The Indic Mathematical Tradition 6000 BCE To ?

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Science in Ancient India

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India's 30-million-page directory of medical wisdom

[Hauma Hamiddha]

We present a note on the dharma shAstra of the bhArgavas:
<b>bhR^igu smR^iti</b>

Contains early scientific speculations of the hindus

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The Origin of Mathematics
by V. Lakshmikantham and S. Leela. University Press of America, Inc., Lanham, MD. Hardcover. 92 pages. www.univpress.com.

Long before the Egyptians, the Greeks, the Mayans, and the Sumerians began civiliz-ing their worlds, mathematics had flourished in India. Does this thesis seem incredible? No, this is not a rhetorical proclamation of some overzealous Indian chauvinists. Two India-born American university professors, V. Lakshmikantham and S. Leela, have documented extensive new data on ancient Indian mathematics and on the bankruptcy of the theory of Aryan invasion of India from the northern-central plains in Asia.
Along with their own meticulous research of original Sanskrit texts and related vernacular literature, the authors draw upon the works of a few European scholars. With the publication of this amazing monograph on Indian mathematics, the cloud of ignorance and deliberate misrepresentation of the many achievements in ancient India is beginning to lift. The authors remind us that the history taught even in Indian schools, colleges, and universities, is still filled with distortions that originated with the founding of the Indian Historical Society (IHS) in the late 18th-century Calcutta, overwhelmed by the prevailing colonial mentality.

These fabrications, passed on as the modern historiography for India, were officially inaugurated with the willful mix-up of Chandragupta Maurya (reigned 1534–1500 B.C.) and Chandragupta (327–320 B.C.) of the Gupta dynasty, by making the former a coeval of Alexander the Great, and by erasing the latter’s reference altogether. Thanks to the inventive and resourceful William Jones of the IHS, the entire chronology of events was summarily shortened by more than 1,200 years. Consequently, the times of ancient astronomers and mathematicians had to be moved into the Christian era. Another ambitious and influential Indologist, Max Mueller, concocted the age of the Rig Veda to be 1200 B.C., with the stipulation it was written by nomadic Aryans (riding on horseback, presumably with a mobile library). Actually, the Rig Veda was compiled well before 3000 B.C. Contrary to popular belief, Gautam Buddha lived during 1887–1807 B.C., and the short but remarkable life’s mission of Adi Shankaracharya was accomplished between 509 and 477 B.C. The first known mathematician and astronomer from India, Aryabhatta, was born in 2765 B.C., and the Sulvasutras, heralding the discipline of geometric algebra, were completed before his birth. But in the occidental “scholarship,” Aryabhatta’s year of birth was changed to 476 C.E. with the misreading of his epoch-making Aryabhatteeum. These were not accidental errors, but were the result of a carefully planned alteration of manuscript copies. Notice that the four Vedas preceded the Sulvasutras. Note also none of the Vedangas, the Upangas, the Brahmanas, the Aranyakas, and the Upanishads could possibly have been written later than the second millennium B.C. So much for the objectivity claimed by and attributed to a few Western historians, which has been mindlessly emulated and replicated by a majority of Indian academicians even after the British had ceased to be the rulers of India.

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I wanted to open the discussion about how can we impart info about our heritage of science and maths to the students at the state and national level. Educatiing at the state level is a major reach out area. Private organizations can also promote by sponsoring quizzies publishing books etc..
Any new ideas????

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<b>Ancient Hindu civilisation and mathematics </b>
By Dr R.N. Das

The ancient Hindu sages discovered the miracles of modern scientific tools. Believe it or not, the following are the glorious examples of them.

I. The Concept of Zero

The concept of zero came from the revered Hindu sages in Vedic times thousands of years ago.

Without the concept of zero the binary system is blind. No counting, no commerce or no computer business. The earliest documented “date” was found in today’s Gujarat [BC 585-586] in an inscription on Sankedia copper plate. In Brahamaphuta—Siddhanta of Brahamagupta (7th century CE), zero was lucidly explained. Muslim invaders from Central Asia crossing the Hindukush mountain ranges invaded Bharat 1300 years ago and plundered its beauty, riches, books, thrones and what not. They plagued the holy land with sword, loot, arson and rape and destroyed and ravaged the whole land in the name of jehad and “Allah”. There was no Steven Spielberg (Schindler’s List) like cinema director who could document this sordid past of our history. There was no patent system at that time. Might was right. They considered those substances of robbery maal-e-ganimat (booty looted from kafirs to be distributed among themselves and friends of theirs) and thus inculcated those invaluable theorems of mathematics, astronomy and geometry in Arabic books in around 770-1200 CE. From there, those extraordinary concepts were carried to Spanish Europe in the 8th century. However the concept of zero was referred to as shunya in the early Sanskrit texts of the 4th century BC and was clearly explained in Pingala’s Chand Sutra of the 2nd century too.

II. The Contribution to Astronomy

Hindu sages told modern scientists how to map the sky in terms of glaring stars almost 4000 years ago. Copernicus published his theory of revolution of the Earth around the Sun in 1543 AD only. But our Aryabhatta in the 5th century had stated that the Earth revolves around the Sun in these specific words: “Just as a person boarding on a boat feels that the trees on the banks are moving, people on the revolving earth also feel that the sun is moving”. Such illustrious teaching of astronomy was rarely seen in the contemporary writings of the Greek astronomers. In his Aryabhatteem, he clearly stated that our Earth was round and it rotated on its own axis, orbited the Sun and was suspended in the space. It also explained that the lunar and solar eclipses occurred by the interplay of the shadows of the Sun, the Moon and the Earth.

III. The Law of Gravity

The Law of Gravity was known to the ancient Hindu astronomer Bhaskaracharya. In his Surya Siddhanta he noted: “Objects fall on the Earth due to force of attraction of the Earth. Therefore, the Earth, planets, constellations, the Moon, and the Sun are all held in the galaxy due to this great cosmic attraction.”

It was in 1687—1200 years later—that Sir Isaac Newton discovered (re-discovered?) the Law of Gravity, which was already invented by the greatest Hindu astronomer Bhaskaracharya, of course which was written in the holiest language, Sanskrit.

IV. The Invention of Trikonmiti

The word geometry seems to have emerged from the Sanskrit word gyaamiti, which means measuring the Earth. And the word trigonometry is similar to trikonmiti meaning measuring triangular forms.

Euclid was famous for the invention of geometry in 300 BC whilst the concept of trikonmiti had emerged in 1000 BC in Bharat. It is evident lucidly from today’s “practice of making fire alters (at homagni kshetra) in different shapes, e.g., round, triangular, hexagonal, pentagonal, square and rectangular”. It was part and parcel of daily pujas and homagnis in ancient times. The treatise of Surya Siddhanta (4th century) described in fascinating details about trigonometry, which was introduced in Europe by Briggs 1200 years later in the 16th century.

