Highest Sageness -4























The Mahakumbh: Its Sacred Significance
By Pankaj Dixit
http://www.timesofindia.com/today/20edit5.htm

WATER is the basis of all life on earth. Of the Panchmahabhut or the five natural elements, water is considered to be the key to life. Human beings feel a close affinity to it, since three-fourths of the human body is constituted of water. In this respect, our body is like a microcosm, as the surface of the earth (the macrocosm) is constituted similarly, being three-fourths, water.
The confluence of three rivers Ganga, Yamuna and Saraswati at Prayag stands for the meeting of Ida, Pingala and Sushumna Nadis at Muladhar Chakra known as Yukta Triveni. Kumbha symbolises the arousing of six chakras to reach Ajna Chakra where these three nadis meet again to form the Mukta (Liberation) Triveni for yogis.
The Ganga always flows and rushes very fast to the sound of Gama-Gam (meaning go-go) while the Yamuna moves slowly with a placid flow to the sound of Yam-Yam (meaning control-control). Likewise whether one acts fast in life or acts after deliberate thinking, it must be decided by his knowledge and temperament. And both these aspects should be supported by the invisible Saraswati, the faculty of Jnan (knowledge). The meeting of these three rivers in the spiritual realm represents the three gunas or qualities of the native, i.e. Sattvic or subtle represented by Saraswati; Rajasic or the vibrant Ganga; and Tamasic or the dark Yamuna. These three rivers also signify the three saktis, Mahalakshmi, Mahakali and Mahasaraswati; the three sacred fires of sacrifice; the three Gods Brahma, Vishnu and Mahesh; and the three notes of music, Sa for Saraswati; Re for Yamuna; and Ga for Ganga.
Further deep in the spiritual sphere, these three rivers represent the three phases of time i.e. present, past and future; the triangle or minimum space enclosed in time; Nad, Bindu and Kala; and the three humours, vata, pitta and kapha. The Triveni also denotes the three basic philosophies of the Gita, i.e. Jnan Yoga, Karma Yoga and Bhakti Yoga.
The Kumbha occurs in a cycle of every 12 years - the most sacred or auspicious time is calculated on the basis of a specific planetary configuration, considering its cosmobiological effect on the human body and mind. Various astronomical conjugations during Kumbha represent various stages of the solar cycle which has a direct influence on human beings and the biosphere. The ritual bath or snan on specific days i.e. full moon, new moon and Basant Panchami have been specifically prescribed on the basis of the bio-effects of lunar phases. The imposed electromagnetic fields on water are transmitted into the human beings taking bath in the Holy Prayag giving them great health benefits. The number 12 here signifies time or Kal as there are 12 adityas, 12 zodiac signs, 12 months, and 12 Jyotirlingas (self-emergent sivalingas). The entire world exists in time, moves in time and space, and is controlled by time. According to Atharvaveda, Kumbh is the representation of space situated in Kal supervising all of us. Spiritually the holding of Kumbha at an interval of 12 years symbolises the need for purifying the body by sublimating the inherent vices of the 12 sense organs, i.e. Panchkarmendriyas (five organs of action), Panchjnanedriyas (five organs of perception, the mind and the intellect - and thereby to arouse the six psychic centres or chakras separated from each other at a distance of 12 angulas for attaining the Amrit Kumbha or pitcher of nectar.
There is another mystical explanation of the Kumbha. The human head and neck form an inverted pitcher or Kumbha from where Amrit or nectar flows downwards into the body. The two eyes represent the sun and moon gods, the nostrils represent Ganga and Jamuna, the tongue is Vani or Saraswati and it spans 12 angulas of space.
Astrologically during Kumbha the three grahas, Jupiter, Sun and Moon, play a prominent role in the two Zodiac signs, Taurus and Capricorn respectively. The presence of Sun in Capricorn or Makara signifies the Swadhishtan Chakra, the centre of procreation representing the water element. Makara also signifies the Kama as Kamdev, popularly knows as Makaradhwaj. Accordingly Madam Blavatsky in her famous book Sacred Doctrine records that Capricorn is universal intelligence, which is transformed into human intelligence through water. It is therefore that one of the famous Shahi Snans occurs on Basant Panchami, the day of Kamdev. Likewise Jupiter's or Jiva's (life force) presence in Taurus signifies the creative power of universe, Shiva Shakti or the Male and female forces.
Trees with spiritual attributes
Pran Nevile
http://www.tribuneindia.com/20011021/spectrum/main5.htm

From time immemorial, certain trees and plants in India have been invested with divine attributes. Hindus were taught to worship and revere trees and plants in the belief that it would influence their own personal well-being. Evergreen trees were regarded as symbols of eternal life and to cut them down was to invite the wrath of the gods. Groves in forests were looked upon as habitations of the gods.
The banyan tree occupies the pride of place amongst the sacred trees of India. It has aerial roots that grow down into the soil forming additional trunks. It is, therefore, called bahupada, the one with several feet. It symbolizes a long life and also represents the divine creator, Brahma. It is invariably planted in front of temples. The numerous stems of the banyan tree are even regarded as the home of gods and spirits. It was under a banyan tree that the Hindu sages sat in a trance seeking enlightenment and it was here that they held discourses and conducted holy rituals. Some banyan trees reached a height of over 100 feet and more than 1000 feet in circumference. No wonder, it is stated that 10,000 men could be covered by a single tree. We come across a mention of the banyan tree in many travelers’ accounts.
Bishop Heber (1825) was so impressed by the sight of this tree that he exclaimed: "What a noble place of worship". Travelers’ tales even inspired the great English poet Milton to give description of the banyan tree in Paradise Lost in the following lines.
The fig-tree at this day to Indians known  
In Malabar or Deccan, spreads her arms,  
Branching so broad and long, that on the ground  
The bended twigs take root, and daughters grow  
About the mother tree, a pillar’d shade,  
High over-arched and echoing walks between."

In Hindu mythology, the tree is called Kalpavriksha, the tree that provides fulfillment of wishes and other material gains. The worship of the tree is also represented in a Buddhist sculpture with its long hanging roots dropping gold pieces in vessels placed below.
Another great tree of India is the peepul to be found all over the country. 
Known for its antiquity, it finds a mention in many Hindu scriptures as a sacred tree whose worship is regarded as homage to the Trinity — Brahma, Vishnu and Shiva.  
The tree is treated as a Brahmin and special offerings made to it in the morning and lamps lit there in the evening. The tree is also associated with the old vedic ritual of lighting a sacrificial fire with a twig of the peepul tree.
Even now, village women may be seen worshipping the tree by watering its roots and placing some milk and eats for the serpents and insects residing there. Every village has its special peepul tree and the village elders hold their councils beneath its hallowed foliage. The most famous of these trees is the sacred peepul at Gaya under which Buddha sat when he attained Enlightenment. Since then the peepul tree is also called the Bo or the Bodhi tree and Prince Sidharath came to be known as Buddha. It is also believed to be a symbol of fertility and women worship it for progeny. The tree waves its leaves in an uncanny way and their trembling with a fluttering sound is attributed to spirits agitating in each leaf. This puts fear of the gods into the hearts of common folk.
The banyan and the peepul trees are symbols of the male and ceremoniously married to those of the female category. James Forbes, in his Oriental Memoirs (1813), mentions about a wedded banyan tree or the Palmyra and Burr tree united, that he saw at Salsette.
The bilva or oak-apple and the Asoka trees are associated with different deities. The Asoka tree is sacred to Kama, the god of love, and according to folklore, its buds will open up in full bloom when the foot of a young beautiful maiden touches its roots. The bilva with its three leaves resembling the trishul, or the trident held by Lord Shiva finds mention in Hindu mythology. Its fruit is a blood purifier.
Besides the sacred trees, there are some sacred plants, notably the tulsi plant which is found everywhere in sandy and fallow lands. It is an ancient variety of the basil. tulsi is considered to be the wife of Vishnu and worshipped by the Hindus. In homes, tulsi is grown in pots and womenfolk offer daily puja and pour an oblation of Ganga water. A mere touch of the plant is believed to purify the person and giving a twig of tulsi to anyone is considered as a protection from dangers and difficulties. Tulsi leaves are also put in the mouth of a dying man for the salvation of the soul. Among other virtues of the tulsi are its medicinal properties. Its leaves have a pleasing aroma and act as a cough elixir and cordial. Leaves are also eaten to help digestion and prevent other maladies like cold and chill. No wonder, the Hindus deified the plant for its numerous qualities.
Darbha or kusha is a sacred grass essential in all sacrifices. This plant is found in damp marshy ground. It is rough to the touch and pointed at the top. According to an old legend, it was produced at the time of the churning of the ocean by the gods and demons. It is also said that the gods while drinking amrita or the nectar of immortality shed some drops on this grass which thus became sacred.
There is a mention of it in the Hindu scriptures and the epics. The Kusha grass is therefore worshipped by Brahmins and used in various religious ceremonies as it is believed to have the virtue of purifying everything. 

Patent Your Heritage 

Globalization has made it easier for companies in wealthy countries to take advantage of poor countries by filing patents for crops, medicines and chemicals that traditional cultures have been cultivating and using for centuries. This year, the poor countries have figured out a way to fight back: they are creating digital libraries for their ancient cultural knowledge.  
India, probably the largest victim, is cataloging its traditional knowledge on a protected Web site and on DVD's it will send to patent examiners worldwide. The next time someone proposes patenting the use of a traditional Indian herb or spice for a particular medicinal purpose, examiners will be able to see if Indian Ayurvedic medicine described the process centuries ago.
In June, the United Nations' World Intellectual Property Organization (WIPO) unveiled a Web site with parts of the Indian digital library, as well as a database of patents based on traditional medicine granted in Beijing to Chinese inventors. WIPO is urging other countries to catalog their cultural and biological patrimony, and is asking patent examiners to search these databases when considering relevant applications.
India began the project after it had to spend almost four years fighting a basmati rice patent granted in America to a company called RiceTec, and two years to get another American patent, on the healing properties of turmeric, revoked. ''There are 2,000 or 3,000 cases of misappropriation of our traditional knowledge in Washington alone,'' says V. K. Gupta, the driving force behind India's digital database. ''It would cost us a billion dollars to invalidate these wrong patents in court. We needed defensive protection.''
The United States patent office, not surprisingly, sees its mission as encouraging innovation through the generous granting of patents, and those who disagree can slug it out before a judge. Woefully overstretched examiners have only a few hours to see whether an idea is new, and they cannot reject a patent application on common sense alone. ''Patent offices have terrible problems knowing who's doing what where, especially outside their home countries,'' says Greg Aharonian, a San Francisco patent consultant. And traditional knowledge -- which often exists only orally -- is especially hard to pin down.
Ayurvedic medicine is written -- in verse. The Indian database translates the verses from Sanskrit to modern languages, updating the names of plants and diseases and grouping them into standard patent classifications. Digital libraries for other Indian traditional medicines are in the works. 
(source: Patent Your Heritagehttp://www.nytimes.com/2002/12/15/magazine/15PATE.html).
The ecological traditions of India, especially Kerala face serious threat in the form of religious conversion, according to noted environmental scientists, technologists and ecologists. This was revealed here on Wednesday by none other than Dr Nanditha Krishna, Chairperson, C P Ramaswami Aiyar Foundation.

