 Can the on average exponential growth rate characterizing SD ever be attributed legitimately to diverging trajectories if their separation is no longer infinitesimal? Examining simple models (e.g., the Baker’s transformation) might seem to indicate yes. However, answering this question requires some care for more complex systems like the Lorenz or Moore-Spiegel attractors. It may turn out that the rate of divergence in the finite separation between two nearby trajectories in a chaotic region changes character numerous times over the course of their winding around in state space, sometimes faster, sometimes slower than that calculated from global Lyapunov exponents, sometimes contracting, sometimes diverging (Smith, Ziehmann and Fraedrich 1999; Ziehmann, Smith and Kurths 2000). But in the long run, some of these trajectories could effectively diverge as if there was on-average exponential growth in uncertainties as characterized by global Lyapunov exponents. However, it is conjectured that the set of initial points in the state space exhibiting this behavior is a set of measure zero, meaning, in this context, that although there are an infinite number of points exhibiting this behavior, this set represents zero percent of the number of points composing the attractor. The details of the kinds of divergence (convergence) neighboring trajectories undergo turn on the detailed structure of the dynamics (i.e., it is determined point-by-point by local growth and convergence of finite uncertainties and not by any Lyapunov exponents). 