The Word-Numeral System :: Hindu numeral system

Hindu numeral system is a pure place-value system, that is why you need a zero. Only the Hindus, within the context of Indo-European civilisations, have consistently used a zero.

It is worth beginning this article with the same quote from Laplace which we give in the article Overview of Indian mathematics. Laplace wrote:-

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. Its simplicity lies in the way it facilitated calculation and placed arithmetic foremost amongst useful inventions. the importance of this invention is more readily appreciated when one considers that it was beyond the two greatest men of Antiquity, Archimedes and Apollonius.

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:

the naming of the first nine digits (eka, dvi, tri, catur, pancha, sat, sapta, asta, nava);

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

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 sutrastyle 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.

 we certainly know that today's symbols took on forms close to that which they presently have in Europe in the 15^th century. It was the advent of printing which motivated the standardisation of the symbols. However we must not forget that many countries use symbols today which are quite different from 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and unless one learns these symbols they are totally unrecognisable as for example the Greek alphabet is to someone unfamiliar with it.

One of the important sources of information which we have about Indian numerals comes from al-Biruni. During the 1020s al-Biruni made several visits to India. Before he went there al-Biruni already knew of Indian astronomy and mathematics from Arabic translations of some Sanskrit texts. In India he made a detailed study of Hindu philosophy and he also studied several branches of Indian science and mathematics. Al-Biruni wrote 27 works on India and on different areas of the Indian sciences. In particular his account of Indian astronomy and mathematics is a valuable contribution to the study of the history of Indian science. Referring to the Indian numerals in a famous book written about 1030 he wrote:-

Whilst we use letters for calculation according to their numerical value, the Indians do not use letters at all for arithmetic. And just as the shape of the letters that they use for writing is different in different regions of their country, so the numerical symbols vary.

It is reasonable to ask where the various symbols for numerals which al-Biruni saw originated. Historians trace them all back to the Brahmi numerals which came into being around the middle of the third century BC. Now these Brahmi numerals were not just symbols for the numbers between 1 and 9. The situation is much more complicated for it was not a place-value system so there were symbols for many more numbers. Also there were no special symbols for 2 and 3, both numbers being constructed from the symbol for 1. 

The system was adopted by Persian (Al-Khwarizmi's c. 825 book On the Calculation with Hindu Numerals) and Arab mathematicians (Al-Kindi's c. 830 volumes On the Use of the Indian Numerals) by the 9th century. It later spread to the western world by the High Middle Ages.

The place-value system is used in the Bakhshali Manuscript. Although date of the composition of the manuscript is uncertain, the language used in the manuscript indicates that it could not have been composed any later than 400. The development of the positional decimal system takes its origins in Indian mathematics during the Gupta period. Around 500, the astronomer Aryabhata uses the wordkha ("emptiness") to mark "zero" in tabular arrangements of digits. The 7th century Brahmasphuta Siddhanta contains a comparatively advanced understanding of the mathematical role of zero. The Sanskrit translation of the lost 5th century Prakrit Jaina cosmological textLokavibhaga may preserve an early instance of positional use of zero.

These Indian developments were taken up in Islamic mathematics in the 8th century, as recorded in al-Qifti's Chronology of the scholars(early 13th century).

The numeral system came to be known to both the Persian mathematician Khwarizmi, who wrote a book, On the Calculation with Hindu Numerals in about 825, and the Arab mathematician Al-Kindi, who wrote four volumes, On the Use of the Indian Numerals (كتاب في استعمال العداد الهندي [kitāb fī isti'māl al-'adād al-hindī]) around 830. These earlier texts did not use the Hindu numerals. Kushyar ibn Labban who wrote Kitab fi usul hisab al-hind(Principles of Hindu Reckoning) is one of the oldest surviving manuscripts using the Hindu numerals.These books are principally responsible for the diffusion of the Indian system of numeration throughout the Islamic world and ultimately also to Europe 

The first dated and undisputed inscription showing the use of a symbol for zero appears on a stone inscription found at the Chaturbhuja Temple at Gwalior in India, dated 876.

