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Squark comments on Solomonoff Cartesianism - Less Wrong
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Comments (45)
UDT may indeed be an aspect of bridging laws. The reason I'm not willing to call it a full solution is as follows:
1) Actually, the current version of UDT that I write down as an equation involves maximizing over maps from sensory sequences to actions. If there's a version of UDT that maximizes over something else, let me know.
2) We could say that it ought to be obvious to the math intuition module that choosing a map R := S->A ought to logically imply that R^ = S^->A for simple isomorphisms over sensory experience for isomorphic reductive hypotheses, thereby eliminating a possible degree of freedom in the bridging laws. I agree in principle. We don't actually have that math intuition module. This is a problem with all logical decision theories, yes, but that is a problem.
3) Aspects of the problem like "What prior space of universes?" aren't solved by saying "UDT". Nor, "How exactly do you identify processes computationally isomorphic to yourself inside that universe?" Nor, "How do you manipulate a map which is smaller than the territory where you don't reason about objects by simulating out the actual atoms?" Nor very much of, "How do I modify myself given that I'm made of parts?"
There's an aspect of UDT that plausibly answers one particular aspect of "How do we do naturalized induction?", especially a particular aspect of how we write bridging laws, and that's exciting, but it doesn't answer what I think of as the entire problem, including the problem of the prior over universes, multilevel reasoning about physical laws and high-level objects, the self-referential aspects of the reasoning, updating in cases where there's no predetermined Cartesian boundary of what constitutes the senses, etc.
My version of UDT (http://lesswrong.com/r/discussion/lw/jub/updateless_intelligence_metrics_in_the_multiverse/) maximizes over programs written for a given abstract "robot" (universal Turing machine + input channels).
Regarding an abstract solution to logical uncertainty, I think the solution given in http://lesswrong.com/lw/imz/notes_on_logical_priors_from_the_miri_workshop/ (which I use in my own post) is not bad. It still runs into the Loebian obstacle. I think I have a solution for that as well, going to write about it soon. Regarding something that can be implemented within reasonable computing resource constraints, well, see below...
The prior space of universes is covered: unsurprisingly it's the Solomonoff prior (over abstract sequences of bits representing the universe, not over sensory data). Regarding the other stuff, my formalism doesn't give an explicit solution (since I can't explicitly write the optimal program of given length). However, the function I suggest to maximize already takes everything into account, including restricted computing resources.