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Math in 12th c England

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Alisha Marie Klapheke
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Math in 12th c England

Post by Alisha Marie Klapheke » Wed March 2nd, 2011, 7:58 pm

When did merchants in medieval England begin using Arabic numerals? And what did they do to keep their account books before that time period? I am sadly ignorant on this point and I can't seem to find clear info on this. Help!

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Post by annis » Thu March 3rd, 2011, 2:45 am

It seems that Roman numerals were still being used until later than you'd think, and were certainly still being used in 12th century England, along with the tally stick system for the less literate. By the 1300s, shopkeepers and moneylenders from Japan to England were using the abacus to track sales and calculate interest. The abacus was made up of beads on parallel wires that represented units of one, 10, 100, 1,000, etc. This allowed people to add or subtract large numbers without losing their place.

Arabic numerals were introduced from the east into Italy from the 10th century, and in the 12th century an Italian merchant and mathematician known as Leonardo Fibonacci studied the Arabic numeric system and wrote several books explaining its use. However it was only during the Renaissance period, when humanists translated the mathematical works of the ancients and disseminated them through the newly developed printing press, that the Arabic numeric system became widely used in Europe. The earliest evidence of use of Arabic numerals in England is in the 15th century.

The other change of significance for merchants was the development of the double bookkeeping system during the fifteenth century for recording transactions.
Last edited by annis on Thu March 3rd, 2011, 3:05 am, edited 4 times in total.

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Alisha Marie Klapheke
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Post by Alisha Marie Klapheke » Thu March 3rd, 2011, 7:21 pm

Thanks, Annis. I'm going to take a look at those links. I think the tally mark info is what I need.

Also, do know anything about the finger counting technique used by merchants? I don't know when exactly and to what extent it was used; I only read an article that displayed pictures of the various hand positions and how merchants used it to establish place value with only ten fingers.

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Post by Ash » Fri March 4th, 2011, 12:06 am

Not sure if its relevant, but its possible in American Sign Language to count to 10 on one hand (6 is thumb and pinky, 7 is thumb and ring finger, 8 is thumb and middle finger, 9 is thumb and index finger, 0 is 'o' shaped hand.) So its possible the merchants in that time used one hand i to count out, the other hand used for placement maybe?

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Post by annis » Fri March 4th, 2011, 1:14 am

I hadn't heard of this finger counting technique, but I've just found this article which explains how it works. It does seem to bear some resemblance to Ash's American sign language approach.

Medieval Finger Counting
http://orion.math.iastate.edu/mathnight ... ntleft.pdf

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Post by Margaret » Fri March 4th, 2011, 1:53 am

This is pretty fascinating! It feels so strange to think that people didn't have the concept of zero as a numeral, although of course they did have a concept of "nothing." I wonder if it changed the way people thought in any way to have the concept of zero (other than the obvious ability to calculate large sums more easily).
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Post by annis » Fri March 4th, 2011, 4:37 am

I'm intrigued by this finger-counting system, which it turns out is very old, and was used in both the east and the west with some small differences. There's always something new to learn- fascinating! The Romans used it as a universal commercial sign language, handy when dealing with traders of the many different nations which made up the Roman Empire. The Venerable Bede mentions it, so it was still being used in what we used to call the Dark Ages, and in fact in Europe and England it only really faded from use when the Arabic numeric system became common. It was pretty much finished by the 16th century.

If you want to follow it up, there's quite a bit of history in Number Words, Number Symbols by Karl Menninger. My link is to the Google Book version and from there you can link to the chapter on Finger Counting from the Contents, and there is also a chapter on Tally Sticks.
Last edited by annis on Fri March 4th, 2011, 4:43 am, edited 4 times in total.

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Post by Alisha Marie Klapheke » Fri March 4th, 2011, 5:38 pm

Thanks for the info Annis. Yes I do think the system is similar to American Sign. I'm going to check out that Number Words, Number Symbols article now. I hope they mention something about the church's stance on varying types of mathematics. I know some new ideas were thought of as an evil type of magic. In my WIP, an intelligent, dangerously forward thinking third son training in the priesthood secretly teaches some mathematical concepts to a young woman whom he has befriended. She later uses her skills while working at an inn. I think I'll include the tally sticks in another area--with a textile merchant scene. This is fun!

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Post by annis » Fri March 4th, 2011, 8:19 pm

The Church definitely played a part in the repression of the use of Arabic numerals, and I saw this mentioned somewhere, but of course can't find the reference now! It was a contributing factor in the surprising amount of time it took before the Arabic numeric system became widely used in the West. The concept of "zero" was particularly hard to for people to deal with, I think, and may have seemed somehow sorcerous. However it has been pointed out that professional abacus users were equally responsible for resistance to Arabic numerals, if not more so. They felt threatened by the new system, as it seemed to make their skills redundant. The use of Arabic numerals (or more strictly Hindu-Arabic numerals) was known in North-Eastern Spain from the 10th century, and Italian merchants who moved freely through the Byzantine Empire knew of them. Fibonnaci was the son of an Italian merchant based in North Africa, and he wrote about them in the 12th century. Fibonnaci, btw, was a favourite with the enlightened Holy Roman Emperor Frederick II, who was considered a heretic and arch-enemy of the Church by various popes. Anything coming out of the east was automatically suspect and tainted with the possibility of heresy according to Church understanding.

Apparently there was yet another method of number-notation used in the Middle Ages, a type of shorthand or cipher used by monks to record information. The medieval monks frequently used shorthand/abbreviations in written work as well. It's very interesting to look at a copy of the Domesday Book in its original form. Translators had their work cut out to make sense out of what would have been commonplace abbreviations when it was written.
Last edited by annis on Sat March 5th, 2011, 12:51 am, edited 8 times in total.

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Post by Kveto from Prague » Sat March 5th, 2011, 11:32 am

Annis, you really know everything :-)

its interesting. I do recall (probably while I was half asleep in algebra class) that the concept of zero is a relatively recent (last 1000 years or so) and revolutionary idea that really aided in the spread of arabic numerals.

can you imagine whiting down a telephone number in roman numerals?

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