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World's Oldest Decimal Multiplication Table Discovered

ananyo writes "From a few fragments out of a collection of 23-century-old Chinese bamboo strips, historians have pieced together what they say is the world's oldest example of a multiplication table in base 10. Each strip is about 7 to 12 millimeters wide and half a meter long, and has a vertical line of ancient Chinese calligraphy painted on it in black ink. The bamboo pieces constitute 65 ancient texts and are thought to be among the most important artifacts from the Warring States period before the unification of China. But 21 bamboo strips contained only numbers and, on closer inspection, turned out to be a multiplication table. As in a modern multiplication table, the entries at the intersection of each row and column in the matrix provide the results of multiplying the corresponding numbers. The table can also help users to multiply any whole or half integer between 0.5 and 99.5. The researchers suspect that officials used the multiplication table to calculate surface area of land, yields of crops and the amounts of taxes owed."

26 of 86 comments (clear)

  1. The ancients by cold+fjord · · Score: 5, Insightful

    It is fascinating that we continue to find artifacts from the ancient world that show far more sophistication that people today generally realize. This finding is one. The Antikythera Mechanism is another. I recently read a fascinating article about ancient Roman military medicine which was so advanced that it was not equaled in some ways until the 1900s. I have little doubt that there is much more to be found. Our ancestors could be quite astonishing in their abilities, and very human in their flaws.

    --
    much of left-wing thought is a kind of playing with fire by people who don't even know that fire is hot - George Orwell
    1. Re:The ancients by cold+fjord · · Score: 4, Interesting

      If you happen into a library that carries Military History magazine you may want to read the Roman medicine article, it is fascinating. Just one tidbit:

      The Best Medicine

      On average the Roman medical corps saved the lives of 70 percent of the wounded that reached the field hospital, a survival rate not equaled until the 1904-05 Russo-Japanese War

      --
      much of left-wing thought is a kind of playing with fire by people who don't even know that fire is hot - George Orwell
    2. Re:The ancients by l0ungeb0y · · Score: 2

      Are you saying that with the rise of Christianity (hello dark ages) that viewed the use of any sort of practical medicinal knowledge and the dissection of human corpses as "devilry" and "witchcraft" had no effect on the general knowledge and practice of medicine?

      There's a damn good reason why the Christian image of a witch depicts and old lady brewing "strange concoctions".
      And there's a damn good reason why "Doctors" were using leeches for damn near everything during the Age of the "Enlightenment"

      It's because the barbarian followers of Jesus were morons without a fucking clue and we lost that knowledge and much more.

    3. Re:The ancients by cold+fjord · · Score: 2

      The article describes a number of innovations the Romans had that weren't copied or equaled for centuries.

      --
      much of left-wing thought is a kind of playing with fire by people who don't even know that fire is hot - George Orwell
    4. Re:The ancients by Laxori666 · · Score: 4, Funny

      You are implying he should read the article before reaching for his keyboard and spouting off the first thought that comes to his self-evaluatedly brilliant mind? You expect too much sir!

    5. Re:The ancients by godrik · · Score: 3, Insightful

      It is fascinating that we continue to find artifacts from the ancient world that show far more sophistication that people today generally realize. This finding is one.

      While I aggree with your first sentence. The second one is puzzling to me. I find it natural that some people understood the concept of multiplication at that time. It is not very old, it is essentially 200BC. There was plenty of commerce, armies and large government at that time which uses lots of multiplications. Pythagoras' work is about 300 years older than that and is much more complex than multiplications.

      It is nice to have the artifact, but it is not very surprising IMHO.

    6. Re:The ancients by cusco · · Score: 5, Interesting

      The Incas (and other Mesoamerican peoples) were doing BRAIN SURGERY before the arrival of the Spanish barbarians. Their style of warfare was to incapacitate the enemy soldiers, then heal them, because what was the purpose of taking over territory if there was no one left to work the land? The weaponry was mostly clubs and slings of various types, which created a lot of head injuries and broken bones that were then healed so that the ex-soldiers could go back to the fields. They really didn't understand the Spanish when they came and killed, and killed, and killed everything that moved. They didn't have the historical background of the glorious Age of Chivalry, where if a European lordling had designs on a neighbors territory he sent his mercenaries to kill all the neighbors peasants, so that there was no one to take in the harvest and the neighbor's mercenaries would defect when he couldn't pay them. In contrast most of the participants of an Incan battle survived, a bit worse for wear but alive and able to work.

