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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 I, 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 standing (Friedrich et al, 1991) and "few
frequency coherence" is a frontier of inquiry in brain wave research.

A heterogeneous collection of coupled nonlinear elements in the form of
widely distributed, multi-location, multifrequency systems such as cross-cortical,
brain stem-thalamic-cortical and interconnected spinal motor neurons can generate

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