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The lower city, which was tightly packed with residential units, was also constructed on a grid pattern consisting of a number of blocks separated by major cross streets. India developed very early, enduring atomist theories of matter. Freedom of the mind created the wondrous world of the intellect — the world of Hindu rishis, philosophers, poets and dramatists.
Vedanta upholds the idea that creation is timeless, having no beginning in time. A fortune minus zero is a fortune. Hindu culture had this unique vision of the infiniteness of time as well as the infinity of space. While the West was still thinking, perhaps, of 6, years old universe — India was already envisioning ages and eons and galaxies as numerous as the sands of the Ganges. Their hair and nails fell out; Pottery broke without apparent cause, And the birds turned white. They evolved the formula that the angle of incidence was equal to the angle of reflection. In line with this eccentricity, the entrance gate is set in a corner rather than the wall.
No other civilization, not even that of the Greeks, could have enjoyed the freedom that we had. We have to remember, Socrates was forced to drink hemlock! The Inquisition burnt the Christian apostates at the stake and Islam beheaded dissenters. Very subtle atoms begin to combine, eventually generating a cosmic wind that blows heavier and heavier atoms together. Souls depending on their karma earned in previous world systems, spontaneously draw to themselves atoms that coalesce into an appropriate body.
While most cultures base their cosmologies on familiar units such as few hundreds or thousands of years, the Hindu concept of time embraces billions and trillions of years.
Hindu sages describe time as cyclic, an endless procession of creation, preservation and dissolution. Scientists such as Carl Sagan have expressed amazement at the accuracy of space and time descriptions given by the ancient rishis and saints, who fathomed the secrets of the universe through their mystically awakened senses.
As in modern physics, Hindu cosmology envisaged the universe as having a cyclical nature. The end of each kalpa brought about by Shiva's dance is also the beginning of the next. The transcendence of time is the aim of every Indian spiritual tradition. Time is often presented as an eternal wheel that binds the soul to a mortal existence of ignorance and suffering. Rather the universe is projected in cycles. Time immemorial is measured in cycles called Kalpas. A Kalpa is a day and night for Brahma, the Lord of Creation.
After each Kalpa, there is another Kalpa. Each Kalpa is composed of 1, Maha Yugas. A Kalpa is thus equal to 4. Kirtha Yuga or Satya yuga golden or truth age is 1,, years; Treta yuga is 1,, years; Dvapara yuga is , years; and Kali Yuga is , years. Total duration of the four yugas is called a kalpa.
At the end of kalyuga the universe is dissolved by pralaya cosmic deluge and another cycle begins. Each cycle of creation lasts one kalpa, that is 12,, human years or 12, Brahma years. One Maha Yuga is 4,32 million years. A Brahma, or Lord of Creation, lives for one hundred Brahma years each of made up of Brahma days.
After that he dies. So a Brahma lives for 36, Kalpas, or 36, x 2, x 4,30, human years — i. After the death of each Brahma, there is a Mahapralaya or Cosmic deluge , when all the universe is destroyed.
Then a new Brahma appears and creation starts all over again. Refer to Sciences of the Ancient Hindus: Time in Hindu mythology is conceived as a wheel turning through vast cycles of creation and destruction pralaya , known as kalpa.
In the words of famous writer, Joseph Campbell: Not so alien to the imagery of modern science that it could not have been put to acceptable use. According to Guy Sorman , visiting scholar at Hoover Institution at Stanford and the leader of new liberalism in France: The Bible had been the yardstick for measuring time, but the infinitely vast time cycles of India suggested that the world was much older than anything the Bible spoke of.
It seem as if the Indian mind was better prepared for the chronological mutations of Darwinian evolution and astrophysics. ISBN 0 p. Subhash Kak - sulekha.
Huston Smith a philosopher, most eloquent writer, world-famous religion scholar who practices Hatha Yoga. Smith has also produced PBS series. The West shied away from this notion. The West likes form, boundaries that distinguish and demarcate.
The trouble is that boundaries also imprison — they restrict and confine. If they express a true infinity. While the West was still thinking, perhaps, of 6, years old universe — India was already envisioning ages and eons and galaxies as numerous as the sands of the Ganges.
The Universe so vast that modern astronomy slips into its folds without a ripple. The Mystic's Journey - India and the Infinite: Carl Sagan in his book Broca's Brain: Reflections on the Romance of Science , remarks: However, in the Bhagavad Gita and in the Vedas , widely divergent numbers of such ages, including an infinity of them, are given; but, more interesting, the duration of the ages between major catastrophes is specified as billions of years.
We simply do not know. The Hindu holy book, the Rig Veda X: Who shall here declare it? Whence was it born, whence came creation? None knows whence creation arose; And whether he has or has not made it; He who surveys it from the lofty skies, Only he knows- or perhaps he knows not.
The theory of animal life and particularly of man was correctly understood by the ancient thinkers. The Brihat Vishnu Purana states that "the aquatic life precedes the monkey life" and that "the monkey life is the precursor of the human life. But evolution, as everything else, was the manifestation of the supreme spirit Atman as is testified by Chandogya Upanishad. Hinduism is the only religion that propounds the idea of life-cycles of the universe.
It suggests that the universe undergoes an infinite number of deaths and rebirths. Hinduism, according to Carl Sagan , " Its cycles run from our ordinary day and night to a day and night of the Brahma, 8. Long before Aryabhata 6th century came up with this awesome achievement, apparently there was a mythological angle to this as well -- it becomes clear when one looks at the following translation of Bhagavad Gita part VIII, lines 16 and 17 ,.
