If we had evolved in an environment in which the only requirement on physical laws/rules was that they are Turing computable (and thus that they didn’t have a lot of symmetries or conservation laws or natural abstractions), then in general the only way to make predictions is to do roughly as much computation as your environment is doing. This generally requires your brain to be roughly equal in computational capacity, and thus similar in size, to the entire rest of its environment (including its body). This is not an environment in which the initial evolution of life is viable (nor, indeed, any form of reproduction). So, to slightly abuse the anthropic principle, we don’t need to worry about it.
Maybe, but if the environment admits NP or PSPACE oracles like this model, you can just make predictions while still being way smaller than your environment again, because you can now just do bounded Solomonoff induction to infer what the universe is like:
If we had evolved in an environment in which the only requirement on physical laws/rules was that they are Turing computable (and thus that they didn’t have a lot of symmetries or conservation laws or natural abstractions), then in general the only way to make predictions is to do roughly as much computation as your environment is doing. This generally requires your brain to be roughly equal in computational capacity, and thus similar in size, to the entire rest of its environment (including its body). This is not an environment in which the initial evolution of life is viable (nor, indeed, any form of reproduction). So, to slightly abuse the anthropic principle, we don’t need to worry about it.
Maybe, but if the environment admits NP or PSPACE oracles like this model, you can just make predictions while still being way smaller than your environment again, because you can now just do bounded Solomonoff induction to infer what the universe is like:
https://arxiv.org/abs/0808.2669