My thoughts !! | எனது எண்ணங்கள் !!

This blog is to express my mind, thoughts and scrabbles. A place to express what I am!

Tuesday, 31 January 2012

BHASKARACHARYA

Thanks to: http://veda.wikidot.com.

This post is just an introduction to one of the greatest astronomer of India Bhaskarachārya! I am in search for his works in detail, will post them here later. I am taking a small step to bring out the works by Indians on field of Astronomy especially solar astronomy. 

Life Cycles of the Universe

The Indians view that the Universe has no beginning or end, but follows a cosmic creation and dissolution. Indians are the one who propounds the idea of life-cycles of the universe. It suggests that the universe undergoes an infinite number of deaths and rebirths. Indians views the universe as without a beginning (anadi = beginning-less) or an end (ananta = end-less). Rather the universe is projected in cycles. Hindu scriptures refer to time scales that vary from ordinary earth day and night to the day and night of the Brahma that are a few billion earth years long.

According to Carl Sagan,


"Millenniums before Europeans were willing to divest themselves of the Biblical idea that the world was a few thousand years old, the Mayans were thinking of millions and the Indians billions".

Continues Carl Sagan,

    "… is the only religion in which the time scales correspond… to those of modern scientific cosmology."

Its cycles run from our ordinary day and night to a day and night of the Brahma, 8.64 billion years long, longer than the age of the Earth or the Sun and about half the time since the Big Bang". One day of Brahma is worth a thousand of the ages (yuga) known to humankind; as is each night." Thus each kalpa is worth one day in the life of Brahma, the God of creation. In other words, the four ages of the mahayuga must be repeated a thousand times to make a "day to Brahma", a unit of time that is the equivalent of 4.32 billion human years, doubling which one gets 8.64 billion years for a Brahma day and night. This was later theorized (possibly independently) by Aryabhata in the 6th century. The cyclic nature of this analysis suggests a universe that is expanding to be followed by contraction… a cosmos without end. This, according to modern physicists is not impossibility.

Bhaskara II or Bhaskarachārya was an Indian mathematician and astronomer who extended Brahmagupta's work on number systems. He was born near Bijjada Bida (in present day Bijapur district, Karnataka state, South India) into the Deshastha Brahmin family. Bhaskara was head of an astronomical observatory at Ujjain, the leading mathematical centre of ancient India. His predecessors in this post had included both the noted Indian mathematician Brahmagupta (598–c. 665) and Varahamihira. He lived in the Sahyadri region. It has been recorded that his great-great-great-grandfather held a hereditary post as a court scholar, as did his son and other descendants. His father Mahesvara was as an astrologer, who taught him mathematics, which he later passed on to his son Loksamudra. Loksamudra's son helped to set up a school in 1207 for the study of Bhāskara's writings

Bhaskara (1114 – 1185) (also known as Bhaskara II and Bhaskarachārya)

Bhaskaracharya's work in Algebra, Arithmetic and Geometry catapulted him to fame and immortality. His renowned mathematical works called Lilavati" and Bijaganita are considered to be unparalleled and a memorial to his profound intelligence. Its translation in several languages of the world bear testimony to its eminence. In his treatise Siddhant Shiromani he writes on planetary positions, eclipses, cosmography, mathematical techniques and astronomical equipment. In the Surya Siddhant he makes a note on the force of gravity:

    "Objects fall on earth due to a force of attraction by the earth. Therefore, the earth, planets, constellations, moon, and sun are held in orbit due to this attraction."

Bhaskaracharya was the first to discover gravity, 500 years before Sir Isaac Newton. He was the champion among mathematicians of ancient and medieval India. His works fired the imagination of Persian and European scholars, who through research on his works earned fame and popularity. Some say Mayans and Chinese too know of gravity some 2000 years before him.

Birth and Education of Bhaskaracharya

Ganesh Daivadnya has bestowed a very apt title on Bhaskaracharya. He has called him ‘Ganakchakrachudamani’, which means, ‘a gem among all the calculators of astronomical phenomena.’ Bhaskaracharya himself has written about his birth, his place of residence, his teacher and his education, in Siddhantashiromani as follows, ‘A place called ‘Vijjadveed’, which is surrounded by Sahyadri ranges, where there are scholars of three Vedas, where all branches of knowledge are studied, and where all kinds of noble people reside, a brahmin called Maheshwar was staying, who was born in Shandilya Gotra (in Hindu religion, Gotra is similar to lineage from a particular person, in this case sage Shandilya), well versed in Shroud (originated from ‘Shut’ or ‘Vedas’) and ‘Smart’ (originated from ‘Smut’) Dharma, respected by all and who was authority in all the branches of knowledge. I acquired knowledge at his feet’.

From this verse it is clear that Bhaskaracharya was a resident of Vijjadveed and his father Maheshwar taught him mathematics and astronomy. Unfortunately today we have no idea where Vijjadveed was located. It is necessary to ardently search this place which was surrounded by the hills of Sahyadri and which was the centre of learning at the time of Bhaskaracharya. He writes about his year of birth as follows,
‘I was born in Shake 1036 (1114 AD) and I wrote Siddhanta Shiromani when I was 36 years old.’

Bhaskaracharya has also written about his education. Looking at the knowledge, which he acquired in a span of 36 years, it seems impossible for any modern student to achieve that feat in his entire life. See what Bhaskaracharya writes about his education,

    ‘I have studied eight books of grammar, six texts of medicine, six books on logic, five books of mathematics, four Vedas, five books on Bharat Shastras, and two Mimansas’.

Bhaskaracharya calls himself a poet and most probably he was Vedanti, since he has mentioned ‘Parambrahman’ in that verse.
Siddhanta Shriomani

Bhaskaracharya wrote Siddhanta Shiromani in 1150 AD when he was 36 years old. This is a mammoth work containing about 1450 verses. It is divided into four parts, Lilawati, Beejaganit, Ganitadhyaya and Goladhyaya. In fact each part can be considered as separate book. The numbers of verses in each part are as follows, Lilawati has 278, Beejaganit has 213, Ganitadhyaya has 451 and Goladhyaya has 501 verses.
One of the most important characteristic of Siddhanta Shiromani is it consists of simple methods of calculations from Arithmetic to Astronomy. Essential knowledge of ancient Indian Astronomy can be acquired by reading only this book. Siddhanta Shiromani has surpassed all the ancient books on astronomy in India. After Bhaskaracharya nobody could write excellent books on mathematics and astronomy in lucid language in India. In India, Siddhanta works used to give no proofs of any theorem. Bhaskaracharya has also followed the same tradition.

Lilawati is an excellent example of how a difficult subject like mathematics can be written in poetic language. Lilawati has been translated in many languages throughout the world. When British Empire became paramount in India, they established three universities in 1857, at Bombay, Calcutta and Madras. Till then, for about 700 years, mathematics was taught in India from Bhaskaracharya’s Lilawati and Beejaganit. No other textbook has enjoyed such long lifespan.
Bhaskara's contributions to mathematics

Lilawati and Beejaganit together consist of about 500 verses. A few important highlights of Bhaskar's mathematics are as follows:
Terms for numbers

In English, cardinal numbers are only in multiples of 1000. They have terms such as thousand, million, billion, trillion, quadrillion etc. Most of these have been named recently. However, Bhaskaracharya has given the terms for numbers in multiples of ten and he says that these terms were coined by ancients for the sake of positional values. Bhaskar's terms for numbers are as follows:

eka(1), dasha(10), shata(100), sahastra(1000), ayuta(10,000), laksha(100,000), prayuta (1,000,000=million), koti(107), arbuda(108), abja(109=billion), kharva (1010), nikharva (1011), mahapadma (1012=trillion), shanku(1013), jaladhi(1014), antya(1015=quadrillion), Madhya (1016) and parardha(1017).
Kuttak

Kuttak is nothing but the modern indeterminate equation of first order. The method of solution of such equations was called as ‘pulveriser’ in the western world. Kuttak means to crush to fine particles or to pulverize. There are many kinds of Kuttaks. Let us consider one example.

In the equation, ax + b = CY, a and b are known positive integers. We want to also find out the values of x and y in integers. A particular example is, 100x +90 = 63y

Bhaskaracharya gives the solution of this example as, x = 18, 81, 144, 207… And y=30, 130, 230, 330…
Indian Astronomers used such kinds of equations to solve astronomical problems. It is not easy to find solutions of these equations but Bhaskara has given a generalized solution to get multiple answers.
Chakrawaal

Chakrawaal is the “indeterminate equation of second order” in western mathematics. This type of equation is also called Pell’s equation. Though the equation is recognized by his name Pell had never solved the equation. Much before Pell, the equation was solved by an ancient and eminent Indian mathematician, Brahmagupta (628 AD). The solution is given in his Brahmasphutasiddhanta. Bhaskara modified the method and gave a general solution of this equation. For example, consider the equation 61x2 + 1 = y2. Bhaskara gives the values of x = 22615398 and y = 1766319049

There is an interesting history behind this very equation. The Famous French mathematician Pierre de Fermat (1601-1664) asked his friend Bessy to solve this very equation. Bessy used to solve the problems in his head like present day Shakuntaladevi. Bessy failed to solve the problem. After about 100 years another famous French mathematician solved this problem. But his method is lengthy and could find a particular solution only, while Bhaskara gave the solution for five cases. In his book ‘History of mathematics’, see what Carl Boyer says about this equation,

‘In connection with the Pell’s equation ax2 + 1 = y2, Bhaskara gave particular solutions for five cases, a = 8, 11, 32, 61, and 67, for 61x2 + 1 = y2, for example he gave the solutions, x = 226153980 and y = 1766319049, this is an impressive feat in calculations and its verifications alone will tax the efforts of the reader’

Henceforth the so-called Pell’s equation should be recognized as ‘Brahmagupta-Bhaskaracharya equation’.
Simple mathematical methods

Bhaskara has given simple methods to find the squares, square roots, cube, and cube roots of big numbers. He has proved the Pythagoras theorem in only two lines. The famous Pascal Triangle was Bhaskara’s ‘Khandameru’. Bhaskara has given problems on that number triangle. Pascal was born 500 years after Bhaskara. Several problems on permutations and combinations are given in Lilawati. Bhaskar. He has called the method ‘ankapaash’. Bhaskara has given an approximate value of PI as 22/7 and more accurate value as 3.1416. He knew the concept of infinity and called it as ‘khahar rashi’, which means ‘anant’. It seems that Bhaskara had not notions about calculus, One of his equations in modern notation can be written as, d (sin (w)) = cos (w) dw.
A Summary of Bhaskara's contributions
    A proof of the Pythagorean Theorem by calculating the same area in two different ways and then canceling out terms to get a² + b² = c².

