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On The Correct Definition of Randomness

Published online by Cambridge University Press:  31 January 2023

Paul Benioff
Paul Benioff*
Affiliation:
Argonne National Laboratory
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Extract

The concept of randomness as applied to number sequences is important to the study of the relationship between the foundations of mathematics and physics. A reason is that while randomness is often defined in mathematical-logical terms, the only way one has to generate random number sequences is by means of repetitive physical processes. This paper will examine the question: What definition of randomness is correct in the sense of being the weakest allowable? Why this question is so important will become clear during the course of the discussion.

The main body of this paper is divided into three sections. Section 1. discusses the use of probability theory to describe various statistical processes and some of the alternative definitions of randomness that have been proposed.

In Section 2. a criterion which a definition of randomness should satisfy is proposed.

Type
Part III. Physical Randomness
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1978 , Issue 2: Volume Two: Symposia and Invited Papers 1978 , 1978 , pp. 62 - 78
Copyright
Copyright © 1981 Philosophy of Science Association

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Footnotes

1

The author wishes to thank Professors Paul Humphreys and Geoffrey Hellman for useful and stimulating discussions on the subject matter of this paper.

References

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