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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. I 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. I 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, I
did psychotherapy with a genuinely spiritual Catholic priest who only some Sundays
served the Eucharist, the corporal presence of our Lord at Communion, wearing no
trousers or underpants beneath his robes. A sudden change in a stock index in
response to the “shock” of a terrorist attack takes much longer to settle down if a
cataclysmically bigger change is in the neighborhood. This extension of the
system’s usual relaxation time is sometimes called critical slowing. In the bifurcation

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