    In Lilavati, solutions of quadratic, cubic and quartic indeterminate equations.

    Solutions of indeterminate quadratic equations (of the type ax² + b = y²).

    Integer solutions of linear and quadratic indeterminate equations (Kuttaka). The rules he gives are (in effect) the same as those given by the Renaissance European mathematicians of the 17th century

    A cyclic Chakravala method for solving indeterminate equations of the form ax² + bx + c = y. The solution to this equation was traditionally attributed to William Brouncker in 1657, though his method was more difficult than the chakravala method.

    His method for finding the solutions of the problem x² − ny² = 1 (so-called "Pell's equation") is of considerable interest and importance.

    Solutions of Diophantine equations of the second order, such as 61x² + 1 = y². This very equation was posed as a problem in 1657 by the French mathematician Pierre de Fermat, but its solution was unknown in Europe until the time of Euler in the 18th century.

    Solved quadratic equations with more than one unknown, and found negative and irrational solutions.

    Preliminary concept of mathematical analysis.

    Preliminary concept of infinitesimal calculus, along with notable contributions towards integral calculus.

    Conceived differential calculus, after discovering the derivative and differential coefficient.

    Stated Rolle's theorem, a special case of one of the most important theorems in analysis, the mean value theorem. Traces of the general mean value theorem are also found in his works.

    Calculated the derivatives of trigonometric functions and formulae. (See Calculus section below.)

    In Siddhanta Shiromani, Bhaskara developed spherical trigonometry along with a number of other trigonometric results.
Arithmetic

Bhaskara's arithmetic text Lilavati covers the topics of definitions, arithmetical terms, interest computation, arithmetical and geometrical progressions, plane geometry, solid geometry, the shadow of the gnomon, methods to solve indeterminate equations, and combinations.

Lilavati is divided into 13 chapters and covers many branches of mathematics, arithmetic, algebra, geometry, and a little trigonometry and mensuration. More specifically the contents include:

    Definitions.
    Properties of zero (including division, and rules of operations with zero).
    Further extensive numerical work, including use of negative numbers and surds.
    Estimation of π.
    Arithmetical terms, methods of multiplication, and squaring.
    Inverse rule of three, and rules of 3, 5, 7, 9, and 11.
    Problems involving interest and interest computation.
    Arithmetical and geometrical progressions.
    Plane (geometry).
    Solid geometry.
    Permutations and combinations.
    Indeterminate equations (Kuttaka), integer solutions (first and second order). His contributions to this topic are particularly important, since the rules he gives are (in effect) the same as those given by the renaissance European mathematicians of the 17th century, yet his work was of the 12th century. Bhaskara's method of solving was an improvement of the methods found in the work of Aryabhata and subsequent mathematicians.

His work is outstanding for its systemisation, improved methods and the new topics that he has introduced. Furthermore the Lilavati contained excellent recreative problems and it is thought that Bhaskara's intention may have been that a student of 'Lilavati' should concern himself with the mechanical application of the method.
Algebra

His Bijaganita ("Algebra") was a work in twelve chapters. It was the first text to recognize that a positive number has two square roots (a positive and negative square root). His work Bijaganita is effectively a treatise on algebra and contains the following topics:

    Positive and negative numbers.
    Zero.
    The 'unknown' (includes determining unknown quantities).
    Determining unknown quantities.
    Surds (includes evaluating surds).
    Kuttaka (for solving indeterminate equations and Diophantine equations).
    Simple equations (indeterminate of second, third and fourth degree).
    Simple equations with more than one unknown.
    Indeterminate quadratic equations (of the type ax² + b = y²).
    Solutions of indeterminate equations of the second, third and fourth degree.
    Quadratic equations.
    Quadratic equations with more than one unknown.
    Operations with products of several unknowns.

Bhaskara derived a cyclic, chakravala method for solving indeterminate quadratic equations of the form ax² + bx + c = y. Bhaskara's method for finding the solutions of the problem Nx² + 1 = y² (the so-called "Pell's equation") is of considerable importance.

He gave the general solutions of:

    Pell's equation using the chakravala method.
    The indeterminate quadratic equation using the chakravala method.

He also solved:

    Cubic equations.
    Quartic equations.
    Indeterminate cubic equations.
    Indeterminate quartic equations.
    Indeterminate higher-order polynomial equations.

Trigonometry

The Siddhanta Shiromani (written in 1150) demonstrates Bhaskara's knowledge of trigonometry, including the sine table and relationships between different trigonometric functions. He also discovered spherical trigonometry, along with other interesting trigonometrical results. In particular Bhaskara seemed more interested in trigonometry for its own sake than his predecessors who saw it only as a tool for calculation. Among the many interesting results given by Bhaskara, discoveries first found in his works include the now well known results for \sin\left(a + b\right) and \sin\left(a - b\right) :
Calculus

His work, the Siddhanta Shiromani, is an astronomical treatise and contains many theories not found in earlier works. Preliminary concepts of infinitesimal calculus and mathematical analysis, along with a number of results in trigonometry, differential calculus and integral calculus that are found in the work are of particular interest.

Evidence suggests Bhaskara was acquainted with some ideas of differential calculus. It seems, however, that he did not understand the utility of his researches, and thus historians of mathematics generally neglect this achievement. Bhaskara also goes deeper into the 'differential calculus' and suggests the differential coefficient vanishes at an extremum value of the function, indicating knowledge of the concept of 'infinitesimals'.

    There is evidence of an early form of Rolle's theorem in his work:
        If f\left(a\right) = f\left(b\right) = 0 then f'\left(x\right) = 0 for some \ x with \ a < x < b

    He gave the result that if x \approx y then \sin(y) - \sin(x) \approx (y - x)\cos(y), thereby finding the derivative of sine, although he never developed the general concept of differentiation.
        Bhaskara uses this result to work out the position angle of the ecliptic, a quantity required for accurately predicting the time of an eclipse.

    In computing the instantaneous motion of a planet, the time interval between successive positions of the planets was no greater than a truti, or a 1⁄33750 of a second, and his measure of velocity was expressed in this infinitesimal unit of time.

    He was aware that when a variable attains the maximum value, its differential vanishes.

    He also showed that when a planet is at its farthest from the earth, or at its closest, the equation of the centre (measure of how far a planet is from the position in which it is predicted to be, by assuming it is to move uniformly) vanishes. He therefore concluded that for some intermediate position the differential of the equation of the centre is equal to zero. In this result, there are traces of the general mean value theorem, one of the most important theorems in analysis, which today is usually derived from Rolle's theorem. The mean value theorem was later found by Parameshvara in the 15th century in the Lilavati Bhasya, a commentary on Bhaskara's Lilavati.

Madhava (1340-1425) and the Kerala School mathematicians (including Parameshvara) from the 14th century to the 16th century expanded on Bhaskara's work and further advanced the development of calculus in India.
Astronomy

Using an astronomical model developed by Brahmagupta in the 7th century, Bhaskara accurately defined many astronomical quantities, including, for example, the length of the sidereal year, the time that is required for the Earth to orbit the Sun, as 365.2588 days which is same as in Suryasiddhanta. The modern accepted measurement is 365.2563 days; it means that Bhaskaracharya was off by only 0.0002%.

His mathematical astronomy text Siddhanta Shiromani is written in two parts: the first part on mathematical astronomy and the second part on the sphere.

The twelve chapters of the first part cover topics such as:

    Mean longitudes of the planets.
    True longitudes of the planets.
    The three problems of diurnal rotation.
    Syzygies.
    Lunar eclipses.
    Solar eclipses.
    Latitudes of the planets.
    Sunrise equation
    The Moon's crescent.
    Conjunctions of the planets with each other.
    Conjunctions of the planets with the fixed stars.
    The patas of the Sun and Moon.

The second part contains thirteen chapters on the sphere. It covers topics such as:

    Praise of study of the sphere.
    Nature of the sphere.
    Cosmography and geography.
    Planetary mean motion.
    Eccentric epicyclic model of the planets.
    The armillary sphere.
    Spherical trigonometry.
    Ellipse calculations.[citation needed]
    First visibilities of the planets.
    Calculating the lunar crescent.
    Astronomical instruments.
    The seasons.
    Problems of astronomical calculations.

