Theoretical interlude—What is randomness? My definitions

  • Gregory J. Chaitin
Part of the Discrete Mathematics and Theoretical Computer Science book series (DISCMATH)


There’s only one definition of randomness (divided into the finite and the infinite case for technical reasons): something is random if it is algorithmically incompressible or irreducible. More precisely, a member of a set of objects is random if it has the highest complexity that is possible within this set. In other words, the random objects in a set are those that have the highest complexity. Applied to the set of all n-bit strings this gives one of our definitions, applied to infinite binary sequences this gives our second definition.


Mutual Information Binary Sequence Maximum Complexity Binary Expansion Infinite Case 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag London 2001

Authors and Affiliations

  • Gregory J. Chaitin
    • 1
  1. 1.IBM Research DivisionThomas J. Watson Research CenterHawthorneUSA

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