V. The Invention of Infinity

The value of “Pi” was first invented by the ancient sages of Bharat. The ratio of circumference and diameter of a circle is known as “Pi” which gives its value as 3.14592657932...

The old Sanskrit text Baudhayna Sulbha Sutra of the 6th century BC mentioned that above-mentioned ratio as approximately equalled to that of Aryabhatta’s ratio [in 499 BC] worked out the value of “Pi” to the fourth decimal place as [3x (177/1250) = 3.1416]. Many centuries later, in 825 AD, Arab mathematician, Mohammed Ibn Musa admitted: “This value of “Pi” was given by the Hindus (62832/20,000 = 3.1416).”

VI. Baudhayna’s Sulbha Sutra versus Pythagoras’s Theorem

The famous Pythagoras’s theorem states: “The square of the hypotenuse angled triangle equals to the sum of the two sides.” This theorem was actually discovered by Euclid in 300 BC but Greek writers attributed this to Pythagoras. But the irony of fate is that our so-called intellectuals (indeed Macaulay’s sons who have forgotten their old but rich and glorious ancient Hindu heritage) had also accepted that theorem as a contribution of Pythagoras. They never read or tried to know that Baudhayna’s Sulbha Sutra which has been existing for many thousands of years (written in the Sanskrit) had already described lucidly the theorem as follows: “The area produced by the diagonal of a rectangle is equal to the sum of the area produced by it on two sides.”

VII. The Measurement of Time or Time Scale

In Surya Siddhanta, Bhaskaracharya calculated the time taken by the Earth to revolve around the Sun up to the 9th decimal place. According to Bhaskaracharya’s calculation it is 365.258756484 days.

Modern scientist accepted a value of the same time as 365.2596 days.

The difference between the two observations made by ancient Hindu sage Bhaskaracharya just by using his super brain (in the 4th century AD) and today’s NASA (National Aeronautic and Space Agency) scientists of America by using super computer (in the 20th century AD) is only 0.00085, i.e., 0.0002 per cent of difference.

The ancient Bharatbhoomi had given the world the idea of the smallest and largest measuring units of Time. In modern time, only Stephen Hockings, Cambridge University Professor of theoretical physics, had the courage to venture into the abysmal depth of the eternity of Time. Astonishingly, our ancient sages taught us the following units of time:

Krati =34,000th of a second
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 Ghadi = 1 Hora (=1 Hour)
24 Hora = 1 Divas (1 Day)
7 Divas = 1 Saptah (1 Week)
4 Saptah = 1 Maas (1 Month)
2 Maas = 1 Ritu (1 Season)
6 Ritu = 1 Varsha (1 Year)
100 Varsha = 1 Satabda (1 Century)
10 Shatabda = 1 Saharabda
432 Saharabda = 1Yug(Kali Yuga))
2 Yuga = 1 Dwapar Yuga
3 Yuga = 1 Treta Yuga
4 Yuga = Kruta Yuga
10 Yuga = 1 Maha Yuga (4,320,000)
1000 Maha Yuga = 1 Kalpa
1 Kalpa = 4.32 Billion Years.
Therefore, the lowest was 34,000th of a second known as krati and the highest of the measurement of the Time was known as kalpa, which equalled to 4.32 billion years. Is it not amazing? Are you not feeling proud to be a Hindu descendent? Swami Vivekananda, the modern sage of Bharat, stated in his famous sermons compiled in his Rousing Call to the Hindu Nation, “Take pride in Hinduism; pronounce yourselves as a descendant of a Hindu. Boast to be a Hindu and give a clarion call to rouse the Hindu nation from its lethargy and slumber.”

VIII. The Invention of Decimal System

It was the ancient Bharatbhoomi that gave us the ingenious methods of expressing all the numbers by means of 10 symbols (decimal systems)—an invaluable and gorgeous idea that escaped the genius of Archimedes and Apollonius, two of the greatest Greek philosophers and mathematician produced by antiquity (100-130BC).

The highest prefix used for raising 10 to the power in today’s mathematics is “D” for 1030 (for Greek Deca).While as early as 100 BC Hindu mathematicians had exact names for figures up to 1053.

a. Ekam = 1

b. Dashkam = 10 (101)

c. 1 Shatam = 100 (102)

d. 10 Shatam = 1 Shahashram = 1000 (103)

e. 10 Dash Shahashram = 10,000 (104)

f. Laksha = 100,000 (105)

g. Dash Laksha = 10,00,000 (106)

h. Kotihi = 10, 00, 0000 (107)

i. Ayutam = 100,000,000 (109)

j. Niyutam = 100,000,000,000 (1011)

k. Kankaram = 10,000,000,000,000 (1013)

l. Vivaram = 10,000,000,000,000,000 (1016)

m. Pararadahaa = 1017

n. Nivahata = 1019

o. Utsangaha = 1021

p. Bahulam = 1023

q. Naagbaalaha = 1025

r. Titlambam = 1027

s. Vyavasthaanapragnaptihi = 1029

t. Hetuhellam = 1031

u. Karahuhu = 1033

v. Hetvindreeyam = 1035

w. Sampaata Lambhaha = 1037

x. Gananaagatihi = 1039

y. Niravadyam = 1041

z. Mudraabalam = 1043

aa. Saraabalam = 1045

ab. Vishamagnagatihi = 1047

ac. Sarvagnaha = 1049

ad. Vibhutangaama = 1051

ae. Tallakshanaam = 1053

Is it not amazing to know that the ancient Hindu sages used to remember them just by using their outstanding memory power or was there some super computer known to them also, which we are quite unaware of?

In Anuyogadwar Sutra, written 100 BC, one numeral had been shown to be raised to as high as 10140 which is beyond our outmost stretches of imagination. All of our remaining hidden treasures, which had not been destroyed or stolen by the foreign mercenaries and invaders, were written in Sanskrit, mother of all languages, which should be revived. It is our legacy to inherit such rich property that our forefather had left for us by their meticulous observations over thousands of years ago.

All hidden treasures are written in Sanskrit, which we are quite ignorant of and our so-called Macaulay’s sons are trying their best to prevent us from knowing about our glorious past. Sir Monier-Williams rightly said: “Hindus are perhaps the only nation, except the Greeks, who have investigated independently and in true scientific manner, the general laws that govern the evolution of languages.”

There was no patent system at that time. Might was right. They considered those substances of robbery maal-e-ganimat (booty looted from kafirs to be distributed among themselves and friends of theirs) and thus inculcated those invaluable theorems of mathematics, astronomy and geometry in Arabic books in around 770-1200 CE.