In 10th century Islamic mathematics, the system was extended to include fractions, as recorded in a treatise by Syrian mathematician Abu'l-Hasan al-Uqlidisi in 952–95.

These symbol sets can be divided into three main families: the Indian numerals used in India, the Eastern Arabic numerals used in Egypt and the Middle East and the West Arabic numerals used in the Maghreb and in Europe.

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).


ekam =1
dashakam =10
shatam =100 (10 to the power of 10)
sahasram =1000 (10 power of 3)
dashasahasram =10000 (10 power of 4)
lakshaha =100000 (10 power of 5)
dashalakshaha =1000000 (10 power of 6)
kotihi =10000000 (10 power of 7)
ayutam =1000000000 (10 power of 9)
niyutam = (10 power of 11)
kankaram = (10 power of 13)
vivaram = (10 power of 15)
paraardhaha = (10 power of 17)
nivahaaha = (10 power of 19)
utsangaha = (10 power of 21)
bahulam = (10 power of 23)
naagbaalaha = (10 power of 25)
titilambam = (10 power of 27)
vyavasthaana
pragnaptihi = (10 power of 29)
hetuheelam = (10 power of 31)
karahuhu = (10 power of 33)
hetvindreeyam = (10 power of 35)
samaapta lambhaha = (10 power of 37)
gananaagatihi) = (10 power of 39)
niravadyam = (10 power of 41)
mudraabaalam = (10 power of 43)
sarvabaalam = (10 power of 45)
vishamagnagatihi = (10 power of 47)
sarvagnaha = (10 power of 49)
vibhutangamaa = (10 power of 51)
tallaakshanam = (10 power of 53)

(In Anuyogdwaar Sutra written in 100 BCE one numeral is raised as high as 10 to the power of 140).

Heliocentric Solar System

Ancient Hindus were first to suggest a heliocentric solar system.  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!.

Rigveda 10.149.1

"The sun has tied Earth and other planets through attraction and moves them around itself as if a trainer moves newly trained horses around itself holding their reins."

Rig Veda 1.164.13

“Sun moves in its orbit which itself is moving. Earth and other bodies move around sun due to force of attraction, because sun is heavier than them.


Rig Veda 1.35.9

“The sun moves in its own orbit but holding earth and other heavenly bodies in a manner that they do not collide with each other through force of attraction.

Yajur-veda 6.21 " Through astronomy, geography, and geology, go thou to all the different countries of the world under the sun. Mayest thou attain through good preaching to statesmanship and artisanship, through medical science obtain knowledge of all medicinal plants, through hydrostatics learn the different uses of water, through electricity understand the working of ever lustrous lightening. Carry out my instructions willingly." 

Aitareya Brahmana(3.44) declares: 

“The Sun does never set nor rise. When people think the Sun is setting (it is not so). For after having arrived at the end of the day it makes itself produce two opposite effects, making night to what is below and day to what is on the other side…Having reached the end of the night, it makes itself produce two opposite effects, making day to what is below and night to what is on the other side. In fact, the Sun never sets….”

 Rig Veda goes: " In the prescribed daily prayers to the Sun we find..the Sun is at the center of the solar system. ..The student ask, "What is the nature of the entity that holds the Earth? The teacher answers, "Rishi Vatsa holds the view that the Earth is held in space by the Sun."

 An ancient Sanskrit couplet also contemplates the idea of multiple suns: 

"Sarva Dishanaam, Suryaham Suryaha, Surya." 

Roughly translated this means, "There are suns in all directions, the night sky being full of them," suggesting that early sky watchers may have realized that the visible stars are similar in kind to the sun. A hymn of the Rig Veda, the Taittriya Brahmana, extols, nakshatravidya (nakshatra means stars; vidya, knowledge)."

"Two thousand years before Pythagoras, philosophers in northern India had understood that gravitation held the solar system together, and that therefore the sun, the most massive object, had to be at its center. "

One frequently encounters the concepts of the Sun being at the center of the solar system (cf Markandeya Purana, 106. 41). All this pales, however, before the concept, startlingly similar to the twentieth-century model, of an oscillating universe, or more accurately, a universe being cyclically created and destroyed, with just about the right time period of about 10,000 million years. 

