There is euphoria in the whole world about India. India's economy and growth is the talk everywhere. Many revolutions are happening. First liberalisation of indian economy, then software boom and finally telecom revolution. There is a march towards knowledge based growth where service sector will have significant place. India' leadership in the form President A.P.J. Abdul kalam and prime Minister Manmohan Singh is major asset. I have been to the two good city of India . Mumbai and Nagpur.Here I can see India transforming into a developed country. Big roads , better tranporation, decent electricity and water, good and knowledgeable people, is what I believe is the evidence of India's growth. I am sure rural areas are also tranforming though not as fast as metros. But surely there life of people is changing.

The reason of difference of growth between Rural and Urban areas is empowered people and PSI (private sector initiative). Empowered people means educated peolple who know what are their rights and what they expect from the government. They force the Govt. to do its duty.If govt. is not performing well they vote them out, approach courts to get justice; and Private sector for the service and always struggle and work hard to get what they deserve. They are quick, learn from their and others ' experience, read a lot and always remain aware of current developments. This enlightenment is due to two reasons , one is the education and secondly their environment. their growth is continous and that is why they are becoming richer and more powerful.
On the other hand rural areas are suffering from collateral side effects of redgressing backwardness. They are becoming more and more poor and less powerful though they are getting benefits of capitalistic consumerism but still they don't have money to buy even basic and cheap commodity. Reasons: history, lack of education and awareness, poor infrastructure( like roads, electricity, water etc), less support from urban counterparts and govt. , big family and sustainance on primary sector only like agriculture and horticulture, lack of funds and capital , very less access to banks and financial institutions. Hence their backwardness is increasing day by day and class struggle is taking roots. Rich are bent on preserving thier stuffs while poors are forced to take other m

Technological discoveries and applications in India

The earliest evidence of technological progress in the Indian subcontinent is to be found in the remains of the Harappan civilization (4000-3000 BC). Archaeological remains point to the existence of well-planned urban centres that boasted of private and public dwellings laid out in orderly fashion along with roads and drainage systems complementing them. The drainage systems were particularly remarkable for the times since they were built underground and were constructed in a manner to allow for regular cleaning. Smaller drains from private homes connected to the larger public drains.

Larger private dwellings were invariably multi-storied and all homes were constructed from standardized fired bricks and provided for separate cooking areas and toilets. Storage facilities for grain and goods for trade were built as were public baths and other buildings intended for various public functions.

Urban centres were often planned near riverine or sea-ports. Accurate weights and measures were in use and ports such as Lothal were developed as export centres of early manufactured products from smelted copper and bronze. Kilns for smelting copper ingots and casting tools were in existence as were metal tools such as curved or circular saws, pierced needles and most significantly, bronze drills with twisted grooves. The drill enabled the production of items with unparalleled precision for the times and could be regarded as an ancient precursor of the modern machine tool.

There is also evidence of planned irrigation systems and it appears that fire and flood control measures to protect farms and villages were also in place. Artisans made use of the wheel and clay pottery was decorated in a variety of colors and designs. Cotton was grown and used to produce textiles.

Urban centres in the Harappan region traded with each other as well as with counterparts in Babylon, the Persian Gulf, Egypt and possibly the Mediteranean. The span of the Harappan civilization was quite extensive, and included much of modern Sindh, Gujarat, Rajasthan, Haryana, Punjab and Western UP.

But prior to it's disappearance, there is also evidence of considerable social decay and disintegration. Excavations from the later phases of the Harappan civilization suggest that population pressures led to greater anarchy in building construction. Urban dwellings became smaller and settlements became more haphazard indicating a breakdown of social mores and structures that promoted urban regulations and enforced construction codes.

Social Conditions and Technological Progress

It is quite possible that the decline in civil society extended to other areas such as agricultural planning and maintenance of irrigations systems making the civilization more vulnerable to natural disasters such droughts, floods, fires or earthquakes - thus contributing to the eventual extinction of that vibrant civilization. This suggests that technological progress cannot be divorced from social conditions that may either encourage the progress of technology or conversely cause civilizations that may be (in relative terms) quite advanced to stagnate and even decline.

For instance, 3000 years after Harappa, we find anecdotal evidence of impressive urban settlements constructed during the Mauryan period. Greek travellers have left behind admiring descriptions of Patliputra - the Mauryan capital. But social strife brought a precipitous end to the grand civilization. The growth of a parasitic, exploitative and socially oppressive elite led to massive social upheavals. In the course of the civil wars, fires and looting destroyed virtually all of the wood-based dwellings including grand palaces and public buildings.

Thus, an entire tradition of wood-based urban construction - (which may have taken several centuries to develop) was destroyed. But it also led to a greater emphasis on the use of more lasting construction materials. The very social conditions that destroyed technological progress in one direction gave birth to technological progress in another. Sculptural finds from the Mauryan period indicate that Mauryan sculptors of that time had achieved a high degree of proficiency in working with stone. They must have had tools and implements that enabled them to create smoothly modelled and highly polished representations of human and animal figures. Later civilizations in India employed these skills not only for the purposes of sculpting but for creating entire monuments constructed from a variety of hard building materials. For instance, various methods for preparing cements were developed, and by the 7th century, cement of highly durable quality came into use in the construction of important monuments that survive to this day.

The Impetus for Metallurgy

Monumental architecture required considerable advances in the technology of lifting, loading and transportation of construction materials, building construction ramps, scaffolding, and related tools and implements. As in ancient Egypt or Babylon, appropriate techniques also had to be developed and implemented in India. But more importantly, stone-based construction presupposes the existence of hard metal based tools and implements for cutting and shaping stone. The discovery of iron thus played an essential role in the development of monumental architecture in India which may have in turn given a further impetus to the development of metallurgical skills.

As early as the 4th C. BC, Kautilya's Arthashastra had a section outlining the processes for metal extraction and alloying. Later Sanskrit texts talk about assessing metal purity and describe techniques for achieving metal purity. Various alloying techniques were in use and some may have had their origin in the Harappan or Vedic periods. (For instance, there are references in the Vedic literature that suggest that copper vessels were coated with tin so as to prevent milk from going sour.)

A combination of scholarly investigation and broad dissemination of practical techniques propelled the development of metallurgical skills. The fifth century Iron Pillar of Delhi is a remarkable example of those skills. Standing over 23 feet high it consists of a single piece of iron and has weathered over 1500 monsoons without showing any signs of rust. The pillar is made of wrought iron with an iron content of 99.72 % and appears to have been protected from rust by the application of a thin coating of manganese dioxide.

By the 12th century, construction engineers were using iron girders and beams on a scale unknown in any other part of the world. The most significant use of iron beams was in the temples of Puri and Konarak. The Puri temple contains 239 iron beams and one of the beams in Konarak is 35 feet long. All are 99.64 percent iron and were produced in a similiar manner to the Delhi iron pillar.

During the middle ages, India acquired a reputation for producing very high quality steel and was also able to extract zinc from it's ore by the 14th century. Bidari (an alloy of copper, lead and tin developed in the Deccan) was also extensively used.

Unsurprisingly, developments in metallurgy also had their impact on artillery production. According to A. Rahman (Science in Medieval India), by the 16th century, the heaviest guns in the world were being cast in India and a variety of weapons were being manufactured in the subcontinent. The Jaigarh cannon factory was one of India's best and before the crucial battle of 1857, the Jaipur Rajputs laid claim to owning Asia's largest cannon. Yet, none of the Rajput cannons were ever used to confront the British who succeeded in conquering the sub-continent without ever having to fight against the country's best equipped armies, thus demonstrating that technological progress is not an end in itself.

Social Needs and Technological Applications

More often than not, social needs (as arising from geographic, climactic or living conditions) have been the primary impetus for technological progress in society. The long dry months that most regions of India had to deal with led to numerous innovations in water-management techniques. Irrigation canals, wells of different types, storage tanks and a variety of water-harvesting techniques were developed throughout the sub-continent. The Harappans were not alone in creating water-management solutions. Irrigation works of enormous size were undertaken time and time again. The reservoirs at Girnar in Kathiawar (built in the 3rd C. BC) had an embankment over 100 ft thick at the base. The artificial lake at Bhojpur (near Bhopal) commisioned by Raja Bhoj in the 11th C covered 250 sq. miles. In the South, also in the 11th C., an artificial lake fed by the Kaveri river had a 16-mile long embankment with stone sluices and irrigation channels. Rajput kings built artificial lakes throughout the desert state of Rajasthan, but irrigation schemes were essential to agricultural prosperity even in Kashmir, Bengal and the delta regions of the South.

The need for accurate prediction of the monsoons spurred developments in astronomy while the intense heat of the summer led to innovations in architecture. In Rajasthan and Gujarat step-wells were built deep into the ground - sometimes descending as much as a hundred feet and large scale observatories were built in Benaras, Mathura and Ujjain to facilitate advances in the astronomical sciences. Bengal became known for it's fine muslins that were light and airy to wear in the warm and humid climate of the state. Techniques for pickling and preserving fruits, vegetables, fish and meats were developed throughout the country to prevent or delay spoilage. Manually operated cooling devices were also invented. The Arthashatra mentions the variyantra (probably a revolving water spray for cooling the air). Technology thus arose in response to compelling material needs.

