Almost 2 decades ago, I was introduced to the fascinating concept called Fibonacci series, by the book “Da Vinci Code” authored by Dan Brown, which was highly circulated among friends & the most talked about book in our college back then.

Thanks to the book, Fibonacci series & its related concepts like Golden Ratio, Phi, Combinatorics, etc had evoked a sense of scientific temper & analytical thought processes.



Image credits: mocomi

In the subsequent semesters, as our professors taught us lessons on Fibonacci & its applications in real world, my respect for Leonardo Fibonacci, (The Italian Mathematician who’s credited for the conceptualization of the numerical series in 13th century AD) had simply skyrocketed. For the next whole decade, I was in awe of the Italian Mathematicians & felt greatly indebted to him for his contribution.

Fast forward to 2015. While browsing through some books of a 20th century Indian Philosopher, I came across an excerpt of his speech in which he made an outright claim that Fibonacci series had actually originated in India, more than 2500+ years ago!! That set my pulse racing, and it was time to go deep into this to find out the truth so that due credit could be given to those who really deserved it. And the results were enthralling to say the least. Let me take this opportunity to concisely narrate the story of this wonderful series & the real scholars behind it.

Way back in the 2nd century BCE, when Sanskrit & Hinduism were at their peak in the Indian sub-continent, Hindus were accumulating knowledge like never before. However, what’s the point in accumulating knowledge without propagating it further? That’s where Sanskrit played a major role. Thanks to the flexible characteristic of the language, it was the ideal language to compose poetry by imbibing these learning into poems & propagating them through oral means.

Hence, the art of poetry in Sanskrit, was not just a matter of entertainment, but actually a methodology to exchange ideas & spread knowledge. Almost all knowledge, be it scientific or medical or philosophical or spiritual or astronomical or astrological, were all in the form of poetry. In fact, some of the mega-epics of India, like the Mahabharata, Ramayana, and the philosophical works like Bhagavad Gita, were all poems. In fact, Mahabharata, in its original poetry form, by itself, has more than 1 lakh shlokas.

With this understanding of how & why Sanskrit Poetry was the ideal medium for knowledge, here comes the next challenge. How to compose the poems efficiently so that it can be relatively easier for the scholars to remember & recite them?

That’s where the concept of “Sanskrit Prosody” comes into picture. This is basically a methodology based on rhythms & arrangement of tones. Not only is it a method, but actually a vast field of study where natural rhythms are determined so as to form a framework for poetry which would be very pleasing to the ears. The poems which are then composed based on this framework, would abide by the laws of nature, hence making the poems sound naturally pleasant, thereby enhancing the probability of it being remembered for a long time in the human mind, with minimal effort.

This “pleasant” effect in Sanskrit is called “Chanda” which is based on the root word “Chand” which means “pleasing”. Hence, this poetry framework, whose aim was to produce pleasant poems, was called “Chandas” in Sanskrit or “Chandassu” in Kannada or Telugu. Since it is like a tool which is to be utilized for fields like poetry, it was considered a sutra/shastra, and hence this methodology was also called “Chandas Sutra” or “Chandas Shastra”.

Now, you might be wondering as to how we started the discussion with something as mathematical as Fibonacci series, but are touching upon topics like poems & Sanskrit Sutras. Well, that’s the beauty of ancient Indian wisdom. What we think is art, is actually beyond that. In ancient India, poems were not merely art forms produced out of creative juices, but had to inculcate highly sophisticated Mathematical concepts in order to pass the test of Sanskrit Shlokas. Chanda Shastra was one such mathematical concept which were widely used by the poets.

In Chanda Shastra, everything finally boils down to 2 syllables: Short syllable which need 1 beat (Laghu) and Long syllable which require 2 beats (Guru). Musicians like Tabla players also use the same concept, where they call Short syllable as “Dhin” & Long syllable as “Dha”.

Now, let’s try to step into the shoes of a poet to understand the significance of this Chanda Shastra. Since every poet begins composing his poem by fixing the total number of beats per line/shloka, his creativity can get drastically constricted because his content in each line must fulfill the criteria of the total beats per line. Hence, there is a need for the poet, well in advance, to be aware of how he can arrange the Laghus & Gurus in each shloka, and how many such combinations are possible for each shloka.

Let’s consider a simple hypothetical case of just 2 beats per shloka.

With this assumption, how many combinations of Laghus (short syllable) & Gurus (long syllables) can be formed?

Simple. Since there are only 2 beats, it can either be filled with 2 Laghus or 1 Guru. Means there are 2 combinations.

Next, what if there are 3 beats? It can have any of the following combinations:

1) 1 Laghu & 1 Guru

2) 1 Guru & 1 Laghu

3) All the 3 Laghus

So, it means, we can have 3 combinations. i.e There are 3 ways of arranging short & long syllables if we are asked to compose a shloka containing 3 beats.

We can go on with these calculations and determine that when we have 4 beats, we can have 5 combinations. When we have 5 beats, we can have 9 combinations. When we have 6 beats, we can have 13 combinations. When we have 7 beats, we can have 21 combinations. For 8 beats, we can have 34 combinations. And so on.

Summarizing the above paragraph, we can have 1, 2, 3, 5, 8, 13, 21, 34 (….. upto infinity) combinations.

If we closely observe the above pattern, we note that it is actually nothing but the series which we today popular refer to as Fibonacci series. This is what the whole subject of Chanda Shastra is based upon.

