For over five thousand years, India has been home to one of the fascinating intellectual endeavours that humankind has ever recorded. India, one of the oldest civilizations in the world, has a strong tradition of science and technology. Ancient India was a land of sages and seers as well as a land of scholars and scientists.

From the ancient Vedic ages till today, the Indians have exhibited unmatchable deep understanding and mastery over knowledge across the spectrum. The ancient Indians have left us a great treasure of knowledge, and the rational interpretation of these ideas, which has become the basis of knowledge discovery across the civilization for several ages now. From astronomy to metallurgy, mathematics to medicine, the contribution of Indians to the global knowledge discovery is enormous.

The origins of the Indian scientific endeavours can be traced to the Vedic period, over three thousand years ago. The Indian scientists have made several discoveries, becoming one of the firsts to shed light on several scientific ideas much earlier than the inception of the very same ideas in the west. In addition to discovering and recording scientific phenomenons, the Indian sages had also absorbed the scientific methods of the other culture-areas in all true spirit, thus displaying a real scientific attitude.

In fact, what interesting is, such an effort by the ancient Indians has been characterised by prolonged observations, especially with the naked eye and simple tools, at times aided by techniques that we seem to discard as crude and primitive.

A fact of great significance is that Indians produced a vast literature on different aspects of astronomy, cosmology, numerology, measures of time, development of observatories, instruments etc. The ancient Indians were also the first to study the planetary motions, design calendars, study time and the inter-disciplinary nature of many of these above aspects.

In a book titled *“Indian Astronomy: A Source-Book”*, the authors – BV Subbarayappa and KV Sharma, have recorded more than 3,000 such observations and discoveries by Indian scientists, astronomers and mathematicians over thousands of years. The book intends to provide a general insight into the scientific discoveries in the field of astronomy, numerology, a measure of times and several other aspects that were accomplished in ancient India.

About 3000 verses, written by the likes of the greatest Indian astronomers and thinkers like Aryabhata, Bhaskarcharya, Brahmagupta etc have been extracted from many original sources, mainly in Sanskrit, and presented with their translations in English and notes by the authors.

Here are few of them that shed light into understanding how ancient India was the cradle for one of world’s greatest scientific discoveries.

### 1. Qualifications of an Astronomer:

These passages in Sanskrit brings out the authenticity of the basic characteristics of Indian astronomy as it outlines the expertise expected of an astronomer in ancient times. The below verse outlines how there was utmost importance to accuracy in ancient ages and how one had to adopt the intricate methodologies to become an astronomer. More significantly, the ancient texts gave importance to observation and mathematically developed documentation to ensure that Indian astronomers did not indulge in speculation but on empirical data.

Here is a verse that sets eligibility standards for individual practising astronomy. The ancient verses written during the Vedic ages set rules to be followed by a person before the performance of sacrifices.

The Vedas state that a certain sequence of actions should be followed at appropriate times before performing sacrifices. Hence, he who knows astronomy, which is the science specifying time, knows the sacrifices and, so, is a Vedist, reads the verse written in Rig Veda.

In his extraordinary encyclopaedia *Brihat Samhita*, the ancient Hindu astrologer, astronomer and polymath Varahamihira, has accounted for the detailed qualification one has to possess to become an astronomer. Varahamihira, who himself was an accomplished astronomer during the 6th century BC, was one of the first in the world to study and detail about the Sun in his treatise – *Surya Siddhanta. *

The below verse details the conditions for an individual to be qualified as an astronomer:

The translation reads:

*Among the astronomical calculations, the astronomer should be conversant with the various sub-division of time such as the yuga, year, solstice, season, month, fortnight, day and night, Yama (a period of an hour and a half), muhurta (forty-eight minutes or two ghatis), Nadi (equal to 24 minutes), prana (time required for one inhalation), truti (a small unit of time) and its further subdivisions, as well as with the ecliptic (or with geometry) that are treated of in the five Siddhantas entitled Paulisa, Romaka, Vasistha, Saura and Paitamaha. (4)*

*He should also be thoroughly acquainted with the reasons for the existence of the four measurement systems of the time, viz. Saura or the solar system, Savana, or the terrestrial time, i.e. the time intervening between the first rising of any given planet or star and its next rising, Nakshatra or sidereal, and Chandra or lunar, as well as for the occurrence of intercalary months and increasing and decreasing lunar days. (5)*

