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--- 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.' altloc: [] chapter: ~ commentary: ~ commref: ~ confdates: ~ conference: ~ confloc: ~ contact_email: ~ creators_id: [] creators_name: - family: Markovitch given: J. S. honourific: '' lineage: '' date: 2004-06 date_type: published datestamp: 2004-06-05 department: ~ dir: disk0/00/00/36/67 edit_lock_since: ~ edit_lock_until: ~ edit_lock_user: ~ editors_id: [] editors_name: [] eprint_status: archive eprintid: 3667 fileinfo: /style/images/fileicons/application_pdf.png;/3667/1/APRI%2DPH%2D2004%2D12b.pdf full_text_status: public importid: ~ institution: ~ isbn: ~ ispublished: ~ issn: ~ item_issues_comment: [] item_issues_count: 0 item_issues_description: [] item_issues_id: [] item_issues_reported_by: [] item_issues_resolved_by: [] item_issues_status: [] item_issues_timestamp: [] item_issues_type: [] keywords: "coincidence\ndata compression" lastmod: 2011-03-11 08:55:37 latitude: ~ longitude: ~ metadata_visibility: show note: ~ number: ~ pagerange: ~ pubdom: FALSE publication: ~ publisher: ~ refereed: FALSE referencetext: | Conway, J. H. and Guy, R. K., The Book of Numbers (Springer-Verlag, New York, 1996), pp. 186-187, 217-226. Dienes, K. R., Dudas, E., and T. Gherghetta, Nucl. Phys. B, 537, 47 (1999). Dimopoulos, S., Raby S., and Wilczek, F., Physics Today, 44, 25 (1991). Feynman, R. P., QED (Princeton University Press, Princeton,1985), pp. 126-130. Georgi, H. and Glashow, S. L., Phys. Rev. Lett., 32, 438 (1974). Georgi, H., Quinn, H. R., and Weinberg, S., Phys. Rev. Lett., 33, 451 (1974). Hardy, G. H. and Wright, E. M., An Introduction to the Theory of Numbers, 5th ed. (Oxford, England: Clarendon Press, 1979), pp. 154-170. Khinchin, A., Continued Fractions, (New York, Dover, 1997), pp. 92-93. Mach, E., Science of Mechanics (Open Court, La Salle, Illinois,1988), pp. 6-8, 577-595. Markovitch, J. S., A Precise, Particle Mass Formula Using Beta-Coefficients From a Higher-Dimensional, Nonsupersymmetric GUT, available at www.slac.stanford.edu/spires/find/hep/www?r=apri-ph-2003-11 (Applied and Pure Research Institute, Nashua, NH, APRI-PH-2003-11, 2003). Mohr, P. J. and Taylor, B. N., "The 2002 CODATA Recommended Values of the Fundamental Physical Constants, Web Version 4.0," available at physics.nist.gov/constants (National Institute of Standards and Technology, Gaithersburg, MD 20899, 9 December 2003). Ramanujan, S., “Modular Equations and Approximations to ”, Quart. J. Pure and Appl. Math., 45, 350-372, 1914. Weisstein, E. W., CRC Concise Encyclopedia of Mathematics (CRC Press, New York, 1999). Zwirner, F. Properties of SUSY particles, Erice 1992, hep-ph/9307293. relation_type: [] relation_uri: [] reportno: ~ rev_number: 12 series: ~ source: ~ status_changed: 2007-09-12 16:52:39 subjects: - comp-sci-complex-theory - phil-sci succeeds: ~ suggestions: ~ sword_depositor: ~ sword_slug: ~ thesistype: ~ title: | Coincidence, data compression, and Mach’s concept of “economy of thought” type: preprint userid: 4003 volume: ~