Ganitadhyaya and Goladhyaya of Siddhanta Shiromani are devoted to astronomy. All put together there are about 1000 verses. Almost all aspects of astronomy are considered in these two books. Some of the highlights are worth mentioning.
Earth’s circumference and diameter

Bhaskara has given a very simple method to determine the circumference of the Earth. According to this method, first find out the distance between two places, which are on the same longitude. Then find the correct latitudes of those two places and difference between the latitudes. Knowing the distance between two latitudes, the distance that corresponds to 360 degrees can be easily found, which the circumference of is the Earth. For example, Satara and Kolhapur are two cities on almost the same longitude. The difference between their latitudes is one degree and the distance between them is 110 kilometers. Then the circumference of the Earth is 110 X 360 = 39600 kilometers. Once the circumference is fixed it is easy to calculate the diameter. Bhaskara gave the value of the Earth’s circumference as 4967 ‘yojane’ (1 yojan = 8 km), which means 39736 kilometers. His value of the diameter of the Earth is 1581 yojane i.e. 12648 km. The modern values of the circumference and the diameter of the Earth are 40212 and 12800 kilometers respectively. The values given by Bhaskara are astonishingly close.
Aksha kshetre

For astronomical calculations, Bhaskara selected a set of eight right angle triangles, similar to each other. The triangles are called ‘aksha kshetre’. One of the angles of all the triangles is the local latitude. If the complete information of one triangle is known, then the information of all the triangles is automatically known. Out of these eight triangles, complete information of one triangle can be obtained by an actual experiment. Then using all eight triangles virtually hundreds of ratios can be obtained. This method can be used to solve many problems in astronomy.
Geocentric parallax

Ancient Indian Astronomers knew that there was a difference between the actual observed timing of a solar eclipse and timing of the eclipse calculated from mathematical formulae. This is because calculation of an eclipse is done with reference to the center of the Earth, while the eclipse is observed from the surface of the Earth. The angle made by the Sun or the Moon with respect to the Earth’s radius is known as parallax. Bhaskara knew the concept of parallax, which he has termed as ‘lamban’. He realized that parallax was maximum when the Sun or the Moon was on the horizon, while it was zero when they were at zenith. The maximum parallax is now called Geocentric Horizontal Parallax. By applying the correction for parallax exact timing of a solar eclipse from the surface of the Earth can be determined.
Yantradhyay

In this chapter of Goladhyay, Bhaskar has discussed eight instruments, which were useful for observations. The names of these instruments are, Gol yantra (armillary sphere), Nadi valay (equatorial sun dial), Ghatika yantra, Shanku (gnomon), Yashti yantra, Chakra, Chaap, Turiya, and Phalak yantra. Out of these eight instruments Bhaskara was fond of Phalak yantra, which he made with skill and efforts. He argued that ‘ this yantra will be extremely useful to astronomers to calculate accurate time and understand many astronomical phenomena’. Bhaskara’s Phalak yantra was probably a precursor of the ‘astrolabe’ used during medieval times.
Dhee yantra

This instrument deserves to be mentioned specially. The word ‘dhee’ means ‘ Buddhi’ i.e. intelligence. The idea was that the intelligence of human being itself was an instrument. If an intelligent person gets a fine, straight and slender stick at his/her disposal he/she can find out many things just by using that stick. Here Bhaskara was talking about extracting astronomical information by using an ordinary stick. One can use the stick and its shadow to find the time, to fix geographical north, south, east, and west. One can find the latitude of a place by measuring the minimum length of the shadow on the equinoctial days or pointing the stick towards the North Pole. One can also use the stick to find the height and distance of a tree even if the tree is beyond a lake.

A GLANCE AT THE ASTRONOMICAL ACHIEVEMENTS OF BHASKARACHARYA

    The Earth is not flat, has no support and has a power of attraction.
    The north and south poles of the Earth experience six months of day and six months of night.
    One day of Moon is equivalent to 15 earth-days and one night is also equivalent to 15 earth-days.
    Earth’s atmosphere extends to 96 kilometres and has seven parts.     There is a vacuum beyond the Earth’s atmosphere.
    He had knowledge of precession of equinoxes. He took the value of its shift from the first point of Aries as 11 degrees. However, at that time it was about 12 degrees.

    Ancient Indian Astronomers used to define a reference point called ‘Lanka’. It was defined as the point of intersection of the longitude passing through Ujjaini and the equator of the Earth. Bhaskara has considered three cardinal places with reference to Lanka, the Yavakoti at 90 degrees east of Lanka, the Romak at 90 degrees west of Lanka and Siddhapoor at 180 degrees from Lanka. He then accurately suggested that, when there is a noon at Lanka, there should be sunset at Yavkoti and sunrise at Romak and midnight at Siddhapoor.

 Bhaskaracharya had accurately calculated apparent orbital periods of the Sun and orbital periods of Mercury, Venus, and Mars. There is slight difference between the orbital periods he calculated for Jupiter and Saturn and the corresponding modern values.

Engineering

The earliest reference to a perpetual motion machine date back to 1150, when Bhāskara II described a wheel that he claimed would run forever.

Bhāskara II used a measuring device known as Yasti-yantra. This device could vary from a simple stick to V-shaped staffs designed specifically for determining angles with the help of a calibrated scale.
References

 Pingree, David Edwin. Census of the Exact Sciences in Sanskrit. Volume 146. American Philosophical Society, 1970. ISBN 9780871691460
    BHASKARACHARYA, Written by Prof. Mohan Apte

Disavowal: I have merely reproduced the content of previous works by people on this subject in a lust to get it to many. Genuineness or question of correctness to be discussed with reference book authors. I have tried to correct maximum I can. If any mistakes are there, kindly ignore those mistakes as some times mistakes will enshroud from eyes!

Labels:

Do You Know? about India your motherland! Be proud of that!!

Courtesy: http://veda.wikidot.com/do-you-know  

From the invention of the decimal system in mathematics to the noble philosophy of ahimsã, Hindus have contributed their share in all fields of knowledge and learning. Over five thousand years ago, when Europeans were only nomadic forest dwellers, ancient Hindus had established a civilization, known as the Harappan culture, in the Indus Valley, the northwestern region of India. When much of the world was still sunk in sleep, people of the Harappan culture were conducting trade workshops in weaving, bead-making, pottery, dying of fabrics, and metallurgy.
Although modern images & descriptions of India often show poverty, India was one of the richest countries till the time of British in the early 17th Century. Christopher Columbus was attracted by India's wealth and was looking for route to India when he discovered America by mistake. If readers, who have diligently read their schoolbooks on India, are surprised that they haven't been told of these ideas before, the fault is of the books they have used. Such books are as worthless as would be books on America, two hundred years from now, that describe only matters of conflict between race, language, and gender, ignoring completely the achievements of science, art, and imagination.
The official Sanskrit name for India is Bharat. INDIA has been called Bharat even in satya yuga.

Charaka Samhita: World’s first physician
 
The west is fond of proclaiming Hippocrates (460 – 377 BC) as the father of medicine, but way before him in 500 BC Maharishi Charaka wrote the famous Charaka Samhita or Physicians’ Handbook. The Charaka Samhita went into great detail to describe human anatomy, pathology, diagnostic procedures, and treatment for various diseases. Charaka defined eight major medical disciplines of Ayur Veda: Shailya Chikitsa (surgery), Shaalakya Chikitsa (head, eye, nose, throat), Kaaya Chikitsa (mental health), Kaumarbhrutya Chikitsa (pediatrics), Agada Tantra (toxicology), Rasaayana Tantra (Pharmacology), Vaajeekarna Tantra (reproductive medicine). Charaka also described the functions of the heart and the circulatory system in great detail. The Charaka Samhita was widely translated in various languages and Charaka was a respected medical authority in both the Arab and Roman empires.


The Worlds Oldest Living Civilisation
 
Did you know that by 7500 B.C. Bharat (India) already had advanced townships with villages of mud-brick houses?
Bharatvarsh (the Indian Subcontinent) is home to the oldest civilization in the world. Mehrgarh which dates to 7500 BC is the oldest city which predates the Indus Valley Civilisation. Recently there have been archaeological findings off the coast of Gujarat in India which confirm a submerged city which is the worlds oldest city. This Indian city dates back to 8000-9000BC.
In 1922, excavations began at Mohenjo-Daro (which means 'hill of the dead') in the Indus Valley, four hundred miles south-west of Harappa, which revealed a rich urban civilization that no one had suspected. Incredibly, Mohenjo-Daro proved to be as sophisticated as a later Greek or Roman city, built on mud-brick platforms to protect it from floods, with a grid-plan reminiscent of New York, and an impressive sewer system - not to mention sit-down toilets. The size of the city indicated that it held about 40,000 people. The large number of female statuettes found there suggested that a female deity - probably the moon goddess - was worshipped. Their seals proved they possessed some form of writing.
A scientifically planned towns and buildings were part of the landscape and about 300 settlements in a belt extending 1,520 km from North to South covering a million square kilometers have been discovered, of which Harappa, Mohenjo-Daro, Kalibangan, and Lothal are important sites. The towns were designed with citadels and defensive walls and the streets and lanes had drains. Individual bathrooms and lavatories were impressively drained into a larger system. Well-developed docks and store houses as well as bullock carts for transportation were very popular.