Scientific Rationalism and Technological Efficacy

But technological progress also requires a favorable social milieu. A foundation of scientific knowledge, rational thinking and practical experimentation can be essential to the process of making technological discoveries (although the application of already known technologies can occur more easily). As mentioned in the essay: Development of Philosophical Thought and Scientific Method in Ancient India numerous technological inventions occurred in parallel with developments in rational philosophy and advances in mathematics and natural sciences.

This is not to say that Indian society was entirely rational. In all ancient societies (and even modern ones), superstitions, religious beliefs, reliance on astrology, numerology or the advice of 'seers', palmists and fortune-tellers have impinged on the scientific process and consequently hindered the progress of technology. In the civilizations of ancient Egypt, Babylon and India - we see numerous instances of scientifically accurate statements and practical truths mixed up with religious myths and popular superstitions. This was especially true in the science of medicine. Genuine cures were listed with unscientific practices without clear distinction. But during the rational period in India the emphasis on the scientific method led to a much greater level of veracity with respect to the efficacy of different medicines and medical procedures.

The more accurately the Indian medical practitioner was able to observe reality, understand bodily functions and test the efficacy of popular medical techniques, the more successful were the prescribed cures. Dissection of corpses and careful monitoring of different diseases was an important component in the study and practice of medicine. With greater success in treatment came greater confidence and allowed medical practitioners to conduct surgical procedures using a variety of surgical tools - albeit primitive in comparison to modern surgical equipment.

Procedures for inducing unconsciousness or numbing body parts that were to be operated on were required and developed. Tools for excision, incision, puncturing, probing, organ or part extraction, fluid drainage, bloodletting, suturing and cauterization were developed. Various types of bandages and ointments were used as were basic procedures for ensuring cleanliness and limiting contamination. The caesarian section was known, bone-setting reached a high degree of skill, and plastic surgery developed far beyond anything known elsewhere at the time. Indian surgeons also became proficient at the repair of noses, ears and lips lost or injured in battle or by judicially mandated mutilation. By the 1st C. AD the foundations of this rather evolved medical system were in place and by the 4th C. - much of this knowledge was standardized and available in the classical textbooks of Charaka and Susruta.

While all ancient societies cherished and admired the skills of the medical practitioner, it was the more determined adoption of the scientific approach that enabled Indian medicine to make a quantum leap over the older medical systems of the time.

{Progress in medicine also led to developments in chemistry and chemical technologies. The manufacture of alkaline substances, medicinal powders, ointments and liquids was systematized, as were chemical processes relating to the manufacture of glass. Advances in food processing (such as manufacture of sugar, condiments and edible oils) took place as did the manufacture of personal hygiene products and beauty aids (such as shampoos, deodorizers, perfumes and cosmetics).}

Cultural Mores and Technological Innovation

Cultural preferences also impelled technological innovations. During the rational period, considerable attention was paid to human psychological processes. The analysis of moods and emotions led to elaborate theories on the role of color and design in inducing psychological well-being. Treatises on art and architecture emphasized the importance of color. As a result, the use of color in decorating household artifacts, textiles, furniture, and public and private dwellings became widely prevalent and a matter of conscious choice.

Discoveries concerning the manufacture and application of natural and artificial dyes quickly followed. Block printing, tie and dye, and other textile-dyeing techniques were popularized. The use of mordents in color-fast dyeing of textiles became known as did the knowledge of lacquers that could be applied to wood

Development of Philosophical Thought and Scientific Method in Ancient India

Contrary to the popular perception that Indian civilization has been largely concerned with the affairs of the spirit and "after-life", India's historical record suggests that some of the greatest Indian minds were much more concerned with developing philosophical paradigms that were grounded in reality. The premise that Indian philosophy is founded solely on mysticism and renunciation emanates from a colonial and orientalist world view that seeks to obfuscate a rich tradition of scientific thought and analysis in India.

Much of the evidence for how India's ancient logicians and scientists developed their theories lies buried in polemical texts that are not normally thought of as scientific texts. While some of the treatises on mathematics, logic, grammar, and medicine have survived as such - many philosophical texts enunciating a rational and scientific world view can only be constructed from extended references found in philosophical texts and commentaries by Buddhist and Jain monks or Hindu scholars (usually Brahmins).

Although these documents are usually considered to lie within the domain of religious studies, it should be pointed out that many of these are in the form of extended polemics that are quite unlike the holy books of Christianity or Islam. These texts attempt to debate the value of the real-world versus the spiritual-world. They attempt to counter the theories of the atheists and other skeptics. But in their attempts to prove the primacy of a mystical soul or "Atman" - they often go to great lengths in describing competing rationalist and worldly philosophies rooted in a more realistic and more scientific perception of the world. Their extensive commentaries illustrate the popular methods of debate, of developing a hypothesis, of extending and elaborating theory, of furnishing proofs and counter-proofs.

It is also important to note that originally, the Buddhist world view was an essentially atheistic world view. The ancient Jains were agnostics, and within the broad stream of Hinduism - there were several heterodox currents that asserted a predominantly atheistic view. In that sense, these were not religions as we think of today since the modern understanding of religion presumes faith or belief in a super-natural entity.

That so many scholars from each of these philosophical schools felt the imperative to prove their extra-worldly theories using rationalist tools of deductive and inductive logic suggests that faith in a super-natural being could not have been taken for granted. This is borne out by the memoirs of Hieun Tsang (the Chinese chronicler who traveled extensively in India during the 7th C. AD) who describes the merchants of Benaras as being mostly "unbelievers"! He also wrote of intense polemics and debates amongst followers of different Buddhist sects.

Similiarly, there is other evidence that suggests that amongst the intellectuals of ancient India, atheism and skepticism must have been very powerful currents that required repeated and vigorous attempts at persuasion and change. Nevertheless, over centuries, the intellectual discords between the believers and non-believers became more and more muted. The advocates of mystic idealism prevailed over the skeptics, so that eventually, (at the popular level) each of these philosophies functioned as traditional religions with their pantheon of gods and goddesses enticing and lulling most into an intellectual stupor. But at no point were the advocates of "pure faith" ever powerful enough to completely extinguish the rationalist current that had so imbued Indian philosophy.

Early Rationalist Schools
One of the most ancient of India's rationalist traditions is the "Lokayata". Maligned and discredited by the evangelicals of mystical Buddhism and Vedantic Hinduism, their world view was sharply atheistic and scientific for their time. Unlike those who believed in reincarnation or an after-life, and in the indestructibility of the human soul - they refused to make artificial distinctions between body and mind. They saw the human mind as part and parcel of the human body - not as some separate entity that could have an independent existence from the human body. They acknowledged nothing but the material human body and the material universe around it. They rejected sacrificial gifts and offerings for the after-life as was common amongst followers of Brahmanical Hinduism during the time of Medhatithi in A.D 900 (a commentator on the writings of Manu who acknowledges that the Lokayatas were atheists or non-believers.)

For instance, they ridiculed the Brahmanical rituals of animal sacrifice: "If a beast slain in the Jyotistoma rite itself goes to heaven, Why then does not the sacrificer also offer his father?"

"If beings in heaven are gratified by our offerings made here, Then why not give the food down below to those who stand on the housetop?"

"If offerings produce gratification to beings who are dead, why make provisions for travellers when they start on a journey?"

"If he who departs from the body goes to another world, How is it that he comes not back again, restless for love of his kindred?"

The Lokayatas dismissed the Vedic priests and their Vedic mantras as nothing but a means of livelihood for those lacking in genuine physical or mental abilities. Instead, they gave primacy to human sense-perception, and through the application of the inferential process - they developed their theories of how the world worked.

One of the most notable aspects of the Lokayata belief system was their intuitive understanding of dialectics in nature. Many argued the mind-body separation as follows: Since the body is made up of things lacking consciousness - but the mind is a conscious entity - mind and body must necessarily be different - and consciousness must imply the existence of something else akin to the "soul". The Lokayatas countered this by citing the example of fermentation - how an intoxicating drink could be produced from something that was not itself an intoxicant. In essence they had discovered the principle that the whole was greater than the sum of it's parts. That physical and chemical processes could lead to dramatic changes in the properties of the substances combined. They were able to understand how special transformations could produce new qualities that were not evident in the constituent elements of the newly-created entity.

As keen observers of nature, they were probably amongst the first to understand the nature of different plants and herbs and their utility to human well-being. As such, it is likely that Indian medicine gradually evolved from the early scientific knowledge and understanding of the Lokayatas. Since the Lokayatas believed that consciousness emerged from the living human body, and ended with it's death - it is more than likely that the widely prevalent Indian custom of cremating the dead also originated amongst them.

This is not to say that the Lokayatas' understanding of the world was as elaborate and precise as that provided by today's science. By the standards of the 20th century, some of their formulations could be considered primitive and inadequate. That is only to be expected. Knowledge of science has expanded considerably since their times. But what is more important is that their world view was driven by a rational and scientific approach.

For instance, some later philosophical schools countered the Lokayata arguments concerning mind-body unity by bringing up the evidence of memory. Nyaya-Vaisesika philosophers like Jayanta and Udayana pointed out that the process of daily eating meant that the human body was constantly changing. The process of ageing also pointed to how the human body was ever-changing. Yet, an old person could remember in detail an incident from childhood. In other words - they tried to argue that memory was evidence of a human soul that existed beyond the mere physical body. Yet, we know today that memory is but a combination of proteins that can survive the length of human existence. There is both continuity and change in nature. The Lokayata world view howsoever sketchy and incomplete was not in contradiction with modern science.

