There are solid formal grounds for saying this won’t happen. Even if the universal Turing machine allows for HALT instructions, the shortest program in an otherwise useful universal Turing machine that predicts the non-halting data so far will always lack a HALT instruction. HALT takes extra bits to encode, and there’s no prior experience with HALT that AIXI can use to rule out the simpler, non-halting programs.
Can someone clarify why this is true? Is it the case that every TM which predicts the data well and has a HALT instruction, can be surgically modified to a slightly smaller state diagram without HALT such that it also predicts the non-HALT data well?
(Also, HALT itself is very hacky; death/outer-world-touchable-cognition seems very nonbinary; even if we solved the HALT problem I doubt we’d solve the rest of reflective reasoning.)
I might be missing something, but it seems to me like the way to modify to a smaller state diagram is to remove the HALT state from the TM and then redraw any state transition that goes to HALT to map to any other state arbitrarily.
This won’t change the behavior on computations that haven’t halted so far, because these computations never reached the HALT state, and so won’t be effected by any of the swapped transitions.
Can someone clarify why this is true? Is it the case that every TM which predicts the data well and has a HALT instruction, can be surgically modified to a slightly smaller state diagram without HALT such that it also predicts the non-HALT data well?
(Also, HALT itself is very hacky; death/outer-world-touchable-cognition seems very nonbinary; even if we solved the HALT problem I doubt we’d solve the rest of reflective reasoning.)
I might be missing something, but it seems to me like the way to modify to a smaller state diagram is to remove the HALT state from the TM and then redraw any state transition that goes to HALT to map to any other state arbitrarily.
This won’t change the behavior on computations that haven’t halted so far, because these computations never reached the HALT state, and so won’t be effected by any of the swapped transitions.