The earliest recorded Indian mathematics was found along the banks of the Indus. Archaeologists have uncovered several scales, instruments, and other measuring devices. The Harappans employed a variety of plumb bobs that reveal a system of weights 27.584 grams. If we assign that a value of 1, other weights scale in at .05, .1, .2, .5, 2, 5, 10, 20, 50, 100, 200 and 500. These weights have been found in sites that span a five-thousand-year period, with little change in size.

Archaeologists also found a “ruler” made of shell lines drawn 6.7 millimeters apart with a high degree of accuracy. Two of the lines are distinguished by circles and are separated by 33.5 millimeters, or 1.32 inches. This distance is the so-called Indus inch. 'In subsequent years, further excavations along the 1800 miles of the Indus river valley revealed more than 150 sites, half a dozen of the cities. The whole area, from the Arabian sea to the foothills of the Himalayas, was once the home of a great civilization that rivaled Egypt or Greece. To the east of the Indus lies a vast desert, the Thar Desert. When remains of towns were found in this desert there was some puzzlement about how they had survived in such arid conditions. Then satellite photography revealed the answer: the Thar Desert was once a fertile plain, traversed by a great river; there were even unmistakable signs of canals. Now only a small part of this river, the Ghaggar, exists. Scholars concluded that the river that had now vanished was the Sarasvati, mentioned in the Vedic hymns.

It seemed that in the heyday of Mohenjo-Daro and Harappa, this whole plain was one of the richest places in the world. At a time when ancient Britons were Bronze Age farmers, and the Greeks were a few Mycenaean warrior tribes, one of the world's greatest civilizations flourished in the land of the Indus and the Sarasvati. It seems that some great catastrophe destroyed this civilization some time after 1900 BC. Evidence shows that the earth buckled, due to the pressure of the tectonic plate that has raised the Himalayas, and the result was a series of earthquakes and volcanic eruptions that literally caused the rivers to sink into the ground. The cost in human life must have been appalling.

 Atomic Theory

Sage Kanad, 600 BC, is recognized as the founder of atomic theory, and classified all the objects of creation into nine elements (earth, water, light or fire, wind, ether, time, space, mind and soul). He stated that every object in creation is made of atoms that in turn connect with each other to form molecules nearly 2,500 years before John Dalton. Further, Kanad described the dimension and motion of atoms, and the chemical reaction with one another.
These Indian ideas about atom and atomic physics could have been transmitted to the West during the contacts created between India and West by the invasion of Alexander.

Life Cycles of the Universe 

The Hindus view that the Universe has no beginning or end, but follows a cosmic creation and dissolution. Hindus are the only one who propounds the idea of life-cycles of the universe. It suggests that the universe undergoes an infinite number of deaths and rebirths. Hindus views the universe as without a beginning (anadi = beginning-less) or an end (ananta = end-less). Rather the universe is projected in cycles. Hindu scriptures refer to time scales that vary from ordinary earth day and night to the day and night of the Brahma that are a few billion earth years long.
According to Carl Sagan,
"A millennium before Europeans were wiling to divest themselves of the Biblical idea that the world was a few thousand years old, the Mayans were thinking of millions and the Hindus billions".
Continues Carl Sagan,
"… is the only religion in which the time scales correspond… to those of modern scientific cosmology."
Its cycles run from our ordinary day and night to a day and night of the Brahma, 8.64 billion years long, longer than the age of the Earth or the Sun and about half the time since the Big Bang". One day of Brahma is worth a thousand of the ages (yuga) known to humankind; as is each night." Thus each kalpa is worth one day in the life of Brahma, the God of creation. In other words, the four ages of the mahayuga must be repeated a thousand times to make a "day ot Brahma", a unit of time that is the equivalent of 4.32 billion human years, doubling which one gets 8.64 billion years for a Brahma day and night. This was later theorized (possibly independently) by Aryabhata in the 6th century. The cyclic nature of this analysis suggests a universe that is expanding to be followed by contraction… a cosmos without end. This, according to modern physicists is not an impossibility.

Heliocentric Solar System 

Ancient Hindus were first to suggest a heliocentric solar system. Speed of light was calculated as 1,85,016 miles/sec. They had even calculated the distance between Earth and Moon as 108 diameters of Moon and Earth and Sun as 108 diameters of Sun. These figures are very close to the modern day values. All these were stated several thousand years before the famous scientist Galileo postulated in the west that sun was the center of the planetary system and Earth was not flat, which was against the prevailing religious doctrines and he died during his house-arrest by clergy. Another astonishing invention was ancient Hindus calculated the age of Earth as 4.3 billion years. The modern estimate is 4.5 billion years. Just remember that the biblical age of the Earth, as per Christians, is just 6,000 years!.

Oldest Systematic Language 

Did you know that Sanskrit is the world’s oldest systematic language?
The word sanskrita, meaning "refined" or "purified," is the antonym of prakrita, meaning "natural," or "vulgar." It is made up of the primordial sounds, and is developed systematically to include the natural progressions of sounds as created in the human mouth. Sanskrit was considered as "Dev Bhasha", "Devavani" or the language of the Gods by ancient Indians. There are 54 letters in the Sanskrit alphabet. Each has masculine and feminine, shiva and shakti. 54 times 2 is 108.

Mother of all Higher Languages

The Sanskrit language has helped shape many European languages including French, German, Russian, and English. It shows many ancient forms of words such as father, through, shampoo, trigonometry, and mouse, while guru, pundit, dharma, bandh, and yoga are among hundreds of Sanskrit words that can now be found in the Oxford dictionary.

Earliest and only known Modern Language

Panini (c 400BC), in his Astadhyayi, gave formal production rules and definitions to describe Sanskrit grammar. Starting with about 1700 fundamental elements, like nouns, verbs, vowels and consonents, he put them into classes. The construction of sentences, compound nouns etc. was explained as ordered rules operating on underlying fundamental structures. This is exactly in congruence with the fundamental notion of using terminals, non-terminals and production rules of moderm day Computer Science. On the basis of just under 4,000 sutras (rules expressed as aphorisms), he built virtually the whole structure of the Sanskrit language. He used a notation precisely as powerful as the Backus normal form, an algebraic notation used in Computer Science to represent numerical and other patterns by letters.
It is my contention that because of the scientific nature of the method of pronunciation of the vowels and consonants in the Indian languages (specially those coming directly from Pali, Prakit and Sanskrit), every part of the mouth is exercised during speaking. This results into speakers of Indian languages being able to pronounce words from any language. This is unlike the case with say native English speakers, as their tongue becomes unused to being able to touch certain portions of the mouth during pronunciation, thus giving the speakers a hard time to speak certain words from a language not sharing a common ancestry with English. I am not aware of any theory in these lines, but I would like to know if there is one.

Yoga - Health of the Body and Mind 

Yoga is a system of exercises for physical and mental nourishment. Apart from being a system of exercise, an important aspect of Yoga is that of self-discipline.
The fundamentals of Yoga were systematically presented by Patanjali in a treatise known as Yogasutras i.e. Yoga Aphorisms. According to Patanjali, within the human body there are channels called Nadi and centres called Chakra. If these are tapped, The energy hidden in the body can be released. This energy is called Kundalini. The release of Kundalini enables the body to acquire many powers which are normally beyond its capability.

Stages of Yoga

Yama (universal moral commandments), Niyama (self-purification through discipline), Asana (posture), Pranayama (breath-control), Pratyahara (withdrawal of mind from external objects), Dharana (concentration), Dhyana (meditation) and Samadhi (state of super-consciousness) .
But though the Yogasutras were formulated 2000 years ago, Yoga has been practiced for countless generations, it is only in the last few years that scientists have begun to recognise the powers of yoga. It has now been established through experiments that by practicing Yoga, several ailments can be cured. Tests conducted on Yogis show that they do acquire extraordinary physical powers. For instance, they can live without oxygen for a long time, they can also adjust their metabolism if they have to remain without food for long periods. Yoga is being increasing applied in the field of Physiotherapy.
There are innumerable asanas (poses) in Yoga. Most of them derive their names from the semblance of the body in those poses to different animals and objects. Yoga is a multifarious system, there are various forms of discipline touching different aspects of human life, which are brought under the heading Yoga.

Asanas (Poses)

Matsyasana (pose like Fish pose), Mayurasana (pose like Peacock), Simhasana (pose like a Lion), Halasana (pose like a Plough), Shavasana (pose like a dead body, in absolute stillness).

Yoga Disciplines

Hathayoga (Bodily exercise), Gyanyoga or Dnyanyoga (Exercise for the mind and intellect), Karmayoga (Discipline in our actions in daily life)


Dice  

 A die found in excavations at a Harappan period site. Note that the six is not opposite the one.

The dice is attributed to India by some accounts. Some of the earliest archaeological evidence of oblong dice have been found in Harrapan sites such as Kalibangan, Lothal, Ropar, Alamgirpur, Desalpur and surrounding territories, some dating back to the third millennium BCE, which were used for gambling. The oblong or cubical dice (akṣa) is the precursor of the more primitive vibhīṣaka—small, hard nuts drawn randomly to obtain factors of a certain integer. Dicing is believed to have later spread westwards to Persia, influencing Persian board games. Early references to dicing can be found in the Ṛig Veda as well as the newer atharvaveda.


