As we study the ancients, we find ourselves revising our own understanding of what was known when. This became quite evident from a study published in January in Science.
In the study, astroarcheologist Mathieu Ossendrijver studied the texts of Babylonian tablets from 350-50 BCE. This Science video and articles from the NY Times and Washington Post show the beautiful tablets with the cuneiform writing.
To his surprise, and upending established history of science, Ossendrijver found a very abstract application of geometry.
Geometry is a very intuitive science
It is used to understand the distance between cities, the extent of pastureland or fields, or volumes of oil and wine.
However the text on these clay tablets dealt with nothing so tangible. They compared speed and time, as is done in calculus.
But calculus was not developed until the mid 17th C, by Leibniz and Newton.
What is calculus?
The word calculus comes the Latin for a small stone or pebble—the kind one might use to count, or in an abacus.
In mathematics, calculus is the study of change. One can estimate the rate of change, in what is known as differential calculus. The reverse process finds the net accumulation due to change, integral calculus.
Integral calculus deals with quantifying the area under a curve.
What did the Babylonians do?
Ossendrijver had long studied several small clay tablets from the British Museum. These tablets spoke of deriving the area of a trapezoid, but there was no context as to what the trapezoid represented. Thanks to an additional clue provided from photos of another tablet from a retired archeologist, he realized that the Babylonians were referring to the planet Jupiter.
Taken all together, the tablets prescribed how to find the area of the trapezoid formed beneath the curve of Jupiter’s velocity against time. Integrating this area gives the distance that the planet has moved during the time period, namely the first one hundred and twenty days following Jupiter’s appearance.
This procedure was thought to have been first used in the 14th C by researchers working out of Merton College in Oxford, England and by the French philosopher, economist, and mathematician Nicholas Oresme.
Why did the Babylonians want to know the position of Jupiter?
It isn’t altogether clear whether the position of Jupiter was necessary for a specific ritual, but Jupiter was identified with the Marduk, god of the city of Babylon.
Given the relative positions of the planetary orbits, shortly after Jupiter appears from the other side of the sun, Earth catches up with Jupiter. Therefore, as seen from Earth, Jupiter’s velocity appears to slow and to reverse itself.
This crossing period or transition point (or Nibiru) could have been an important religious marker for the Babylonians.
Who is Marduk anyway?
As is the case of many ancient deities, and especially with fragmented records, Marduk morphed over time: from god of thunderstorms to ruler of the cosmos to god of order and fate. At at one time he was known as the god of fifty names.
After vanquishing Tiamat, the monster of chaos, he became the Lord of the Gods of Heaven and Earth. This is just one more of the many cases where patriarchal gods overcame the ancient ones, but that’s a story for another time.
Ancient Greek astronomers used similar geometric methods as seen in these tablets
However, as noted in Ossendrijver’s original article, the Babylonians weren’t calculating the area of a tangible physical object.
The area defined by speed relative to time is abstract. There is no record of similar sophistication until fourteen hundred years later.
The ruler of the cosmos, vanquisher of chaos, wouldn’t have expected anything less.