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30-Science in Ved-2
See also   Jyotish in Ved;    Numbers in Ved;     Science in Ved-3

For more details on Vaidik science the seekers of Vaidik knowledge can see "Glimpses of Vaidik Metaphysics" for on line reading and even taking print at no cost on Website http://www, /OR through search engine of, or,

Medicine in Ved
Although our traditional or herbal medicine is a part of Atharv Ved, but the modern type of medicine is also mentioned in our Ved.

Attaching artificial limbs, which is mentioned in Rig Ved (Mandal 1, Sookt, 116; Ashtak 1, chapter 8 Mantra 15) came to the modern world only during 20th century.

Cloning came to the modern world only in 1997, while Rig Ved mentions the birth of Prithu from the dead body of King Ven. Read his story in Bhaagvat Puraan, 4/4,   Padm Puraan, 1/9;   Padm Puraan, 2/4;   Vishnu Puraan, 1/6;   Vishnu Puraan, 1/7.

In Mahaabhaarat, Gun Vidhi indicates chromosomes. This came to our knowledge only in 1910 AD.

Astronomy and astrology are the part of Ved's six parts - (Shat-Ang) - Shikshaa, Vyaakaran (Grammar), Nirukt, Kalp, Jyotish (astrology), and Chhand (meters). For detailed description on this topic read Jyotish in Ved.

Mathematics in Ved
Taken from Ved-Vigyaan     See its picture

In Shaarngdhar's one manuscript, there is a Shlok, demonstrating, that one does not have to go near to an object for its measurement. By its Gochar Lakshan (characteristics) itself, its whole knowledge can be attained. Based on these mathematical arguments, he proves that it is not required to go to a planet to know its Kiran (rays), Gochaar, Shaakhaa, Chalanaa (movement) rules. The mathematical formulae which calculate these kinds of parameters accurately are grouped under "Khagol Ganit". So the qery is as follows -

There is a lotus plant in a pond. It stands a bit high from the water level. If a mathematician wishes to calculate the total legth of the lotus stalk, depth of water from the tip of stalk floating up, he can do that. It is the power of Beej Ganit (Algebra) and Rekhaa Ganit (Geometry).

Ved Sootra
Anaarambhane Tadaveeryethaa Rani sthaane Naaree Deshe Samudre |
Yadashwinaa Oohthujai astu Shat patram Oon trayam Astumekam ||

Kaavya Sootra
Chakra Kraunchaa Kulit Salile Kwaapi Drishtam Tadaage Toyaa Doordhwam Kamal Kalikaagram Vitasti Pramaanam |
Mand Mand Chalitam Nilenaahatam Hast Yugme Tasminmagnam Ganak kathaya Kshipra Mambu Pramaanam ||

Trigonometry can be used here, but it will be a bit difficult, then what is the other solution?
This problem from Leelaavatee can be solved without going through the complexity of Trigonometry or other higher concepts. All you need is the concepts of Pythagoras Theorem, Binomial Expansion and Linear Equation in One Variable. All three concepts were known at the time of Bhaaskar II. The Pythagoras Theorem is known from Shulb Sootra, and Binomial Expansion coefficients can be known from what Halaayud calls it "Meru Prastaar" (an old concept attributed to Pingal
Vitasti Pramaanam (one hand span); and
Hast Yugme (lotus submerges in the pond at a distance of 2 hand spans from its original location).

Its solution is by ER Narayanan
Padm Syaagram Sprishati Salilam Maanasched Vitastam |
Nityaanando Ganan Kushalah Sangan yyeti Tattwam ||
Ardhaadardh Pragati ruditaa Taav Doordhwa Tadaage |
Saadyankaa saa Jal Parimiti Haryuchch Laddhast Yugmaa ||

The following is not from the Ved, but it is from our very important and popular scripture.

Heinemann in the 18th century found that a disease can be cured by the same germs which cause that disease.
But Bhaagvat Puraan (1.5.53) has mentioned this long before.

The Vedas and the Birth of Science
Posted April 6, 2013 by Professor Subhash Kak in Gods of Science and Discovery

The Vaidik texts present a tripartite and recursive view of the physical world. The universe is viewed as three regions of Earth, space, and sky which in the human being are mirrored in the physical body, the breath (Praan), and mind.