Invention of Decimal System 

Did you know that Hindus gave us the method of expressing numbers by means of a decimal system?
The so called Arabic numerals are actually Hindu numerals and even many Arab mathematicians admit that. During the 700's, the Arabs learned Hindu arithmetic from scientific writings of the Hindus and the Greeks. Then, in the 800's, a Persian mathematician wrote a book that was translated into Latin about 300 years later. This translation brought the Hindu-Arabic numerals into Europe.



Hindu mathematicians used a system based on 10. The Hindus had symbols for each number from one to nine. They had a name for each power of 10, and used these names when writing numerals. For example, Hindus wrote "1 sata, 3 dasan, 5" to represent the number we write as 135. They wrote "1 sata, 5" for the number we write as 105. Hindus found a way of eliminating place names. They invented the symbol shunya (meaning empty), which we call zero. With this symbol, they could write "105" instead of "1 sata, 5."
The largest numbers the Greeks and the Romans used were 106 whereas Hindus used numbers as big as 1053 (i.e 10 to the power of 53) with specific names (Tallakshana) as early as 5000 B.C. during the Vedic period. Even today, the largest used number is Tera: 1012 (10 to the power of 12).
"It is India that gave us the ingenuous method of expressing all numbers by the means of ten symbols, each symbol receiving a value of position, as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit, but its very simplicity, the great ease which it has lent to all computations, puts our arithmetic in the first rank of useful inventions, and we shall appreciate the grandeur of this achievement when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest minds produced by antiquity."
— French mathematician Pierre Simon Laplace (1749 - 1827)
 The Game of Chess 

The game of chess was invented in India and was originally called Ashtapada (sixty-four squares).
"Ashtapada" Sanskrit for spider -"a legendary being with eight legs" was played with dice on an 8x8 checkered board. There were no light and dark squares like we see in today's chess board for 1,000 years. Other Indian boards included the 10×10 Dasapada and the 9×9 Saturankam.

 Krishna and Radha playing chaturanga on an 8x8 Ashtāpada.

Later this game came to be known as chaturanga. The Sanskrit name Chaturanga means 'quadripartite' — the four angas (divided into four parts). The earliest known form of chess is two-handed chaturanga, Sanskrit for "the 4 branches of the army." Like real Indian armies at that time, the pieces were called elephants, chariots, horses and foot soldiers. Unlike modern chess, chaturanga was mainly a game of chance; results depended on how well you rolled the dice.
SpreadofChessfromIndia.jpg
Map showing origin and diffusion of chess from India to Asia, Africa, and Europe, and the changes in the native names of the game in corresponding places and time.
Chaturanga is well recognized as the earliest form of chess. Played on an authentic cloth game surface by 2, 3 or 4 players, Chaturanga combines the basic strategy of chess with the dynamic challenge of chance as each move is determined by the random roll of wooden dice. There is evidence of ‘chaturanga’ having been played with dice, which is still not uncommon, although it involved more skill than chance in this version. In fact, Yudhishthira and Duryodhana, in the Mahabharata, played a version of chaturanga using a dice. The game Chaturanga was a battle simulation game which rendered Indian military strategy of the time.


In 600 AD this game was learned by Persians who named it Shatranj. Shatranj is a foreign word among the Persians and the Arabians, whereas its natural derivation from the term Chaturanga is obvious. Again affix the Arabic name for the bishop, means the elephant, derived from alephhind, the Indian elephant.
Even the word 'checkmate' is derived from the Persian term Shah Mat which means 'the king is dead!'. The Sanskrit translation of this term would be Kshatra Mruta. Another term viz. 'the rooks' which is the name for one set of the counters used in chess, originated from the Persian term Roth which means a soldier. The Persian term is derived from the Indian term Rukh, which obviously seems to have originated in the Sanskrit word Rakshak which means a soldier from Raksha which means 'to protect'.
About the introduction of this game into Persia, the Encylopedia Britannica says that the Persian poet Firdousi, in his historical poem, the Shahnama, gives an account of the introduction of Shatranj into Persia in the reign of Chosroes I Anushirwan, to whom came ambassadors from the sovereign of Hind (India), with a chess-board and men asking him to solve the secrets of the game, if he could or pay tribute. The king asked for seven days grace, during which time the wise men vainly tried to discover the secret. Finally, the king's minister took the pieces home and discovered the secret in a day and a night.
indian-chess.jpg
Chaturanga.
The Encyclopedia Britannica concludes that "Other Persian and Arabian writers state that Shatranj came into Persia from India and there appears to be a consensus of opinion that may be considered to settle the question. Thus we have the game passing from the Hindus to the Persians and then to the Arabians, after the capture V of Persia by the Caliphs in the 7th century, and from them, directly or indirectly, to various parts of Europe, at a time which cannot be definitely fixed, but either in or before the 10th century. That the source of the European game is Arabic is clear enough, nor merely from the words "check" and "mate", which are evidently from Shah mat ("the king is dead"), but also from the names of some of the pieces.

Local Variations

Tamil variations of chaturanga are ‘puliattam’ (goat and tiger game), where careful moves on a triangle decide whether the tiger captures the goats or the goats escape; the ‘nakshatraattam’ or star game where each player cuts out the other; and ‘dayakattam’ with four, eight or ten squares, a kind of ludo. Variations of the ‘dayakattam’ include ‘dayakaram’, the North Indian ‘pachisi’ and ‘champar’. There are many more local variations.

Surgery: 300 different types Operations, and 125 Surgical Instruments 

The ancient Indians were also the first to perform amputation, cesarean surgery and cranial surgery. Sushruta as early as 600 BC used cheek skin to perform plastic surgery to restore and reshape human nose, ears, and lips with incredible results. In his treatise, Shushruta Samhita, he classified surgery into eight types:
  1. aaharya (extracting solid bodies),
  2. bhedya (excision),
  3. eshya (probing),
  4. lekhya (sarification),
  5. vedhya (puncturing),
  6. visravya (extracting fluids), and
  7. sivya (suturing).
Shushruta describes the details of more than 300 operations such as extracting solid bodies, excision, incision, probing, puncturing, evacuating fluids and suturing. Ancient Indians were also the first to perform amputations, caesarean and cranall surgeries with 42 surgical processes. He worked with 125 kinds of surgical instruments including scalpels, lancets, needles, catheters, etc. Sushruta even devised non-invasive surgical treatments with the aid of light rays and heat. Sushrata & his team conducted complicated surgeries like cataract, artificial limbs, cesareans, fractures, urinary stones and also plastic surgery and brain surgeries.
Chanakya's Arthashãstra describes post-mortems, and Bhoja Prabandha describes brain surgery, successfully performed in 927 AD by two surgeons on King Bhoja to remove a growth from his brain. Usage of anesthesia was well known in ancient India medicine. Detailed knowledge of anatomy, embryology, digestion, metabolism, physiology, etiology, genetics and immunity is also found in many ancient Indian texts.

Vedic roots of Mathematics 

Did you know that Geometry, Trigonometry, Calculus and Algebra are studies which originated in India?
The word Geometry seems to have emerged from the Sanskrit word gyaa-miti which means "measuring the Earth". And the word Trigonometry is similar to tri-kona-miti meaning "measuring triangular forms". Euclid is credited with the invention of Geometry in 300 BCE while the concept of Geometry in India emerged in 1000 BCE, from the practice of making fire altars in square and rectangular shapes. The treatise of Surya Siddhanta describes amazing details of Trigonometry, which were introduced to Europe 1200 years later in the 16th century by Briggs. All Hindu as well as Buddhist mandalas and yantras are complex forms of Geometrical shapes.

Bhaskaracharya otherwise known as Bhaskara is probably the most well known mathematician of ancient Indian today. Bhaskara wrote his famous Siddhanta Siroman in the year 1150 A.D. It is divided into four parts; Lilavati (arithmetic), Bijaganita (a treatise on algebra), Goladhyaya (celestial globe), and Grahaganita (mathematics of the planets). An Arabic Scholar Al Zabar translated a Bhaskara's work Bijaganita from Sanskrit. It was later known as Algebra in European languages.
From India the sine function was introduced to the Arab world in the 8th century, where the term jya was transliterated into jiba or jyb. Early Latin translations of Arabic mathematical treatises mistook jiba for the Arabic word jaib, which can mean the opening of a woman's garment at the neck. Accordingly, jaib was translated into the Latin sinus, which can mean "fold" (in a garment), "bosom," "bay," or even "curve." Hence our word "sine."
The word “Algorithm” was actually supposed to be pronounced “Al-Khwarizmi”, which was the name of an eminent 9th century Arab scholar, who played important roles in importing knowledge on arithematic and algebra from India to the Arabs. In his work, De numero indorum (Concerning the Hindu Art of Reckoning), it was based presumably on an Arabic translation of Brahmagupta where he gave a full account of the Hindu numerals which was the first to expound the system with its digits 0,1,2,3,…,9 and decimal place value which was a fairly recent arrival from India. The new notation came to be known as that of al-Khwarizmi, or more carelessly, algorismi; ultimately the scheme of numeration making use of the Hindu numerals came to be called simply algorism or algorithm.

Oral tradition of Vedic Chanting is declared an intangible heritage of humanity by UNESCO 

The oral tradition of Vedic chanting has been declared an intangible heritage of humanity by UNESCO. In a meeting of jury members on November 7, 2003, at Paris, Mr. Koichiro Matsuura, Director-General of UNESCO, declared the chanting of Vedas in India an outstanding example of heritage and form of cultural expressions. The proclamation says that in the age of globalization and modernization when cultural diversity is under pressure, the preservation of oral tradition of Vedic chanting, a unique cultural heritage, has great significance.

