Showing posts with label hinduism science. Show all posts
Showing posts with label hinduism science. Show all posts

Thursday, July 23, 2015

Ancient Indian's contribution in science-Reminder

Ancient India contributed to what science is today. After havoc created by occupying forces of Islamist, Greek, British, Europeans from beginning of this century, where islamist and Christians burned many scientific books, India did loose its edge in science. NOW time is changing for India to come and lead world again- 1. India invented the Number system. Pingalacharya invented ‘zero.’ in 200 BC.

2. Indians discovered the size, shape, rotation and gravity of earth about 1000 years before Kelvin,Galileo,Newton and 

Copper Nicus. Aryabhatta I was the first to explain spherical shape,size ,diameter,rotaion and correct speed of Earth in 499 


3. Newton’s law of Gravitational force is an ancient Indian discovery. In Siddhanta Siromani ( Bhuvanakosam 6 ) 

Bhaskaracharya II described about gravity of earth about 400 years before Sir Isaac Newton.

4. Bhaskaracharya II discovered Differential calculus.

5. Theory of Continued Fraction was discovered by Bhaskaracharya II.

6. The place value system, the decimal system was developed in India in 100 BC.

7. Indians discovered Arithmetic and Geometric progression. Arithmetic progression is explained in Yajurveda.

8. Govindaswamin discovered Newton Gauss Interpolation formula about 1800 years before Newton.

9. Vateswaracharya discovered Newton Gauss Backward Interpolation formula about 1000 years before Newton.

10. Madhavacharya discovered Taylor series of Sine and Cosine function about 250 years before Taylor.

11. Madhavacharya discovered Newton Power series.

12. Madhavacharya discovered Gregory Leibnitz series for the Inverse Tangent about 280 years before Gregory.

13. Madhavacharya discovered Leibnitz power series for pi about 300 years before Leibnitz.

14. Parameswaracharya discovered Lhuiler’s formula about 400 years before Lhuiler.

15. Nilakanta discovered Newton’s Infinite Geometric Progression convergent series.

16. Theorems relating the diameter,volume and circumference of circles discovered by Madhavacharya, Puthumana 

Somayaji, Aryabhatta, Bhaskaracharya…….

17. The value of pi was first calculated by Aryabhatta I in 499 AD,ie more than 1350 years before Lindemann

18. Boudhayana discovered Pythagorus Theorem in 800BC. ie 300 years before Pythagorus.

19. Algebra, trigonometry and calculus came from India. Quadratic equations were by Sridharacharya in the 11th Century.

20. While the Greeks were using only upto a maximum value 1000, Indians could go upto 18th power of 10 level during 

Vedic period.

21. Infinity was well known for ancient Indians. BhaskaracharyaII in Beejaganitha (stanza-20) has given clear explanation 

with examples for infinity

22. Positive and Negative numbers and their calculations were explained first by Brahmagupta in his book Brahmasputa 


23. Sterling formula was discovered by Brahmagupta about 1000 years before Sterling.

24. Demovier’s theorem of positive integral was discovered by Brahmagupta in 628 A.D, i.e around 1000 years before 


25. Puthumana Somayaji discovered Demovier’s infinite series in 1140 AD,i.e more than 200 years before Demovier.

26. Maharshi Sushruta is the father of surgery. 2600 years ago he and health scientists of his time conducted surgeries like 

cesareans, cataract, fractures and urinary stones. Usage of anesthesia was well known in ancient India. He was the first 

person to perform plastic surgery.

27. When many cultures in the world were only nomadic forest dwellers over 5000 years ago, Indians established Harappan 

culture in Sindhu Valley (Indus Valley Civilization).

28. The world’s first University was established in Takshila in 700BC. More than 10,500 students from all over the world 

studied more than 60 subjects. The University of Nalanda built in the 4th century BC was one of the greatest achievements 

of ancient India in the field of education.

29. According to the Forbes magazine, Sanskrit is the most suitable language for computer software.

30. Ayurveda is the earliest school of medicine known to humans.

31. Although western media portray modern images of India as poverty stricken and underdeveloped through political 

corruption, India was once the richest empire on earth.

32. According to the Gemmological Institute of America, until 1896, India was the only source of diamonds to the world.

33. USA based IEEE has proved what has been a century-old suspicion amongst academics that the pioneer of wireless 

communication was Professor Jagdeesh Bose and not Marconi.

34. The earliest reservoir and dam for irrigation was built in Saurashtra.

35. Chess was invented in India.

36. The first philosopher who formulated ideas about the atom in a systematic manner was Kanada who lived in the 6th 

century B.C.

37. All the atomic reactors in the world are in Shiva Linga Shape which is an Indian contribution.

38. Padanjali maharshi discovered Sound waves.

39. Yoga is an ancient Indian gift to the world.

40. Shayanacharya discovered velocity of light.

41. Maharshi Bharadwaja discovered different types of light rays.

42. Maharshi Bharadwaja was the first person to give definition about aeroplane. He explained about different types 

aeroplanes in his book “Vimana Thantra” about 2000 years before Right Brothers.

43. Maharshi Bharadwaja discovered spectrometer. In his “Yantra Sarvaswa” he explained about more than 100 instruments.

44. The different colours of light, VIBGYOR are mentioned in Rigveda which was written more than 6000 years ago.

45. Maharshi Charaka discovered Psychology and Quantum healing system.

46. Varahamihira discovered the concept of “Budding of plants”.

47. Varahamihira discovered Comets in 505 AD, i.e more than 1100 years before Haley.



48. Gouthama Maharshi discovered the wave nature of sound about 1400 years before Hyghen.

49. Seven continents are mentioned in Padmapurana.

1. Bhaaskaraachaaryan - I (early 6th century AD) 

Formost among Ganithajnans (astrologer / mathematician) in the entire Bhaaratham (India), Bhaskaran-I, hailed from 

Kerala, according to experts. In 522 AD he wrote "Mahaa Bhaaskareeyam", also known as "Karma Nibandhham". A 

Vyaakhyaanam (explanations and discussions) on Aaryabhateeyam as well as a condensed version - "Laghu 

Bhaaskareeyam" - of Aaryabhateeyam, have also come down to us. 

