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 astronomy books. But there I go, using Greek and Latin words for Sanskrit.

Let me rephrase. Ganitam गणितं was a chapter in Jyotisham ज्योतिषं books. Jyotisha is astrology, isnt it? 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 revolutionised astronomy. But astronomy was a science for several thousands of years before the telescope.

All ancient cultures such as Egypt, Sumeria, China, India practised 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 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 political history 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:

1. Vedic era (before 5th century BC)

2. Eighteen Siddhantas era (5th century BC to 5th century AD)

3. Classical era (5th century AD to 17th century AD)

4. Post-colonial era (after 17th century)

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 that 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 Vedangas, were devised to help students learn, interpret and understand the Vedas. These Vedangas are:

1. Shiksha (Pronunciation)

2. Vyaakarna (Grammar)

3. Chandas (Prosody)

4. Nirukta (Etymology)

5. Kalpa (Ritual)

6. Jyotisha (Astronomy)

The first four of these deal primarily with language (Linguistics) and the last two primarily 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 given to Jyotisha.

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 complex figures like birds.

The bird shaped altar consisted of several hundred rectangles, trapeziums, triangles, etc. and constructing them with bricks of a 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 cultures, 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 30 thithis, 15 from new moon to full moon (called waxing fortnight in English and shukla paksha in Sanskrit), and 15 from full moon to new moon (called waning fortnight in English and krishna paksha in Sanskrit).

This 30 thithi period is maasa. Note that each thithi or lunar day is slightly shorter than each solar day. Twelve lunar maasas will total up to 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 6,000 stars in the night sky, but Indian astronomy has a named cycle of 27. Why? There is a very scientific reason. These 27 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 cycle…. Ashwini, Bharani, Kriththika, Rohini….with series ending in Revathy on the 27th night.

So, each night or day was called by that star… or nakshatram; the English astronomical term for this is Stellar Day. They also noted that moon became a full moon, only when it was next to some of these 27; 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 and so on.

Notice that this system of individual stars contrasts starkly with the 12 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 themselves 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 2,000 years after Lagadha, who is considered 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.

Also read: Not Only Of Religion And Literature, Sanskrit Was Also The Language Of Science