Hindu Kush 

'Hindu Kush' means Hindu slaughter. The Indian name for Hindu Kush mountain range was 'Paariyaatra Parvat'. Until 1000 A.D. the area of Hindu Kush was a full part of Hindu cradle. The name 'Hindu Kush' was given by the muslim conquerors indicating the Hindu genocide that took place in this region.

The oldest book in the library of humans is the Rigveda 

The existence of the Vedas go beyond recorded history and are said to be passed down from the Gods to the great seers of Bharat. For many human generations the Vedas were passed on through word of mouth, until finally documented by the great Rishis and Swamis.
'The Vedas are written in Sanskrit, a complex language that Sir William Jones - in 1786 - demonstrated to be related to Greek, Latin, German and Celtic (giving rise to the expression 'Indo-European languages'). And if the Vedas speak of the Sarasvati River, then it would seem clear that they were written before about 2000 BC, and not later than 1500 BC, as scholars originally believed. And if - as seems likely - Sanskrit was the language of the Aryans, then it was also clear that they could not have invaded as late as 1500 BC.
There are four major collections of Vedic hymns - the Rig-Veda, the Samaveda, the Yajurveda and the Atharvaveda, of which the Rigveda is recognized as the oldest and most important.
In the 1980's, a Vedic scholar, David Frawley, observed that the hymns of the Rigveda are full of an oceanic symbolism that seems to argue that they sprang from the maritime culture - which certainly contradicted the assumption that the Aryans came from somewhere in central Europe. He also noted hymns that spoke of the 'ancestors' as coming from across the sea, having been saved from the great flood.
Studying the astronomical references in the Vedic hymns, Frawley concluded that one reference to a summer solstice in Virgo indicated a date of about 4000 BC, while a reference to a summer solstice in Libra pointed to about 6000 BC. He also concluded that the authors of the Vedas were familiar with the precession of the equinoxes. These revolutionary ideas were set out in a book called Gods, Sages and Kings (1991).

The Place Value System 

The place value system is built into the Sanskrit language and so whereas in English we only use thousand, million, billion etc, in Sanskrit there are specific nomenclature for the powers of 10, most used in modern times are dasa (10), sata (100), sahasra (1,000=1K), ayuta (10K), laksha (100K), niyuta (106=1M), koti (10M), vyarbuda (100M), paraardha (1012) etc. Results of such a practice were two-folds. Firstly, the removal of special importance of numbers. Instead of naming numbers in grops of three, four or eight orders of units one could use the necessary name for the power of 10. Secondly, the notion of the term "of the order of". To express the order of a particular number, one simply needs to use the nearest two powers of 10 to express its enormity.

Ayurveda - the Science of Longevity 

Ayurveda is the indigenous system of medicine in India. Ayurveda literally means 'the science of living' (longevity). Ayu means "Life" and Veda means "Knowledge". The origins of this system of medicine are lost in the hoary past, and the body of knowledge that comes under the heading Ayurveda constitutes ideas about diseases, diagnosis and cure, which have been accumulated over the ages past.
The feature that distinguishes this system of medicines from other systems like Allopathy and Homeopathy is that it is solely based on herbs and herbal compounds. The medical system of Ayurveda draws heavily from the doctrines developed in the Charaka-Samahita. The main quality which Ayurveda has borrowed from Charaka is its aim of removing the cause for illness and not just curing the disease itself. In Ayurveda there are no such things as instant relievers, pain killers or antibiotics. The herbs used in Ayurvedic remedies do not operate against the body's metabolism, their effect is registered gradually and hence there are minimum side-effects. The constituents of Ayurvedic medicines are largely based on organic matter. The absence of fast registering inorganic compounds which are at times corrosive, contributes to the absence of side-effects from Ayurvedic medicines.
Unique quality of Ayurveda is that it uncovers and cures the root cause of illness, it is safe, gentle and inexpensive, it sees 6 stages of disease development (where modern medicine only sees the last two stages), it treats people in a personalized manner according to their dosha or constitution and not in any generic manner.

Mokshapat: Snake and Ladder had its origin in India 

The game had its origin in India and was called Moksha Patam or Parama Padam or Mokshapat. It was used to teach Hindu Dharma and Hindu values to children. The British renamed it as Snakes and Ladders.
The game was created by the 13th century poet saint Gyandev. The ladders in the game represented virtues and the snakes indicated vices. The game was played with cowrie shells and dices. Later through time, the game underwent several modifications but the meaning is the same i.e good deeds take us to heaven and evil to a cycle of re-births. There are certain references which take the game back to 2nd century BC.
indian-snakes-n-ladders.jpg
Indian Snakes and Ladders game (1700’s AD)
In the original game square 12 was faith, 51 was Reliability, 57 was Generosity, 76 was Knowledge, and 78 was Asceticism. These were the squares were the ladder was found. Square 41 was for Disobedience, 44 for Arrogance, 49 for Vulgarity, 52 for Theft, 58 for Lying, 62 for Drunkenness, 69 for Debt, 84 for Anger, 92 for Greed, 95 for Pride, 73 for Murder and 99 for Lust. These were the squares were the snake was found. The Square 100 represented Nirvana or Moksha.
Also known as ‘paramapadam’, there are a hundred squares on a board; the ladders take you up, the snakes bring you down. The difference here is that the squares are illustrated. The top of the ladder depicts a God, or one of the various heavens (kailasa, vaikuntha, brahmaloka) and so on, while the bottom describes a good quality. Conversely, each snake’s head is a negative quality or an asura (demon). As the game progresses, the various karma and samskara, good deeds and bad, take you up and down the board. Interspersed are plants, people and animals.
The game serves a dual purpose: entertainment, as well as dos and don’ts, divine reward and punishment, ethical values and morality. The final goal leads to Vaikuntha or heaven, depicted by Vishnu surrounded by his devotees, or Kailasa with Shiva, Parvati, Ganesha and Skanda, and their devotees. In this age of moral and ethical degeneration, this would be a good way of teaching values to children who think they already know more than their parents.
If paramapadam teaches moral values, pallankuli develops skill and quick thinking. Two players compete on a board consisting of between seven and twenty pits per player; each player has to collect the coins or shells or seeds with which the game is played, the player with the maximum number being the winner. There are nine variations of this game, each a ‘pandi’, with regional, caste and religious variations. It was very popular among women and required a good memory and alertness, as they had to count and remember the number of coins or seeds accumulated by the opponent.
The British took the game to England in 1892 and named it Snakes and Ladders and changed it according to Victorian values.

Hindsa 


The Arabs borrowed so much from India in the field of mathematics that even the subject of mathematics in Arabic came to known as Hindsa which means 'from India' and a mathematician or engineer in Arabic is called Muhandis which means 'an expert in Mathematics'

Hindu Kālagaņanā (chronologies) is the Oldest in the World! 

According to Indian tradition or Hindu Kālagaņanā, three chronologies are in currency. Firstly, the Kali era or Kalyabda, which has begun from the present Kaliyuga and hence it is 5107 years old. Secondly, the Kalpābda which has begun with the present Svetavārāha Kalpa, and hence it is 1,971,221, 107 years old. And thirdly, the Sŗsţābda, which has begun with the creation of this universe and hence it is 155,521,971,221,107 years old. One should notice that. Kalyabda is fit for narrating historical events of recent past while Kalpābda and Sŗstābda are suitable for narrating much older cosmological, geological, geographical, biological and other events such as the creation of this earth, creation of the sun, beginning of life on earth and so on. So the scientists may find in them the most suitable alternative to the geological time frame which they are now extensively using for describing such older events.
Today, there are many chronologies, much older than the Christian chronology, extant in the world, as shown below:
Chronology Antiquity in years
Roman 2,753
Greek 3,576
Turkish (new) 4,294
Chinese (new) 4,360
Hindu (Kalyabda) 5,106
Jewish 5,764
Iran (new) 6,008
Turkish (old) 7,610
Egyptian 28,667
Iran (old) 189,971
Chinese (old) 96,002,301
Hindu (Kalpābda) 1,971,221,106
Hindu (Sŗşābda) 155,521,971,221,106
So a rational mind may ask — despite having so many older chronologies, why the shortest of them, the Christian chronology has been given the status of an international calendar? Why the 21st birth centenary of a person is to be observed as the 21st century of the entire world? If a genuine thought is given to the matter, without any racial, regional, political, sectorial or religious prejudice, the Hindu alone deserves the right to be treated as the calendar of the world, since it is the oldest and based entirely astronomical science. So, it carries much more scientific sense in saying that we have entered the 52nd century of Kalyabda in 1998, than in saying that we have entered the 21st century of the Christian calendar in 2001.