Delivering the introductory speech of the seminar on “ Conservation of Ecological Traditions and Sacred Sites of India”, with special emphasis on Kerala, Dr Nanditha pointed out that religious conversion happening all over the country at an alarming rate has destroyed forests and holy groves (popularly known as Kaavus in Kerala). “The proselityzers and the newly converts do not have any emotional attachments with the holy groves. In most of the cases, the newly converted people see to it that the holy groves are destroyed at the earliest,” Dr Nanditha said. She pointed out with statistics that many dense forests and groves in north east India became the main target of the Christian missionaries engaged in the harvesting of souls in the areas.

Dr Nanditha said that the Kaavus, especially the sarppakaavus ( fanily temples where the snakes were worshipped) were destroyed indiscriminately as a result of urbanization and religious conversion. “This is causing havoc all over the country. The team of scientists from the CRP Foundation found to their dismay that Kerala, popularly known as God’s Own Country, is fast emerging as a drought stricken state. The new generation among the Hindus show scant regard to the traditional Kaavus and groves,” Dr Nanditha said.

Substantiating the findings of the CRP Foundation team were the revelations by Shri M Amrithalingam, a well known botanist and ecologist. Shri Amrithalingam, with more than two decades of research experience in the ecological system of south India told the seminar that unless and other wise something is done to arrest the destruction of the holy groves, the country is in for serious crises, like drought and shortage of water.

“While we had small sized forests attached to the Hindu tharavadus in Kerala, urbanization and religious conversion have denuded them. There were many scientific reasons for worshipping forests, animals and groves,” Amrithalingam explained.

Shri T Madhava Menon, formerly of the Indian Administrative Service spoke on the Tribal Communities and Heritages of Kerala. Dr C R Rajagopalan, Dr S Rajasekharan, Shri E Unnikrishnan, Dr K P Thrivikramji and Dr Ashalatha Thampuran presented papers on the various aspects of ecology and environment.

Earlier, Adoor Gopalakrishnan, noted film maker who inaugurated the seminar expressed apprehension over the findings of the CPR Foundation. More than hundred college students from various parts of the state attended the seminar.
(source: Haindava Kerala Correspondent - THIRUVANANTHAPURAM). For more refer to chapter on Conversion

German scientist trains farmers on ancient Indian vedic homa therapy

To deal with the impact of climate change in agriculture, farmers in Himachal Pradesh are being trained by a German scientist in the ancient Indian vedic homa therapy.
Ulrich Berk claims the Vedic homa therapy, which invokes prayers, has been found to aid farming.

This farming technique is called 'Homa' (traditional vedic farming method through prayers) farming here. Berk has made some alterations in the centuries old technique to make it contemporary.

Berk said that if the farmers practice 'Homa' therapy it might rain in their farms as the therapy creates microclimate around one's farm.

"It is possible that if the farmers practice 'Homa' farming here that it might rain as it creates microclimate around your farm and you will be safe. The capacity of soil to absorb the moisture will be increased," said Berk.

Lalit Mohan Sharma, a farmer in Rampur , said that by practicing 'Homa' farming pollution can be controlled to a large extent.

"Earlier in Hindu culture, life used to revolve around Vedas and today he has given a demonstration of 'Homa' farming and also told us that by practicing this technique pollution can be controlled," said Sharma.

The farmers are very delighted to adopt the traditional methods of farming and offering prayers. They believe that the prayers offering will help the farmers to purify the atmosphere and bring timely rainfall to have good crop.
Can wisdom be patented?

I grew up watching my father stand on his head every morning. He was doing sirsasana, a yoga pose that accounts for his youthful looks well into his 60s. Now he might have to pay a royalty to an American patent holder if he teaches the secrets of his good health to others.

The U.S. Patent and Trademark Office has issued 150 yoga-related copyrights, 134 patents on yoga accessories, and 2,315 yoga trademarks. There's big money in those pretzel twists and contortions - $3 billion a year in America alone. It's a mystery to most Indians that anybody can make that much money from the teaching of a knowledge that is not supposed to be bought or sold like sausages.

The Indian government is not laughing. It has set up a task force that is cataloging traditional knowledge, including ayurvedic remedies and hundreds of yoga poses, to protect them from being pirated and copyrighted by foreign hucksters. The data will be translated from ancient Sanskrit and Tamil texts, stored digitally, and available in
five international languages, so that patent offices in other countries can see that yoga didn't originate in a San Francisco commune.

It is worth noting that the people in the forefront of the patenting of traditional Indian wisdom are Indians, mostly overseas. We know a business opportunity when we see one and have exported generations of gurus skilled in peddling enlightenment for a buck. But as Indians, they ought to know that the very idea of patenting knowledge is a
gross violation of the tradition of yoga.

In Sanskrit, "yoga" means "union." Indians believe in a universal mind - brahman - of which we are all a part, and which ponders eternally. Everyone has access to this knowledge.

Knowledge in ancient India was protected by caste lines, not legal or economic ones. The term "intellectual property" was an oxymoron: the intellect could not be anybody's property. 
Perhaps it is for this reason that Indians do not feel obligated to pay for knowledge. Pirated copies of my book are openly sold on the Bombay streets, for a fourth of its official price. Many of the plots and the music in Bollywood movies are lifted wholesale from Hollywood . Still, Indians get upset every time they hear reports - often overblown - of Westerners' stealing their age-old wisdom through the mechanism of copyright law. The fears may be exaggerated, but they are widespread and reflect India 's mixed experience with globalization.

Western pharmaceutical companies make billions on drugs that are often first discovered in developing countries. But herbal remedies like bitter gourd or turmeric, which are known to be effective against everything from diabetes to piles, earn nothing for the country whose sages first isolated their virtues. The Indian government estimates
that worldwide, 2,000 patents are issued a year based on traditional Indian medicines.

Drugs and hatha yoga have the same aim: to help us lead healthier lives. India has given the world yoga for free. No wonder so many in the country feel that the world should return the favor by making lifesaving drugs available at reduced prices, or at least letting Indian companies make cheap generics. If the lotus position belongs to
all mankind, so should the formula for Gleevec, the leukemia drug over whose patent a Swiss pharmaceuticals company is suing the Indian government.

For decades, Indian law allowed its pharmaceutical companies to replicate Western-patented drugs and sell them at a lower price to countries too poor to afford them otherwise. In this way, India supplied half of the drugs used by HIV-positive people in the developing world.

But in March 2005, the Indian Parliament, under pressure to bring the country into compliance with the World Trade Organization's rules on intellectual property, passed a bill declaring it illegal to make generic copies of patented drugs.

This has put life-saving antiretroviral medications out of reach of many of the nearly 6 million Indians who have AIDS. Yet the very international drug companies that so fiercely protect their patents oppose India 's attempts to amend World Trade Organization rules to protect its traditional remedies.

There's more at stake than just the money. There is also the perception that the world trading system is unfair, that the deck is stacked against developing countries. If the copying of Western drugs is illegal, so should be the patenting of yoga. It is also intellectual piracy, stood on its head.

Suketu Mehta is the author of " Maximum City : Bombay Lost and Found
(source: Can wisdom be patented? - by Suketu Mehta International Herald Tribune May 7 2007).
An Indian herbal formulation with regenerative properties.  
While all attention is riveted on the furore over CPI(M) The Communist Party of India-Marxist leader Brinda Karat's diabolical attempt to denigrate and discredit Ayurveda and Ayurvedic drugs which together are rapidly gaining popularity and posing a challenge to multinational drug companies, few would have noticed that an American firm has surreptitiously patented Jeevani, an Indian herbal formulation with regenerative properties.   
The Kani tribe of Kerala had harnessed native knowledge and used indigenous plants to create this wonder diet supplement. Subsequently, Tropical Botanical Garden and Research Institute, in collaboration with the tribe, had developed Jeevani as a packaged product. That was nearly a decade ago. Although a local patent was procured, nobody bothered to take note of patent laws that have come into force in the post-WTO era.  
The American firm, Good Earth Companies Inc, has made full use of this lapse and, after patenting the brand, released its own product labelled as 'Jeevani Jolt 1000' whose ingredients are the same as those in the original Indian formulation.  
Technically, Good Earth has not violated any law. Given the smash-and-grab attitude of American enterprise, it would be silly to expect any US firm to be guided by ethics. If anybody is to blame, it is the sprawling bureaucracy of India which is too slothful to respond to the changing times. By the time a file makes its way from one desk to another in its inexorable journey through the hierarchy of India's babudom, someone somewhere would have outwitted those charged with - and paid by taxpayers - to protect India's interests.  
We have seen this happening in the past with Neem, Haldi and Basmati being patented and our babudom waking up from their paid-for-slumber with a start only after reports appeared in the media. This time, too, we can expect our bureaucrats to feign ignorance and their political bosses to voice faux indignation. 
There are other reasons, too, why we continue to lose out on indigenous medicines, often to foreign firms. To begin with, Indian systems of medicine are poorly documented. Modern medicine demands proof on the efficacy of a particular formulation, which is most often not documented in the case of traditional drugs. The Government's effort to overcome this obstacle through a partnership between CSIR, ICMR and Department of Ayush is welcome, but the pace is far too slow to merit any applause.  
Moreover, the marketing of indigenous medicines is poor. A last point: Indigenous systems have not cultivated a culture of quality control as is understood in the context of modern, consumer-driven markets.  
We need to introduce standardisation across industry. The State drug controller's establishment does not have the expertise to check Ayurvedic samples. The Government is at last talking about creating the post of an additional director-general in the proposed National Drug Authority and four AYUSH inspectors. But given the snail's pace at which Government works, and the pro-active campaign by MNCs to prevent the emergence of indigenous medicines as a challenger to their hegemony, adequately backed by the campaign of calumny launched by their stooges in the Left, we can only wait for all this to happen.
(source: Our loss, US's gain - The Pioneer Edit Desk - Jan 7' 2006).
***
The Japanese have worked really hard to understand the basic concepts in ayurveda and now they know that the discipline offers solutions for a number of ailments, which cannot be cured by modern medicine alone. It is true that the country has one of highest life expectancies in the world and now they are striving for longer quality of life with the help of ayurveda. The life style diseases including diabetes, hypertension and cardiac problems are also growing in Japan and people are turning to traditional medicine.

