Did ancient Babylonians anticipated integral calculus with velocity v time graphs!

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MSI
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Did ancient Babylonians anticipated integral calculus with velocity v time graphs!

Post by MSI » Sat Jan 30, 2016 6:29 pm

From a New York Times article Signs of Modern Astronomy Seen in Ancient Babylon
Which begins:
  • For people living in the ancient city of Babylon, Marduk was their patron god, and thus it is not a surprise that Babylonian astronomers took an interest in tracking the comings and goings of the planet Jupiter, which they regarded as a celestial manifestation of Marduk.

    What is perhaps more surprising is the sophistication with which they tracked the planet, judging from inscriptions on a small clay tablet dating to between 350 B.C. and 50 B.C. The tablet, a couple of inches wide and a couple of inches tall, reveals that the Babylonian astronomers employed a sort of precalculus in describing Jupiter’s motion across the night sky relative to the distant background stars. Until now, credit for this kind of mathematical technique had gone to Europeans who lived some 15 centuries later.
And includes:
  • “That is a truly astonishing find,” said Mathieu Ossendrijver, a professor at Humboldt University in Berlin, who describes his archaeological astronomy discovery in an article on Thursday in the journal Science.
    “It anticipates integral calculus,” Dr. Ossendrijver said. “This is utterly familiar to any modern physicist or mathematician.”
The paper by Ossendrijver is:
  • Abstract
    • The idea of computing a body’s displacement as an area in time-velocity space is usually traced back to 14th-century Europe. I show that in four ancient Babylonian cuneiform tablets, Jupiter’s displacement along the ecliptic is computed as the area of a trapezoidal figure obtained by drawing its daily displacement against time. This interpretation is prompted by a newly discovered tablet on which the same computation is presented in an equivalent arithmetical formulation. The tablets date from 350 to 50 BCE. The trapezoid procedures offer the first evidence for the use of geometrical methods in Babylonian mathematical astronomy, which was thus far viewed as operating exclusively with arithmetical concepts.
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