LATIN VIA FABLES: AESOPUS

Aesop's Fables... in Latin!

Ning Diary: Jan. 26 - Roman counting game

Synchronicity: just last night I was showing somebody this game AND this morning someone wrote and asked me to explain it to her again... which is the perfect excuse to publish it here.

Just like we do, the Romans counted on their fingers. The Roman numerals I, V and X are NOT letters. They may look like letters... but they are not! They are symbols for fingers of the hand and/or for notches made on sticks (compare our tally system of IIII with the fifth mark being a diagonal through the group, and then starting a new group of five next to it). So, you can think about it this way:

I is one finger
II is two fingers
III is three fingers
IIII is four fingers
V can be seen as five fingers (a schematic outline view of "V" made by a hand with all fingers extended; see below - it just looks like the letter V)
X is two sets of five, one above and one below (it just looks like the letter X, but it's really two Vs, one up and one down)

The use of "IV" to indicate 4 came later, and IIII continued to be used as a representation of the number 4 (it makes sense, doesn't it?).

Now learn how to multiple numbers 5 and higher using finger counting! Here is an illustrated guide to the Roman counting game which lets you multiply numbers 5-9 on your fingers. Showing the numbers 1, 2, 3, or 4 with your fingers is easy; you just hold up that number of fingers. To be able to do this trick, you also need to know how to show the numbers 6, 7, 8 and 9 with ONE HAND ONLY, being able to show those numbers with either your left or your right hand. Here is how it goes:

LEFT
RIGHT
To show the number 5,
hold no fingers down,
palm facing you, so all fingers are extended;
here is how the number 5 looks when made with your left hand, and with your right hand:
To show the number 6,
hold one finger down,
palm facing you;
here is how the number 6 looks when made with your left hand, and with your right hand:
To show the number 7,
hold two fingers down,
palm facing you;
here is how the number 7 looks when made with your left hand, and with your right hand:
To show the number 8,
hold three fingers down,
palm facing you;
here is how the number 8 looks when made with your left hand, and with your right hand:
To show the number 9,
hold four fingers down,
palm facing you;
here is how the number 9 looks when made with your left hand, and with your right hand:

To multiply, do the numbers with both hands, and then COUNT the number of fingers down and multiply those by 10, and then MULTIPLY the number of fingers standing up, and then add the two numbers:

6 multiplied by 7:

3 fingers down = 30
4 x 3 fingers up = 12

TOTAL 42

9 multiplied by 9:

8 fingers down = 80
1 x 1 fingers up = 1

TOTAL 81

7 multiplied by 8:

5 fingers down = 50
3 x 2 fingers up = 6

TOTAL 56

8 multiplied by 5:

3 fingers down = 30
2 x 5 fingers up = 10

TOTAL 40

Try some more - it works!

I learned this trick in a medieval Latin graduate seminar, and I recall somehow that the source was the venerable Bede. Does anybody know exactly where to find that in Bede? I'd love to know more about how math was done with Roman numbers in general - if anybody has reading suggestions for that, online or in print, please leave a comment here! :-)

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Comment by Laura Gibbs on January 26, 2009 at 2:39pm
From Mark Bordelon over at the LatinTeach list, an algebraic demonstration!

OK. There's how it works: First of all some notation. Fingers down on one hand will be D1 and fingers down on the other hand will be D2. To show a number five and up on either hand you lower a finger. Increasing the amount of lowered fingers increases the value of the hand. The product of two numbers using the notation above looks like this: (5 + D1) (5 + D2), which, multiplied out, gives
25 + 5D1 + 5D2 + D1D2 (Equation 1)
Now the method of reading the result combines notions of fingers down and fingers up, which are related like this (U = "up"): U1 = 5 - D1 and U2 = 5 - U2.
The product is supposedly the sum of downed fingers times 10 plus the product of the up fingers, using our notation:
10 * (D1 + D2) + (5 - D1) (5 - D2),
which, multiplied out, gives
10D1 + 10D2 + 25 - 5D1 - 5D2 + D1D2
which is equivalent to
5D1 + 5D2 + 25 + D1D2 (Equation 2)

Comparing these two expressions (Equation 1) and (Equation 2) shows that they are identical quantities.

QVOD ERAT DEMONSTRANDVM (whoo hooo...get to USE that!)

Gratias agamus Marco!!!!!!!
Comment by Laura Gibbs on January 26, 2009 at 1:51pm
HOW COOL. But then he has the benefit of Arabic numerals - which he credits very admirably!
Tandem Arabes excogitarunt ingeniose Cifras decem: 0 1 2 3 4 5 6 7 8 9
What's interesting, too, is that Comenius does refer to the Roman numerals as letters, as if they were somehow comparable to the Greek use of letters for numbers, when they are not at all -
Romani septem literas adhibuerunt: I V X L C D M
Greek use follows Hebrew use, actual alphabetic characters used to represent numbers - but the Romans had symbols that LOOKED like letters (and were increasingly made to look like letters, as the odd history of L and D both show) ... it's interesting that Comenius was not more aware that they only look like letters, rather than actually being letters - that's the biggest clue, of course, because once you know that C is centum and M is mille, you see that the "wrong" letters are being used for unum, quinque, decem etc. :-)

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