Gödel Machines: Towards a Technical Justification of Consciousness

The growing literature on consciousness does not provide a formal demonstration of the usefulness of consciousness. Here we point out that the recently formulated Godel machines may provide just such a technical justification. They are the first mathematically rigorous, general, fully self-referential, self-improving, optimally efficient problem solvers, “conscious” or “self-aware” in the sense that their entire behavior is open to introspection, and modifiable. A Godel machine is a computer that rewrites any part of its own initial code as soon as it finds a proof that the rewrite is useful, where the problem-dependent utility function, the hardware, and the entire initial code are described by axioms encoded in an initial asymptotically optimal proof searcher which is also part of the initial code. This type of total self-reference is precisely the reason for the Godel machine’s optimality as a general problem solver: any self-rewrite is globally optimal—no local maxima!—since the code first had to prove that it is not useful to continue the proof search for alternative self-rewrites.