Sunday, 30 March 2025

Sanskrit and other Languages of Science

In 1999, I read the Tamil historical novel Sivakaamiyin Sabatham. Set in the seventh century, the novel tells of the siege of Kanchipuram, the capital of the Pallavas, by their rivals, the Chalukyas. It is still one of the most popular books in Tamilnadu, seventy years after its first publication. At one point in the story, Aayanar, an artist and sculptor tells the Pallava king Mahendra Varma, that his deepest desire is to know the secret technology of  Ajanta paintings, which have lasted a thousand years without fading. The paintings of Ajanta are still there, a thousand years after the Pallavas and Chalukyas disappeared.

In Kanchipuram, the Kailasanatha temple built by Mahendra Varma’s great grandson Rajasimha Pallava in the eighth century, has paintings in the Ajanta style, which have sustained damage but what remains hasn’t faded. The contemporary Pandyas built a Jain cave temple of Sittannavasal, which has equally remarkable paintings.

A heritage of science and technology

These struck a severely discordant note. How many advertisements do we see on television for the latest paints that last twenty years? Enamel paints manaufactured in large chemical plants, based on the very latest technology brought to life by the most brilliant chemical engineers of the last century. Their great selling point is that they last twenty years – one hundredth of the two thousand years that Ajanta paintings have lasted, in primitive caves, sculpted by hammer and chisel.

What other remarkable scientific and technological achievements of ancient Indians was I missing?

By sheer coincidence, I happened to attend a series of lectures about the “Oral Traditions of the Sanskrit” language, by Prof Swaminathan, a retired IIT Delhi professor of mechanical engineering. He explained the Siva sutras (also called Maheshvara sutras) and how Panini used them to write extremely compact rules of grammar for Sanskrit. The Siva Sutras and Panini’s sutras reminded me starkly of the Backus-Naur notation, that every computer science or engineering student learns in college. But, wait! What was Panini doing, composing Sanskrit grammar in Backus-Naur notation?

Why is Panini never mentioned in any computer science course? Why is not a single discovery  of Baudhayana, Aryabhata, Brahmagupta or Bhaskara ever taught in a mathematics or engineering course? In any school or college? Seventy years after independence, you can hardly blame British colonialism.

The ignorance is not merely about Indian science, it is about all non European science and technology, in general. Sumeria, Egypt, China, MesoAmerica (Olmecs-Mayans-Aztecs), Persia, all ancient civilizations are totally ignored, and we get an entirely European perspective of all science and technology.

English is the language of science, we are told, though most of the scientific vocabulary is in Greek or Latin. The very names of the sciences Physics, Biology, Zoology, Geology, Astronomy come from Greek. Chemistry, is an exception, adapted from the Arabic word AlChimia (or Alchemy). The  different fields of mathematics, Geometry, Trigonometry, Arithmetic have Greek origins. But Algebra comes from an Arabic word; Calculus from a Latin word. Newton wrote his most famous physics book, “Principa Mathematica de Naturalis” in Latin, not English. When Antoine Lavoisier coined new words for the modern chemistry he discovered, he did not use French; he chose Greek and Latin. English words like soda and pot ash, were Latinized into Sodium and Potassium.

A mathematical vocabulary

Did the Sumerians, Chinese, or ancient Indians use Latin or Greek? Or even need them? Obviously not. It was when I started reading the Aryabhateeyam in its original Sanskrit (with English translation assisting), that I realized what a rich vocabulary we are ignorant of.

Do you recognize the following words: vishkambha, parinaaha, kakshya, vishuvat, karna, jyaa?

How about these words : diameter, circumference, orbit, equator, hypotenuse, sine?

Here’s the stunnner. The first row of Sanskrit words have the exact same meaning as the second row of English words.

समपरिणाहस्यार्ध विष्कम्भार्धहतमेव वृत्तफलम्

Transliteration sama pariNaahasya ardha vishkamba ardha hatameva vrtta phalam

Let me explain this Sanskrit statement, word by word:

Sama – equal
Parinaaha – diameter
Ardha – half
Vishkambha – circumference
Hatam – multiply
Eva – exactly
Vrtta – circle
Phalam – result 

Literarlly “Equal diameter-half circumference-half mutliply-exactly circle’s-result”

Rephrased grammatically in English : “A circle’s area equals half the diameter  multiplied by half the circumference”.

This was stated in Sanskrit by none other than Aryabhata. It is the seventh sloka in his Aryabhateeyam.

Let me propose two quick quizzes: there are two lists of names side by side, one European, the other Indian. Just write down what they invented or discovered, as a self-test.