But for the soul that reaches my Kingdom, O son of Kunti, there is no more reincarnation. One day of Brahma is worth a thousand of the ages [yuga] known to humankind; as is each night. Thus each kalpa is worth one day in the life of Brahma, the God of creation.
In other words, the four ages of the mahayuga must be repeated a thousand times to make a "day ot Brahma", a unit of time that is the equivalent of 4. This was later theorized possibly independently by Aryabhata in the 6th century. The cyclic nature of this analysis suggests a universe that is expanding to be followed by contraction This, according to modern physicists is not an impossibility. Astronomy and Mathematics in Ancient India. Count Maurice Maeterlinck was a Belgian writer of poetry, a wide variety of essays.
He won the Nobel Prize for literature. In his book Mountain Paths , says: Mountain Paths - By Maurice Maeterlinck. In Hindu thought, interspersed between linear, time-limited existences lie timeless intervals of non-existence. The scale of this space or time is indeed staggering. It has taken more than two thousand years to come up again with a similar concept.
Hindu culture had this unique vision of the infiniteness of time as well as the infinity of space. When modern astronomy deals with billion of years, Hindu creation concepts deal with trillions of years.
Vedanta upholds the idea that creation is timeless, having no beginning in time. Each creation and dissolution follows in sequence. The whole cosmos exists in two states -- the unmanifested or undifferentiated state and the manifested or differentiated state.
John Bowle , categorically declares that Plato was influenced by Indian ideas. They have just fired their latest volley at that belief, saying there could be a timeless cycle of expansion and contraction.
The theorists acknowledge that their cyclic concept draws upon religious and scientific ideas going back for millennia — echoing the "oscillating universe" model that was in vogue in the s, as well as the Hindu belief that the universe has no beginning or end, but follows a cosmic cycle of creation and dissolution. What about those who developed a sophisticated system of medicine with its mind-body approach known as Ayurveda, detailed anatomical and surgical knowledge of the human body, metallurgical methods of extraction and purification of metals including the so called Damascus blade, chemical techniques to transform compounds, knowledge of various constellations and planetary motions that was good enough to assign motion to the Earth in the fifth century A.
The ancient Hindus used a complex calendar that used the sun and the moon in defining the day, month and year.
While days and months were defined by the moon, the year was defined by the sun. All stars, but not planets, were at rest in this theory. Science was institutionalized among the ancient Hindus. It was considered sacred and as good as their moral codes for society. Scientific activities had important functions that were valued in society.
The role of astronomers to fix the calendar, to set dates of religious festivals, and to predict eclipses or other astronomical events became as important as their moral codes. On the contrary, India attracted scholars from China, the Middle East, and even from the Mediterreanean. This is in contrast to the Greek tradition in which many young Greek scholars undertook arduous journeys to Egypt, Babylon, Persia, and even to India for learning. He is cofounder of Omni magazine and has written: Indian cosmologists, the first to estimate the age of the earth at more than 4 billion years.
Meanwhile Brahma is but one of untold numbers of other gods dreaming their own universes. The ancient Hindus believed that each Brahma day and each Brahma night lasted a kalpa, 4. That the Hindus could conceive of the universe in terms of billions. The Hindus, according to Sir Monier-Williams , were Spinozists more than 2, years before the advent of Spinoza, and Darwinians many centuries before Darwin and Evolutionists many centuries before the doctrine of Evolution was accepted by scientists of the present age.
He served with competence for eighteen years and in officiated as Chief Justice. Publishers Date of Publication: Thus, in Hinduism, science and religion are not opposed fundamentally , as they often seem to be in the West, but are seen as parts of the same great search for truth and enlightenment that inspired the sages of Hinduism.
Fundamental to Hindu concept of time and space is the notion that the external world is a product of the creative play of Maya illusion. To the philosophers of India, however, Relativity is no new discovery, just as the concept of light years is no matter for astonishment to people used to thinking of time in millions of kalpas. Vishwa Hindu Parishad of America. Inc - calendar. The fact that the wise men of India have not been concerned with technological applications of this knowledge arises from the circumstance that technology is but one of innumerable ways of applying it.
It is, indeed, a remarkable circumstance that when Western civilization discovers Relativity it applies it to the manufacture of atom-bombs, whereas Oriental civilization applies it to the development of new states of consciousness. The late scientist, Carl Sagan , asserts that the Dance of Nataraja Tandava signifies the cycle of evolution and destruction of the cosmic universe Big Bang Theory. According to Carl Sagan, astro-physicist, in his book Cosmos says: It is the only religion in which the time scales correspond, to those of modern scientific cosmology.
For modern physicists, then, Shiva's dance is the dance of subatomic matter. Hundreds of years ago, Indian artist created visual images of dancing Shiva's in a beautiful series of bronzes. Today, physicist have used the most advanced technology to portray the pattern of the cosmic dance. Thus, the metaphor of the cosmic dance unifies, ancient religious art and modern physics.
Its cycles run from our ordinary day and night to a day and night of Brahma, 8. Longer than the age of the Earth or the Sun and about half the time since the Big Bang. And there are much longer time scales still. Fritjof Capra - Austrian-born famous theoretical high-energy physicist and ecologist wrote: As in Hindu mythology, it is a continual dance of creation and destruction involving the whole cosmos; the basis of all existence and of all natural phenomenon.
Hundreds of years ago, Indian artists created visual images of dancing Shivas in a beautiful series of bronzes. In our times, physicists have used the most advanced technology to portray the patterns of the cosmic dance. The Tao of Physics: In private life she was known as Mrs.
