T1.JPGA concept essential to modern calculus was understood 1500 years earlier than historians have ever seen.  Jupiter’s erratic pace across the sky (appearing to slow down and speed up from day to day based on the combination of its orbit and Earth’s) must have perplexed ancient astronomers and tested their best computational techniques. A surprisingly modern technique was used to calculate how far the bright dot traveled through the sky over the course of months. Their process requires a leap in understanding in how position and speed relate to time, one that wouldn’t appear again until 1350 and that was a precursor to modern calculus.  The connections between speed, position and time are known to most modern travelers (people easily understand speed as a measure of miles or kilometers per hour). Locations are often described in terms of time (it’s only an hour away) rather than distance. The insight that led to calculus demonstrated the connection between a graph of the traveler’s changing speed and the total distance traveled.  Examining the tablets at the British Museum, Mathieu Ossendrijver figured out that the trapezoid calculations were a tool for calculating Jupiter’s displacement each day along the ecliptic, the path that the sun appears to trace through the stars.  The computations recorded on the tablets covered a period of 60 days, beginning on a day when the giant planet first appeared in the night sky just before dawn.  The distance travelled by Jupiter after 60 days, 10º45′, is computed as the area of the trapezoid whose top left corner is Jupiter’s velocity over the course of the first day, in distance per day, and its top right corner is Jupiter’s velocity on the 60th day. In a second calculation, the trapezoid is divided into two smaller ones with equal area to find the time in which Jupiter covers half this distance.  It’s like a precursor if you like of what we know today as integral calculus, which allows us to calculate the movements of decelerating or accelerating objects.  Further, the little tablet Text A(officially named BH40054) had markings that served as a kind of abbreviation of a longer calculation that looked familiar to him. By comparing Text A to the four previously mysterious tablets, he was able to decode what was going on: This was all about Jupiter. The five tablets computed the predictable motion of Jupiter relative to the other planets and the distant stars.