Imaginary Fields

Nonlinear dynamical modeling of interaction between automatic and conscious processes in the human brain is considered in terms of the quaternion fields. The interaction is due, particularly, to the nonlinear firing rate of neu-rons. Possible connection of consciousness with the general field theory is indicated. A new type of symmetry between dynamics of real and imaginary fields is pointed out. From the physical-mathematical point of view consciousness (C) is a mystery. It is desired to catch C into some sort of equations. The common knowledge is that C is somehow connected with the electrochemical activity in the brain. So, it seems logical to start with equations for these processes. The brain activity revealed the regime of scale-similarity [1-3], which is typical for systems with strong interaction of many degrees of freedom (particularly, for turbulence [4]). Corresponding equations can be formally written and are rather complicated. However, at this stage of our understanding of C, the precise form of equations is not critical. One can use various simplified models. The important question is how to connect these equations with C? The C-processes are subjective and, as far as we know, they can not be measured directly by the objective methods, which are used for measuring the electrochemical (automatic) processes. At the same time, there are reasons to believe that C-processes can interact with automatic (A) processes. We need equations for A-fields and C-fields, which interact despite the fact that C-field have a different nature and can not be measured directly by the same methods as A-fields. In recent papers [5-8] an approach to nonlinear dynamical modeling of interaction between these two processes was presented. The idea is to use the quaternion field with real and imaginary components representing A-and C-processes. The subjective C-experiences were divided into three major groups: sensations (S), emotions (E) and reflections (R). Note, that subjective S should be distinguished from the automatic sensory input into the neuron system of the brain [9]. The A − C interaction is due to the nonlinearity of the system. This approach was illustrated on the nonlinear equation for the current density in the cortex.. The nonlinearity is determined by the sigmoidal firing rate of neurons. Perspective for the laboratory testing of this approach were also indicated as well as some more general approaches [5-8]. To be specific, consider quaternion: q = α + i p ψ p (1) Here α(t) is …