*He should also be well-versed with the calculation of the beginning and ending times of the cycle of sixty years, a yuga (a five-year period), a year, a month, a day, a horn (hour), as well as of their respective lords. (6)*

*He should also be capable of explaining, using arguments, the similarities and dissimilarities, and the appropriateness or otherwise of the different systems of measurement of time according to the solar and allied systems. (7)*

*Despite differences of opinion among the Siddhantas regarding the expiry or ending time of an Ayana (solstice), he should be capable of reconciling them by showing the agreement between correct calculation and what has been actually observed in the circle drawn on the ground using the shadow of the gnomon as well as water-instruments. (8)*

*He should also be well acquainted with the causes that are responsible for the different kinds of motions of the planets headed by the Sun, viz. fast, slow, southerly, northerly, towards perigee and apogee. (9)*

*He must be able to forecast, by calculation, the times of commencement and ending, direction, magnitude, duration, intensity and colour at the eclipses of the Sun and the Moon, as well as the conjunctions of the Moon with the five Taragrahas or non-luminous planets and the planetary conjunctions. (10)*

*He should also be an expert in determining accurately for each planet, its motion in yojanas, its orbit, other allied dimensions etc., all in terms of yojanas. (11)*

*He must be thoroughly acquainted with the Earth’s rotation (on its own axis around the Sun) and its revolution along the circle of constellations, its shape and such other details, the latitude of a place and its complement, the difference in the lengths of the day and night (lit. diameter of the day-circle), the carakhandas of a place, rising periods of the different signs of the zodiac at a given place, the methods of converting the length of shadow into time (in ghatis) and time into the length of the shadow and such other things, as well as those to find out the exact time in ghatis that has elapsed since sunrise or sunset at any required time from the position of the Sun or from the Ascendant, as the case may be. (12)*

### 2. Concepts of Astronomy:

#### Shape of Earth:

Even thousands of years before the Western astronomers discovered the shape of the Earth, Indian astronomers had accurately predicted Earth’s shape as ‘spherical’.

During Varahamihira’s period, the development of astrological and astronomical sciences reached a pinnacle. In his book *Paulisa Siddhanta*, Varahamihira gives an exact description of not only the share of the earth, i.e., spherical but also provides its topographical study in detail.

The verse in *Paulisa Siddhanta* accounts, *Earth is spherical and constituted of the five elements, which stands poised in the region of space as if it is an iron ball held in position in a cage of magnets.* (1)

*The whole earth surface is spotted by trees, mountains, cities, rivers, oceans, etc. The Meru mountain (forming the North pole) is the abode of the devas (gods). The Asuras (demons) are down below (i.e. at the South pole). (2) *

*Just as the reflection of the objects on the bund of a water source is upside down, so the asuras are (with respect to the devas.) The asuras, too, consider the devas to be upside down. (3) *

*Just as the flame of the fire, observed by men here, flares upwards, and anything is thrown up falls down towards the earth, the same upward flaring of the flame and the downward falling of a heavy object is experienced by the asuras (at the antipodal region). (4) *

Below is another documentation by Varahamihira describing Earth and its close correspondence with *Panchabhutas*.

*This sphere of Earth, made of akasa, air, fire, water and clay and thus having all the properties of the five elements, surrounded by the orbits (of the Moon, etc.), and extending up to the sphere of stars, remains in (the centre of) space. (1)*

Just as a ball of iron, when placed amidst pieces of magnets, remains suspended in space, in the same manner, this globe of Earth remains in space unsupported, while itself remaining the abode of all. (2)

*The third verse says – Yamakoti is to the east of Lanka (which is in the middle of the Earth), and Romaka (Rome) is to the west. Siddhapura is beneath Lanka (just opposite); the Meru (mountains) is to the north, and the abode of the demons is to the south. (3)*

*These (four cities) are on islands. Meru is on the land, and the abode of the demons (in the south) is surrounded by water. These six places are believed to be situated transversely at a distance of one-fourth of the Earth’s circumference (that is 90°), each from the next one. (4)*

*Those who are at a distance of half the Earth’s circumference from each other are antipodes, just as a man (standing on the bank of a river) and his reflection in the water. The sky is above all. This (globe of Earth) is beneath it. The inhabitants are on the surface of the Earth. (5)*

#### Cause of Earthquakes:

Kamalakara, an Indian astronomer and mathematician, who lived in Varanasi in the 17th century AD, gave the first detailed account of the causes of earthquake within Earth’s crust. However, the European geologists took another century to publish a basic understanding of Earth’s interiors and the phenomenon of Earthquakes.

