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%A J. S. Markovitch %T Coincidence, data compression, and Mach?s concept of ?economy of thought? %X 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. %D 2004 %K coincidence data compression %L cogprints3667