When people think the sun is setting, he only changes about after reaching the end of the day and makes night below and day to what is on the other side. In truth, he does not see at all. In Hindu cosmology, immutable Brahman, at fixed intervals, draws back into his beginningless, endless Being the whole substance of the living world. Lord Vishnu sleeping on a coiled serpent. Relief in Sanctuary 9, Aihole,. Lord Vishnu is said to rest in the coils of Ananta, the great serpent of Infinity, while he waits for the universe to recreate itself.
Heinrich Zimmer , the great German Indologist, a man of penetrating intellect, the keenest esthetic sensibility observed: The Boar, carrying on his arm the goddess Earth whom he is in the act of rescuing from the depths of the sea, passingly remarks to her: For the Western mind, which believes in single, epoch-making, historical events such as, for instance, the coming of Christ this casual comment of the ageless god has a gently minimizing, annihilating effect.
Professor Arthur Holmes geologist, professor at the University of Durham. He writes regarding the age of the earth in his great book, The Age of Earth as follows: The most remarkable of these occult time-scales is that of the ancient Hindus, whose astonishing concept of the Earth's duration has been traced back to Manusmriti, a sacred book.
When the Hindu calculation of the present age of the earth and the expanding universe could make Professor Holmes so astonished, the precision with which the Hindu calculation regarding the age of the entire Universe was made would make any man spellbound. Hinduism and Scientific Quest - By T. The Upanishads developed this spirit of inquiry, and traces of naturalistic and scientific thought in them are quite significant. The Samkhya system, which has been described as the ruling philosophy of pre-Buddhist India and an orthodox system having its roots in the Upanishads, is essentially rational, anti-theistic, and intellectual.
According to Richard Garbe, it was in Samkhya doctrine that complete independence and freedom of the human mind was exhibited for the first time in history. Samkhya, probably the oldest Indian philosophical system, furnished the background for the Yoga system, and the early Buddhist biography Lalitavistara includes both Samkhya and Yoga in the curriculum of study for the young Buddha.
Ideas of natural selection, atomic polarity and evolution. Like in other ancient civilizations, in Hindu India priests and scientists were often the same persons; the conflict between religion and reason is not the primitive condition but a contingent historical development in post-classical Europe, paralleled to an extent by the stagnation of Muslim culture from the 12th century onwards. The Sankya philosophy of Kapila, in short, is devoted entirely to the systematic, logical, and scientific explanation of the process of cosmic evolution from that primordial Prakriti, or eternal Energy.
There is no ancient philosophy in the world which was not indebted to the sankhya system of Kapila. The idea of evolution which the ancient Greeks and neo-Platonists had can be traced back to the influence of this Sankhya school of thought.
India and World Civilization - By D. Before the sixth century B. If there were but one or two of these cases, they might be set aside as accidental coincidences, but such coincidences are too numerous to be the result of change. And again he writes: The Gnostic ideas in regard to a plurality of heavens and spiritual worlds go back directly to Hindu sources.
Soul and light are one in the Sankhyan system, before they became so in Greece, and when they appear united in Greece it is by means of the thought which is borrowed from India. The famous three qualities of the Sankhyan reappear as the Gnostic 'three classes.
Some sources even credit Pythagoras with having traveled as far as India in search of knowledge, which may explain some of the close parallels between Indian and Pythagorean philosophy and religion.
According to Greek tradition, Pythagoras, Thales, Empedocles, Anaxagoras, Democritus and others undertook journey to the East to study philosophy and science. The crest of the peacock: For more refer to chapter on India and Greece.
Modern people divide the day into 24 hours, the hour - into 60 minutes, the minute - into 60 seconds. Ancient Hindus divided the day in 60 periods, lasting 24 minutes each, and so on and so forth. The shortest time period of ancient Hindus made up one-three-hundred-millionth of a second.
Ancient nuclear blasts and levitating stones of Shivapur - By Alexander Pechersky - pravda. In his commentary on the fourth verse of the hymn 1. O Sun , bow to you, you who travers 2, yojanas in half a minute. Further support for the genuineness of the figure in the ancient book comes from one of the earliest Puranas, the Vayu, conservatively dated to at least 1, years old. The Puranas speak of the creation and destruction of the universe in cycles of 8.
In the realm of physics, remarkable contributions have been made by Indian scientists. Some hint at the theory may be contained in the views of Uddalaka Aruni, preserved in the Chandogya Upanishad.
In order to develop names-and-forms, to discriminate things from one another, or to set them in order, the universal spirit came not in its universal form but as the living, principle, and entered into Fire, Water and Earth.
After separating their component but qualitatively distinct parts dhatus , it made numerous new combinations of them. By propounding the theory of combination and separation of particles, Uddalaka anticipated the atomic theory of Kannada. Kanaada, the founder of the Vaisesika system of philosophy , expounded that the entire matter in this world consists of atoms as many in kind as the various elements. Kanaada's atom would then correspond to the modern atom.
It is due to the operation of this metempirical force that atoms start moving to get together in order that they may be integrated into countless varieties of things. Some Jain thinkers went a step further. They thought that all atoms are the same kind and variety emerged because they entered into different combinations. Kanaada taught that light and heat are variations of the same reality. Vacaspati interpreted light as composed of minute particles emitted by substances and striking the eyes.
This is a clear anticipation of the corpuscular theory of light, which was proposed by Newton but rejected till the discovery of the proton.
Modern physics confirmed that the sun's rays travel in a curved way, but not in a straight line. Our ancestors told that the sun's chariot was drawn by seven horses tied by snakes.
As the movements of the snakes are crooked and curved, so also the sun's ray. The phenomenon is described in a metaphysical poetic line bhujagana mita sapta turaga. The chapter on light says that there are seven colors in the white ray of the sun.
