back to article Forget trigonometry, 'cos Babylonians did it better 3,700 years ago – by counting in base 60!

Those of you who can remember trigonometry can feel free to forget it, because ancient Babylonian mathematicians had a better way of doing it – using base 60! That's the conclusion of a new paper, Plimpton 322 is Babylonian exact sexagesimal trigonometry, in the new issue of the journal Historia Mathematica. The “Plimpton 322 …

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  1. HkraM

    Copyright

    The Babylonians knew a thing or two about copyright as well if the tablet is still protected after over 3000 years.

    1. eldakka Silver badge

      Re: Copyright

      While I did upvote....

      technically, I don't think it's the tablet that is protected by copyright, it's the images of the tablet that are copyrighted.

      If you had access to the physical tablet, you could take your own photos, and you would own the copyright in those photos (or release them public domain if you so choose).

      1. Pompous Git Silver badge

        Re: Copyright

        "If you had access to the physical tablet, you could take your own photos, and you would own the copyright in those photos (or release them public domain if you so choose)."

        There are images already in the public domain, so not much point. I suspect HkraM was only trying to get a laugh...

        The Babylonian tablet Plimpton 322

    2. Anonymous Coward
      Anonymous Coward

      Re: Copyright

      It's not well known but Walt Disney descended from the Babylonians.

      1. Symon Silver badge
        Happy

        Re: Copyright

        Yep.

        http://cyberlaw.stanford.edu/blog/2007/03/fairy-use-tale

        1. Ugotta B. Kiddingme

          Re: Copyright

          Symon: "Yep. http://cyberlaw.stanford.edu/blog/2007/03/fairy-use-tale"

          Wow, thank you. That is absolutely brilliant. And quite possibly the best example of passive-aggressive trolling I have ever seen.

          1. Destroy All Monsters Silver badge

            Re: Copyright

            That is absolutely brilliant.

            Andrew is probably already penning an article about the starving Babylonian artists and scribes forced to live in Akkad dumpsters.

      2. LDS Silver badge
        Joke

        Walt Disney descended from the Babylonians

        If so Babylonians would have used octal arithmetic....

        1. herman Silver badge

          Re: Walt Disney descended from the Babylonians

          The Babylonians must have been polydactyl.

          https://www.google.ae/search?q=cat+with+60+toes

    3. MyffyW Silver badge
      Paris Hilton

      Re: Copyright

      Paris COS she's bound to have a TAN

      1. Pompous Git Silver badge

        Re: Copyright

        "Paris COS she's bound to have a TAN"
        A bit hard to tell from the bedroom scenes she's made...

        1. Anonymous Coward
          Anonymous Coward

          Re: Copyright

          "Paris COS she's bound to have a TAN"

          "A bit hard to tell from the bedroom scenes she's made..."

          Well, that's the SIN right there.

          1. Antron Argaiv Silver badge
            Coat

            Re: Copyright

            "Paris COS she's bound to have a TAN"

            "A bit hard to tell from the bedroom scenes she's made..."

            "Well, that's the SIN right there."

            I'll watch the video again, and this time, I'll try to ignore the SECs and pay more ATAN-tion to the skin tones...

            1. handleoclast Silver badge
              Coat

              Re: Copyright

              @Antron Argaiv

              With puns like that, don't be surprised if somebody hits you with a COSH. Then you'll end up in a hospital COT.

              BTW, what's a nortna? The second part of your name is obvious, but not the first (not to me, anyway, I expect about 200 replies pointing out what I've missed).

            2. DropBear Silver badge
              Paris Hilton

              Re: Copyright

              "I'll watch the video again, and this time, I'll try to ignore the SECs and pay more ATAN-tion to the skin tones..."

              There's a direct connection to ATAN insomuch every programmer unfortunate enough to have dabbled in geometry-handling maths knows it's an unreliable bitch - you really should use ATAN2 instead...

