Science & Vedanta

Nobel laureate physicist Albert Einstein’s comment on ‘Science and Religion’ [Ref. “The world Treasury of Physics, Astronomy and Mathematics” Block bay books etc.1991] are as follows:

Science without religion is LAME 

Religion without science is BLIND.

Hindu Calendar

The year of 2005 is the centennial year of the theory of Relativity where “Time” was assumed by Professor Einstein as a variable entity in contrast to the absolute nature of the “Newtonian Time”. The concept of “Time” lured even the ancient Vedic Seers and they looked upon the “MOON” as the time-marker. Although, these Seers recognized the fact that “TIME” had no beginning or end but the time intervals are needed to calculate the recurring phenomenon of nature such as day and night, new moon, full moon and especially Seasons, in order to formulate a Calendar for daily use of the people. The Calendar was essential for the ancients for the cultivation of the land, to trade with the other countries by sea route and the seasonal as well as the daily rituals of the people.

As the changing cycle of the moon is the most visible phenomenon, these Vedic Seers or the first astronomer observed the lunar fact that the moon took slightly more than twenty seven nights to complete one revolution in the sky and thus this path of the moon was divided into twenty seven divisions among the cluster of stars. Each of this division [ or lunar mansion] of this cluster of stars was designated as “ NAKSHATRA” [ Sanskrit name of the lunar mansion]. Each Nakshatra (star) was named after the most visible star among that particular star cluster.The ancient Seers also observed that the new moon took place when both the Sun and the Moon stayed in the same Nakshatra and likewise the full moon occurred when the Sun and the Moon remained in the opposing Nakshatra. Each month of a year gets one new moon and one full moon and the name of the month was designated after the name of the most visible star of that Nakshatra where the full moon occurred.

 These ancients also observed that the moon took nearly twenty nine and half nights to move from one new moon or full moon to the next, thereby taking 354 days to have 12 new moons or full moons in a year. It must be noted that the first astronomers of India already divided a year into 12 months of 365 days. Thus ,in order to adjust the discrepancy of 11days between the solar year and the lunar year, at the interval of every third year , an extra month [ intercalary month] was added to the lunar year to synchronize with the solar year. Furthermore, the ancient recognized that the earth’s yearly path around the Sun and the moon’s path among the Nakshatras , intersect each other at two points , where the length of the period of the day and night became equal[ equinoxes].The meeting of these two paths happen twice a year : on 21st of march point known as “Vernal equinox”and on 22nd of September, known as “Autumnal equinox”.These two dates are the most important reference points in order to develop a Calendar system. The Vernal equinox is the beginning of the spring [or Vasanta] whereas the autumnal equinox is the first month of the fall term [Sarad]. Hindu rituals begin from the first newmoon following the Vernal equinox and the Autumnal equinox , such as Vasanti puja and Durga puja respectively.

 Before independence, the different parts of India followed different Calendar systems, so to standardize the Calendar of India, the first Prime Minister of free India Mr. Nehru, established the Calendar reform committee in 1952 and the renowned astronomer of India Professor Meghnad Saha was selected as its Chairman. Professor Saha along with a few others, did an extensive research on the Calendars of the world as well as the different systems of Calendars of India and submitted their report in 1955 to the Council of Scientific and Industrial Research[ CSIR}.In 1992, CSIR published this report entitled “ History of the Calendar” , which is a valuable document not only about the Indian Calendar systems as well as the Calendars of the World.

 Thus “TIME” was the foremost concept which the ancient Vedic Seers tried to interpret and developed the “Hindu Calendar” but still at this age of the scientific progress the understanding of the concept of “TIME” remains as mysterious as before.

Dr. Ramananda Chatterjee

Professor Emeritus


[After receiving the doctorate degree in Theoretical Physics, from the University of Calcutta in 1963, the author started to teach physics at the University of Calgary, until 1997 when he took retirement & got involved in the service to the Indian community of Calgary, such as giving lectures on Vedic astronomy & mother Goddesses as well as performing the Hindu rituals etc.] 