(Bhaaskaraachaaryan-II who wrote "Leelaavathy" lived in the 11th century). 

2. Haridathan (650 - 750 AD) 

Though the Aarybhata system had been followed in calculating the planetary positions, Namboothiri scholars recognised 

variations between the computed and observed values of longitudes of the planets. A new system called "Parahitham" was 

proposed by Haridathan through his famous works "Graha-Chakra-Nibandhhana" and "Mahaa-Maarga-Nibandhhana". In 

683 AD, this system was accepted throughout Kerala on the occasion of the 12-yearly Mahaamaagha festival at 

Thirunavaya, and is recorded in many later works. Haridathan introduced many improvements over Aarybhata system, like 

using the more elegant Katapayaadi (Click here) system of notation in preference to the more complicated Aarybhataa's 


Haridathan introduced the unique system of enunciating graded tables of the sines of arcs of anomaly (Manda-jya) and of 

conjugation (Seeghra-jya) at intervals of 3° 45' to facilitate the computation of the true positions of the planets. One of the 

corrections introduced by Haridathan to make the Aarybhata's results more accurate, is the "Sakaabda Samskaaram". 

3. Aadi Sankaran (788 - 820 AD) 

Sree Sankaran was born in Kalady in Central Kerala (nearly 50 km north east of Kochi) on the banks of river Periyar as the 

son of Kaippilly Sivaguru Namboothiri and Arya Antharjanam (Melpazhur Mana). Scientific concepts naturally evolved from 

this highly logical and rational intellect. It is believed that Sree Sankaran was the first mathematician to moot the concept of 

Number Line. [Ref: "Sankara Bhaashyam" (4-4-25) of the "Brihadaaranyaka Upanishad"]. It was Sree Sankaran who first 

expounded the idea of assigning a set of natural numbers to a straight line. As the number of elements in a set of natural 

numbers is infinite, it requires a symbol of infinity to represent them. A straight line can be considered to be infinitely long. 

Sankaran adopted a straight line as a symbol of infinity. A straight line can be divided to infinite number of parts and each of 

these parts can be assigned the value of a particular number. This is called number line. Though his concept lacks the 

perfection of modern number line theory, Sree Sankaran exhibited his intellectual ingenuity in conceiving such a novel idea. 

Yet another example for Sree Sankaran's unbiased and pure scientific pursuit of knowledge could be seen in the second 

"Slokam" of "Soundarya Lahari" [a collection of 100 Slokams in praise of Goddess Durga written by Sree Sankaran]. In the 

Slokam "Thaneeyaamsam paamsum thava charana pankeruhabhavam", we can see a hint to the theory of inter-

convertibility of mass and energy. Famous scientist Albert Einstein put forward this theory much later. Einstein said mass 

can be converted to energy and vice-versa according to the equation E = MC², where E = Energy released, M = Mass of the 

substance, and C = Velocity of light = 3 x 10¹º cm/sec. 

In another context, Sree Sankaran postulated that the diameter of Sun is 1 lakh "Yojanas". Later the modern scientific 

community calculated the diameter which agreed very closely with (just 3% error) the value provided by Sankaran. 

4. Sankaranarayanan (9th century) 

This scholar from "Kollapuri" (Kollam) in Kerala has written a commentary (Vyaakhhyaanam) of the "Laghu Bhaaskareeyam" 

of Bhaaskaraachaaryan-I, titled "Sankaranaaraayaneeyam". The Granthham is dated 869 AD (ME 44). 

5. Sreepathy (around 1039 AD) 

Sreepathy (Kaasyapa Gothram) has described methods for calculating the "Shadbalam" of the planets and stars. 

Prescribing of consequences should be based on these "Balams". His works include "Aarybhateeya Vyaakhhyaanams" 

such as "Ganitha Thilakam", "Jaathaka Karma Padhhathi" and "Jyothisha Rathna Maala". 

6. Thalakkulathu Bhattathiri (1237 - 1295 AD) 

This Govindan Bhattathiri is believed to have been born in ME 412 in Thalakkulam of Aalathur Graamam, about three 

kilometer south of Tirur. The Illam does not exist anymore. His mother was apparently from Paazhoor. He is said to have left 

Keralam (to Paradesam, possibly Tamil Nadu) and studied the "Ulgranthhams" in Jyothisham under a scholar by name 

Kaanchanoor Aazhvaar, returned and prayed for a dozen years to Vadakkunnathan at Thrissur. 

Bhattathiri's major work is the renowned Jyothisha Granthham "Dasaadhhyaayi". It is a majestic "Vyaakhyaanam" of the first 

ten chapters of the famous 26-chapter "Brihajjaathakam" in the field of Jyothissaasthram, written by Varaahamihiran of 

Avanthi, a sixth century scholar. Bhattathiri felt that the "Aachaaryan" had not covered anything significantly more in the rest 

of the chapters and therefore, left them altogether. There are also other works like "Muhoortha Rathnam" to his credit. 

7. Sooryadevan 

This Namboothiri (Somayaaji) scholar is better known as Sooryadeva Yajwaavu. "Jaathakaalankaaram" is Sooryadevan's 

Vyaakhyaanam for Sreepathy's (No. 5, above) "Jaathaka Karma Padhhathi". His other works include a "Laghu 

Vyaakhhyaanam" (simple explanation) of Aaryabhateeyam, called "Bhataprakaasam", as well as Vyaakhhyaanams for 

Varaahamihiran's "Brihadyaathra" and for Mujjaalakan's "Laghu Maanava Karanam". 

8. Irinjaatappilly Madhavan Namboodiri (1340 - 1425) 

Madhavan of Sangamagraamam, as he is known, holds a position of eminence among the astute astronomers of medieval 

Kerala. He hailed from Sangama Graamam, the modern Irinjalakuda, near the railway station. Madhavan was the treacher 

of Parameswaran, the promulgator of Drigganitha school of Astronomy, and is frequently quoted in the medieval 

astronomical literature of Kerala as Golavith (adept in spherics). 