( Mahabharata Santi Parva, or Markandeya Purana, 81, 57-58).  

The Rig Veda repeatedly asks, "How is it that though the Sun is not bound and is directed downwards, it does not fall?" A question asked by Isaac Newton more than three thousand years later, and no one else, because the Greeks had furnished the crystal spheres to which these objects were attached!

Aryabhata (476–550), in his magnum opus Aryabhatiya (499), propounded a planetary model in which the Earth was taken to be spinning on its axis and the periods of the planets were given with respect to the Sun. He accurately calculated many astronomical constants, such as the periods of the planets, times of the solar and lunar eclipses, and the instantaneous motion of the Moon. Early followers of Aryabhata's model included Varahamihira, Brahmagupta, and Bhaskara II.

 Aryabhata advocated an astronomical model in which the Earth turns on its own axis. His model also gave corrections (the śīgra anomaly) for the speeds of the planets in the sky in terms of the mean speed of the sun. Thus, it has been suggested that Aryabhata's calculations were based on an underlying heliocentric model, in which the planets orbit the Sun.

The Indian astronomers went even further, giving a physical reason for how the dual star or binary motion might allow the rise and fall of human consciousness to occur. They said that the Sun (with the Earth and other planets) traveled along its set orbital path with its companion start, it would cyclically move close to, then away from, a point in space referred to as Vishnunabhi, a supposed magnetic center or "grand center".

Pythagorean Theorem or Baudhayana Theorem?

 It was ancient Indians mathematicians who discovered Pythagoras theorem. This might come as a surprise to many, but it’s true that Pythagoras theorem was known much before Pythagoras and it was Indians who actually discovered it at least 1000 years before Pythagoras was born!

It was Baudhāyana who discovered the Pythagoras theorem. Baudhāyana listed Pythagoras theorem in his book called Baudhāyana Śulbasûtra (800 BCE). Incidentally, Baudhāyana Śulbasûtra is also one of the oldest books on advanced Mathematics appendices to the Vedas giving rules for the construction of altars—called the Baudhāyana Śulbasûtra, which contained several important mathematical results. He is older than the other famous mathematician Āpastambha. He belongs to the Yajurveda school.. The actual shloka (verse) in Baudhāyana Śulbasûtra that describes Pythagoras theorem is given below :

“dīrghasyākṣaṇayā rajjuH pārśvamānī, tiryaDaM mānī, cha yatpṛthagbhUte kurutastadubhayāṅ karoti.”

Interestingly, Baudhāyana used a rope as an example in the above shloka which can be translated as – A rope stretched along the length of the diagonal produces an area which the vertical and horizontal sides make together. As you see, it becomes clear that this is perhaps the most intuitive way of understanding and visualizing Pythagoras theorem (and geometry in general) and Baudhāyana seems to have simplified the process of learning by encapsulating the mathematical result in a simple shloka in a layman’s language.

He is accredited with calculating the value of pi before pythagoras,

Some people might say that this is not really an actual mathematical proof of Pythagoras theorem though and it is possible that Pythagoras provided that missing proof. But if we look in the same Śulbasûtra, we find that the proof of Pythagoras theorem has been provided by both Baudhāyana and Āpastamba in the Sulba Sutras! To elaborate, the shloka is to be translated as -

The diagonal of a rectangle produces by itself both (the areas) produced separately by its two sides.

The implications of the above statement are profound because it is directly translated into Pythagorean Theorem (and graphically represented in the picutre on the left) and it becomes evident that Baudhāyana proved Pythagoras theorem. Since most of the later proofs (presented by Euclid and others) are geometrical in nature, the Sulba Sutra’s numerical proof was unfortunately ignored. Though, Baudhāyana was not the only Indian mathematician to have provided Pythagorean triplets and proof. Āpastamba also provided the proof for Pythagoras theorem, which again is numerical in nature but again unfortunately this vital contribution has been ignored and Pythagoras was wrongly credited by Cicero and early Greek mathematicians for this theorem. Baudhāyana also presented geometrical proof using isosceles triangles so, to be more accurate, we attribute the geometrical proof to Baudhāyana and numerical (using number theory and area computation) proof to Āpastamba. Also, another ancient Indian mathematician called Bhaskara later provided a unique geometrical proof as well as numerical which is known for the fact that it’s truly generalized and works for all sorts of triangles and is not incongruent  (not just isosceles as in some older proofs).

