Localized theories and conditional complexity

7 jimmy 19 October 2009 07:29AM

Suppose I hand you a series of data points without providing the context. Consider the theory v = a*t for t<<1, v = b for t>>1. Without knowing anything a priori about the shapes of the curves, one must have enough data to make sure that v follows the right lines at the two limits since there is complexity that must be justified.  Here we have two one-parameter curves, so we need at least two data points to pick the right slope and offset, as well as at least a couple more to make sure it follows the right shape.

This is what I’ll call a completely local theory – see data, fit curve.  Dealing with problems at this level does not leave much room for human bias or error, but it also does not allow for improvement by including  background knowledge.

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