      --
      "Think about how stupid the average person is. Now, realise that half of them are dumber than that." - George Carlin
    7. Re:The ancients by Nutria · · Score: 2, Insightful

      And there's a damn good reason why "Doctors" were using leeches for damn near everything during the Age of the "Enlightenment"

      Sure: because Galen said so.

      It's because the barbarian followers of Jesus were morons without a fucking clue and we lost that knowledge and much more.

      Or... it was because Augustine of Hippo crawled so far up Aristotle's ass (men have more teeth than women and so men obviously are superior) that the Church only considered a need to think about maybe crawling out 1900 years later.

      Thank goodness for those Evil Crusaders, though, looting Arab libraries and bringing Greek, Roman & Islamic ideas back to Europe.

      --
      "I don't know, therefore Aliens" Wafflebox1
    8. Re:The ancients by gstoddart · · Score: 2

      hahaha. Medicine was largely unchanged during that time. Wasn't until the end of the 19th century before actual science started being applied to medicine, for the most part.

      Don't think for one minute the acients people weren't using stuff like science.

      Just because the West went through the dark ages and rooted around in the muck for a couple of centuries, there was an awful lot of things people knew before.

      There's a reason why Latin is still the language of science. And there's also a reason why several thousand years ago people had some pretty sophisticated cultures.

      That the Church made everybody live for a few centuries with little or no advancement doesn't mean it didn't happen before, or elsewhere. But there's plenty of things we are still learning that ancient cultures had that we didn't think they would.

      --
      Lost at C:>. Found at C.
    9. Re:The ancients by icebike · · Score: 2

      Since the article is not available on-line (or even in google books) what else can be expected?

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      Sig Battery depleted. Reverting to safe mode.
    10. Re:The ancients by umafuckit · · Score: 2

      Good call! The Antikythera Mechanism is from more or less the same period (about 2100 years ago) as these multiplication tables yet it was a very sophisticated mechanical calculator. The Mechanism is currently on display in the Athens Archaeological museum. If you ever have the opportunity: you should go. It's very well displayed and is shown alongside modern replicas (not all the parts were found so some creative reconstruction was necessary) and movies of it working. Furthermore, the Mechanism was just one find out of many from the Antikythera Shipwreck. The other significant finds are also shown in the same exhibit. There's some really stunning bronze art there. There's info and a video here: http://www.antikythera-mechanism.gr/ It says there that the exhibit closes this month, but I was there in September and at the time there was printed material with dates indicating that the exhibit should already have ended. So maybe they're keeping it going indefinitely. This is Greece, so who knows. There's also the Mycenaean room in the same museum which is full the most stunning jewellery, art, etc from about 1,500 BC.

    11. Re:The ancients by K.+S.+Kyosuke · · Score: 2

      Well, apparently, I hit jackpot with magzdb since I posted that. ;) Now let me bury myself in comparing sources.

      --
      Ezekiel 23:20
    12. Re:The ancients by DNS-and-BIND · · Score: 2

      So...I can't help but notice you left the word "slavery" out of your description of the glorious Incan Empire. Huh. That's odd, why could that be?

      --
      Shutting down free speech with violence isn't fighting fascism. It IS fascism!
  2. Re:The researchers suspect that... by bob_super · · Score: 2

    By opposition to what, homework?

  3. Re:China, it figures... by K.+S.+Kyosuke · · Score: 5, Insightful

    And who's surprised it wasn't found in Africa?

    I, for one, would be really surprised if an ancient Chinese multiplication table were discovered in Africa.

    --
    Ezekiel 23:20
  4. Re:Chinese also used hexadecimal... by VortexCortex · · Score: 2

    Waiting for the next Indiana to thus discover a two thousand year old computer! Evidence of those time travellers we heard recently about on /.

    Their mathematics may have been more advanced than we guessed, but I'm pretty sure they didn't have time machines in 14AD. It would be an amazing feat to be that old and still working. Sometimes symbols change in sound over time, with the emphasis on intonation I wonder if linguists would still be able to talk to a computer from so long ago, before audio recordings. It would be interesting to find out if they had a Y0K crisis, and exactly how they worked, what they ate, who they were related to...

    Wait, we're talking about the operator of this tablet, right?

