Analysis of ancient Babylonian tablets reveals that, to calculate the position of Jupiter, the tablets' makers used geometry, a technique scientists previously believed humans had not developed until at least 1,400 years later, in 14th century Europe. These tablets are the earliest known examples of using geometry to calculate positions in time-space and suggest that ancient Babylonian astronomers may have influenced the emergence of such techniques in Western science. In this Report, Mathieu Ossendrijver discusses the translation of four almost completely intact tablets that were most likely written in Babylon between 350 and 50 BCE. They depict two intervals from when Jupiter first appears along the horizon, calculating the planet's position at 60 and 120 days. The texts contain geometrical calculations based on a trapezoid's area, and its "long" and "short" sides; previously, it was thought that Babylonian astronomers operated exclusively with arithmetical concepts. The ancient astronomers also computed the time when Jupiter covers half of this 60-day distance by partitioning the trapezoid into two smaller ones of equal area. While ancient Greeks used geometrical figures to describe configurations in physical space, these Babylonian tablets use geometry in an abstract sense to define time and velocity, Ossendrijver notes. These tablets redefine our history books, revealing that European scholars in Oxford and Paris in the 14th century, who were previously credited with developing such calculations, were in fact centuries behind their ancient Babylonian counterparts. This paper is featured on the cover, with a special cover caption describing how *Science* photo editors created a striking image of a 3-D printed replica of the ancient tablet, positioned aptly under a prominent Jupiter in the Babylonian night sky.

**American Association for the Advancement of Science**

## Comments