ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Rabinovich M. I., Varona P. . Mathematics of mind. Izvestiya VUZ. Applied Nonlinear Dynamics, 2017, vol. 25, iss. 3, pp. 5-51. DOI: 10.18500/0869-6632-2017-25-3-5-51

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Mathematics of mind

Rabinovich Mihail Izrailevich, University of California, San Diego
Varona Pablo , Universidad Autonoma de Madrid

In this slide-lecture we formulate a novel paradigm for the mathematical description of mental functions such as consciousness, creativity, decision making and prediction of the future based on the past. Such cognitive functions are described in the framework of canonical nonlinear dynamical models that form joint global hierarchical networks. Subnetworks cooperate and compete with each other by inhibition. The suggested approach uses heteroclinic dynamics to represent transitivity and sequential interaction of different cognitive modalities at all levels of network hierarchy. For the first time we build a model of global network dynamics based on a set of kinetic ecological equations describing the interaction with emotion at each level of the hierarchy. This makes the model applicable for the description and understanding of perception, creativity and other complex cognitive processes. We discuss the creativity phenomenon, for example, in a joint «human-robot mind» considering the approximation in which the artificial partner is responsible for the binding and retrieving of multimodal perception information. The formation of chunks and the creation of working memory is a joint effort – human-robot mind. The human mind is responsible for the evaluation of the information in working memory. Creativity is estimated by Kolmogorov–Sinai entropy. As an example, we discuss joint human-robot musical improvisation, which can be generalized for many applications, in particular, in the context of artificial intelligence applications and to address several psychiatric disorders. 

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