You can the internet to verify your answers. But did you get all answers correctly in the first list? How did you fare with the second list? Did you even recognize all the names? (Confession: I didn’t know three of them ten years ago). If you guessed that Aryabhata invented zero or discovered gravity or the heliocentric theory, give yourself negative marks. He didn’t.

But the people on the second list had one things in common. They all used Sanskrit as the language of science. Why Sanskrit? Sanskrit was not only the language of religion, and literature, it was also the language of several sciences, law, justice, administration, economics, rhetoric, logic, and several arts, namely music, dance, painting, sculpure, architecture etc. It served the same function in India and countries to the east of India, that Latin first in the Roman empire, then in Europe until perhaps the twentieth century; what Mandarin did in China from Confucian times upto perhaps today; what Arabic did in the realms of Islam. It was the link language of a cultural continent, across several kingdoms over the span of several centuries, even millennia.

Consider these somewhat famous books.


I have provided only one example in each field. In reality, each field has several books, written by scholars from various regions or cities, across several centuries. We never hear of them, because over time, Sanskrit has become more alien in India than Greek or Latin.

Now consider that quiz, again. Why is that ignorance of the inventions or discoveries of Europeans considered scientific illiteracy, but ignorance of the inventions of discoveries of Indians considered normal? It may be tempting to Islamic desturction or European colonialism. But I don’t think that is an acceptable excuse, seventy years after Independence.

When most Indians, hear Sanskrit or hear of it, we only hear of it as the language of the Vedas, or at best the language of beautfiul poetry as in Kalidasa or Jayadeva. One popular understanding is that it is a dead language, steeped in the superstition of religion. The only people talking in public about anything Sanskrit are people quoting philosophy; once in a blue moon, perhaps a musician or a dancer. Or, a chorus chanting Sanskrit mantras as background music in a Star Wars movie.

Buddhist and Jain Sanskrit literature

Sanskrit was not the only language in which science was written, in ancient and medieval India. The Jains and Buddhists wrote books on some sciences in several Prakrits, primarily Ardha Magadhi and Pali. They believed that Sanskrit was the language of the elite, and to reach the common man, the local languages should be used. But this soon led to severe fragmentation of literature. The Kushana king Kanishka convened a Buddhist Sangha in Kashmir, at which scholars began to translate several Buddhist canonical texts from Pali to Sanskrit. From then on, several original works, including on mathematics, were composed in Sanskrit also. Similarly, Jains composed Sanskrit works from the fifth century onwards, after the Valabhi Sangham. The first Sanskrit book where mathematics is the primary subject, not a chapter in an astronomy book, is Ganita Sara Sangraha, composed by the 9th century Jain mathematician Mahavira. A few stanzas of his first chapter, beautifully outline the use and power of mathematics. It should be declared the Mathematics Anthem, and printed on the first page of ever math text book. I suspect Finland or Cambodia will do it, and then India will rush to follow. Here it is, with my translation:

लौकिके वैदिके वापि तथा सामायिकेऽपि य: |
व्यापारस्तत्र सर्वत्र संख्यानमुपयुज्यते || ९

कामतन्त्रेऽर्थतन्त्रे च गान्धर्वे नाटकेऽपि वा|
सूपशास्त्रे तथा वैद्ये वास्तुविद्यादिवस्तुषु || १०

छन्दोऽलङ्कारकाव्येषु तर्कव्याकरणादिषु |
कलागुणेषु सर्वेषु प्रस्तुतं गणितं परम् || ११

Translation

In worldly life, in Vedic learning, in religious practice, 
In business, in everything, Mathematics is useful.

In romance, economics, in music dance and drama,
In cooking, medicine and in architecture, 

In prosody, poetry, logic and grammar,
In all the arts, Mathematics reigns supreme.


The libraires of Alexandria and Nalanda may have been destroyed by iconoclastic invaders, but the library of all Sanskrit knowledge is vandalized every day, by our collective ignorance and negligence.

That is ridiculous. We can change that.