    4. Anonymous Coward
      Anonymous Coward

      Re: Copyright

      >The Babylonians knew a thing or two about copyright

      And like the Greeks their best days are far behind them and they have been coasting ever since.

  2. Nick Kew Silver badge

    So much for digital

    If the relative lack of divisors of 10 is a shortcoming, why has the modern world moved so far towards pure binary (and powers of 2 in specific contexts)?

    1. Dave 126 Silver badge

      Re: So much for digital

      I don't know... Something to do with Napoleon possibly?

      Whilst I work (measure and cut) in mm, I estimate in feet and inches. However I may be missing a trick because of the way that 12 can be easily divided by 3 and by 4 (and obviously 2 and 6). For centuries, carpenters have been able to make beautiful pieces without a unit of measurement by means of dividers - it is only important that they can express a length as a rational of another.

      1. Anonymous Coward
        Anonymous Coward

        Re: So much for digital

        Thought that was why there was 60 seconds / minutes in a hour. Because it was easy to work out divide by 2, 3, 4, 5, 6, 10, 12, 15, 20, 30

        1. alain williams Silver badge

          Re: So much for digital

          I always thought that they used 60 because 6*60 gives you about the number of days in a year and that a circle has 360 degrees because every day you move about one degree around the zodiac.

          1. Omgwtfbbqtime Silver badge
            Mushroom

            Re: So much for digital

            That's why I prefer mils for angles.

            6400 mils to a circle.

            1mil subtends 1m at 1km.

            or at least close enough for artillery.

        2. Doctor Syntax Silver badge

          Re: So much for digital

          "Thought that was why there was 60 seconds / minutes in a hour."

          I think that's also derived from the Babylonians as do the divisions of a circle. But, of course, it was they who had the wit to use a number base that was convenient for integer division rather than an inconvenient one based simply on counting their fingers.

        3. Anonymous Coward
          Anonymous Coward

          Re: So much for digital

          "Thought that was why there was 60 seconds / minutes in a hour. "

          And 360 degrees in a circle.

        4. Anonymous Coward
          Anonymous Coward

          Re: So much for digital

          > Thought that was why there was 60 seconds / minutes in a hour. Because it was easy to work out divide by 2, 3, 4, 5, 6, 10, 12, 15, 20, 30

          And by 37⅙, if you're not too bothered about integer results (or your time source shows serious short-term stability issues).

        5. TimNevins
          Thumb Up

          Re: So much for digital

          Correct. Numbers like 12 and 60 were used by street market traders due to their high level of divisibility.

          This was especially important when buying selling items that could not be easily divided such as fruit/vegetables which would spoil once cut. A cart of 60 apples could be split into 10 different uniform units.

      2. Anonymous Coward
        Anonymous Coward

        Napoleon?

        Metric units came much later than base 10 arithmetic.. metric units match the base 10 positional system, while imperial units don't.

        1. PNGuinn Silver badge
          Headmaster

          Re: Napoleon?

          Pedant.

          Why waste a good opportunity to blame the French?

          He's a pedant. It's Friday. He looks slightly French. >>

      3. Chris G Silver badge

        Re: So much for digital

        Plus carpenters and builders have used the 3.4.5. formula to get a right angle for centuries too.

        Dividers, a piece of string or a length of wood is enough to provide the measurements for building almost anything including round towers and staircases.

      4. Dazed and Confused Silver badge

        Re: So much for digital

        > Whilst I work (measure and cut) in mm

        Is this for lengths or cross sections?

        I was amused to note when ordering a replacement thermostat for my posh German shower that the fittings are 3/4" ones.

    2. Pen-y-gors Silver badge

      Re: So much for digital

      Obvious. Using base 10 evolved because we have 10 digits (most of us). Using base two reflects the decline in education standards, which means that many people count hands rather than fingers.

      Of course, binary is also handy for smart-arse techies because we can count to 1023 on our fingers.

