This smoothness-dependent intuition of determinism breaks down in nonlinear equations as well as in a wide variety of the machines of experimental physics, from the sudden coherent lasing of previously incoherent light to the vortices and turbulence in suitably bounded rotating or flowing fluid. It took me a while for these topological still shots and movies of the head to become real. Nevertheless, the enrichment of intuition was well worth it. Of course one could smoothly increase the normal factor weight of a ship until it gradually sank, but if one moved the center of gravity splitting factor to an eccentric position in the ship in the parameter region of the bifurcation set, a sudden global capsize before weight-induced gradual sinking made sense. | could see it. Indeed, increasing normal factor tension in a prison population that was identified, not alienated, from the officials and mores of the penal institution, would increase social symptomotology gradually. However, increasing the splitting factor of social and institutional alienation results in the cataclysmic change of a riot with increasing tension. | could see it. Do we need to know the causal equations to anticipate instability and discontinuity in our lives? Zeeman making Thom’s thoughts accessible to us plain mortals said no. He suggested that we could use _ several diagnostic phenomenological signs to make a good guess about whether we are near or within the bifurcation set. Depending upon the route that the causal variables take through the shadow of the bifurcation set, we may see very large fluctuations in our observable. The Dow or S&P stock indices in the neighborhood of a sudden large change is often presaged, sometimes for weeks, by a marked increase in volatility, fluctuations between extreme values. Theorists call the statistical properties of a time series of values behaving this way anomalous variance. For several months, | did psychotherapy with a genuinely spiritual Catholic priest w