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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."

50 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.

    --
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    1. Re:The ancients by geekoid · · Score: 1

      The difference between people then and people now is almost entirely culture.

      " which was so advanced that it was not equaled in some ways until the 1900s
      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.

      --
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    2. 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
    3. 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.

    4. 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
    5. 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!

    6. 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.

    7. 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.

      --
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    8. Re:The ancients by Anonymous Coward · · Score: 1

      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

      Maybe the Romans only brought people to the hospital who they thought had a chance of living.

    9. Re:The ancients by cold+fjord · · Score: 1

      They actually performed a form of triage similar to modern practice, but they also had dedicated medical staff to both treat battlefield wounded and evacuate them. I recommend the article.

      --
      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
    10. Re:The ancients by Forty+Two+Tenfold · · Score: 1

      That's triage. Also part of medicine and also re-developed in XXth century.

      --
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    11. Re:The ancients by UnknownSoldier · · Score: 1

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

      Uh, not to be condescending, but try reading more. :-)

      "The easiest form of parochialism to fall into is to assume that we are smarter than the past generations, that our thinking is necessarily more sophisticated. This may be true in science and technology, but not necessarily so in wisdom."

      That quote is from the introduction to this brilliant essay: "Macaulay on Copyright"
      http://www.kuro5hin.org/story/2002/4/25/1345/03329

    12. 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.

      --
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    13. 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.

      --
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    14. 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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    15. Re:The ancients by icebike · · Score: 1

      Yeah, so what?
      Selecting only those you can save, by simple expedients of cauterizing wounds while the rest aren't even removed from the battle field is not exactly the best medicine, but it helps your "patients saved" stats, especially when the badly wounded never darken your door.

      Triage is not medicine.

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    16. 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.

    17. 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
    18. Re:The ancients by cold+fjord · · Score: 1

      Triage is a critical function that supports battlefield medicine especially in mass casualty events. Pretty much any ancient battle is going to be a mass casualty event. If you don't do triage you will end up wasting limited medical resources and losing more lives and limbs than you would if you had done it properly. Roman medicine was much more sophisticated than simple expedients. The Romans weren't doing to for the purpose of "stats," but to save lives and return trained soldiers to duty. They were more successful at it than other peoples for more than a millennia after the fall of the empire.

      --
      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
    19. Re: The ancients by clickclickdrone · · Score: 1

      On the other hand, I don't find any of this very suprising. At school we learned all about various ancient civilizations gong back thousands of years, Romans, Greeks, Egyptians, Chinese etc so grew knowing all about the amazing things they got up to and the things they invented across science, engineering, medicine etc. Jarred Diamond has some good books on this.

      --
      I want a list of atrocities done in your name - Recoil
    20. 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!
    21. Re:The ancients by dargaud · · Score: 1

      It was rather implied. In contrast the Aztec empire wanted the loosing soldiers to survive just long enough so that they would have open heart surgery on top of a pyramid...

      --
      Non-Linux Penguins ?
    22. Re:The ancients by minstrelmike · · Score: 1

      Wasn't until the end of the 19th century before actual science started being applied to medicine, for the most part.

      Not really. If you regard science as experimentation method invented by Bacon and DesCartes, then yes.
      But if we're talking about medically experimenting on slaves and then trying the procedures on kings, that process has occurred in ancient Egyptian and Peruvian Inca times. The whole point of ethnobotanists investigating the medicines of indigenous peoples is based on the extensive knowledge our ancestors gained.

      There are many ways to learn about the physical world and modern technology is not needed for all of them.

    23. Re:The ancients by cusco · · Score: 1

      There were very few societies in the world that didn't practice slavery at the time. I didn't mention that people believed the sun went around the Earth either, it was as unnecessary to the post as mention of slavery was.

      --
      "Think about how stupid the average person is. Now, realise that half of them are dumber than that." - George Carlin
  2. Re:The researchers suspect that... by geekoid · · Score: 1

    No, he is saying the maybe this was a tool to aid them.

    --
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  3. Re:The researchers suspect that... by ebno-10db · · Score: 1, Flamebait

    Didn't you see that it could be used for taxes? We'll have half a hundred teabaggers piling on before you can say Ayn Rand.