In the Vaidik world view, the processes in the sky, on earth, and within the mind are all connected. The Vaidik seers insist that all rational descriptions of the universe lead to logical paradox. The one category transcending all oppositions is Brahm. Understanding the nature of consciousness is of paramount importance in this view but this does not mean that other sciences are ignored. Vaidik ritual is a symbolic retelling of this world view. Knowledge is classified in two ways: the lower or dual, and the higher or unified. The seemingly irreconcilable worlds of the material and the conscious are taken as aspects of the same transcendental reality. The idea of complementarity is at the basis of the systematization of Indian philosophic traditions, so that complementary approaches are paired together.

We have the groups of: logic (Nyaaya) and physics (Vaisheshikaa), cosmology (Saankhya) and psychology (Yog), and language (Meemaansaa) and reality (Vedaant). These six views are like the six sides of a cube. Although these philosophical schools were formalized in the post-Vaidik age, we find the basis of these ideas in the Vaidik texts.

The Saankhya and the Yog systems take the mind as consisting of five components: Manas, Ahankaar, Chitta, Buddhi, and Aatmaa.
Manas is the lower mind which collects sense impressions. Ahankaar is the sense of I-ness that associates some of those perceptions to a subjective and personal experience. Once those sensory impressions have been related to I-ness by Ahankaar, their evaluation and resulting decisions are arrived at by Buddhi, the intellect. Chitta is the memory bank of the mind. These memories constitute the foundation on which the rest of the mind operates. But Chitta is not merely a passive instrument. The organization of the new impressions throws up instinctual or primitive urges which creates different emotional states. This mental complex surrounds the innermost aspect of consciousness, which is Aatmaa (Self or Brahm) . In this view, matter appears inert only because it has not expressed its potential. By process of transformation, nature (Prakriti) attains the capacity for freedom. Sentient beings are free to varying degrees.

Physics and Chemistry
The Vaisheshikaa system considers nine classes of substances, some of which are non-atomic, some atomic, and others are all-pervasive. The non-atomic ground is provided by the three substances Ether, Space, and Time, which are unitary and indestructible; a further four, Earth, Water, Fire, and Air are atomic substances composed of indivisible, and indestructible atoms; self (Aatmaa), which is the eighth, is omnipresent and eternal; and, lastly, the ninth, is the mind (Manas), which is also eternal but of atomic dimensions, that is, infinitely small. The atoms combine to form different kinds of molecules that break up under the influence of heat. The molecules come to have different properties based on the influence of various potentials (Tanmaatraa). Heat and light rays are taken to consist of very small particles of high velocity. Being particles, their velocity is finite. The gravitational force was perceived as a wind. The other forces were mediated by atoms of one kind or the other. Indian chemistry developed many different alkalis, acids and metallic salts by processes of calcination and distillation, often motivated by the need to formulate medicines. Metallurgists developed efficient techniques of extraction of metals from ore.

Geometry and Mathematics
Indian geometry began very early in the Vaidik period in altar problems as in the one where the circular altar (Earth) is to be made equal in area to a square altar (Heavens). Two aspects of the Pythagoras' Theorem are described in the texts by Baudhaayaan and others. The geometric problems are often presented with their algebraic counterparts. The solution to the planetary problems also led to the development of algebraic methods. Binary numbers were known at the time of Pingalaa's Chhand Shaastra. Pingalaa, who is believed to have lived about the 5th century BC used binary numbers to classify Vaidik meters. The knowledge of binary numbers indicates a deep understanding of arithmetic.

For many years the mainstream view was to take Indian astronomy as being essentially derivative, based on Mesopotamian and Greek sources. This view arose from the belief that the Indians did not possess a tradition of sound observation. This view was proven wrong for the Saiddhaantik period by Roger Billard who, using computer analysis, showed that the parameters used in the Siddhant were accurate for the date of the texts, establishing that they couldn't have been borrowed from some old source outside of the country.