Artharveda says that there are seven types of sun's rays, sapta surayasya rasmayah. The law of gravitation discovered by Brahmagupta anticipated Newton by declaring "all things fall to the earth by law of nature; for it is the nature of the earth to attract and keep things.
For more information refer to the chapter ' Advanced Concepts. Kannada was an expounder of the law of causation and of the atomic theory.
He classified all the objects of creation into nine elements, namely: According to his theory every object of creation is made of atoms, which in turn are joined with each other to form molecules. His statement ushered in the Atomic theory for the first time in the world, early years before John Dalton. Kanaada has also described the dimension and motion of atoms and their chemical reactions with each other.
Colebrooke , has said: Calendar - VHP of America. Umasvati , who lived in the first century A. Commenting on these theories, A. Gravity was considered a peculiar cause of primary descent or falling In the absence of counter-balancing cause, as adhesion, velocity or some act of volition, descent results from this quality.
Thus a coconut is withheld from falling by adhesion of the foot-stalk, but this impediment ceasing on maturity of the fruit, it falls. The penetrative diffusion of liquid was explained by capillary motion and the conduction of water in pipes was said to be due to the pressure of air.
They were familiar with an accurate method of calculating velocity which facilitated the measurement of the relative pitch of musical tones with great precision. They anticipated the Pythagorean law of vibration of stretched strings. The believed that energy was indestructible and thus anticipated the law of conservation and energy.
Heat and light were viewed as only different forms of the same essential substance. One of the scientists succeeded in suggesting a scientific explanation of the phenomenon of ebullition and rarefaction in evaporation. They were familiar with refraction and chemical effects of light rays, causes of translucency, opacity and shadows.
They evolved the formula that the angle of incidence was equal to the angle of reflection. They discovered that a magnet possessed the power of attracting iron. Bhoja , a writer of the eleventh century, therefore, suggested that iron should not be used in the construction of a ship to avoid the danger of being drawn into a magnetic field by magnetic rocks.
They also discovered the mariner's compass centuries before its discovery in Europe. It was called matsya-yantra and consisted of an iron fish which floated in a vessel of oil and pointed at the North. The Indians came closest to modern ideas of atomism, quantum physics, and other current theories. India developed very early, enduring atomist theories of matter.
Possibly Greek atomistic thought was influenced by India, via the Persian civilization. The Rig-Veda, is the first Indian literature to set down ideas resembling universal natural laws. Cosmic law is connected with cosmic light, with gods, and, later, specifically with Brahman.
Sanskrit Vedas from thousands of years before Christ implied that matter could not be created, and that the universe had created itself. Reflecting this, in his Vaiseshika philosophy, Kanada B. C claimed that elements could not be destroyed. Kanada's life is somewhat a mysterious, but his name is said to mean "one who eats particle or grain" likely referring to his theory that basic particles mix together as the building blocks for all matter.
Two, three, four, or more of these elements would combine, just as we conceive of atoms doing. The Greeks would not stumble on this concept for another century. Further progress was made in knowing the qualities and functions of earth, water, heat, sound etc. Especially in sound the ancient Indians reached great heights very early.
The octave was divided into 22 shrutis quarter-tones and their proportions were measured with great accuracy. Their love of accuracy and precision is testified by their tables of weights, and measures. The measurement of time was, for example, based on the unit of time taken by a wink nimisha. J R Oppenheimer and Atom bomb in modern times. Only seven years after the first successful atom bomb blast in New Mexico, Dr. Oppenheimer of the Manhattan Project , who was familiar with ancient Sanskrit literature, was giving a lecture at Rochester University.
During the question and answer period a student asked a question to which Oppenheimer gave a strangely qualified answer: Was the bomb exploded at Alamogordo during the Manhattan Project the first one to be detonated? In modern times, of course. An incandescent column of smoke and flame As bright as ten thousand Suns Rose in all its splendor The Entire race of the Vrishnis and the Andhakas Their hair and nails fell out; Pottery broke without apparent cause, And the birds turned white.
After a few hours all foodstuffs were infected To escape from this fire. The soldiers threw themselves in streams to wash themselves and their equipment One is reminded of the yet unknown final effect of a super-bomb when we read in the Ramayana of a projectile: And on it sits Death Both laboratories have a statue of the Hindu god Shiva, which depicts this God performing a dance called the Nataraja to destroy a weary universe in preparation to restart creation.
Teller explained nuclear fusion in the following words: Compression and nuclear reaction occurs in a tiny dot at the middle of the sphere. Apparatus practically filling a whole building feeds the twenty pipes, or the arms of the god Shiva.
According to Hindu Creed, Shiva had three eyes; two for seeing, and one usually kept closed to emit annihilating radiation. The Hindus obviously know about lasers. Mathematics - The Language of Science. In mental abstraction and concentration of thought the Hindus are proverbially happy. Apart from direct testimony on the point, the literature of the Hindus furnishes unmistakable evidence to prove that the ancient Hindus possessed astonishing power of memory and concentration of thought.
The science of mathematics, the most abstract of all sciences, must have an irresistible fascination for the minds of the Hindus. The great German critic, Schlegel wrote in his History of Literature , p. Mathematics is the science to which Indians have contributed the most.
Our decimal system, place notation, numbers 1 through 9, and the ubiquitous 0, are all major Indian contributions to world science. Without them, our modern world of computer sciences, earth-launched satellites, microchips, and artificial intelligence would all have been impossible. The earliest recorded Indian mathematics was found along the banks of the Indus. Archaeologists have uncovered several scales, instruments, and other measuring devices.
