Indian Mathematics: Invention of Zero
We Indians are very proud that zero was invented in India. Most people are under the impression that nobody knew about zero before Indians came up with the concept, however that is not exactly true. In this article lets learn the details about zero and clearly understand what contribution ancient Indians made towards the concept of zero and why is it very important.
The term “Zero” comes from the Arabic word “Sifr” which come from the Sanskrit word “Shunya”. Shunya as most Indians know philosophically means empty or Void. Considering zero to be a mathematical quantity that represents nothing then such a zero has been present in many other cultures. Ancient Egyptians represented such a zero with a word “nfr”. In the late Mesopotamian culture the zero was represented by two slanting parallel lines and was used as a place-holder indicating nothing here. Ancient Chinese had zero represented as an empty space again indicating the presence of nothing. The only civilization, which did not make much use of the zero were the Greeks who were mostly inclined towards geometry. Greeks were not very arithmetically inclined as they considered it to be associated with relations of equality and therefore an activity of the slaves.
The zero that comes closest to Indian zero is the Mayan zero, however more on that later. Lets first understand what is so special about Indian zero and why did such a zero was invented in India out of all the other places. To understand this lets get a little bit into Indian philosophy and metaphysics. According to Hindu philosophy this world goes through various cycles which are called Mahayuga. Each Mahayuga consists of four Yugas, Satya Yuga, Treta Yuga, Dwapara Yuga and Kali Yuga with the time span of 1728000, 1296000, 864000 and 432000 years respectively. As you can see these are large numbers. Now if you consider Jain and Buddhist philosophy then you see huge numbers getting mentioned. As an example in the Jain text Anuyoga Dvara Sutra the number of people in the world are mentioned to be 2⁹⁶. All this shows is that in our ancient scriptures there was a need to represent huge numbers as compactly as possible. It is this need that lead to the development of Indian zero, which then was adapted worldwide. The other factor in the reverence for zero is the metaphysical concept of Shunyata in Indian philosophy, which we will discuss when we will talk about Indian Philosophy.
Understand that it is not the inherent superiority of a certain group of people that leads them to development of sophisticated concepts. It is the needs of that particular group that forces them to the development of such abstract concepts. This is true for all the scientific development in our human history. So thinking that you are a superior race to the other or the other race is superior to you is plain ignorance.
Coming back to the zero, as must be evident to you, most cultures around the world knew about zero as a term representing nothing in mathematics. The beauty of Indian zero is that it was considered a number. Indians not only used zero in representing nothing, but also used it as a place value in decimal number system. It might not appear much of an achievement to many of you, but you must realize the significance of changing zero from a concrete concept (nothing) to an abstract concept (number). As an example compare roman number X with Indian number 10. The fact that Indian mathematicians could conceive putting zero after 1 to represent ten on a base ten number system is a pure work of genius. This development made representing large numbers in short form and made multiplication and division of numbers very easy. India has a long tradition of doing mathematical calculations in mind, even now in India the use of calculator for doing basic mathematical operations is frowned upon and this could also be a reason for the development of Indian zero as it helped in doing the mathematical operation easily in the mind.
The very first mention of Indian zero is in the Jain text Lokavibhaga, of the 5 thcentury BCE. For the next few centuries the concept was further developed as decimal place value notation of numbers was developed. The representation of zero in the beginning started of with two symbols one was a solid dot and other the circle. Eventually the present representation of zero as a circle came out to be universally accepted, as the concept of zero spread from India to rest of the world.
I mentioned earlier that Mayan zero comes closest to Indian zero. Mayans developed the number representation system similar to Indian decimal representation, with the difference being that they used a base of 20 and with a peculiarity that second place value was a base of 18. So a number abcd in Mayan representation with the equal to
a*20*18*20 + b*20*18 + c*20 + d*1.
Keep in mind that Mayan had developed this sophisticated system by about 4 thcentury BCE, around the same times as Indian system and way before many other civilizations understood zero as a number. Again this happened because Mayans just like Indians needed to represent large numbers in short form. Just like the Yugas in Indian system Mayans also had the need to calculate time precisely. The reasoning for Mayans was that the Mayans believed that their Gods had to be satisfied with sacrifice at defined intervals to avoid their wrath. So Mayans came up with an elaborate calendar with periodization just as in India. If Mayans had been in contact with the rest of the world, it may be possible that we might have been using base 20 numbers, instead of Indian base 10 numbers.
Originally published at https://stoicsadhu.com on July 20, 2019.
