TY - JOUR

T1 - Dynamical duality of type- and token-computation as an abstract brain

AU - Gunji, Yukio Pegio

AU - Miyoshi, Hiroyuki

AU - Takahashi, Tatsuji

AU - Kamiura, Moto

N1 - Funding Information:
This research was supported by the 21st century COE program from the JSPS.
Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2006/3

Y1 - 2006/3

N2 - In brain science, there are few researches focusing on the theoretical relation between cognition (top-down processing) and perception (bottom-up processing). Philosophically they were regarded as the alternative leading to the dualism of mind and body, while it is an adequate problem for the endo-physics. Qualia are conjectured as the hard problem under those situations. To overcome such an impasse, we propose an abstract brain model featuring the dynamical duality of two parts of computations in a brain, in a term of endo-physics and internal measurement. Two parts of computations are expressed as binary relations, and the relationship between them is expressed as a pair of maps, called an infomorphism [Barwise J, Seligman J. Information flow, the logic of distributed systems. Cambridge University Press 1997]. Dynamical duality is implemented by the interaction between a binary relation and an infomorphism, and that leads to a dynamical change of a pair of binary relations. When a binary relation is expressed as a partial ordered set, one can check whether a part of computation is closed with respect to logical operations (i.e., a lattice) or not. By estimating a binary relation in terms of properties of lattice, we show that dynamical infomorphism robustly develops to a pair of logical computations corresponding to type cognition and non-logical one corresponding to qualia perception. It implies origin of differentiation and robust co-existence of type-cognition and qualia-perception. It is easy to see that dynamical infomorphism can also develop to a pair of singleton sets corresponding to savants' special cognitive style.

AB - In brain science, there are few researches focusing on the theoretical relation between cognition (top-down processing) and perception (bottom-up processing). Philosophically they were regarded as the alternative leading to the dualism of mind and body, while it is an adequate problem for the endo-physics. Qualia are conjectured as the hard problem under those situations. To overcome such an impasse, we propose an abstract brain model featuring the dynamical duality of two parts of computations in a brain, in a term of endo-physics and internal measurement. Two parts of computations are expressed as binary relations, and the relationship between them is expressed as a pair of maps, called an infomorphism [Barwise J, Seligman J. Information flow, the logic of distributed systems. Cambridge University Press 1997]. Dynamical duality is implemented by the interaction between a binary relation and an infomorphism, and that leads to a dynamical change of a pair of binary relations. When a binary relation is expressed as a partial ordered set, one can check whether a part of computation is closed with respect to logical operations (i.e., a lattice) or not. By estimating a binary relation in terms of properties of lattice, we show that dynamical infomorphism robustly develops to a pair of logical computations corresponding to type cognition and non-logical one corresponding to qualia perception. It implies origin of differentiation and robust co-existence of type-cognition and qualia-perception. It is easy to see that dynamical infomorphism can also develop to a pair of singleton sets corresponding to savants' special cognitive style.

UR - http://www.scopus.com/inward/record.url?scp=24944491234&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=24944491234&partnerID=8YFLogxK

U2 - 10.1016/j.chaos.2005.01.067

DO - 10.1016/j.chaos.2005.01.067

M3 - Article

AN - SCOPUS:24944491234

VL - 27

SP - 1187

EP - 1204

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

SN - 0960-0779

IS - 5

ER -