Aabhas Ancient India

Pingala & Fibonnaci Series

A thread by Aabhas Maldahiyar 🇮🇳

n #SadarPranam to Ishwara within you @TonyPannWBAL ji. Since you are talking about the “gorgeous sequence” I being an “Indian Architect” couldn’t hold back but to share India’s contribution in originating it.

Read this thread👇🏼

Tony Pann

It’s 11/23 or 1123. . The Fibonacci sequence is a series of numbers where every number is the sum of the two preceding it. Why important? It’s nature’s code! Fibonacci spirals are seen in everything from flowers to storm systems to the shape of galaxies.

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n Till 7yrs back I too believed that it was Fibonacci who crafted this beautiful sequence.

I did my UG Archi thesis on “Role of Applied Mathematics in Deriving Architectural Forms” in year 2011 but while continuing this research beyond B.Arch I came across Prof Deshpande. n He was retired HOD(Architecture) at VNIT,Nagpur. Reading about the use of Fibonacci Sequence in my thesis he revealed the Indian part of it. Which goes as below:

@TonyPannWBAL pl read carefully 👇🏼 n Way longer before “Jesus of Nazareth” is deemed to be born Sanskrit was at its peak in Bharata (what you call India) & Hindus we’re accumulating knowledge like there is no tomorrow.

Interestingly you always wish to circulate & spread your knowledge or else it’s of no use. n Sanskrit played a major role in propagation for its highly flexible characteristic.

Sanskrit was perfect Bhasha to compose poetry incorporating these learning & propagating them orally. n But our ancestors had a big challenge: finding a way to compose poems efficiently enough SK that they are relatively easier to remember as well as recite.

& then “Sanskrit Prosody” came in play: a methodology based on rhythms + arrangement of tones. n Prosody is a vast field of study where natural rhythms are determined in order to create a framework for poetry which would appealing to the ears.

Being naturally pleasant,the probability of it being remembered for a long time with minimal effort is giant. n This “pleasant” effect in Sanskrit is called “Chanda”. Hence, this poetry framework, whose aim was to produce pleasant poems, was called “Chandas” in Sanskrit. Hence the field was & is called “Chandaḥśāstra”. n @TonyPannWBAL ,you might be wondering that why am I touching upon Sanskrit Sutras & Poems.

😊Well, that’s the beauty of ancient Indian wisdom. Our art, is actually way beyond what west perceives it to be. n Our ancestors composed poems not merely as art forms but as highly sophisticated Mathematical concepts in order to pass the test of Sanskrit Shlokas. “Chandaḥśāstra” was one such mathematical concept which were widely used by the poets. n Let me elaborate. In Chanda Shastra,it’s all about 2 syllables: Short syllable which need 1 beat (Laghu) and Long syllable which require 2 beats (Guru).

One uses same concept while playing Tabla too. Here we call Short syllable as “Dhin” & Long syllable as “Dha”. n Now, let’s try to significance of this Chandaḥśāstra from a poet’s perspective.

Composition of each poem begins by fixing the total number of beats per shloka, hence creativity gets drastically confined as the content in each line must suffice “total beats per line.” n Hence, it’s essential for the composer to know well in advance, how he can arrange the Laghus & Gurus in each shloka & the probabilities for each shloka.

Let me put forward a simple hypothetical case of 2 beats per shloka. n With this assumption,since there are only 2 beats,it can either be filled with 2 Laghus or 1 Guru. It implies that there are 2 combinations.

Next, let’s consider 3 beats. Following combinations shall occur:
•1 Laghu & 1 Guru
•1 Guru & 1 Laghu
•All the 3 Laghus n Hence, we can have 3 combinations if we are asked to compose a shloka containing 3 beats.

If we follow this sequence,with 4 beats,we can have 5 combinations. With 5 beats,we can have 9 combinations & so on. n With 6 beats, we can have 13 combinations. With 7 beats, we can have 21 combinations. The game of sequence goes on and on.

What does it seem like? 1,2,3,5,8,13,21…

Fibonacci Series. Isn’t it? This is the base of “Chandaḥśāstra”

It gets more interesting. Pl read in👇🏼 n Rishi Pingala framed the so called “Fibonacci Series” that is root of Chandaḥśāstra ( 4th Cen BCE or earlier).

Apart from that he also laid concept for the pyramid of stacked numbers which globe calls as “Pascal’s Triangle” today. 😊 n Back then Mount Meru was common reference to the centre of Hindu civilization. Pingala had called his stack of numbers as “Maatra Meru” which claimed to converge towards the Golden Mean Ratio.

Source: “Venus Blueprint: Uncovering the Ancient Science of Sacred Spaces”

n We find a lot more in this book & the explanations are just too interesting. This is link for the book:

Hence Rishi Pingala had conceptualised it 2.5 Ka bp (books.google.com/books/about/Th…) n Though I don’t want to get into this right now but just briefing a bit. RigVeda (composed at least 24ka bp) too has mention of “Meru”. (Relate with 19/n).

Will share details of it in case you are interested. n Apart from Sanskrit poets, Hindustani & Carnatic musical Forms too have used this series perfectly.

In this video one can observe rhythms in Konnakol form (Carnatic music)that use so called Fibonacci Series.

n For ages,so called “Fibonacci Series”have been in use especially by Indian poets,classical musicians, as well as Architects.

There have been detailed commentaries of Pingala Chandaḥśāstra made by many ancient Indian scholars for their respective fields. n The Indian Astronomer-Mathematician Varahamihira(6th Cen CE) used this sequence in his works related to Binomial Coefficients.

Source: “An Algorithm to Generalize the Pascal and Fibonacci Matrices” by
Ilhan M. Izmirli (June,2015)

n Pingala & Varahamihira used the number series for their respective fields like Sanskrit Prosody & Astronomy.

Acharya Henchandra (12th Cen) wrote one of the most comprehensive commentary on it applying it to various other fields. n Acharya Hemachandra compiled his treatise in 1150 CE. Leonardo Fibonacci presented his thesis only in 1202 CE. (identical to that of Hemachandra).

Hence,even in the form of a treatise, it was presented by Hemachandra, before Leonardo Fibonacci by almost 5 decades. n Actually series is already known as “Hemchandra Fibonacci Numbers”, though yetthe originator Pingala is to get due credit.

Source: Butterfly in the Quantum World

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