The problem of Solomonoff induction having 100% probability in being a computable isn’t actually, by itself logically contradictory with seeing universes that are uncomputable.
Now, to address the post’s claims:
Because what matters is not whether the universe is computable, but whether our methods of reasoning are computable. Or in other words, whether the map is computable.
So to answer the question, the answer is basically yes, because of the fact that humans have a finite and fixed memory + finite speed of computation, meaning that it’s trivial to compute all reasoning strategies that a human does by a Turing Machine.
In general the Church-Turing thesis that the set of reasoning strategies/the set of computers is equal to the set of Turing machines is false, as the set of computers/the set of reasoning strategies are way, way bigger than the set of Turing machines.
So either the Church-Turing thesis is tautologically true, or if we wanted to generalize it is simply false.
So Solomonoff induction, as it’s usually considered would beat any strategy that’s computable, or recursively enumerable strategies that doesn’t have the complement of the set, but compared to the set of all computers/strategies as we currently know of, Solomonoff induction doesn’t do very well, as it’s only on the first floor of a halting oracle, or equivalently it’s at the 2nd floor of the arithmetical hierarchy, but compared to the vastness of reasoning and computation, it’s still way, way worse than the current optimal reasoners/optimal computers in math. It’s superior to the Accelerating Turing Machine, an uncomputable machine, and superior to all other computable strategies, but is inferior to the Malament-Hogarth machine, possibly an infinite time turing machine depending on how many time steps we allow, and the 3 equivalent current champions of reasoning machines/computers.
The infinite state turing machine.
The Blum-Shub-Smale machine over the reals.
A recurrent neural network with real valued weights with exponential time to compute.
Solomonoff induction isn’t ideal, compared to the current champions of computation/reasoning engines.
The problem of Solomonoff induction having 100% probability in being a computable isn’t actually, by itself logically contradictory with seeing universes that are uncomputable.
Now, to address the post’s claims:
So to answer the question, the answer is basically yes, because of the fact that humans have a finite and fixed memory + finite speed of computation, meaning that it’s trivial to compute all reasoning strategies that a human does by a Turing Machine.
In general the Church-Turing thesis that the set of reasoning strategies/the set of computers is equal to the set of Turing machines is false, as the set of computers/the set of reasoning strategies are way, way bigger than the set of Turing machines.
So either the Church-Turing thesis is tautologically true, or if we wanted to generalize it is simply false.
So Solomonoff induction, as it’s usually considered would beat any strategy that’s computable, or recursively enumerable strategies that doesn’t have the complement of the set, but compared to the set of all computers/strategies as we currently know of, Solomonoff induction doesn’t do very well, as it’s only on the first floor of a halting oracle, or equivalently it’s at the 2nd floor of the arithmetical hierarchy, but compared to the vastness of reasoning and computation, it’s still way, way worse than the current optimal reasoners/optimal computers in math. It’s superior to the Accelerating Turing Machine, an uncomputable machine, and superior to all other computable strategies, but is inferior to the Malament-Hogarth machine, possibly an infinite time turing machine depending on how many time steps we allow, and the 3 equivalent current champions of reasoning machines/computers.
The infinite state turing machine.
The Blum-Shub-Smale machine over the reals.
A recurrent neural network with real valued weights with exponential time to compute.
Solomonoff induction isn’t ideal, compared to the current champions of computation/reasoning engines.