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## World's Oldest Decimal Multiplication Table Discovered86

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."
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## World's Oldest Decimal Multiplication Table Discovered

• #### The ancients (Score:5, Insightful)

on Tuesday January 07, 2014 @07:42PM (#45893125)

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 [livescience.com] is another. I recently read a fascinating article about ancient Roman military medicine [historynet.com] 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.

• #### Re: (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.

• #### Re:The ancients (Score:4, Interesting)

on Tuesday January 07, 2014 @08:14PM (#45893335)

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 [historynet.com]

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

• #### Re: (Score:1)

...which could simply mean that in the centuries before the R-J war, we were using more lethal weapons. Or something about the transport of the wounded. Without context, this number might be indicative of nothing really useful.
• #### Re: (Score:2)

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

• #### Re:The ancients (Score:5, Funny)

on Tuesday January 07, 2014 @08:33PM (#45893499) Homepage
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!
• #### Re: (Score:3)

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

• #### Re: (Score:3)

Well, apparently, I hit jackpot with magzdb [magzdb.org] since I posted that. ;) Now let me bury myself in comparing sources.
• #### Re: (Score:1)

by Anonymous Coward

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 [historynet.com]

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.

• #### Re: (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.

• #### Re: (Score:2)

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.

• #### Re: (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

• #### Re: (Score:1)

That's triage. [wikipedia.org] Also part of medicine and also re-developed in XXth century.
• #### Re: (Score:3)

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 becau

• #### Re:The ancients (Score:5, Interesting)

<brian...bixby@@@gmail...com> on Tuesday January 07, 2014 @09:18PM (#45893785)

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.

• #### Re: (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?
• #### Re: (Score:2)

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...
• #### Re: (Score:2)

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.

• #### Re: (Score:3, 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 [wikipedia.org].

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.

• #### Re: (Score:3)

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 th

• #### Re: (Score:2)

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

• #### Re: (Score:1)

I'm not saying it was aliens...but it was totally aliens!
• #### Re:The ancients (Score:4, Insightful)

on Tuesday January 07, 2014 @08:49PM (#45893617)

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.

• #### Re: (Score:2)

> 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: "Macaula

• #### Re: (Score:3)

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 on
• #### Re: The ancients (Score:2)

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.
• #### The dumbing down of Slashdot (Score:1, Interesting)

by Anonymous Coward

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 shoul

• #### Re: The dumbing down of Slashdot (Score:1)

Yes, this. The level of arrogance here can be amazing.
• #### Chinese also used hexadecimal... (Score:2)

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 /.

• #### Re: (Score:3)

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, w

• #### Re: (Score:3)

Hexadecimal nothing! And you can can leave aside these tables as well. The Ancient Chinese were able to solve linear systems using Guass Elimination [ncsu.edu]. 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.

• #### I really don't find this surprising (Score:4, Interesting)

on Tuesday January 07, 2014 @09:21PM (#45893811)
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.
• #### Characters (Score:5, Interesting)

on Tuesday January 07, 2014 @10:04PM (#45894009)
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.
• #### Math is hard! (Score:1)

Who decided to use a hexadecimal multiplication table as the lead image for a story about base-10 multiplication tables?
• #### Decimal pah (Score:1)

All their bases are belong to us

• #### Get over with it... (Score:1)

The China at the time was India...!!
• #### 27600-Month-old Chinese bamboo strips... (Score:2)

See, I can be a moron too.

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