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Mathematics and the Brain: A Category Theoretical Approach to Go Beyond the Neural Correlates of Consciousness

by Georg Northoff 1,2,3,*,†, Naotsugu Tsuchiya 4,5,6,7,† and Hayato Saigo 8,†
1
Mental Health Centre, Zhejiang University School of Medicine, Hangzhou 310058, China
2
Institute of Mental Health Research, University of Ottawa, Ottawa, ON K1Z 7K4 Canada
3
Centre for Cognition and Brain Disorders, Hangzhou Normal University, Hangzhou 310036, China
4
School of Psychological Sciences, Faculty of Medicine, Nursing and Health Sciences, Monash University, Melbourne, Victoria 3800, Australia
5
Turner Institute for Brain and Mental Health, Monash University, Melbourne, Victoria 3800, Australia
6
Advanced Telecommunication Research, Soraku-gun, Kyoto 619-0288, Japan
7
Center for Information and Neural Networks (CiNet), National Institute of Information and Communications Technology (NICT), Suita, Osaka 565-0871, Japan
8
Nagahama Institute of Bio-Science and Technology, Nagahama 526-0829, Japan
*
Author to whom correspondence should be addressed.
All authors contributed equally to the paper as it was a conjoint and equally distributed work between all three authors.
Entropy 2019, 21(12), 1234; https://doi.org/10.3390/e21121234
Received: 18 July 2019 / Revised: 29 September 2019 / Accepted: 9 October 2019 / Published: 17 December 2019
(This article belongs to the Special Issue Integrated Information Theory)
Consciousness is a central issue in neuroscience, however, we still lack a formal framework that can address the nature of the relationship between consciousness and its physical substrates. In this review, we provide a novel mathematical framework of category theory (CT), in which we can define and study the sameness between different domains of phenomena such as consciousness and its neural substrates. CT was designed and developed to deal with the relationships between various domains of phenomena. We introduce three concepts of CT which include (i) category; (ii) inclusion functor and expansion functor; and, most importantly, (iii) natural transformation between the functors. Each of these mathematical concepts is related to specific features in the neural correlates of consciousness (NCC). In this novel framework, we will examine two of the major theories of consciousness, integrated information theory (IIT) of consciousness and temporospatial theory of consciousness (TTC). We conclude that CT, especially the application of the notion of natural transformation, highlights that we need to go beyond NCC and unravels questions that need to be addressed by any future neuroscientific theory of consciousness. View Full-Text
Keywords: consciousness; mathematics; category theory; neural correlates of consciousness; integrated information theory; temporospatial theory of consciousness consciousness; mathematics; category theory; neural correlates of consciousness; integrated information theory; temporospatial theory of consciousness
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Northoff, G.; Tsuchiya, N.; Saigo, H. Mathematics and the Brain: A Category Theoretical Approach to Go Beyond the Neural Correlates of Consciousness. Entropy 2019, 21, 1234.

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