And that takes us to the actual topic now. What we call as Chanda Shastra, was pioneered by a Saint-Scholar (Rishi) named Pingala in the 2nd century BC. (Although recent archeological evidences suggest that it was 4th century BC).

In fact, not only did Pingala conceptualize the series (what we call as Fibonacci series today) as part of Chanda Shastra, but even extended it to the concept of a pyramid of stacked numbers which we call as “Pascal’s Triangle” today. However, during Pingala’s era, since Mount Meru was commonly used as a reference to the centre of Hindu civilization, he had called his stack of numbers as “Maatra Meru” which he had claimed converges towards the Golden Mean.

An excerpt from a well researched book titled The “Venus Blueprint: Uncovering the Ancient Science of Sacred Spaces” has illustrated it very well, and an excerpt of it (Page 50 to be precise) is presented below:

Reference:

https://books.google.co.in/books?id=OrdrXuS15XQC&pg=PA50#v=onepage&q&f=false

As we can see, Fibonacci Series & its extension i.e Pascal’s Triangle, were already described by Pingala 2500 years ago as part of Chandas Shastra, with reference to Matra-Meru, & the concept has been used by Sanskrit Poets for 2000+ years.

Not only by Sanskrit poets, but by Indian classical musicians (including Hindustani & Carnatic forms) as well.

For example, here is an interesting demonstration (video embedded under this paragraph) of rhythms in Konnakol form, which is a part of Carnatic music, and one can see how it is in accordance with Pingala’s Chandas Shastra, which we call as Fibonacci Series now.

If the above embedded video is not working on your PC/Device, you can watch it directly on YouTube by clicking the following link:

https://www.youtube.com/watch?v=Zc7WMbVW-3s

For centuries, these number series have been in use especially by Indian poets & classical musicians, and there have been detailed commentaries of Pingala Chandas Shastra made by ancient Indian scholars as well for their respective fields. For instance, in the 5th century AD, the Indian Astronomer-Mathematician Varahamihira had used the same sequence in his works related to Binomial Coefficients. This is in fact well acknowledged by the Mathematical community now and is nowadays being cited in their research works as well.

Following is an excerpt from a paper published at “Scientific Research Publishing” where this historical fact is being acknowledged & credit is given the above mentioned Ancient Indian Scholars.

Reference:

https://file.scirp.org/pdf/AM_2015061016154083.pdf

While Pingala & Varahamihira had used the number series for their respective fields like Sanskrit Prosody & Astronomy, one of the most comprehensive commentary on it applying it to various other fields, was later done by a Hindu Jain Scholar named Acharya Hemachandra in the 12th century AD.

Documentary evidences show that Acharya Hemachandra had compiled his treatise in 1150 AD, whereas Leonardo Fibonacci had presented his thesis only in 1202 AD, which looked identical to that of the commentary made by Hemachandra. Hence, this proves that even in the form of a treatise, the number series presented by the Indian Scholar Hemachandra, had preceded that of Leonardo Fibonacci by more than half a century!!

Thanks to the awareness spread by Indian scientists worldwide about this fact & evidence, almost all the Mathematicians, and the Scientific Community in general, have started acknowledging this, and are giving credit where it is due, by mentioning Fibonacci numbers as “Hemachandra-Fibonacci numbers”, which is the first step in the awareness process, with the hope that it will some day in future be referred to as “Pingala-Hemachandra numbers”.

Following is an excerpt from a Quantum Mechanics book in which the author has given due credit to Ancient Indian Scholars & has referred to the series as Hemachandra-Fibonacci numbers.



Reference:

https://books.google.co.in/books?id=toIRDQAAQBAJ&pg=SA4-PA2#v=onepage&q&f=false

Meanwhile, one such Mathematician from Indian descent, who is putting immense efforts into spreading this awareness about the origins of Fibonacci series in India, is Manjul Bhargava, who is currently a Professor of Mathematics at Princeton University. On a regular basis, he conducts workshops & seminars in which he shares insights into these concepts & makes them interesting by relating them with real world applications, including poetry & music.

If you can spare a few mins, I strongly suggest you to watch one of his recent talks (video embedded below this paragraph) in which Manjul Bhargava, in his signature style, explains how Hemachandra numbers (Fibonacci numbers) are being an integral part of various fields like nature, poetry, art & music:

If the above embedded video is not working on your PC/Device, you can watch it directly on YouTube by clicking the following link:

https://www.youtube.com/watch?v=siFBqH-LaQQ

As more professors like Manjul Bhargava continue to rise up to the occasion to spread further awareness about this concept and its origins, the rest of the world will not be able to ignore it anymore, and start acknowledging our ancient Rishis who deserve real credit. Also, thanks to the advent of internet technologies & social media, more Indians are also becoming aware of their own glorious history, helping in inculcating national pride within themselves, which our previous Govts had carefully chosen to ignore, for reasons best known to them.

With all these evidences & explanations, we can now see how the fascinating number series, which we call as Fibonacci series today, had originated in India and has been in use for centuries, thanks to the foundation laid by Pingala 2500 years ago, and the legacy strengthened by Hemachandra more than 1000 years ago.

Now, the least we can do, is to acknowledge the roles of our ancient Indian scholars & Rishis, and start giving them due credit, by referring to the Fibonacci series as “Pingala-Hemachandra” series. The global scientific community has already started the process (by including Hemachandra’s name). It is now the turn of Indian academicians & educationalists to imbibe these into school textbooks as well, so that future generations can be proud of our Rishis in particular & our ancient wisdom in general.