This was not accepted by all. In particular, David Pingree, who had invested his career in the paradigm that Greek astronomy was the source of Indian astronomy attacked Billard. The distinguished historian of astronomy BL van der Waerden stepped in as a referee. He wrote a famous paper called "Two Treatises on Indian Astronomy" in the Journal for History of Astronomy (1970), where he stated the problem as: "If Pingree is right, Billard is wrong, and conversely. Proceeding to summarize the works of each, he concluded, that --
"Billard's methods are sound, and his results shed new light on the chronology of Indian astronomical treatises and the accuracy of the underlying observations. We also have seen that Pingree's chronology is wrong in several cases. In one case, his error amounts to 500 years Billard's book is reliable and contains very valuable new information. I have checked several of his results, and Billard always proved right.

Meanwhile, our understanding of Vaidik astronomy has changed in which my discovery of an astronomical code in the organization has played a role. These discoveries indicate that there was a long tradition of astronomical observation in India. The origins of Indian mathematics are also much ancient than previously thought. An amulet seal from Rehman Dheri (2400 BC) indicates that the Nakshatra system is an old one. The seal shows a pair of scorpions on one side and two antelopes on the other. It has been argued that this seal represents the opposition of the Orion (Mrigashiraa, or antelope head) and the Scorpio (Rohinee) Nakshatra. There exists another relationship between Orion and Rohinee, this time the name of alpha Tauri, Aldebaran.

The famous Vaidik myth of Prajaapati as Orion, as personification of the year, desiring his daughter (Rohinee) (for example Aitareya Braahman 3.33) represents the age when the beginning of the year shifted from Orion to Rohinee. For this transgression, Rudra (Sirius, Mrigavyaadh) cuts off Prajapati's head. It has been suggested that the arrow near the head of one of the antelopes represents the decapitation of Orion, and this seems a very reasonable interpretation of the iconography of the seal.

It is likely then that many constellations were named in the 3rd millennium BC or earlier. This would explain why the named constellations in the Rig Ved and the Braahman, such as the Riksha (the Great Bear and the Little Bear), the two divine dogs (Canis Major and Canis Minor), the twin Asses (in Cancer), the Goat (Capricornus) and the Heavenly Boat (Argo Navis), are the same as in Europe. Other constellations described similar mythical events: Prajaapati as Orion upon his beheading; Osiris as Orion when he is killed by Seth.

The Vedaang Jyotish (VJ) of Lagadha (1300 BC) is one of the subsidiary Vaidik texts, so its contents must be considered to be roughly coeval with the Braahman and other post-Vaidik texts although the Vaidik Jyotish text that has come down to us is definitely of a later period. The Puraan also contain a lot of very old material and their astronomy appears, on all counts, to be earlier than Aaryabhat so they provide us with clues regarding the evolution of astronomical thought. It was long popular to consider the Saiddhaantik astronomy of Aaryabhat to be based mainly on mathematical ideas that originated in Babylon and Greece. This view was inspired, in part, by the fact that two of the five pre-Aaryabhat Siddhant in Varaahamihira's Panch Saiddhaantikaa (PS), namely Romak and Paulish, appear to be connected to the West through the names Rome and Paul. But the planetary model of these early Siddhaant is basically an extension of the theory of the orbits of the Sun
and the Moon in the Vedaang Jyotish. Furthermore, the compilation of the Panch Siddhaant occurred after Aaryabhat and so the question of the gradual development of ideas can hardly be answered by examining it. I have presented the technical details of these discoveries elsewhere.

The main conclusion of these findings is that the earliest Indian astronomy is prior to the Mesopotamian one. We have traced certain Indian ideas in Mesopotamia in the 2nd and the 1st millennium BC. There they were further developed and subsequently transmitted to Greece. Using hitherto neglected texts, an astronomy of the third millennium BC has been discovered. Yaagyavalkya, who perhaps lived around 1800 BC, knew of a 95-year cycle to harmonize the motions of the Sun and the Moon and he also knew that the Sun's circuit was asymmetric. The 2nd millennium text Vedaang Jyotish of Lagadha went beyond the earlier calendrical astronomy to develop a theory for the mean motions of the Sun and the moon. This marked the beginnings of the application of mathematics to the motions of the heavenly bodies. An epicycle theory was used to explain plan The Birth of Science 55 etary motions. Later theories consider the motion of the planets with respect to the Sun, which in turn is seen to go around the earth.

