changes in results. The Nobel Prize winning solid-state physicist, Phillip Anderson, in a short but memorable piece in Science in the 1970’s said it tersely, “More is different.” This general, qualitative mathematical theory of discontinuous change models nicely the sudden delivery of the first and second second winds from gradually and continuously increasing running distances as well as the abrupt transmission of the guru’s “energy”, shaktipat, from smoothly increasing amounts of chanting, meditation, guru service and Baba love. Gradually changing forces leading to sudden changes in an energy-equivalent result are found in most rigorous form in Rene’ Thom’s singularity-bifurcation-catastrophe theory applied to rational mechanics and geometric optics. Here the existence of already solvable computational formalisms makes this more qualitative approach superfluous. On the other hand, the power of this both basic and applied mathematical orientation and method lies in its approach to the qualitative understanding of variously induced global and sudden changes in an energy-equivalent observable in biological, psychological, spiritual and social systems, fields of study in which little abstract and formal lawfulness presently exists. Oxford’s Chris Zeeman’s more accessible applications of Thom’s deeper, more generally ramifying, almost mystical (due to their apparent wide generality) results, include approaches to real world problems such those above as well as the sudden change in excitable membrane potential accompanying the generation of the heart beat and neuronal discharge; mechanisms of opinion change, stock market crashes and, as noted above, the social science of riots. Whereas Thom’s On Structural Stability and Morphogenesis can be said to be scriptural, Zeeman’s Selected Papers, 1972-1977 constitute the Book of Common Prayer of this church.
To review and place catastrophe and bifurcation theories in the context of the differential equations of mathematical physics and biology, causal determinism implied by differential equations conventionally requires continuity and smoothness in behavior to be credible. Our intuitions as well as the formal conditions for the generic differential equations of mathematics and physics imply that smoothly increasing amounts of cause lead to smoothly increasing results and yield at least
local predictability: a little more leads to a little more, a little less leads to a little less.
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