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Billiard balls, butterfly wings, and the Goracle
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The Goracle
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Jules Henri Poincare once pointed out the obvious: there are fundamental limits to our mathematical equations and use of mathematical models in predicting future events. His reasoning is simple to understand: in order to project future conditions, you need ever-increasing precision in modeling the dynamics OF THE PAST because of the nonlinear compounding effects of error. Small effects lead to severe consequences.
Poincare showed this with his “three-body problem.” When modeling two planets in a solar system with nothing else affecting their courses, you may be able to predict with precision those two planets’ behavior over long periods of time. When you add a third planet or other body to the system and try to predict their behaviors, the errors in your predictions become greater the further in the future you predict. Small errors in the precision of initial conditions and the dynamics modeled “blow up” into huge errors over increased time the model runs.
For a more easily-understood model, consider a pool table: if you have only one or two balls it is fairly simple to predict how collisions affect each ball’s path. As you add more balls, the importance of things like bumps in the table’s slate, variances in the coefficient of friction between areas of the table’s covering, differences in the “bounce” of the bumpers, etc. all add variances to the path each ball takes. Michael Berry demonstrated that by the ninth impact, you need to take into account the gravitational pull of someone standing next to the table! To compute the 56th impact every single elementary particle in the universe needs to be accommodated in your model and assumptions!
Edward Lorenz rediscovered this fact in the 1960s while trying to build a computer model of weather dynamics. He found that running the same simulation of a few days’ weather twice using (what he thought were) the exact same initial conditions gave wildly different results. After much head-scratching and investigation, he found that small rounding errors in his input parameters caused this divergence of results. This became known as the “Butterfly Effect:” a butterfly moving its wings in India could cause a hurricane in New York two years later!
While computer capabilities and measurement precision have undoubtedly improved in the last 40 years, the problem remains: NO ONE CAN PRECISELY PREDICT THE PAST MUCH LESS THE FUTURE! Think about that next time you hear the Goracle bloviating dire predictions of impending, inevitable Global Warming disasters.
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