INTRODUCTION #
The Ancient Indian Scholars were highly aware of the fundament concepts of nature. They marveled in the field of medicine, Astronomy, Metallurgy, Mathematics, medicines, etc. which is yet to be fully explored and understood.
ASTRONOMERS AND THEIR CON- STRIBUTION #
The following table shows the astronomers, their contribution and the instruments used by them, which are briefly described in this module:
Surya Siddhanta #
In India people had started the use of the astro- nomical instruments before 1000 BC. During this period one of the prominent books ‘Suryasidhanta’ was written for astronomical calculations.
Please note that there are several works with the same name, BUT the Original writer of Surya Siddhanta is UNKNOWN. The title ‘Suryasidhanta’ means sun theory and it highlights the calculations of positions of stars and planets. Some of the Indian mathematicians later have developed their own instruments and developed their own methods to facilitate the theory of ‘Suryasidhanta’. Introduction of zero in mathematics and the decimal method of calculation is one of such invaluable contribution. We should note that Varahamihira had contrasted Surya Siddhanta along with his 4 other treatises in
the panchsiddhantika viz. Paitamaha Siddhantas, Paulisha , Romaka Siddhantas and Vasishta Sid- dhanta. Citation of the Surya Siddhanta is also found in the works of Aryabhata.
Panchasiddhanta of Varahamihira (505 AD) #
He has done a valuable job of compilation of five astronomical theories, which were in use before Christ, and suryasidhanta is one of them. This com- piled book is known as ‘Panchasidhanta’. He had developed some ring and string instruments.
THE TWELVE YANTRAS OF LALLA (700 AD) #
Lalla was an Indian astronomer and mathema- tician who followed the tradition of Aryabhata-I. Lalla’s most famous work was entitled Shishya- dhividdhidatantra. He was well known because of twelve instruments which he brought into practice.
Lalla describes the 12 Instruments as follows:
Sphere, ring, dial, bow, time measuring water vessel, Gnomon, divider, scissor. Circular seat with central stick, semicircle with stick, combination of sticks, are the twelve instuments along with a stick.
The 12 instruments are as follows:
- The Gola yantra is a type of armilliary sphere used to locate planetary positions.
- Bhangana is a ring with angular graduations
along its circumference, it is a type of pro- tractor.
- Chakra is a circular disk with angular gradu- ations. It is also a type of protractor.
- Dhanu is a semicircular disk with angular graduations and a stick pivoted at the center, it is a type of protractor with a plumb bob arrangement.
- Ghati is a small vessel with a hole at the bottom. It was used to measure time.
- Shanku is a type of gnomon, a long vertical cone used to identify East-West-North-South direction based on shadow of its tip.
- A special geometrical construction known a ‘Matsya’ was used for the above purpose. Altitude of sun and day time was also measured with this instrument based on the shadow.
- Shakata consists of two ‘V’ shaped sticks, pivoted at the end.
- Kartari means a seizer. This instrument is made up of two sticks both pivoted together. It was used like a caliper, and also to measure angle with the help of protractor.
- Pitha is a horizontal disk with a vertical stick at its center. It was used to measure local time based on its shadow, it was used to measure the height with the help of special geometrical contruction.
- Shalaka is combination of two sticks with a string.
- Yasti is just a long stick having standard dimensions. It was used to measure height and distances. Special geometrical constructions were framed to facilitate the use of this stick. These proposed geometrical constructions were to construct the proportionate triangles with the help of which heights of terrestrial objects could be calculated.
THE SIDDHANT SHIROMANI & YASTI YANTRA OF BHASKARACHARYA (1072 AD) #
He was one of the promonent Indian math- ematician and astronomer, who wrote a book
‘Sidhantshiromani’. In his book, he has documented valuable ancient liturature and given the references of many of the instruments used by the astrono- mers before him. Similarly, he has documented the various methods for the use of these instruments. Yasti means a stick. Yasti Yantra was developed by Bhaskaracharya and has also been refered to as Dhi Yantra. The same type of instrument has also been described by ancient sages and astronomers, but Bhaskaracharya has developed this Yantra as unique methods to calculate the height of terrestrial objects like trees and mountains. The usage and principles have been described in the ‘Shidhantashiromani’ of Bhaskaracharya.
Time: Vipal, Pala, Gati, Hora, and Dina #
Sixty Vipala makes one pala. Sixty pala makes one ghati. 150 Pala makes one Hora. 24 Hora (Hours) makes one Dina (a day).
Geometry in Vedic Age- Sulvasutras #
Some scholars have shown on the basis of evi- dence in Shatapatha Brahmana that Indian geometry predates Greek geometry by centuries. It has been argued that Geometry and Mathematics had a ritu- alistic beginning in India centuries before Greeks or Babylon. In these rituals, Earth was represented by Circular altar and heavens were represented in Squar altar. There were eagle shaped altars also. The examples are as follows:
The Ritual consisted of coverting the Circle into a square of identical area. As per a paper by Seidenberg: Babylonia [1700 BC] got the theorem of Pythagoras from India or that both Old-Babylonia and India got it from a third source. The source quoted was Sulvasutras.
Sulvasutras deal with complex fire altars of vari- ous shapes constructed with bricks of specific shapes and area. The total area of the altar must always be carefully respected. This proves that despite of no existance of algebra, there was an awareness of precise purely geometrical calculations.
