(Ehlers et al, 1995); indicating the presence or absence of septic encephalopathy (Straver et al, 1998); using time series from jejunal manometry to discriminate objectifiable somatic from psychological conversion related irritable bowel syndrome (Wackerbauer et al, 1998); analyzing time-dependent patterns in plasma hormone levels to discriminate between the presence or absence of a functioning tumor (Hartman et al, 1994, Mandell and Selz, 1997a); automated differentiation of ataxic from normal speech (Accardo and Menulo, 1998); and discrimination of temporomandibular joint dysfunction from normal patterns of chewing motions (Morinushi et al, 1998). Styles of Orbital Motions in Chaotic Dynamical Systems In chaotic dynamics, in various specific ways, an initial hypothetical handful of points lined up along the trajectory and acted on over time by the nonlinear differential equation (“operator”), get out of order in an unpredictable way. Here the hypothetical handful can come from a statistical aggregate of initial conditions or from a single recursive orbit studied over long times. As noted above, ergodic theorists call this getting out of order “mixing” and how and to what degree this happens consumes many mathematical theorems but for purposes of brain research, it can be best described using a variety of statistical measures. For example, visualizing the Lorenz attractor (see above) as a butterfly in phase space, the points get out of order because as they spiral out (“stretching”) to the edge of one wing and return (“folding”) to the unstable fixed point on the butterfly’s body whence they either jump to some place on the other wing to spiral to its edge or return to the same wing to spiral out again. Which one of these is chosen is exquisitely sensitive to very small changes in where the trajectory started and very small fluctuations in where it returned to the unstable fixed point on the butterfly’s body. In fact, specification of these locations is beyond the