  5. Re:The researchers suspect that... by Anonymous Coward · · Score: 2, Insightful

    Well, the researchers probably know better than you, bob_super.

    Not likely. Most of the "science" here is just doing things like surveying and dating objects.
    Figuring out what things were used for is usually a matter of Wild Speculation, heavily influenced by the "researchers'" own personal prejudices, which is then taken as Truth until someone finds some actual evidence. Usually the evidence proves the speculation was complete bullshit.

    Yes, a multiplication table COULD be used for figuring crop yield. It could also be used for figuring logistics for an army. Or calculating how many sex slaves are needed for an upcoming party. Real science is far less concerned about what it COULD be used for an more interested in what it actually WAS used for. In this case, they have no idea what use DID occur, so they're speculating with nothing to back it up.

    Thus, bob_super's opinion is likely to be just as close to the truth as the "researcher"'s opinion.

  6. Re:This is impossible by Anonymous Coward · · Score: 2, Funny
    That is EXACTLY what I am saying. That computer you're using? It owes everything to NASA and the Apollo project. No space, no computers. That simple. All those people before 1957? All just single-celled mouth breathers. Space came along, THEN the human species got smart.

    No one was smart before space. Only space provides the proper stimulation and motivation for progress. War? Please. You don't actually believe all those stories from WWII about computers, encryption, jet engines, radar, nuclear bombs? Come ON. No one is that smart. But you put a test pilot in a rubber suit?

    Boom. Spinoffs. Right there.

  7. I really don't find this surprising by BeanBagKing · · Score: 4, Interesting

    I mean, Babylonians were doing this (granted in a different base) some 1,500 to 2,000 years prior. That's a long time. If nobody, between then and 600(ish) BC thought of doing the same thing, I would lose hope in the creativity of humans. So this really doesn't surprise me, it's not like they were idiots back then.

  8. Re:China, it figures... by Forty+Two+Tenfold · · Score: 5, Interesting

    Well, those primitive African tribes went far beyond that. They invented fractals.

    --
    Upward mobility is a slippery slope - the higher you climb the more you show your ass.
  9. Characters by manu0601 · · Score: 4, Interesting

    What is impressive is how the characters hardly evolved since that time. The picture is not easy to read, but it seems that only 7 and 9 are different from modern characters.

  10. Re:The researchers suspect that... by icebike · · Score: 4, Interesting

    I tend to agree. Just as likely a schooling aid as something actually used day to day.

    Someone wrote a sifi short story about the anthropologists far in the future speculating about the religious cult of the rings, and the tossing of rings as a penance for personal transgressions. He speculated that people wore the rings as disposable penance, to be cast at the scene after self inflicting a minor cut of penitence. Each ring seemed sized just right to fit over a finger, and had a semi sharp spoon shaped attachment for self flagellation.

    Nothing else could explain the wide scattering of these things all over the world.

    They were called by the name of the Deity to which they were related: Pop Tops. The sect died out after a while.

    --
    Sig Battery depleted. Reverting to safe mode.
  11. Re:The researchers suspect that... by Anonymous Coward · · Score: 2, Insightful

    Since you can't spell "sci fi" (or scifi, if you like) your opinion is hereby annulled.

  12. It isn't war, but money by Taco+Cowboy · · Score: 2, Interesting

    Chinese don't like war too much. They are not a warring tribe.

    However, they love money.

    Ask any Chinese, and I mean, any Chinese and you will find each and every single one of them love money.

    How I know ? I am a Chinese.

    The multiplication table wasn't the only Chinese invention. The ancient Chinese also invented the Abacus ( http://eileen-lian.com/wp-content/uploads/2009/09/abacus-1-AJHD.jpg ) because they needed something to count their money.

    --
    Muchas Gracias, Señor Edward Snowden !
    1. Re:It isn't war, but money by wonkey_monkey · · Score: 4, Funny

      you will find each and every single one of them love money.

      How I know ? I am a Chinese.

      All British people think that's a bit of a generalisation.

      --
      systemd is Roko's Basilisk.
  13. Re:Chinese also used hexadecimal... by ObsessiveMathsFreak · · Score: 2

    Hexadecimal nothing! And you can can leave aside these tables as well. The Ancient Chinese were able to solve linear systems using Guass Elimination. Most undergraduate still aren't able to do that.

    I personally suspect that many of our basic and even advanced mathematical methods are much older than we assumme. Much, much older.

    --
    May the Maths Be with you!