If some of their characterizations required later revisions or refinement, or even corrections, it didn't take away from their fundamentally scientific approach. Their inadequacies were a consequence of incomplete knowledge and the understandable inability to see all the complexities of nature that we are now able (through advanced scientific instruments and centuries of accumulated knowledge). Their errors did not, however, stem from stubborn faith or deliberate rejection of reality and real-world phenomenon.

In practice, (according to some historians) India's ancient Tantric followers may have also had a largely rational world view, which sprang from a practical mindset and was impaired only by the limited amount of scientific knowledge available to humanity at that time. Critics of the tantrics dismissed them as sexually obsessed hedonists. But they failed to acknowledge that the early tantrics had an intuitive scientific streak and their understanding of sexual reproduction is probably what may have also impelled them to develop basic agricultural tools and other implements. In that sense, they were India's early technologists.

The Age of Science and Reason
But even amongst those Indian philosophers who accepted the separation of mind and body and argued for the existence of the soul, there was considerable dedication to the scientific method and to developing the principles of deductive and inductive logic. From 1000 B.C to the 4th C A.D (also described as India's rationalistic period) treatises in astronomy, mathematics, logic, medicine and linguistics were produced. The philosophers of the Sankhya school, the Nyaya-Vaisesika schools and early Jain and Buddhist scholars made substantial contributions to the growth of science and learning. Advances in the applied sciences like metallurgy, textile production and dyeing were also made.

In particular, the rational period produced some of the most fascinating series of debates on what constitutes the "scientific method": How does one separate our sensory perceptions from dreams and hallucinations? When does an observation of reality become accepted as fact, and as scientific truth? How should the principles of inductive and deductive logic be developed and applied? How does one evaluate a hypothesis for it's scientific merit? What is a valid inference? What constitutes a scientific proof?

These and other questions were attacked with an unexpected intellectual vigour. As keen observers of nature and the human body, India's early scientist/philosophers studied human sensory organs, analyzed dreams, memory and consciousness. The best of them understood dialectics in nature - they understood change, both in quantitative and qualitative terms - they even posited a proto-type of the modern atomic theory. It was this rational foundation that led to the flowering of Indian civilization.

This is borne out by the testaments of important Greek scientists and philosophers of that period. Pythagoras - the Greek mathematician and philosopher who lived in the 6th C B.C was familiar with the Upanishads and learnt his basic geometry from the Sulva Sutras. (The famous Pythagoras theorem is actually a restatement of a result already known and recorded by earlier Indian mathematicians). Later, Herodotus (father of Greek history) was to write that the Indians were the greatest nation of the age. Megasthenes - who travelled extensively through India in the 4th C. B.C also left extensive accounts that paint India in highly favorable light (for that period).

Intellectual contacts between ancient Greece and India were not insignificant. Scientific exchanges between Greece and India were mutually beneficial and helped in the development of the sciences in both nations. By the 6th C. A.D, with the help of ancient Greek and Indian texts, and through their own ingenuity, Indian astronomers made significant discoveries about planetary motion. An Indian astronomer - Aryabhata, was to become the first to describe the earth as a sphere that rotated on it's own axis. He further postulated that it was the earth that rotated around the sun and correctly described how solar and lunar eclipses occurred.

Because astronomy required extremely complicated mathematical equations, ancient Indians also made significant advances in mathematics. Differential equations - the basis of modern calculus were in all likelihood an Indian invention (something essential in modeling planetary motions). Indian mathematicians were also the first to invent the concept of abstract infinite numbers - numbers that can only be represented through abstract mathematical formulations such as infinite series - geometric or arithmetic. They also seemed to be familiar with polynomial equations (again essential in advanced astronomy) and were the inventors of the modern numeral system (referred to as the Arabic numeral system in Europe).

The use of the decimal system and the concept of zero was essential in facilitating large astronomical calculation and allowed such 7th C mathematicians as Brahmagupta to estimate the earth's circumferance at about 23,000 miles - (not too far off from the current calculation). It also enabled Indian astronomers to provide fairly accurate longitudes of important places in India.

The science of Ayurveda - (the ancient Indian system of healing) blossomed in this period. Medical practitioners took up the dissection of corpses, practised surgery, developed popular nutritional guides, and wrote out codes for medical procedures and patient care and diagnosis. Chemical processes associated with the dying of textiles and extraction of metals were studied and documented. The use of mordants (in dyeing) and catalysts (in metal-extraction/purification) was discovered.

The scientific ethos also had it's impact on the arts and literature. Painting and sculpture flourished even as there were advances in social infrastructure. Universities were set up with dormitories and meeting halls. In addition, according to the Chinese traveller, Hieun Tsang, roads were built with well-marked signposts. Shade trees were planted. Inns and hospitals dotted national highways so as to facilitate travel and trade.

India's rational age was thus a period of tremendous intellectual ferment and vitality. It was a period of scientific discovery and technological innovation. Accompanied by challenges to caste discrimination and rigidity and religious obscurantism - it was also a period of great social upheaval that eventually led to society becoming more democratic, allowing greater social interaction between members of different castes and expanding opportunities for social mobility amongst the population. Social ethics drew considerable attention in this period. Rules of engagement during war were constructed so as to eliminate non-military casualties and destruction of pasture-land, crop-land or orchards. The notion of chivalry in war was popularized - it meant not attacking fleeing or injured soldiers. It also required warring armies to provide safe passage to women, children, the elderly and other non-combatants.

The rational period thus saw progress on several fronts. Not only did it create an enduring foundation for India's civilization to develop and mature - it has also had it's impact on the growth of other civilizations. In fact, India's rational period served as a vital link in the long and varied chain of human progress. Although colonial history has attempted to usurp this collective heritage of the planet and make it exclusively euro-centric, it is important to note that fundamental and important discoveries in science and innovations in technology have come from many different parts of the globe, albeit at different times and stages of world civilization. India made significant contributions in this regard. If India is to fully recover from the depredations of colonial rule, it is imperative that we don't forget the achievements of this inspiring epoch.

Note: References to Greece and India are used in a very broad way. In the ancient world, the 'Greek' world included most Mediterranean nations - including those of North Africa, Palestine, modern-day Turkey, Bulgaria and Yugoslavia. References to India apply to the general expanse of the sub-continent.

For a somewhat more detailed outline of the different rational schools and their emergence in India, see Philosophical development from Upanishadic theism to scientific realism which outlines the epistemology of the Nyaya school, the Jain system of Syadavada, theories of causality and the atomic theories of Jain and Buddhist philosophers

Technorati Profile

History of the Physical Sciences in India

In all early civilizations, the study of the physical sciences was neither formalized nor separated from other branches of knowledge. And at least initially, there were few conscious attempts to study the theory of science independently of the practical innovations and technologies that required some application of scientific principles. In most cases, technological discoveries took place without any knowledge of the underlying scientific principles, through hit and trial, and by experience. Sometimes there was a vague or approximate awareness of the science, but the predominant focus remained on the utilitarian aspects of the technique, on practical efficacy, as opposed to how and why something worked or didn't work.

In India, the earliest applications of chemistry took place in the context of medicine, metallurgy, construction technology (such as manufacture of cement and paints) and in textile production and dyeing. But in the process of understanding chemical processes, there also emerged a concomitant interest in attempting to describe the basic elements of matter - what they were composed of, and how they interacted with each other to produce new substances. Natural phenomenon were studied in the context of tides, rainfall, appearance of the sun, the moon and stellar formations, changes in season, weather patterns and agriculture. (For instance, Vedic literature mentions the condensation of water vapour from seas and oceans due to evaporation (caused by the sun's heat) and the subsequent formation of clouds and rain.) This naturally led to theories about physical processes and the forces of nature that are today studied as specific topics within the fields of chemistry and physics.

Philosophy and Physical Science

While it is hard to say which precedes which - theory or practice - clearly there is a dialectical relationship between both, and the neglect of either leads to the death of science. Religious beliefs, particularly religious taboos and irrational indoctrination towards mystical or magical phenomenon, or adherence to false superstitions can often pose as serious impediments to the advance of science, and play an important role in whether the why and the how of physical causes can be safely and usefully explored.

Societies that believed that only the "gods" knew the secrets of nature, and that it was futile for humans to attempt to unravel the mysteries of the universe were naturally incapable of making any substantial progress in the realm of the sciences. Even in societies where there were no formal religious taboos in understanding real-world phenomenon in a scientific way, the power and the influence of the priests could serve as an obstacle to scientific progress. For instance, in a society where ritual practices alone were considered sufficient in achieving desired goals, there would naturally be little scope for serious investigation into the properties and laws of nature.

While ancient India did not generally suffer from the first affliction (of religious opposition to science), it did suffer from the second (the proliferation of rituals and superstitions). The progress of science in India was thus inextricably linked to challenges to the domination of the priests, and resistance to the proliferation of rituals and sacrifices. It was necessary to at least argue that rituals alone were insufficient in producing desired results, and that some measure of rational observation of the world was necessary in shaping human destiny. It is therefore no accident that, by and large, developments in science and technology came in parallel with the advance of rational philosophy in India. (See Development of Philosophical Thought and Scientific Method).

