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Tests, Anomalies, and Monsters 107word-frequency distribution in mathematical linguistics and half on statisticalthermodynamics; to the Institute for Advanced Study in Princeton in 1953–54as the last postdoc of John von Neumann; to Geneva “to attempt a collaborationwith Jean Piaget,” the famous developmental psychologist; then to a professorshipof mathematics at Lille. 24In the summer of 1958, Mandelbrot found a congenial intellectual home:the IBM Research Center at Yorktown Heights in Westchester County, justnorth of New York City. Soon to occupy the landmark modernist buildingdesigned for it by Eero Saarinen, the IBM Research Center was at its peak“the world’s largest campus for computer science research” (Knowles andLeslie 2001, p. 17). It freed Mandelbrot from the constraints of standard academicdisciplines without subjecting him to undue pressure to work on pragmaticallyuseful topics. IBM was big enough and successful enough to allowits research “stars” considerable freedom, and their contributions to corporateprofits were not yet under close scrutiny.Talking with Mandelbrot, it is hard not to be reminded of Imre Lakatos’s1976 book Proofs and Refutations, especially as re-interpreted in the light of thework of the anthropologist Mary Douglas (1970a,b) by the sociologist ofknowledge David Bloor (1978). The issue on which Lakatos and Bloor focusis reaction to mathematical anomalies (Lakatos calls them “monstrosities” or“monsters” 25 ) such as counterexamples to a putative proof.Mathematicians can simply be indifferent to counterexamples. Alternatively,they can “bar” monsters, for example redefining “polyhedron” 26 so that ananomalous polyhedron isn’t a polyhedron at all. (Lakatos’s main example is atheorem concerning the relationship between the numbers of vertices, edges,and faces of any polyhedron. 27 ) Other ways to preserve a theorem in the faceof a counterexample are “exception-barring” (for example, restricting thetheorem’s domain so that it no longer includes the anomaly) and “monsteradjustment”(that is, redefining terms so that the anomaly is no longer acounterexample).The approach to monsters that Lakatos recommends, however, involvesembracing them as spurs to conceptual innovation: the “dialectical method,”Lakatos calls it (1976, p. 94 ff.). That has been Mandelbrot’s attitude: “I’malways ready to look at anything curious and bizarre.” (Mandelbrot interview)For example, Mandelbrot became interested in linguistics after reading areview (Walsh 1949) that his uncle had thrown into his wastepaper basket. Thereview alerted him to Zipf ’s law, 28 a regularity in word frequencies that holdsacross languages. It was apparently a mere curiosity from a field in which Mandelbrothad no training, and others might have disregarded it, but Mandelbrotdid not. It was part of the circuitous route that took him to finance.