I don’t think it’s a string of objections; it’s one (reasonable) objection made at length.
The objection is that you’re not really doing Solomonoff induction or anything like it unless you’re considering actual programs and people saying things like “many worlds is simpler than collapse” never actually do that.
As I say, I think this is a reasonable criticism, but (in the specific context here of comparing MW to collapse) I think there’s a reasonable response to it: “Collapse interpretations have to do literally all the same things that many-worlds interpretations do—i.e., compute how the wavefunction evolves—as well as something extra, namely identifying events as measurements, picking measurement results at random, and replacing the wavefunction with one of the eigenfunctions. No matter how you fill in the formal details, that is going to require a longer program.”
(For the avoidance of doubt, the “picking measurement results at random” bit isn’t reckoning the random numbers as part of the complexity cost—as discussed elsewhere in this discussion, it seems like that cost is the same whatever interpretation you pick; it’s the actual process of picking results at random. The bit of your code that calls random(), not the random bits you get by calling it.)
This is still a bit hand-wavy, and it’s not impossible that it might turn out to be wrong for some subtle reason. But it does go beyond “X sure seems simpler to me than Y”, and it’s based on some amount of actual thinking about (admittedly hypothetical) actual programs.
(I guess there are a few other kinda-objections in there—that Solomonoff induction is underspecified because you have to say what language your programs are written in, that someone said “Copenhagen” when they meant “collapse”, and that some interpretations of QM with actual wavefunction collapse in aren’t merely interpretations of the same mathematics as every other interpretation but have actual potentially observable consequences. The first is indeed an issue, but I haven’t heard anyone seriously suggest that any plausible difference in language would change the order of preference between two complete physical theories, if we were actually able to codify them with enough precision; the second is a terminological nitpick, though certainly one worth picking; the third isn’t really an objection at all but is again an observation worth making. But the main point of that comment is a single objection.)
I don’t think it’s a string of objections; it’s one (reasonable) objection made at length.
The objection is that you’re not really doing Solomonoff induction or anything like it unless you’re considering actual programs and people saying things like “many worlds is simpler than collapse” never actually do that.
As I say, I think this is a reasonable criticism, but (in the specific context here of comparing MW to collapse) I think there’s a reasonable response to it: “Collapse interpretations have to do literally all the same things that many-worlds interpretations do—i.e., compute how the wavefunction evolves—as well as something extra, namely identifying events as measurements, picking measurement results at random, and replacing the wavefunction with one of the eigenfunctions. No matter how you fill in the formal details, that is going to require a longer program.”
(For the avoidance of doubt, the “picking measurement results at random” bit isn’t reckoning the random numbers as part of the complexity cost—as discussed elsewhere in this discussion, it seems like that cost is the same whatever interpretation you pick; it’s the actual process of picking results at random. The bit of your code that calls
random()
, not the random bits you get by calling it.)This is still a bit hand-wavy, and it’s not impossible that it might turn out to be wrong for some subtle reason. But it does go beyond “X sure seems simpler to me than Y”, and it’s based on some amount of actual thinking about (admittedly hypothetical) actual programs.
(I guess there are a few other kinda-objections in there—that Solomonoff induction is underspecified because you have to say what language your programs are written in, that someone said “Copenhagen” when they meant “collapse”, and that some interpretations of QM with actual wavefunction collapse in aren’t merely interpretations of the same mathematics as every other interpretation but have actual potentially observable consequences. The first is indeed an issue, but I haven’t heard anyone seriously suggest that any plausible difference in language would change the order of preference between two complete physical theories, if we were actually able to codify them with enough precision; the second is a terminological nitpick, though certainly one worth picking; the third isn’t really an objection at all but is again an observation worth making. But the main point of that comment is a single objection.)