More than this, the Hindus had made considerable advances in astronomy, algebra, arithmetics, botany and medicine, not to mention their superiority in grammar, long before some of these sciences were cultivated by the most ancient nations of Europe.

Indeed, Hindus were Spinozists 2000 years before the birth of Spinoza, Darwinians many centuries before the birth of Darwin, and evolutionists, centuries before the doctrine of evolution had been accepted by Aldus Huxley’s of our times, and before any word like evolution existed in any language in this world.

We should take a vow to work together to search those hidden treasures out, propagate the notion that Sanskrit is not a dead language. Sanskrit is the elite of the elitist, classic of the classics and it should be revived once again. We will again sit in the seat of the world assembly with our head held high and with pride. I would like to draw the final touch with the quotation from Swami Vivekananda, “I do not see into the future nor do I care to see. But one vision I see clear as life before me, that the ancient Mother has awakened once more sitting on her throne rejuvenated, more glorious than ever. Proclaim her to all the world with the voice of peace and benediction.”

(The writer is Associate Professor, Department of Medicine, Manipal Teaching Hospital, Pokhara, Nepal,

E-mail:dar_rabindranath@hotmail.com)
http://www.organiser.org/dynamic/modules.p...pid=114&page=31

[shamu]

From the above notations we generally use

eka,
dasa,
shatha,
sahasra,
lakh,
crore

Currently our population itself is 100 Crore and we talk about 10000 crores of rupees.

At present we are using billion and trillion to refer to numbers of such magnitude. I think it is high time Indians start using corresponding Indian notations simultaneously.

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http://www.asiantribune.com/show_article.php?id=2978

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<b>Vedic Math — Vedic Science & Mathematics — Ancient India's Vedanta — Architecture & Vastu Sastra </b>

Mathematics and the Spiritual Dimension

Unfortunately, I think I went too far to the other side. I threw reason to the wind, so to speak, and unceremoniously became a self-ordained "spiritual person." Science, the foundation of which is mathematics, as I saw it, had nothing to offer. It was only years later, when the cloud of my sentimentalism was dissipated by the sun of my soul's integrity, that I was able to separate myself from yet another delusion-the first being the advice of my father, and the second being the idea that I could wish myself into a more profound understanding of the nature of reality.


Math cannot take the mystery out of life without doing away with life itself, for it is life's mystery, its unpredictability-the fact that it is dynamic, not static-that makes it alive and worth living. We may theoretically explain away God, but in so doing we only choose to delude ourselves; I = everything is just bad arithmetic.

However, before we can connect with our heart of hearts, our real spiritual essence, we cannot cast reason aside. With the help of the discriminating faculty we can know at least what transcendence is not. Withdrawing our heart from that is a good beginning for a spiritual life.

Mathematics has only recently risen to attempt to usurp the throne of Godhead. Ironically, it originally came into use in human society within the context of spiritual pursuit. Spiritually advanced cultures were not ignorant of the principles of mathematics, but they saw no necessity to explore those principles beyond that which was helpful in the advancement of God realization. Intoxicated by the gross power inherent in mathematical principles, later civilizations, succumbing to the all-inviting arms of illusion, employed these principles and further explored them in an attempt to conquer nature. The folly of this, as demonstrated in modern society today, points to the fact that "wisdom" is more than the exercise of intelligence. Modern man's worship of intelligence blinds him from the obvious: the superiority of love over reason.

Archimedes and Pythagoras

A common belief among ancient cultures was that the laws of numbers have not only a practical meaning, but also a mystical or religious one. This belief was prevalent amongst the Pythagoreans. Prior to 500 B.C.E., Pythagoras, the great Greek pioneer in the teaching of mathematics, formed an exclusive club of young men to whom he imparted his superior mathematical knowledge. Each member was required to take an oath never to reveal this knowledge to an outsider. Pythagoras acquired many faithful disciples to whom he preached about the immortality of the soul and insisted on a life of renunciation. At the heart of the Pythagorean world view was a unity of religious principles and mathematical propositions.

In the third century B.C.E. another great Greek mathematician, Archimedes, contributed considerably to the field of mathematics. A quote attributed to Archimedes reads, "There are things which seem incredible to most men who have not studied mathematics." Yet according to Plutarch, Archimedes considered "mechanical work and every art concerned with the necessities of life an ignoble and inferior form of labor, and therefore exerted his best efforts only in seeking knowledge of those things in which the good and the beautiful were not mixed with the necessary." As did Plato, Archimedes scorned practical mathematics, although he became very expert at it.

The Abacus: A mechanical counting device
The Greeks, however, encountered a major problem. The Greek alphabet, which had proved so useful in so many ways, proved to be a great hindrance in the art of calculating. Although Greek astronomers and astrologers used a sexagesimal place notation and a zero, the advantages of this usage were not fully appreciated and did not spread beyond their calculations. The Egyptians had no difficulty in representing large numbers, but the absence of any place value for their symbols so complicated their system that, for example, 23 symbols were needed to represent the number 986. Even the Romans, who succeeded the Greeks as masters of the Mediterranean world, and who are known as a nation of conquerors, could not conquer the art of calculating. This was a chore left to an abacus worked by a slave. No real progress in the art of calculating nor in science was made until help came from the East.

Shulba Sutra

In the valley of the Indus River of India, the world's oldest civilization had developed its own system of mathematics. The Vedic Shulba Sutras (fifth to eighth century B.C.E.), meaning "codes of the rope," show that the earliest geometrical and mathematical investigations among the Indians arose from certain requirements of their religious rituals. When the poetic vision of the Vedic seers was externalized in symbols, rituals requiring altars and precise measurement became manifest, providing a means to the attainment of the unmanifest world of consciousness. "Shulba Sutras" is the name given to those portions or supplements of the Kalpasutras, which deal with the measurement and construction of the different altars or arenas for religious rites. The word shulba refers to the ropes used to make these measurements.

Math cannot take the mystery out of life without doing away with life itself, for it is life's mystery, its unpredictability — the fact that it is dynamic, not static — that makes it alive and worth living.

Although Vedic mathematicians are known primarily for their computational genius in arithmetic and algebra, the basis and inspiration for the whole of Indian mathematics is geometry. Evidence of geometrical drawing instruments from as early as 2500 B.C.E. has been found in the Indus Valley. [1] The beginnings of algebra can be traced to the constructional geometry of the Vedic priests, which are preserved in the Shulba Sutras. Exact measurements, orientations, and different geometrical shapes for the altars and arenas used for the religious functions (yajnas), which occupy an important part of the Vedic religious culture, are described in the Shulba Sutras. Many of these calculations employ the geometrical formula known as the Pythagorean theorem.