One thing that is really interesting is that Pythagoras was not credited for this theorem till at least three centuries after! It was much later when Cicero and other Greek philosophers/mathematicians/historians decided to tell the world that it was Pythagoras that came up with this theorem! How utterly ridiculous! In fact, later on many historians have tried to prove the relation between Pythagoras theorem and Pythagoras but have failed miserably. In fact, the only relation that the historians have been able to trace it to is with Euclid, who again came many centuries after Pythagoras!

This fact itself means that they just wanted to use some of their own to name this theorem after and discredit the much ancient Indian mathematicians without whose contribution it could’ve been impossible to create the very basis of algebra and geometry!

                     Many historians have also presented evidence for the fact that Pythagoras actually travelled to Egypt and then India and learned many important mathematical theories (including Pythagoras theorem) that western world didn’t know of back then! So, it’s very much possible that Pythagoras learned this theorem during his visit to India but hid his source of knowledge he went back to Greece! This would also partially explain why Greeks were so reserved in crediting Pythagoras with this theorem!

Bodhayana also states that if a and b be the two sides and c be the hypotenuse, such that 'a' is divisible by 4( as in all pythogorean triplets one of the two shorter sides ateast is divisible by 4).Now, c = (a - a/8) + b/2 This method makes us solve without using squares and square roots.

This appears to be referring to a rectangle or a square(in some cases as interpreted by some people), although some interpretations consider this to refer to a square. In either case, it states that the square of the hypotenuse equals the sum of the squares of the sides. If restricted to right-angled isosceles triangles, however, it would constitute a less general claim, but the text seems to be quite open to unequal sides.

If this refers to a rectangle, it is the earliest recorded statement of the Pythagorean theorem.

Baudhāyana also provides a non-axiomatic demonstration using a rope measure of the reduced form of the Pythagorean theorem for an isosceles right triangle:

The cord which is stretched across a square produces an area double the size of the original square.

Another problem tackled by Baudhāyana is that of finding a circle whose area is the same as that of a square (the reverse of squaring the circle). His sūtra gives this construction:

Draw half its diagonal about the centre towards the East-West line; then describe a circle tog with a third part of that which lies outside the square.

Baudhāyana (elaborated in Āpastamba Sulbasūtra ) gives the length of the diagonal of a square in terms of its sides, which is equivalent to a formula for the square root of 2:

samasya dvikaraṇī. pramāṇaṃ tṛtīyena vardhayet

tac caturthenātmacatustriṃśonena saviśeṣaḥ

The diagonal of a square. The measure is to be increased by a third and by a fourth decreased by the 34th. That is its diagonal approximately.which is correct to five decimals.

Other theorems include: diagonals of rectangle bisect each other, diagonals of rhombus bisect at right angles, area of a square formed by joining the middle points of a square is half of original, the midpoints of a rectangle joined forms a rhombus whose area is half the rectangle, etc.

Note the emphasis on rectangles and squares; this arises from the need to specify yajña bhūmikās—i.e. the altar on which a rituals were conducted, including yajña.

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'.

Ganit (Mathematics) has been considered a very important subject since ancient times. We find very elaborate proof of this in Veda(which were compiled around 6000 BC). The concept of division, addition et-cetera was used even that time. Concepts of zero and infinite were there. We also find roots of algebra in Vedah. When Indian Beez Ganit reached Arab, they called it Algebra. Algebra was name of the Arabic book that described Indian concepts. This knowledge reached to Europe from there. And thus ancient Indian Beez Ganit is currently referred to as Algebra.

This fact was well known to intellectuals of India that is why they gave special importance to the development of Mathematics, right from the beginning. When this knowledge was negligible in Arab and Europe, India had acquired great achievements.

People from Arab and other countries used to travel to India for commerce. While doing commerce, side by side, they also learnt easy to use calculation methods of India. Through them this knowledge reached to Europe. From time to time many inquisitive foreigners visited India and they delivered this matchless knowledge to their countries. This will not be exaggeration to say that till 12th century India was the World Guru in the area of Mathematics.