In his book – *Siddhāntatattvaviveka*, Kamalakara has stated that the Earth’s crust is hard and rocky. Explaining the process of the earthquake, he writes, *a fissure occurs due to lack of strength, gases emerge forcibly, causing the Earth to quake when there would also be constant terrific noise.*

#### Motion of Earth:

Similarly, Lalla, an Indian mathematician, astronomer, and astrologer, had discovered in the 8th century AD that the Earth travelled from west to east and if anyone viewed it from the north pole star Polaris, Earth turns left, i.e., counterclockwise.

The Indian astronomers made accurate discoveries on earth’s rotation and direction of rotation; centuries before, European astronomers came up with such predictions explaining concepts of Earth’s rotation.

Lallas’s documentation on Earth’s rotation on its axis and the direction of its rotation:

The translation of Lalla’s work reads: *The celestial sphere, at the Earth’s equator, is constantly carried towards the west by the Pravaha wind. To the gods (at the north pole), it appears to move (from the left) to the right and the demons (at the south pole from the right) to the left. (3).*

#### Rotation of Earth:

Chaturveda Prithudaka Swami, another astronomer, known for his exemplary work on mathematical equations, explained that it is only the Earth that is regularly rotating once a day, and the sphere of the stars is fixed, causing the rising and setting of the stars and the planets.

In his book – ‘Commentaries on *Brahmasphuṭasiddhanta*‘, Prithudaka Swami explain the causes behind the phenomenon of days and nights.

The translation of one of his works reads:* The Earth’s rotation had been accepted by Aryabhata also, vide his words, ‘The Earth rotates through (an angle of) one second per one prana (of time). On account of (possible) adverse criticism by people, Bhaskara I and others explained the verse to give it a different meaning. *

Aryabhata, arguably the world’s oldest astronomer, had explained the rotation of Earth on its own axis. The above work of Aryabhata is mentioned in his masterpiece – *Aryabhatiyam*, which translated into, *Rotation of the Earth also has been accepted by Acarya (Aryabhata). Note that there is a variant reading as ‘The Earth rotates through (an angle of) one second per one prana (of time).*

In his book, Aryabhata explains, *Just as a man in a boat moving forward sees the stationary objects (on either side of the river) as moving backwards, so are the stationary stars seen by people at Lanka (on the equator), as moving exactly towards the west. (9)*

*(It so appears as if) the entire structure of the asterisms, together with the planets, moved exactly towards the west of Lanka, being constantly driven by the pro-vector wind to cause their rising and setting. (10) *

The earlier texts also had reference to the direction of the earth’s rotation. Makkibhatta, too has discovered that the Earth rotates on its own axis from west to east.

#### Dimensions of the Earth:

Rig Vedic verses, written more than 5,000 ago, had estimated the dimensions of Earth. Here is a Rig Vedic verse that mentions Mother Earth and its dimensions. It is by far the oldest document to speak, even though it does not explain details about the dimensions and size of the earth.

The translation of the Rigvedic verse translated into: *Oh (God) Indra, were this Earth to magnify itself tenfold (i.e., infinitely) and men who live on it multiplied day by day, then and then alone will the lauded might and glory of yours be as vast as the heavens. *

In his seminal work, Varahamihira builds on assumptions of Rigvedic times and accurately estimates the circumference of the earth as 3200 yojanas. Furthermore, each Yojana is estimated to be 12-15 km, which translates into nearly 38,000 km to 45,000 km, which is almost accurate to the current estimates.

Earth’s circumference is the distance around Earth and it is Measured around the Equator, it is 40,075.017 km.