In the earliest scientific texts such has those of the Vaisheshikas (6th C BC or possibly earlier), (see Philosophical Development from Upanishadic Theism to Scientific Realism), there was a rudimentary attempt at recording the physical properties of different types of plants and natural substances. There was also an attempt at summarizing and classifying the observations made about natural phenomenon. Intuitive formulations and approximate theories about the composition of matter and physical behavior followed. Thus, although the earliest applications of physics and chemistry in India (as in other ancient societies), took place without involving much theoretical knowledge or insight into these branches of science, there were elements of basic scientific investigation and scientific documentation in these early rational treatises. Primitive and tentative as these steps were, they were nevertheless crucial to humanity reaching it's present stage of knowledge in the fields of physics, chemistry, botany, biology and other physical sciences.

Particle Physics

Although particle physics is one of the most advanced and most complicated branches of modern physics, the earliest atomic theories are at least 2500 years old. In India, virtually every rational school of philosophy (whether Hindu, Buddhist or Jain - see Philosophical Development from Upanishadic Theism to Scientific Realism) had something to say on the nature of elementary particles, and various schools of thought promoted the idea that matter was composed of atoms that were indivisible and indestructible. Later philosophers further elaborated on this notion by positing that atoms could not only combine in pairs (dyads) but also in threes (triads) - and that the juxtaposition of dyads and triads determined the different physical properties of substances seen in nature. The Jains also postulated that the combinations of atoms required specific properties in the combining atoms, and also a separate "catalyst" atom. In this way, the earlier atomic theories became converted into a molecular theory of matter. While many details of these theories no longer stand the test of scientific validity, there was much in these formulations that was conceptually quite advanced and sophisticated for it's time.

{Although it may be just a coincidence, but the development of the Jain molecular theory appears to parallel practical developments in other fields such as medicine or metallurgy where the vital role of catalysts had been observed and carefully documented. Indian medical texts had postulated that proper human digestion and the successful absorption of medicinal pills and potions also required the presence of "catalytic" substances. The requirement of catalytic substances relating to the manufacture of acids and alkalis (relevant to medicinal and surgical applications) had also been documented, as had the role of suitable catalysts in metallurgical processes, and in the manufacture of color-fast dyes. (Today, much more is known about catalytic processes, as a variety of minerals, vitamins and enzymes have been identified as playing a key role (as catalysts) in a range of essential chemical processes that take place in our bodies, as do catalytic compounds in other physical processes).}

Atomic/molecular theories were also utilized in (albeit speculative) explanations of chemical changes caused by heat. Prasastapada proposed that the taijasa (heat) factor affected molecular groupings (vyuhas), thus causing chemical changes. Two competing theories attempted to provide a more detailed explanation of the process (as applied to the baking/coloring of a clay pot through firing): the Pilupakavada theory, as proposed by the Vaisesikas held that the application of heat (through fire, for instance) reduced the molecules of the earthen pot into atoms; and the continued application of heat caused the atoms to regroup creating new molecules and a different color. The Pitharapakavada theory offered by the Nyayikas (of the Nyaya school) disagreed, suggesting that the molecular changes/transformations took place without a breakdown of the original molecules into basic atoms, arguing that if that happened, there would also have to be a disintegration of the pot itself, which remained intact, but only changed color.

An intuitive understanding of kinetic energy appears in the texts of Prasastapada and the the Nyaya-Vaisesikas who believed that all atoms were in a state of constant activity. The concept of parispanda was propounded to describe such molecular/atomic motion, whether it be whirling, circling, or harmonic.

Optics and Sound

The earliest of the Indian rationalists also attempted to provide theories on the nature of light and sound. Like the ancient Greeks, the eye was assumed to be a source of light by the early Indian philosophers, and this error wasn't corrected until the 1st C AD when Susruta posited that it was light arriving from an external source at the retina that illuminated the world around us. (This was reiterated by Aryabhatta in the 5th C). In other respects, the earlier philosophers were more on the mark, with Cakrapani suggesting that both sound and light traveled in waves, but that light traveled at a much higher speed. Others like the Mimamsakas imagined light to comprise of minute particles (now understood to be photons) in constant motion and spreading through radiation and diffusion from the original source.

The wave character of sound was elaborated on by Prastapada who hypothesized that sound was borne by air in increasing circles, similar to the movement of ripples in water. Sound was understood to have its own reflection - pratidhvani (echo). Musical pitches (sruti) were seen as caused by the magnitude and frequency of vibrations. A svara (tone) was believed to consist of a sruti (fundamental tone) and some anuranana (partial tones or harmonics). Musical theory was elaborated on the basis of concepts such as jativyaktyoriva tadatamyam (genus and species of svara), parinama (change of fundamental frequency), vyanjana (manifestation of overtones), vivartana (reflection of sound), and karyakaranabhava (cause and effect of the sound).

In the 6th C. Varahamihira discussed reflection as being caused by light particles arriving on an object and then back-scattering (kiranavighattana, murcchana). Vatsyayana referred to this phenomenon as rasmiparavartana, and the concept was adapted to explain the occurrence of shadows and the opacity of materials. Refraction was understood to be caused by the ability of light to penetrate inner spaces of translucent or transparent materials and Uddyotakara drew a comparison with fluids moving through porous objects - tatra parispandah tiryaggamanam parisravah pata iti.

(Al Haytham (b, Basra, worked in Cairo, 10th C) who may have been familiar with the writings of Aryabhatta, expounded a more advanced theory of optics using light rays, diagrammatically explaining the concepts of reflection and refraction. He is particularly known for elucidating the laws of refraction and articulating that refraction was caused by light rays traveling at different speeds in different materials.)

Astronomy and Physics

Just as the study of Mathematics in India received an impetus from the study of astronomy, so did the study of Physics. As mentioned in the essay on mathematics, Aryabhatta (5th-6th C) made pioneering discoveries in the realm of planetary motion. This led to advances in the definition of space and time measuring units and better comprehension of concepts such as gravitation, motion and velocity.

{For instance, Yativrasabha's work Tiloyapannatti (6th C) gives various units for measuring distances and time and also describes a system of infinite time measures. More significantly, Vacaspati Misra (circa AD 840) anticipated solid (co-ordinate) geometry eight centuries before Descartes (AD 1644). In his Nyayasuchi-nibandha, he states that the position of a particle in space could be calculated by assuming it relative to another and measuring along three (imaginary) axes.

The study of astronomy also led to a great interest in quantifying very large and very small units of time and space. The solar day was considered to be made up of 1,944,000 ksana (units of time), according to the Nyaya-Vaisesikas. Each ksana thus correspnded to .044 seconds. The truti was defined as the smallest unit of time i.e. 2.9623*10-4. The Silpasastra records the smallest measure of length as the paramanu i.e. 1/349525 of an inch. This measurement corresponds to the smallest thickness of the Nyaya-Vaisesika school - the trasarenu, which was the size of the smallest mote visible on a sunbeam as it shone into a dark room. Varahamihira (circa AD sixth century) posited that 86 trasarenu were equal to one anguli i.e. three-fourths of an inch. He also suggested that 64 trasarenu were equal to the thickness of a hair.}

The Laws of Motion

Although the earliest attempts at classifying different types of motion were made by the Vaisesikas, Prasastapada took the study of the subject much further in the 7th C AD, and it appears from some of his definitions that at least some of the concepts he enunciated must have emerged from a study of planetary motion. In addition to linear motion, Prasastapada also described curvilinear motion (gamana), rotary motion (bhramana) and vibratory motion. He also differentiated motion that was initiated by some external action from that which took place as a result of gravity or fluidity.

He was also aware of motion that resulted from elasticity or momentum, or as an opposite reaction to an external force. He also noted that some types of actions result in like motion, and others in opposite motion, or no motion at all - the variations arising from the internal and inherent properties of the interacting objects.

Prasastapada also noted that at any given instance, a particle was capable of only a single motion (although a body such as a blowing leaf composed of multiple particles may experience a more complex pattern of motion due to different particles moving in different ways) - an important concept that was to facilitate in later quantifications of the laws of motion.

In the 10th C. Sridhara reiterated what had been observed by Prasastapada, and expanded on what he had documented. Bhaskaracharya (12th C), in his Siddhanta Siromani and Ganitadhyaya, took a crucial first step in quantification, and measured average velocity as v=s/t (where v is the average velocity, s is distance covered, and t is time).

For their time, Prasastapada's work, and Sridhara and Bhaskaracharya's later elaborations ought to be considered quite significant. However, one of the weaknesses of later Indian treatises was a failure to follow up with further attempts at quantification and conceptual elaboration. For instance, several types of motion had been earlier assigned to unseen causes. There was no subsequent attempts to solve these mysteries, nor was there the realization that the invisible cause behind various types of motion could be conceptually generalized and formally characterized and expressed in an abstract way, through a mathematical formula as was done by Newton a few centuries later.

Experimentation versus Intuition

In fact, the next major step in the study of motion was to take place in England, when the ground for scientific investigation was prepared by the likes of Roger Bacon (13th C) who described the great obstacles to learning as regard for authority, force of habit, theological prejudice and false concept of knowledge. A century later, Merton scholars at Oxford developed the concept of accelerated motion (an important precursor to the understanding that force=mass*acceleration) and took rudimentary but important steps in the measurement and quantification of heat in a rod. One of the hallmarks of British (and European) science thereafter was the fusion of theory and practice, unlike the generally intuitive approach followed by Indian scientists when investigating fields other than astronomy.