"10th place value method" dispersed from India to Arab. From there it got transferred to Western countries. This is the reason that digits from 1-9 are called "hindsa" by the people of Arab. In western countries 0,1,2,3,4,5,6,7,8,9 are called Hindu-Arabic Numerals. 

Roots of the Modern Trignometry lie in the book titled Surya Siddhanta . It mentions Zya(Sine), Otkram Zya(Versesine), and Kotizya(Cosine). Please remember that the same word (Zia) changed to "Jaib" in Arab. The translation of Jaib in Latin was done as "Sinus". And this "Sinus" became "Sine" later on.

It is without doubt that like Aank Ganit (Numerical Mathematics) Beez Ganit (Later the name Algebra became more popular) reached Arab from India. Arab mathematician Al-Khowarizmi (780-850 AD) has described topics based on Indian Beez Ganit in his book titled "Algebr". And when it reached Europe it was called Algebra.

Shridharacharya (850 AD) book titled "Pati Ganit" has been translated into Arabic by the name "Hisabul Tarapt".

The Hindu-Arabic numeral system is a decimal place-value numeral system that uses a zero glyph.

Its glyphs are descended from the Indian Brahmi numerals. The full system emerged by the 8th to 9th centuries, and is first described in Al-Khwarizmi's On the Calculation with Hindu Numerals (ca. 825), and Al-Kindi's four volume work On the Use of the Indian Numerals (ca. 830). Today the name Hindu-Arabic numerals is usually used.

Singaporean historian of mathematics Lam Lay Yong (National University of Singapore) claims that the computation in Kitab al-Fusul fi al-Hisab al Hindi (925) by al-Uqlidisi, and another Latin translation of the Arab manuscript written by the Persian mathematician Khwarizmi (825), are almost identical to algorithms for square root extraction, multiplication and division of Indian Mathematics.

Before the rise of the Arab Empire, the Hindu-Arabic numeral system was already moving West and was mentioned in Syria in 662 AD by the Nestorian scholar Severus Sebokht who wrote the following:

"I will omit all discussion of the science of the Indians, ... , of their subtle discoveries in astronomy, discoveries that are more ingenious than those of the Greeks and the Babylonians, and of their valuable methods of calculation which surpass description. I wish only to say that this computation is done by means of nine signs. If those who believe, because they speak Greek, that they have arrived at the limits of science, would read the Indian texts, they would be convinced, even if a little late in the day, that there are others who know something of value."

According to al-Qifti's chronology of the scholars:

"... a person from India presented himself before the Caliph al-Mansur in the year [776 AD] who was well versed in the siddhanta method of calculation related to the movement of the heavenly bodies, and having ways of calculating equations based on the half-chord [essentially the sine] calculated in half-degrees ... This is all contained in a work ... from which he claimed to have taken the half-chord calculated for one minute. Al-Mansur ordered this book to be translated into Arabic, and a work to be written, based on the translation, to give the Arabs a solid base for calculating the movements of the planets ..."

The work was most likely to have been Brahmagupta's Brahmasphutasiddhanta (Ifrah)  (The Opening of the Universe) which was written in 628. Irrespective of whether Ifrah is right, since all Indian texts after Aryabhata's Aryabhatiya used the Indian number system, certainly from this time the Arabs had a translation of a text written in the Indian number system. 

In his text The Arithmetic of Al-Uqlîdisî (Dordrecht: D. Reidel, 1978), A.S. Saidan's studies were unable to answer in full how the numerals reached the Arab world:

"It seems plausible that it drifted gradually, probably before the 7th century, through two channels, one starting from Sind, undergoing Persian filtration and spreading in what is now known as the Middle East, and the other starting from the coasts of the Indian Ocean and extending to the southern coasts of the Mediterranean."