The Harappans employed a variety of plumb bobs that reveal a system of weights If we assign that a value of 1, other weights scale in at. These weights have been found in sites that span a five-thousand-year period, with little change in size.
The debt owed by the West to other civilizations, and to India in particular, go back to the earliest epoch of the "Western" scientific tradition, the age of the classical Greeks, and continued up until the dawn of the modern era, the renaissance, when Europe was awakening from its dark ages.
Dr Gray goes on to list some of the most important developments in the history of mathematics that took place in India, summarizing the contributions of luminaries such as Aryabhatta, Brahmagupta, Mahavira, Bhaskara and Maadhava. He concludes by asserting that " the role played by India in the development of the scientific revolution in Europe is no mere footnote, easily and inconsequentially swept under the rug of Eurocentric bias. To do so is to distort history, and to deny India one of its greatest contributions to world civilization.
Pingala 3rd C AD , author of Chandasutra explored the relationship between combinatorics and musical theory anticipating Mersenne author of a classic on musical theory. His contributions to mathematics include: The formation of a matrix. Invention of the binary number system while he was forming a matrix for musical purposes. The concept of a binary code, similar to Morse code. First use of the Fibonacci sequence. First use of Pascal's triangle , which he refers to as Meru-prastaara.
His work, along with Panini's work, was foundational to the development of computing. Science and Mathematics in India. Refer to chapter on Hindu Music and Indian Mathematics.
Fascination with numbers has been an abiding characteristic of Indian civilization, not only large numbers but very small ones as well. Operations with zero attracted the interest of both Bhaskaracharya b. In Ramayana , the great Indian epic, there is a description of two armies facing, each other. Hundred hundred thousands make a Crore Hundred thousand crores make a Sankhu Hundred thousand sankhus make a Maha-sankhu Hundred thousand maha-sankhus make a Vriundam Hundred thousand vriundam make a Maha-vriundam Hundred thousand maha-vriundams make a Padmam Hundred thousand padmams make a Maha-padmam Hundred thousand maha-padmams make a Kharvam Hundred thousand kharvams make a Maha-kharvam Hundred thousand maha-kharvams make a Samudra Hundred thousand samudras make a Maha-ougham.
The importance of number names in the evolution of the decimal place value notation in India cannot be exaggerated. The word-numeral system was the logical outcome of proceeding by multiples of ten. Thus, in an early system, 60, is denoted by the Sanskrit word sastim 60 , shsara thousand , sapta seven satani hundred , navatim nine ten times and nava nine. Such a system presupposes a scientifically based vocabulary of number names in which the principles of addition, subtraction and multiplication are used.
To understand why word numerals persisted in India, even after the Indian numerals became widespread, it is necessary to recognize the importance of the oral mode of preserving and disseminating knowledge. An important characteristic of written texts in India from times immemorial was the sutra style of writing, which presented information in a cryptic form, leaving out details and rationale to be filled in by teachers and commentators.
In short pithy sentences, often expressed in verse, the sutras enabled the reader to memorize the content easily. In the Vedic age, India was ahead of the rest in mathematics and astronomy. The first decimal system and the oldest names of "astronomical" numbers such as quadrillions and quintillions. Arabs still call the decimal system rakmu 'l-Hind , from Hind, "India. Highly intellectual and given to abstract thinking as they were, one would expect the ancient Indians to excel in mathematics.
Ancient Indians developed a system of mathematics far superior, to that of the Greeks. Ancient Vedic mathematicians devised sutras for solving mathematical problems with apparent ease. Among the most vital parts of our heritage are the numerals and the decimal system. Hindsaa numerals in Arabic means from India. Jawaharlal Nehru has said, " The clumsy method of using a counting frame and the use of Roman and such like numerals had long retarded progress when the ten Indian numerals, including the zero sign, liberated the human mind from these restrictions and threw a flood of light on the behavior of numbers.
Vedanga Jyotisa says "As are the crests on the heads of peacocks, as are the gems on the hoods of the snakes so is the ganita Mathematics at the top of the sciences known as Vedanga. In this period, ganita is a comprehensive term which included arithmetic, algebra and astronomy. Geometry was also investigated but was placed in a different general science known as kalpa. Indians were the first to use the decimal either to increase or decrease the value of the figure which was presided by Laplace, the great French mathematician.
Indians were the first to use the 'zero' as a symbol in mathematics. They invented the present numerical system. India teachers taught arithmetic and algebra, Vedic Sulva Sutras were earlier than the Alexandrian geometry of Hero. The earliest available work was Bakshali Manuscript. The approximate value of an 'irrational number' i. In the geometry of the circle, "Arybhatta I" gave a value for pi tyajya which is correct to the four decimal places in a sloka Sankara Varman's treatise on astronomy, Sadratnamala theorems and their deductions: John Pell discovered this in the 17th century.
Indians discovered it a 1, years earlier. The most fundamental contribution of ancient India in mathematics is the invention of decimal system of enumeration, including the invention of zero. The decimal system uses nine digits 1 to 9 and the symbol zero for nothing to denote all natural numbers by assigning a place value to the digits. The Arabs carried this system to Africa and Europe.
The Vedas and Valmiki Ramayana used this system, though the exact dates of these works are not known. MohanjoDaro and Harappa excavations which may be around B. Aryans came years later, around B. Being very religious people, they were deeply interested in planetary positions to calculate auspicious times, and they developed astronomy and mathematics towards this end.
They identified various nakshatras constellations and named the months after them. They could count up to 10 12 , while the Greeks could count up to 10 4 and Romans up to 10 8.