      1. DailyLlama

        Re: So much for digital

        1024 if you undo your fly

        1. Anonymous Coward
          Anonymous Coward

          Re: So much for digital

          Or 2047?

          Oh well, there are 10 types of people in the world.

        2. Doctor Syntax Silver badge

          Re: So much for digital

          "1024 if you undo your fly"

          No, that would be 2047.

          1. Anonymous Coward
            Anonymous Coward

            Re: So much for digital

            > No, that would be 2047.

            Depends on how much youthful vigour you have left.

        3. Pen-y-gors Silver badge

          Re: So much for digital

          1024 if you undo your fly

          No, 2047! But only if you're a bloke.

          1. herman Silver badge

            It is getting nippy

            Well, the ladies win. They can use their nips.

        4. Allan George Dyer Silver badge

          Re: So much for digital

          @DailyLlama - Downvoted for:

          1) sexism

          2) Failure to calculate 2^11-1

        5. This post has been deleted by its author

        6. Borg.King

          Re: So much for digital

          1024 if you undo your fly

          That must be your least significant digit.

        7. wayne 8

          Re: So much for digital

          That's sexist. Check your male patriarchal privilege in a safe space.

        8. Someone Else Silver badge
          Coat

          Re: So much for digital

          1024 if you undo your fly

          Uhhh...that would be 2047. Or maybe -1024? (Possibly depending on the stiffness of the digit...)

        9. herman Silver badge

          Re: So much for digital

          Hey don't be so misogynistic. How must the lady vultures feel now?

        10. Anonymous Coward
          Anonymous Coward

          Re: So much for digital

          Big or little Endian?

      2. Jos V

        Re: So much for digital

        Well, it might be because we have 10 fingers, but in the older days, trades folks used their thumbs to count the phalanx bones of the fingers. 12 on each hand, for a total of 12 x 12 =144.

        1. Justin Clift

          Re: So much for digital

          Interesting. With that method, using one hand to count units (up to 12), and the other hand to count the groups of 12... it's possible to count up to 60 using your hands.

          Hadn't realised that before, but it makes sense as to a practical way to count up to 60 in early historical times.

          1. Charles 9 Silver badge

            Re: So much for digital

            It's entirely possible to handle 0-9 with just one hand. Use the same system with the other hand and you can do 0-99 easily.

      3. Anonymous Coward
        Anonymous Coward

        Using base 10 evolved because we have 10 digits

        @Pen-y-gors

        I was waiting for someone to post that.

        Therefore if the Babylonians used base 60 they had 60 fingers.

        There we have it, proof Aliens built the pyramids and I didn't even need my trusty hat.

      4. Joe Harrison Silver badge

        Re: So much for digital

        You can do better than 1023 if you count up to 2 on each finger, I mean finger down = 0, finger halfway up = 1, finger completely up = 2. You could probably have even more finger positions but then it gets confusing.

        1. handleoclast Silver badge

          Re: So much for digital

          @Joe Harrison

          You are using ternary (or trinary) digits. Confusingly abbreviated as "tits."

    3. Doctor Syntax Silver badge

      Re: So much for digital

      "why has the modern world moved so far towards pure binary (and powers of 2 in specific contexts)?"

      Imperial measurement made considerable use of binary. Weights from pounds down to drachms were binary as were volumes from gallons down to gills. In general they seem to have been based on measures which were a convenient size for some purpose with a strong inclination to subdivide on a binary basis. It's a natural thing to do. If you have a standard of weight, for instance, you can weigh out that amount of sand, flour or whatever on scales and then, using the same scales, divide that into two equal portions and subdivide further.

      The problem arises when two different scales of measurement overlap and we end up with a stone of 14 pounds. Other stones were available - I've seen reference to a stone of 15lbs in the C18th - but I suppose a atone of 16lbs would have required too much adjustment to reconcile with the larger scales in use for other purposes.

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