By EDWARD ROTHSTEIN Published: November 26, 2010
If the cost of digging a trench is 9 gin, and the trench has a length of 5 ninda and is one-half ninda deep, and if a worker’s daily load of earth costs 10 gin to move, and his daily wages are 6 se of silver, then how wide is the canal?
The tablet called Plimpton 322 at the Institute for the Study of the Ancient World, part of a new exhibition, “Before Pythagoras.”
A tablet in the exhibition that shows an installation of numbers in ancient Babylon.
A tablet bearing a rough sketch of a square and its diagonals.
Or, a better question: if you were a tutor of Babylonian scribes some 4,000 years ago, holding a clay tablet on which this problem was incised with cuneiform indentations — the very tablet that can now be seen with 12 others from that Middle Eastern civilization at the Institute for the Study of the Ancient World — what could you take for granted, and what would you need to explain to your students? In what way did you think about measures of time and space? How did you calculate? Did you believe numbers had an abstract existence, each with its own properties?
And how would you have figured out the width of that canal (which, the tablet tells us, is one-and-a-half ninda)?
Spend some time at this modest yet thoroughly intriguing exhibition,“Before Pythagoras: The Culture of Old Babylonian Mathematics,” and you begin to realize that the answers can be far more cryptic than these tablets were before great scholars likeOtto E. Neugebauer began to decipher them during the first half of the 20th century.
The institute, part of New York University, has gathered together a remarkable selection of Old Babylonian tablets from the collections of three universities — Columbia, Yale and the University of Pennsylvania — that cover a wide mathematical range. Made between 1900 and 1700 B.C., they include student exercises, word problems and calculation tables, as well as more abstract demonstrations. Under thecuratorship of Alexander Jones, a professor at N.Y.U., and Christine Proust, a historian of mathematics, the tablets are used to give a quick survey of Babylonian mathematical enterprise, while also paying tribute toNeugebauer, the Austrian-born scholar who spent the last half of his career teaching at Brown University and almost single-handedly created a new discipline of study through his analysis of these neglected sources.