The traditional medicine system in Japan has its root in oriental system as practised in China, but it has its own limitations. The country has been fast enough to realise the significance of inter-disciplinary approach in medicine system, taking the best out of every medicine system. "India also needs to take a leaf out of this practice in Japan, if it is wishing to address a wide range of diseases and improve health conditions," added Dr. Krishna.
(source: Japan Making a better use of Ayurveda - timesofindia.com).
Did you Know?
Sissa's request and Chess
Among the fascinating legends told about the origin of chess is the story of Sissa, a scientist and the inventor of the game. In western India, Raja Balhait had asked his advisers to create a game that demonstrated the values of prudence, diligence, foresight, and knowledge. Sissa brought a chessboard to the raja and explained that he had chosen war as a model for the game because war was the most effective school in which to learn the values of decision, vigor, endurance, circumspection, and courage. The raja was delighted with the game and ordered its preservation in temples. He considered its principles the foundation of all justice and held it to be the best training in the art of war.

The raja said to his subject Sissa, "Ask any reward. It will be yours." Being a scientist, Sissa felt rewarded by the pleasure his invention was giving others; but the kind insisted, and finally Sissa said, "Give me a reward in grains of corn on the chessboard (ashtapada). On the first square one grain, on the second two, on the third four, on the fourth double of that, and so on until the 64th and last square."

The raja would not hear of it. He insisted that Sissa ask for something of more worth than grains of corn. But Sissa insisted he had no need of much and that the grains of corn would suffice. Thereupon the raja ordered the corn to be brought; but before they had reached the 30th square, all the corn of India was exhausted. Perturbed, he looked at Sissa, who laughed and told his raja that he knew perfectly well he could never receive the reward he had asked because the amount of corn involved would cover the whole surface of the earth to a depth of nine inches. 
The raja did not know which to admire more: the invention of chess or the ingenuity of Sissa's request. The number involved is 18,446,744,073,709,551,615 grains. This number had been previously calculated by the early Indian mathematicians, who incidentally, had invented the decimal system long before it reached the Arabs and Europe. 
(source: Feast of India: A Legacy of Recipes and Fables - By Rani p. 84).

Hindu Culture -1

"India is the world's most ancient civilization. Nowhere on earth can you find such a rich and multi-layered tradition that has remained unbroken and largely unchanged for at least five thousand years. 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 transmitting its unmistakable imprint down five millennia to no less than a billion modern bearers. Indians have demonstrated greater cultural stamina than any other people on earth. The essential basis of Indian culture is Religion in the widest and most general sense of the world. An intuitive conviction that the Divine is immanent in everything permeated every phase of life," says Stanley Wolpert.

Indic civilization has enriched every art and science known to man. Thanks to India, we reckon from zero to ten with misnamed "Arabic" numerals (Hindsaa - in Arabic means from India), and use a decimal system without which our modern computer age would hardly have been possible.

Science and philosophy were both highly developed disciplines in ancient India. However, because Indian philosophic thought was considerably more mature and found particular favor amongst intellectuals, the traditions persists that any early scientific contribution came solely from the West, Greece in particular. Because of this erroneous belief, which is perpetuated by a wide variety of scholars, it is necessary to briefly examine the history of Indian scientific thought. Jawaharlal Nehru wrote in his book The Discovery of India:  "Till recently many European thinkers imagined that everything that was worthwhile had its origins in Greece or Rome ." From the very earliest times, India had made its contribution to the texture of Western thought and living. Michael Edwardes, author of British India, writes that throughout the literatures of Europe, tales of Indian origin can be discovered. European mathematics  - and, through them, the full range of European technical achievement – could hardly have existed without Indian numerals. But until the beginning of European colonization in Asia, India’s contribution was usually filtered through other cultures.
"Many of the advances in the sciences that we consider today to have been made in Europe were in fact made in India centuries ago." - Grant Duff British Historian of India. Dr. Vincent Smith has remarked, "India suffers today, in the estimation of the world, more through the world's ignorance of the achievements of the heroes of Indian history than through the absence or insignificance of such achievement."
Introduction
According to American Historian Will Durant in his book, The Story of Civilizations - Our Oriental Heritage ISBN: 1567310125 1937 p.391-396:
"From the time of Megasthenes, who described India to Greece ca 302 B.C., down to the eighteenth century, India was all a marvel and a mystery to Europe. Marco Polo (1254-1323) pictured its western fringe vaguely, Columbus blundered upon America in trying to reach it, Vasco da Gama sailed around Africa to rediscover it, and merchants spoke rapaciously of "the wealth of the Indies." 
" It is true that even across the Himalayan barrier India has sent to us such questionable gifts as grammar and logic, philosophy and fables, hypnotism and chess, and above all our numerals and our decimal system. But these are not the essence of her spirit; they are trifles compared to what we may learn from her in the future. As invention, industry, and trade bind the continents more closely, and shall absorb, even in enmity, some of its ways and thoughts." 
"The indications are that Mohenjadaro was at its height when Cheops built the first great pyramid; that it had commercial, religious and artistic connections to Sumeria and Babylonia...as Sir John Marshall believes, Mohenjadaro represents the oldest of all civilizations known."
Yaqubi (9th century) Muslim historian has written: 
"The Hindus are superior to all other nations in intelligence and thoughtfulness. They are more exact in astronomy and astrology than any other people.

"
The Siddhanta is a good proof of their intellectual powers; by this book the Greeks and Persians have also profited. In medicine their opinion ranks first."
Al-Jahiz 9th century Muslim historian writes:
"The Hindus excel in astrology, mathematics, medicine and in various other sciences. They have developed to a perfection arts like sculpture, painting, and architecture. They have collections of poetry, philosophy, literature and science of morals. From India we received the book called Kalilah wa Dimnah. These people have judgment and are brave. They posses the virtues of cleanliness and purity. Contemplation has originated with them."
(source: The Vision of India - By Sisirkumar Mitra p. 226).
The medieval Arab scholar Sa'id Ibn Ahmad al-Andalusi (1029-1070) wrote in his Tabaqat al-'umam, one of the earliest books on history of sciences:
"The first nation to have cultivated science is India. ... India is known for the wisdom of its people. Over many centuries, all the kings of the past have recognized the ability of the Indians in all the branches of knowledge... The kings of China have stated that the kings of the world are five in number and all the people of the world are their subjects. They mentioned the king of China, the king of India, the king of the Turks, the king of the Persians, and the king of the Romans... They referred to the king of India as the "king of wisdom" because of the Indians' careful treatment of ulum (sciences) and all the branches of knowledge. ... The Indians, known to all nations for many centuries, are the metal (essence) of wisdom, the source of fairness and objectivity. They are people of sublime pensiveness, universal apologues, and useful and rare inventions. ... To their credit the Indians have made great strides in the study of numbers and of geometry. They have acquired immense information and reached the zenith in their knowledge of the movements of the stars (astronomy).... After all that they have surpassed all other peoples in their knowledge of medical sciences.."
“That which has reached us from the discoveries of their clear thinking and the marvels of their inventions is the (game) of chess. The Indians have, in the construction of its cells, its double numbers, its symbols and secrets, reached the forefront of knowledge. They have extracted its mysteries from supernatural forces. While the game is being played and its pieces are being maneuvered, there appear the beauty of structure and the greatness of harmony. It demonstrates the manifestation of high intentions and noble deeds, as it provides various forms of warnings from enemies and points out ruses as well as ways to avoid dangers. And in this, there is considerable gain and useful profit.” 
(source: The Categories of Nations - By Said al-Andalusi. A translation was published by University of Texas Press : “Science in the Medieval World”. This is the first English translation of this eleventh-century manuscript. Quotes are from Chapter V: “Science in India ”). A Concise History of Science in India   eds. D. M. Bose, S. N. Sen & B. V. Subbarayappa. New Delhi . Indian National Science Academy , 1989), p. i and The Invasion That Never Was - By Michel Danino and Sujata Nahar p. 16 and How 'Gandhara' became 'Kandahar' - By Rajiv Malhotra and The Making of the Indo-Islamic World. Volume I – Early Medieval India and the Expansion of Islam 7th-11th Centuries - By Andre Wink. Oxford University Press, New Delhi 1999. p.112 -193).
Abu’l Hasan al-Qifti ( ? ) Arab scholar and author of Chronology of the Scholars, speaks of  Arab admiration for Indian place-value system and methods of calculation.
“Among those parts of their sciences which came to us, the numerical calculation….it is the swiftest and most complete method of calculation, the easiest to understand and the simplest to learn; it bears witness to the Indians’ piercing intellect, fine creativity and their superior understanding and inventive genius.”
(source:  The Universal History of Numbers - By Georges Ifrah   p. 530 - 531).
For more refer to chapter on Quotes.