References

  • 1.     Facets of Indian Astronomy, KV Sarma, 1975
  • 2.     The Aryabhatiya of Aryabhata, Walter Eugene Clark, 1930
  • 3.   Mahavira's Ganita Saara Sangraha, Prof Rangacharya, Univ of Madras, 1912 

__________

This was the first of a series of essays published in Swarajya magazine online

For the entire series click this link --> Indian Astronomy and Mathematics   

Related Links

My blogs on Astronomy and Mathematics

Shilpam Science Sundaram - TEDx lecture at Saveetha Eco Pupil school

Wednesday, 29 January 2025

A Sculptor's muse


Softly O softly she floated ashore
On the waves of his dream to his mind's very core
Like the dew on the grass from the soul of the breeze
In the still of the night with the greatest of ease

Smoothly O smoothly he etched in her shape
For devas to gasp and manushas to gape
Firmly O firmly he hammered the stone
'Til rock came alive as flesh blood and bone

Her lips promised love, her breasts spoke in rhyme
Her hips gently prodded her anklets to chime
She smiled with her eyes and laughed with her heart
As he breathed into her the essence of art

On the return from Jhansi after January 2025 THT Site Seminar in northern Madhya Pradesh, this sculpture popularly known as Gyaraspur lady, now kept in the Gujari Mahal museum in Gwalior fort, inspired this poem above. "Gyaraspur lady" is the sculpture of a shaala-bhanjika from a place called Gyaraspur near Vidisha, which is south of Gwalior. In 2019, THT site seminar was conducted in areas around Bhopal including Vidisha and Gyaraspur. That's when we came to know about it, when Vallabha Srinivasan gave a preparatory lecture about it. Mr Venkatesiah, retired Regional Director of ASI, accompanied us as an expert, and informed us that this statue was under high security, behind a barricade, because of several attempts at stealing it. While some were waxing eloquent about the grace, beauty, allure, posture and other aspects of this sculpture, I was reminded of an apsara sculpture from Nageshvaran temple in Kumbakonam, Tamilnadu - one of four such beautiful apsara figures in that temple. This particular apsara, west of the Dakshinamurthy shrine, is soft, supple, demure, enchanting. When I mentioned this, Sowparnika, who was nearby showed it from her photo collection in her phone. The Gyaraspur lady photo is by Suresh Priyan, who was also on the Site Seminar.

Phrases and the tune of Sarojini Naidu's poem, "The Palanquin Bearers", which I had read in school, and loved for the very Indian sounding chandas/yaappu (prosody) of this English poem, floated into my thoughts. On the return journey by train on January 27, I wrote this poem - it applies to both sculptures and the shilpis who sculpted them.

Gyaraspur lady - photo by Suresh Priyan





Apsara at Kumbakonam Nageshvaran temple - photo by Sowparnika


Related Essays in my Blog



Sunday, 29 December 2024

Muthuswamy Deekshithar - Notes from a 2017 lecture by V Sriram

These are my notes from a lecture at Vani Mahal, Thyagaraya Nagar in December 2017.

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Marvelous lighting at the mini hall in Vani Mahal, such that the speaker Sriram Venkatakrishnan was well lit, without shining on the large the screen displaying his PowerPoint and pictures. There were some projector hiccups halfway but overcome.

From an early move out of Vellore because of a power struggle in the fort, to the expertise of Ramaswami Deekshitar, in Jayadeva's Ashtapathi, to the travels, career and musical virtuosity of his son, Muthuswamy, born by the blessing of the eponymous God in Vaideesvaran temple, it was a comprehensive lecture, as profuse in scholarship as it was delightful in diction and delivery, in not one but three languages.

One could write a twenty page book just from the lecture. I'll list some highlights.

A background of Tanjavur Mahratta politics including Amarasimha, Tulaji, saraboji, Father Schwartz.

Early life in Govindapuram.

Sonti Venkataramana, guru of Thyagayya, was impressed by Deekshitars teaching skills.

Venkatamakhin and his Chatur Dandika Prakasika, containing the melakartas, whose rare copy Muthuswamy had the good fortune of receiving.

Patronage by Manali Muthukrishna Mudali, the Dubash of Madras, and by his son. Songs lauding them, which contrast with other accounts of their lives.

The band in Fort st George, which inspired the nottu swarams, and the adoption of the violin in carnatic music.

Two wives.

A deep knowledge of Tevaram songs, which reflected in several compositions in Sanskrit.

Later settlement in Kanchipuram and encounter with Upanishad Brahmendra, whose mutt survives. Songs on the Somaskanda of Ekamreshvara, with poetic description of the sthala purana, and word play on ma skanda and moola skanda.

A tour of several nearby temples including Kalahasti, Tiruvannamalai, Tirupati. Perhaps a reference to laddu!

A reference to Gnanasambanda as Uttamavipra in his song on Arunachala and his legend of sighting the hill from a distance, and how this episode repeated later in the life of Ramana.

