THE FORGOTTEN SCIENTIFIC HERITAGE: THE INDIA STORY (PART 1)

 India is a land of great diversity. This diversity is seen not only in its culture but also in the advancements that the country has made in the field of science and mathematics. Our textbooks and journals often attribute groundbreaking scientific ideas to foreign 'geniuses,' while many of these discoveries actually have their origins here in India. As a result, we are neglecting the Indian roots and contributions that formed the foundations of most of those theories.

The term 'foreign' is inappropriate in the context of science, as scientific discoveries, regardless of where they originate, have a global impact and contribute to the collective knowledge of humanity, without assigning exclusive credit to any one country or individual.

The purpose of this blog is to highlight the significant advancements in science and mathematics made in India, which have often been overshadowed or credited to other countries or scientists.

In this blog we will be discussing about the Kerala School of Astronomy and Mathematics.

बकुलाधिष्ठितथ्वेना 

विहारो यो विष्यथे 

ग्रुहानमणि सोयं स्याथ 

निजनमणि माधव |

-Madhava (13th sloka, Venuroham)

Astronomical and mathematical development in India is not well known after 10^th century AD and many important works that prove the presence of many great astronomers and mathematicians of Kerala remain little known in the field of history of science. One such great astronomer-mathematician was Madhava of Sangamagrama. Sangamagrama Madhava’s work Venuaroham was used for the computation of the true longitude of the moon. Sangamagrama Madhava was one of the great geniuses of the time before Kepler and Newton.

Sangamagrama Madhava and his school were known to the western world through a series of papers published by Charles Whish in 1834 in the journal called Transactions of Asiatic Society of Great Britain and Ireland. In his series of papers, Whish showed that works of Newton, Leibnitz, Gregory and others (who lived during 17^th -18^th century) were just rediscoveries of the mathematics contributed by the Kerala School. 

 Portrait 1: Madhava of Sangamagrama

While Europe was divided in modeling solar system to geocentric and heliocentric systems even in the 17th century, an astronomer-mathematician from Kerala during the 16th century described observational studies as geocentric which can be transformed into a mathematical model with the Sun as the centre. 

Neelakanda Somayaji, born in present day Malappuram district of Kerala, a 16^th century astronomer-mathematician belonging to a long guru-sishyaparampara chain of five hundred years of length, described in his work, Tantra Sangraha, the subject of  observational astronomy along with necessary mathematical techniques. 

Neelakanda also made a significant contribution by revising Aryabhata's model for the interior planets, Mercury and Venus. His modifications provided a more precise calculation of the equation of the center for these planets, surpassing existing models in Islamic and European astronomy prior to Johannes Kepler, who emerged 130 years later. This provides a significant insight into the groundbreaking contributions of Indian scientists, demonstrating their achievements in comparison to global advancements at that time.

In his work, Aryabhatiyabhasya, Neelakanda devised a computational scheme for planetary motion that outperformed later models, including Tycho Brahe's. His approach suggested a heliocentric system where Mercury, Venus, Mars, Jupiter, and Saturn orbited the Sun, which itself circled the Earth.

Figure 1: The Temple in Kerala were Madhava made his great discoveries.

MADHAVA'S ANOMAMLISTIC CYCLES

Figure 2: Moon's Synodic and Sidereal cycle

The fundamental lunar cycles in relation to the Earth are the Synodic cycle  (refer my blog on the Moon), which has a period of 29.5 days (New Moon to New Moon) and the Anomalistic cycle (perigee to perigee) which is 27 days 13hrs 18min 34.45s (about 27.5 days). Anomalistic cycles from a zero period will end at cycle number, days, hours, minutes, seconds respectively as follows:

1, 27,13 18 34.45

2, 55, 02,37, 08.90

3, 82, 15, 55, 43.35

4, 110, 05, 14, 17.79

5, 137, 18, 32, 52.24

6, 165, 07, 51, 36.69

7, 192, 21, 10, 01.14

8, 220, 10, 38, 35.59

9, 247, 23, 47, 10.04

As you can see the difference between successive cycles is 12 hours and alternate cycles is 24 hours. This means that successive durations corresponds to alternate day-night difference.

Let's discuss the way in which Madhava devised this entire concept.

The Madhava Algorithm

Before going into the algorithm it is important to understand some terms:

1) ध्रुव कालम् (Dhruva Kalam)

    It is the time at which the Moon and its apogee (the point in the Moon's orbit which is farthest away from Earth) lines up. 

