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Effective Complexity as a Measure of Information Content

Published online by Cambridge University Press:  01 January 2022

James W. McAllister
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Abstract

Murray Gell-Mann has proposed the concept of effective complexity as a measure of information content. The effective complexity of a string of digits is defined as the algorithmic complexity of the regular component of the string. This paper argues that the effective complexity of a given string is not uniquely determined. The effective complexity of a string admitting a physical interpretation, such as an empirical data set, depends on the cognitive and practical interests of investigators. The effective complexity of a string as a purely formal construct, lacking a physical interpretation, is either close to zero, or equal to the string's algorithmic complexity, or arbitrary, depending on the auxiliary criterion chosen to pick out the regular component of the string. Because of this flaw, the concept of effective complexity is unsuitable as a measure of information content.

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Type
Research Article
Information
Philosophy of Science , Volume 70 , Issue 2 , April 2003 , pp. 302 - 307
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

‡

I thank an anonymous referee of this journal for constructive comments on a previous draft.

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