Sir William Wilson Hunter ( ? )author of the book, The Indian Empire, said India," has even contributed to modern medical science by the discovery of various chemicals and by teaching you how to reform misshapen ears and noses. Even more it has done in mathematics, for algebra, geometry, astronomy, and the triumph of modern science -- mixed mathematics -- were all invented in India, just so much as the ten numerals, the very cornerstone of all present civilization, were discovered in India, and are in reality, Sanskrit words."
Beginning with the earliest known Indian civilization, the Indus Valley, with its pottery wheel, cotton textiles, Indus script, and two wheeled carts, there is a good deal of material and texts to work from. By the beginning of the third millennium B.C. in India, as in China, Egypt, and Mesopotamia, scientific development was well advanced. Excavations carried on at the sites of the Indus civilization have revealed remnants of an ancient civilization unsurpassed in civil engineering accomplishments, particularly baths and drainage. Whilst much is known of the hygienic measures of the period, little is known of the scientific knowledge upon which it was based. From the town Planning and Great Baths of Indus Valley it is evidence in the neat arrangement of the major buildings contained in the citadel, including the placement of a large granary and water tank or bath at right angles to one another. 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. Baked-brick houses faced the street, and domestic life was centered around an enclosed courtyard. The cities had an elaborate public drainage system, Sanitation was provided through an extensive system of covered drains running the length of the main streets and connected by chutes with most residences. In the valley of the Indus River of India, the world's oldest civilization had developed its own system of mathematics. 
This civilization is known for its well planned cities, brick built houses, excellent drainage system and water storage tanks. Benjamin Rowland (1904-1972) author of Art and Architecture of India wrote: "Indeed it could be said that the population of the Indus cities lived more comfortably than did their contemporaries in the crowded and ill-built metropolises elsewhere. People were literate and had their own script. Dance and music formed essential part of their daily life."
They had wide main streets and were magnificently laid out in grid form, reflecting careful town planning. They had sewers, municipal water systems, public baths, and well-fortified citadels. The private houses were well built, of fine solid baked bricks which have not crumbled over the centuries. Many of them were two stories high, and had seat latrines and chutes for refuse. Homes were built around courtyards. The people of the Indus Valley civilization had an advanced technology. They knew how to make cotton cloth and copper and bronze castings and forgings. Some of their art objects have a wonderful simple realism. The torso of one small dancing figure is so unbelievably alive that one can almost feel the easy muscles at work under the smooth skin. 
(source: India: A World in Transition - By Beatrice Pitney Lamb p. 20).
"Mohenjo-daro had some of the most advanced toilets and sewers, with lavatories built into the outer walls of houses. There were “Western-style” toilets made from bricks with wooden seats on top. They had vertical chutes, through which waste fell into street drains or cesspits. Sir Mortimer Wheeler, the director-general of archaeology in India from 1944 to 1948, wrote: “The high quality of the sanitary arrangements could well be envied in many parts of the world today.” 
Nearly all of the hundreds of houses excavated had their own bathing rooms. Generally located on the ground floor, the bath was made of brick, sometimes with a surrounding curb to sit on. The water drained away through a hole in the floor, down chutes or pottery pipes in the walls, into the municipal drainage system. Even the fastidious Egyptians rarely had special bathrooms."
The Indian architects designed sewage disposal systems on a large scale, building networks of brick effluent drains following the lines of the streets. The drains were seven to ten feet wide, cut at two feet below ground level with U shaped bottoms lined with loose brick easily taken up for cleaning. At the intersection of two drains, the sewage planners installed cesspools with steps leading down into them, for periodic cleaning. By 2700 B.C. these cities had standardized earthenware plumbing pipes with broad flanges for easy joining with asphalt to stop leaks."  
The Harappans employed a variety of plumb bobs that reveal a system of weight based on a decimal scale. For example, a basic Harappan plumb bob weighs 27.584 grams. If we assign that a value of 1, other weights scale in at 0.5, .1., 2, .5, 2, 5, 10, 20 50, 100, 200, and 500. Archaeologists have found a “ruler” made of shell lines drawn 6.7 millimeters apart with a high degree of accuracy. Two of the lines are distinguished by circles and are separated by 33.5 millimeters or 1.32 inches. This distance is the so-called Indus inch.
Harappan bricks contain no straw or binding material and are still in usable shape after five thousand years. Most interesting are their dimensions: while found in fifteen different sizes, their length, width, and thickness are always in the ration of 4:2:1.

(source: Lost Discoveries - Dick Teresi   p. 351-352 and 59 - 62).
In ancient India, as in Greece, there was much speculative thought about astronomy, mathematics, physics, and biology. But mathematics and mysticism were inextricably mixed in early Greek thought, and Greek belief in magic, divination and oracles was perhaps more pronounced than its counterpart in India.

It is therefore untrue to assert, as recent European writers particularly have done, that Greece was the home of pure science. 

Both India and Greece, whilst having their own traditions, had direct and indirect effects on each other in science as they did in philosophy. In fact, long before the Greeks, the Indians had learned to employ the dialectic method to grasp empirical and transcendental truths, although in India, more perhaps than in ancient Greece or the modern West, reason and truth, logic and mysticism, the visible and invisible, have always been regarded as inseparable. The practical application of science to human affairs, was as poor in India as it was in any other ancient society. In fact, this was not achieved until the eighteenth century, until then science and technology developed separately. When it did as in the case of Galileo Galilei, who was the first to employ the modern scientific method in its fullness, he incurred the wrath of the Church and was incarcerated by the Inquisition at the advanced age of seventy. There is hardly any parallel in India where a difference in interpretation either in metaphysics or scientific thought was so unkindly suppressed. 

The spirit of scientific enquiry and a rigorous correlation of cause and effect in explaining natural phenomenon were particularly evident in ancient India. The connection between Indian philosophy and medicine, mathematics, astronomy, and technology is, strangely enough seldom realized much less recognized.
Ancient Indians "measured the land, divided the year, mapped out the heavens, traced the course of the sun and the planets through the zodiacal belt, analyzed the constitution of matter, and studied the nature of birds and beasts, plants and seeds." Whilst in Western civilizations the  interest has been increasingly focused on single sciences, in the Indian world the ontological viewpoint has been generally preferred, and it would appear that "in India, through all periods,  the special sciences are rooted in and developed on the underlying cosmic concepts and presuppositions. This universal vision in India has never been lost. 
India's contribution to the sciences of mathematics and medicine have been unique. In other sciences, especially linguistics, metallurgy, and chemistry, Indians made trail-blazing discoveries. 

(source: An Introduction to India - By Stanley Wolpert  p. 192).

The Vedic Shulba Sutras (fifth to eighth century B.C. E.) meaning "codes of the rope," show that the earliest geometrical and mathematical investigations among the Indians arose from certain requirements of their religious rituals. When the poetic vision of the Vedic seers was externalized in symbols, rituals requiring altars and precise measurement became manifest, providing a means to the attainment of the unmanifest world of consciousness. "Shulba Sutras" is the name given to those portions or supplements of the Kalpasutras, which deal with the measurement and construction of the different altars or arenas for religious rites. The word Shulba refers to the ropes used to make these measurements. Although Vedic mathematicians are known primarily for their computational genius in arithmetic and algebra, the basis and inspiration for the whole of Indian mathematics is geometry. Evidence of geometrical drawing instruments from as early as 2500 B.C.E. has been found in the Indus Valley.
The beginnings of algebra can be traced to the constructional geometry of the Vedic priests, which are preserved in the Shulba Sutras. Exact measurements, orientations, and different geometrical shapes for the altars and arenas used for the religious functions (yajnas), which occupy an important part of the Vedic religious culture, are described in the Shulba Sutras. Many of these calculations employ the geometrical formula known as the Pythagorean theorem.
This theorem (c. 540 B.C.E.), equating the square of the hypotenuse of a right angle triangle with the sum of the squares of the other two sides, was utilized in the earliest Shulba Sutra (the Baudhayana) prior to the eighth century B.C.E. Thus, widespread use of this famous mathematical theorem in India several centuries before its being popularized by Pythagoras has been documented. The exact wording of the theorem as presented in the Sulba Sutras is: "The diagonal chord of the rectangle makes both the squares that the horizontal and vertical sides make separately." The proof of this fundamentally important theorem is well known from Euclid's time until the present for its excessively tedious and cumbersome nature; yet the Vedas present five different extremely simple proofs for this theorem. 
One historian, Joseph Needham, has stated, "Future research on the history of science and technology in Asia will in fact reveal that the achievements of these peoples contribute far more in all pre-Renaissance periods to the development of world science than has yet been realized." 
Meticulous planning and architectural brilliance in the layout of the city are the established and striking features of the Harappan civilisation. 
Recent excavations at the small township of Dholavira, in Kutch, Gujarat, have presented to the world some of the oldest stadiums and sign board.  
One of the stadiums is huge. The multipurpose structure, with terraced seats for spectators, around 800 feet in length (around 283 metres) can accommodate as many as 10,000 persons. The other stadium is much smaller in size.    
The dimensions of the town of Dholavira (777.1 metres in length and 668.7 meters in width) establishes that the Harappans had great knowledge of trigonometry.   They were also mathematical experts as all the dimensions at the site are based on squares and cubes, 
(source: Oldest Harappan signboard at Kutch township - timesofindia.com). 
Ancient Indians already operated with a time span of astronomical proportions long before the earliest signs of natural science in ancient Greece. It is undeniable that ancient Indian texts present astonishingly exact scientific calculations even by today's latest scientific standards, such as the speed of light, exact size of the smallest particles and the age of the universe. 
The Surya Siddhanta, a textbook on astronomy of ancient India - last compiled in 1000 BC, believed by Hindus to be handed down from 3000 BC by aid of complex mnemonic recital methods still known today - computed the earth's diameter to be 7,840 miles, the distance earth - moon as 253,000 miles. These compare to modern measurements resp. as 7,926.7 miles and 252,710 miles for max. dist. moon-earth.
Manu's texts in Sanskrit propounded evolution thousands of years before Lamarck & Darwin. "The first germ of life was developed by water and heat. Man will traverse the universe, gradually ascending and passing through the rocks, the plants, the worms, insects, fish, serpents, tortoises, wild animals, cattle, and higher animals. These are the transformations declared, from the plant to Brahma, which have to take place in the world."
Brihath Sathaka operates with divisions of the time of one day into:- 60 kalas or ghatika - 24 mins each. Subdivided into 60 vikala (24 secs.each) 60 para then into tatpara, then into vitatpara then into ima then into kasha.... the smallest unit, equal to approx. o.ooooooo3 of a second (one 300 millionth). This smallest unit (3 X 10 -8 second) is surprisingly close to the life-spans of certain mesons and hyperons, according to some Western physicist who was interviewed on the BBC World Service in the early 1990s. 
The 14th century 'Rigveda of the Sun' (dated by manuscript age only), says that the sun covers 2,202 yoganas in half a mimesa - which calculates as 300,000 metres a second, fairly exactly the speed of light.
(source: Science, the Critical mind and Dissent - By Robert C Priddy).
Francois Marie Arouet Voltaire (1694-1774) France's greatest writers and philosophers, was a theist, and a bitter critic of the Church said :
" It is very important to note that some 2,500 years ago at the least Pythagoras went from Samos to the Ganges to learn geometry...But he would certainly not have undertaken such a strange journey had the reputation of the Brahmans' science not been been long established in Europe....We have already acknowledged that arithmetic, geometry, astronomy were taught among the Brahmans. From time immemorial they have known the precession of the equinoxes and were in their calculation far closer to the real figure than the Greeks who came much later. Mr. Le Gentil (a French astronomer who spent several years in India) has with admiration acknowledged the Brahmans' science, as well as the immensity of time these Indians must have needed to reach a knowledge of which even the Chinese never had any notion, and which was unknown to Egypt and to Chaldea, the teacher of Egypt."
(source:  Fragments historiques sur l'linde - By Voltaire  p. 444 - 445.). 
Beginning of Indian Scientific Thought
The beginning of Indian scientific thought are traced to the same source as those of Indian metaphysics and religion, the Rig Veda. The Vedas, being essentially works of poetic imagination, cannot be expected to contain much spirit of scientific inquiry, yet there are remarkable flashes of intuitive conjecture and reason. 
They explain the nature of the universe, of life, while admitting that Creation itself is the one unknowable mystery.
To the Vedic sages, creation indicated that point before which there was no Creator, the line between indefinable nothingness and something delineated by attributes and function, at least. Like the moment before the Big Bang Theory. These concepts preoccupy high wisdom, the Truth far removed from mere religion.  