He is the author of several important treatises on Mathematics and Astronomy. The "Venvaaroham" explaining the method 

for computation of the moon and the moon-sentences, "Aganitham", an extensive treatise on the computation of planets, 

"Golavaadam", "Sphhuta-Chandraapthi", "Madhyama Nayana Prakaaram" are some of his important works. 

Besides these works, a number of stray verses of Madhavan are quoted by later astronomers like Neelakandha Somayaaji, 

Narayanan the commentator of Leelaavathy, Sankaran the commentator of Thanthrasangraham, etc. One of his significant 

contributions is his enunciatiation of formulae for accurate determination of the circumference of a circle and the value of p 

by the method of indeterminate series, a method which was rediscovered in Europe nearly three centuries later by James 

Gregory (1638 - 75 AD), Gottfried Wilhelm Leibniz (1646 - 1716 AD) and Newton (1642, "Principia Mathematicia"). His five 

Paraspara-Nyaaya contains the enunciation for the first time in the world, of the formula for the sine of sum of two angles. 
sine (A + B) = sine A cos B + cos A sine B 
This is known as "Jeeve Paraspara Nyaaya". 

The ideas of Calculus and Trigonometry were developed by him in the middle of the 14th century itself, as can be verified 

by his extensive mathematical and astronomical treatises and quotations by later authors. 

Madhavan deserves, in all respects, to be called the Father of Calculus and Spherical Trigonometry. For a detailed 

appreciation of his contribution, refer to the excellent paper of R G Gupta,"Second Order of Interpolation of Indian 

Mathematics", Ind, J.of Hist. of Sc. 4 (1969) 92-94. 

Again Madhavan provides the power series expansions for sin x and cos x for an arc x correct to 1/3600 of a degree.

9. Vatasseri Parameswaran Namboodiri (1360 - 1455) 

Vatasseri was a great scientist who contributed much to Astronomy and Mathematics. He was from Vatasseri Mana on the 

north bank of river Nila (Bhaarathappuzha) near its mouth in a village called Aalathiyur (Aswathha Graamam). This is near 

the present Tirur of Malappuram district. He was a Rigvedi (Aaswalaayanan) of Bhrigu Gothram. 

"Drigganitham" was his greatest contribution. The seventh century "Parahitha Ganitham" for calculations and projections in 

Astronomy continued its popularity for a few centuries, with some later modifications made by Mujjaalakan, Sreepathy and 

others, for correcting the differences found with actual occurences. But it was Parameswaran who, as a result of over fifty 

years of systematic observations and research on movements of celestial bodies, estimated the error factor and established 

a new method called Drig Sidhham as explained in his popular Drigganitham (ME 606, 1430-31 AD). He suggested the use 

of "Parahitham" for "Paralokahitham" such as Thithhi, Nakshthram, Muhoortham, etc., and his own "Drigganitham" for 

"Ihalokahitham" like "Jaathakam", "Graha Moudhhyam", "Grahanam", etc. Unfortunately, Drigganitham Granthham has not 

been traced so far. 

Yet another of his contribution was a correction to the angle of precision of equinox mentioned by his disciple, Kelalloor 

Somayaaji (vide 15, below) in his "Jyothirmeemaamsa" (ch. 17). The 13 ½° suggested by Mujjaalakan was rectified by him 

to 15°. 

There are numerous works to his credit, apart from Drigganitham. The 3-volume, 302 verse "Gola Deepika" (1443 AD) 

explaining about the stars and earth in very simple terms, "Jaathaka Padhhathy" in 41 verses, "Soorya Sidhhantha 

Vivaranam", "Grahana Mandanam", "Grahanaashtakam", "Vyatheepaathaashtaka Vrththi" in 500 verses or Slokams. (The 

last three are believed by experts to be his works), "Aachaarya Samgraham", "Grahana Nyaaya Deepika", "Chandra-

Chhaayaa-Ganitham", "Vaakya Karmam" and "Vaakya Deepika" are his well-known works. 

He has written superb commentaries such as "Sidhhantha Deepika" on Govindaswamy's Mahaa Bhaaskareeyam; "Karma 

Deepika" or "Bhata Deepika" on Aarya Bhateeyam; "Muhoortha Rathna Vyaakhyaa" on Govindaswamy's Muhoortha 

Rathnam; Leelavathee Vyaakhyaa on the famous mathematical treatise, Leelavathy of Bhaaskaraachaarya-II; "Laghu 

Bhaaskareeya Vyaakhyaa" on Laghu Bhaaskareeyam of Bhaaskaraachaarya-I; "Jaathaka Karma Padhhathee Vyaakhyaa" 

on Sreepathy's 8-chapter work on Jyothisham; the one on "Laghu Maanasam" of Mujjaalakan; "Jaathakaadesa Vyaakhyaa"; 

and "Prasna-Nashta Panchaasikaavrthy" also called "Paarameswari" based on the work of Prathhuyasass, son of 


Undoubtedly, there had not been many scholars of his calibre in the annals of history in the realm of Astronomy. 

10. Damodaran Namboodiri 

Damodaran Namboodiri is known for his work "Muhoorthaabharanam". It is believed that he had an ancestor by name 

Yajnan whose brother's son, Kesavan, was a great scholar, and that Damodaran was Kesavan's younger brother. His family 

is said to have belonged to a village near Thriprangod, but it is clear that it was in Taliparamba Graamam. Mazhamangalam 

(Mahishamangalam, vide 17, below) has recognised "Muhoorthaabharanam" as a reference work similar to "Muhoortha 

Rathnam" and other earlier works. 

11. Narayanan Namboodiri 

He has authored "Muhoortha Deepikam". He could be the same Narayanan, one of Vatasseri Parameswaran Namboodiri's 

teachers (Guru), as mentioned by Kelallur Chomaathiri (Neelakandha Somayaaji, 15, below). "Muhoortha Deepikam" is also 

recognised as an authoritative work, by Mazhamangalam (17, below). 

12. Puthumana Somayaaji (Chomaathiri) 

He belonged to Puthumana Illam (Sanskritised as Noothana Graamam) of Chovvaram (Sukapuram) Graamam. He is 

believed to have been a contemporary of Vatasseri Namboodiri, during the 15th century AD. 

