The Tablet known as Plimpton 322

Maev Kennedy, a special writer for the Guardian, puts forward that “[m]athematicians have been arguing for most of a century about the interpretation of the tablet known as Plimpton 322, ever since the New York publisher George Plimpton bequeathed it to Columbia University in the 1930s as part of a major collection. He bought it from Edgar Banks, a diplomat, antiquities dealer and flamboyant amateur archaeologist said to have inspired the character of Indiana Jones – his feats included climbing Mount Ararat in an unsuccessful attempt to find Noah’s Ark – who had excavated it in southern Iraq in the early 20th century”.¹

The Professor of Ancient Near Eastern History Eleanor Robson explains that “Plimpton 322 is the modern label given to a cuneiform tablet written in the ancient Iraqi city of Larsa in the mid-18th century BCE. Old Babylonian (OB) mathematics, the oldest known body of ‘pure’ mathematics in the world, derived from two separate traditions in early Mesopotamia: an orally-based ‘surveyors’ algebra’ and a bureaucratic accountancy culture. The ‘surveyors’ algebra’ is heavily based on riddles concerning cut-and-paste geometry and has its origins outside the literate scribal tradition in the late third millennium . . . Scribes, on the other hand, had been directly concerned with the quantitative control of goods, time, and labour since the advent of writing at the end of the fourth millennium . . . Their complex system of metrology,work norms,andother technical constants also reached its apex at the end of the third millennium, under the so-called Third Dynasty of Ur III . . . The two traditions coalesced into the mathematics of the OB humanist scribal schools of the early second millennium, where education appears to have comprised far more than the acquisition of professionally useful skills”.² Professor Robson goes on to say that “[a]lthough the archaeology of Old Babylonian schools is not clear-cut and the large majority of OB mathematical tablets known are completely unprovenanced, [she is] convinced that virtually all of the OB mathematical corpus as we have it should be interpreted as the products of scribal training, or, at the very least, as the products of a scholastic milieu”.³ And, going down to the nitty-gritty, she postulates that “Plimpton 322 is, physically at least, a typical product of OB mathematical culture . . . It is a clay tablet, measuring some 12.7×8.8 cm as it is preserved, ruled into four columns. It was excavated illegally sometime during the 1920s, along with many thousands of other cuneiform tablets, not from Babylon but from the ancient city of Larsa (modern Tell Senkereh, 31◦140 N, 45◦510 E)”.⁴

The mathematician Daniel Mansfield relates that the “huge mystery [of Plimpton 322], until now, was its purpose – why the ancient scribes carried out the complex task of generating and sorting the numbers on the tablet. Our research reveals that Plimpton 322 describes the shapes of right-angle triangles using a novel kind of trigonometry based on ratios, not angles and circles. It is a fascinating mathematical work that demonstrates undoubted genius. The tablet not only contains the world’s oldest trigonometric table; it is also the only completely accurate trigonometric table, because of the very different Babylonian approach to arithmetic and geometry. This means it has great relevance for our modern world. Babylonian mathematics may have been out of fashion for more than 3,000 years, but it has possible practical applications in surveying, computer graphics and education. This is a rare example of the ancient world teaching us something new”.⁵ The mathemtician Norman Wildberger, for his part, adds that “Plimpton 322 predates [the Greek astronomer] Hipparchus by more than 1,000 years. It opens up new possibilities not just for modern mathematics research, but also for mathematics education. With Plimpton 322 we see a simpler, more accurate trigonometry that has clear advantages over our own”, also explaining that a veritable “treasure trove of Babylonian tablets exists, but only a fraction of them have been studied yet. The mathematical world is only waking up to the fact that this ancient but very sophisticated mathematical culture has much to teach us”.⁶ Mansfield and Wildberger have published their fiindings on the Babylonian tablet in an article published in the journal Historia Mathematica.

1Maev Kennedy, “Mathematical secrets of ancient tablet unlocked after nearly a century of study” The Guardian (24 August 2017). https://www.theguardian.com/science/2017/aug/24/mathematical-secrets-of-ancient-tablet-unlocked-after-nearly-a-century-of-study#img-2.

2Eleanor Robson, “Neither Sherlock Holmes nor Babylon: A Reassessment of Plimpton 322” Historia Mathematica 28 (2001), 167–206.

3Eleanor Robson, “Neither Sherlock Holmes nor Babylon: A Reassessment of Plimpton 322”.

4Eleanor Robson, “Neither Sherlock Holmes nor Babylon: A Reassessment of Plimpton 322”.

5Maev Kennedy, “Mathematical secrets of ancient tablet unlocked after nearly a century of study”.

6Maev Kennedy, “Mathematical secrets of ancient tablet unlocked after nearly a century of study”.

Oxford University Chancellor: “Grow up!”

“Louise Richardson, Oxford’s vice-chancellor, told students had to ‘understand the true nature of freedom of inquiry and expression.’ Oxford University installed its first female vice-chancellor this week, Louise Richardson, who boldly stressed the importance of free speech and critical thinking at university amid roiling student protests. Addressing students for the first time in her new role, Richardson urged them to be open-minded and tolerant; and to engage in debate rather than censorship, alluding to countless calls from students at Oxford and other universities across the U.K. to ban potentially offensive speakers and rename or remove historical monuments.” . . . Oxford University just hired their first female chancellor, and she has a message for the student body: “Grow up!” Ana Kasparian, Becca Frucht, Jimmy Dore (The Jimmy Dore Show), and Elliot Hill (The LipTV) hosts of The Young Turks discuss. (Published on Jan 15, 2016).

The Oxford website for the Social Sciences offers this short bio by way of introduction: ‘Professor Richardson is an internationally renowned scholar of terrorism and security studies, on which she has advised policy makers and others internationally. Her publications include the ground-breaking study: What Terrorists Want: Understanding the Enemy Containing the Threat. Whilst at Harvard she received several honours for the quality of her teaching, including the Joseph R Levenson Memorial Teaching Prize, bestowed by Harvard’s undergraduate body in recognition of exceptional teaching. Born in the Republic of Ireland, Professor Richardson holds a BA in History from Trinity College, Dublin, an MA in Political Science from the University of California, Los Angeles (UCLA) and an MA and PhD in Government from Harvard University’. Professor Richardson has led St Andrews for more than six years, combining strong institutional advancement with a distinguished academic career in the study of terrorism and security issues. Prior to joining St Andrews in 2009, Professor Richardson lived and worked in the United States where she was Executive Dean of the Radcliffe Institute for Advanced Study at Harvard University’.[1]

[1] “Professor Louise Richardson nominated as next Vice-Chancellor” Social Sciences (29 May 2015). http://www.socsci.ox.ac.uk/news/professor-louise-richardson-nominated-as-next-vice-chancellor.