An Introduction to Indian Astronomy

Vedic Mathematics is a popular catchphrase. Vedic Architecture is another. Rarely have I heard the phrase Vedic Astronomy though. Which is odd. Aryabhata, famous for being a mathematician, was primarily an astronomer. Mathematics was a chapter in his astronomy book.

In fact, for several centuries, Mathematics was a chapter in Indian Astronomy books. Let me rephrase. Ganitam was a chapter in Jyotisham books. Isn't Jyotisha astrology or is it astronomy? Was it superstition or science or an inseparable mix of both?

Jyoti is the Sanskrit word for light. In this particular context, it means “celestial object that emits light”. Jyotisham is the science of such objects, which includes the Sun, the Moon, the planets, and stars. A jyotishaH studies these celestial objects.

We think of the telescope as the instrument that revolutionized astronomy. But astronomy was a science for several thousands of years before the telescope. All ancient culutres, Egypt, Sumeria, China, India practiced extensive astronomy long before the ancient Greeks, who adopted or acquired quite a bit of their astronomical knowledge from some these cultures. The most important tool for astronomy was not just the naked eye, but observation and recording.  The second most important tool was mathematics.

So entwined was mathematics with astronomy in India, that the word gaNakaH (mathematician) was effectively a synonym for astronomer.

Kaala Dik Desha Jnaanam

What was the point of studying these? Surely, to cast horoscopes, find a bride or groom, the right time to perform a wedding, build a house or palace or temple, start a journey, etc? That is the popular belief. I’ve rarely seen a dissenting opinion anywhere, especially from atheist scientists. The oldest surviving jyotisham texts we have, the Rg Vedanga Jyotisha and Yajur Vedanga Jyotisha very clearly explain the purpose of studying this field.

तस्माद् इदं कालविधानशास्त्रं यो ज्योतिषं वेद स वेद यज्ञान् ॥

tasmaad idam kaala-vidhaana-shaastram yo jyotisham veda sa veda yajnaan

 

"kaala-vidhaana-shaastram" means “the science of determining time ”. The second half of the sloka means : “He who knows jyotisham knows the yajnaas”. The primary purpose was to calculate time, so that the right yajnaas can be performed at the correct time.

Another work expands this definition to “Kaala-dik-desha-jnaanaartham” : To find time, direction and geography.

All personal uses of jyotisham were secondary.

Eras of Indian astronomy

We divide Indian history political into several eras, usually as Hindu era, Muslim era, British era, and post Independence. We can similarly divide the history of Indian Astronomy into several eras:

Eras of Indian Astronomy
---	Vedic Era
1400 BC	Vedanga Jyotisha
500BC - 500 AD	Rishi Siddhantas
500AD - 1500 AD	Classical Era

 

The only surviving text of the Vedic period are the Rg and Yajur Vedanga Jyotishas. They both have 36 identical slokas, but the Yajur version has one extra sloka. The author of both Vedanga Jyotishas  was Lagadha, of whom we know extremely little. He compiled that knowledge preceded him.

The Vedas themselves are about ritual, revelation, philosophy, prayer, etc. Their purpose is not astronomy or mathematics. Six additional subjects of study, called Vedaanga-s, were devised to help students learn, interpret and understand the Vedas. These Vedaangas are:

The Six Vedangas
Shiksha Phonetics   VyaakaraNa Grammar Chandas  Prosody        Nirukta         Etymology	Linguistics
Kalpa             Ritual        Jyotisha    Astronomy	Mathematics

The first four of these deal primarily with language (Linguistics) and the last two primariy with mathematics. It is worth observing, that the Sangam Tamil book Tolkappiyam deals with the first three subjects, for Tamil, as three different sections.

A beautiful sloka describes the importance give to Jyoisha

यथा शिखा मयुराणां नागानां मणयो यथा ।
तद्वद् वेदाङ्गशास्त्राणां ज्योतिषं मूर्धनि स्थितम् ॥ 

yathaa shikhaa mayurANAm naagaanaam maNayo yathaa
tadvad vedaanga shAstrANAm jyotisham murdhani sthitam 

Yathaa - Just as
shikhaa - crest
mayurANAm – among peacocks
naagaanaam – among serpents
maNayo - jewels
tadvad – thus too
vedaanga  shAstrANAm – among vedanga shastras
jyotisham – astronomy
murdhani – on the head
sthitam – stands 

Just like crests on peacocks, and jewel on serpents
Thus among vedanga shaastras, Jyotisham crowns the head 

Sulba sutras

Texts called the Sulba sutras are part of Kalpa, and they describe the geometry of Vedic altars. Altars for the yajnas were to be constructed in various shapes, including circle, semicircle, square, octagon and compex figures like birds. The bird shaped altar consisted of several hundred rectangles, trapezeums, triangles, etc. and constructing them with bricks of predetermined size was a complex geometrical exercise. These were measured using ropes (sulba or rajju). This is one noticeable practical difference between the practical origins of Indian versus Egyptian or Greek geometry. In the latter culutres, the primary practical motivation was measurement of land, especially farmland. Hence the subject was named geo (earth) metry (measurement). This is also a major difference between Vedic and Jain or Buddhist mathematics; since the latter religions did not need performance of yajnas, the theoretical pursuit of scholars of those faiths were also somewhat different.

