**By Justice Markandey Katju**

### The decimal system was perhaps the most revolutionary and greatest scientific achievement in the ancient world, and it was an achievement of Indians.

The numbers in the decimal system were called Arabic numerals by the Europeans, but surprisingly the Arab scholars called them Hindu numerals. Were they really Arabic or Hindu ? In this connection it may be mentioned that the languages Hebrew, Arabic, Persian and Urdu are written from right to left, but if you ask any speaker of these languages to write any number e.g. 257 he will write the number from left to right.

This shows that these numbers were taken from a language which was written from left to right and not from right to left. It is accepted now that these numbers came from India and they were copied by the Arabs from us, who later passed them on to Europeans.

#### I would like to explain the revolutionary significance of the decimal system.

As we all know, ancient Rome was a great civilization, the civilization of Caesar and Augustus, but if one would have asked an ancient Roman to write the number one million he would have almost gone crazy, because to write one million he would have to write the letter M which stands for millennium (or one thousand) one thousand times.

This is because the Romans wrote their numbers in alphabets, I denoting 1, II denoting 2, III denoting 3, V denoting 5, X denoting 10, L denoting 50, C denoting 100, D denoting 500, and M denoting 1000.

The Romans had no alphabet denoting a number greater than 1000. So if a Roman wanted to write 2000 he had to write MM, if he wanted to write 3000 he had to write MMM, and so on. To write 1 million he would have to write M 1 thousand times.

In fact an ancient Roman started feeling uncomfortable with numbers above 1000.

On the other hand, under our system to express one million we have just to write the number one followed by six zeros.

In the Roman numerals there is no zero. Zero was an invention of ancient India and scientific progress was not possible without this invention.

Let me explain the importance of zero.

The numbers 1,2,3,4, etc do not really exist in the objective Universe. What exists is 1 man, 2 cars, 3 tables, 4 trees, etc. 1,2,3,4 etc are just abstractions.

Now to conceive of 0 men, 0 cars, 0 tables etc required a further abstraction, and a further flight of imagination, which the Europeans never achieved in ancient times.

Many scientific thinkers consider the invention of the decimal system by Hindus the greatest invention ever made by man. Without it modern civilization would be impossible. Thus, in his three volume work, ‘ The Universal History of Numbers ‘, the French scholar Georges Ifrah writes :

“Finally, it all came to pass, as though across the ages and the civilizations, after the human mind had tried all the possible solutions to the problem of writing numbers, before universally adopting the one which seemed the most abstract, the most perfect and the most effective of all. The measure of genius of the Indians, to which we owe our decimal system, is all the greater in that it was they only in all history and of all people in the world to have achieved this triumph “.

I am not going into details about the contributions of our great mathematicians like Aryabhatta, Brahmagupta, Bhaskar, Varahamihira etc. and you can read about them by using Google. However, I may just give two simple illustrations in this connection.

The number 1,000 is called sahastra in the Indian numeral system. If we add two zeroes to it we get 1 lac. By adding two more zeroes we get 1 crore, With two more zeroes we get 1 arab, with two more we get 1 kharab, with two more we get 1 neel, with two more we get 1 padma, with two more we get 1 shankh, with two more we get 1 mahashankh, etc. Thus one mahashankh will be the number 1 followed by 19 zeros (for further details you may see V.S. Apte's Sanskrit English Dictionary on the internet by using Google). Thus, with the use of zero we can write astronomical numbers in very brief.

On the other hand the ancient Romans could not express any number larger than one thousand except by repeating M and the other numerals again and again.

Take another illustration. According to the Vishnu Purana, the Kaliyuga in which we are living consists of 4, 32, 000 years. The preceding Yuga is known as the Dwapar Yuga ( in which Lord Krishna lived ) and is twice as long as the Kaliyuga. Preceding the Dwapar Yuga, is the Treta Yuga ( in which Lord Ram lived ) which is thrice the duration of the Kaliyuga. The Yuga preceding Treta Yuga is the Satyuga which was said to be four times longer than the Kaliyuga.

One Kaliyuga, one Dwapar Yuga, one Treta Yuga and one Satyuga are collectively known as one Chaturyugi (or 43 lacs 20 thousand years). Fifty Six Chaturyugis are known as one Manovantar. Fourteen Manovantars is known as one Kalpa. Twelve Kalpas make one day of Brahma. Brahma is believed to have lived for billions or trillions of years.

When our people do the sankalp, which is to be done everyday by orthodox people, they have to mention the exact day, month and year of the Kaliyuga ( and this date changes daily ) as well as the Chaturyugi, Manovantar and kalpa in which we are living. It is said that we are living today in the 28th Chaturyugi in our present Manovantar, that is to say half the Manovantar of our Kalpa is over, but the remaining Manovantar is yet to be completed. We are living presently in the Vaivasvata Manuvantar.

One may or may not believe the above system, but one can only marvel at the flight of imagination of our ancestors who could conceive of billions or trillions of years in history.

Aryabhatta in his famous book called the Aryabhatiya wrote about algebra, arithmetic, trigonometry, quadratic equations and the sine table. He calculated the value of Pi at 3.1416, which is close to the actual value which is about 3.14159. Aryabhatta's works were later adopted by the Arabs, and then the Europeans.

I am not going into the contribution of the other mathematicians e.g. Brahmagupta, Bhaskar, Varahamihira etc. as that will take too much time.

Many Westerners assume that Indians lack a scientific bent of mind and that their contribution to scientific progress is negligible, but this is false.

The truth is that Indians have a natural aptitude for science, and this is proved by the fact that at one time India was leading the whole world in science. Ancient and medieval scholars of Arabia, Spain, China and Greece acknowledged their indebtedness to Indian science.

Thus, the prominent medieval Muslim Arab scholar Sa’id ibn Ahmad al-Andalusi (1029-1070 ) wrote in his book Tabaqat al-‘umam, one of the earliest books on the history of science :

“The first people in the world to have cultivated science are the Hindus, who are renowned for their wisdom. Over many centuries, all the scholars of the past have recognized the excellence of the Hindus in all branches of knowledge. They have made great strides in the study of numbers and geometry. They have acquired immense information and reached the zenith in their knowledge of astronomy. They have surpassed all other peoples in their knowledge of the medical sciences ''.

I am quoting all this not to gloat over past achievements, but to inspire the Indian people on their onward march, by knowing about the great achievements of their ancestors.

**(Justice Katju is a retired judge of the Supreme Court of India. These are his personal views.)**