2) चन्द्र तुंगा योग (Chandra Thunga Yogam)

    After Dhruva Kalam, for nine revolutions of the Moon around the Earth, the position of the Moon  shifts by 3 degrees every day. These nine shifts are called the Chandra Thunga Yogams.

3) सूर्योदय मध्य (Suryodaya Madya)

    The starting reference point for the calculations is when the Chandra Thunga Yogam occurs at sunrise. This is known as Suryodaya Madhya. 

4) ध्रुवः (Dhruvas -D1 to D9): These are specific points in time (measured in days) when a particular cycle of the Moon's alignment with its apogee (farthest point from Earth) completes. Each Dhruva represents the end of a particular anomalistic cycle of the Moon.

5) चन्द्रवाक्यम् (Chandravakya - S1 to S9): These are the angular positions of the Moon in its orbit (measured in degrees) when each of the Dhruva cycles ends. Essentially, they tell us where the Moon is in its orbit when these Dhruva cycles complete.

With this reference in mind, let us delve deeper into the details.

Position of the moon and the apogee coincide during a time called dhruva kalam. The algorithm of Madhava is based on the computation of 9 dhruvas (D1, … D9). 

When position of the moon and the apogee coincide during a time, dhruva kalam, from that  point of time there will be 9 Chandrathungayogam which can be computed as follows:

For each moon revolution around the earth, the Chandrathungayogam will get shifted by 3 degrees every day. To start with a reference point, the starting point will be when Chandra thunga yogam happens at sunrise (Suryodaya Madhya). 

The number of days of this type is 188611 and the completed moon’s orbiting around the earth is 6845. From this we can calculate the moon orbiting period as:

188611/ 6845 = 27.5 days approximately (27 days 13h 18m 34.45s to be exact). 

Based on Madhava’s algorithm, we can find that anomalistic cycles from a zero period will end respectively at Dhruvas D1 to D9 at 6460, 3411, 362, 4158, 1109, 4905, 1856, 5652, and 2603 respectively and corresponding chandravakya S1 to S9 as 0, 28, 56, 83, 111, 138, 166, 193, and 221 respectively.

D1: After 6,460 days, the first Dhruva cycle completes.

• S1 (Chandravakya at D1): 0 degrees. This means that at the end of the first Dhruva cycle, the Moon is at 0 degrees in its orbit, marking the start of the next cycle.

D2: After 3,411 days, the second Dhruva cycle completes.

• S2 (Chandravakya at D2): 28 degrees. This means that when the second cycle ends, the Moon is at 28 degrees in its orbit.

D3: After 362 days, the third Dhruva cycle completes.

• S3 (Chandravakya at D3): 56 degrees. At the end of this third cycle, the Moon is positioned at 56 degrees in its orbit.

D4: After 4,158 days, the fourth Dhruva cycle completes.

• S4 (Chandravakya at D4): 83 degrees. The Moon's position at the end of the fourth cycle is 83 degrees.

D5: After 1,109 days, the fifth Dhruva cycle completes.

• S5 (Chandravakya at D5): 111 degrees. At the conclusion of the fifth cycle, the Moon is at 111 degrees in its orbit.

D6: After 4,905 days, the sixth Dhruva cycle completes.

• S6 (Chandravakya at D6): 138 degrees. The Moon is positioned at 138 degrees at the end of the sixth cycle.

In summary,

D1: 6,460 days → S1: 0 degrees

D2: 3,411 days → S2: 28 degrees

D3: 362 days → S3: 56 degrees

D4: 4,158 days → S4: 83 degrees

D5: 1,109 days → S5: 111 degrees

D6: 4,905 days → S6: 138 degrees

D7: 1,856 days → S7: 166 degrees

D8: 5,652 days → S8: 193 degrees

D9: 2,603 days → S9: 221 degrees                                                                                                                                                                                                                                                                                Each Dhruva represents a significant point in the Moon’s alignment cycle, and the Chandravakya values provide the specific angular positions at these points.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              TO BE CONTINUED...                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    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Kerala School of Astronomy and Mathematics - Dr. M.D. Srinivas; Centre of Policy Studies, Chennai; Indian Institute of Technology Guwahati.

Kerala School of Astronomy and Mathematics: Contributions and Contemporary Reference - Indira Gandhi National Centre for the Arts, Government of India.

The Legacy of Sangamagrama Madhava and Kerala School of Astronomy and Mathematics - Science India Magazine                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  *All the media published in this blog belongs to their original creators and 'Knowledge Through Science' does not claim any right over it.