This theorem (c. 540 B.C.E.), equating the square of the hypotenuse of a right angle triangle with the sum of the squares of the other two sides, was utilized in the earliest Shulba Sutra (the Baudhayana) prior to the eighth century B.C.E. Thus, widespread use of this famous mathematical theorem in India several centuries before its being popularized by Pythagoras has been documented. The exact wording of the theorem as presented in the Sulba Sutras is: "The diagonal chord of the rectangle makes both the squares that the horizontal and vertical sides make separately." [2] The proof of this fundamentally important theorem is well known from Euclid's time until the present for its excessively tedious and cumbersome nature; yet the Vedas present five different extremely simple proofs for this theorem. One historian, Needham, has stated, "Future research on the history of science and technology in Asia will in fact reveal that the achievements of these peoples contribute far more in all pre-Renaissance periods to the development of world science than has yet been realized." [3]

The Shulba Sutras have preserved only that part of Vedic mathematics which was used for constructing the altars and for computing the calendar to regulate the performance of religious rituals. After the Shulba Sutra period, the main developments in Vedic mathematics arose from needs in the field of astronomy. The Jyotisha, science of the luminaries, utilizes all branches of mathematics.

The need to determine the right time for their religious rituals gave the first impetus for astronomical observations. With this desire in mind, the priests would spend night after night watching the advance of the moon through the circle of the nakshatras (lunar mansions), and day after day the alternate progress of the sun towards the north and the south. However, the priests were interested in mathematical rules only as far as they were of practical use. These truths were therefore expressed in the simplest and most practical manner. Elaborate proofs were not presented, nor were they desired.

Evolution of Arabic (Roman) Numerals from India

A close investigation of the Vedic system of mathematics shows that it was much more advanced than the mathematical systems of the civilizations of the Nile or the Euphrates. The Vedic mathematicians had developed the decimal system of tens, hundreds, thousands, etc. where the remainder from one column of numbers is carried over to the next. The advantage of this system of nine number signs and a zero is that it allows for calculations to be easily made. Further, it has been said that the introduction of zero, or sunya as the Indians called it, in an operational sense as a definite part of a number system, marks one of the most important developments in the entire history of mathematics. The earliest preserved examples of the number system which is still in use today are found on several stone columns erected in India by King Ashoka in about 250 B.C.E. [4 ] Similar inscriptions are found in caves near Poona (100 B.C.E.) and Nasik (200 C.E.). [5] These earliest Indian numerals appear in a script called brahmi.

After 700 C.E. another notation, called by the name "Indian numerals," which is said to have evolved from the brahmi numerals, assumed common usage, spreading to Arabia and from there around the world. When Arabic numerals (the name they had then become known by) came into common use throughout the Arabian empire, which extended from India to Spain, Europeans called them "Arabic notations," because they received them from the Arabians. However, the Arabians themselves called them "Indian figures" (Al-Arqan-Al-Hindu) and mathematics itself was called "the Indian art" (hindisat).

Evolution of "Arabic numerals" from Brahmi
(250 B.C.E.) to the 16th century.


Mastery of this new mathematics allowed the Muslim mathematicians of Baghdad to fully utilize the geometrical treatises of Euclid and Archimedes. Trigonometry flourished there along with astronomy and geography. Later in history, Carl Friedrich Gauss, the "prince of mathematics," was said to have lamented that Archimedes in the third century B.C.E. had failed to foresee the Indian system of numeration; how much more advanced science would have been.
Prior to these revolutionary discoveries, other world civilizations-the Egyptians, the Babylonians, the Romans, and the Chinese-all used independent symbols for each row of counting beads on the abacus, each requiring its own set of multiplication or addition tables. So cumbersome were these systems that mathematics was virtually at a standstill. The new number system from the Indus Valley led a revolution in mathematics by setting it free. By 500 C.E. mathematicians of India had solved problems that baffled the world's greatest scholars of all time. Aryabhatta, an astronomer mathematician who flourished at the beginning of the 6th century, introduced sines and versed sines-a great improvement over the clumsy half-cords of Ptolemy. A.L. Basham, foremost authority on ancient India, writes in The Wonder That Was India,

Medieval Indian mathematicians, such as Brahmagupta (seventh century), Mahavira (ninth century), and Bhaskara (twelfth century), made several discoveries which in Europe were not known until the Renaissance or later. They understood the import of positive and negative quantities, evolved sound systems of extracting square and cube roots, and could solve quadratic and certain types of indeterminate equations." [6] Mahavira's most noteworthy contribution is his treatment of fractions for the first time and his rule for dividing one fraction by another, which did not appear in Europe until the 16th century.

Equations and Symbols

B.B. Dutta writes: "The use of symbols-letters of the alphabet to denote unknowns, and equations are the foundations of the science of algebra. The Hindus were the first to make systematic use of the letters of the alphabet to denote unknowns. They were also the first to classify and make a detailed study of equations. Thus they may be said to have given birth to the modern science of algebra." [7] The great Indian mathematician Bhaskaracharya (1150 C.E.) produced extensive treatises on both plane and spherical trigonometry and algebra, and his works contain remarkable solutions of problems which were not discovered in Europe until the seventeenth and eighteenth centuries. He preceded Newton by over 500 years in the discovery of the principles of differential calculus. A.L. Basham writes further, "The mathematical implications of zero (sunya) and infinity, never more than vaguely realized by classical authorities, were fully understood in medieval India. Earlier mathematicians had taught that X/0 = X, but Bhaskara proved the contrary. He also established mathematically what had been recognized in Indian theology at least a millennium earlier: that infinity, however divided, remains infinite, represented by the equation oo /X = oo." In the 14th century, Madhava, isolated in South India, developed a power series for the arc tangent function, apparently without the use of calculus, allowing the calculation of pi to any number of decimal places (since arctan 1 = pi/4). Whether he accomplished this by inventing a system as good as calculus or without the aid of calculus; either way it is astonishing.

Spiritually advanced cultures were not ignorant of the principles of mathematics, but they saw no necessity to explore those principles beyond that which was helpful in the advancement of God realization.

By the fifteenth century C.E. use of the new mathematical concepts from India had spread all over Europe to Britain, France, Germany, and Italy, among others. A.L. Basham states also that

The debt of the Western world to India in this respect [the field of mathematics] cannot be overestimated. Most of the great discoveries and inventions of which Europe is so proud would have been impossible without a developed system of mathematics, and this in turn would have been impossible if Europe had been shackled by the unwieldy system of Roman numerals. The unknown man who devised the new system was, from the world's point of view, after the Buddha, the most important son of India. His achievement, though easily taken for granted, was the work of an analytical mind of the first order, and he deserves much more honor than he has so far received.

