As noted above, the cross-disciplinary cohesiveness of such a vaguely defined field occurred as the result of the unanticipated discovery of a relatively small set of nonlinear phenomena, universalities, that implicated many fields of mathematics, from differential geometry to number theory, and were found in a broad range of physical and biological realizations, from turbulent plasmas and chemical and enzymatic reactions to neuroendocrine hormone release patterns. It is perhaps counter-intuitive but, whereas linear systems can generate an infinite number of solutions locating points anywhere the person writing the equations wants them to go, nonlinear systems are generally restricted to a finite set of global dynamics and these emerge on their own from the intrinsic dynamics of the system. Trying to make these systems follow orders, not unlike finding the most clinically effective dosage range of a psychopharmacological agent, require the empiricism of trial and error experiments. A second class of computational accidents involving nonlinear systems resulted in unanticipated coherence rather than unpredictable disorder. Using one of the early “high speed” digital computers at Los Alamos, MANIC |, Enrico Fermi with Pasta and Ulam (1955) attempted to obtain a many-body statistical thermodynamic equilibrium analogous to heat generated noise by coupling 64 particles together with nonlinear springs. They found only a few low period modes that oscillated indefinitely. Instead of equidistribution of the energy into 128 degrees of freedom (64 locations x 64 velocities in 128 dimensional phase space), they found it gathered up into only few coherent modes. Although the relevance to biological science of nonlinear multifrequency coherence is a bit off from our focus, it is worthwhile noting that a recent (Karhunen-Loeve) decomposition of the alpha band of the resting alert human EEG revealed only three dominant temporal—spatial modes: anterior-posterior, rotational and stan