AP: Any two deterministic, reversible automata with state space of the same cardinality are isomorphic, no?
BH: If so, wouldn't that involve an isomorphism whose information content is potentially the same size as the state space itself?
AP: I am not sure how the information content of the isomorphism matters here. Surely it's a question of degree. In some cases, there will be very little content. In others, a lot. I do not think one can draw a line between "most trivial" and "less trivial".
Making comparisons doesn't require drawing lines, it only requires a comparison operator. For the purpose of the induction problem, we only care whether the fact of isomorphisms would undermine our conclusions drawn about the relative frequencies of two kinds of worlds -- those with noticed irregularities, and those without. I don't see how it would.
BH: the straightforward bitstring encoding of an automaton stands as a first-class instance of a world, and cannot be waved away as just one of the many ways that the "concrete" world in question can be described.
AP: Very well, but if it is not up to isomorphism, then we get a lot of contingent and utterly inscrutable facts, such as what encoding was used for the bitstrings. Reality becomes complex in uninteresting ways.
I would make the same guess for alternative encoding methods as for isomorphisms: that they don't undermine our frequency calculations above. At any rate, the problem of uninteresting complexity probably applies to any notion of modal realism. If the only criterion for being a world is that it is a causal closure without internal contradiction, then there will be lots of uninteresting ways for worlds to differ from other, and lots of worlds that are hard to decide if they are interestingly different.
BH: I noted earlier that my perspective "depends on the thesis that physicalism is right and that qualia and consciousness are epiphenomena".
AP: You need a stronger claim. Physicalism is compatible, e.g., with the idea that no simulation can be conscious, because it might turn out that consciousness is an epiphenomenon of some but not other physical processes. It is logically compatible with physicalism and epiphenomenalism, though intuitively absurd, that no anti-matter-based beings could be conscious. It is less absurd to suppose that no simulated beings could be conscious.
That depends on what you mean by simulation. In this context, a simulation can be just the infinite collection of facts that together say all that can be said of a world, including e.g. all the facts about my mental state(s) as I write this sentence. My speculation is that the phenomenological experience associated with those facts is the same regardless of whether the world in question is "real" as scored by people who distinguish worlds as "real" or not in some non-indexical way. (For my part, I don't see how we can know that we have such a way.) But yes, I wouldn't dispute that my perspective requires claiming e.g. the systems reply to Searle's Chinese Room argument.
BH: irregularity doesn't undermine induction if the irregularity is unnoticed.
AP: It depends on how ambitious the inductive claims are. If you merely want to get the claim that you will not SEE any irregularity, maybe.
Right, the claim here is about irregularity that is either undetectable or undetected (or perhaps even so tenuously detected that it's reasonable to doubt the detection).
AP: But normally in science we want to know that the things we infer are really so, and not merely appear so.
If the undetectedness and indefectibility of the irregularities can be statistically guaranteed to the same extent as the sorts of guarantees we get in thermodynamics and quantum mechanics, then that's scientific enough for me. :-)