A voyage to Kashi with all its perils, almost surely, entirely by foot. The episode of Ganga gifting a veenai to Baluswamy Deekshitar his brother. Let's just say he came back with a veena, quipped Sriram. A very small veena, perhaps three feet long, which the family preserved and showcased at the Music academy in 1975, the 200th anniversary of Deekshitar.

Life in Tiruvarur, famous also for the life of Nayanmar Sundaramoorthy. The mysteries of the Thyagesa idol, eternally covered from the neck down,which inspired a superb song by another composer. A mysterious closed shrine perhaps of Vishnu behind it, and the oft ignored Valmikinatha, the real moolavar. More on Kamalambal, Katyayani both more celebrated than Neelotpalambal, the primary consort. Katyayani is the Lord's concubine or main Rudra ganika, and the model for all devadasis. In fact it is believe that the devadasi tradition began at this temple. And the erotic sculpture of Uchishta Ganapathi, and it's tantric worship, which Muthuswamy must have practiced as a Sri Vidya upasaka.

The variety and range of his disciples from different communities, including devadasis and the Tanjavur quartet.

Muthuswamy composed music for Rama Ashtapathi, composed by someone else, but unfortunately these haven't survived. Or else we would have known how he set others composition to music, as musician Sriram Parasuram (present at the lecture) observed elsewhere, the speaker adds. (Another singer Ramakrishna Murthy was also in the audience).

Songs on several temples around the Kaveri built including Tayumanavar whom he calls Matrubutha, and various navagraha shrines. Waxing eloquent at Tirukannamangai, where bhkatas believe the devas reside as bees, and the Thayar shrine still has a beehive perhaps two centuries old, that the archaka shows to visitors. Tirumangai Alwar has a mischevous passuram here, where he advises not just Vaishnavas but also Vishnu himself that singing his ten songs will benefit the singer.

Ratnagiri temple, populated by monkeys, where the devotees fill a large copper vessel from the Kaveri, eight km away, and then take it up the thousand steps for abishekam. They did it during his times, as recorded in his song, and they do it today.

Songs on navagraha shrines in the hinterland. Travel to Madurai and Ettayapuram , famous for its betrayal of Kattabommu, but whose king Deekshitar praised. The court appreciated the novelty of the violin as a carnatic instrument. Songs on Meenakshi and Azhagar.

We should recognize that Deekshitar was human, needed patrons, was practical, and not just cover him in saintliness, said Sriram. Final samadhi there. Now, there is a memorial mandapam, which a collector recently wanted to demolish as an illegal structure. Fortunately, it survives.

Originally posted to Facebook on 29 December 2017. Dedicated to Rajagopalan Venkatraman who could not be there, who otherwise would have provided marvelous slide by slide coverage.

Related Posts

Lecture Notes

Blogs on Music


Friday, 13 December 2024

Aryabhata 2025 - ghana citi - Formula for sum of series of cubes

Aryabhata ghana citi
Aryabhata's ghana citi for 2025

Most of us studied not only numbers, but also series of numbers and sums of series in school in mathematics. I am sure most people remember, that the sum of the series from 1 to any number N is given by the formula N*(N+1)/2.

In other words, 1+2+3+4…..+N =  (N * (N+1))  /2

In some school mathematic text books, the name of Carl Friedrich Gauss, the great German genius, is mentioned in association with this series. It seems a German teacher asked his class of nine or ten year olds, what is the sum of the first hundred natural numbers. And Gauss, who was in this class quickly responded, 5050. When asked how we calculated it so quickly, Gauss responded, that he added the smallest and largest numbers 1 and 100, which came to 101; then he added 2 and 99 the second smallest and second largest numbers, which also came to 101; next 3 and 98, then 4 and 97, also each adding to 101. He realized that there were 50 such pairs, each adding to 101, so the sum is 50 times 101 which is 5050. Gauss went on to do amazing things in mathematics, and became one of the greatest mathematical geniuses the world ever saw.

Nice story. Every student and teacher can relate to it. Why don’t we have such stories about Indian mathematicians, except for the famous taxi number 1729 of Ramanujan?

While some formulae in mathematics have names attributed to their inventors or discoverers, there are several mathematical formulae that remain anonymous. All the formula that have names in either physics or mathematics have European or American scientist or mathematician’s names. So, we have Pythagoras theorem, Newton’s formula, Einstein’s formula, Euler identity, and so on. Have you ever wondered why? Why is this Gauss story told without mentioning that Aryabhata gave us this formula for sum of series?

We also learnt that Indians invented zero – we are wrongly told that Aryabhata invented zero. No, Aryabhata did not invent zero. Zero was at least a few hundred years old before Aryabhata was even born. Besides Aryabhata at least Bhaskara is famous as a great mathematician in India. Why do we never learn about some Aryabhata theorem or Bhaskara formula.

