ones and zeroes

In fourteenth century AD a Keralite mathematician and astronomer wrote about the infinite series. He is known as the Madhava of Sangamagrama to avoid confusion with other Madhavacharyas. In seventeenth century Issac Newton and Wilhelm Leibnitz also discovered the series. However for a long time Newton and Leibnitz continued to take credit for the discovery. It is heartening to know that Madhava’s contribution now has been recognised and the series is now known as Madhava series or Madhava – Leibnitz series.

But many other mathematical discoveries of ancient India are yet to be recognised. As I have mentioned in my chapter on Jyotisha, all the great astronomers of India have been great mathematicians as well. However, it seems experts of fields like music too contributed to mathematics.

Chhanda Shastra is a treatise on composition of verses written by Pingala Muni. Chhanda means rhythm. In terms of syllables Pingala Muni talks of two types – light (laghu) and heavy (Guru). For example take the following line from Gita Govindam :

yahi madhava yahi keshava mavada kaitabha vadam 

Taking the bold letter as Guru, the combination is Laghu-Guru, Laghu-Guru, Laghu-Guru, Laghu-Guru, Laghu-Guru, Laghu-Guru. This is a simple but very popular style of composition. The poet can work out various types of such combinations and depending upon the combinations various names are assigned. What is more, Pingala gives a formula for the possible number of such combinations. He says that a line with ‘n’ syllables can be written in 2ⁿ possible ways. If we take a three syllable line, it can be written in eight (2³) ways: LLL, LLG, LGL, GLL, LGG, GGL, GLG, GGG.

If you replace guru with one and laghu with zero, that is exactly the binary system for you. While Pingala’s Chhanda Shastra was written not later than the second century BC, Leibnitz was born in seventeenth century. However, Leibnitz continues to take credit as being the first person to have worked out the binary system.

I feel that two concepts of modern day computer programming which were extensively used by Panini in his treatise on Grammar known as Astadhyayi are algorithm and data compression. Sanskrit grammar seems very difficult to master until you understand its algorithm. Once you understand the algorithm of Sanskrit language it will be easy for you to master its seemingly complicated structure of grammar. This thoughtful algorithm also empowers the language to construct an infinite number of meaningful words out of finite number of root words using prefix, suffix and sandhi.

In my earlier post ‘The Language of Gods’ I have already discussed about the Maaheswara Sutra in connection with the origin of the alphabets. All the alphabets are put into fourteen groups. Panini uses a short hand method or a code to recall all the alphabets of a particular group. This code or shorthand method, or coding method to avoid lengthy repetitioning is known as pratyahara. Today’s data compression techniques are based on similar principles. Of course here I do not want to claim that the person who invented data compression was inspired by Panini’s Astadhyayi. All I want to convey is that many of the so called modern concepts and methods were in extensive use in ancient India.

It is also claimed that the study of Sanskrit phonetics has been helpful in developing speech recognition software. I will discuss in detail about this aspect of Sanskrit language in a subsequent post. There was also extensive use of the features of the branch of a mathematics known as combinatorics. The numbers inside Sri Yantra and other Yantras belong to intricate number series.

Another misplaced credit is in connection with the intricate number series Fibonacci. While the Italian mathematician Fibonacci himself makes references to Indian mathematicians for the inspiration of his work and there is proof of the use of ‘Fibonacci series’ in ancient Indian texts, Mr. Fibonacci continues to hog the limelight as the inventor of the series.

Hope, as awareness increases and more research is done, due credit will come to the original inventors. As in the case of Madhava of Sangamagrama some corrections have been done. More should follow.

**********************************

This is the alphabet O post of Blogchatter AtoZ Challenge 2021. My theme this year is ‘The beauty of Sanskrit and Sanskrit texts’, where in I explore selected compositions in Sanskrit and also some unique aspects of Sanskrit language and texts. Join with me in my journey to understand India’s spiritual and intellectual heritage. All the posts of AtoZ Challenge 2021 can be accessed here.