Cognitive Computation

, Volume 1, Issue 2, pp 177–193 | Cite as

Ultimate Cognition à la Gödel

  • Jürgen SchmidhuberEmail author


“All life is problem solving,” said Popper. To deal with arbitrary problems in arbitrary environments, an ultimate cognitive agent should use its limited hardware in the “best” and “most efficient” possible way. Can we formally nail down this informal statement, and derive a mathematically rigorous blueprint of ultimate cognition? Yes, we can, using Kurt Gödel’s celebrated self-reference trick of 1931 in a new way. Gödel exhibited the limits of mathematics and computation by creating a formula that speaks about itself, claiming to be unprovable by an algorithmic theorem prover: either the formula is true but unprovable, or math itself is flawed in an algorithmic sense. Here we describe an agent-controlling program that speaks about itself, ready to rewrite itself in arbitrary fashion once it has found a proof that the rewrite is useful according to a user-defined utility function. Any such a rewrite is necessarily globally optimal—no local maxima!—since this proof necessarily must have demonstrated the uselessness of continuing the proof search for even better rewrites. Our self-referential program will optimally speed up its proof searcher and other program parts, but only if the speed up’s utility is indeed provable—even ultimate cognition has limits of the Gödelian kind.


Universal cognitive systems Ultimate cognition  Optimal general problem solver Self-reference  Goedel machine Global optimality theorem  AI becoming a formal science 



Thanks to Alexey Chernov, Marcus Hutter, Jan Poland, Ray Solomonoff, Sepp Hochreiter, Shane Legg, Leonid Levin, Alex Graves, Matteo Gagliolo, Viktor Zhumatiy, Ben Goertzel, Will Pearson, and Faustino Gomez for useful comments on drafts or summaries or earlier versions of this article. I am also grateful to many others who asked questions during Gödel machine talks or sent comments by email.


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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.IDSIAManno-LuganoSwitzerland
  2. 2.TU MünchenGarching bei MünchenGermany

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