Astronomia Vedica IV

Subbarayyappa remarked that " Indian mathematics too owes its primary inspiration to Vedic practices. The Shulba sutras, part of another Vedic auxiliary called the Kalpa sutras, deal with the construction of several types of brick altars and in that context with certain geometrical problems including the Pythagorean theorem, squaring a circle, irrational numbers and the like. Yet another Vedic auxiliary, Metrics (chandah), postulated a triangular array for determining the type of combinations of 'n' syllables of long and short sounds for metrical chanting. This was mathematically developed by Halayudha who lived in Karnataka (10th Century) into a pyramidal expansion of numbers. Such an exercise appeared six centuries later in Europe, known as Pascal's triangle. Vedic mathematics and astronomy were pragmatic and integrated with Vedic religio-philosophical life."

"During the three centuries before and after the Christian era, there were new impulses. Astronomy became mathematics-based. In the succeeding centuries, while astronomy assimilated Hellenic ideas to some extent mathematics was really innovative. Indian astronomers were able mathematicians too. The doyen among them, Aryabhatta I (b.476 A.D.) gave the value of pi (3.1416 approx., a value used even today) worked out trigonometrical tables, areas of triangles and other plane figures, arithmetical progression, summation of series, indeterminate equations of the first order and the like. He expounded that the earth rotates about its own axis and the period of one sidereal rotation given by him is equivalent to 23h 56m 4s.1, while the modern value is 23h 56m 4s.091. He discarded the mythical Rahu-Ketu postulate concerning eclipses in favour of a scientific explanation. Aryabhatta's junior contemporary Varahamihira, was well known for his compendium, the Panchasiddhantika, a compilation of the then extant five astronomical works called the Siddhantha- Surya, Paulisha, Romaka, Vasishta, and Paitamaha. Of them, the Suryasiddhanta, which he regarded as the most accurate, underwent revisions from time to time and continues to be an important text for computing pancangas.

Brahmagupta was a noted astronomer mathematician of the 7th Century. His remarkable contribution was his equation for solving indeterminate equations of the second order - an equation that appeared in Europe a thousand years later known as Pell's equation. His lemmas in this connection were rediscovered by Euler (1764) and Lagrange (1768). Brahmagupta was also the first to enunciate a formula for the area of a rational cyclic quadrilateral. In the latter half of the first millenium A.D. there were other noted astronomers and mathematicians like Bhaskara I, Lalla, Pruthudakasvamin, Vateshvara, Munjala, Mahavira (Jaina mathematician), Shripati, Shridhara, Aryabhatta II , and Vijayanandin. The tradition of astronomy and mathematics continued unabated - determination of procession of equinoxes, parallax, mean and true motions of planet, permutations and combinations, solving quadratic equations, square root of a negative number and the like.

Using nine digits and zero, the decimal place value system had established itself by about the 4th century A.D. Says historian of science, George Sarton, "Our numbers and the use of zero were invented by the Hindus and transmitted by Arabs, hence the name Arabic numerals which we often give them.' Brahmagupta's Brahmasphuta Siddhanta and Khandakhadyaka were also rendered into Arabic in the 9th-10th century. The Brahmi numerical forms with some modifications along with the decimal place-value system developed in India have since become universal."

Eirik L Harris remarked that "Additionally, the Vedics, who developed the Hindu-Arabic number system, were far enough advanced in mathematics to make many calculations, including that of the complete cycle of the progression of the equinoxes, though, again, as the Vedas were mainly religious, there is no mention as to how results like this were derived. Overall, the Vedic culture was very rich in astronomical thinking, and it is a shame that non religious texts did not last through the centuries, for they could have shone more light on the matter of the astronomical accomplishments of the Vedic people." The ancient Indians divided the path of the moon into 27 equal parts called nakshatras, showing the variation of the relative position of the moon in comparison to the rest of the stars visible to the Vedic people. These nakshatras were quite important for determining times of the year, as can be seen in combination with Vedic mythology, and can also be used to determine how far back in history Vedic astronomy extended.

The myth of the god Janus shows both of these factors, the determination of the age of Vedic astronomy and different periods of the year. Janus had four heads, each of which represented a phase of the moon in Sagittarius (one of the nakshatras) which marked the four seasons. One head was the full moon (in Sagittarius) which gave the time of the spring equinox, another was the new moon, during which time the autumn equinox fell, still another was the half waning moon, marking the winter solstice, and finally came the head representing the half waxing moon, during which time came the summer solstice. From current knowledge of the movement of the sphere of stars surrounding the earth, it can be calculated that the observations leading to the myth of Janus were made around 4000 BC. Additionally, within the Rg Veda is a verse observing the winter solstice in Aries, which would have placed it at around 6500 BC.

It is possible to date the Rg Veda like this because a complete cycle in the procession of the equinoxes takes place either every 25,870 to 24,500 years according to modern astronomers (the exact time period is still disputed by modern day astronomers), meaning that the moon is only full in Sagittarius during the spring equinox every 25,000 years or so. Modern astronomers, however, were not the first to make the difficult calculations to discover the length of this cycle. The Vedics were able to do this and came up with the value of 25,870 years. How these ancient people were able to make these calculations, however is "as great a mystery as the origin of life itself".

Further observations which could only have taken place around 4000 BC have also been recorded. These included the constellation Hydra, the god of darkness. The only time Hydra was fully visible to the people of northern India was in mid-winter, when the sun shone the fewest hours, hence the allusion to the god of darkness. More importantly, however, was the fact that the rains came when Hydra ceased to be completely visible. This was very important to the farmers of North India, for they needed to know when the rains would come, so as to know when to prepare their fields and plant their crops." ( Astronomy of Vedic India )Astronomical Mysticism in the Rig Veda The five fundamental circles, the Celestial Equator ( Vishuvat Vritta) , the Celestial Meridien ( Khagoleeya Dhruva Rekha ), the Ecliptic ( Kranti Vritta ), the Nodal Circle ( Vikshepa Vritta ) and the Celestial Horizon ( Kshithija ) were called by the Seers as Shahasra Seersha, Sahasra Purusha, Sahasra Kha, Sahasra Path & Sahasra Bhoomi. This is given in the Hymn, the Purusha Sooktha, that the Zodiacal Man or Time Eternal lies coiled as the mighty Zodiac ! Yogic or Philosophical Piece The Downward Pull of the Mind The Downward Pull of the Mind is when the negative elements in the collective mind or the social mind triumph. Socrates is poisoned. Rimbau flees to the Abyssinian desert. History is replete with such incidents, when " the adverse forces " or " the hostile forces " triumph over the positive forces in the collective or social mind. The Upward Pull of the Mind This happens only in the minds of Initiates. " In Ire " in Latin means to go within. Initiates are those who are always in touch with the Divine Self in themselves. The four faculites of the Intuitive Reason - Revealation, Inspiration, Intuition & Illumination - are experienced by them. The river of inspiration flowing from the Truth Consciousness pulls the mind to the higher regions of the Superconscient. In Geo-Biology, this is the pull of the mind from the Telluric level to the Cosmic level. The mind experiences Bliss during this Upward Pull. The Upward Pull is the master movement of Nature. The upward movement is that which pulls us from Death ( the senseless attachment to the sensory world ) to Immortality ( Self- Actualisation) and realises in this body of earth the luminous Kingdom of Heaven !