The Complex Number Space of Brain's Self and Bohm´s Mind-Matter Theory

Matti Bergström, Helsinki University and Pia Ikonen, Helsinki School of Economics

The physicist David Bohm presented a new theory of the relationship of mind and matter (1986, 1990). He founded this theory on his own work on relativity and quantum theory, where he developed the concept of "implicate" order, which means that the whole of the universe is enfolded in everything, so that everything implicates everything. In the explicate order, which dominates our experience and thinking, each thing is seen as separate. Bohm’s basic proposal is that the implicate order is the more fundamental order and common to both mind and matter, so that these two are not as different as they may appear.

Bohm made use of his ontological interpretation of quantum theory (Bohm and Hiley 1993): the Schrödinger wave function contains information which acts upon particles, so that their movements cannot be wholly determined by their local interactions. Instead, a nonlocal factor, a quantum potential Q, is involved . Bohm considers the wave-function as analogous to “mind”, and the local particles and their microscopic behaviour ("dance") in the physical space as corresponding to “matter”. In the end, mind and matter are not separate but forming the same common process.

In earlier presentations in conferences on consciousness (Skövde 2001, Tucson 2002 and 2004, Copenhagen 2005) we presented an empirically based mathematical model of the brain´s limbic "Self", where the system between brain stem and neocortical effects (MacLean 1973) was considered as an empty border. The Self is a 2-dimensional (i,r)-space: r is a real number dimension recording the physical environmental effects via cortex, i is an imaginary number dimension (Bergström 1964) recording the effects of mental feelings and values via brain stem. The Self-space is a complex number space, reflecting the interaction between “mental”, brain stem macrostates and cortically mediated “physical” microstates (Bergström 1967, 1972, 1986).

The objective microstate is represented in the r-dimension. But because the observer is involved, the situation also has a projection on the i-dimension. The observed particle moves (in nonpredictable "dance") in the (i,r) space, where the i-dimension describes "active information" in observer’s mental nonlocal "consciousness potential” (Bohm´s Q-potential).

Since the i-projection of the perceived particle describes the mental content and the r-projection the physical content, we can say with Bohm that mind and matter are not separated but forming the same common process.

The square root of (-1) of the observer´s i-dimensional mental Self is the main obstacle for the r-dimensional physics and its r-mathematics to penetrate to the fundamental reality of mind and matter. Our results indicate that implicate order is imaginary order. In our earlier model of the Self-space in the brain (see above references) we have a 3:rd dimension (p) for free "possibilities" of mental acts of the subject. Since the word "tempus" originally means "opportunity" (possibility), this p-dimension apparently describes time, not the physical, but the imaginary time (simultaneous, as in the "Child-brain") described by Hawking.

These findings explain Heisenberg´s Uncertainty principle as caused by the thinking process in the brain of observer !

Summary

1. Our model of brain´s Neuro-mental Self being a complex number space is based on the finding that whereas suprathreshold experiences corresponded to real number quantities of physical stimuli, sub-threshold experiences had to be described with imaginary number quantities (Bergström 1964).



2. The Neuromental space consequently is a complex number space with a real number dimension (r) describing the physical environment, and an imaginary number dimension (i) describing the mental content of an observer.



3. Applying to this Mandelbrot type complex space (i,r) of the Self the Julia equation, the iteration of the space vector can be considered as describing the thinking of the observer in an observation situation. Hereby the non-local effect of the imaginary, subconscious mental content of the observer affects the local behaviour of the physical object. In the vector mind and matter are same !



4. This can be considered as being conform with Bohm´s theory of mind and matter, where the mind, Schrödinger´s wave function (our i-effect) acts on matter, the particles (our r-objects), the effect being "non-local". This explaines the "dance" of the observed particles being caused by the thinking (Heisenberg´s "Questioning" causing time reversal) in the act of a physical observation.

Figure 1.

Figure 2.

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