trivialism…

4: We’re not talking about Wheeler any more

I don’t know that Wheeler’s it from bit and laws without law imply what you seem to think they imply. Multiverse, yes, depending of course on your definition thereof, but unlimited, untestable multiverse... I don’t think so.

With your 4th question you’ve ventured away from Wheeler and into the ideas of Max Tegmark and his ilk. Tegmark proposes the idea of a multiverse in which every mathematically expressible idea is made manifest. It’s like the ultimate multiverse where every possible mathematical system is just as physically real as every other. And he even came up with a way to test it!

I wouldn’t recommend it though… It’s called the Quantum Suicide Experiment, and it’s pretty messy. Seriously, do not attempt this experiment!