The doctrine of the three constituent qualities: Sattwa, Rajas, and Tamas, plays an important role in the Saankhya physics and metaphysics. In its undeveloped state, cosmic matter has these qualities in equilibrium. As the world evolves, one or the other of these become preponderant in different objects or beings, giving specific character to each. The recursive Vaidik world-view requires that the universe itself go through cycles of creation and destruction. This view became a part of the astronomical framework and ultimately very long cycles of billions of years were assumed. Indian evolution takes the life forms to evolve into an increasingly complex system until the end of the cycle. The categories of Saankhya operate at the level of the individual as well. Life mirrors the entire creation cycle and cognition mirrors a life-history. Cosmological speculations led to the belief in a universe that goes through cycles of creation and destruction with a period of 8.64 billion years. Related to this was the notion that light traveled with a speed of 186,000 miles per second. Since these numbers were not obtained through
experimentation, the accuracy of these figures must be seen as remarkable coincidence.

Panini's grammar (5th century BC) provides 4,000 rules that describe the Sanskrit of his day completely. This grammar is acknowledged to be one of the greatest intellectual achievements of all time. The great variety of language mirrors, in many ways, the complexity of nature and, therefore, success in describing a language is as impressive as a complete theory of physics.
It is remarkable that Paanini set out to describe the entire grammar in terms of a finite number of rules. Scholars have shown that the grammar of Paanini represents a universal grammatical and computing system. From this perspective it anticipates the logical framework of modern computers.

Aayur Ved, the Indian medicine system, is a holistic approach to health that builds upon the tripartite Vaidik approach to the world. Health is maintained through a balance between three basic humors (Dosh) of wind (Vaat), fire (Pitta), and water (Kaph). Charak and Sushrut are two famous early physicians of this system. Indian surgery was quite advanced. The caesarian section was known, bone-setting reached a high degree of skill, and plastic surgery was also known.

The Yog Vasishth
Let me take a single book, the Yog Vasishtha (YV), to summarize main ideas about space, time, matter, and man in the universe. The internal evidence indicates that it was authored or compiled later than the Raamaayan. Scholars have dated it variously as early as 1st century AD or as late as the 13th or the 14th century AD. Yog Vashishth may be viewed as a book of philosophy or as a philosophical novel. It describes the instruction given by Vashishth to Raam, the hero of the epic Raamaayan. Its premise may be termed radical idealism and it is couched in a fashion that has many parallels with the notion of a participatory universe argued by Wheeler and others. Its most interesting passages from the scientific point of view relate to the description of the nature of space, time, matter, and consciousness. It should be emphasized that the Yog Vashishth ideas do not stand in isolation.

Similar ideas are to be found in the earlier Vaidik books. At its deepest level the Vaidik conception is to view reality in a monist manner; at the next level one may speak of the dichotomy of mind and matter. Ideas similar to those found in Yog Vashishth are also encountered in Puraan and Tantric literature. Three kinds of motion are alluded to in the Vaidik books: these are the translational motion, sound, and light which are taken to be equivalent to Earth, Air, and Sky. The fourth motion is assigned to consciousness; and this is considered to be infinite in speed. It is most interesting that the books in this Indian tradition speak about the relativity of time and space in a variety of ways. Universes defined recursively are described in the famous episode of Indra and the ants in Brahm Vaivart Puraan (4.47.100-160), the Mahaabhaarat 12.187, and elsewhere. These flights of imagination are to be traced to more than a straightforward generalization of the motions of the planets into a cyclic universe.

They must be viewed in the background of an amazingly sophisticated tradition of cognitive and analytical thought. Selected Passages of Yog Vashishth consists of 6 books where the 6th book itself has two parts. The numbers in the square brackets refer to the book, (part), section, verse.