*When situated on the equator, the Sun is visible from pole to pole at all latitudes, making the day and night equal). The middle of the Earth (the North pole is meant here) is north of Ujjain by 586 2/3 yojanas. It is north of Lanka by 800 yojanas. *

#### Earth: Diameter and Circumference

Similarly, in his book *Khandakhadyaka*, Brahmagupta had also estimated the circumference of the Earth. The above documentation in his book suggests that he had mathematically derived an accurate measurement of Earth’s circumference.

The translation of Brahmagupta’s work reads: *Multiply 5000 by thejja of the colatitude of the place and divide the product by the trijyd. The result is the correct circumference of the Earth at that place. (6a)*

Deva, another ancient astronomer, too had come up with an accurate measurement of the Earth’s circumference. In addition to it, Deva had also calculated the distance between Ujjain (Madhya Pradesh) and Lanka (Sri Lanka), which was nearly 200 yojanas, approximately 3,000 km.

The translation of the above reads: *3299 (yojanas) is the Earth’s circumference; this divided by 16 gives the distance between Lanka and Avanti (or Ujjayini.) *

Similarly, Bhaskara II – in his major treatise *Siddhanta Siromani*, had said that that the circumference of the Earth sphere is said to be 4967 yojanas.

*Its diameter is 1581 1/24 yojanas. The surface area thereof is 7,85,034 square yojanas, for it is obvious that, as in the case of a spherical ball, the product of the Earth’s circumference and its diameter gives its surface area. (52),” Bhaskara II wrote in Siddhanta Siromani. *

Interestingly, Bhaskar was one of the first to provide an accurate mathematical model to derive the circumference of the Earth. According to his estimation, Earth was 4967 yojana and its diameter 1581.

As per Bhaskara II, a yojana is equal to the *(distance between the two places*360)/(circumference-(difference in the latitudes of two places on the same terrestrial meridian in degrees)*.

In his book, Bhaskara II notes, *The equatorial circumference of the earth multiplied by cos 0 and divided by R, or multiplied by 12 and divided by the hypotenuse of the right-angled triangle formed by the gnomon and the equinoctial midday shadow thereof, (hereafter called equinoctial hypotenuse), gives the circumference of the Earth parallel to the equator and passing through the locality (hereafter called the rectified circumference)*.

Estimating the earth’s circumference, Astronomer Nilakantha had accurately measured that the earth’s diameter is around 1050 yojans, i.e., 12,000 km.

His above work reads: *The terrestrial sphere is 1050 yojanas in diameter and it stands in the sky in the centre of the celestial sphere, as the lowest point.*

Here is another ancient text giving us the mathematical formulae to determine the circumference of the earth.

The above verse reads: *Having fixed upon two places situated exactly north and south, determine their latitudes and the number of yojana-s between them. Then apply the rule of three: If their difference in latitudes causes the distance between the two places, how much (will the distance be) for the degrees in a circle (i.e., 360°)? The result will be the circumference of the Earth. (12-13)*

The next verse explains: *If the difference in degrees of the two latitudes is the yojanas between them, how many will the yojanas be for 90°, which is the latitude of Meru? This will give a quarter of the circumference of the Earth. (14). *

### 3. Decimal numbers:

Indian mathematicians first recorded the Decimal number system, which is the basis of modern mathematics today. The ancient and medieval Indian mathematical works, all composed in Sanskrit, consisted of several sutras discussing the Decimal system of numbers.

It was Indians who gave the ingenious method of expressing all numbers by means of ten symbols – the decimal system. The simplicity of the decimal notation facilitated calculation, and this system invented by the Indians made the uses of arithmetic in practical inventions much faster and easier.

In his work *Aryabhatiyam*, Aryabhata explains the decimal system of numbers, where the corresponding place value of a digit is always 10 times as great as the place value of the digit to its right.

The translation of Aryabhata’s work, originally written in Sanskrit: *Eka (unit’s place), DaSa (tens place), Shatha (hundreds place), Sahasra (thousands place), Ayuta (ten thousand place), Niyuta (hundred thousand place), Prayuta (millions place), Koti (ten million place), Arbuda (hundred million place), and Vrnda (thousand million place) are, respectively, from place to place, every ten times the preceding. (2) *

Astronomer-mathematician Sankara Varman, in the later part of the medieval era, also explained the decimal system that was enumerated by the likes of Aryabhata.

