They don't. To get the probabilities about something occuring in our universe, you need to get the information about our universe first. Solomonoff Induction tells you how to do that, in a random universe. After you get enough evidence to understand the universe, only then you start getting good results.
Yes, but we already have lots of information about our universe. So, making use of all that, if we could start using SI to, say, predict the weather, would its predictions be well-calibrated? (They should be - modern weather predictions are already well-calibrated, and SI is supposed to be better than how we do things now.) That would require that, of all predictions compatible with currently known info, ALL of them would have to occur in EXACT PROPORTION to their bit-length complexity.
Is there any evidence that this is the case?
of all predictions compatible with currently known info, ALL of them would have to occur in EXACT PROPORTION to their bit-length complexity
I admit I am rather confused here, but here is my best guess:
It is not true, in our specific world, that all predictions compatible with the past will occur in exact proportion to their bit-length complexity. Some of them will occur more frequently, some of them will occur less frequently. The problem is, you don't know which ones. Because all of them are compatible with the past, so how could you tell the difference... (read more)
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.