Time cannot be analyzed; for however much it is divided it survives indestructible. [1.23]
There is another aspect of this time, the end of action (Kritaant), according to the law of nature (Niyati). [1.25.6-7]
The world is like a potter's wheel: the wheel looks as if it stands still, though it revolves at a terrific speed. [1.27]
Just as space does not have a fixed span, time does not have a fixed span either. Just as the world and its creation are mere appearances, a moment and an epoch are also imaginary. [3.20]
Infinite consciousness held in itself the notion of a unit of time equal to one millionth of the twinkling of an eye: and from this evolved the time-scale right upto an epoch consisting of several revolutions of the four ages, which is the lifespan of one cosmic creation. Infinite consciousness itself is un involved in these, for it is devoid of rising and setting (which are essential to all time-scales) , and it is devoid of a beginning, middle and end. [3.61]

There are three types of space - the psychological space, the physical space and the infinite space of consciousness. [3.17]
The infinite space of undivided consciousness is that which exists in all, inside and outside. The finite space of divided consciousness is that which created divisions of time, which pervades all being. The physical space is that in which the elements exist. The latter two are not independent of the first. [3.97]

Other Universes/wormholes
I saw within [the] rock [at the edge of the universe] the creation, sustenance and the dissolution of the univers. I saw innumerable creations in the very many rocks that I found on the hill. In some of these creation was just beginning, others were populated by humans, still others were far ahead in the passage of their times. [6.2.86]
I perceived within each molecule of air a whole universe. [6.2.92]

In every atom there are worlds within worlds. [3.20]
I saw reflected in that consciousness the image of countless universes. I saw countless creations though they did not know of one another's existence. Some were coming into being, others were perishing, all of them had different shielding atmospheres (from five to thirty-six atmospheres) . There were different elements in each, they were inhabited by different types of beings in different stages of evolution. [In] some there was apparent natural order in others there was utter disorder, in some there was no light and hence no time-sense. [6.2.59]

Direct experience alone is the basis for all proofs. That substratum is the experiencing intelligence which itself becomes the experiencer, the act of experiencing, and the experience. [2.19-20]
Everyone has two bodies, the one physical and the other mental. The physical body is insentient and seeks its own destruction; the mind is finite but orderly. [4.10]
I have carefully investigated, I have observed everything from the tips of my toes to the top of my head, and I have not found anything of which I could say "This I am." "Who is I? I am the all-pervading consciousness which is itself not an object of knowledge or knowing and is free from self-hood. I am that which is indivisible, which has no name, which does not undergo change, which is beyond all concepts of unity and diversity, which is beyond measure. [5.52]
I remember that once upon a time there was nothing on this Earth, neither trees and plants, nor even mountains. For a period of eleven thousand years the Earth was covered by lava. In those days there was neither day nor night below the polar region: for in the rest of the Earth neither the Sun nor the Moon shone. Only one half of the polar region was illumined. Then demons ruled the Earth. They were deluded, powerful and prosperous, and the Earth was their playground. Apart from the polar region, the rest of the Earth was covered with water. And then for a very long time the whole earth was covered with forests, except the polar region. Then there arose great mountains, but without any human inhabitants. For a period of ten thousand years the Earth was covered with the corpses of the demons. [6.1]

The same infinite self conceives within itself the duality of oneself and the other. [3.1]
Thought is mind, there is no distinction between the two. [3.4]
The body can neither enjoy nor suffer. It is the mind alone that experiences. [3.115]
The mind has no body, no support and no form; yet by this mind is everything consumed in this world. This is indeed a great mystery. He who says that he is destroyed by the mind which has no substantiality at all, says in effect that his head was smashed by the lotus petal … The hero who is able to destroy a real enemy standing in front of him is himself destroyed by this mind which is [nonmaterial] . The intelligence which is other than self-knowledge is what constitutes the mind. [5.14]

The absolute alone exists now and for ever. When one thinks of it as a void, it is because of the feeling one has that it is not void; when one thinks of it as notvoid, it is because there is a feeling that it is void. [3.10]
All fundamental elements continued to act on one another as experiencer and experience and the entire creation came into being like ripples on the surface of the ocean. And, they are interwoven and mixed up so effectively that they cannot be extricated from one another till the cosmic dissolution. [3.12]