Al-Uqlidisi developed a notation to represent decimal fractions. The numerals came to fame due to their use in the pivotal work of the Persian mathematician Al-Khwarizmi, whose book On the Calculation with Hindu Numerals was written about 825, and the Arab mathematician Al-Kindi, who wrote four volumes "On the Use of the Indian Numerals" (Ketab fi Isti'mal al-'Adad al-Hindi) about 830. They, amongst other works, contributed to the diffusion of the Indian system of numeration in the Middle-East and the West.

The significance of the development of the positional number system is described by the French mathematician Pierre Simon Laplace (1749–1827) who wrote:

"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."

Tobias Dantzig, the father of George Dantzig, had this to say in Number:

"This long period of nearly five thousand years saw the rise and fall of many a civilization, each leaving behind it a heritage of literature, art, philosophy, and religion. But what was the net achievement in the field of reckoning, the earliest art practiced by man? An inflexible numeration so crude as to make progress well nigh impossible, and a calculating device so limited in scope that even elementary calculations called for the services of an expert [...] Man used these devices for thousands of years without contributing a single important idea to the system [...] Even when compared with the slow growth of ideas during the dark ages, the history of reckoning presents a peculiar picture of desolate stagnation. When viewed in this light, the achievements of the unknown Hindu, who some time in the first centuries of our era discovered the principle of position, assumes the importance of a world event."

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 and Tulsi Das. These forms an important part of the Hindu canon (smṛti), considered to be itihāsa. It depicts the duties of relationships, portraying ideal characters like the ideal father, ideal servant, the ideal brother, the ideal wife and the ideal king.The name Ramayana is a tatpurusha compound of Rāma and ayana ("going, advancing"), translating to "Rama's Journey". The Ramayana consists of 24,000 verses in seven books (kāṇḍas) and 500 cantos (sargas), and tells the story of Rama (an avatar of the Hindu preserver-God Vishnu), whose wife Sita is abducted by the king of Sri Lanka, Ravana. Thematically, the Ramayana explores human values and the concept of dharma.

Verses in the Ramayana are written in a 32-syllable meter called anustubh. The Ramayana was an important influence on later Sanskrit poetry and Indian life and culture. The Ramayana is not just a story: it presents the teachings of ancient Hindu sages (Vedas) in narrative allegory, interspersing philosophical and devotional elements. The characters Rama, Sita, Lakshmana, Bharata, Hanuman and Ravana are all fundamental to the cultural consciousness of India, Nepal, and many South-East Asian countries such as Thailand and Indonesia.

There are other versions of the Ramayana, notably the Ramavataram in Tamil, Buddhist (Dasaratha Jataka No. 461) and Jain adaptations, and also Cambodian, Indonesian, Philippine, Thai, Lao, Burmese and Malay versions of the tale.

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.

its epic narrative of the Kurukshetra War and the fates of the Kauravas and the Pandava princes, theMahabharata contains much philosophical and devotional material, such as a discussion of the four "goals of life" or purusharthas. (Among the principal works and stories that are a part of the Mahabharata are theBhagavad Gita, the story of Damayanti, an abbreviated version of the Ramayana, and the Rishyasringa, often considered as works in their own right.

Traditionally, the authorship of the Mahabharata is attributed to Vyasa. There have been many attempts to unravel its historical growth and compositional layers. The oldest preserved parts of the text are not thought to be appreciably older than around 400 BCE, though the origins of the story probably fall between the 8th and 9th centuries BCE.  The title may be translated as "the great tale of the Bhārata dynasty". According to the Mahabharata itself, the tale is extended from a shorter version of 24,000 verses called simply Bhārata.

The Mahabharata is the longest Sanskrit epic. Its longest version consists of over 100,000 shloka or over 200,000 individual verse lines (each shloka is a couplet), and long prose passages. About 1.8 million words in total, the Mahabharata is roughly ten times the length of the Iliad and Odyssey combined, or about four times the length of the Ramayana. W. J. Johnson has compared the importance of the Mahabharata to world civilization to that of the Bible, the works of Shakespeare, the works of Homer, Greek drama, or the Qur'an.

Atomic Theory ::by John Dalton or ACHARYA KANADA

 Kanada (Sanskrit: कणाद); was a sage and philosopher who founded the philosophical school of Vaisheshika and authored the text Vaisheshika Sutra. He probably lived around the 2nd century BCE,while other sources claim he lived in the 6th Century BCE. It is believed that he was born in Prabhas Kshetra (near Dwaraka) in Gujarat,India.