His famous works are "Karana Padhhathi" which is a comprehensive treatise on Astronomy in ten chapters completed in the 

year ME 606 (1430-31 AD), the same year as Vatasseri Namboodiri's "Drigganitham"; "Nyaaya Rathnam", an 8-chapter 

Ganitha Granthham; "Jaathakaadesa Maargam"; "Smaartha-Praayaschitham"; "Venvaarohaashtakam"; "Panchabodham"; 

"Grahanaashtakam"; and "Grahana Ganitham". 

To his credit is also an important mathematical equation to calculate the tangent (tan) value of an angle

13. Chennas Narayanan Namboodiripad (mid 15th century) 

He was considered to be an authority in the fields of Vaasthusaastram (Indian Architecture), Mathematics and Tanthram. 

Born in 1428, Chennas Narayanan Namboodiripad authored a book titled "Thanthra Samuchayam" which is still considered 

as the authentic reference manual in the field of temple architecture and rituals. In this Granthham , while elaborating on 

various points of Indian architectural practices, he has dealt with many mathematical principles also. The following are 


a) A method of arriving at a circle starting with a square, and successively making it a regular octagon, a regular 16-sided, a 

32-sided, 64-sided polygons, etc. In this method some geometrical steps have been suggested. 
b) Co-ordinate system of fixing points in a plane. 
c) Converting a square to a regular hexagon having approximately equal area. 
d) Finding the width of a regular octagon, given the perimeter. 

14. Ravi Namboodiri 

He is one of the teachers of Kelallur Chomaathiri, and was a scholar in both Astronomy and Vedaantham. His treatise 

"Aachaara Deepika" is on Jyothisham. 

15. Kelallur Neelakandha Somayaaji (1465 - 1545) 

He is one of the foremost astronomers of Kerala and considered an equal to Vatasseri Parameswaran Namboodiri, and 

known popularly as Kelallur Chomaathiri. He was born to Jathavedan and Arya in Kelallur (or Kerala Nallur, Kerala-Sad-

Graamam in Sanskrit) Mana of Thrikkandiyur (Sree Kundapuram in Sanskrit), near Tirur, and belonged to Gaargya 

Gothram, Aaswalaayana Soothram of Rigvedam. Kelallur Mana later became extinct and their properties merged with 

Edamana Mana. They were staunch devotees at Thriprangot Siva temple. 

He is said to be a disciple of one Ravi who taught him Vedaantham and the basics of Astronomy and of Vatasseri 

Damodaran Namboodiri (son of the famous Parameswaran Namboodiri) who trained him in Astronomy and Mathematics. 

According to Ulloor, he lived during 1465 and 1545 (roughly), though according to another version, he was born on June 17, 

1444 on a Wednesday. 

His most important work is "Thanthra Samgraham" (a treatise on Mathematics and Astronomy) in eight chapters with 432 

verses, and apparently written in an unbelievable six days from Meenam 26 of 676 ME to Metam 1 the same year! The lucid 

manner in which difficult concepts are presented, the wealth of quotations, and the results of his personal investigations 

and comparative studies make this work a real masterpiece. Two commentaries on this work, "Yukthi Bhaasha" (in 

Malayalam) by Paarangot Jyeshthhadevan Namboodiri (No. 16 below) and "Yukthi Deepika" by Sankara Varier, themselves 

indicate the importance of the original work. 

Another of his important works is a "Bhaashyam" (commentary) on "Aaryabhateeyam". In his book "Jyorthir Meemaamsa", 

he demonstrates his intellectual and scientific thinking. Some of his other works are "Chandra Chhaayaa Ganitham" 

(calculations relating to moon's shadow), "Sidhhantha Darpanam" (mirror on the laws of Astronomy) and its Vyaakhyaa, 

"Golasaaram" (quintessence of spherical Astronomy), "Grahana Nirnayam", "Grahanaashtakam", "Graha Pareekshaa 

Kramam", and "Sundara Raaja Prasnotharam". He postulated that the ratio of circumference to diameter of a circle could 

never be a rational number. His commentary on Aaryabhateeyam shows that his scholastic abilities extend beyond 

Jyothisham and Vedaantham, to the realms of Meemaamsa, Vyaakaranam and Nyaayam. 

16. Paarangottu Jyeshthhadevan Namboodiri (1500 - 1610) 

He was born in Paaragottu Mana situated near Thrikkandiyur and Aalathur on the banks of river Nila. Vatasseri Damodaran 

Namboodiri was his teacher. He wrote a Malayalam commentary, "Yukthi Bhaasha" for "Thanthra Sangraham" of Kelallur 

Neelakandha Somayaaji. It forms an elaborate and systematic exposition of calculation methods in Mathematics in its first 

part and Astronomy in the second part. The treatment is in a rational and logical manner, and may turn out to be an asset to 

our scientific community, if properly translated and studied. He is also the author of "Drik Karanam", a comprehensive 

treatise in Malayalam on Astronomy, composed in 1603 AD. 

17. Mahishamangalam Narayanan Namboodiri (1540 - 1610) 

He was a member of Mahishamangalam (Mazhamangalam) Mana of Peruvanam in Thrissur district. His father Sankaran 

Namboothiri has written several Granthhams on Astronomy in Malayalam. Renouned scholar Sankara Varier has written a 

commentary "Kriyaakramakari" in Malayalam for the popular Mathematical manual "Leelavathy" (of Bhaskaraachaarya) but 

before commencing the 200th Slokam, he expired. It was Mahishamangalam Narayanan Namboodiri who, at the age of 18, 

took up the challenge of completing it. He was popularly known as "Ganitha Vith" [Maths wizard]. After successfully 

completing "Kriyaakramakari", Narayanan Namboodiri wrote his own commentary "Karmadeepika" for "Leelavathy". "Upa 

Raaga Kriyaa Kramam" was his original work in the related topic. He has authored many Granthhams on subjects other 

than Astronomy, including Smaartha Praayaschitha Vimarsanam, Vyavahaara Mala [ethical code of conduct], 

Mahishamangalam Bhaanam, Uthara Raamaayana Champu, Raasa Kreedaa Kaavyam, Raaja Ratnaavaleeyam [in praise of 

Kerala Varma, Prince of Kochi), Daarikavadham, and Paarvatheesthuthi. 

