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A computational journey into the mind. (English) Zbl 1251.30054
Summary: The first half of this paper 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 \(\zeta\) function.

30G35 Functions of hypercomplex variables and generalized variables
17A30 Nonassociative algebras satisfying other identities
03F60 Constructive and recursive analysis
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