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Critical truths about power laws

Michael P. H. Stumpf, Mason A. Porter

posted on 15 July 2013

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The ability to summarize observations using explanatory and predictive theories is the greatest strength of modern science. A theoretical framework is perceived as particularly successful if it can explain very disparate facts. The observation that some apparently complex phenomena can exhibit startling similarities to dynamics generated with simple mathematical models has led  to empirical searches for fundamental laws by inspecting data for qualitative agreement with the behavior of such models. A striking feature that has attracted considerable attention is the apparent ubiquity of powerlaw relationships in empirical data. However, although power laws have been reported in areas ranging from finance and molecular biology to geophysics and the Internet, the data are typically insufficient and the mechanistic insights are almost always too limited for the identifi cation of power-law behavior to be scientifically useful. Indeed, even most statistically "successful" calculations of power laws offer little more than anecdotal value.