Neither Sherlock Holmes nor Babylon: A Reassessment of Plimpton 322

Ancient mathematical texts and artefacts, if we are to understand them fully, must be viewed in the light of their mathematico-historical context, and not treated as artificial, self-contained creations in the style of detective stories. I take as a dramatic case study the famous cuneiform tablet Plimpton 322. I show that the popular view of it as some sort of trigonometric table cannot be correct, given what is now known of the concept of angle in the Old Babylonian period. Neither is the equally widespread theory of generating functions likely to be correct. I provide supporting evidence in a strong theoretical framework for an alternative interpretation, first published half a century ago in a different guise. I recast it using regular reciprocal pairs, Hoyrup's analysis of contemporaneous “naive geometry,” and a new reading of the table's headings. In contextualising Plimpton 322 (and perhaps thereby knocking it off its pedestal), I argue that cuneiform culture produced many dozens, if not hundreds, of other mathematical texts which are equally worthy of the modern mathematical community's attention. Wir mussen fruhe mathematische Texte und Objekte im Hinblick auf ihre mathematisch-historische Umgebung betrachten und sie nicht als kunstliche, vollstandige Schopfungen im Stile von Detektivgeschichten behandeln, wollen wir sie verstehen. Als dramatische Fallstudies dient mir die Keilschrifttafel Plimpton 322. Ich zeige auf, dass die weitverbreitete Ansicht, so etwas wie eine trigonometrische Tabelle vor uns zu haben, nicht richtig sein kann, und zwar aufgrund unseres Wissens uber die Vorstellung des Winkels in altbabylonischer Zeit. In gleiche Weise ist die gangige Theorie uber erzeugende Funktionen wahrscheinlich falsch. Ich kann meine Neuinterpretation, die in einen stark theoretischen Rahmen eingebettet wird, mit Texten belegen. Hinter meiner Neuinterpretation liegt eine funfzigjahrige Theorie, die auf Bruins zuruckgeht. Sie fundiert auf den Gebrauch von regelmassigen, reziproken Paaren, auf Hoyrups Analyse der naiven Geometrie und auf eine neue Lesung der Uberschriften der Tabelle. Indem ich die Keilschrifttafel Plimpton 322 in ihren historischen Kontext stelle, pladiere ich dafur, dass viele andere mathematische Texte mesopotamischen Ursprungs es ebenso verdienen, von uns beachtet zu werden. Copyright 2001 Academic Press. AMS Subject Classifications: 01A17; 01A85.

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