By: Karl H. Pribram
As did Appalachian I, Appalachian II resolved, for me, certain hitherto intractable problems that plague the mind/brain relationship. In Appalachian I, the problem was: how can psychological processes reflect brain activity? Psychological processes such as language seem to be organized so differently from the recorded activity of the neurons and neural systems known to be critically involved. The answer came in the form of an identity at the subneuronal, synaptodendritic and cytoskeletal level. At that level, descriptions of the organization of the elementary neural process and descriptions of the organization of the elementary psychological process are identical: assuming that the brain is an information processing organ, the description of the organization of synaptodendritic cortical receptive fields is identical with the description of the organization of information processing in communication devices such as those that process language--e.g. telephony, and those that process images--e.g., tomography and television.
Appalachian II addressed a problem that emerges as a direct consequence of this identity. The form of the identity is symmetrical. The informational process is a two-way interaction: in a manner of speaking, the organization of the subneuronal process produces (causes) the organization of the elementary psychological process; but at the same time, this organization shapes (causes) the subneuronal process. The identity of organization, the information process involved, makes this way of speaking seem awkward and old fashioned, rooted in a pervasive Cartesian dualism. But it does call attention to the fact that identity implies symmetry.
Life and mind are not governed completely by the laws of symmetry. In fact, one might define an all important characteristic of life and mind is that symmetries become broken--especially time symmetry. In biology, birth, growth, procreation and death; in psychology, learning and memory, attention, intuition and thought are all time-symmetry breaking processes.
Prigogine's keynote addresses this issue and clarifies, for me, the "how" of time symmetry breaking. As I understand Prigogine's presentation (with help from Kunio Yasue and Mari Jibu), there are formulations in which spectral representations do not render both real and virtual "images" when Fourier transformed. Prigogine's discussion is restricted to certain quantum and/or classical systems driven by (non-self-adjoint) Hamiltonian operators (for quantum systems) and/or Liouville operators (for classical systems) which are "chosen" so that their time developments are kept contractive (i.e. loose information) and dissipative (i.e. loose energy). Thus, as Prigogine states in a letter to me in response to a question:
The difference between real and complex spectrum is very simple. Take the Hamiltonian in Hilbert space, it has real eigenvalues E1, E2...
Similarly the evolution operator U(t)=e-iHt has complex eigenvalues such as e-iE1t.