For instance, right up to the 16th C, Indian scientists continued to record useful scientific observations, but without serious attempts at quantification, or deeper investigation into the physical and chemical causes of what they observed. Magnetism is referred to by Bhoja (10th-11th C) as well as by Sankara Misra later. Udayana (10th-11th C) recognized solar heat as the heat-source of all chemical changes, and also that air had weight in a discussion of balloons in his Kiranawali. Vallabhacharya (13th C) in his Nyaya-lilavati pointed out the resistance of water to a sinking object, but did not go on to discuss the principle any further. Sankara Misra (15th-16th C) noted the phenomenon of electrostatic attraction after he had observed how grass and straw were attracted by amber. But the cause was deemed adrishta (unseen cause). He also recorded some awareness of the concept of kinetic energy and in his Upaskara dwelt on the properties of heat, and tried to relate the process of boiling to evaporation. In the same treatise, Sankara Misra also gave examples of capillary motion citing the ascent of sap from root to stem in a plant and the ability of liquids to penetrate porous vessels. He also wrote about surface tension, and posited sandrata (viscosity) as the cause behind the cohesion of water molecules and the smoothness of water itself.

The Social Milieu

Yet, unlike in astronomy, where many Indian scientists got very intensely involved, and were driven to work towards a considerable degree of accuracy, no such compulsions appeared to guide Indian scientists in other fields. Whereas Indian astronomers were compelled to develop useful mathematical formulae and explore the mysteries of the universe in greater depth - in other fields of scientific investigation, Indian scientists seemed to remain content with intuitive and general observations, tolerating a far greater degree of vagueness and imprecision. The answer to this apparent inconsistency may lie in the social milieu. The study of astronomy was triggered partly by practical considerations such as the need for accurate monsoon prediction and rainfall mapping, but perhaps even more so, by the growing demand for "good" astrologers. The obsession with astrological charts - both amongst the royalty and mercantile classes led to considerable state patronage of intellectuals who wished to pursue the study of astronomy. Patronage was also available for alchemists - for those attempting to discover the "elixir" of life. But support for modern scientific research as was beginning to take shape in 14th C Oxford was generally lacking.

The situation prevalent in 15th-16th C Italy was not significantly different, and Leonardo Da Vinci (1452-1519) was particularly frustrated that there was not sufficient interest in his many inventions and how those with means failed to distinguish genuine scientific activities from quackery and the work of charlatans. But Da Vinci was convinced that dedication to scientific truth would eventually prevail. "For nature, as it would seem, takes vengeance on such as would work miracles and they come to have less than other men who are more quiet. And those who wish to grow rich in a day shall live a long time in great poverty, as happens and will to all eternity happen to the alchemists, the would-be creators of gold and silver, and to the engineers who think to make dead water stir itself into life with perpetual motion, and to those supreme fools, the necromancer and the enchanter."

Although Raja Bhoja's Somarangana-sutradhara (circa AD 1100) describes many useful mechanical inventions, and the use of levers and pulleys is described in numerous other Urdu, Persian and Arabic texts in India and the Middle East, Da Vinci's notes on mechanics, the study of levers of different kinds, cantilevers, pulleys and gears in combination, varied gadgetry, bridges, and studies of flight were of a truly pioneering nature, and exceeded in complexity and breadth any civil and mechanical engineering treatise that had preceded him.

And even though in his time, Da Vinci's works were not especially appreciated, Western Europe was in the midst of a monumental change in it's attitude towards science and technology. A century later, the momentum towards the modern scientific era was to gather considerable pace, and eventually the European Renaissance created an environment where the ideas of Da Vinci and Francis Bacon (15-16th C England - who stressed the importance of the experimental method in science) were able to blossom and flourish.

But at the same time in India, several factors posed as hindrances to the development of modern science. In comparison to Europe, India enjoyed a relatively milder climate, and the production of necessities was deemed sufficient to satisfy the population of the time. The courts - whether Mughal or regional spent a good part of their rich treasuries on cultivating the fine arts and promoting the manufacture of luxury goods and decorative objects of exquisite beauty. Science and technology simply attracted little attention (except when it came to improving the tools of war).

The growing influence of religion - whether Quranic or Brahminical also had it's negative effect. While the Quran claimed that all the world's knowledge was already described in it, Brahminical orthodoxy created a sharp divide between the mental and the physical and thus prevented scientists from going beyond passive observation and intuition to practical experimentation, active theorizing and quantification. Whereas Akbar and Jehangir were not averse to science, and the latter took an active interest in books on botany and zoology, it appears from anecdotal accounts that Aurangzeb had a decidedly skeptical attitude towards the sciences. Although some patronage was available in the regional courts, (and outside the courts), alchemy, astrology, study of omens, numerology and other semi-rational and irrational traditions drew much more attention, and thus distracted from genuine scientific pursuits.

On the other hand, European scientists drew on the best works produced in the East - studying foreign documents with due diligence, often accepting little at face value - but instead verifying the results with apparatus and scientific measuring tools of their own creation. There was a time when such had also been the case in ancient India - but over time (due to both internal and external factors) - India's scientific spirit got eroded. Thus Europe was not only able to catch up with the knowledge of India and the East, it was able to rapidly surpass it.

Since independence, Indian scientists have been provided the opportunity of narrowing the gap, and in some fields have done especially well. However, the quality of science education for the masses still needs considerable improvement. On the one hand, the study of the physical sciences in India needs to be accompanied with practical demonstrations and more experimentation as is common practice in the West. In many instances, tools and apparatus used to demonstrate and quantify scientific phenomenon need to be modernized or improved. On the other hand, there also needs to be somewhat greater appreciation of the intuitive approach that has been the hallmark of ancient and medieval Indian science. The conceptual elegance of some earlier formulations, and the facility to inform and educate through analogy is also something that can be learned from the Indian tradition.

It may also be noted that in terms of pedagogy, the standard Western texts are not always as useful. Often, the teaching of physics and chemistry becomes too esoteric for the average student. There is excessive abstraction in most text books, and undue theoretical complexity is thrust upon relatively young students. In contrast, the Indian approach with it's stress on observation of natural phenomenon, and epistemological approach to understanding each field are much easier to grasp for beginners and intermediate students. Once the student understands the basics, and develops a good intuitive way of perceiving scientific phenomenon - the complexities and mathematical abstractions can follow - and the world of the physical sciences can be opened up to more than just the few who are able to transcend the complexities and difficulties that accompany the study of these branches of science today.

History of Mathematics in India

In all early civilizations, the first expression of mathematical understanding appears in the form of counting systems. Numbers in very early societies were typically represented by groups of lines, though later different numbers came to be assigned specific numeral names and symbols (as in India) or were designated by alphabetic letters (such as in Rome). Although today, we take our decimal system for granted, not all ancient civilizations based their numbers on a ten-base system. In ancient Babylon, a sexagesimal (base 60) system was in use.

The Decimal System in Harappa

In India a decimal system was already in place during the Harappan period, as indicated by an analysis of Harappan weights and measures. Weights corresponding to ratios of 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 200, and 500 have been identified, as have scales with decimal divisions. A particularly notable characteristic of Harappan weights and measures is their remarkable accuracy. A bronze rod marked in units of 0.367 inches points to the degree of precision demanded in those times. Such scales were particularly important in ensuring proper implementation of town planning rules that required roads of fixed widths to run at right angles to each other, for drains to be constructed of precise measurements, and for homes to be constructed according to specified guidelines. The existence of a gradated system of accurately marked weights points to the development of trade and commerce in Harappan society.

Mathematical Activity in the Vedic Period

In the Vedic period, records of mathematical activity are mostly to be found in Vedic texts associated with ritual activities. However, as in many other early agricultural civilizations, the study of arithmetic and geometry was also impelled by secular considerations. Thus, to some extent early mathematical developments in India mirrored the developments in Egypt, Babylon and China . The system of land grants and agricultural tax assessments required accurate measurement of cultivated areas. As land was redistributed or consolidated, problems of mensuration came up that required solutions. In order to ensure that all cultivators had equivalent amounts of irrigated and non-irrigated lands and tracts of equivalent fertility - individual farmers in a village often had their holdings broken up in several parcels to ensure fairness. Since plots could not all be of the same shape - local administrators were required to convert rectangular plots or triangular plots to squares of equivalent sizes and so on. Tax assessments were based on fixed proportions of annual or seasonal crop incomes, but could be adjusted upwards or downwards based on a variety of factors. This meant that an understanding of geometry and arithmetic was virtually essential for revenue administrators. Mathematics was thus brought into the service of both the secular and the ritual domains.

Arithmetic operations (Ganit) such as addition, subtraction, multiplication, fractions, squares, cubes and roots are enumerated in the Narad Vishnu Purana attributed to Ved Vyas (pre-1000 BC). Examples of geometric knowledge (rekha-ganit) are to be found in the Sulva-Sutras of Baudhayana (800 BC) and Apasthmaba (600 BC) which describe techniques for the construction of ritual altars in use during the Vedic era. It is likely that these texts tapped geometric knowledge that may have been acquired much earlier, possibly in the Harappan period. Baudhayana's Sutra displays an understanding of basic geometric shapes and techniques of converting one geometric shape (such as a rectangle) to another of equivalent (or multiple, or fractional) area (such as a square). While some of the formulations are approximations, others are accurate and reveal a certain degree of practical ingenuity as well as some theoretical understanding of basic geometric principles. Modern methods of multiplication and addition probably emerged from the techniques described in the Sulva-Sutras.