Unfortunately, Eurocentrism has effectively concealed from the common man the fact that we owe much in the way of mathematics to ancient India. Reflection on this may cause modern man to consider more seriously the spiritual preoccupation of ancient India. The rishis (seers) were not men lacking in practical knowledge of the world, dwelling only in the realm of imagination. They were well developed in secular knowledge, yet only insofar as they felt it was necessary within a world view in which consciousness was held as primary.

In ancient India, mathematics served as a bridge between understanding material reality and the spiritual conception. Vedic mathematics differs profoundly from Greek mathematics in that knowledge for its own sake (for its aesthetic satisfaction) did not appeal to the Indian mind. The mathematics of the Vedas lacks the cold, clear, geometric precision of the West; rather, it is cloaked in the poetic language which so distinguishes the East. Vedic mathematicians strongly felt that every discipline must have a purpose, and believed that the ultimate goal of life was to achieve self-realization and love of God and thereby be released from the cycle of birth and death. Those practices which furthered this end either directly or indirectly were practiced most rigorously. Outside of the religio-astronomical sphere, only the problems of day to day life (such as purchasing and bartering) interested the Indian mathematicians.

Poetry in Math

One of the foremost exponents of Vedic math, the late Bharati Krishna Tirtha Maharaja, author of Vedic Mathematics, has offered a glimpse into the sophistication of Vedic math. Drawing from the Atharva-veda, Tirtha Maharaja points to many sutras (codes) or aphorisms which appear to apply to every branch of mathematics: arithmetic, algebra, geometry (plane and solid), trigonometry (plane and spherical), conics (geometrical and analytical), astronomy, calculus (differential and integral), etc.

Utilizing the techniques derived from these sutras, calculations can be done with incredible ease and simplicity in one's head in a fraction of the time required by modern means. Calculations normally requiring as many as a hundred steps can be done by the Vedic method in one single simple step. For instance the conversion of the fraction 1/29 to its equivalent recurring decimal notation normally involves 28 steps. Utilizing the Vedic method it can be calculated in one simple step. (see the next section for examples of how to utilize Vedic sutras)

In order to illustrate how secular and spiritual life were intertwined in Vedic India, Tirtha Maharaja has demonstrated that mathematical formulas and laws were often taught within the context of spiritual expression (mantra). Thus while learning spiritual lessons, one could also learn mathematical rules.

Tirtha Maharaja has pointed out that Vedic mathematicians prefer to use the devanagari letters of Sanskrit to represent the various numbers in their numerical notations rather than the numbers themselves, especially where large numbers are concerned. This made it much easier for the students of this math in their recording of the arguments and the appropriate conclusions.

Tirtha Maharaja states, "In order to help the pupil to memorize the material studied and assimilated, they made it a general rule of practice to write even the most technical and abstruse textbooks in sutras or in verse (which is so much easier-even for the children-to memorize). And this is why we find not only theological, philosophical, medical, astronomical, and other such treatises, but even huge dictionaries in Sanskrit verse! So from this standpoint, they used verse, sutras and codes for lightening the burden and facilitating the work (by versifying scientific and even mathematical material in a readily assimilable form)!" [8] The code used is as follows:

The Sanskrit consonants

ka, ta, pa, and ya all denote 1;
kha, tha, pha, and ra all represent 2;
ga, da, ba, and la all stand for 3;
Gha, dha, bha, and va all represent 4;
gna, na, ma, and sa all represent 5;
ca, ta, and sa all stand for 6;
cha, tha, and sa all denote 7;
ja, da, and ha all represent 8;
jha and dha stand for 9; and
ka means zero.

Vowels make no difference and it is left to the author to select a particular consonant or vowel at each step. This great latitude allows one to bring about additional meanings of his own choice. For example kapa, tapa, papa, and yapa all mean 11. By a particular choice of consonants and vowels one can compose a poetic hymn with double or triple meanings. Here is an actual sutra of spiritual content, as well as secular mathematical significance.

gopi bhagya madhuvrata
srngiso dadhi sandhiga
khala jivita khatava
gala hala rasandara

While this verse is a type of petition to Krishna, when learning it one can also learn the value of pi/10 (i.e. the ratio of the circumference of a circle to its diameter divided by 10) to 32 decimal places. It has a self-contained master-key for extending the evaluation to any number of decimal places.

The translation is as follows:

O Lord anointed with the yogurt of the milkmaids' worship (Krishna), O savior of the fallen, O master of Shiva, please protect me.

At the same time, by application of the consonant code given above, this verse directly yields the decimal equivalent of pi divided by 10: pi/10 = 0.31415926535897932384626433832792. Thus, while offering mantric praise to Godhead in devotion, by this method one can also add to memory significant secular truths.

This is the real gist of the Vedic world view regarding the culture of knowledge: while culturing transcendental knowledge, one can also come to understand the intricacies of the phenomenal world. By the process of knowing the absolute truth, all relative truths also become known. In modern society today it is often contended that never the twain shall meet: science and religion are at odds. This erroneous conclusion is based on little understanding of either discipline. Science is the smaller circle within the larger circle of religion.

We should never lose sight of our spiritual goals. We should never succumb to the shortsightedness of attempting to exploit the inherent power in the principles of mathematics or any of the natural sciences for ungodly purposes. Our reasoning faculty is but a gracious gift of Godhead intended for divine purposes, and not those of our own design.

Vedic Mathematical Sutras

Consider the following three sutras:

1. "All from 9 and the last from 10," and its corollary: "Whatever the extent of its deficiency, lessen it still further to that very extent; and also set up the square (of that deficiency)."
2. "By one more than the previous one," and its corollary: "Proportionately."
3. "Vertically and crosswise," and its corollary: "The first by the first and the last by the last."

The first rather cryptic formula is best understood by way of a simple example: let us multiply 6 by 8.

1. First, assign as the base for our calculations the power of 10 nearest to the numbers which are to be multiplied. For this example our base is 10.
2. Write the two numbers to be multiplied on a paper one above the other, and to the right of each write the remainder when each number is subtracted from the base 10. The remainders are then connected to the original numbers with minus signs, signifying that they are less than the base 10.

6-4
8-2

3. The answer to the multiplication is given in two parts. The first digit on the left is in multiples of 10 (i.e. the 4 of the answer 48). Although the answer can be arrived at by four different ways, only one is presented here. Subtract the sum of the two deficiencies (4 + 2 = 6) from the base (10) and obtain 10 - 6 = 4 for the left digit (which in multiples of the base 10 is 40).

6-4
8-2
4

4. Now multiply the two remainder numbers 4 and 2 to obtain the product 8. This is the right hand portion of the answer which when added to the left hand portion 4 (multiples of 10) produces 48.

