Chaos theory, Wikipedia tells us, "is the field of study in mathematics that studies the behavior of dynamical systems that are highly sensitive to initial conditions – a response popularly referred to as the butterfly effect." The butterfly effect refers to the flapping of a butterfly's wings having an impact on the creation of strong winds, maybe even a hurricane.

Events, I venture to say, are connected causally. (I don't believe in miracles.) We don't know enough to conclude that the world outside our heads is completely predetermined and that chaos is an illusion. But some want to overcome our limited knowledge and overcome uncertainties about the future with complex math formulas. Mathematicians try to calculate possibilities, probabilities, and improbabilities, and some have claimed that mathematics can capture the infinite complexity of nature. But t I am skeptical. All I can do is point to the French mathematician Jacques Hadamard (1865-1963), who made major contributions in number theory, complex function theory, differential geometry and partial differential equations. He argued that any solution exhibiting sensitive dependence (such as the flapping of butterfly wings) is a sign of a mathematical model that incorrectly describes its target system.

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