Universal Turing Machine
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- Form a hypothesis that explains the observation: use a Universal Turing Machine to find all possible hypotheses
Find all the hypotheses that would predict the observation by trying every possible hypothesis through the Universal Turing Machine and keeping the ones that output the observation.
all algorithms are represented by Turing machine, and all Turing machine are represented by inputs to the Universal Turing Machine.
Which Universal Turing Machine? There are actually infinite sets of rules that can simulate all other rules, which is to be used for Solomonoff Induction. This choice affects the length of the hypotheses, and thus the probability we place on them. (doesn’t Eliezer Yudkowsky have something to say about this? he seemed to have an explanation of Occam’s Razor that might assume a specific Universal Turing Machine). In any case, different Universal Turing Machine rules don’t significantly change the hypothesis length relative to the compiler.
Given two states, the one that takes fewer lines of code to create on a Universal Turing Machine is simpler.