The entire universe is forever the same as the consciousness that dwells in every atom, even as an ornament is non-different from gold. [3.4]
The five elements are the seed of which the world is the tree; and the eternal consciousness is the seed of the elements. [3.13]
Cosmic consciousness alone exists now and ever; in it are no worlds, no created beings. That consciousness reflected in itself appears to be creation. [3.13]
This consciousness is not knowable: when it wishes to become the knowable, it is known as the universe. Mind, intellect, egotism, the five great elements, and the world—all these innumerable names and forms are all consciousness alone. [3.14]
The world exists because consciousness is, and the world is the body of consciousness. There is no division, no difference, no distinction. Hence the universe can be said to be both real and unreal: real because of the reality of consciousness which is its own reality, and unreal because the universe does not exist as universe, independent of consciousness. } [3.14]
Consciousness is pure, eternal and infinite: it does not arise nor cease to be. It is ever there in the moving and unmoving creatures, in the sky, on the mountain and in fire and air. [3.55]
Millions of universes appear in the infinite consciousness like specks of dust in a beam of light. In one small atom all the three worlds appear to be, with all their components like space, time, action, substance, day and night. [4.2] 60 The Wishing Tree The universe exists in infinite consciousness. Infinite consciousness is unmanifest, though omnipresent, even as space, though existing everywhere, is manifest. [4.36]
The manifestation of the omnipotence of infinite consciousness enters into an alliance with time, space and causation. Thence arise infinite names and forms. [4.42]
Rudra is the pure, spontaneous self-experience which is the one consciousness that dwells in all substances. It is the seed of all seeds, it is the essence of this world-appearance, it is the greatest of actions. It is the cause of all causes and it is the essence of all beings, though in fact it does not cause anything nor is it the concept of being, and therefore cannot be conceived. It is the awareness in all that is sentient, it knows itself as its own object, it is its own supreme object and it is aware of infinite diversity within itself. The infinite consciousness can be compared to the ultimate atom which yet hides within its heart the greatest of mountains. It encompasses the span of countless epochs, but it does not let go of a moment of time. It is subtler than the tip of single strand of hair, yet it pervades the entire universe. It does nothing, yet it has fashioned the universe. All substances are non-different from it, yet it is not a substance; though it is non-substantial it pervades all substances. The cosmos is its body, yet it has no body. [6.1.36]

The Yog Vashishth Model of Knowledge
Yog Vashishth is not written as a systematic text. Its narrative jumps between various levels: psychological, social, and physical. But since the Indian tradition of knowledge is based on analogies that are recursive and connect various domains, one can be certain that our literal reading of the passages is valid. Yog Vashishth appears to accept the idea that laws are intrinsic to the universe. In other words, the laws of nature in an unfolding universe will also evolve. According to Yog Vashishth, new information does not emerge out of the inanimate world but it is a result of the exchange between mind and matter. It accepts consciousness as a kind of fundamental field that pervades the whole universe. One might speculate that the parallels between Yog Vashishth and some recent ideas of physics are a result of the inherent structure of the mind.

Other Texts
Our readings of the Yog Vashishth are confirmed by other texts such as the Mahaabhaarat and the Puraan as they are by the philosophical systems of Saankhya and Vaisheshikaa, or the various astronomical texts. Here is a reference to the size of the universe from the Mahaabhaarat 12.182:36 - "The sky you see above is infinite. Its limits cannot be ascertained. The Sun and the Moon cannot see, above or below, beyond the range of their own rays. There where the rays of the Sun and the Moon cannot reach, are luminaries which are self-effulgent and which possess splendor like that of the Sun or the fire. Even these last do not behold the limits of the firmament in consequence of the inaccessibility and infinity of those limits. This space which the very gods cannot measure is full of many blazing and self-luminous worlds each above the other."

The Mahabharata has a very interesting passage (12.233), virtually identical with the corresponding material in Yog Vashishth, which describes the dissolution of the world. Briefly, it is stated how a dozen Suns burn up the Earth, and how elements get transmuted until space itself collapses into wind (one of the elements). Ultimately, everything enters into primeval consciousness. If one leaves out the often incongruous commentary on these ideas which were strange to him, we find al-Biruni in his encyclopedic book on India written in 1030 speaking of essentially the same ideas. Here are two little extracts ---
"The Hindus have divided duration into two periods, a period of motion, which has been determined as time, and a period of rest, which can only be determined in an imaginary way according to the analogy of that which has first been determined, the period of motion. The Hindus hold the eternity of the Creator to be determinable, not measurable, since it is infinite. They do not, by the word creation, understand a formation of something out of nothing. They mean by creation only the working with a piece of clay, working out various combinations and figures in it, and making such arrangements with it as will lead to certain ends and aims which are potentially in it."

