(Hemi-Sync® Journal, Vol. IX, No 4, Fall 1991) HEMI-SYNC® RECOVERING THE ATTRACTORS by Glenn Pearce Glenn Pearce, professor of philosophy, completed undergraduate work at William and Mary and graduate studies at Duke University. He has been a member of the faculty of the University of Western Ontario for twenty-four years and served as chairman of the philosophy department. His main interests are cognitive science and metaphysics. This presentation discusses preliminary results from the application of chaos theory mathematics to Hemi-Sync and brainwave frequencies. My research on the encephalography of conscious states has three main goals: 1. Since the EEG data I am studying pertain to subjects exposed to Hemi-Sync® signals, there is some chance of providing feedback for the further development of Hemi-Sync technology. 2. By studying the cerebral activity underlying conscious states, one may hope to gain insight into the laws governing cognitive phenomena. Of course, what we can discover in this way depends crucially on the nature of the relation between neural behavior and states of consciousness. 3. This brings me to my long-range interest, which is philosophical, namely: to increase our basic understanding of the mind-brain relation itself. As noted by Henri Bergson almost a
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century ago, this relation has been studied very little. There are many theories, to be sure, but not much in the way of testable hypotheses. Thus, contrary to tradition, the study of human EEG records seems a very natural way to address this perennial question. Before describing my current work, a brief summary of the chaos-theoretic approach involved will be useful. The behavior of a dynamic system may be represented in phase space, a multidimensional mathematical space with one dimension for each variable needed to describe the system. Each point in this space represents a possible state (“phase”) of the system; a trajectory through this space represents the possible behavior of the system over time; and an attractor for the system exists when nearby trajectories are drawn into a given one. For example, a pendulum is representable in two dimensions, for position and momentum. If it is free-swinging (so that it slows down and stops due to friction) its “phase portrait” spirals in to the central fixed point, which is its attractor. If it has a regular period (as when driven by a motor) then its phase portrait coincides with the attractor, which is a closed loop. A system is chaotic when the dimension of its phase space is fractal (fractional); its attractor is said to be strange. Strange attractors never cross themselves or repeat—that would mean a periodic system—yet the behavior they describe is nonrandom. (By contrast, the portrait of
truly random activity would visit every point in an infinite dimensional space.) Many strange attractors have become familiar; one of the best known is the attractor for the Lorenz weather model. [Ed.: For more background information on chaos theory, see HEMI-SYNC JOURNAL, Fall 1990, Vol. VIII, No. 4.] [see: Topics/Perceptual Studies/Consciousness] One can computer-generate a system’s attractor from its governing equations, if they are known. If not, we must somehow reconstruct the attractor for the system’s behavior. The application of chaos theory to natural systems has been greatly advanced in the last decade by the development of accurate and reliable reconstruction methods, using time-series data from a single variable of the system. One such—the method of delays—is used in my current work, to which I now turn. The investigation is motivated by the following questions: Are there neural attractors characteristic of specific cognitive processes or conscious states (e.g., TMI focus levels)? Are any (such) attractors correlated with specific Hemi-Sync signals? What implications would affirmative answers have for the prospect of controlled access to specific conscious states, and for the development of Hemi-Sync-related technologies? I began to address these questions in February of 1991, when I was able to spend a week in the TMI lab, examining files from the NRS-24 brain mapping system. Subsequently, I have