Values of irrational numbers were also known to them to a high degree of approximation. Pythagoras Theorem can be also traced to the Aryan's Sulbasutras.
These Sutras, estimated to be between B. Said the great and magnanimous Pierre Simon de Laplace , French mathematician, philosopher, and astronomer, a contemporary of Napoleon: But its very simplicity, the great ease which it has lent to all computations, puts our arithmetic in the first rank of useful inventions, and we shall appreciate the grandeur of this achievement the more when we remember that it escaped the genius of Archimedes and Appollnius, two of the greatest men produced by antiquity.
Brilliant as it was, this invention was no accident. In the Western world, the cumbersome Roman numeral system posed as a major obstacle, and in China the pictorial script posed as a hindrance.
But in India, almost everything was in place to favor such a development. There was already a long and established history in the use of decimal numbers, and philosophical and cosmological constructs encouraged a creative and expansive approach to number theory. Panini's studies in linguistic theory and formal language and the powerful role of symbolism and representational abstraction in art and architecture may have also provided an impetus, as might have the rationalist doctrines and the exacting epistemology of the Nyaya Sutras, and the innovative abstractions of the Syadavada and Buddhist schools of learning.
Panini and Formal Scientific Notation. A particularly important development in the history of Indian science that was to have a profound impact on all mathematical treatises that followed was the pioneering work by Panini 6th C BC in the field of Sanskrit grammar and linguistics. Besides expounding a comprehensive and scientific theory of phonetics, phonology and morphology, Panini provided formal production rules and definitions describing Sanskrit grammar in his treatise called Asthadhyayi.
Basic elements such as vowels and consonants, parts of speech such as nouns and verbs were placed in classes. The construction of compound words and sentences was elaborated through ordered rules operating on underlying structures in a manner similar to formal language theory.
Today, Panini's constructions can also be seen as comparable to modern definitions of a mathematical function. G G Joseph, in The crest of the peacock argues that the algebraic nature of Indian mathematics arises as a consequence of the structure of the Sanskrit language.
Ingerman in his paper titled Panini-Backus form finds Panini's notation to be equivalent in its power to that of Backus - inventor of the Backus Naur Form used to describe the syntax of modern computer languages. Thus Panini's work provided an example of a scientific notational model that could have propelled later mathematicians to use abstract notations in characterizing algebraic equations and presenting algebraic theorems and results in a scientific format.
In his book, Pi in the Sky: Counting, thinking and Being he has observed: It has spread and been adopted almost universally, far more extensively, even than the letters of the Phoenician alphabet which we now employ. Pi in the Sky: Counting, thinking and Being - by John D Barrow p. The decimal system was known to Aryabhatta and Brahmagupta long before its appearance in the writings of the Arabs and the Syrians; it was adopted by China from Buddhist missionaries; and Muhammad Ibn Musa al-Khwarazni, the greatest mathematician of his age ca A.
Zero, this most modest and most valuable of all numerals is one of the subtle gifts of India to mankind. The earliest use of the zero symbol, so far discovered, is in one of the scriptural books dated about B. The zero, called shunya or nothing, was originally a dot and later it became a small circle. It was considered as a number like any other. This giving to airy nothing, not merely a local habitation and a name, a picture, a symbol but helpful power, is the characteristic of the Hindu race whence it sprang.
It is like coining the Nirvana into dynamos. No single mathematical creation has been more potent for the general on-go of intelligence and power. It's all, as the Hindus knew, a play between the void and the absolute. Yet another modern mathematician has grown eloquent over this historic event. Dantzig in his 'Number' writes: But what was the net achievement in the field of reckoning, the earliest art practiced by man?
An inflexible numeration so crude as to make progress well nigh impossible, and a calculating device so limited in scope that even elementary calculations called for the services of an expert When viewed in this light the achievements of the unknown Hindu, who sometime in the first centuries of our era discovered the principle of position, assumes the importance of a world event. Dantzig is puzzled at the fact that the great mathematicians of Greece did not stumble on this discovery.
But if so, how is it that the nation that gave us geometry and carried this science so far did not create a rudimentary algebra? An important Mathematics book prescribed by the New York State Education Department acknowledges the debt in the following words: It was developed by an unknown Indian more than years ago.
Without it most of the great discoveries and inventions including computers of western civilization would never have come about. This invention was the decimal system of numerals - nine digits and a zero. The science and technology of today including the computers could not have developed if we had only the Roman system of numerals. That system is too clumsy to be used as a scientific too. Today we take the decimal system for granted. We don't think about how brilliant the man who invented zero must have been.
Yet without zero we could not assign a place value to the digits. That ancient mathematician, whoever, he was, deserves much honor. Very early in their history they developed a simple system of geometry. This system was used to plan outdoor sites for Indian religious ceremonies. Indians also added to our knowledge of even more complicated branches of mathematics such as trigonometry and calculus.
They studied these branches of mathematics in order to apply them to astronomy. For more refer to The Infinitesimal Calculus: He holds an M. The Biography of a Dangerous Idea says: For Indians, the void of Sunya was the very font of all potential; nothingness was liberation. No surprise then that it is from this sophisticated culture that we inherit the mathematical analog of nothing, zero. Like Sunya, zero is a kind of place holder, a symbol signifying a pregnant space where any other number might potentially reside.
The Biography of a Dangerous Idea: It's weird, it's counterintuitive and the Greeks hated it. Why did the Church reject the use of zero? Lancelot Thomas Hogben English zoologist and geneticist, has written: The concept of Debits and negative numbers originated in India, and why were they not accepted until recently?