His primary area of study was Rasavādam, considered to be a type of alchemy. He is said to have believed that all living beings are composed of five elements: water, fire, earth, air, ether. Vegetables have only water, insects have water and fire, birds have water, fire, earth and air, and Humans, the top of the creation, have ether—the sense of discrimination (time, space, mind) are one. He theorized that Gurutva(Hindi/Sanskrit for Gravity) was responsible for the falling of objects on the Earth.

He 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.

Many believe that Kanada originated the concept of atom. An interesting story states that this theory occurred to him while he was walking with food in his hand. As he nibbled at the food in his hand, throwing away the small particles, it occurred to him that he could not divide the food into further parts and thus the idea of a matter which cannot be divided further came into existence. He called that indivisible matter as ' Anu ' .i.e. atom.

Vaisheshika:: 

It was Kanada who originated the idea that paramanu (atom) was an indestructible particle of matter. An interesting story states that this theory occurred to him while he was walking with food in his hand. As he nibbled at the food in his hand, throwing away the small particles, it occurred to him that he could not divide the food into further parts and thus the idea of a matter which cannot be divided further came into existence. He called that indivisible matter anu, i.e. atom.

Adherents of the school of philosophy founded by Kanada, considered the atom to be indestructible, and hence eternal. They believed atoms to be minute objects invisible to the naked eye which come into being and vanish in an instant. Vaiseshikas further held that atoms of same substance combined with each other to produce dvyanuka (biatomic molecules) and tryanuka (triatomic molecules). Kanada also put forward the idea that atoms could be combined in various ways to produce chemical changes in presence of other factors such as heat. He gave blackening of earthen pot and ripening of fruit as examples of this phenomenon.

This Indian conception of the atom was developed independently and possibly prior (depending on which dates one accepts for the life of Kanada) to the development of the idea in the Greco-Roman world. Indian theories about the atom are greatly abstract and enmeshed in philosophy as they were based on logic and not on personal experience or experimentation. Thus the Indian theories lacked an empirical base, but in the words of A.L. Basham, the veteran Australian Indologist “they were brilliant imaginative explanations of the physical structure of the world, and in a large measure, agreed with the discoveries of modern physics.”

According to author Dilip M. Salwi, "if Kanada’s sutras are analysed, one would find that his atomic theory was far more advanced than those forwarded later by the Greek philosophers, Leucippus and Democritus. Kanada founded this system. This system is believed to be as old as Jainism and  Buddhism.  Kanada presented his detailed atomic theory in Vaisheshika-Sutra. Basically, Vaisheshika is a pluralistic realism. It explains the nature of the world with seven categories: Dravya (substance), guna (quality), karma(action), samanya(universal), vishesha (particular), amavaya(inherence) and abhava (non-existence). Vaisheshika contends that every effect is a fresh creation or a new beginning. Thus this system refutes the theory of pre-existence of the effect in the cause. Kanada does not discuss much on God. But the later commentators refer to God as the Supreme Soul, perfect and eternal.  This system accepts that God (Ishvara ) is the efficient cause of the world. The eternal atoms are the material cause of the world. Vaisheshika recognizes nine ultimate substances : Five material and four non-material substances. The five material substances are: Earth, water, fire, air and akasha. The four non-material substances are: space, time, soul and mind. Earth, water, fire and air are atomic but akasha is non-atomic and  infinite. Space and time are infinite and eternal. The concept of soul is comparable to that of the self or atman. This system considers consciousnessas an accidental property. In other words, when the soul associates itself to the body, only then it ‘acquires’ consciousness. Thus, consciousness is not considered an essential quality of the soul. The mind (manas) is accepted as atomic but indivisible and eternal substance. The mind helps to establish the contact of the self to the external world objects. The soul develops attachment to the body owing to ignorance. The soul identifies itself with the body and mind. The soul is trapped in the bondage of  karma, as a consequence of actions resulted from countless desires and passions. It can be free from the bondage only if it becomes free from actions. Liberation follows the cessation of the actions.