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Ancient Babylonians Figured Out Forerunner of Calculus (sciencemag.org)

sciencehabit writes: Tracking and recording the motion of the sun, the moon, and the planets as they paraded across the desert sky, ancient Babylonian astronomers used simple arithmetic to predict the positions of celestial bodies. Now, new evidence reveals that these astronomers, working several centuries B.C.E., also employed sophisticated geometric methods that foreshadow the development of calculus. Historians had thought such techniques did not emerge until more than 1400 years later, in 14th century Europe.

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  1. Re:Archimedes had calculus by jbeaupre · · Score: 4, Interesting

    It was more than that, and he did have an inkling of the use. But he treated it as academic. In college, we had to study his technique for integrating the area under a curve. Specifically, the area of a spiral. And he got it right. We even applied it to other geometry with success.

    What made it painful was that it was done without algebra or even the symbol pi. Think long wordy descriptions involving limits and ratios and you end up with 3 pages of text for what takes half a line in modern notation. Heck, even his result takes a couple lines to write.

    --
    The world is made by those who show up for the job.
  2. Re:Archimedes had calculus by AthanasiusKircher · · Score: 5, Interesting

    No. What the church brought was stagnation and illiteracy. Anyone caught translating the bible was burned at the stake.

    Another myth. (Note -- before I go on, I'm NOT Catholic, and I have no interest in defending the Catholic Church. But I do think we have a moral duty to accurate history.)

    The Catholic Church punished people who translated the Bible AND threatened heresy/schism, etc. Yes, there were some incidents in medieval Europe where translators were punished, but that was because they were associated with political movements against the church. If you wanted to translate the Bible AND lead an insurrection, sure they might kill you.

    On the other hand, there are plenty of examples where portions or the entirety of the Bible were translated in the years 1000-1500, and the Church didn't do anything to the translators. It only became a significant controversy after the whole Luther thing and the Counter-Reformation.

    By the way, I don't mean this to be argumentative or even that you should have known this. Errors in scholarship have a long life, and there were some influential studies done on this stuff based on incomplete evidence and erroneous interpretations of medieval documents in the early 1900s. That's why this myth endures.

    But it's a myth nonetheless.

    And illiteracy was just a consequence of lack of utility. Parchment was expensive -- how many animals did you have to kill and skin to make a book? So, why would literacy be common until paper became cheap in the 1400s (due to a sudden excess of scrap linen that could be pulped)?

    Preserving the bad ideas of the Greeks may or may not have been a good thing. We might have been better off flushing the whole thing and starting over completely from scratch.

    Well, that's all very debatable. Arguably the major medieval renaissance in knowledge was in part driven by reclaiming the knowledge of the ancients, which in turn led to what most people think of as the real "Renaissance," which in turn led to Humanistic enterprises that were no longer dominated by the Church, which led to the Scientific Revolution.

    That's only one way of telling the story, of course. But there's some truth to it.

    The real problem was not being able to challenge bogus crap for 1000 years.

    You really have no idea what medieval Scholasticism was about, then, do you? Medieval universities were largely started by priests and monks. Debates were the norm. Empiricism and logical argument were combined into a new method. Challenging accepted facts was commonplace. In fact, some historians of science actually argue that the reason why the West had a "Scientific Revolution" and other places (e.g., China, the Arab world) didn't was because of the accepted level of scholarly debate that occurred in the West compared to other areas of the world... which didn't have the same kinds of debates.