It was much more than years ago. It wasn't accepted elsewhere because the Church did not think it possible. Then, the problem would be one of explaining how the so called 'Pascal's triangle' continues to bear his name, or how the British reference books like the Encyclopedia Britannica persisted till well into the 20th century in crediting Newton with the discovery of the binomial theorem.
India Through The Ages: The Hindus knew mathematics much early. Aa dvabhyam haribhyamindryahya chaturbhirashadabhi rhuya manah ashtabhirdashabhih. Also in Vajasaneya Samhita Eka cha dasha cha dasha cha shatam cha shatam cha sahasram cha sahasram cha yutam cha ayutam cha niyutam cha niyutam cha prayutam cha.
In Mahabharata there are references to addition and subtraction. Adhikam more , Unam less , Shesham remaining , multiplication and division are indicated. In Rig Veda It seems that gambling was very common in the Vedic days, and it involved dices and numbers. According to Yajur Veda, Vajasneya Samhita 4. In another kind of gambling, the dice Aksha used four names of the four Ages namely Krita, Treta, Dvapar and Kali and they were numbered 4, 3, 2 and 1. The numbers from one to one thousand billion are found in the Vajasneya Samhita and also in Taitteriya, Maitrayani and Kathaka Samhitas.
In Sama Veda , in the 25 th Brahmana, there is a reference to how much fees dakshina should be given to a priest in sacrifice Yajna. It may be at least 12 Krishnala milligrams of gold, and doubling the figure, it can go up to 3,93, The system they adopt in giving page numbers in old manuscripts in Malabar and in Andhra was to have 34 digits of consonants from Ka to La and then to have the next 34 digits by adding vowels Kaa to Laa. Burma also had the same system for pagination.
There is a beautiful definition of the infinite in the following line of a Vedic mantra, which forms the introductory verse to the Isa Upanishad: Take the whole Infinite Brahman from the whole, and the whole still remains. This is almost like the mathematician, Cantor's definition of infinity.
The very names of the numerals are of Sanskrit origin. Thus, though we call the latter science by an Arabic name, it is a gift we owe to India. The linkage of God with the infinite is found in the Bhagavad Gita , by tradition spoken by Lord Krishna himself, we read: It is equated with the Supreme Brahman — infinitely powerful and so infinitely free.
It is bigger than any quantity that can be imagined; it is bigger than any finite number. Infinity is one of the fundamental axioms upon which contemporary mathematics is based. Sanskrit grammar and interpretation in ancient India were closely linked to the handling of high value numbers.
Studies relating to poetry and metrics initiated sastragnaas or scientists to both arithmetic and grammar. Grammarians were just as competent at calculations as professional mathematicians. Indian sastragnaas or scientists, philosophers, astronomers and cosmographers — in order to develop their arithmetical, metaphysical and cosmological speculations concerning ever higher numbers — became at once mathematicians, grammarians and poets.
They gave their spoken counting system a truly mathematical structure which had the potential to lead directly to the discovery of the decimal place-value system. In Indian mysticism, the concept of infinity and zero are very closely linked. To mathematically explain this, we have to assume that the first poornam represents infinity and the second, zero. In Sanskrit, poornam means both full and zero.
Indian mathematicians knew perfectly well how to distinguish between these two notions which are mutually contradictory and which are the inverse of each other. They knew that division by zero gave them infinity. The concept of infinity has always remained an enigma. The Taittiriya Upanishad says: In Indian cosmology, Ananta refers to the Adisesha or the great serpent on which Lord Vishnu reclines, taking His yoga nidra or anantasayanam.
The symbol for infinity is called the leminiscate. English mathematician John Wallis introduced this symbol for the first time in Hindu mythological iconography contains a similar symbol representing the same idea. The symbol is that of Ananta, the great Adisesha of infinity and eternity, which is always represented, coiled up in a horizontal figure of 8 just like the leminiscate. Negative numbers had been rejected as solutions of problems in early times.
They were eventually admitted in Hindu practical mathematics through problems involving money transactions, since the idea of receiving and owing money was a simple and obvious one — a negative number could be interpreted as a debt. Objection to negative numbers continued up to the early 19th century. Negative numbers are the mirror image of positive numbers. The invention of Cartesian geometry brought the X, Y co-ordinates and numbers came to be represented on a graph.
Today, the series of negative natural numbers go up to infinity. Raju - holds a Ph. He taught mathematics for several years before playing a lead role in the C-DAC team which built Param: He has has revealed how calculus, an Indian invention, was picked up by the Jesuit priests from Kerala in the second half of the 16th century and taken to Europe. This is how the Westerners got their calculus. Overtime, people forgot this link and the Europeans began to claim calculus as their own invention.
This myth still persists despite calculus texts existing in India since thousands of years. It took them about years to fully comprehend its working. Why were these texts imported into Europe? These texts, and the accompanying precise sine values computed using the series expansions, were useful for the science that was at that time most critical to Europe: How were these Indian texts imported into Europe?
Jesuit records show that they sought out these texts as inputs to the Gregorian calendar reform. The Jesuits were equipped with the knowledge of local languages as well as mathematics and astronomy that were required to understand these Indian texts. How the mathematics given in these Indian ancient texts subsequently diffused into Europe e. No one else, however, has so far studied the connection of these Indian developments to European mathematics.
Columbus and Vasco da Gama used dead reckoning and were ignorant of celestial navigation. Navigation, however, was both strategically and economically the key to the prosperity of Europe of that time. C K Raju - indianrealist. Her Right to Freedom - Rev. French historian of Mathematics and author of the book, The Universal History of Numbers has written: So much so that Indian culture regarded the science of numbers as the noblest of its arts A thousand years ahead of Europeans, Indian savants knew that the zero and infinity were mutually inverse notions.