Also, even if Aryabhata discovered or invented zero, he must have invented something else also?

Let us discuss one set of things Aryabhata presented, which are given in school textbooks throughout India and the world without mentioning his name. Aryabhata gave not just the formula for the sum of series of numbers, he gave formula for the sum of series of squares and the sum of series of cubes.

In Sanskrit books, the word citi is used for series. Citi  (Sanskrit चिति Tamil சிதி) is literally the word for series of bricks with which a yagna or fire altar for Vedic rituals is made. Aryabhata uses these terms for these formulae

citi: for sum of series of numbers  (1+2+3+4… +N) = N*(N+1)/2

varga citi: for sum of series of squares (1^2 + 2^2 + 3^2+ 4^2 …. + N^2) = N*(N+1)*(2N+1)/6

ghana citi: for sum of series of cubes (1^3 + 2^3 + 3^3+ 4^3 …. + N^3) = (N*(N+1)/2)^2

Varga (वर्ग வர்க) and ghana (घन கன)are the words used in most Indian languages for square and cube. Varga moola and ghana moola are the words used for square root and cube root – incidentally Aryabhata also gave us algorithms to calculate varga moola and ghana moola, but that is a topic for another day.

We learn these formulae in school with Greek notations, invented by European mathematicians in the 18th and 19th century like sigma for sum.

Interestingly the sum of the series of the cubes upto 9, that is, 1^3 + 2^3 + 3^3+ 4^3+…9^3 is equal to 2025, which is the Christian year that comes up shortly. I am sure social media will be full of posters and jpegs and gifs and short videos telling you this interesting fact, and perhaps bated breath narrations of Gauss. And zero mention of Aryabhata. So, here is Aryabhata wishing you a happy 2025.

Ironically Aryabhata knew nothing about this Christian calendar adopted in Constantinople and the Roman empire, a few decades before he was born. He used the Kali Yuga notation in his book on astronomy, giving his own year of birth as 23 years before the 3600th year of the Kali calendar. As 499 AD is Kali year 3600, historians of mathematics believe he was born in 473 AD. In the Kali yuga calendar 2025 is the year 5126 – I am sure enterprising mathematicians will come up with interesting ways to compute this number using Aryabhata’s various formulae.

Related Links

Other essays about Indian Mathematics and Astronomy

My essay in The week magazine on Aryabhata

My essay in Swarajya magazine about Aryabhata

Aryabhata -  CSIR NiScPR Posters

Thursday, 3 October 2024

எல்லோரும் இந்நாட்டு மன்னன்


எல்லோரும் இந்நாட்டு மன்னன்

எல்லோரும் இந்நாட்டு மந்திரி

எல்லோரும் இந்நாட்டு தொண்டன்

எல்லோரும் இந்நாட்டு குமாஸ்தா

எல்லோரும் இந்நாட்டு அறிவாளி

எல்லோரும் இந்நாட்டு அடிமுட்டாள்

எல்லோரும் இந்நாட்டு மாவீரன்

எல்லோரும் இந்நாட்டு படுகோழை

எல்லோரும் இந்நாட்டு காவலன்

எல்லோரும் இந்நாட்டு திருடன்

எல்லோரும் இந்நாட்டு செல்வந்தன்

எல்லோரும் இந்நாட்டு ஏழை

எல்லோரும் இந்நாட்டு வள்ளல்

எல்லோரும் இந்நாட்டு கஞ்சன்

எல்லோரும் இந்நாட்டு முனிவன்

எல்லோரும் இந்நாட்டு முரடன்

எல்லோரும் இந்நாட்டு ஆசிரியன்

எல்லோரும் இந்நாட்டு மாணவன்

எல்லோரும் இந்நாட்டு கிழவன்

எல்லோரும் இந்நாட்டு குழந்தை

எல்லோரும் இந்நாட்டு மன்மதன்

எல்லோரும் இந்நாட்டு சந்நியாசி

எல்லோரும் இந்நாட்டு வண்ணான்

எல்லோரும் இந்நாட்டு நாவிதன்

எல்லோரும் இந்நாட்டு உழவன்

எல்லோரும் இந்நாட்டு குயவன்

எல்லோரும் இந்நாட்டு நெசவாளன்

எல்லோரும் இந்நாட்டு வண்டிக்காரன்

எல்லோரும் இந்நாட்டு நடிகன்

எல்லோரும் இந்நாட்டு ரசிகன்


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என் கவிதைகள்