Seidenberg’s conclusion of India being the source of the geometric and mathematical knowledge of the ancient world has been included now in chronology of the texts. Please note that Sulva sutras belong to a bigger text Shrauta Sutras. The four major Sulva
Sutras, which are mathematically the most signifi- cant, are those composed by Baudhayana, Manava, Apastamba and Katyayana. Out of them the oldest belongs to Baudhayana and dates back to 600BC. They discuss the cases of the Pythagorean Theorem and Pythagorean triples.
The Baudhayan Sulbasutra 1.48 says: The diag- onal of a rectangle produces both areas produced seperately by its two sides.It is represented as follows
In the Baudhayan’s Sulva Sutras we should note that the Right angles were made by ropes marked to give the triads 3, 4, 5 and 5, 12, 13 (32 + 42 =
52, 52 + 122 = 132)
Sulva Sutra also mentions a ritual which included “Squaring the circle” (and vice-versa), thus geometrically constructing a square having the same area as a given area. It has worked out the square root of 2 to 1.414215, up to last 5 decimals.
Knowledge of Days of Year #
There have been found symbols that prove that the Aryans knew about the year. In a ritual, pebbles were placed around the altars for the earth, the atmosphere, and the sky. The number of these pebbles was 21, 78, and 261, respectively. These numbers add up to the 360 days of the year. There were other features related to the design of the altars which suggested that the ritualists were aware that the length of the year was between 365 and 366 days.
Saraswati Script #
Most probably, the first true alphabetic script was Saraswati Script that was practiced on the banks of Saraswati River. It has been hypothesized that symbol of Zero was devised by unknown Indians who were inspired with the Fish sign of Brahmi script that refered to 10. However, it was not till 6-8th century AD, when practical calculations were carried out using zero.
Knowledge of Binary Numbers – Pingala #
The Indian scholar Pingala (circa. 5th-2nd cen- tury BC) used binary numbers in the form of short and long syllables (the latter equal in length to two short syllables).
Pingala used in his Chhandahshastra. The knowledge of binary numbers indicates his deep
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understanding of arithmetic. Binary repersentation has now become the basis of information storage in terms of sequences of 0s and 1s in modern-day computers.
Ghati Yantra #
The meaning is that a Ghatika or (bowl) is a hemispherical vessel made of copper with a small aperature at the bottom so that it sinks into the water 60 times in a day and night.
The clepsydra (Ghatî -yantra) was used in India for astronomical purposes until recent times. Brah- magupta of Bhilamala in Rajasthan, who was born in 598 A.D, wrote his masterpiece, Brahmasphuta Siddhanta, in 628 A.D. His school, which was a rival to that of Aryabhata, has been very infuential in western and northern India. Brahmagupta’s work was translated into Arabic in 771 or 773 at Baghdad and it became famous in the Arabic world as Sin- dhind. One of Brahmagupta’s chief contributions is the solution of a certain second order indeterminate equation which is of great significance in number theory. Another of his books, the Khandakhadyaka, remained a popular handbook for astronomical com- putations for centuries.
The gahtiyantra theory interprets that the vessel sinks in 24 Minutes.
Panini’s Grammar #
The Panini’s grammar was composed in 6th century B.C or earlier. This grammar has provided 4,000 rules that describe the Sanskrit of his day completely. It has been shown that grammar of Panini represents a universal grammatical and com- puting system. From this perspective it anticipates the logical framework of modern computers.
Concept of Tridosha in Ayurveda #
Ayurveda adopts the physics of the five elements viz. Prithvi(earth), Jala(water), Agni (fire), Vayu(air) and Akasha (ether)). It notes that these five elements compose the Universe as well as human body. The Ayurveda divides the human body in SaptaDhatu or 7 constituent elements viz.
- Rasa dhatu (Chyle, Lymph, Plasma).
- Rakta dhatu (Haemoglobin fraction in blood).
- Mamsa dhatu (Muscle tissue).
- Medas dhatu (Fat or Adipose tissue).
- Asthi dhatu (Bone-tissue including cartilage).
- Majja dhatu (Bone Marrow).
- Sukra dhatu (Semen, Sperm, Ovum).
Then, Ayurveda talks about the balance of three elemental energies called:
- Vata: Air.
- Pitta : Bile and
- Kapha: Phlegm.
Unbalance in any of the above three causes illness and this is called Tridosha. Plato in Greek medicine has also described the same 3 issues and it appears to be derived from the earlier tridosha theory of Ayurveda.
The Lilavati of Bhaskara #
Bhaskara (born 1114), who was from the Karna- taka region, was an outstanding mathematician and astronomer. Amongst his mathematical contributions is the concept of differentials. He was the author of Siddhanta Shiromani, a book in four parts:
- Lilavati on arithmetic.
- Bijaganita on algebra.
- Ganitadhyaya on astronomy.
- Goladhyaya on astronomy.
Bhaskara’s epicyclic eccentric theories of plane- tary motions are more developed than in the earlier siddhantas.
Madhava #
Madhava (c. 1340-1425) developed a procedure to determine the positions of the moon every 36 minutes. He also provided methods to estimate the motions of the planets. He gave power series expansions for trigonometric functions, and for pi correct to eleven decimal places.
Yoga vashishtha of Valmiki #
Valmiki, the author of Ramayana has written Yoga Vashishtha in which there are some passages on scientific point of view relating to the description of the nature of space, time, matter, and conscious- ness. For example, one of the passage says: The world is like a potter’s wheel: the wheel looks as if it stands still, though it revolves at a terriffic speed. Valmiki has also written Akshara Lakshana in which he deals with mathematics in general, algebra, trig- onometry, chemicals and heat.
