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Sunday, July 19, 2009

The Mystery of Arabic Numerals

Like most people educated in the West, I was always told from a very early age that there were two major number systems in the world, Roman numerals and Arabic numerals. The Roman numerals were lightly touched upon as their use in modern times have been relegated to fancy clocks and copyright dates at the end of movies. All of those X's, L's, V's, C's and M's are rarely seen anymore much less understood. Like Latin, it is the numerical equivalent of that dead language (why the Latin language died is also a mystery to me). There is a good reason for the Roman numerals' demise which I will cover later.

So my whole life I thought that I had been using Arabic numerals on a daily basis. My watch, my speedometer, my electronic calculator, my bank statement, etc., were all in Arabic numerals, or so I thought until moving to the Middle East.

Take a look the photo above of a bi-numeral pay telephone keypad and you will immedeately see that REAL Arabic numerals look nothing like the ones I had come to know and love. The 1 looks kind of like a 1, the 2 and 3 bear no resemblance to the ones I am used to, the 4 looks like a backwards 3, the 5 a zero, The 6 a shaky 7, the 7 a V, the 8 a tent, the 9 looked vaguely familiar and the poor zero is nothing but a dot.

This surprised me as I thought that living in the middle of Arabia I would at least recognize the digits, after all that's what I was learning according to my educators from a very early age. Written Arabic is equally inscrutable. Like Japanese, it is written and read from right to left, but the cruel twist is that the numbers are written and read from left to right. Are you still with me?

A quick internet search revealed that India initially developed the current number system we all use. Indian mathematicians invented the concept of "zero" as a place holder and the concept of "positional notation" which simply means that a number positioned to the left of another number has 10X (in a base 10 system) the value of the number to its right. The zero acts as a place holder with no value but it moves the leftmost number one or more positions to the left which increases that number's value by 10X. For example: we all know the number 23 to mean 2 tens and 3 ones, add a place holder zero in the middle and the valueless zero promotes the 2 to represent 2 hundreds and three ones....203.

Well, this concept proved invaluable to the development of higher mathematics and spread Westward where some Arabian mathematicians developed algebra (the fiends!) and eventually the Western countries caught on to this better idea as a lot of them were still using Roman numerals which were very limited in mathematical utility.

The reason the Roman numeral system was flawed was that although it was a decimal system using 10 symbols (I-X....1 to 10) there was no zero to act as a place holder therefore there was no orderly way to multiply the numbers, no positional notation. IX=9 even though the I was to the left of the X, it subtracted from instead of neatly multiplying the number to the right 10X as the Hindu-Arabic system did. This made advanced mathematics unwieldy for the Roman system and it was quickly abandoned.

Because of its utility, the Hindu-Arabic system quickly spread Westward and became the world standard. The symbols for Hindu-Arabic numbers morphed into what we commonly recognize today in Western countries (0-9), but it is cool to see the original symbols still in use here in the Middle East!

One caution: at 2AM after several lagers in a dark pub, one would be advised to count the dots (zeros) on the local Dirham bills used to pay the tab. Those dots to the right are easy to miss in a dim light with compromised vision and will provide an expensive lesson in the role of zeros in positional notation when one pays a 50 Dirham tab with a 500 Dirham note. Ask me how I know!
See the corner of a 200 UAE Dirham bill above.


nikita said...

as I understood from your post indian and arabic numbers are the same. I was also wonder about the numbers in the middle east and heard the "indian" version, but when i was talking to an indian guy who was stydying with me he told that they were using different numbers in india. He told that the numbers in india differs either from used in europe or from used in arabic.. so the third one ))

Ace said...

India developed the concepts of modern number systems with the invention of the zero and positional notation which the Roman numeral system that Europe used at the time didn't have.

While India invented the CONCEPTS, each region has different symbols for each number. Indian numbers look different from Arabic numbers that look different than the numbers the West uses. We all share the same underlying system though.

I hope this clears things up!