Indeed, in one of the most remarkable of the Vedic hymns - In the Hymn of Creation (Rig Veda 10.129.3)   a searching inquiry as to the origin of the world is made; it is certainly the earliest known record of philosophic doubt. 
" There was not non-existent nor existent;
There was no realm of air, no sky beyond it.
What covered it, and where? and what gave shelter?
Was water there, unfathomed depth
of water?

Yet the Vedas go further, being philosophy, or really spiritual sciences, rather than myth.  The hymn goes to say that in the beginning there was neither death nor immortality, nor day nor night. All that existed was void and formless. Then arose, desire, the primal seed and germ of spirit. But,

Who verily knows and
who can declare it,
Whence it was born and
Whence comes this creation?

The gods are later than this
world's production
Who knows, then, whence it
first came into being?
Vedas are the most sophisticated, most profoundly beautiful, and most complete presentations of what Aldous Huxley termed the “perennial philosophy” that is at the core of all religions. In modern academia, of course, there is not supposed to be any “ancient wisdom”.  In this hymn, which contains the essence of monism, can be seen a representation of the most advanced theory of creation. The germ of free speculation and skepticism were already present in the Rig Veda. 
(source: The Empire of the Soul: Some Journeys into India - By Paul William Roberts  published by Riverhead Books ASIN: 1573226351 p 300-301).
The statue of Nataraja (dance pose of Lord Shiva) is a well known example for the artistic, scientific and philosophical significance of Hinduism. 
Freedom was born in India. Doubt, the mother of freedom, was born with the Rig Veda, the most sacred scripture of the Hindus which has the following:

What are words, and what are mortal thoughts!
Who is there who truly knows and who can say,|
Whence this unfathomed world
And from what cause!

Freedom of the mind created the wondrous world of the intellect — the world of Hindu rishis, philosophers, poets and dramatists. It was the freedom of the mind and freedom of the senses which led to India’s diversity and contributed to the richness of its civilization. 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

Concept of Time
"After a cycle of universal dissolution, the Supreme Being decides to recreate the cosmos so that we souls can experience worlds of shape and solidity. 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." - The Prashasta Pada.
***
Grandiose time scales
Hinduism’s understanding of time is as grandiose as time itself. 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. The Puranas describe time units from the infinitesimal truti, lasting 1/1,000,0000 of a second to a mahamantavara of 311 trillion 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.
(source: Hinduism Today April/May/June 2007 p. 14).
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. Rebirth follows destruction.
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. "Release" from time's fateful wheel is termed moksha, and an advanced ascetic may be called kala-attita (' he who has transcended time').
Hindus believe that the universe is without a beginning (anadi= beginning-less) or an end (ananta = end-less).  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 1,000 Maha Yugas. 
A Kalpa is thus equal to 4.32 billion human years. Kirtha Yuga or Satya yuga (golden or truth age) is 1,728,000 years; Treta yuga is 1,296,000 years; Dvapara yuga is 864,000 years; and Kali Yuga is 432,000 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 12,000,000 human years ( or 12,000 Brahma years).
One Maha Yuga is 4,32 million years.  
Krita or Satya 
golden age 
1,728,000 years
Treta
silver age
1,296,000 years
Dvapara
copper age
864,000 years
Kali 
iron age
432,000 years
 
Watch Carl Sagan and Hindu cosmology – video
A Brahma, or Lord of Creation, lives for one hundred Brahma years (each of made up of 360 Brahma days). After that he dies. So a Brahma lives for 36,000 Kalpas, or 36,000 x 2,000 x 4,30,000 human years – i.e., a Brahma lives for 311.4 trillion human years. 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. 
(source: Am I a Hindu - by Ed Viswanathan  p. 292 - 293). For more on Yugas, refer to One Cosmic Day of Creator Brahma)
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:

"The Hindus with their grandiose Kalpas and their ideas of the divine power which is beyond all human category (male or female). 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: 
"Temporal notions in Europe were overturned by an India rooted in eternity. 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." 
(source: The Genius of India - By Guy Sorman  ('Le Genie de l'Inde') Macmillan India Ltd. 2001. ISBN 0333 93600 0 p. 195). For more on Guy Sorman refer to chapter Quotes201_220).(Refer to Visions of the End of the World - By Dr. Subhash Kak
Huston Smith a philosopher, most eloquent writer, world-famous religion scholar who practices Hatha Yoga.  Has taught at  MIT and is currently visiting professor at Univ. of California at Berkley. Smith has also produced PBS series. He has written various books,  The World's Religions,  "Science and Human Responsibility", and "The Religions of Man" says: 
“Philosophers tell us that the Indians were the first ones to conceive of a true infinite from which nothing is excluded. 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.”  
“India saw this clearly and turned her face to that which has no boundary or whatever.” “India anchored her soul in the infinite seeing the things of the world as masks of the infinite assumes – there can be no end to these masks, of course. If they express a true infinity.” And It is here that India’s mind boggling variety links up to her infinite soul.” 
“India includes so much because her soul being infinite excludes nothing.” It goes without saying that the universe that India saw emerging from the infinite was stupendous.” 
While the West was still thinking, perhaps, of 6,000 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.”   
(source: The Mystic's Journey - India and the Infinite: The Soul of a People – By Huston Smith). For more on Huston Smith refer to chapter Quotes41_60).
Dr. Carl Sagan in his book Broca's Brain: Reflections on the Romance of Science, remarks:
"Immanuel Velikovsky (the author of Earth in Upheaval) in his book Worlds in Collision, notes that the idea of four ancient ages terminated by catastrophe is common to Indian as well as to Western sacred writing. 
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. .. "
"The idea that scientists or theologians, with our present still puny understanding of this vast and awesome cosmos, can comprehend the origins of the universe is only a little less silly than the idea that Mesopotamian astronomers of 3,000 years ago – from whom the ancient Hebrews borrowed, during the Babylonian captivity, the cosmological accounts in the first chapter of Genesis – could have understood the origins of the universe. We simply do not know.
The Hindu holy book, the Rig Veda (X:129), has a much more realistic view of the matter: 
“Who knows for certain? Who shall here declare it?
Whence was it born, whence came creation?
The gods are later than this world’s formation;
Who then can know the origins of the world?
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."
(source: Broca's Brain: Reflections on the Romance of Science - By Carl Sagan   p. 106 - 137). Watch Carl Sagan and Hindu cosmology – video
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." The same theory was explained in an interesting way by the dashavatara (ten incarnations). But evolution, as everything else, was the manifestation of the supreme spirit (Atman) as is testified by Chandogya Upanishad.
(source: Ancient Indian History and Culture - By Chidambara Kulkarni Orient Longman Ltd. 1974. p.268).
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, "... is the only religion in which the time scales correspond... to those of modern scientific cosmology. Its cycles run from our ordinary day and night to a day and night of the Brahma, 8.64 billion years long, longer than the age of the Earth or the Sun and about half the time since the Big Bang" 
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), 
"All the planets of the universe, from the most evolved to the most base, are places of suffering, where birth and death takes place. 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 4.32 billion human years, doubling which one gets 8.64 billion years for a Brahma day and night. 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... a cosmos without end. This, according to modern physicists is not an impossibility. 

(source: Astronomy and Mathematics in Ancient India).

Count Maurice Maeterlinck (1862-1949) was a Belgian writer of poetry, a wide variety of essays. He won the 1911 Nobel Prize for literature. In his book Mountain Paths, says:
"he falls back upon the earliest and greatest of Revelations, those of the Sacred Books of India with a Cosmogony which no European conception has ever surpassed." 
(source: Mountain Paths - By Maurice Maeterlinck).
In Hindu thought, interspersed between linear, time-limited existences lie timeless intervals of non-existence. The creation hymn of the Hindus, Nasadiya-sukta of Rig-Veda, affirms an absolute beginning of things and describes the origin of the universe as being beyond the concepts of existence and non-existence

“The Hindu ... pictured the universe as periodically expanding and contracting and gave the name Kalpa to the time span between the beginning and the end of one creation. 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.

(source: The Origin of the Universe - By K B N Sarma - sulekha.com).

John Bowle, categorically declares that Plato was influenced by Indian ideas. 
(source: A New Outline of World History - By John Bowle p. 91).
Princeton University’s Paul Steinhardt and Cambridge University’s Neil Turok, have recently developed The Cyclical Model. 
They have just fired their latest volley at that belief, saying there could be a timeless cycle of expansion and contraction. It’s an idea as old as Hinduism, updated for the 21st century. 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 1930s, as well as the Hindu belief that the universe has no beginning or end, but follows a cosmic cycle of creation and dissolution.

(source: Questioning the Big Bang -  msnbcnews.com).  

Dick Teresi ( ? ) author and coauthor of several books about science and technology, including The God Particle. He is cofounder of Omni magazine and has written:
"The big bang is the biggest-budget universe ever, with mind-boggling numbers to dazzle us – a technique pioneered by fifth-century A.D. Indian cosmologists, the first to estimate the age of the earth at more than 4 billion years. The cycle of creation and destruction continues forever, manifested in the Hindu deity Shiva, Lord of the Dance, who holds the drum that sounds the universe’s creation in his right hand and the flame that, billions of years later, will destroy the universe in his left. Meanwhile Brahma is but one of untold numbers of other gods dreaming their own universes.  The 8.64 billion years that mark a full day-and-night cycle in Brahma’s life is about half the modern estimate for the age of the universe. The ancient Hindus believed that each Brahma day and each Brahma night lasted a kalpa, 4.32 billion years, with 72,000 kalpas equaling a Brahma century, 311,040 billion years in all. That the Hindus could conceive of the universe in terms of billions."
(source: Lost Discoveries: The Ancient Roots of Modern Science - By Dick Teresi   p. 159 and 174 -212).
The Hindus, according to Sir Monier-Williams, were Spinozists more than 2,000 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.