6-4
8-2
----
4/8

Another method employs cross subtraction. In the current example the 2 is subtracted from 6 (or 4 from 8) to obtain the first digit of the answer and the digits 2 and 4 are multiplied together to give the second digit of the answer. This process has been noted by historians as responsible for the general acceptance of the X mark as the sign of multiplication. The algebraical explanation for the first process is

(x-a)(x-b)=x(x-a-b) + ab

where x is the base 10, a is the remainder 4 and b is the remainder 2 so that

6 = (x-a) = (10-4)
8 = (x-b) = (10-2)

The equivalent process of multiplying 6 by 8 is then

x(x-a-b) + ab or
10(10-4-2) + 2x4 = 40 + 8 = 48

These simple examples can be extended without limitation. Consider the following cases where 100 has been chosen as the base:

97 - 3 93 - 7 25 - 75
78 - 22 92 - 8 98 - 2
______ ______ ______

75/66 85/56 23/150 = 24/50

In the last example we carry the 100 of the 150 to the left and 23 (signifying 23 hundred) becomes 24 (hundred). Herein the sutra's words "all from 9 and the last from 10" are shown. The rule is that all the digits of the given original numbers are subtracted from 9, except for the last (the righthand-most one) which should be deducted from 10.

Consider the case when the multiplicand and the multiplier are just above a power of 10. In this case we must cross-add instead of cross subtract. The algebraic formula for the process is: (x+a)(x+b) = x(x+a+b) + ab. Further, if one number is above and the other below a power of 10, we have a combination of subtraction and addition: viz:


108 + 8 and 13 + 3
97 - 3 8 - 2
_______ ______

105/-24 = 104/(100-24) = 104/76 11/-6 = 10/(10-6) = 10/4


The Sub-Sutra: "Proportionately" Provides for those cases where we wish to use as our base multiples of the normal base of powers of ten. That is, whenever neither the multiplicand nor the multiplier is sufficiently near a convenient power of 10, which could serve as our base we simply use a multiple of a power of ten as our working base, perform our calculations with this working base and then multiply or divide the result proportionately.

To multiply 48 by 32, for example, we use as our base 50 = 100/2, so we have

Base 50 48 - 2
32 - 18
______

2/ 30/36 or (30/2) / 36 = 15/36

Note that only the left decimals corresponding to the powers of ten digits (here 100) are to be effected by the proportional division of 2. These examples show how much easier it is to subtract a few numbers, (especially for more complex calculations) rather than memorize long mathematical tables and perform cumbersome calculations the long way.

Squaring Numbers

The algebraic equivalent of the sutra for squaring a number is: (a+-b)2 = a2 +- 2ab + b2 . To square 103 we could write it as (100 + 3 )2 = 10,000 + 600 + 9 = 10,609. This calculation can easily be done mentally. Similarly, to divide 38,982 by 73 we can write the numerator as 38x3 + 9x2 +8x + 2, where x is equal to 10, and the denominator is 7x + 3. It doesn't take much to figure out that the numerator can also be written as 35x3 +36x2 + 37x + 12. Therefore,

38,982/73 = (35x3 + 36x2 +37x + 12)/(7x + 3) = 5x2 + 3x +4 = 534

This is just the algebraic equivalent of the actual method used. The algebraic principle involved in the third sutra, "vertically and crosswise," can be expressed, in one of it's applications, as the multiplication of the two numbers represented by (ax + b) and (cx + d), with the answer acx2 + x(ad + bc) + bd. Differential calculus also is utilized in the Vedic sutras for breaking down a quadratic equation on sight into two simple equations of the first degree. Many additional sutras are given which provide simple mental one or two line methods for division, squaring of numbers, determining square and cube roots, compound additions and subtractions, integrations, differentiations, and integration by partial fractions, factorisation of quadratic equations, solution of simultaneous equations, and many more. For demonstrational purposes, we have only presented simple examples.

Bibliography

1. E.J.H. Mackay, Further Excavations at Mohenjo-daro, 1938, p. 222.

2. Saraswati Amma, Geometry in Ancient and Medieval India, Motilal Banarsidas, 1979, p. 18.

3. Dr. V. Raghavan, Presidential Address, Technical Sciences and Fine Arts Section, XXIst AIOC, New Delhi, 1961.

4. Herbert Meschkowski, Ways of Thought of Great Mathematicians, Holden-Day Inc., San Francisco, 1964.

5. Howard Eves, An Introduction to the History of Mathematics, Rinehart and Company Inc., New York, 1953, p. 19.

6. A.L. Basham, The Wonder That Was India, Rupa & Co., Calcutta, 1967.

7. B.B. Dutta, History of Hindu Mathematics, Preface.

8. Jagadguru Swami Shri Bharati Krishna Tirthaji Maharaja, Vedic Mathematics, Motilal Banarsidass, Delhi, 1988.

http://www.gosai.com/chaitanya/saranagati/...dic-Mathematics

[Guest]

<b>Who remembers ancient India's scientific wealth?</b>
<i>By Md. Vazeeruddin - Syndicate Features</i>

Sessions of Indian Science Congress are held with monotonous regularity at fixed periodicity. Eminent persons use them to think aloud on what breakthroughs India needs to achieve. For instance, Prime Minister Manmohan Singh has just told such a session that India should aim at a second Green Revolution. That was a laudable sentiment. <b>But is it not the duty of the notables to use such sessions to tell the masses what ancient India had achieved in the field of science?</b>

Is Indian heritage only spiritual and cultural, and not scientific? On the contrary, it is at least as scientific as it is spiritual or cultural. It is, however, true that any claim that India's scientific heritage is as great as its spiritual and cultural heritage may baffle many Indians because we have for decades, <b>if not centuries, believed that science is the West's contribution to humanity while India made the world aware of, and prize, cultural and moral values.</b>

That is the reason why we talk day in and day out of our spiritual and cultural heritage but seldom, if ever, of our scientific heritage. Do we have any? Not many know the true answer. <b>In the book "Changing Perspectives in the History of Science: Essays in Honour of Joseph Needham", edited by Mikulas Teich and Robert Young, Dr Rahman, "speaking for India", convincingly exploded the myth that science and technology were essentially European.</b>

The Director of the National Institute of Science, Technology and Development Studies called for co-ordination among various agencies for the allocation of funds for the promotion of research into the history and philosophy of science in India.