Pythagoras - the Greek mathematician and philosopher who lived in the 6th C B.C was familiar with the Upanishads and learnt his basic geometry from the Sulva Sutras. An early statement of what is commonly known as the Pythagoras theorem is to be found in Baudhayana's Sutra: The chord which is stretched across the diagonal of a square produces an area of double the size. A similar observation pertaining to oblongs is also noted. His Sutra also contains geometric solutions of a linear equation in a single unknown. Examples of quadratic equations also appear. Apasthamba's sutra (an expansion of Baudhayana's with several original contributions) provides a value for the square root of 2 that is accurate to the fifth decimal place. Apasthamba also looked at the problems of squaring a circle, dividing a segment into seven equal parts, and a solution to the general linear equation. Jain texts from the 6th C BC such as the Surya Pragyapti describe ellipses.

Modern-day commentators are divided on how some of the results were generated. Some believe that these results came about through hit and trial - as rules of thumb, or as generalizations of observed examples. Others believe that once the scientific method came to be formalized in the Nyaya-Sutras - proofs for such results must have been provided, but these have either been lost or destroyed, or else were transmitted orally through the Gurukul system, and only the final results were tabulated in the texts. In any case, the study of Ganit i.e mathematics was given considerable importance in the Vedic period. The Vedang Jyotish (1000 BC) includes the statement: "Just as the feathers of a peacock and the jewel-stone of a snake are placed at the highest point of the body (at the forehead), similarly, the position of Ganit is the highest amongst all branches of the Vedas and the Shastras."

(Many centuries later, Jain mathematician from Mysore, Mahaviracharya further emphasized the importance of mathematics: "Whatever object exists in this moving and non-moving world, cannot be understood without the base of Ganit (i.e. mathematics)".)

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 Normal 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.

Philosophy and Mathematics

Philosophical doctrines also had a profound influence on the development of mathematical concepts and formulations. Like the Upanishadic world view, space and time were considered limitless in Jain cosmology. This led to a deep interest in very large numbers and definitions of infinite numbers. Infinite numbers were created through recursive formulae, as in the Anuyoga Dwara Sutra. Jain mathematicians recognized five different types of infinities: infinite in one direction, in two directions, in area, infinite everywhere and perpetually infinite. Permutations and combinations are listed in the Bhagvati Sutras (3rd C BC) and Sathananga Sutra (2nd C BC).

Jain set theory probably arose in parallel with the Syadvada system of Jain epistemology in which reality was described in terms of pairs of truth conditions and state changes. The Anuyoga Dwara Sutra demonstrates an understanding of the law of indeces and uses it to develop the notion of logarithms. Terms like Ardh Aached , Trik Aached, and Chatur Aached are used to denote log base 2, log base 3 and log base 4 respectively. In Satkhandagama various sets are operated upon by logarithmic functions to base two, by squaring and extracting square roots, and by raising to finite or infinite powers. The operations are repeated to produce new sets. In other works the relation of the number of combinations to the coefficients occurring in the binomial expansion is noted.

Since Jain epistemology allowed for a degree of indeterminacy in describing reality, it probably helped in grappling with indeterminate equations and finding numerical approximations to irrational numbers.

Buddhist literature also demonstrates an awareness of indeterminate and infinite numbers. Buddhist mathematics was classified either as Garna (Simple Mathematics) or Sankhyan (Higher Mathematics). Numbers were deemed to be of three types: Sankheya (countable), Asankheya (uncountable) and Anant (infinite).

Philosophical formulations concerning Shunya - i.e. emptiness or the void may have facilitated in the introduction of the concept of zero. While the zero (bindu) as an empty place holder in the place-value numeral system appears much earlier, algebraic definitions of the zero and it's relationship to mathematical functions appear in the mathematical treatises of Brahmagupta in the 7th C AD. Although scholars are divided about how early the symbol for zero came to be used in numeric notation in India, (Ifrah arguing that the use of zero is already implied in Aryabhatta) tangible evidence for the use of the zero begins to proliferate towards the end of the Gupta period. Between the 7th C and the 11th C, Indian numerals developed into their modern form, and along with the symbols denoting various mathematical functions (such as plus, minus, square root etc) eventually became the foundation stones of modern mathematical notation.

The Indian Numeral System

Although the Chinese were also using a decimal based counting system, the Chinese lacked a formal notational system that had the abstraction and elegance of the Indian notational system, and it was the Indian notational system that reached the Western world through the Arabs and has now been accepted as universal. Several factors contributed to this development whose significance is perhaps best stated by French mathematician, Laplace: "The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India. The idea seems so simple nowadays that its significance and profound importance is no longer appreciated. It's simplicity lies in the way it facilitated calculation and placed arithmetic foremost amongst useful inventions."

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.

Influence of Trade and Commerce, Importance of Astronomy

The growth of trade and commerce, particularly lending and borrowing demanded an understanding of both simple and compound interest which probably stimulated the interest in arithmetic and geometric series. Brahmagupta's description of negative numbers as debts and positive numbers as fortunes points to a link between trade and mathematical study. Knowledge of astronomy - particularly knowledge of the tides and the stars was of great import to trading communities who crossed oceans or deserts at night. This is borne out by numerous references in the Jataka tales and several other folk-tales. The young person who wished to embark on a commercial venture was inevitably required to first gain some grounding in astronomy. This led to a proliferation of teachers of astronomy, who in turn received training at universities such as at Kusumpura (Bihar) or Ujjain (Central India) or at smaller local colleges or Gurukuls. This also led to the exchange of texts on astronomy and mathematics amongst scholars and the transmission of knowledge from one part of India to another. Virtually every Indian state produced great mathematicians who wrote commentaries on the works of other mathematicians (who may have lived and worked in a different part of India many centuries earlier). Sanskrit served as the common medium of scientific communication.

The science of astronomy was also spurred by the need to have accurate calendars and a better understanding of climate and rainfall patterns for timely sowing and choice of crops. At the same time, religion and astrology also played a role in creating an interest in astronomy and a negative fallout of this irrational influence was the rejection of scientific theories that were far ahead of their time. One of the greatest scientists of the Gupta period - Aryabhatta (born in 476 AD, Kusumpura, Bihar) provided a systematic treatment of the position of the planets in space. He correctly posited the axial rotation of the earth, and inferred correctly that the orbits of the planets were ellipses. He also correctly deduced that the moon and the planets shined by reflected sunlight and provided a valid explanation for the solar and lunar eclipses rejecting the superstitions and mythical belief systems surrounding the phenomenon. Although Bhaskar I (born Saurashtra, 6th C, and follower of the Asmaka school of science, Nizamabad, Andhra ) recognized his genius and the tremendous value of his scientific contributions, some later astronomers continued to believe in a static earth and rejected his rational explanations of the eclipses. But in spite of such setbacks, Aryabhatta had a profound influence on the astronomers and mathematicians who followed him, particularly on those from the Asmaka school.

Mathematics played a vital role in Aryabhatta's revolutionary understanding of the solar system. His calculations on pi, the circumferance of the earth (62832 miles) and the length of the solar year (within about 13 minutes of the modern calculation) were remarkably close approximations. In making such calculations, Aryabhatta had to solve several mathematical problems that had not been addressed before including problems in algebra (beej-ganit) and trigonometry (trikonmiti).

Bhaskar I continued where Aryabhatta left off, and discussed in further detail topics such as the longitudes of the planets; conjunctions of the planets with each other and with bright stars; risings and settings of the planets; and the lunar crescent. Again, these studies required still more advanced mathematics and Bhaskar I expanded on the trigonometric equations provided by Aryabhatta, and like Aryabhatta correctly assessed pi to be an irrational number. Amongst his most important contributions was his formula for calculating the sine function which was 99% accurate. He also did pioneering work on indeterminate equations and considered for the first time quadrilaterals with all the four sides unequal and none of the opposite sides parallel.

Another important astronomer/mathematician was Varahamira (6th C, Ujjain) who compiled previously written texts on astronomy and made important additions to Aryabhatta's trigonometric formulas. His works on permutations and combinations complemented what had been previously achieved by Jain mathematicians and provided a method of calculation of nCr that closely resembles the much more recent Pascal's Triangle. In the 7th century, Brahmagupta did important work in enumerating the basic principles of algebra. In addition to listing the algebraic properties of zero, he also listed the algebraic properties of negative numbers. His work on solutions to quadratic indeterminate equations anticipated the work of Euler and Lagrange.

Emergence of Calculus

In the course of developing a precise mapping of the lunar eclipse, Aryabhatta was obliged to introduce the concept of infinitesimals - i.e. tatkalika gati to designate the infinitesimal, or near instantaneous motion of the moon, and express it in the form of a basic differential equation. Aryabhatta's equations were elaborated on by Manjula (10th C) and Bhaskaracharya (12th C) who derived the differential of the sine function. Later mathematicians used their intuitive understanding of integration in deriving the areas of curved surfaces and the volumes enclosed by them.

Applied Mathematics, Solutions to Practical Problems

Developments also took place in applied mathematics such as in creation of trigonometric tables and measurement units. Yativrsabha's work Tiloyapannatti (6th C) gives various units for measuring distances and time and also describes the system of infinite time measures.

In the 9th C, Mahaviracharya ( Mysore) wrote Ganit Saar Sangraha where he described the currently used method of calculating the Least Common Multiple (LCM) of given numbers. He also derived formulae to calculate the area of an ellipse and a quadrilateral inscribed within a circle (something that had also been looked at by Brahmagupta) The solution of indeterminate equations also drew considerable interest in the 9th century, and several mathematicians contributed approximations and solutions to different types of indeterminate equations.