18. Mathur Nambudiripad 

The Granthham, "Muhoortha Padavi" (the second) is credited to Mathur Nambudiripad, whose name is not known. He has 

condensed the old "Muhoortha Padavi" into an amazingly short version with just 35 Slokams (verses). Since 

Mazhamangalam of mid-sixteenth century AD, in his "Baala Sankaram" has referred to Muhoortha Padavi, it is possible that 

Mathur Nambudiripad lived during the second half of the 15th century AD. Apart from Mazhamangalam's commentary on 

this Granthham, there are: a short one in Sanskrit, "Muhoortha Saranee Deepam" (author unknown); a detailed one in 

Sanskrit, "Varadeepika" by Purayannur Parameswaran Nambudiripad; and yet another one in Malayalam, "Muhoortha 

Bhaasha" by Aazhvaancheri Thampraakkal. 

19. Narayanan Namboodiri 

One Narayanan has written a commentary on Bhaaskaraachaaryan's Leelaavathy, which has been variously referred to as 

"Karmadeepika", "Karmadeepakam" and "Kriyaakramakari". The work is well-focussed and neither too elaborate nor too 


Another of his works is " Karmasaaram" which discusses "Grahasphhutaanayanam" and other aspects of the Drik tradition. 

It is in four chapters and may have been written during the second half of the 16th century AD. 

20. Chithrabhanu Namboodiri (16th century) 

Born in Chovvara (Sukapuram) Graamam, Chithrabhanu Namboodiri was a mathematician and has written a Granthham 

titled "Eka Vimsathi Prasnothari". It is said that Sankara Varier, another scholar (mentioned earlier) who wrote the 

commentary "Kriyaakramakari" was Chithrabhanu Namboodiri's disciple. Varier has, at several occasions, quoted his master. 

Chithrabhanu Nambudiri's "Eka Vimsathi Prasnothari" gives a method of solving the binomials (A + B), (A - B), (A² + B²), (A³ + B³), (A³ - B³), AB, etc. Given any two of these, the book gives twentyone different ways to solve for A and B. As he is believed to be the master of Sankara Varier, his period could be 16th century.

The achievements of such and other Kerala mathematicians were, at first, brought to the notice of scholars, both Indian and western, by Charles M Whilsh who presented a paper on the subject before the Royal Asiatic Society of Great Britain and Ireland, 3 (1835) (509 - 523).

Monday, April 13, 2015

Vedic Hinduism explained

The Supreme One who represents selflessness, controls the entire universe, is present everywhere and is the Devata of all Devatas, alone is source of bliss. Those who do not understand Him remain drenched in sorrow and those who realize Him achieve unconditional happiness. (Rigveda 1.164.39)

Q: How many Ishwar are there in Vedas? We heard there are huge number of Ishwar in Vedas.

A: You have heard from wrong sources. Vedas clearly specify that there is One and only One Ishwar. And there is no mantra in Vedas that can be interpreted to imply multiple Ishwars.
Not only this, Vedas also refuse existence of any angel or Prophet or incarnation who is necessarily required to act as an agent between You and Ishwar.
To give a rough analogy:
Ishwar of Vedas = God of Christianity minus the concept of Trinity minus the necessity to surrender to Jesus
Ishwar of Vedas = Allah of Islam minus the necessity to accept Muhammad as final Prophet.
In other words, If someone says first part of Shahada : lâ ilâha illallâh (There is no other God except one and only Allah) but rejects the second part : Muḥammadur rasûlullâh (Muhammad is his messenger), that is close to concept of Vedic God.
In Islam, it is Shirk or greatest sin to worship anything except Allah. If you take this concept further and also refuse to accept any Muhammad or Gabriel as necessary to be remembered apart from Allah, you are avoiding Shirk as per Vedas.

Q: What about the various Gods or Devatas mentioned in Vedas? What about 33 crore Gods?

1. As mentioned earlier, Devata refers to entities that are useful for us. But nowhere it is mentioned in Vedas that we should worship these entities. Of course, Ishwar is the Devata or Devatas and hence called ‘Mahadeva’. He alone is to be worshipped.
2. The Vedas refer to not 33 crore Devatas but 33 types (Koti in Sanskrit) of Devatas. They are explained in Shatpath Brahman very clearly. These include –
8 Vasus (Earth, Water, Fire, Air, Sky, Moon, Sun, Stars/ Planets) that form components of universe where we live,
10 Life Forces in our body or Prana (Prana, Apana, Vyana, Udana, Samaana, Naga, Kurma, Kukala, Devadatta) and 1 Soul called Rudra,
12 Aditya or months of year,
1 Vidyut or Electromagnetic force that is of tremendous use to us
1 Yajna or constant noble selfless deeds done by humans
The master of these 33 Devatas is the Mahadeva or Ishwar who alone is to be worshipped as per 14th Kanda of Shatpath Brahman.
The concept of 33 Devatas is a great research based subject in itself and requires in-depth study for proper understanding. However, it has been made very clear in all Vedic texts that they are NOT Ishwar and hence NOT to be worshipped.
3. Ishwar has huge number of properties. Ignorant people wrongly consider these properties of Ishwar to be different Ishwars. For example, in today’s newspaper there were 2 headlines – One referred to Dr Singh and other to Manmohan. That does not mean India has two Prime Ministers!
4. To dispel such confusions, there are several mantras in Vedas that clearly state that there is One and Only One Ishwar without any assistants, agents, prophets or juniors to liaison between Him and Us. For example:
Yajurveda 40.1:
This entire world is embedded within and managed by the One and Only One Ishwar. Never dare do any injustice or desire riches through unjust means. Instead follow the righteous path and enjoy His bliss. After all He alone is source of all bliss!
Rigveda 10.48.1:
Ishwar alone is omnipresent and manager of entire universe. He alone provides victory and eternal cause of world. All souls should look up only to Him in same manner as children look up to their Father. He alone provides for our sustenance and bliss.
Rigveda 10.48.5
Ishwar enlightens the entire world. He is undefeated and undying. He is the creator of the world. All souls should seek bliss through seeking knowledge and acting thereupon. They should never shun the friendship of Ishwar.
Rigveda 10.49.1
Ishwar alone provides true knowledge to truth seekers. He alone is promoter of knowledge and motivates virtuous people into noble actions to seek bliss. He alone is the creator and manager of the world. Hence never worship anyone else except one and only Ishwar.
Yajurveda 13.4
There is One and only One Creator and Maintainer of the entire world. He alone is sustaining the earth, sky and other heavenly bodies. He is Bliss Himself! He alone deserves to be worshipped by us.
Atharvaveda 13.4.16-21
He is neither two, nor three, nor four, nor five, nor six, nor seven, nor eight, nor nine, nor ten. He is, on contrary, One and Only One. There is no Ishwar except Him. All devatas reside within Him and are controlled by Him. So He alone should be worshipped, none else.
Atharvaveda 10.7.38Ishwar alone is greatest and worth being worshipped. He is the source of all knowledge and activities.
Yajurveda 32.11
Ishwar resides at each point in universe. No space is devoid of Him. He is self-sustaining and does not need help of any agent, angel, prophet or incarnation to perform His duties. The soul which is able to realize this One and only One Ishwar achieves Him and enjoys unconditional ultimate bliss or Moksha.
There are innumerable such mantras in Vedas that explain One and Only One Ishwar and instructs us to worship Him directly without invoking any other entity – Incarnation, Prophet, Angel or Agent.