Inaugurating in Delhi a meeting of experts on "approach and logistics of supporting research into history and philosophy in India", Dr Ashok Jain said that critical studies in the historical and philosophical contexts of science and technology were vital for the sustenance of an innovative tradition. <b>Research in this area is not only of cultural and academic significance but is responsible also for bringing to life the "foundational aspect of science" which is vital for the development of theoretical science.</b>

Unfortunately, a meeting, jointly organized by the Institute and the National Commission on History and Philosophy of Science, went more or less unnoticed by the public; understandably because the view is gaining ever-increasing acceptance that interest in the history of science is a sign of failing powers. Mercifully, however, medical practitioners who are usually enthralled by the history of medicine do not hold this low opinion. The possible reason is that physicians and surgeons, like all who are executants rather than theorists, are great hero-worshippers, and hero-worship is a great incentive to the study of historical records.

What, anyway, is the Indian science whose history needs to be known? <b>Take, for instance, zinc. Europe learnt to produce it in 1746, but it was distilled in India more than 2,000 years ago through the use of a highly sophisticated pyro-technology. </b>Distillation of this metal in India was brought to light through a series of nearly intact structural remains of ancient Indian zinc distillation furnaces at Zawar near Udaipur in Rajasthan. In late 17th century zinc was imported in small quantities from the East and used in the production of brass. After all, before the advent of present-day high-pressure technology, zinc had inevitably to be produced as a vapour because of the vast difficulties in its distillation process at Bristol in Britain in 1747. <b>The discoveries at Zawar nevertheless prove that Indians knew the process some 2,000 years ago.</b>

Or consider astronomy. According to Dr B.G.Sidhartha, Director of the B.M. Birla Planetarium at Hyderabad, Rig Vedic authors had already discovered the spherecity of the Earth and established the heliocentric (Sun-cantered) theory much before Copernicus. <b>The Rig Veda, according to him, is the oldest textbook on modern astronomy.</b> As such, its seers were scientists in the modern sense. Yet they deliberately concealed this knowledge in hymns, probably because the subject was the preserve of priests. In the hymns themselves, however, can be found through new interpretations the information that light is composed of seven colours, a discovery attributed by modern science to Newton. Thus, when Indra lets loose his seven rivers, it means the splitting of sunlight. Therefore, the rainbow is called "Indradhanush" in the Atharveda.

Three ancient astronomers, the "Ribhus", were the first to establish that the Earth was round and that Mercury and Venus revolved round the Sun. But these sacred texts came down from father to son and thus lost their form and structure till they were lost by about 1400 B.C.

The computer is the reigning fad today and, therefore, India's scientific achievements of the past, some argue, pale into insignificance. But were our ancient scientists totally ignorant of what has developed into the computer? Aryabhata, the ancient Indian mathematician, it is true, had no computer, but some of the techniques that he developed were precisely the ones used in solving problems with today's computer. <b>What is more, computer designers in the West are now studying the works of ancient Indian mathematicians to learn a thing or two about writing software. </b> Aryabhata's algorithm, called "kuttaka" and meant to solve linear intermediate equations, has been found by the West to be extremely efficient computationally. <b>Similarly, the method of Brahmagouta, Jayadeva and Bhaskara-II (rediscovered in Europe 1000 years later) was "optimum in minimizing the number of steps for solving a problem".</b>

<b>Dr Rick Briggs, an American computer engineer, in a paper published in the 1985 issue of "Artificial Intelligence", said that ancient Indians had developed a method for paraphrasing Sanskrit "in a manner that is identical not only in essence but also in form with the current work of artificial intelligence". According to him, "Sanskrit grammarians had already found a way of solving what is perhaps the most important problem in computer science—natural language understanding and machine translation".</b>

Now take physics. Dr Erwin Schrodinger, in an essay, "Seek For The Road", written in 1925, <b>said that science, like Vedantic philosophy, used analogy to comprehend phenomena, as logic had its own limitations and left the scientist in the lurch after taking him up to a certain point. </b>Dr Schrodinger, who won the Nobel Prize for his wave equation that placed the revolutionary quantum concept (as opposed to the Newtonian mechanistic interpretation) on a firm scientific basis, <b>found support for Vedanta in the new physics with its element of indeterminism and idea of "collapse of the wave function", mathematical entity to describe nature for no discernible physical reason.</b>

The most important link between science and the Sastras is an uncompromising logical attitude to everything. According to Prof. T.S.Shankara, who took up "sanyas" and became Swami Parmananda Bharati after teaching physics for 15 years in the prestigious Indian Institute of Technology at Chennai, some basic concepts of modern-day physics are found in the Sastras. For example, the concept of relativity is to be found in them. Basic ideas of relative velocity (velocity not being absolute but only relative) are extensively referred to by Shankaracharya, quoting the Vedas.

The Brahmashastras contain a profound discussion on the same subject. According to Swamiji, "if only some of our students had known this, one of them could have developed Einstein's theory of relativity much before it was done. Pithy statements in the Sastras can help our scientists make significant contributions".

Or consider what the eminent nuclear physicist D.S.Kothari has to say. In a prestigious lecture on "Science and Values" delivered at the Indian National Science Academy on the concluding day of its golden jubilee celebrations, he claimed that the view of the universe provided by physics proclaimed the moral insight of philosophy. "Plank's constant, which explains movement of electrons at various levels of energy, does lead to the moral conclusion that in practicing truth lies immortality as stated in the Rig Veda," he explained. "Plank's constant has a message that either we hang together or will be destroyed together," he said, and referred to the Rig Vedic invocation to the Sun that stressed the wisdom of practicing truth. <b>How can we lament lack of national pride in Indians without first acquainting them with the country's phenomenal scientific achievements in the dim distant past?</b>

http://www.asiantribune.com/show_article.php?id=2978

[Hauma Hamiddha]

A stream of the kubjikA tradition has evolved out of the more archaic atharvanic tradition. One of the most important links between the kubjikA mata and the older atharvan tradition is the kubjikA upaniShad. kubjikA is identified with pratya~NgirA or atharvaNa bhadrakAlI the spirit of the atharva veda. The kubjikA mata also preserves certain other connections to the atharvan tradition in the form of the medico-magical use of herbs. The kubjikA traditon deploys two famous herb grids that are reminiscent of the herb collection used in the atharvanic upAkarma or dIksha rite, the herb collection used for consecrating and offering during the atharvaNa mahAshAnti and the most exalted and awful dhUmAvatI rite of the atharvaNa kalpa. The first of these is the 4X4 grid. These within the squares of this grid are placed the following 18 oShadhis:
bhR^i~ngarAja (16), sahadevI (3), mayUrashikhA (8), putra~NjIva (2), kR^itanjalI (7), adhaHpuShpA (14), rudantikA (11), kumArI (8), rudrajaTa (10), viShNukrAnta (6), shvetArka (4), lajjAlukA (9), mohalatA (6), kR^iShNadhattUra (12), gorakSha(1), karkaTI (15), meShashR^i~ngI (5) and snuhI (13).
They are coded thus:
1= chandramAH; 2=pakShau; 3=vahanayaH; 4=vedaH; 5=bANa; 6=rasAH+R^itavaH; 7=muni/abdhiH; 8=nAgAH+vasavaH; 9=grahAH; 10=dik; 11=shiva; 12=ravi/sUrya; 13=tridasha; 14=manu; 15=tithayaH; 16=R^itvijaH

