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@misc{cogprints3667, month = {June}, title = {Coincidence, data compression, and Mach?s concept of ?economy of thought? }, author = {J. S. Markovitch}, year = {2004}, keywords = {coincidence data compression}, url = {http://cogprints.org/3667/}, abstract = {A case is made that Mach?s principle of ?economy of thought?, and therefore usefulness, is related to the compressibility of data, but that a mathematical expression may compress data for reasons that are sometimes coincidental and sometimes not. An expression, therefore, may be sometimes explainable and sometimes not. A method is proposed for distinguishing coincidental data compression from non-coincidental, where this method may serve as a guide in uncovering new mathematical relationships. The method works by producing a probability that a given mathematical expression achieves its compression purely by chance.} }