Claiming India to be the true birthplace of our numerals, Ifrah salutes the Indian researchers saying that the " Of particular interest is the work by Indian mathematician Bhaskaracharya known as Bhaskara BC where he makes a reference to zero and the place-value system were invented by the god Brahma. The early passion which Indian civilization had for high numbers was a significant factor contributing to the discovery of the place-value system, and not only offered the Indians the incentive to go beyond the "calculable" physical world, but also led to an understanding much earlier than in our civilization of the notion of mathematical infinity itself.
Sanskrit notation had an excellent conceptual quality. It was easy to use and moreover it facilitated the conception of the highest imaginable numbers. This is why it was so well suited to the most exuberant numerical or arithmetical-cosmogonic speculations of Indian culture. We owe the discovery of modern numeration and the elaboration of the very foundations of written calculations to India alone. The discoveries of these men doubtless required much time and imagination, and above all a great ability for abstract thinking.
These major discoveries took place within an environment which was at once mystical, philosophical, religious, cosmological, mythological and metaphysical. In short, Indian science was born out of a mystical and religious culture and the etymology of the Sanskrit words used to describe numbers and the science of numbers bears witness to this fact. In fact, this language is extremely elaborate , almost artificial, and is capable of describing multiple levels of meditation, states of consciousness and psychic, spiritual and even intellectual processes.
As for vocabulary, its richness is considerable and highly diversified. Sanskrit has for centuries lent itself admirably to the diverse rules of prosody and versification.
Thus we can see why poetry has played such a preponderant role in all of Indian culture and Sanskrit literature. Sometimes in certain remote places and mountainous terrain cave temples existed. It was only later that temples were made out of stones and bricks. In fact the earliest structures that indicate idol worship can be traced back to 4th or the 5th century AD. There was significant growth and rise of the Hindu temples between the 6 th and 16 th century and a great part of it can be contributed to the various dynasties that ruled India during that period.
They considered that building temples was an extremely pious act and hence kings, wealthy men were ready to put their hands down and help in the building of the temples for its growth and perform various religious activities. The pagoda style temple has several masterpieces of 5th and 12th century Nepalese art. According to legends Changu Narayan temple existed as early as A. In the grounds there is a stone pillar inscription of great importance recording the military exploits of King Man Deva who reigned from A.
The first epigraphic evidence of Nepalese history found in the temple premises during the reign of the Licchavi King Mandeva dating back to A. It is the earliest inscription known in Nepal. The temple was restored during the lifetime of Ganga Rani, consort of Siva Simha Malla who reigned from to Bhubaneswar the capital of Orissa is a city of temples, several of which are important from an architectural standpoint.
The Lingaraj temple — the largest of these is about a thousand years old. Bhubaneswar, Konarak and Puri constitute the Golden triangle of Orissa, visited in large numbers by pilgrims and tourists. This feet high grand temple is dedicated to Lord Shiva and is considered to be the finest example of purely Hindu style of temple architecture. The Lingaraj Temple has a jagamohana, natamandir, bhogamandapa and is surrounded by a massive 7 feet thick wall.
The sculptures in this temple date back to AD to the Somavamsis. Outer square x meters surrounded by a 1 meter boundary wall. All the three squares have gates to connect the other squares. The outer square do not have temples. Inside the middle square there are Perwara temples which are arranged in 4 rows of temples. The first row consists of 68 temples, followed by the second row 60 temples , the third row 52 temples and the fourth row 44 temples. The arrangement of temples is in such a way that shorter temples lies in the outside and getting higher toward the center.
Inside the center square are sixteen small and big temples. The Brihadeeswarar temple combines the best in the tradition of temple building — architecture, sculpture, painting and other allied arts.
It is composed of many interconnected structures such as the Nandi pavilion, a pillared portico and a large hall. Its Vimana the roof like structure that towers above the sanctum sanctorum or main shrine is 66 metres high.
The Kailash temple in Ellora was built as a dedication to Lord Shiva, the destroyer. It was carved in perfect proportion and alignment to its adjacent structures, which include columns, flying bridges, stone arches, and statues and buildings — all made out of a single piece of rock. Situated on the banks of the Yagachi River, the Chennakesava temple was an early masterpiece of the Hoysala Period.
It was built by the Vijaynagara ruler to commemorate their victory over the Cholas and is solely dedicated to Vishnu as most of the figural carvings depict aspects of Vishnu, particularly the incarnations and the God seated with Lakshmi. The temple is quite small, and hence only 10 people are allowed in at a time. Located in the temple town of India, Kumbakonnam, the Adi Kumbeswarar temple dates back to the Vijaynagara period.
Adi Kumbeswarar is the presiding deity of the temple and the shrine is located in the centre.
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So much so that Indian culture regarded the science of numbers as the noblest of its arts A 10 th century traveler Masaudi, in his Arabic work Meadows of Gold, records that a Hindu Raja called Pandit who counted nine digits by memory. Kanaada taught that light and heat are variations of the same reality.
Today, Panini's constructions can also be seen as comparable to modern definitions of a mathematical function. Relief in Sanctuary 9, Aihole,.
Bowing low before the onslaught of armies, and elements, India has survived every invasion, every natural disaster, every mortal disease and epidemic, the double helix of her genetic code hindu dating sites its unmistakable imprint down five millennia to no less than a billion modern bearers. These major discoveries took place within an environment which was at once mystical, philosophical, religious, cosmological, mythological and metaphysical. That ancient mathematician, whoever, he was, deserves much honor. Smith hindu dating sites also produced PBS series. Panini and Formal Scientific Notation.
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