Numbers and digits
Posted by alhayetamal on 9 December 2007
10+1=11, even a little child at primary school can perform this “simple” mathematical calculation. He can also explain that 10 > 1 because in the first number we have a one on the tens position and in the second number the one is in the units position. But can you convince the little child how it took a very long time for humanity to discover what he consider as a “simple” calculation system. How the Indian was the first to use these digits and to make some relatively big calculation. How Arabs used the same system in the 8th century, developed new mathematical calculation methods and helped it propagating and how it didn’t spread in Europe until the 12th century.
In the Roman numeral system different symbols were used to represent a numerical value. they used I for one, V for five, X for ten, L for fifty, C for one hundred…using these symbols is not adapted for big numbers, in fact representing numbers can become rapidly hard and confusing.
For instance, the number 487 is represented as follow: CCCCLXXXVII. Such representation can not enable using big numbers and does not permit calculations.
On their side, the Indians used only one symbol for every digit and used a positional numeral system to make numbers. In their system, every position has a specific value; the first position on the right is for units the second for tens, the third for hundreds, the forth for thousands…
Using the positional numeral system simplifies too much the representation of numbers. Up to the 6th century, the positional numeral system was used only by the Hindus and the Mayas, therefore they was the only ones able to carry out big mathematical calculations.
But until the year 400, there was no digit representing the naught. To write down the number 408, Hindus put a symbol between the four and the eight to differentiate it from 48, and they called it a hollow. They used to put a dot or a circle in this hollow and then it became a digit, the nought.
In the year 776, after meeting an Indian mathematician and astronomer, the Abbasid caliph, Al-Mansur, ordered to translate numerous books about astronomy and calculations into Arabic. We site as example the book “Sind Hind”. These books helped Arabs to know Indians numbers and the positional numeral system so they started using it. Understanding the new systems needed a lot of effort, but still that it was rapidly spread and used by Arabs.
At the same period, “Al-Khwārizmī”, who is an Islamic mathematician, astronomer and geographer, wrote a little book to explain how to use the Indian system of numeration. He explained the operations of addition, subtraction, multiplication, division and calculating quotients. He also wrote a book about resolving the linear and quadratic equations “al-Kitab al-mukhtasar fi hisab al-jabr wa’l-muqabala” which means “The Compendious Book on Calculation by Completion and Balancing”. This book was first translated into Latin in the twelfth century, and the word algebra is derived from the name of the book.
Thanks to the books of Al-Khwārizmī, the west learnt how to use digits and to make calculations. Note that the word “algorithm” derives from the name of this mathematician.
Shams al-‘Arab tasta‘ ‘ala al-Gharb – Arabic translation of the book “Allahs Sonne über dem Abendland” – Sigrid Hunke