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Randomness and determinism in the interplay between the continuum and the discrete†

Published online by Cambridge University Press:  01 April 2007

FRANCIS BAILLY and
GIUSEPPE LONGO
FRANCIS BAILLY
Affiliation:
Physique, CNRS, Meudon Email: bailly@cnrs-bellevue.fr
GIUSEPPE LONGO
Affiliation:
LIENS, CNRS ENS and CREA, Paris Web site: http://www.di.ens.fr/users/longo
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This paper provides a conceptual analysis of the role of the mathematical continuum versus the discrete in the understanding of randomness as a notion with a physical meaning or origin. The presentation is ‘informal’ as we will not write formulas; however, we will refer to non-obvious technical results from various scientific domains, and we will also propose a conceptual framework for understanding randomness (and predictability), which we believe is, essentially, original. As a matter of fact, unpredictability and randomness may be conveniently identified in various physico-mathematical contexts. This will allow us to explore these concepts in continuous versus discrete frameworks, with particular emphasis on the relationships and differences between classical approaches and quantum theories in Physics.

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Type
Paper
Information
Mathematical Structures in Computer Science , Volume 17 , Issue 2 , April 2007, pp. 289 - 305
Copyright
Copyright © Cambridge University Press 2007

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