The Game of Cards 

The popular game of cards originated in ancient India and was known as Krida-patram. It was one of the favorite pastimes of Indians in ancient times. This game was patronized especially by the royalty and nobility. In medieval India, playing cards was known as Ganjifa cards which were played in practically all royal courts. This game is recorded to have been played in Rajputana, Kashyapa Meru (Kashmir), Utkala (Orissa) the Deccan and even in Nepal. The Mughals also patronized this game, but the Mughal card-sets differed from those of the ancient Indian royal courts.
According to Abul Fazal's (author of the Ain-e-Akbari) description of the game, the following cards were used. The first was Ashvapati which means 'lord of horses'. The Ashvapati which was the highest card in, the pack represented the picture of the king on horseback. The second highest card represented a General (Senapati) on horseback. After this card come ten other with pictures of horses from one to ten.
Another set of cards had the Gajapati (lord of elephants) which represented the king whose power lay in the number of elephants. The other eleven cards in this pack represented the Senapati and ten others with a soldier astride an elephant. Another pack has the Narpati, a king whose power lies in his infantry. We also had other cards known as the Dhanpati, the lord of treasures, Dalpati the lord of the squadron, Navapati, the lord of the navy, Surapati, the lord of divinities, Asrapati, lord of genii, Vanapati, the king of the forest and Ahipati, lord of snakes, etc.
On the authority of Abul Fazal we can say that the game of playing cards had been invented by sages in ancient times who took the number 12 as the basis and made a set of 12 cards. Every king had 11 followers, thus a pack had 144 cards. The Mughals retained 12 sets having 96 cards. These Mughal Ganjifa sets have representations of diverse trades like Nakkash painter, Mujallid book binder, Rangrez, dyer, etc., In addition there were also the Padishah-i-Qimash, king of the manufacturers and Padishah-izar-i-Safid, king of silver, etc.
Cards were known as Krida-patram in ancient India. These cards were made of cloth and depicted motifs from the Ramayana, Mahabharata, etc. A tradition carried on today with floral motifs and natural scenery.
The pre-Mughal origin of the game of cards is evident if we examine the pattern of painting the cards. We also find that despite the observation of Abul Fazal that Akbar introduced the pack with 8 sets, we find that even earlier, in Indian (Hindu) courts we have packs with 8, 9 and 10 sets apart from the usual 12. The numbers were derived from the eight cardinal directions Ashtadikpala, for the pack with 8 set, from the nine planets Navagraha for the one with 9 sets and from ten incarnations Dashavatara of Vishnu for the pack with 10 sets.
Themes from the Ramayana and Mahabharata are painted on these cards. The largest number of such cards are to be found in Orrisa. The largest number of such cards are to be found in Orissa. The painters from Orissa have represented various illustrations like the Navagunjara, a mythical birdhuman animal which was the form assumed by Sri Krishna to test Arjuna's fidelity, illustrations from the Dashavatata of Vishnu are also portrayed.
All these cards were hand-made and were painted in the traditional style. This required considerable patience and hard meticulous work. The kings usually commissioned painters to make cards as per their preference. The commoners got their cards made by local artists who were to be ; found in urban and rural areas. In order to -obtain the required thickness a number of sheets of pieces of cloth were glued together. The outlines of the rim were painted in black and then the figures were filled with colors.
As cards were played by members all strata of society we find different types of cards. Some cards were also made of ivory, tortoise shell, mother of pearl, inlaid or enameled with precious metals. The cards were of different shapes; they were circular, oval rectangular, but the circular cards were more common. The cards were usually kept in a wooden box with a lid painted with mythological figures. This art of handmade, hand painted cards which had survived for hundreds of years. gradually feel into decay and became extinct with the introduction of printed paper cards by the Europeans in the 17-18th centuries. With the extinction of the art of making and painting cards also was erased the memory that Indians ever had played the game of cards with their own specific representations of the Narapati, Gajapati and Ashvapati.

 The Concept of 'Zero' 

Did you know that the ancient Hindus originated the concept 'zero'?
The concept of zero is referred to as shunya in the early Sanskrit texts and it is also explained in the Pingala’s Chandah Sutra (200 AD). In the Brahma Phuta Siddhanta of Brahmagupta (400-500 AD), the zero is lucidly explained. The Hindu genius Bhaskaracharya proved that x divided by 0 = 4 (infinity) and that infinity however divided remains infinity. This concept was recognized in Hindu theology millennia earlier. The earliest recorded date for an inscription of zero (inscribed on a copper plate) was found in Gujarat (585 – 586 AD). Later, zero appeared in Arabic books in 770 AD and from there it was carried to Europe in 800 AD.
The Indian place-value numeration with zero sign ranks among humanity's fundamental discoveries.


 Ancient root of Navigation 

The art of Navigation was born in the river Sindhu 6000 years ago. The very word Navigation is derived from the Sanskrit word 'Navgatih'. The word navy is also derived from Sanskrit 'Nou'.


The Value of Pi 

Did you know that the ratio of the circumference and the diameter of a circle known as Pi (a value of 3.141592657932…) was first calculated by Hindus?
The Sanskrit text, by the famous Hindu mathematician, Baudhayana in his Baudhayana Sulbha Sutra of the 6th century BC mentions this ratio as approximately equal to 3. The Hindu mathematician, Aryabhatta, in 499 AD worked out the value of Pi to the fourth decimal place as [3x (177/1250) = 3.1416]. In 825 AD one Arab mathematician Mohammad Ibna Musa said: This value has been given by the Hindus [Indians] (62832/20,000 = 3.1416).

The Word-Numeral System 

The word-numeral system was the logical outcome of proceeding by multiples of ten. Thus, in an early system, 60,799 is denoted by the Sanskrit word sastim (60), shsara (thousand), sapta (seven) satani (hundred), navatim (nine ten times) and nava (nine). Such a system presupposes a scientifically based vocabulary of number names in which the principles of addition, subtraction and multiplication are used. It requires:
  1. the naming of the first nine digits (eka, dvi, tri, catur, pancha, sat, sapta, asta, nava);
  2. a second group of nine numbers obtained by multiplying each of the nine digits in 1 by ten (dasa, vimsat, trimsat, catvarimsat, panchasat, sasti, saptati, astiti, navati): and
  3. a group of numbers which are increasing integral powers of 10, starting with 102 (satam sagasara, ayut, niyuta, prayuta, arbuda, nyarbuda, samudra, Madhya, anta, parardha…).
To understand why word numerals persisted in India, even after the Indian numerals became widespread, it is necessary to recognize the importance of the oral mode of preserving and disseminating knowledge. An important characteristic of written texts in India from times immemorial was the sutra style of writing, which presented information in a cryptic form, leaving out details and rationale to be filled in by teachers and commentators. In short pithy sentences, often expressed in verse, the sutras enabled the reader to memorize the content easily.

 Mother of Martial Arts

Do you know that Kalari is considered to be the most complete and scientific martial art and is the mother of all martial arts?
Bodhidharma, a Buddhist monk from India, introduced Kalari into China and Japan in the 5th century. He taught this art in a temple This temple is today known as the Shaolin temple. The Chinese called him Po-ti-tama. What he taught has evolved into Karate and Kung Fu. One can find a lot of similarities among the three.
Thus Judo, Karate, Kung Fu and other similar marshal arts which are today identified with the far-east actually originated from India. At times the changes made in the original nature of the Indian sport-forms were so many and so fundamental that the game lost all similarity with its original form in India. Some Indian games were not transmitted abroad and remained confined to India.
For instance we have Kabbadi, Kho-Kho, AtyaPatya, Malkhamb, Gulli-danda, etc., which are being played today exclusively in India. In this chapter we shall look into how the games like Chess and Ludo (Snakes and Ladders), the martial art of Karate, and Playing cards had existed in India for the past 2000 years and how in some cases the indigenous form of the game became totally extinct erasing the fact that the game had ever been played in India.
The teacher here is not looked upon only as a coach as in western martial arts like boxing and fencing. This relationship between a teacher and student in Judo and Karate could have its roots in the Guru-Shishya tradition of India.

Bharatanatyam 

Bharatanatyam is amongst the oldest of the classical dance forms of India, with a history that goes back more than two thousand years. Integrating elements of music, theatre, poetry, sculpture, and literature, this multi-dimensional art has come down through the centuries, as part of a dynamic, vital, living tradition, that offers infinite scope for understanding and exploring the body, mind and spirit.

Time taken for Earth to orbit Sun 

The famous Hindu mathematician, Bhaskaracharya, in his treatise Surya Siddhanta, calculated the time taken for the earth to orbit the sun to nine decimal places (365.258756484 days).
Bhaskaracharya rightly calculated the time taken by the earth to orbit the sun hundreds of years before the astronomer Smart. His calculations was - Time taken by earth to orbit the sun: ( 5th century ) 365.258756484 days.
Today’s accepted measurement is 365.2564 days. Therefore, assuming that today’s figures are correct, it means that Bhaskaracharya was off by only 0.0002%.

Metallurgy  

India was the world-leader in Metallurgy for more than 5,000 years. Gold jewelery is available from 3,000 BCE. Brass and bronze pieces are dated back to 1,300 BCE. Extraction of zinc from ore by distillation was used in India as early as 400 BCE while European William Campion patented the process some 2,000 years later. Copper statues can be dated back to 500 CE. There is an iron pillar in Delhi dating back to 400 CE that shows no sign of rust or decay.
The earliest know book on metallurgy was known to be written by Nagarjuna in 10th century. The book Rasaratnanakara addresses various metallurgical topics such as:
  • Preparation of liquids (rasas) such as Mercury
  • Extraction of metals like Gold, Silver, Tin, and Copper from their ores and their purification
  • The processes of liquefaction, distillation, sublimation, and roasting
India was invaded by Mohammedans during the time of Nagarjuna. It is possible that Nagarjuna's texts fell into the hands of the invaders, who could have transmitted these Indian Metallurgical sciences to the outside world.

