Words and Pictures: New Light on Plimpton 322

1. INTRODUCTION. In this paper I shall discuss Plimpton 322, one of the world's most famous ancient mathematical artefacts [Figure 1]. But I also want to explore the ways in which studying ancient mathematics is, or should be, different from researching modern mathematics. One of the most cited analyses of Plimpton 322, published some 20 years ago, was called " Sherlock Holmes in Babylon " [4]. This enticing title gave out the message that deciphering historical documents was rather like solving a fictional murder mystery: the amateur detective-historian need only pit his razor-sharp intellect against the clues provided by the self-contained story that is the piece of mathematics he is studying. Not only will he solve the puzzle, but he will outwit the well-meaning but incompetent professional history-police every time. In real life, the past isn't like an old-fashioned whodunnit: historical documents can only be understood in their historical context.

[1]  Jens Høyrup.  Algebra and Naive Geometry. An Investigation of Some Basic Aspects of Old Babylonian Mathematical Thought I , 1990 .

[2]  Jens Høyrup,et al.  In Measure, Number, and Weight: Studies in Mathematics and Culture , 1994 .

[3]  Geoff Emberling.  :The Study of the Ancient Near East in the Twenty‐First Century: The William Foxwell Albright Centennial Conference , 2003 .

[4]  fl. nd cent. Ptolemy,et al.  Ptolemy's Almagest , 1986 .

[5]  E. Robson.  Mesopotamian mathematics: some historical background , 2000 .

[6]  Eleanor Robson,et al.  The uses of mathematics in ancient Iraq, 6000-600 BC , 2000 .

[7]  Jöran Friberg,et al.  Methods and traditions of Babylonian mathematics: Plimpton 322, Pythagorean Triples, and the Babylonian Triangle Parameter Equations , 1981 .

[8]  A. Keaveney.  Cuneiform texts and the writing of history , 2000 .

[9]  A. Kuhrt.  The Ancient Near East , 1996 .

[10]  T. G. Pinches.  Babylonian Records in the Library of J. Pierpont Morgan . Edited by Albert T. Clay. Part I: Babylonian Business Transactions of the first millennium b.c. 12 × 9¼ inches. New York: privately printed, 1912. , 1913, Journal of the Royal Asiatic Society of Great Britain & Ireland.

[11]  Pythagorean Triads in Babylonian Mathematics , 1957 .

[12]  R. Creighton Buck.  Sherlock Holmes in BABYLON , 1981, Cryptologia.

[13]  A. Kuhrt.  The Ancient Near East c. 3000-330 bc , 2003 .

[14]  E Robson,et al.  Mathematical cuneiform tablets in Philadelphia, I: problems and calculations , 2000 .

[15]  A. Sachs,et al.  Mathematical Cuneiform Texts. , 1946 .

[16]  Peter Damerow,et al.  Archaic Bookkeeping: Early Writing and Techniques of Economic Administration in the Ancient Near East , 1994 .

[17]  J. Høyrup.  Algebra and Naive Geometry. An Investigation of Some Basic Aspects of Old Babylonian Mathematical Thought I , 1987 .

[18]  J. Friberg.  Methods and Traditions of Babylonian Mathematics, II: An Old Babylonian Catalogue Text with Equations for Squares and Circles , 1981, Journal of Cuneiform Studies.

[19]  O. Schmidt.  On Plimpton 322. Pythagorean Numbers in Babylonian Mathematics , 1980 .

[20]  M. Mieroop.  Cuneiform texts and the writing of history , 1999 .

[21]  M. Roaf.  Cultural Atlas of Mesopotamia and the Ancient Near East , 1990 .

[22]  Eleanor Robson,et al.  Mesopotamian Mathematics 2100-1600 BC: Technical Constants in Bureaucracy and Education , 1999 .

[23]  R. W. Sloley.  Mathematical Cuneiform Texts , 1946, Nature.

[24]  Eleanor Robson,et al.  Neither Sherlock Holmes nor Babylon: A Reassessment of Plimpton 322 , 2001 .

[25]  David Brown.  Mesopotamian planetary astronomy-astrology , 2000 .

[26]  J. V. Rauff.  Mathematics across Cultures: The History of Non-Western Mathematics , 2002 .

[27]  O. Neugebauer.  The exact sciences in antiquity , 1952 .

[28]  E. Ebeling,et al.  Reallexikon der Assyriologie , 1963 .

[29]  C. Boyer.  Episodes from the Early History of Mathematics. , 1964, Science.

[30]  R. Netz.  The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History , 1999 .

[31]  Asger Aaboe.  Episodes from the early history of mathematics , 1963 .