There were several Sulba sutras, authored by different people and named after them like Baudhaayana, Aapastambha, Kaatyaayana etc.

But us let get back to astronomy now. And the determination of time.

Solar, Lunar, Stellar Days

The period from one sunrise to another, is called a dina, divasa or aha in Sanskrit. Since the Sun causes the day, he is called Dina-kara (the maker of the Day). The English astronomical term for this is Solar Day.

The period from one moonrise to another, is called a thithi in Sanskrit. (Lunar Day).

There are thirty thithi-s, fifteen from new moon to full moon(called waxing fortnight in English and shukla paksha in Sanskrit), and fifteen from full moon to new moon (called waning fortnight inEnglish and krishna paksha in Sanskrit). This thirty thithi period is maasa. Note that each thithi or lunar day is slightly shorter than each solar day. Twelve lunar maasa-s will total upto 354 rather than 365 solar days. This quickly led to a mismatch between lunar year of  and solar years, and was resolved using a concept called adhika maasa (or extra month). Once every five years, adhika maasas were used to realign solar and lunar years. According to Vedanga jyotisha, this five year period was called yuga. But in all later siddhantas, the yuga is a much longer period of several lakh years.

We can see about six thousand stars in the night sky, but Indian astronomy has a named cycle of twenty seven. Why? There is a very scientific reason. These twenty seven stars lie along the orbit of the moon around the earth.

Each night the moon changes its position in the sky against the background stars (because it is orbiting the earth). Oriental historians called these lunar mansions. The name of the brightest star next to the moon on each night was observed to fall in a certain cylce…. Ashwini, Bharani, Kriththika, Rohini….with series ending in Revathy on the twenty seventh night. So each night or day was called by that star… or nakshatram; the English astronomoical term for this is Stellar Day. They also noted that moon became  a full moon, only when it was next to some of these twenty seven; hence the months were named after those stars. So the month where the full moon was next to Chitra was called Chaitra; when next to Visaka was called Vaisaaki, when next to Kritthikaa was called Kaarthika, when next to Mrigasirsha the month was called Maargasirsha….and so on. You can see local adaptations of these names in various languages. So Vaisakhaa is called Baisaaki in some languages, Sravishtam is called Avittam in Tamil, etc.

Notice that this system of individual stars, contrasts starkly with the twelve Sumerian/Greek constellations called the zodiac

Divisions of the Day

The sun moon and the stars form natural clocks in the sky. These were useful to divide years into days and months, but the days themselve were divided into naadi and vinaadi using artificial devices like water pots of particular volume. These terms evolved over the ages.

A verse by Aryabhata concisely explains these divisions

वर्ष द्वादश मासास्त्रिंशद्दिवसो भवेत् स मासस्तु ।
षष्टिर्नाड्यो दिवसः षष्टिश्च विनाडिका नाडी ॥

varsha dvaadasha mAsA   trimshad divasO bavEd sa mAsa tu
shashTi naaDIya divasa    shashti vinaaDikaa naaDee 

varsha - Year
dvaadasha - twelve
mAsA   - months
trimshad - thirty
divasO - days
bavEd - become
shashTi – sixty 

A year is twelve months, a month thirty days
A day is sixty naadi-s, a naadi is sixty vinaadi-s 

Aryabhata is estimated to have lived nearly two thousand years after Lagadha, the most ancient Indian astronomer; what a pity most of us have never heard of him. In fact, we are chronologically closer to Aryabhata than he was to Lagadha. How did the science develop in those two millennia? We will discuss these next.

References

• 1.      Facets of Indian Astronomy, KV Sarma, 1975
• 2.      The Aryabhatiya of Aryabhata, KV Sarma and KS Shukla
• 3.      Oral Traditions of Sanskrit, Powerpoint presentations of Prof S Swaminathan

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This essay was first published in a series in Swarajya magazine

Related Links

My blogs on Astronomy and Mathematics

Video of my Lecture at Indian Science Festival, Pune: 

The men who knew Zero to infinity January 2020

The 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 9^th 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 

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

Related Links

My blogs on Astronomy and Mathematics

Shilpam Science Sundaram - TEDx lecture at Saveetha Eco Pupil school