But would you agree with the claim that a real-world agent is going to have to use a formulation that fits inside limits on the length of usable proofs?
I’m not defining an agent here, I’m defining a mathematical function which evaluates agents. It is uncomputable (as is the Legg-Hutter metric).
Upon further reflection, I think the problems are not with your distribution… but with the neglect of bridging laws or different ways of representing the universe.
N defines the ontology in which the utility function and the “intrinsic mind model” are defined. Y should be regarded as the projection of the universe on this ontology rather than the “objective universe” (whatever the latter means). Thus H implicitly includes both the model of the universe and the bridging laws. In particular, its complexity reflects the total complexity of both. For example, if N is classical and the universe is quantum mechanical, G will arrive at a hypothesis H which combines quantum mechanics with decoherence theory to produce classical macroscopic histories. This hypothesis will have large t(H) since quantum mechanics correctly reproduces the classical dynamics of M at the macroscopic level. This shouldn’t come as a surprise: we also perceive the world as classical. More precisely, there would be a dominant family of hypothesis differing in the results of “quantum coin tosses”. That is, this ontological projection is precisely the place where the probability interpretation of the wavefunction arises.
I’m not defining an agent here, I’m defining a mathematical function which evaluates agents. It is uncomputable (as is the Legg-Hutter metric).
N defines the ontology in which the utility function and the “intrinsic mind model” are defined. Y should be regarded as the projection of the universe on this ontology rather than the “objective universe” (whatever the latter means). Thus H implicitly includes both the model of the universe and the bridging laws. In particular, its complexity reflects the total complexity of both. For example, if N is classical and the universe is quantum mechanical, G will arrive at a hypothesis H which combines quantum mechanics with decoherence theory to produce classical macroscopic histories. This hypothesis will have large t(H) since quantum mechanics correctly reproduces the classical dynamics of M at the macroscopic level. This shouldn’t come as a surprise: we also perceive the world as classical. More precisely, there would be a dominant family of hypothesis differing in the results of “quantum coin tosses”. That is, this ontological projection is precisely the place where the probability interpretation of the wavefunction arises.