including those involving the choice of the embedding space vis a vis the “true” dimension of the attractor. This becomes an issue when, for example, the attractor shrinks over time to some subspace of the initial embedding (Liebert et al, 1991 and references therein). If we imagine the process of time series reconstruction to inscribe an attractor’s untidy ball-of-string of recurrent trajectories in three dimensions, we can then, by making the z-dimension a constant value, cut the ball with a two dimensional plane, a “Poincaré surface of section.” This could yield a roundish cloud of discrete points on the x,y plane and t,-; — th would be the time between two piercings of this surface. It has been proven that almost any cut, as long as it is made transverse to the direction of the orbital trajectories, is equally valid and useful for further analyses (Oseledec, 1968). If the original embedding and subsequence section was in high enough dimension to allow invertability, we might have enough (trial and error) knowledge to be able to write a discrete equation, a “return map,” f, that would move one point to the next on the plane as (x,y)/, , <> (x,y)¢,. What can sometimes be case with real systems (Coffman et al, 1986), is that reducing the geometric reconstruction still one dimension further, accepting non- invertability, ironing down the points in the plane onto the x axis line (normalized to [0,1]), and plotting the values at x; against x1 (“mapping the unit interval to itself”), can generate points in the general shape of a parabola with dynamics representable by the same family of one parameter, single maximum discrete equations that generated May's sequence of bifurcations, Feigenbaum’s scaling and Metropolis, Stein and Stein’s (and Sharkovskii’s) U sequence (see discussions of qualitative and quantitative universalities above). Although sometimes a significant change in brain system physiology, such as penicillin-induced epileptic neuron spiking activity is