Q: How do you establish existence of Ishwar?

A: Through direct and indirect evidences.

Q: But direct evidence of Ishwar cannot be possible. How do you then establish Ishwar?

1. Evidence means the clear knowledge determined through stimuli received from sense organs. But note that sense organs capture the properties and not the ’cause of these properties’.
For example, when you read this article, you do not capture existence of Agniveer, but only certain images coming on your screen that you interpret into meaningful knowledge. And then you conclude that there has to be some writer of this article and claim that you have evidence of existence of Agniveer. So this is ‘indirect evidence’ even though it appears ‘direct’.
Similarly, this whole creation that we observe via its properties through sense organs imply existence of Ishwar.
2. When you can link a sensory input directly to an entity, you claim to have ‘direct evidence’. For example when you eat a mango, you feel the property of sweetness and associate it with the mango that you consumed. What is important is that you can associate such ‘direct evidence’ ONLY with specific sense organ that was used to observe that property.
Thus in previous example, you cannot have ‘direct evidence’ of mango through ‘ears’ but only through ‘tongue’ or ‘nose’ or ‘eyes’.
Also in reality this is also ‘indirect evidence’ though we term it ‘direct evidence’ for sake of simplicity.
Now since Ishwar is the most subtle entity existing, it is impossible to have ‘direct evidence’ of Ishwar through coarse sense organs like eyes, nose, tongue, skin or ears. For example we cannot see subatomic particles even through most powerful microscopes, we cannot hear ultrasonic sound, we cannot feel the touch of each individual molecule.
In other words, Ishwar is impossible to be evidenced through these coarse and weak sense organs just as mango cannot be sensed through ears or subatomic particles cannot be sensed through any sense organ for that matter.
3. The only organ that can sense Ishwar is mind or Mana. When mind is fully controlled and devoid of involuntary disturbances (like thousands of thoughts coming all the time) and adequate knowledge about properties of Ishwar has been obtained through study and practice, Ishwar can be evidenced directly through intellect in same manner as a mango is evidenced through its taste.
This is the goal of life and this is what a Yogi attempts to do through all the various methods of mind control that include cultivating traits like non-violence, truth-seeking, compassion, seeking bliss for all, high moral character, fighting against injustice, unity among people, etc etc.
4. In a way we get hints of direct evidence of Ishwar everyday in our life. When we try to indulge in any wrong act like theft, cheating, brutality, we hear that faint ‘inner voice’ in form of fear, shame, doubt etc. And when we indulge in noble deeds like helping others, blessing a child etc, we again hear that ‘inner voice’ in form of fearlessless, sense of satisfaction, enthusiasm and feeling of bliss.
This ‘inner voice’ is from Ishwar. Often we reduce its audibility by trying to silence it through loud DJ Music of stupid tendencies around. But then we all at times feel this ‘inner voice’ getting louder now and then, when things are relatively silent.
5. And when the soul purifies itself from mental disturbances and gets away from the DJ club, it is able to directly evidence itself as well as Ishwar.
Hence both through direct and indirect evidence, Ishwar is established as clearly as other entities witnessed by us.

Q: Where does Ishwar live?

1. Ishwar is omnipresent and hence resides everywhere. Had Ishwar been living at a particular place like some special sky or on some special throne, He could not have been omniscient, omnipotent, manager of all, creator of all and destructor of all. You cannot perform actions at a place where you are not present.
2. If you say that Ishwar manages the world from one place just like sun illuminates earth from far off or you watch TV through remote control, this is defective logic. Because sun is able to illuminate the earth or remote control is able to operate the TV only through radiation waves that travel through the interim space. Just because we are unable to see them we call it remote control. In reality there is nothing like a remote control. Thus the very fact that Ishwar is able to manage something implies that it is present there to manage it.
Vedic God3. Further, if Ishwar is omnipotent, why would He be scared to restrict Himself to a small space. This makes Ishwar limited. Christians say God is on 4th sky and Muslims say that Allah is on 7th sky. And their followers keep fighting each other to prove themselves right. Is it that God and Allah decided to live in separate skies so that they also do not start fighting like their angry followers?
In reality these are childish talks. When Ishwar is All-Powerful and controls entire universe, there is no reason why He would be scared to limit himself to a small part of universe. And if He is, he cannot be termed All-Powerful.

Q: Does it mean Ishwar is also in dirty things like alcohol, urine, excreta?

