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Comment Dated Jan 3, 2010
Curve fitting is the art of constructing a graph that will best fit a given set of data points. The versatility that comes as the number of independently variable paramaters increases can be astonishing. In a famous quote, cited here, by the mathematician John Von Neumann during a conversation with Enrico Fermi, as told to Freeman Dyson: “Give me four parameters, and I can fit an elephant. Give me five, and I can wiggle its trunk."
According to astrophysicist Sallie Baliunas in a Testimony to the Senate Committee on Environment and Public Works, 2002, entitled Separating Climate Fact From Fiction , "The complexity of the computer simulations of climate is one reason the forecasts are unreliable. The simulations must track over 5 million parameters. To simulate climate change for a period of several decades is a computational task that requires 10,000,000,000,000,000,000 degrees of freedom."
(Actually, Von Neumann was stretching things a bit to make his point. Fitting the points that defined the elephant above required 30 parameters--see Mahalanobis, the web log of Michael Stastny.)