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Ancient Babylonians Figured Out Forerunner of Calculus ( 153

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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Ancient Babylonians Figured Out Forerunner of Calculus

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  • Since today is Friday, the most important issue regarding this story will be whether or not the ancient Babylonians were white men.

    For the record, Stormfront says, "Bet your ass they were". When asked for comment, Donald Trump said that if elected president, he'll make sure the US has "the classiest calculus of any country."

    • Re: (Score:2, Offtopic)

      by Hognoxious ( 631665 )

      From what I've seen of sculptures and stuff they look awfully like murzlums.

      I think we should err on the side of caution and bomb them back into the bronze age, just to be sure.

      • by kbonin ( 58917 )

        Babylonian religion predates Judaism and Islam by a long time, they worshiped lots of gods, lots of statues, a good deal of it adapted from Sumerians. []

        • Babylonian religion predates Judaism and Islam by a long time, they worshiped lots of gods, lots of statues, a good deal of it adapted from Sumerians.

          Well, it sure didn't take long for this discovery to spark a war over priority. I guess "The Babylonians ripped off proto-calculus from the Sumerians" is the new "Leibniz was actually using calculus years before Newton."

        • by Anonymous Coward on Friday January 29, 2016 @04:14PM (#51398487)

          There's a good reason that Judaism, Islam, and Christianity are called "Abrahamic" religions.

          Abraham (Abram) had a son by a concubine (Hagar). That son was named Ishmael. The Arabs claim ancestry back to him. He also had a son by his wife (Sarai/Sarah). That son was named Isaac. The Jews claim ancestry back to him. Jesus (Christ) was a Jew.

          Abraham was from "Ur of the Chaldeans", also known as Uruk. The name hasn't changed. That place is still called Iraq. (Say both of those names out loud if you don't "get it".) Specifically, the city of Ur was in the southern part of the Euphrates basin, right about where it curves east and runs to the Persian Gulf.

          Babylon was much farther to the north and a little east, where the Euphrates and Tigris run closest to each other. You can still see where Babylon was on Google Maps. It's immediately north west of Al-Iqsandariya (Alexandria), Iraq. It's a scorch mark, basically. Nothing grows there, nothing lives there. There was a prophecy issued about that in the 800's BC. (Isaiah 13:20, specifically.) Interestingly, it holds true despite many attempts to make use of that portion of land. Make of that what you will.

          • by Camel Pilot ( 78781 ) on Friday January 29, 2016 @07:30PM (#51399901) Homepage Journal


            Looks pretty lush actually.


      • Dem murzlums beat ya to it. []

    • Also, from what I have read on Slashdot, all astronomers are misogynist pigs who harass women. And they try to build their telescopes on native lands. So basically: boo astronomy! Plus I don't trust any astronomy article that doesn't link to Forbes.
  • Archimeded in the first century AD may have built upon Babylonian and Egyptian mathto create true calculus. []

    • by pjt33 ( 739471 )

      If Archimedes did create calculus then it was considerably earlier than that, because he died more than 200 years before the first century AD.

      • by epine ( 68316 )

        Furthermore, SMS service was a bit spotty back then, so let's just assume that whatever Archimedes accomplished, he mostly accomplished ab initio.

        Furthermore again, calculus isn't really calculus without the notion of continuous functions over an algebraic coordinate system.

        Merely inscribing exterior and interior polygons around a circle and then amping up the edge count is obviously a pretty good place to start, but Newton or Leibniz it sure the heck wasn't.

    • by HiThere ( 15173 )

      Archimedes didn't discover the calculus. He didn't discover the theory of limits. He discovered what I to be a more accurate thing, the method of approximation.

      As I don't believe in infinities or continuity, I consider the calculus to be a useful but false approximation of reality, just as I consider the real number line. I mean just think a minute about one of the proofs: You make two copies of all the real numbers between 1 and 0, and you paint one red and the other blue.... What does that even MEAN!

  • by haruchai ( 17472 ) on Friday January 29, 2016 @03:01PM (#51397873)

    How does "several centuries BCE" plus 1400 years = 14th century??

    • by Aighearach ( 97333 ) on Friday January 29, 2016 @03:05PM (#51397913) Homepage

      Because the youngest end of their date range is less than 100 years BCE, and off-by-one is close-enough. Likely it 200 years older, but that isn't certain. 350 to 50 BCE is the range given.

    • Good spot, I didn't notice that.

      Neither, of course, did the editors. [snigger] Perhaps shitandpiss and dimmothy are working out their notice periods.

      • Whenever I try to picture Timothy, I keep coming up with this:

        http://fairlyoddparents.wikia.... []

        Is that wrong?

