Minds and Machines

, Volume 12, Issue 4, pp 503-517

First online:

Incompleteness, Complexity, Randomness and Beyond

  • Cristian S. CaludeAffiliated withDepartment of Computer Science, University of Auckland

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Gödel's Incompleteness Theorems have the same scientific status as Einstein's principle of relativity, Heisenberg's uncertainty principle, and Watson and Crick's double helix model of DNA. Our aim is to discuss some new faces of the incompleteness phenomenon unveiled by an information-theoretic approach to randomness and recent developments in quantum computing.

complexity incompleteness Omega Number quantum computing randomness Turing barrier