The French historian Louis Jacolliot says,  "Here to mock are conceit, our apprehensions, and our despair, we may read what Manu said, perhaps 10,000 years before the birth of Christ about Evolution:
 
' The first germ of life was developed by water and heat.' (Book I, sloka 8,9 )
' Water ascends towards the sky in vapors; from the sun it descends in rain, from the rains are born the plants, and from the plants, animals.'  (Book III, sloka 76).

(source:  Philosophy of Hinduism  - By T C Galav  ISBN: 0964237709  p 17).
Sir John Woodroffe, (1865-1936) the well known scholar, Advocate-General of Bengal and sometime Legal Member of the Government of India. He served with competence for eighteen years and in 1915 officiated as Chief Justice. He has said: 
"Ages before Lamarck and Darwin it was held in India that man has passed through 84 lakhs (8,400,000) of birth as plants, animals, as an "inferior species of man" and then as the ancestor of the developed type existing to-day. 
"The theory was not, like modern doctrine of evolution, based wholly on observation and a scientific enquiry into fact but was a rather (as some other matters) an act of brilliant intuition in which observation may also have had some part."

(source: Is India Civilized: Essays on Indian Culture - By Sir John Woodroffe Publisher: Ganesh & Co. Publishers Date of Publication: 1922 p. 22).

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, (A kalpa is about 4,320,000 years). 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." 
(source: Spiritual Practices of India - By Frederic Spiegelberg  Introduction by Alan Watts p. 8-9). 
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, (1934-1996) astro-physicist, in his book Cosmos says:

"The Hindu religion  is the only one of the world's great faiths dedicated to the idea that the Cosmos itself undergoes an immense, indeed an infinite, number of deaths and rebirths. It is the only religion in which the time scales correspond, to those of modern scientific cosmology. 

 "It is the clearest image of the activity of God which any art or religion can boast of." Modern physics has shown that the rhythm of creation and destruction is not only manifest in the turn of the seasons and in the birth and death of all living creatures, but also the very essence of inorganic matter.

 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. 

"The Hindu religion  is the only one of the world's great faiths dedicated to the idea that the Cosmos itself undergoes an immense, indeed an infinite, number of deaths and rebirths. It is the only religion in which the time scales correspond, to those of modern scientific cosmology.  Its cycles run from our ordinary day and night to a day and night of Brahma, 8.64 billion years long. 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 (1939 - ) Austrian-born famous theoretical high-energy physicist and ecologist wrote:
"Modern physics has thus revealed that every subatomic particle not only performs an energy dance, but also is an energy dance; a pulsating process of creation and destruction. The dance of Shiva is the dancing universe, the ceaseless flow of energy going through an infinite variety of patterns that melt into one another’’. For the modern physicists, then Shiva’s dance is the dance of subatomic matter. 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."
(source: The Tao of Physics: An Exploration of the Parallels Between Modern Physics and Eastern Mysticism - By Fritjof Capra p. 241-245).
Nancy Wilson Ross (1901 -1986) made her first trip to Japan, China, Korea and India in 1939. She was the author of several books including The World of Zen and Time's Left Corner. Miss Ross lectured on Zen Buddhism at the Jungian Institute in Zurich. She served on the board of the Asia Society of New York which was founded by John D. Rockefeller III since its founding in 1956 and was on the governing board of the India Council. In private life she was known as Mrs. Stanley Young.
She has written:
"Anachronistic as this labyrinthine mythology may appear to the foreign mind, many of India’s ancient theories about the universe are startlingly modern in scope and worthy of a people who are credited with the invention of the zero, as well as algebra and its application of astronomy and geometry; a people who so carefully observed the heavens that, in the opinion of Monier-Williams, they determined the moon’s synodical revolution much more correctly than the Greeks."
" Many hundreds of years before those great European pioneers, Galileo and Copernicus, had to pay heavy prices in ridicule and excommunication for their daring theories, a section of the Vedas known as the Brahmanas contained this astounding statement: 
“The sun never sets or rises. 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. Then, when people think he rises in the morning, he only shifts himself about after reaching the end of the day night, and makes day below and night to what is on the other side. In truth, he does not see at all.” 
"The Indians, whose theory of time, is not linear like ours – that is, not proceeding consecutively from past to present to future – have always been able to accept, seemingly without anxiety, the notion of an alternately expanding and contracting universe, an idea recently advanced by certain Western scientists. In Hindu cosmology, immutable Brahman, at fixed intervals, draws back into his beginningless, endless Being the whole substance of the living world. There then takes place the long “sleep” of Brahaman from which, in course of countless aeons, there is an awakening, and another universe or “dream” emerges. "
"This notion of the sleeping and waking, or contracting and expanding, of the Life Force, so long a part of Hindu cosmology, has recently been expressed in relevant terms in an article written for a British scientific journal by Professor Fred Hoyle, Britain’s foremost astronomer. "  

"Plainly, contemporary Western science’s description of an astronomical universe of such vast magnitude that distances must be measured in terms as abstract as light-years is not new to Hinduism whose wise men, millennia ago, came up with the term kalpa to signify the inconceivable duration of the period elapsing between the beginning and end of a world system.  
"It is clear that Indian religious cosmology is sharply at variance with that inherited by Western peoples from the Semites. On the highest level, when stripped of mythological embroidery, Hinduism’s conceptions of space, time and multiple universes approximate in range and abstraction the most advanced scientific thought. "
(source: Three Ways of Asian Wisdom – By Nancy Wilson Ross  p. 64 - 67 and 74 - 76).
Dr. Heinrich Zimmer (1890-1943), the great German Indologist, a man of penetrating intellect, the keenest esthetic sensibility observed:
“In one of the Puranic accounts of the deeds of Vishnu in his Boar Incarnation or Avatar, occurs a casual reference to the cyclic recurrence of the great moments of myth. 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: 
“Every time I carry you this way….” 
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."
(source: The Myth and Symbols in India Art and Civilization – By Heinrich Zimmer p. 18 and 152 - 155
Professor Arthur Holmes (1895-1965) geologist, professor at the University of Durham. He writes regarding the age of the earth in his great book, The Age of Earth (1913) as follows:
"Long before it became a scientific aspiration to estimate the age of the earth, many elaborate systems of the world chronology had been devised by the sages of antiquity. 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.
(source: Hinduism and Scientific Quest - By T. R. R. Iyengar p. 20-21).
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. Samkhya is generally ascribed to Sage Kapila and Yoga to Sage Patanjali. 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. 
(source: India and World Civilization - By D. P. Singhal - Chapter V - Naturalism and Science in Ancient India -  p.153 - 188).
Professor Edward Washburn Hopkins (1857-1932)  Indologist, Chair of Sanskrit Studies of Yale, says:
"Plato is full of Sankhyan thought, worked out by him, but taken from Pythagoras. Before the sixth century B.C. all the religious-philosophical idea of Pythagoras are current in India (L. Schroeder, Pythagoras). 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: "Neo-Platonism and Christian Gnosticism owe much to India. 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.'
(source: Religions of India - By Edward Washburn Hopkins   p. 559-560).
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. These parallels include: 
  1. a belief in the transmigration of souls;
  2. the theory of four elements constituting matter;
  3. the reasons for not eating beans;
  4.  the structure of the religio-philosophical character of the Pythagorean fraternity, which resembled Buddhist monastic orders; and
  5. the contents of the mystical speculations of the Pythagorean schools, which bear a striking resemblance of the Hindu Upanishads
According to Greek tradition, Pythagoras, Thales, Empedocles, Anaxagoras, Democritus and others undertook journey to the East to study philosophy and science. By the time Ptolmaic Egypt and Rome’s Eastern empire had established themselves just before the beginning of the Common era, Indian civilization was already well developed, having founded three great religions – Hinduism, Buddhism and Jainism – and expressed in writing some subtle currents of religious thought and speculation as well as fundamental theories in science and medicine.
(source: The crest of the peacock: Non-European roots of Mathematics - By George Gheverghese Joseph   p. 1 - 18). For more refer to chapter on India and Greece).
A 9th century Hindu scripture, The Mahapurana by Jinasena claims the something as modern as the following: (translation from [5])

"Some foolish men declare that a Creator made the world. The doctrine that the world was created is ill-advised, and should be rejected. If God created the world, where was he before creation?... How could God have made the world without any raw material? If you say He made this first, and then the world, you are faced with an endless regression... Know that the world is uncreated, as time itself is, without beginning and end. And it is based on principles."
(source: Astronomy and Mathematics in Ancient India). (Refer to Visions of the End of the World - By Dr. Subhash Kak - sulekha.com).
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.
(source: Ancient nuclear blasts and levitating stones of Shivapur - By Alexander Pechersky - pravda.ru.com).
Speed of Light: 
Sayana (c. 1315-1387) was a minister in the court of King Bukka I of the Vijayanagar Empire in South India; he was also a great Vedic scholar who wrote extensive commentaries on several ancient texts. In his commentary on the fourth verse of the hymn 1.50 of the Rig Veda on the sun, he says:
Tatha cha smaryate yojananam sahasre dve dve shate dve cha yogane ekena nimishardhena kramamana namo ‘stu ta iti   

Thus it is remembered: (O Sun), bow to you, you who travers 2,202 yojanas in half a minute. 
The Puranas define 1 nimesha to be equal to 16/75 seconds. 1 yojana is about 9 miles. Substituting in Sayana’s statement we get 186,000 per second.  
Sayana’s statement was printed in 1890 in the famous edition of Rig Veda edited by Max Muller, the German Sanskritist . He claimed to have used several three or four hundred year old manuscripts of Sayana’s commentary, written much before the time of  Romer. 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 1,500 years old. The Puranas speak of the creation and destruction of the universe in cycles of 8.64 billion years, that is quite close to currently accepted value regarding the time of the big bang.
(source: The Wishing Tree - By Subhash Kak   p. 75 - 77 and Sayana's Astronomy - By Subhash Kak)

Physics

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. Uddalaka says: "matter was at first a chaotic mass, like the juices of various trees indiscriminately blended together in honey. 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.'
(image source: Vishwa Hindu Parishad of America. Inc - 2002 calendar).
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. He said:

 "The cause of creative motion is believed to be adrsta, unseen moral force which guides the destiny of souls according to their karma and requires them to be provided with properly equipped bodies and an appropriate objective world for the experience of pleasure and pain. 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." 
(source: Hinduism and Scientific Quest - By T R. R. Iyengar p. 153-154 and History of Science and Technology in Ancient India - by Debiprasad Chattopadhya volume II p. 297-299). 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: earth, water, light, wind, ether, time, space, mind and soul. 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 2500 years before John Dalton. Kanaada has also described the dimension and motion of atoms and their chemical reactions with each other. 
T. N. Colebrooke, has said: "Compared to the scientists of Europe, Kanaada and others Indian scientists were the global masters in this field."
(source: Calendar 2002 - VHP of America).
Umasvati, who lived in the first century A.D. suggested that atoms of opposite qualities alone combined and the atoms attracted or repelled as they were heterogeneous or homogenous. Commenting on these theories, A. L Basham remarks: "Indian atomic theories were not of course, based on experiment, but on intuition and logic..."
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. viz. the number of vibrations varies inversely as the length of the string.
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. (for more information refer to chapters War in Ancient India and Seafaring in Ancient India). It was called matsya-yantra and consisted of an iron fish which floated in a vessel of oil and pointed at the North.
(source: Main Currents in Indian Culture - By S. Natarajan p. 68 - 69 Indo-Middle East Cultural Studies Hyderabad 1960). 
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." It was the Vedic Aryans... who gave the world some of the earliest philosophical texts on the makeup of matter and the theoretical underpinnings for the chemical makeup of minerals. 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 (600 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."
(source: Lost Discoveries: The Ancient Roots of Modern Science - By Dick Teresi  p. 1 - 8 and 159 and 174 -239). For more on Dick Teresi refer to chapters Quotes301_320, GlimpsesVI and GlimpsesVII ).
Historian A. L. Basham has written:
"The atomic theories of ancient India are brilliant imaginative explanations of the physical structure of the world..."
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). 
(source: Ancient Indian History and Culture - By Chidambara Kulkarni Orient Longman Ltd. 1974. p. 272).

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:

Student: Was the bomb exploded at Alamogordo during the Manhattan Project the first one to be detonated?

Dr. Oppenheimer: "Well -- yes. In modern times, of course.

Charles Berlitz goes on to quote a number of passages from the Mahabharata that describe the impact of a weapon that I suspect  must be the brahmaastra, although he neither names the weapon nor cites those sections of the text from which his quotations are drawn (he lists Protap Chandra Roy's translation of 1889 in his bibliography):...a single projectile Charged with all the power of the Universe.

An incandescent column of smoke and flame As bright as ten thousand Suns Rose in all its splendor......it was an unknown weapon, An iron thunderbolt, A gigantic messenger of death, Which reduced to ashes. The Entire race of the Vrishnis and the Andhakas....the corpses were so burned As to be unrecognizable. 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:
...So powerful that it could destroy
The earth in an instant -
A great soaring sound in smoke and flames...
And on it sits Death...

(source: Doomsday 1999 - By Charles Berlitz Doubleday ASIN: 038515982X  p. 118-122). For more on Oppenheimer, refer to Quotes21_40 and GlimpsesX).
Mathematics - The Language of Science

“Like the crest of a peacock, like the gem on the head of a snake, so is mathematics at the head of all knowledge --- Vedanga  Jyotisa.

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. 123: "The decimal cyphers, the honor of which, next to letters the most important of human discoveries, has, with the common consent of historical authorities, been ascribed to Hindus."
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.

(source: An Introduction to India - By Stanley Wolpert  p. 194).

Hermann Hankel (1839 - 1873) born in Halle, Germany in his History of Mathematics says:
 “ It is remarkable to what extent Indian Mathematics enters into the Science of our time”
(source: Is India Civilized? - Essays on Indian Culture - By Sir John Woodroffe Ganesh & Co. Publishers 1922 p. 182).
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 27.584 grams. If we assign that a value of 1, other weights scale in at .05, .1, .2, .5, 2, 5, 10, 20, 50, 100, 200 and 500. These weights have been found in sites that span a five-thousand-year period, with little change in size. 
Archaeologists also found a “ruler” made of shell lines drawn 6.7 millimeters apart with a high degree of accuracy. Two of the lines are distinguished by circles and are separated by 33.5 millimeters, or 1.32 inches. This distance is the so-called Indus inch.
(source: Lost Discoveries - Dick Teresi  p. 59).
Dr. David Gray writes:
"The study of mathematics in the West has long been characterized by a certain ethnocentric bias, a bias which most often manifests not in explicit racism, but in a tendency toward undermining or eliding the real contributions made by non-Western civilizations. 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." 
Mathematics and Music
Pingala (3rd C AD), author of Chandasutra explored the relationship between combinatorics and musical theory anticipating Mersenne (1588-1648) 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.
Used a dot (.) to denote zero.
His work, along with Panini's work, was foundational to the development of computing.

(source: 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. 1114) and Srinivas Ramanujan (1887-1920).
In Ramayana, the great Indian epic, there is a description of two armies facing, each other. The size of  the larger army led by Rama is given as follows in a 17th century translation of the epic by Kottayam Kerala varma Thampuran
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, 60,799 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. It requires: 
  1. the naming of the first nine digits (eka, dvi, tri, catur, pancha, sat, sapta, asta, nava);
  2. a second group of nine numbers obtained by multiplying each of the nine digits in 1 by ten (dasa, vimsat, trimsat, catvarimsat, panchasat, sasti, saptati, astiti, navati): and
  3. a group of numbers which are increasing integral powers of 10, starting with 102 (satam sagasara, ayut, niyuta, prayuta, arbuda, nyarbuda, samudra, Madhya, anta, parardha…).
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. 
(source: The crest of the peacock: Non-European roots of Mathematics - By George Gheverghese Joseph  p.401 - 403).
In the Vedic age, India was ahead of the rest in mathematics and astronomy. Thus, the geometry of the Shulba Sutras (The Rules of the Cord),  geometrical appendices to the manuals of ritual (Shrauta Sutras) include the oldest known formulation of the theorem named after Pythagoras, developed in the context of Vedic altar-building. 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."
(source: Mathematics as Known to the Vedic Samhitas - By M. D. Pandit p. 20).
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. The miscalled "Arabic" numerals are found on the Rock Edicts of Ashoka (250 B.C.), a thousand years before their occurrence in Arabic literature. 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."

(source: The Discovery of India - By Jawaharlal Nehru Oxford University Press. 1995 p. 216).

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. Ganita-Sara-Sangraham of Mahavira acarya who lived between Brahmagupta and Bhaskaracharya. 
The 'Pythagoras theorem' which stated in Sulva Sutras by Baudhayana's (6th century C. E): "The diagonal of a rectangle produces both areas, which its length and breadth produce separately." Arya Bhatta discovered the method of finding out the areas of a triangle, a trapezium and a circle. The approximate value of an 'irrational number' i.e. 2 (dvikarani) (1.143256) and 3 (1.7320513) can be obtained, Baudhayana and Apastamba.
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:
"Lemma of Brahmagupta for integral solution or the indeterminate equation of second degree. John Pell (1611-1685) discovered this in the 17th century. Indians discovered it a 1,000 years earlier. 
(source: Hinduism and Scientific Quest - By T R. R. Iyengar p. 151-152).
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 3000 B.C. old) also give specimens of writing in India. Aryans came 1000 years later, around 2000 B.C. 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 1012, while the Greeks could count up to 104 and Romans up to 108. 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 800 B.C. and 500 B.C., cover a large number of geometric principles. 
Said the great and magnanimous Pierre Simon de Laplace, (1749-1827) French mathematician, philosopher, and astronomer, a contemporary of Napoleon :
" It is India that gave us the ingenious method of expressing all numbers by ten symbols, each receiving a value of position as well as an absolute value, a profound and important idea which appears so simple to us now that we ignore its true merit. 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."
(source: The Discovery of India - By Jawaharlal Nehru Oxford University Press. 1995 p. 217).
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.
(source: Science and Mathematics in India).
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 850 A.D.), seems to have introduced it into Baghdad.

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 200 B.C. 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. Professor G. B. Halsted, in his book ' Mathematics for the Million' (London 1942)  thus emphasizes the vital significance of this invention:

"The importance of the creation of the zero mark can never be exaggerated. 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 was India that first domesticated zero, through the Hindu familiarity with the concepts of infinity and the void. Neither pagan Rome nor the Christian Europe of the Middle Ages had any truck with it. 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:

"This long period of nearly five thousand years saw the rise and fall of many a civilization, each leaving behind a heritage of literature, art, philosophy, and religion. 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.

 "Is it that the Greeks had such a marked contempt for applied science, leaving even the instruction of their children to the slaves? 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? that corner-stone of modern mathematics, also originated in India, and at about the same time that positional numeration did?"

(source: The Discovery of India - By Jawaharlal Nehru Oxford University Press. 1995 p. 218)
The Unsung Mathematician:

An important Mathematics book prescribed by the New York State Education Department acknowledges the debt in the following words:

"The Western world owes a great deal to India for a simple invention. It was developed by an unknown Indian more than 1500 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."

Indians also made advances in other areas of mathematics. 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."

(source: Harry Shor and Gloria Meng, Exploring Algebra).  

For more refer to The Infinitesimal Calculus: How and Why it Was Imported into Europe - By C. K. Raju and 
Computers, mathematics education, and the alternative epistemology of the calculus in the Yuktibhâsâ  - By C. K. Raju.

Refer to Visualizing Indian heritage Digital Library Metaphor – By Nagnath R Ramdasi - CDAC.
Charles Seife, a journalist with Science magazine, has also written for New Scientist, Scientific American, The Economist, Science, Wired UK, The Sciences, and numerous other publications. He holds an M.S. in mathematics from Yale University and his areas of research include probability theory and artificial intelligence. He is a mathematician and science writer, author of  Zero: The Biography of a Dangerous Idea says:
"Perhaps no one has embraced nothing as strongly as the Indians who, Seife notes, "never had a fear of the infinite or of the void." Hinduism has embedded within it, a complex philosophy of nothingness, seeing everything in the world as arising from the pregnant void, known as Sunya.
"The ultimate goal of the Hindu was to free himself from the endless cycle of pain found in continual reincarnation and reconnect with the Nothingness that is the source and fundament of the All. 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."
(source: Zero: 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?
http://www.calendarlive.com/top/1,1419,L-LATimes-Books-X!ArticleDetail-26133,00.html
http://www.salon.com/books/review/2000/03/03/seife/index.html
).