 The Christian Chronology 

From the days of British colonial rule we have developed a habit of following the Christian, or rather the Gregorian calendar. The main difficulty of this chronology is that, it originated only nearly 2000 years ago and hence incapable of accommodating events of long past as stated above. The geological time-frame invented by the scientists can take care of events which happened not earlier than 4 billion years ago. Most importantly, the origin and the process of counting months and years in Gregorian calendar are in no way linked to astronomical events. That is the reason why it was a matter of dispute whether the month February in 2000 A.D. would contain 29 days or 30 days.
Some texts try to establish a link between the birth of Jesus and the beginning of this Christian or Gregorian calendar and say that a bright star then appeared in the sky. According to the famous German astronomer Johannes Kepler, it was a conjunction of the planets Jupiter and Saturn in the zodiacal sign Pisces and the incident look place in 7 B.C. Most of the historians and researchers on Jesus believe that he was born somewhere in between 6 B.C. and 4 B.C. Moreover, the people who are connected with the origin of this calendar, possess entirely childish and amusing ideas about the creation of this universe and its antiquity. The Irish prelate James Ussher in 17th century openly declared, without giving any thought to the possible repercussions of his statement that this universe originated on February 26, 4004 B.C. at 9 a.m. Even today most of them believe that God created this earth and heaven within six days from nothingness and finished His task on that day.
In fact, the present Christian chronology originated in 753 B.C., the year of foundation of the city of Rome. In its original form, 304 days divided into 10 months made a year and its present form bears the testimony of this fact. At that time the parting 4 months, namely September, October. November and December were the 7th, 8th, 9th and 10th months of the year and their names were coined from septem, octo, novem and decem, the Latin words for 7.8.9 and 10. This shows the colossal lack of knowledge the Romans of that time had about the solar cycle and one can easily imagine the frightening disharmony it had with the solar cycle. Here one should also notice the striking similarity between the Latin words for 7, 8, 9 and 10 as mentioned above and the Sanskrit words saptam, astam, navam and dasam. This shows that the Romans learned the art of counting from India. However, in 46 B.C. emperor Julius Caesar introduced, quite arbitrarily, the month July after his name and then emperor Augustus Caesar introduced the month August after his name and made 12 months or 355 days a year. Then onwards it was called the Julian calendar.
In 1582, Pope Gregori XIII, in his endeavour to make it in harmony with the solar cycle, introduced some vital revisions. He introduced the practice of counting a year normally of 365 days and, a leap year of 366 days every fourth year. Furthermore, he made the rule that, a centesimal year will be treated as a leap year only when it is divisible by 400. Despite all such efforts it was seen that, a discrepancy of 11 days had crept in the year 1700 A.D. A compromise was made in that year by skipping those 11 days and in fact, 4th September was counted as 15th September in that year. In the Eastern Europe the said correction was done in 1917, when the discrepancy reached 13 days. According to the old calendar the Bolshevik revolution in Russia took place in October, but in November after correction. That is the reason why the Communists some times call it the Great October Revolution and some times the Great November Revolution. It is important to note here that, there is no scope of occurrence of such a discrepancy in Hindu calendar because months and years are counted here according to actual position of the sun in the sky. However, in 1752, only 5 years before the battle of Palāśī, this Gregorian calendar was adopted as the royal calendar of Britain and with the gradual expansion of the British Empire, it ultimately acquired the present status of an international calendar. So, one should notice that the Gregorian calendar has achieved the status of an international calendar not due to its superior scientific basis but due to military success of its followers.

34000th of a Second to 4.32 Billion Years 

The ancient Hindus had given the world the idea of the smallest and largest measuring units of Time. Astonishingly, the ancient Hindus used the following units of time:
Unit Equivalent Equivalent
Krati
34,000th of a second
1 Truti
300th of a second
2 Truti 1 Luv
2 Luv 1 Kshana
30 Kshana 1 Vipal
60 Vipal 1 Pal
60 Pal 1 Ghadi 24 minutes
2.5 Gadhi 1 Hora 1 Hour
24 Hora 1 Divas 1 Day
7 Divas 1 Saptaah 1 Week
4 Saptaah 1 Maas 1 Month
2 Maas 1 Rutu (season)
6 Rutu 1 Varsh 1 Year
100 Varsh 1 Shataabda 1 Century
10 Shataabda 1 Sahasraabda 10 Centuries or 1000 Years
432 Sahasraabda 1 Yuga 4320 Centuries or 432000 Years
10 Yuga 1 Mahayuga 43200 Centuries or 4320000 Years
1000 Mahayuga 1 Kalpa 43200000 Centuries or 4.32 Billion Years
India gave the largest measurement of time as 8.64 billion years.
The Gregorian calendar on your desk simply adds on one day for every 4 years and is not in coherence with the movement of sun. But, Hindu calendar is in coherence as the short fall is corrected in the month itself by adding Adhikamasa as postulated by Maharshi Vishwamitra. Rig Veda 1.164.1, 2, 14 and 15 describe sun's motion, ritus and colours of spectrum. Kalyana varma, Varahamihira, Jaimini, Vidyanatha Deekshita, Kalidasa, Mantreshwara, Satyacharya, Venkatadri, Parashara, Ramadayalu and Garga have immensely contributed for the development of Hindu astrology.

Raising 10 to the Power of 53 ! 


The highest prefix used for raising 10 to a power in today’s math is ‘D’ for 10 to a power of 30 (from Greek Deca). While, as early as 100 BCE Indian Mathematicians had exact names for figures upto 10 to the power of 53.
1= Ekam =1, 10 was Dashakam, 100 was Shatam (10 to the power of 10), 1000 was Sahasram (10 power of 3), 10000 was Dashasahasram (10 power of 4), 100000 was Lakshaha (10 power of 5), 1000000 was Dashalakshaha (10 power of 6), 10000000 was Kotihi (10 power of 7)……Vibhutangamaa (10 power of 51), Tallaakshanam (10 power of 53).

First and Longest Poetry of the World 

The Ramayana is the first poetry of the world. It is a glorious Sanskrit epic written by the Divine Sage Valmiki. The Ramayana begins with the author, Sage Valmiki, asking Narada: "O Venerable Rishi, please tell me, is there a perfect man in this world who is virtuous, brave, dutiful, truthful, noble, kind to all beings, and adored by all?" Narada replies: "Rama." The Ramayana has 24,000 Samkskrit verses. It later translated by Kamban into Tamil and Tulsi Das into Hindi.

The Mahabarata is the longest poetry ever written. Its 100,000 verses encompass all facets of Dharma or human way of life. It narrates the story about the great Mahabarata war between the noble Pandavas and their evil cousins the Kauravas.

Pythagorean Theorem or Baudhayana Theorem? 

Did you know that the so-called Pythagoras Theorem that the square of the hypotenuse of a right-angled triangle equals to the sum of the square of the other two sides was documented by the famed Hindu mathematician Baudhayana in his 6th century BC treatise called Baudhayana Sulba Sutra?
Baudhayana states:
"The area produced by the diagonal of a rectangle is equal to the sum of area produced by it on two sides."

Chakras Centres of Consciousness 

Humans have fourteen great nerve centers in the physical body, in the astral body and in the body of the soul. These centers are called chakras in Sanskrit, which means "wheel." These spinning vortices of energy are actually regions of mind power, each one governing certain aspects of our inner being. Together, they are the subtle components of all people.
When inwardly perceived, they are vividly colorful and can be heard by sages and mystics. When awareness flows through any one or more of these regions, the various functions of consciousness operate, such as memory, reason and willpower. In any one lifetime, one may predominantly be aware in two or three centers, thus setting the pattern for the way one thinks and lives. One develops a comprehension of these seven regions in a natural sequence, the perfection of one leading logically to the next. Thus, though we may not psychically be seeing spinning forces within ourself, we nevertheless mature through memory, reason, willpower, cognition, universal love, divine sight and spiritual illumination.
There are six chakras above the muladhara, which is located at the base of the spine. When awareness is flowing through these chakras, consciousness is in the higher nature. There are also seven chakras below the muladhara, and when awareness is flowing through them, consciousness is in the lower nature.
Through personal sadhana, prayer, meditation, right thought, speech and action and love of God, we lift our own consciousness and that of others into the chakras above the muladhara, bringing the mind into the higher nature. The functions of the chakras are aspects of our being that we use every day. In the same way, we use our arms and hands everyday without thinking. The chakras do not awaken—they are already awakened in everyone.

Bhaskaracharya's Law of Gravity 

Did you know that the famous Hindu astronomer, Bhaskaracharya in his Surya Siddhanta wrote:
"Objects fall on the earth due to a force of attraction by the earth. Therefore, the earth, planets, constellations, moon and sun are held in orbit due to this attraction."
It was not until 1687, 1200 years later did Issac Newton "rediscover" the Law of Gravity.
In Surya Siddhanta, dated 400-500 AD, the ancient Hindu astronomer Bhaskaracharya states,
"Objects fall on the earth due to a force of attraction by the earth. Therefore, the earth, planets, constellations, moon, and sun are held in orbit due to this force."
Approximately 1200 years later (1687 AD), Sir Isaac Newton rediscovered this phenomenon and called it the Law of Gravity.

Quotes

Albert Einstein:
We owe a lot to the Indians, who taught us how to count, without which no worthwhile scientific discovery could have been made.
Mark Twain:
India is the cradle of the human race, the birthplace of human speech, the mother of history, the grandmother of legend and the great grand mother of tradition.
French scholar Romain Rolland:
If there is one place on the face of earth where all dreams of living men have found a home from the very earliest days when man began the dream of existence, it is India.

Labels: