It supports Occam’s Razor pretty well, but does it also offer good evidence that that those likelihoods will manifest in real-world probabilities IN EXACT PROPORTION to the bit-lengths of their inputs?
Nope, and we have no idea where we’d even start on evaluating this precisely because of the various problems relating to different languages. I think this is an active area of research.
It does seem though, by observation and inference (heh, use whatever tools you have), that more efficient languages tend to formulate shorter hypotheses that tend to hint at this.
There’s also been some demonstrations of how well SI works for learning and inferring about a completely unknown environment. I think this was what AIXI was about, though I can’t recall specifics.
Nope, and we have no idea where we’d even start on evaluating this precisely because of the various problems relating to different languages. I think this is an active area of research.
It does seem though, by observation and inference (heh, use whatever tools you have), that more efficient languages tend to formulate shorter hypotheses that tend to hint at this.
There’s also been some demonstrations of how well SI works for learning and inferring about a completely unknown environment. I think this was what AIXI was about, though I can’t recall specifics.