Source: Dr. Ramananda Chatterjee, Emeritus Professor of Physics, The University of Calgary

 The Bakshali Manuscript

 In 1881, a farmer of lndia found- an old-manuscript inside a tree trunk in the village called “Bakshali” within fifty miles of the city of Pesahar. The farmer handed this unknown manuscript to the local government and it was exported to the Bodelien library in oxford, England for safe keeping. Since then a lot of research work has been done on this manuscript which was written on birch-bark and only thirtyfive leaves out of seventy, were in legible condition. Written in early Sharada script {a modified version of Sanskrit} this manuscript has been claimed as a valuable mathematical treatise and its author is yet to be known. The mathematical rules in this ancient manuscript were written in the form of verses-in “Anushtubh” meter where the sentence consists of thirtytwo syllables.

Recently, a Japanese scholar named Takao Hayashi from Brown University, USA has published his doctoral thesis entitled: “The Bakshali Manuscript” {Groningen Oriental Studies-1995}. In this manuscript, the ~”Rule of Three” [traisika] was applied to solve the problems for the business community, travelers and goldsmiths. This “Rule of Three” was known to the European in the thirteen century as the famous “Golden Mean” from the book written by the Italian Mathematician Leonardo of Pisa, known as Fibonacci [filius bonacci]. Fibonacci obtained the necessary informations from the Arabic book on Hindu Mathematics. In the Bakshali Manuscript the “Rule of Three” was applied to prove a theorem of transforming a rectangle into a series of squares [continued fraction]. The “Golden Mean” is the ratio of the larger to the smaller side of the rectangle and it is always close to a constant value of 1.618 ,provided the sides of the rectangle are proportional to two consecutive numbers such as 2, 3, 5, 8,13, 21 so on, these numbers are called Fibonacci numbers and they are generated by adding the two preceding numbers.

 Most of the Bakshali Manuscript contains problems and their final solutions. A simplified version of a problem can be stated as follows: A certain King asked his goldsmith to distribute eleven gold coins among his three daughters in the ratio of a half,a quarter and one sixth. The goldsmith added one more gold coin from his own pocket and out of total twelve gold coins,he took the ratio of one half which was six and gave it to the first daughter. The second daughter got a quarter of twelve which was three gold coins. Finally, the third daughter received one sixth of twelve which amounts to two gold coins. The goldsmith took back his own gold coin but satisfied everyone. The application ofthe”Rule of Three” can be traced in the 20th century “Quantum Physics” where any basic model can be built by using THREE operators, named as The Creation Operator[Brahma], The Number Operator [Vishnu] and The Annihilation Operator [Shiva] {JJ Sakurai, Advanced Quantum Mechanics, Addison- Wesley, 1967}. Similarly, the basic constituents of the particles such as proton, neutron, mesons etc., consists of the THREE fundamental particles “QUARK” {this name quark was taken from the name ofa character of the Irish writer James Joyces’s “Finnegans Wake”}.

 The ”Rule of Three” has been extended to other prime numbers such as 5,7,etc., and was applied not only in science but also in various other sectors of the society. In fact, the number 3 was considered to be a divine number in most of the ancient civilizations. After the excavation in India where the two cities Mohenjo-Daro and Harappa of the Indus-Sarasvati Civilization {~5000 B.C.} were discovered, the “TREFOIL” motif has been found on the robe of the statue ofa priest {J.M. Kenoyer, Ancient cities of the Indus Valley Civilization, Oxford, 1998}. The next prime number 5 is mentioned in the “Taittiriya” and “Brihadaranyaka” Upanishads as the most important number because the entire universe is FIVE-FOLD. In fact, in the Hindu ritualist worship, one needs minimum five items such as: flowers, sandelpaste, incense stick, light and food [naivedya] which represent the Five basic elements of the constituents of the universe: Space, Earth, Air, Fire and Water respectively.

 In Physics” a quasi-periodic tiling with a crystallographically impossible Five-fold quasi-symmetry” has been observed {Roger Penrose, The Emperor’s New Mind, 1989, Oxford}. In the Rig-Veda, the SEVEN sages are considered as the founder of the Vedic Aryans linages and they are represented as the SEVEN bright stars associated with northern celestial pole, known as ” The Great Bears” {Ursa Major}. Most of the “Hindu Wedding” follows the Rig-Vedic framework of marriage where “The Seven Steps” {Saptapadi} is one of the most important part of this ritual. Thus, at the dawn of the civilization,the prime numbers were very auspicious even at present age it is very significant to understand the Universe yet, it remains as mysterious as before. 

Source: Dr. Ramananda Chatterjee, Emeritus Professor of Physics, The University of Calgary