    • On a related note how does 1st and 2nd century BC count as "Ancient Babylon". That was toward the end of the Hellenistic period of what was barely left of Babylon. Ancient Babylon by archaeological standards (to avoid conflating it with any number of other empires that just happened to share the same geographical area) had ended some 1000 years before. In fact the article suggests that the 2nd century BC tablets were actually copies handed down from as far back as actual ancient Babylonian mathematical

  • ancient Babylonians were just poor students of calculus, which their ancient astronaut alien overlords kept trying to teach them unsuccessfully.

  • And their VCR's didn't flash "12:00" all day

  • Please, everybody knows that Glorious Nation of North Korea invented calculus long time before that.

    This post was brought to you by People's Hacking Army.
  • by Anonymous Coward

    Using it analytically to derive the familiar differential and integral calculus is not.

    • by HiThere ( 15173 )

      The concept of limit is not only not simple, I believe it to be false. It's a very useful theoretical concept, as is the real number line, but I do not believe that it has any actual existence in the world outside of mathematics. Just because you can't look at something close enough to see where it dissolves into pieces doesn't mean that it's actually continuous. This is why Xeno's paradoxes were so annoying. Most of them rely simplicity on the assumption of continuity, which is intuitive, but false. (

  • So if calculus is derived from this Babylonian knowledge, should we rename it threerunner?
  • Not surprising (Score:5, Insightful)

    by rasmusbr ( 2186518 ) on Friday January 29, 2016 @04:21PM (#51398527)

    Civilizations tend to "discover" philosophy, mathematics, literature, drama and great works of music in the centuries after they invent ways of writing those things down.

    What's probably going on is that these things have been cropping up intermittently for thousands of years (or tens of thousands of years), but the ideas would usually not survive for very long because it would take unreasonable amounts of human effort to remember and transmit them.

    By the way, video finally made it possible to commit dancing to permanent media in the early 1900's, so future historians will probably think of the 1900's and 2000's as the centuries when great dancing was first invented.

    • How do you have "advanced" mathematics ( or perhaps a better term might be "non-trivial" ) without at least a rudimentary writing system?

      • How do you have "advanced" mathematics ( or perhaps a better term might be "non-trivial" ) without at least a rudimentary writing system?

        You can't. You can do a lot of basic arithmetic and basic geometry.

        But you could for example come up with the hypothesis that stars are faraway suns, just by noticing that different stars vary in brightness and guessing that the brighter ones are closer to Earth, with the Sun being much closer than all the others. You could argue that spherical objects are more efficient than other objects because they minimise both their surface area and the distance of any surface feature to the center of themselves for a

  • ... our last best hope for peace.
  • These orbits are all elliptic curves, second order curves basically. With enough observations one could construct some kind of regression, extrapolation based predictions. So what the clay tablets contain could be simple prediction tables. Can one tell the difference between extrapolation or regression prediction and trapezoidal quadrature?
  • by hey! ( 33014 ) on Friday January 29, 2016 @08:01PM (#51400027) Homepage Journal

    How do you think they figured out the formula for the volume of a sphere? Or proved that the area of a circle was proportional to the square of its radius when it's impossible to construct a square of the same area in a finite number of steps with ruler-and-compass methods? The same techniques were rediscovered in China around the 3rd century CE, again as a result of trying to calculate the area of a circle.

    I think the basic ideas behind integral calculus are pretty much inevitable when you have mathematicians messing with geometry problems that can only be solved with successive approximations -- although inevitable only because eventually someone really smart will get bored with doing things the long way.

    What's distinctive about modern calculus is it's connections to analytic geometry and algebra (algebra with good notation, I might add). This allows us to generalize problems in a way that transcends geometric resemblance, e.g., the area under the curve of any polynomial.

    • I think the basic ideas behind integral calculus are pretty much inevitable when you have mathematicians messing with geometry problems that can only be solved with successive approximations

      I agree with this, and I suspect any adoption problems, if any, were with the notation. Until algebraic notation came along, I bet integration, like Greek geometry, was a serious pita for the Babylonians. I took a class that included a long division problem using Roman numerals for extra credit in one test. OMG... if the Babylonians were using cruciform numbers for their calculations, holy cow...

  • by colinrichardday ( 768814 ) <> on Saturday January 30, 2016 @02:13AM (#51401271)

    The article mentions trapezoids. Did the Babylonians approximate curved regions with trapezoids, or did they just use trapezoids? Finding the area of a trapezoid doesn't require calculus.

  • What bothers me really is after thousands of years and reading tons of history, we failed to understand the simple thing the biggest culprit was/is the Religion. Why don't we just try to get rid of it.

I've finally learned what "upward compatible" means. It means we get to keep all our old mistakes. -- Dennie van Tassel