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Mitchell_Porter comments on Open Problems Related to Solomonoff Induction - Less Wrong
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The interesting bit is that if you could actually use Solomonoff induction as prior, I'm pretty sure you'd be an irreparable aether believer and 'relativity sceptic', with confidence that has so many nines nothing would ever convince you. That's because the absolute-speed irreversible aether universes like 3d versions of Conway's game of life are so much more computationally compact than highly symmetric universe with many space-time symmetries (to the point of time and space intermixing in the equations) and the fully reversible fundamental laws of physics. Saying this to you as applied mathematician with experience actually implementing laws of physics in software.
The priors are only a free parameter if all you care for is not getting Dutch-booked on your bets about physics but do not give a damn to have any useful theories.
Discrete universes introduce an unobserved parameter (a fundamental length) as well as a preferred frame. Abandoning complex numbers for a countable group in QM would also be very difficult. There is a complexity theory for real-valued objects and if Solomonoff induction could be adapted to that context, continuum theories ought to be favored.
Yep. Well, in any case, the point is that the Solomonoff probability is not in any way 'universal prior', you have to pick the machine, then you can't actually compute anything useful because its uncomputable and you'll never get anything non-trivial all the way down to minimum length.
If you go for changing the machine, you could use laws of physics as you know them as the machine, too (then you'll be irreparable sceptic of any new physics). In the context of laws of physics its just the emulation of one universal computation (laws of physics) with another (what ever stuff you pick). We are only discussing this because some highly self-important people heard of Solomonoff induction and Kolmogorov complexity, modelled those with something ill defined and fuzzy (lacking not only sufficient understanding of those things but the understanding of the concepts in which to understand those, and so on several layers deep, as is usually the case when you choose something really complicated without having spent a lot of time studying towards it) and then used it as universal smart sounding word to say (e.g. here or here or here ). Name-dropping and nothing more.