Thank you for your reply. It does clear up some of the virtues of SI, especially when used to generate priors absent any evidence. However, as I understand it, SI does take into account evidence—one removes all the possibilities incompatible with the evidence, then renormalizes the probablities of the remaining possibilities. Right?
If so, one could still ask—after taking account of all available evidence—is SI then well-calibrated? (At some point it should be well-calibrated, right? More calibrated than human beings. Otherwise, how is it useful? Or why should we use it for induction?)
Essentially the theory seems to predict that possible (evidence-compatible) events or states in the universe will occur in exact or fairly exact proportion to their relative complexities as measured in bits. Possibly over-simplifying, this suggests that if I am predicting between 2 (evidence-compatible) possibilities, and one is twice as information-complex as the other, then it should actually occur 1⁄3 of the time. Is there any evidence that this is actually true?
(I can see immediately that one would have to control for the number of possible “paths” or universe-states or however you call it that could lead to each event, in order for the outcome to be directly proportional to the information-complexity. I am ignoring this because the inability to compute this appears to be the reason SI as a whole cannot be computed.)
You suggest above that SI explains why Occam’s razor works. I could offer another possibility—that Occam’s Razor works because it is vague, but that when specified it will not turn out to match how the universe actually works very precisely. Or that Occam’s Razor is useful because it suggests that when generating a Map one should use only as much information about the Territory is as is necessary for a certain purpose, thereby allowing one to get maximum usefulness with minimum cognitive load on the user.
I am not arguing for one or the other. Instead I am just asking, here among people knowledgeable about SI—Is there any evidence that outcomes in the universe actually occur with probablities in proportion to their information-complexity? (A much more precise claim than Occam’s suggestion that in general simpler explanations are preferable.)
Maybe it will not be possible to answer my question until SI can at least be estimated, in order to actually make the comparison?
(Above you refer to “all mathematically possible universes.” I phrased things in terms of probabilities inside a single universe because that is the context in which I observe & make decisions and would like SI to be useful. However I think you could just translate what I have said back into many-worlds language and keep the question intact.)
Hi, my name is Jason, this is my first post. I have recently been reading about 2 subjects here, Calibration and Solomoff Induction; reading them together has given me the following question:
How well-calibrated would Solomonoff Induction be if it could actually be calculated?
That is to say, if one generated priors on a whole bunch of questions based on information complexity measured in bits—if you took all the hypotheses that were measured at 10% likely—would 10% of those actually turn out to be correct?
I don’t immediately see why Solomonoff Induction should be expected to be well-calibrated. It appears to just be a formalization of Occam’s Razor, which itself is just a rule of thumb. But if it turned out not to be well-calibrated, it would not be a very good “recipe for truth.” What am I missing?