    Thus showing that math is a Statist conspiracy.

  4. The dumbing down of Slashdot by Anonymous Coward · · Score: 1, Interesting

    300BC is anything but a pre-historic era. Do the owners of Slashdot REALLY think you are that thick? Do any of you think that the great achievements of that period could occur WITHOUT the ability to do simple maths, like multiplying numbers?

    Strict base number counting systems are arbitrary. Knowledge of one is knowledge of all of them, yet only a few weeks ago we had the humiliatingly cretinous suggestion that BINARY could be invented AFTER the concept of base number systems was understood. Even betas should be above the propaganda ploy that goes "you are geniuses, but your ancestors were know-nothing thickos". Every salesperson knows that the most idiotic 'marks' are those that fall for simple flattery.

    What is true, when you go back far enough, is that practical maths skills would frequently have been treasured as 'industrial secrets' by collectives or guilds or the like- and there was little widespread desire to universally educate the 'common man'. This did NOT mean things were not known, simply that some knowledge remained well known only amongst certainly tightly knit groups of people. It was, recall, the age of the printing press that changed this situation. Before the printing press, replication of written material was painful and costly.

    Google "Antikythera mechanism". If this device had not been discovered, and I said here the people of 100BC had the ability to make such a computer, the usual vile shills would immediately reply, calling me a "tin foil hat wearing conspiracy theorist". The scum who tell you betas to be 'amazed' at the idea of Humans multiplying two numbers together want you to be this dumb and uninformed about levels of Human achievement in the past.

  5. Re:The researchers suspect that... by bob_super · · Score: 2

    By opposition to what, homework?

  6. 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
  7. Chinese also used hexadecimal... by ChunderDownunder · · Score: 1

    According to wikipedia at least.

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

    1. 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?

    2. 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!
    3. Re: Chinese also used hexadecimal... by minstrelmike · · Score: 1

      I believe the poster is talking about a one-way time machine, one that can only move you into the future faster.
      So far, each of those has merely resulted in the untimely death of the inventor ;-)

  8. 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.

  9. 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.

  10. 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.

    1. Re:I really don't find this surprising by hawkfish · · Score: 1

      When thinking about human abilities way back when it's useful to remember St. Ambrose.

      Living around 400AD, St Ambrose is reported to be the first human to read without moving his lips.

      Yes, before him, no one thought to read a book without saying the words aloud...

      I don't know about the first. Plutarch records that Julius Caesar had the same skill. (The context is pretty funny too - Caesar was reading a mash note from Cato's sister during a Senate meeting, but Cato thought it was an incriminating letter from an enemy of the state and demanded to read it, much to Cato's embarrassment. The fact that Cato threw it back at him, calling him a drunkard, is also funny because Cato was himself a notorious drunk whose Stoic principles didn't allow him to even buy good wine...)

      --
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  11. 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.
  12. 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.

  13. Re:The researchers suspect that... by icebike · · Score: 1

    My thoughts exactly.

    Sounds to me it like it would just as likely be a teaching aid as a commerce aid.

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  14. 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.

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  15. Math is hard! by NadNad · · Score: 1

    Who decided to use a hexadecimal multiplication table as the lead image for a story about base-10 multiplication tables?

  16. 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.

  17. 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.

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    1. Re: It isn't war, but money by AvitarX · · Score: 1

      Aside from being the "warring states" period, what your post makes me think of most is idiacracy where the guy says something to the effect of "I can't believe you like money too".

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    2. 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.
  18. Re:The researchers suspect that... by icebike · · Score: 1

    Recycling you Neanderthal!

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  19. Get over with it... by freshlimesoda · · Score: 1

    The China at the time was India...!!

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  20. 27600-Month-old Chinese bamboo strips... by DarthVain · · Score: 1

    See, I can be a moron too.

  21. Re:The researchers suspect that... by Impy+the+Impiuos+Imp · · Score: 1

    Way back then, government was just the local warlord who had slaughtered everyone around into submission, and then demanded a cut, which he called "taxes". This continues in many countries to this day.

    Inventing memes that make you feel all warm and fuzzy towards that warlord, as he teaches you you should be grateful to this, was an invention thousands of years in the future.

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