1. The entire creation is within Ishwar. Because Ishwar is also outside these things but these things do not exist outside Ishwar. So all things in world are pervaded by Ishwar. To give a very rough analogy, we are within Ishwar in similar manner as a pice of cloth within tub of water. There is water within, outside and all around the cloth. There is no portion of cloth which is not wet with water but there is water beyond the cloth as well.
2. Anything is dirty or good for us depending upon our duty towards it. The same set of atoms that form the tasty mango we eat is so lovely for us. But when the atoms disintegrate, interact with other chemicals and form excreta, that becomes dirty for us. But in essence all these are merely different combinations of particles of nature. Since we have a mission on this earth, we analyze each thing with regards to the mission and accept some/ reject rest. What we reject is dirty or trash for us and what we accept is good for us. But for God, such duty does not exist and hence nothing is dirty for Him. On contrary, His duty is different from ours – to help us achieve bliss in just manner – and hence nothing in His entire creation is untouchable for Him.
3. If you look from another analogy, Ishwar is not like a pampered social worker who would prefer to plan remotely in his air-conditioned office but would desist from visiting the slums where actual social work has to be done. He, on contrary, exists to manage the most dirty of the places for our benefit.
4. And since He alone is most perfect, despite He being everywhere and everything being within Him, He is separate and different from these things.

Q: Is Ishwar Kind and Just?

A: Yes. He is the epitome of kindness and justice.

Q: But these are opposite traits. Kindness means to forgive a criminal. And justice means giving punishment to criminal. How can both exist at same time?

A: Kindness and Justice are basically one and same. Because both serve the same purpose.
1. Kindness does not mean forgiving a criminal. Because if that be done, several innocent people would become victims. Thus unless justice is meted out to a criminal, one cannot be kind to innocents. It will also be not justice to the criminal because he would not be prevented from further crimes.
For example, if a dacoit is forgiven, he would harm several innocent people. And if he is imprisoned, it would not only prevent harm to innocents but also allow him opportunity to improve himself and not do further crimes. So in justice alone lies kindness for one and all.
2. In reality, kindness refers to the purpose of Ishwar and justice to the process. When Ishwar punishes a criminal, He does it to prevent the criminal from doing further crimes. And he also prevents innocent people from getting punished for no offense of theirs. Thus the entire purpose of justice is kindness to all.
3. As per Vedas, and observation, the source of sorrow is ignorance which causes one to do wrong acts called crimes. So when a soul does such wrong acts, Ishwar restricts his freedom to do crimes and allows him opportunities to remove his ignorance and remove sorrow.
4. Mere saying sorry is not sufficient to receive pardon of Ishwar. The source of sin or crimes is ignorance and until that is removed, the soul would continue to get rightful punishments or rewards for its actions every moment throughout several births and deaths. And the purpose of all this justice is His kindness towards the soul to gift it with ultimate bliss.

Q: Does that mean, Ishwar will never pardon my sins? Islam or Christianity are better. There, if I confess or say sorry, all my past records are deleted and I am given fresh opportunity.

1. Ishwar does pardon your sins. His pardon lies in the just results of your actions that He provides and not in deleting your past records.
2. If He were to delete your past records, He would be doing greatest injustice and brutality to you. Because in this case, He has allowed you to be promoted to next class even when you have not gained the competence to pass the present class. And in process he is doing injustice to others also who interact with you.
3. Pardoning means providing opportunity to improve your competence and not giving you 100% when you deserved a zero. This is exactly what Ishwar does. And remember that improving competence does not happen in one moment or through one word of ‘Sorry’. It demands dedicated practice and efforts over a period of time. Only lazy people seek shortcuts like trying to get 100% without even studying the course.
4. Unfortunately, those who attract people to their religion by saying that God will forgive their sins are fooling themselves and people. Suppose someone has diabetes. Does it get treated merely by saying sorry? When a physical disease takes much more than a sorry to be treated, how can mind – the most complex thing known to humanity – be treated by a sorry?
5. Actually these ideologies have a blatant flaw – they believe in one life and do not believe in rebirth. So they want to create artificial hurry formula to attract people. And scare them to Hell of they do not agree to them. We have already covered the loopholes of One Life theory in God must be crazy!
6. Vedic philosophy is much more natural, amenable to logic and reasonable. Neither is there a Hell where you would be thrown to burn forever by an Ishwar who is as loving as Mother, nor would He debar you from opportunities to actually raise your competence through efforts and achieve what you truly deserve. After all what is more satisfying:
a. Rank 1 through a fake mark sheet when we know that actually we had got zero, or
b. A proud Rank 1 through hard work and burning midnight oil, when we know that we did the best we could to become masters of the subject!
So in vedas, there are no shortcuts or longcuts to success. There is only the right cut! And the success is much more satisfying than what any illusionary and illusive shortcut can be imagined to provide!

Q: Is Ishwar with form or formless?

A: He is formless as per Vedas and commonsense.
1. He cannot be omnipresent if He has form. Because form implies existence of boundary. And hence He should not exist beyond the boundary if He has form.
2. Form can be seen only if Ishwar is coarse. Because any object finer than what can reflect light waves cannot be seen. Now Vedas clearly define Ishwar as the most finest, without gaps and uniform everywhere. (Refer Yajurveda 40.8 for example). Hence He cannot have form.
3. If Ishwar has a form, it means that someone created His form. This is not possible. If you say that He himself made His form, it means He was formless earlier.
4. If you say that Ishwar is both formless and with form, it is not possible because both are contradictory.
5. If you say that He takes divine forms at times, kindly specify what divine means. Say Ishwar took divine form of a man. Now how will you define boundary of Ishwar atoms and non-Ishwar atoms. Further since He is present everywhere with same density (uniformity), how we distinguish between man-Ishwar and rest of world. And if Ishwar is same everywhere, how are we seeing the boundary?
6. What we see as human body is actually continuous exchange of matter and energy with rest of the world. It is impossible to distinguish each atom as part of human body or rest of the world. So it will be impossible to segregate even body of man-Ishwar. For example, will the spit, urine, sweat and other excreta from man-Ishwar also be divine?
7. In Vedas there is no concept of Ishwar being with form. Further there is nothing that Ishwar cannot do without form that He must assume a form.
8. What we normally consider as divine Ishwar forms – for example people like Ram and Krishna – were actually divinely inspired. Remember, we talked about ‘inner voice’ of Ishwar? These legends were epitome of Ishwar worship and purity of mind. And hence for normal people, they were Ishwar themselves. However Vedas prohibit worship of anyone except Ishwar. Thus, these persons should instead be emulated (their examples be followed in our own real lives) to offer our gratitude to them. This hero-followership is as per Vedas and explained in The power of Now! – Know Vedas.
9. Had Ishwar taken form and worship of these forms been the recipe for salvation, Vedas would have detailed description on this topic. But Vedas do not even hint at such concepts.