The mystery of consciousness is a recurring theme in Indian texts. Unfortunately, the misrepresentation that Indian philosophy is idealistic, where the physical universe is considered an illusion, has become very common. For an authoritative modern exposition of Indian ideas of consciousness one must turn to Aurobindo.

It appears that Indian understanding of physics was informed not only by astronomy and terrestrial experiments but also by speculative thought and by meditations on the nature of consciousness. Unfettered by either geocentric or anthropocentric views, this understanding unified the physics of the small with that of the large within a framework that included metaphysics.

This was a framework consisting of innumerable worlds (solar systems), where time and space were continuous, matter was atomic, and consciousness was atomic, yet derived from an all-pervasive unity. The material atoms were defined first by their subtle form, called Tanmaatraa, which was visualized as a potential, from which emerged the gross atoms. A central notion in this system was that all descriptions of reality are circumscribed by paradox. The universe was seen as dynamic, going through ceaseless change.

The Medieval Period
Astronomical texts called Siddhaant begin appearing sometime in the 1st millennium BC. According to tradition there were 18 early Siddhaant of which only a few have survived. Each Siddhaant is an astronomical system with its own constants. Some of the famous astronomer mathematicians that arose in India's long medieval period are listed below.

Aaryabhat (born 476) took the Earth to spin on its axis; this idea appears to have been his innovation. Aaryabhat was aware of the relativity of motion as is clear from this passage in his book, "Just as a man in a boat sees the trees on the bank move in the opposite direction, so an observer on the equator sees the stationary stars as moving precisely toward the West.

Brahmagupt, who was born in 598 in Raajasthaan, wrote his masterpiece, "Brahm Sphoot Siddhaant" in 628. His school, which was a rival to that of Aaryabhat, has been very influential in Western and Northern India. Brahmagupt's work was translated into Arabic in the 8th century at Bagdaad and it became famous in the Arabic world as Sindhind and it influenced Islamic astronomy. One of Brahmagupt's chief contributions is the solution of a certain second order indeterminate equation which is of great significance in number theory.

Belonging to the Karnaatak region, Bhaaskar (born 1114), was an outstanding mathematician and astronomer. Amongst his mathematical contributions is the concept of differentials. He was the author of Siddhaant Shiromani, a book in four parts: (I) Leelaavatee on Arithmetic, (ii) Beej Ganit on algebra, (iii) Ganit Adhyaaya, (iv) Gol Adhyaaya on astronomy. His epicyclic-eccentric theories of planetary motions are more developed than in the earlier Siddhaant. Subsequent to Bhaaskar we see a flourishing tradition of mathematics and astronomy in Kerala which saw itself as a successor to the school of Aaryabhat.

Of these, 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 11 decimal places.
A very prolific scholar who wrote several works on astronomy, Neelakanth (c. 1444-1545) found the correct formulation for the equation of the center of the planets and his model must be considered a true heliocentric model of the solar system. He also improved upon the power series techniques of Madhava. The methods developed by the Kerala mathematicians were far ahead of the European mathematics of the day. Another noteworthy contribution was by the school of New Logic (Navya Nyaaya) of Bangaal and Bihaar.

At its zenith, during the time of Raghunath (1475- 1550), this school developed a methodology for a precise semantic analysis of language. Its formulations are equivalent to mathematical logic. With all these brilliant achievements behind them, why didn't the Indians create a scientific revolution that touched the entire fabric of society? Clearly, the social, political and economic conditions were not ripe for such change. Europe had the advantage of the wealth obtained from the New World part of which went to the support of institutions of higher learning and the development of instruments to aid navigation.


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Created by Sushma Gupta on 3/15/06
Updated on 05/22/13