The translation of the above work reads: *Eka (1), Dasa (10), Shatha (100), Sahasra (1000), Ayuta (10,000), Niyuta (or Lakh, 10s), Prayuta (10^6 ), Koti (10^7), Arbuda (10^8), Vrnda (10^9), Kharva (10^10), Nikharva (10^11), Mahapadma (10^12), Sanku (10^13), Varidhi (10^14), Antya (10^15), Madhya (10^16), Parardha (10^17) are numbers, each tenfold of the previous.*

Here is a Yajurvedic verse that also cites the usage of the decimal system of numbers in the Vedic era. In addition, the Yajurvedic hymns mention the usage of the decimal value system in its ritual practises.

The translation of the hymn reads: *O Agni, may these (sacrificial) bricks be my own milch-kine: one and a ten, a ten and a hundred, a hundred and a thousand, a thousand and a ten thou¬ sand, a ten thousand and a hundred thousand, a hundred thousand and a million, a ten million, a hundred million, a thousand million, a ten thousand million, a hundred thousand million, a million-million or billion. May these bricks be mine milch-kine in yonder world and in this world.”*

### 4. Measures of Time

In India, a system of time measurement was in place as early as in Early Vedic Era, dating 2500 BCE. There are several references to the measurement of time in sa and Upanishads.

Here is a Rigvedic hymn explaining the way time was measured in the Vedic age. The above hymn reads that the division of time in Vedic era was on the basis of Year, Months and Days.

The translation of the Rigveda hymn says: *The wheel (of time) formed with twelve spokes revolves round the heavens without wearing out. O Agni! on it are 720 sons (viz. days and nights)*.

The above verse says time was divided into 12 spokes (hourly), with a combined 720 days and nights – making it 360 calendar days.

Another Rig Vedic hymn says:* The fellies (or arcs) are twelve; the wheel is one; three-(partitioned) are the axles (or hubs); but who knows it? Within it are collected 360 (spokes), which are, as it were, movable and unmovable.*

According to Rig Veda, sage Dhrtavrata knew the twelve months. He also knows the month that is created, the Vedic documents reveals suggesting that the Vedic people knew and practised a sophisticated system of time consisting of 360 days, 12 months, which is almost identical to the Gregorian system of calendars which came thousands of years later and continued to be used even today.

Here is another Yajurveda prayers for hailing interstellar objects such as sun, moon, stars, responsible for formation of day and nights.

*Oblation to (the intercalary month) Samsarpa, an oblation to the Moon, an oblation to the luminaries, an oblation to (the intercalary month) Malimluca, an oblation to the Sun,* reads the Yajurveda verse.

Taittiriya Brahmanas also list the names of 13 months as per the Lunar system of calendar.

The names of the thirteen months: *Aruna, Arunarajas, Pundarika, Visvajit, Abhijit, Ardra, Pinvamana, Anna- van, Rasa-van, Iravan, Sarvausadha, Sambhara and Mahasvan.*

The Taittiriya Brahmanas also mentions the names of 24 half-months (pakshas):

The names of the 24 half-months are: *Pavitra, Pavisyan, Puta, Medhya, YaSas, Yasasvan, Ayus, Amrta, Jiva, Jivisyan, Sarga, Loka, Sahasvan, Sahlyan, Ojasvan, Sahamana, Jayan, Abhijayan, Sudravina, Dravinodas, Ardrapavitra, Harikesa, Moda and Pramoda.*

The Satapatha Brahmanas also mentions the Lunar year consisting of 354 days.

*Verily, they who perform the Full and New Moon sacrifices run a race. One ought to perform it for fifteen years. But, in these fifteen years, there are three hundred and sixty full moons and new moons. And, there are, in a year, three hundred and sixty nights; it is the nights he thus gains. (10)*, reads the Satapatha Brahmana.

Further, *He should then sacrifice for another fifteen years. In these fifteen years, there are three hundred and sixty full moons and new moons, and there are in a year three hundred and sixty days; it is the days he thus gains, and the year itself he thus gains. (11)*

The authors have documented more than 3,000 verses in their magnum opus, that shed light on the major scientific accomplishments by Indians hundreds of years even before their western counterparts had conceptualised these ideas.