Grounding Occam's Razor in a Formal Theory of Simplicity
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It is proposed that the Occam's Razor heuristic – when in doubt, choose the simplest hypothesis – requires a theory of simplicity in order to become fully rigorous and meaningful. With this in mind, a simple formal theory of simplicity is introduced. The relationship between simplicity and computation is explored, with simplicity shown reducible to a variant of computational complexity under certain special assumptions. The theory of simplicity is then used as a foundation for a theory of pattern, and a theory of hierarchy and heterarchy in systems of patterns. The conceptual end result is to re-envision Occam's Razor as something like the following: In order for a mind to effectively understand the world, it should interpret itself and the world in the context of some simplicity measure obeying certain basic criteria. Doing so enables it to build up hierarchical and heterarchical pattern structures that help it interpret the world in a subjectively meaningful and useful way.
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