Extensive literature on the identification of chaotic dynamics in the brain, as expressed in the EEG's trajectories, suggests a wider picture than that advanced by Wright, Kydd and Liley (1993). The model they advance is not incompatible with chaotic dynamics at the level of mass action, but it does not address more serious difficulties which arise in the analysis of real data from the intact cortex. It is not necessary to postulate symmetrical couplings within networks, and models of cognitive processes already exist which do not have this formal constraint.
2. Wright et al.'s close, almost exclusive, focussing on two models fails markedly to do justice to many other studies on brain dynamics and the analysis of the EEG in its spatio-temporal evolution, for example those edited by Basar (1990). The conclusions in their paragraphs 50 and 51 seem tenable but are not strictly dependent on the arguments they advance; they could have gotten there through other mathematics. But having said that, their caveat in paragraph 53, "provided allowance is made for additional features of the brain" is too open-ended.
3. I must admit to a preference for theories that begin with a detailed review of available relevant data on the EEG and chaos (indicating all the subtle difficulties which have been observed both in data collection and analysis) and that then offer a model which respects those data. Wright et al.'s bibliography has, from that perspective, an excess of autocitation and some very surprising gaps (Gallez and Babloyantz, 1991; Gregson, Campbell and Gates, 1992; Nan and Jinghua, 1988; Pessa, De Pascalis and Marucci, 1989; Rapp, Albano and Mees, 1988; Roschke and Aldenhoff, 1991; and Soong and Stuart, 1989 will suffice for examples).
4. Finding, or failing to find, strange attractor dynamics in brain recording through the intact skull is still a hazy activity. It is expedient to distinguish:
a. chaos as analytically defined in purely mathematical models;
b. chaos as found in computer simulations with truncated accuracy of
calculation;
c. chaos as detectable in sources with suspected mixed low and high
Lyapunov indices;
d. chaos as inferred from posterior numerical analysis, with heavy
roll-off filtering, of EEGs treated as the trajectories of
attractor dynamics;
e. suspected chaos in psychophysiological experiments, with measures
of performance even further removed from cortical activity.
I am not satisfied that the authors have kept these distinctions sufficiently in mind.
5. One specific point puzzles me: In paragraph 35, Wright et al. state "Standard artificial network models depend upon symmetry of couplings." What is meant by "standard"? Is this merely a tautology, or does it mean only those models which the authors have noticed in their (hidden) review of the literature? If they really believe that "the class of dynamics applicable is a matter of scale," which is true of many disciplines besides physics -- for example, population biology, human psychophysics, social networks, macroeconomics, all of which have used or use dynamic models and chaotic metaphors -- then their comment on standard models is not true.
6. A fair conclusion is that the perspective on theory construction here is not sufficiently useful because it is rooted too much in the authors' own algebra. On the specific question of the merits of Freeman's approach, one awaits Freeman's potential rejoinder. As both models postulate or allow chaotic dynamics, and temporal transitions into and out of chaos, then at the gross level of observable EEGs, based on a wide montage of scalp electrode placements or electrode implants, it is still unclear what useful distinction emerges.
Basar, E. (1990) Chaos in Brain Function. Berlin: Springer-Verlag.
Freeman, W.J. (1991) Predictions on neocortical dynamics derived from studies in paleocortex. In: Induced rhythms of the brain, eds. E. Basar & T.H. Bullock. Cambridge MA, Birkhaeuser Boston Inc.
Gallez, D. and Babloyantz, A. (1991) Predictability of Human EEG: a Dynamical Approach. Biological Cybernetics, 64, 381-391.
Gregson, R.A.M., Campbell, E.A. and Gates, G.R. (1992) Cognitive Load as a Determinant of the Dimensionality of the Electroencephalo- gram: a Replication Study. Biological Psychology, 35, 165-178.
Nan, X. and Jinghua, X. (1988) The Fractal Dimension of EEG as a Physical Measure of Conscious Human Brain Activities. Bulletin of Mathematical Biology, 50, 559-565.
Pessa, E., De Pascalis, V. and Marucci, P.S. (1989) The Detection of Strange Attractors in Brain Dynamics through EEG Data Analysis. International Journal of Psychophysiology, 7, 350-351.
Rapp, P.E., Albano, A.M. and Mees, A.I. (1988) Calculation of Correlation Dimension from Experimental Data: Progress and Problems. In J.A.S. Kelso, A.J. Mandell and M.F. Schlesinger (Eds.) Dynamic patterns in complex systems. Singapore: World Scientific, pp. 191-205.
Roschke, J. and Aldenhoff, J. (1991) The Dimensionality of Human's Electroencephalogram During Sleep. Biological Cybernetics, 64, 307-313.
Soong, A.C.K. and Stuart, C.I.J.M. (1989) Evidence of Chaotic Dynamics Underlying the Human Alpha Rhythm Electroencephalogram. Biological Cybernetics, 62, 58-62.
Wright, J.J., Kydd, R.R. and Liley, D.T.J. (1993) EEG Models: Chaotic and Linear. PSYCOLOQUY 4(60) eeg-chaos.1.wright.