Lancelot Thomas Hogben (1895-1975) English zoologist and geneticist, has written:
"In the whole history of Mathematics, there has been no more revolutionary step than the one which the Hindus made when they invented the sign ‘0’ for the empty column of the counting frame."
(source: Mathematics for the Million - By Lancelot Thomas Hogben p. 47).

The concept of Debits and negative numbers originated in India, and why were they not accepted until recently? It was much more than 2000 years ago. It wasn't accepted elsewhere because the Church did not think it possible.

The paper of Reuben Burrow (1798-1868)  "A Proof that the Hindus had the Binomial Theorem." (published in 1790) Asiatic Researches 2 (1790): 487-97 is more proof for us that the western world was aware of the Indian achievement in the field of combinational mathematics. 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.
(source: India Through The Ages: History, Art Culture and Religion - By G. Kuppuram p. 672-673).
The Hindus knew mathematics much early. In the Rig Veda (2-18, 4 to 6), there are references to ‘two’, ‘four’, ‘eight’, ‘ten.’ 
Aa dvabhyam haribhyamindryahya
chaturbhirashadabhi rhuya manah ashtabhirdashabhih 
Also in Vajasaneya Samhita (17.2), there is the passage referring to 1, 10, 100, 1000 etc. 
Eka cha dasha cha dasha cha shatam cha shatam cha
sahasram cha sahasram cha yutam cha ayutam cha
niyutam cha niyutam cha prayutam cha. Etc.
In Mahabharata there are references to addition and subtraction. Adhikam (more), Unam (less), Shesham (remaining), multiplication and division are indicated. For example, “60 thousand camels and twice the number of horses” are referred to. 
In Rig Veda (10.62.7), Nabhanedishta praises King Savarni for giving in charity one thousand cows, who had the figure 8 on their ears and so were called Ashta Karni. It seems that gambling was very common in the Vedic days, and it involved dices and numbers. According to Yajur Veda, Vajasneya Samhita (4.3,3), in the Rajasuya sacrifice, five was called Abhiburasi. 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 25th 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 3,93,216. 
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. They can number pages upto 408 (34  x 12). Burma also had the same system for pagination.

(source: Hinduism: Its Contribution to Science and Civilization - By Prabhakar Balvant Machwe  p. 10 -14).
The Notion of Infinity and zero:
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:
It says: 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. Professor Arthur Macdonell says in his A History of Sanskrit Literature: "During the eighth and ninth centuries, the Indians became the teachers in arithmetic and algebra of the Arabs, and through them of the nations of the west. Thus, though we call the latter science by an Arabic name, it is a gift we owe to India."
(source: Indian Culture and the Modern Age - By Dewan Bahadur K. S. Ramaswami Sastri  Annamalai University. 1956 p.66-67).
The linkage of God with the infinite is found in the Bhagavad Gita, by tradition spoken by Lord Krishna himself, we read: 
“O Lord of the universe, I see You everywhere with infinite form…Neither do I see the beginning nor the middle nor the end of Your Universal Form.” 
(source: Infinity: The Quest to Think the Unthinkable - By Brian Clegg p. 54).
Zero to Infinity in Indian Mysticism

Ananta is Sanskrit for infinity. 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. In the Isavasya Upanishad, there’s a line: “Poornasya poornam aadaya poornameva visish-yate”. 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: yatho vacho nivartante, apraapya manasa saha — where mind and speech return (being) unable to comprehend. 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 1655. 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.

(source: Zero to Infinity in Indian Mysticism - By T R Rajagopalan - Times of India). 

‘Calculus is India ’s Gift to Europe ’

Dr. C.K. Raju (1954 - ) holds a Ph.D. from the Indian Statistical Institute. He taught mathematics for several years before playing a lead role in the C-DAC team which built Param: India ’s first parallel supercomputer. His earlier book ‘Time: Towards a Consistent Theory’ (Kluwer Academic, 1994) set out a new physics with a tilt in the arrow of time. He has been a Fellow of the Indian Institute of Advanced Study and is a Professor of Computer Applications.  
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.
“Indian infinite series has been known to British scholars since at least 1832, but no scholar tried to establish the connection with the calculus attributed to Newton and Leibnitz,” he said.
Dr. Raju’s 10-year research that included archival work in Kerala and Rome was published in a book “Cultural Foundations of Mathematics.” It established that the Jesuit priests took trigonometric tables and planetary models from the Kerala mathematicians of the Aryabhata school and exported them to Europe starting around 1560 in connection with the European navigational problem.
“When the Europeans received the Indian calculus, they couldn’t understand it properly because the Indian philosophy of mathematics is different from the Western philosophy of mathematics. It took them about 300 years to fully comprehend its working. The calculus was used by Newton to develop his laws of physics,”
It is well known that the “Taylor-series” expansion, that is at the heart of calculus, existed in India in widely distributed mathematics / astronomy / timekeeping (“jyotisa”) texts which preceded Newton and Leibniz by centuries.
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 : navigation. The ‘jyotisa’ texts were specifically needed by Europeans for the problem of determining the three “ells”: latitude, loxodrome, and longitude.
How were these Indian texts imported into Europe ? Jesuit records show that they sought out these texts as inputs to the Gregorian calendar reform. This reform was needed to solve the ‘latitude problem’ of European navigation. The Jesuits were equipped with the knowledge of local languages as well as mathematics and astronomy that were required to understand these Indian texts.
The Jesuits also needed these texts to understand the local customs and how the dates of traditional festivals were fixed by Indians using the local calendar (“panchânga”). How the mathematics given in these Indian ancient texts subsequently diffused into Europe (e.g. through clearing houses like Mersenne and the works of Cavalieri, Fermat, Pascal, Wallis, Gregory, etc.) is yet another story.
The calculus has played a key role in the development of the sciences, starting from the “Newtonian Revolution”. According to the “standard” story, the calculus was invented independently by Leibniz and Newton . This story of indigenous development, ab initio, is now beginning to totter, like the story of the “Copernican Revolution”.
The English-speaking world has known for over one and a half centuries that “Taylor series” expansions for sine, cosine and arctangent functions were found in Indian mathematics / astronomy / timekeeping (‘jyotisa’) texts, and specifically in the works of Madhava, Neelkantha, Jyeshtadeva, etc. No one else, however, has so far studied the connection of these Indian developments to European mathematics.
The connection is provided by the requirements of the European navigational problem, the foremost problem of the time in Europe . 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.
Jesuits such as Matteo Ricci who trained in mathematics and astronomy under Clavius’ new syllabus were sent to India . In a 1581 letter, Ricci explicitly acknowledged that he was trying to understand the local methods of time-keeping (‘jyotisa’) from the Brahmins and Moors in the vicinity of Cochin .
Cochin was then the key centre for mathematics and astronomy since the Vijaynagar Empire had sheltered it from the continuous onslaughts of Islamic raiders from the north. Language was not a problem for the Jesuits since they had established a substantial presence in India .
For more refer to The Infinitesimal Calculus: How and Why it Was Imported into Europe - By C. K. Raju and 
Computers, mathematics education, and the alternative epistemology of the calculus in the Yuktibhâsâ  - By C. K. Raju. 

(source: ‘Calculus is India ’s Gift to Europe ’ - By Dr. C K Raju - indianrealist.com).
In his speech introducing the Indian Budget March 1st, 1926, Sir Basil Blackett said:
"India long ago revolutionized mathematics, and provided the West with the key to the most far reaching of all the mechanical instrument on which its control of nature has been built, when it presented to Europe through the medium of Arabia the device of the cypher (and the decimal notation) upon which all modern system of numeration depend. even so, India today or tomorrow, will, I am confident, revolutionize western doctrines of progress by demonstrating the insufficiency and lack of finality of much of the West's present system of human values."
(source: India in Bondage: Her Right to Freedom - Rev. Jabez T. Sunderland p.356-357).
Georges Ifrah ( ?  ) French historian of Mathematics and author of the book, The Universal History of Numbers has written:
"The Indian mind has always had for calculations and the handling of numbers an extraordinary inclination, ease and power, such as no other civilization in history ever possessed to the same degree. 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."
(source: Histoire Universelle des Chiffres - By Georges Ifrah  Paris - Robert Laffont, 1994, volume 2.  p. 3).
“The real inventors of [the numeral system], which is no less important than such feats as the mastery of fire, the development of agriculture, or the invention of the wheel, writing or the steam engine, were the mathematicians and astronomers of Indian civilization: scholars who, unlike the Greeks, were concerned with practical applications and who were motivated by a kind of passion for both numbers and numerical calculations.”
Claiming India to be the true birthplace of our numerals, Ifrah salutes the Indian researchers saying that the "...real inventors of this fundamental discovery, which is no less important than such feats as the mastery of fire, the development of agriculture, or the invention of the wheel, writing or the steam engine, were the mathematicians and astronomers of the Indian civilization: scholars who, unlike the Greeks, were concerned with practical applications and who were motivated by a kind of passion for both numbers and numerical calculations."
He refers to 24 evidences from scriptures from India, whose dates range from 1150 BC until 458 BC. Of particular interest is the work by Indian mathematician Bhaskaracharya known as Bhaskara (1150 BC) where he makes a reference to zero and the place-value system were invented by the god Brahma. In other words,  these notions were so well established in Indian thought and tradition that at this time they were considered to have always been used by humans, and thus to have constituted a "revelation" of the divinities.
"It was only after the eighth century BC, and doubtless due to the influence of the Indian Buddhist missionaries, that Chinese mathematicians introduced the use of zero in the form of a little circle or dot (signs that originated in India),...".
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."
"The Indian people were the only civilization to take the decisive step towards the perfection of numerical notation. We owe the discovery of modern numeration and the elaboration of the very foundations of written calculations to India alone."
"It is clear how much we owe to this brilliant civilization, and not only in the field of arithmetic; by opening the way to the generalization of the concept of the number, the Indian scholars enabled the rapid development of mathematics and exact sciences. 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 India, an aptitude for the study of numbers and arithmetical research was often combined with a surprising tendency towards metaphysical abstractions; in fact, the latter is so deeply ingrained in Indian thought and tradition that one meets it in all fields of study, from the most advanced mathematical ideas to disciplines completely unrelated to 'exact sciences. 
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. "
"Sanskrit means “complete”, “perfect” and “definitive”. 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. "
(source:  The Universal History of Numbers - By Georges Ifrah  p 365 - 441).









Om Tat Sat
                                                        
(Continued...)  




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