Q: Does it mean all these temples and worship of Ram, Krishna, Durga, Lakshmi wrong?

A: Take example of a pious mother living in a remote village. Her son gets bitten by snake. She rushes to local Tantrik for Jhaad Phoonk in an attempt to save life of her child. Would you call her wrong or right?
The bulk of Ishwar worshippers today, be it Hindu, Muslim, Christian or whatever are in same state. Their intentions are genuine and worth greatest respect. But out of ignorance, they adopt wrong practices of worshipping Ishwar. This is obvious from the fact that hardly anyone even knows about the Vedas, even though, at least the Hindus agree that Vedas are supreme.
The right way to show our gratitude to great legends of past should be by imbibing their virtues and doing noble deeds accordingly. For example, we see Ravans all around in form of corruption, terrorism, immorality etc. If we can unite to counter these in rightful manner, that would be true glorification of Ram. Same with Krishna, Durga, Hanuman etc.
I have been a fan of Hanumanji throughout my life. My way of his glorification has been preservation of my moral character and putting efforts for a strong and healthy body that serves the society. What point is in worshipping Hanuman with weak body and irritable stomach yet consuming heavy laddus!
While the motive behind all these modes of worship is worth greatest respect and we humbly bow to the purity of true devotees of any cult, it is our wish to see all devotees to adopt the same methods of worship that Ram or Krishna adopted in their own lives!

Q: Is Ishwar Omnipotent or All-Powerful?

Yes, He is omnipotent. But that does not mean He can do whatever He wants. Doing whatever one may want is sign of indiscipline. On contrary, Ishwar is most disciplined. Omnipotence means that Ishwar does not need help of any other entity to conduct His duties – creation, management, destruction of universe. He is self-sufficient to conduct His duties.
But He would act only as per His duties. For example, He will not kill Himself to create another Ishwar. He cannot make Himself an idiot. He cannot do theft or dacoity etc.

Q: Does Ishwar has a beginning?

Ishwar is without any beginning and without any end. He was always present and will always remain. Further His properties remain same at all times.
Soul and Nature are two other beginningless and endless entities.

Q: What does Ishwar want?

A: Ishwar wants bliss for all souls and wants them to achieve this bliss through deserving efforts purely on basis of merit.

Q: Should we worship Ishwar or not? Why? After all He never forgives!

A: Ishwar should be worshipped and He alone should be worshipped.
It is true that by worship of Ishwar, you will not receive any shortcut pass certificate when you have actually failed. Only lazy and cheaters desire such unscrupulous means to success.
The benefits of worship of Ishwar are different:
a. By worship of Ishwar one is able to understand Ishwar and His creation better.
b. By worship, one is able to better understand His properties and adopt those in his own life.
c. By worship, one is able to hear ‘inner voice’ better and get constant clearer guidance from Him.
d. By worship, one eradicates ignorance, gains strength and is able to withstand toughest challenges in life with confidence and aplomb.
e. Ultimately, one is able to remove ignorance completely and achieve Moksha or salvation with ultimate bliss.
Please note that worship does not mean some mechanical recitations or blankness of mind. It is a proactive approach to imbibe wisdom through actions, knowledge and contemplation.
We shall discuss this in detail subsequently. For now, you can refer to: How to worship?

Q: When Ishwar does not have limbs and sense organs, how does He conduct His actions?

A: He does not need coarse organs for his actions that happen at most microscopic level. He does so through His inherent powers. He sees without eyes because his eyes are present at every points in space, He does not have legs, but is fastest, He does not have ears but listens to everything, He knows everything but is beyond complete cognizance of everybody. This shloka comes in Upanishad. Ishopanishad also describes this in detail.

Q: Does Ishwar know His limits?

A: Ishwar knows everything. This means that He knows whatever is truth. Since Ishwar is limitless, He knows Himself as limitless. It would render Him ignorant if He tries to know His limits when none exist.

Q: Is Ishwar Saguna or Nirguna?

A: Both. Ishwar is Saguna if you refer to properties like Kindness, Just, Creator, Maintainer etc. But He is Nirguna, if you refer to properties that He does not possess – like dumbness, senselessness, anger, cheating, birth, death etc. Its only a semantic difference.

Q: Please summarize major properties of Ishwar as per Vedas.

A: His properties are infinite and cannot be expressed in words. But here are some major properties:
– He exists
– He is animate
– He is source of all bliss and happiness
– He is formless
– He is unchangeable
– He is all-powerful
– He is just
– He is kind
– He is unborn
– He never dies
– He is infinite
– He is omnipresent
– He has no defects
– He has no beginning and no end either in time or space
– He is uncomparable
– He maintains entire universe
– He creates entire universe
– He knows everything
– He never deteriorates and remains perfect always
– He is fearless
– He is pure
– He has no agents and establishes direct relationship with all souls.
He alone deserves to be worshipped without invoking anyone else.
This alone is the path to bliss and removal of all miseries!

Ishwar of Vedas = God of Christianity minus the concept of Trinity minus the necessity to surrender to Jesus
Ishwar of Vedas = Allah of Islam minus the necessity to accept Muhammad as final Prophet.
In other words, If someone says first part of Shahada : lâ ilâha illallâh (There is no other God except one and only Allah) but rejects the second part : Muḥammadur rasûlullâh (Muhammad is his messenger), that is close to concept of Vedic God.