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number spectra; (4) Non-Gaussian distributions with heavy tails and correlations reflected in their Hurst, Fano, Allan and Levy exponents; (5) Statistical dynamical descriptions of trajectories of the system in their embedding space such as Lyapounov exponents, Hausdorff-Mandelbrot dimensions, Sinai-Ruelle-Bowen measures, and Adler-Weiss-Ornstein topological and metric entropies.

Characteristics which discriminate between experimental versus control conditions in parametric computational and real physiological and pharmacological experiments serve to generate and test ideas and imagery arising out of behavior observed in both biological and abstract dynamical realms. New experiments can be suggested by the implicative structure of dynamical systems theory as well as neurobiological findings and intuitions. As examples, the sudden “switch” of manic-depressive bipolarity syndromes may be a “bifurcation” in nonlinear dynamical systems; the “noise” of the statistical physicist may be the “arousal” of the brain stem-thalamic biogenic amine and reticular formation neurophysiologist; aspects of “thought disorder” in the pathophysiology of schizophrenic patients may be an entropic sequencing idiosyncrasy in the “symbolic dynamics” of a particular brain system attractor; neuronal “bursting” may be the “intermittency” of a neurodynamical system; a multiplicity of “discrete ion channel conductances” may be a single “global scaling hierarchy” of conductances times. The number of published examples of this fusion of ideas and methodology in the biological-relevant literature is already in the several hundreds and Medline counts indicate is growing exponentially. Representative samples of these are described below.

In addition to the technological advances in computational hardware and software, the major scientific surprise making this new era possible is the discovery of universalities, the finite set of behaviors characteristic of most, if not all nonlinear systems, across most if not all of the specific equations or neural systems being explored. This makes the emergence of semi-quantitative equivalence relations between model and data not only possible but likely, even though we don’t now and perhaps never will know enough to either write or solve completely the specific and detailed equations for the biological system of interest. We neuroscientists need not be apologetic for using these ideas and tools qualitatively and empirically. In fact,

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