In the late 9th C, Sridhara (probably Bengal) provided mathematical formulae for a variety of practical problems involving ratios, barter, simple interest, mixtures, purchase and sale, rates of travel, wages, and filling of cisterns. Some of these examples involved fairly complicated solutions and his Patiganita is considered an advanced mathematical work. Sections of the book were also devoted to arithmetic and geometric progressions, including progressions with fractional numbers or terms, and formulas for the sum of certain finite series are provided. Mathematical investigation continued into the 10th C. Vijayanandi (of Benares, whose Karanatilaka was translated by Al-Beruni into Arabic) and Sripati of Maharashtra are amongst the prominent mathematicians of the century.

The leading light of 12th C Indian mathematics was Bhaskaracharya who came from a long-line of mathematicians and was head of the astronomical observatory at Ujjain. He left several important mathematical texts including the Lilavati and Bijaganita and the Siddhanta Shiromani, an astronomical text. He was the first to recognize that certain types of quadratic equations could have two solutions. His Chakrawaat method of solving indeterminate solutions preceded European solutions by several centuries, and in his Siddhanta Shiromani he postulated that the earth had a gravitational force, and broached the fields of infinitesimal calculation and integration. In the second part of this treatise, there are several chapters relating to the study of the sphere and it's properties and applications to geography, planetary mean motion, eccentric epicyclical model of the planets, first visibilities of the planets, the seasons, the lunar crescent etc. He also discussed astronomical instruments and spherical trigonometry. Of particular interest are his trigonometric equations: sin(a + b) = sin a cos b + cos a sin b; sin(a - b) = sin a cos b - cos a sin b;

The Spread of Indian Mathematics

The study of mathematics appears to slow down after the onslaught of the Islamic invasions and the conversion of colleges and universities to madrasahs. But this was also the time when Indian mathematical texts were increasingly being translated into Arabic and Persian. Although Arab scholars relied on a variety of sources including Babylonian, Syriac, Greek and some Chinese texts, Indian mathematical texts played a particularly important role. Scholars such as Ibn Tariq and Al-Fazari (8th C, Baghdad), Al-Kindi (9th C, Basra), Al-Khwarizmi (9th C. Khiva), Al-Qayarawani (9th C, Maghreb, author of Kitab fi al-hisab al-hindi), Al-Uqlidisi (10th C, Damascus, author of The book of Chapters in Indian Arithmetic), Ibn-Sina (Avicenna), Ibn al-Samh (Granada, 11th C, Spain), Al-Nasawi (Khurasan, 11th C, Persia), Al-Beruni (11th C, born Khiva, died Afghanistan), Al-Razi (Teheran), and Ibn-Al-Saffar (11th C, Cordoba) were amongst the many who based their own scientific texts on translations of Indian treatises. Records of the Indian origin of many proofs, concepts and formulations were obscured in the later centuries, but the enormous contributions of Indian mathematics was generously acknowledged by several important Arabic and Persian scholars, especially in Spain. Abbasid scholar Al-Gaheth wrote: " India is the source of knowledge, thought and insight”. Al-Maoudi (956 AD) who travelled in Western India also wrote about the greatness of Indian science. Said Al-Andalusi, an 11th C Spanish scholar and court historian was amongst the most enthusiastic in his praise of Indian civilization, and specially remarked on Indian achievements in the sciences and in mathematics. Of course, eventually, Indian algebra and trigonometry reached Europe through a cycle of translations, traveling from the Arab world to Spain and Sicily, and eventually penetrating all of Europe. At the same time, Arabic and Persian translations of Greek and Egyptian scientific texts become more readily available in India.

The Kerala School

Although it appears that original work in mathematics ceased in much of Northern India after the Islamic conquests, Benaras survived as a center for mathematical study, and an important school of mathematics blossomed in Kerala. Madhava (14th C, Kochi) made important mathematical discoveries that would not be identified by European mathematicians till at least two centuries later. His series expansion of the cos and sine functions anticipated Newton by almost three centuries. Historians of mathematics, Rajagopal, Rangachari and Joseph considered his contributions instrumental in taking mathematics to the next stage, that of modern classical analysis. Nilkantha (15th C, Tirur, Kerala) extended and elaborated upon the results of Madhava while Jyesthadeva (16th C, Kerala) provided detailed proofs of the theorems and derivations of the rules contained in the works of Madhava and Nilkantha. It is also notable that Jyesthadeva's Yuktibhasa which contained commentaries on Nilkantha's Tantrasamgraha included elaborations on planetary theory later adopted by Tycho Brahe, and mathematics that anticipated work by later Europeans. Chitrabhanu (16th C, Kerala) gave integer solutions to twenty-one types of systems of two algebraic equations, using both algebraic and geometric methods in developing his results. Important discoveries by the Kerala mathematicians included the Newton-Gauss interpolation formula, the formula for the sum of an infinite series, and a series notation for pi. Charles Whish (1835, published in the Transactions of the Royal Asiatic Society of Great Britain and Ireland) was one of the first Westerners to recognize that the Kerala school had anticipated by almost 300 years many European developments in the field.

Yet, few modern compendiums on the history of mathematics have paid adequate attention to the often pioneering and revolutionary contributions of Indian mathematicians. But as this essay amply demonstrates, a significant body of mathematical works were produced in the Indian subcontinent. The science of mathematics played a pivotal role not only in the industrial revolution but in the scientific developments that have occurred since. No other branch of science is complete without mathematics. Not only did India provide the financial capital for the industrial revolution (see the essay on colonization) India also provided vital elements of the scientific foundation without which humanity could not have entered this modern age of science and high technology.

Languages in India

India has number its own language and that is why English is still ruling India after 40 years after independence also.
There are a great no. of languages in India, but the Number of languages those are officially recognised is 18. These languages can be divided into mainly 6 groups. Those are as follows:

Negroid Dravidian Sine Tibetan
Austric Indo Aryan Other Speaches

From the above six groups the IndoAryan and Dravidian groups dominate the other languages.
Hindi is the national language of India.Although this is so many of the educated people have English as first language and a great number of Indians who speak more than one language it will be their secind language. thus if you don't know even a little of the local language, you can communicate any local person in English.

Hindi Although only about 20% of Indians speaks Hindi as their mother toung like people in Bihar, Madhya Pradesh, Rajasthan, and uttar Pradesh, Hindu is the most important language in India. This is the official language of the Indian Goernment as well as all the states. Primarily Hindi was spoken in Delhi and some part of the UPdistrict.

Assamese It is a member of Indo-Aryan Language. This one is the state language of Assam. More than 58% of the poopulation of the state Assam speaks this language.Developed as a separate language in 13th century.

Bengali It is a member of Indo-Aryanlanguage. It is the state language of Bangladesh. About 200 millions of people speaks Bengali. It has its origine in 1000AD.

Gujarathi Being a member of an Indo-Aryan family, Gujarathi is the state language of the state Gujarat, has its origin as an independent language from AD1200. Because of the rapid development it is one of the most developed languages in India.

Kannada Being the state language of the state Karnataka, Kannada belongs to the Dravidian family. As it has its origine in 9th century Kannada has a rich literary tradition. About 65% of the state's population speakes Kannada.

Kashmiri Kashmiri language is a member of an Indo-Aryan family. Although it is not the state language of the state Jammu and Kashmir, 55% of the population speaks Kashmiri and has its origin in 1200AD.

Malayalam It is one of the Dravidian languages. Malayam struck out in 10th century AD. It the state language of Kerala.

Marathi It is a state language of the state Maharashtra. It belongs to the Indo-Aryan family. Its literary career began in 13th century. It has today a fully developed literature of the modern type.

Oriya It is one of the branches of the Indo-Aryan family. Belongs to tteh state Orrisa as its state language and spoken by nearly about 87% of the total population of the state.Found in 10th century but began its literary in 14th century.

Punjabi Being the member of the Indo-Aryan family it is the state language of Punjab. It is based on the script 'Gurumukhi' which is written in a 16th century created by the Sikh Guru Angad.Since 19th century Punjabi shows a vigourous developmentin all branches of literature.

Sanskrit Being one of the oldest languages in world, Sanskrit is a classical language of India.It start with Rig Veda, which has its origin 2000BC. Early Sunskrit is known as Vedic Sunskrit and covers the period between 2000 to 500BC and Classical Sunskrit covers the period between 500 to 1000 BC.

Sindhi It is one of the branches of the Indo-Aryan family. About 10.5 millions of people from India speakes Sindhi. Sindhi speakers in India mainly uses Devanagari script. sindhi has developed noteworthy literature also.

Tamil An ancient Dravidian language has its origin at least 2000 years old. It is the state language of Tamil Nadu. the language is spoken by 73 millions of people and judging by its modern publications.

Tellugu Numarically the biggest language in the Dravidian family. Next to Hindi, it is the biggest linguistic unit in India, having its origin in 7th centuryAD, but it was broke out into a literary language in 11th century.

Urdu Being with Hindi Urdu is evolved in early Delhi, Urdu is the state language of jammu and Kashmir. This language is spoken by more than 28 million people in India. The name Urdu is derived from 'Zaben-e-Urdu-Muala' which means the language of the exalted camp or court. Urdu and Hindi have same source and was a spoken language which prevailed around Delhi since the 13th century

Nepali Being language of Nepal it is related to the languages of North India.It is spoken in some parts of West Bengal, Up, Bihar and Assam.

