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most relevantly by their computational procedures and what are computed are empirical scaling exponents describing real observables as limited by the precision of the observations, their resolution and series lengths (Smith, 1988; Eckmann and Ruelle, 1992). The "correlation integral," the probability that two vectors chosen at random from the phase space reconstruction lie within "r" distance of each other, not unrelated to the phase randomization controlled, D2 measure, yields statements about amount of "nonlinearity" (not accountable by the linear regressively capturable component of the power spectrum), which are also difficult to translate into experimentally or theoretically useful concepts (Casdagli et al, 1997). These efforts contrast with a more direct attempt to establish a spiking neuron system’s dynamical "dimension" using trial and error prediction in which "dimension" was defined as the number of potentially physiologically relevant variables required to make the predictive equations fit (Segundo et al, 1998).

Computations of scaling exponent descriptors of orbital point distributions on reconstructed attractors of the brain sciences have proven to be most useful as atheoretical, empirical techniques discriminating experimental, clinical and/or treatment conditions with various approaches to statistical significance. In this regard, one can say that D2 is often found to be superior to central tendency oriented statistics in making these discriminations. Dimension and correlation integral descriptors appear least useful when dealing with global issues such as chaos, randomness, linearity and the "underlying dimensions" of (unknown) differential equations. We discuss below the possibility that the failure to find chaos in the more recent EEG studies (Theiler and Rapp, 1996; Prichard et al, 1996) may be because the EEG attractor is better characterized as a "strange nonchaotic atttractor" with orbital patterns manifesting fractional scaling exponents but no λ(+) (Grebogi et al, 1984; Mandell and Selz, 1993).

The relatively subtle influence of high altitude (Mt. Everest) oxygen concentrations was not seen in the central moments of the cardiac interbeat intervals, but the D2 of the attactor was reduced significantly (Yamamoto et al, 1993). The latencies and amplitudes of the visual evoked potential failed to

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