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A computational journey into the mind

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Abstract

The first half of this paper is the written version of the invited talk presented at Unconventional Computing UC10, The University of Tokyo, Japan, June 21–25, 2010. It describes some salient features of hypercomputation in Dickson algebras. Such quadratic algebras form an appropriate framework for nonlinear computations which does not limit a priori the computational power of multiplication. They underlie paradoxical mathematics whose potential interest to analyse some computational aspects of the human mind which resist the classical approach is presented. In its last part, the paper offers new glimpses on the organic logic for hypercomputation by developing a fresh look at plane geometry in relation with the ζ function.

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Abbreviations

SVD:

Singular Value Decomposition

FTA:

Fundamental Theorem of Algebra

iff:

if and only if

IFS:

Iterated function system

MGG:

Matrix graph grammar

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Acknowledgements

The author wishes to thank the two referees whose constructive remarks led to a substantial clarification of the paper. She is grateful to C. Calude for inviting her to talk at UC2010 and to G. Chaitin for his words of encouragement.

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  1. CERFACS, 42 Avenue Gaspard Coriolis, 31057, Toulouse Cedex 01, France

    Françoise Chatelin

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  1. Françoise Chatelin
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Correspondence to Françoise Chatelin.

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Chatelin, F. A computational journey into the mind. Nat Comput 11, 67–79 (2012). https://doi.org/10.1007/s11047-011-9269-6

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