Kokani This is the official language of Goa spoken by thousands of Kokanies in Maharashtra, Karnataka and Kerala.

Manipuri This is the local language of the people of the valley and the hill of Manipur. About 70% of the Manipur's population speaks the language.

Heritage of India

Heritage of India

The roots of Indian civilization stretch back in time to pre-recorded history. The earliest human activity in the Indian sub-continent can be traced back to the Early, Middle and Late Stone Ages through 400,000-200,000 BC. Throughout its history armies, traders, and immigrants from all over the world have invaded India. India's heritage is like a rainbow of multiple facets like performing arts, crafts, religion, customs, traditions, beliefs, philosophy, history, health, medicine, travel, cuisine, monuments, literature, painting and languages. Each one of these heritages of India reflects the influence of prevailing cultures. These were the cultures primarily taken birth from the amalgamation of migrating cultures with the Indian ones. Nevertheless today its medical, scientific and philosophical heritage has made a mark of its own in the world.
While some of this heritage is well documented and commonly known, much of it still needs to be unveiled. HeritageinIndia.com would provide you with all the information that you need on Indian Heritage in order to understand this great country and prepare yourself for the tour of India. To understand the heritage and culture of India and a much better way, select one of our Heritage Tours of India. These are the most comprehensive and visitor friendly tours coming out of India. Our heritage tours capture the essence of India in all forms and colors.
The cultural heritage of India has its roots in the different components of culture i.e. musical heritage, dances, sculpturing and other fine arts, festivities, languages spoken, traditional beliefs and customs, food and many more like these. It is the development in these aspects of life that makes the heritage of India one of the most vibrant and most exhaustive.
Traditional health and medicines of India have their roots in the ancient treatise like Ayurveda, Charak Sanhita, and the experiments done by ancient Indian gurus. These health systems not only aimed at curing people from different diseases, they were also aimed at cleaning your body and mind. In fact, these systems give more emphasis on protection than the cure. Traditional health sciences of different parts of India mainly originate from Ayurvedic System of Medicines. Another important way of keeping your body and soul fit was Yoga, practiced by the great souls of ancient India.


India's artistic heritage:
Indian culture has intrigued and sometimes awed visitors through the ages, from megasthenes, a Greek traveler of the third century BC, hsuan tsang, the Chinese pilgrim of the seventh century, Arab travelers of the 13th century like ibn bat Utah, and the British and other Europeans, down to our own day. For Indians, too Indian civilization remains elusive, too vast and varied to comprehend in its entirety. Art histories characterize Indian art as the handmaiden of religion. But it is perhaps more appropriate to credit geography with being the dominant influence in the development of Indian culture. The high mountain ranges in north have inspired poets and philosophers and, in mythology, the Himalayas are the abode of the god. The forest and river valleys, the desert and coastal plains, have been home to people for thousands of years. The elephant, lion and bull, as well as numerous flowers and plants, became motifs in sculpture, painting and poetry. In India's monochrome desert, the inhabitants of rajastan and Gujarat adorn themselves in a rainbow of colors; in the tropical forest, people wear white, perhaps reluctant to compete with the exuberant colors of nature.
One feature of Indian civilization is its antiquity and the continuity of its age-old tradition and aesthetic principles, which even today influence artistic activity. in Madhya Pradesh , at bhimbetka , near Bhopal , are some natural caves , their walls and ceilings covered with painting of running deer, stags with magnificent antlers and delightful drawings of hunting , dancing and merry-making , dating back to stone age , some 8,000 years ago. The dancers in the pictures are often shown wearing ritual masks and there are depictions of flutes and blades found in these caves represent the beginnings of India's rich and diverse material culture.

Ancient city cultures:
In the early 20th century, archaeologists unearthed ruined cities over 5,000 years old: Harappa and mohenjodaro (now in Pakistan), kalibangan and lothal. This urban cultures are knows as the harappan or Indus civilization, as the cities were concentrated on the banks of the Indus River. Lothal (Gujarat) is a well-pre-served site with brick building laid out along broad streets. Each house has a 'living room'. Kitchen, well and bathing area. This civilization produced elegantly shaped well-thrown pottery with painted designs, which still serve as models for pottery produced in India today. clay toys in the form of animals, birds an bullock-carts found at the sites display a sense of artistry and hum our . Tiny seals bearing an undeciphered pictographic script and emblems, possibly used as traders and merchant, have long fascinated histories. Tools and bronze images, such as the celebrated dancing girl and the bullock cart and bulls, testify to the harappans'skill in metallurgy. The national museum in New Delhi and Indian museum in kolkata have sizeable collection of artifacts from this period, contemporary with the ancient cultures of Mesopotamia and Egypt.
Prosperous villages along the Ganges and Indus rivers supported these large cities and supplied them with food. It was in these villages that artifacts in clay, wood and others perishable materials were produced. As new techniques developed, it happened most dramatically around the second century BC and accompanied the spread of Buddhism.


Taj Mahal
The greater significance of a monument like Taj Mahal to the world is much more than being a part of the Seven Wonders of the World. Taj Mahal has become a symbol of endless love and devotion. Taj has been a visual delight for viewers over the ages.

Taj Mahal - The Symbol of Love in Agra IndiaHistory Of The Taj Mahal
Set against the backdrop of Yamuna River, this tribute of love was built by the third Mughal emperor of India, Shah Jahan in the memory of his beloved wife Mumtaz Mahal, who died during childbirth. Although it is not known for sure who planned the Taj Mahal, the name of an Indian architect of Persian descent, Ustad Ahmad Lahori, has been cited in many sources. As soon as construction began in 1630, masons, craftsmen, sculptors, and calligraphers were summoned from Persia, the Ottoman Empire, and Europe to work on the masterpiece.
It took 12 years of hard labour and 20,000 labourers to build the mausoleum. The architectural complex is comprised of five main elements: the 'Darwaza' or main gateway, the 'Bageecha' or garden, the Masjid or mosque, the 'Naqqar Khana' or rest house, and the 'Rauza' or the Taj Mahal mausoleum. The actual Tomb is situated inside the Taj.
The marble stature memorial has got embellishments of beautiful marble inlay work known as "Pietra Dura" that is a very integral part of Agra's art culture and traditions. But the most fascinating feature in this wonder is the garden with its water channels, lotus pools and colourful flowerbeds and trees.
Various Moods Of Taj Mahal
Taj Mahal travel is a joy forever and for any imaginative visitor rare experience. Internationally, Taj Mahal represents India; designed like a palace and finished like a jewel. Pure, gloriously perfect and superbly lovely, and like a jewel made of white marble, the Taj sparkles under the moonlight. During the early morning hours its white beauty takes a blushing soft pinkish colour and in the dusk hours Taj Mahal reflects the fiery shades of the setting sun. Nicely depicting the different moods of a woman, right!
Taj Mahal India Travel
Taj Mahal travel brings you within the close proximity of one of the most celebrated monument and heritage site of India - the Taj Mahal. Visit Agra city, the home of Taj that encloses some of the best monumental grandeur of the Mughal era, beside the Taj Mahal.

Khajuraho Temples India

Even if situated in the middle of nowhere, the Khajuraho temple complex site is one the most popular places both foreign and Indian tourists. Temples of Khajuraho hold the attention of a visitor with their sculptural art, which is so exquisite and intricate, that one cannot even dream of cloning it now. Perfect in execution and sublime in expressions these Khajuraho temples are a dedication to the womanhood. The artist's creative instincts have beautifully captured various facets and moods of life in stone.World known Khajuraho Temples in M.P., India
Khajuraho, the ancient "Kharjjuravahaka", was the principal seat of authority of the Chandella rulers who adorned it with numerous tanks, scores of lofty temples of sculptural grace and architectural splendour. The local tradition lists eighty-five temples but now only twenty-five are standing examples in various stages of preservation. But for Chausath-Yogini, Brahma and Mahadeva, which are of granite, all the other temples are of fine-grained sandstone, buff, pink or pale yellow in colour.
Khajuraho Temples - A Celebration Of Life
The existing temple of Khajuraho can be divided into three groups, Western, Eastern and Southern. The famous Western Group, designated a World Heritage site, is enclosed within a beautifully laid-out park. Yasovarman (AD 954) built the temple of Lord Vishnu, now famous as Lakshmana temple is an ornate and evolved example of its time proclaiming the prestige of the Chandellas.
The Vishvanatha, Parsvanatha and Vaidyanatha temples in Khajuraho belong to the time of king Dhanga, the successor of Yasovarman. The Jagadambi, Chitragupta, are noteworthy among the western group of royal temples of Khajuraho. The largest and grandest temple of Khajuraho is the immortal Kandariya Mahadeva, which is attributed to king Ganda (AD 1017-29).
The other examples that followed viz., Vamana, Adinatha, Javari, Chaturbhuj and Duladeo, are smaller but elaborately designed. The Khajuraho group of temples are noted for lofty terraces (jagati) and functionally effective plans. The sculptural embellishments include, besides the cult images; 'Parivara', 'Parsva', 'Avarana' 'Devatas', 'Dikpalas', the 'Apsaras' and 'Sura-Sundaris' which win universal admiration for their delicate, youthful female forms of ravishing beauty. The attire and ornamentation embrace the winsome grace and charm.