gorakSha(1)=Adansonia digitata
putra~NjIva (2)=Putranjiva roxburghii
sahadevI (3)=Conyza cinerea
shvetArka (4)= Calotropis procera
meShashR^i~ngI (5)= Gymnema sylvestra
viShNukrAnta (6)=Clitoria ternatea, Evolvulus alsinoides (?)
mohalatA (6) =Bergenia ligulata
kR^itanjalI (7)= Mimosa pudica
mayUrashikhA (8)= Adiantum caudatum
kumArI (8)=Aloe barbadensis/ Aloe vera
lajjAlukA (9)= Biophytum sensitivum
rudrajaTa (10)=Aristolochia indica
rudantikA (11)=Cressa cretica
kR^iShNadhattUra (12)=Datura fastuosa
snuhI (13)= Euphorbia species (E.neriifolia or E.nivulia)
adhaHpuShpA (14)=Trichodesma indicum
karkaTI (15)=Trichosanthes anguina
bhR^i~ngarAja (16)= Eclipta alba

Using this grid and numerical system various prescriptions may be coded by the practioner. Thus, we are told of a prescription thus: tri-dashAkShesha-bhujagair lepAt strI sUyate sukhaM ||
Which means: For easy delivery a woman may use a paste made from tri (3); dasha (10); akShi (eyes=2); isha (rudra=11); bhujaga (nAga=8).
Some applications might have a magical slant: tithi-dig-yuga-bANaish cha guTikA tu vasha~NkarI | bhakShye bhojye tathA pAne dAtavyA guTikA vashe ||
This means: a pill made from tithi (15); dik (10); yuga (ages=4); and bANa (5) can be used for vashikaraNa. This pill should be given in eatables, food-stuff and drinks for the purpose of vashikaraNa.

R^itvig-grahAkShi-shailaish cha shastra-stambhe mukhe dhR^itA |
For protection against palsy on the face caused by stambhana prayogas one may use R^itvik(16); graha (9); akShi (eyes=2); shaila (mountains=7).

The second grid is a larger one of 6X6 squares (know as the grid of brahmA-rudra-indra), with 36 plants: (1) harItakI (2) akShi (3) dhAtrI (4) marIcha (5) pippalI (6) shlphA (7) vahni (8) ShuNThi (9) green pippalI (10) guDUchI (11) vachA (12) nimbakA (13) vAsaka (14) shatamUli (15) saindhava (16) sindhu-vAraka (17) kaNTakArI (18) gokShuraka (19) bilva (20) paunarnavA (21) balA (22) eraNDamuNDI (23) ruchaka (24) bhR^ingarAja (25) kShara (26) parpaTa (27) dhanyAka (28) jIraka (29) ShatapuShpI (30) javAnikA (31) viD~Nga (32) khadira (33) kR^itamAla (34) haridrA (35) vachA (36) siddhArtha

It seems vachA is reused twice in the grid. The plants are dried, ground to powder, treated with soma and mixed with jaggery into modaka, or mixed with ghee and some tailas for use. The recommended doses are from .5 karsha to 1 pala by weight.

[Guest]

Hello there!

Indian science and heritage are often known as arab in Europe.

<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->The exhibition " The golden age of the Arab science ", which has just closed its doors at "l’Institut du Monde Arabe (Institut of the Arab World, Paris), tries to present to the French public the importance of what is presented like "an injustice " : " the history of Western sciences " would "have occulted for a long time what it owe to Arab science ".

The topic of the exhibition is simple : the " Arab-Islamic world " would have experienced a " brilliant development of its civilization ", which has been translated in particular by " fulgurating progress in several scientific fields ".

It is clear that a such point is far from the vision we have of this world today. We only see chaos, intellectual misery, corruption, dictatorships, religious fanaticism and economic disaster. We can easily imagine that those who are inhabited by " the Arab-Islamic identity " feel daily wounded when evolving in an environment organized mainly by concepts forged in Occident. Certainly, a majority needs recognition which would be formulated as follows : " we also, we invented, created, innovated ".

In truth, it is necessary to acknowledge that history taught in our schools leans little on the European extra influences which could mark its development. However, major inventions come from elsewhere, forwards by the "Arab-Islamic world". We owe them in particular the techniques which were crucial for the development of mathematics : numbering system, equations of the third degree etc. Without speaking about the other disciplines like astronomy, medicine etc...
<!--QuoteEnd--><!--QuoteEEnd-->

http://www.north-of-africa.com/article.p...rticle=259

[Bharatvarsh]

Well not surprising, what the arabs did most of the time was to copy Indian science, all this entered Europe through them which is why people used to think arabs made these discoveries but today we know many of the discoveries were made by Indians and its stupid to claim that its "arab science".

[agnivayu]

Let them claim what they want. Hindus dont' recognize their claim. Besides, considering the large number of Hindu Engineers, teachers and doctors who work in the Gulf is proof positive of where the brain power is. I don't see Any High Tech Industrial growth happening in the Arab world.





<!--QuoteBegin-Bharatvarsh+Apr 28 2006, 05:29 PM-->QUOTE(Bharatvarsh @ Apr 28 2006, 05:29 PM)<!--QuoteEBegin-->Well not surprising, what the arabs did most of the time was to copy Indian science, all this entered Europe through them which is why people used to think arabs made these discoveries but today we know many of the discoveries were made by Indians and its stupid to claim that its "arab science".
[right][snapback]50413[/snapback][/right]
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[Guest]

<!--c1-->CODE<!--ec1-->Let them claim what they want. Hindus dont' recognize their claim. Besides, considering the large number of Hindu Engineers, teachers and doctors who work in the Gulf is proof positive of where the brain power is. I don't see Any High Tech Industrial growth happening in the Arab world.

Well not surprising, what the arabs did most of the time was to copy Indian science, all this entered Europe through them which is why people used to think arabs made these discoveries but today we know many of the discoveries were made by Indians and its stupid to claim that its "arab science".
[right][snapback]50413[/snapback][/right]

[right][snapback]50426[/snapback][/right]
[/quote]<!--c2--><!--ec2-->

It is not just Science, Mathematics have been plagiarized but the very civilization of Arabs stands on the Hindu blood, money and brain power.

A bunch of blood thirsty thugs' aka Ghazni/Ghauri/Turks' only contribution to this world is 'Taqaiiya' or deceit during ambush and redistribution of women folks captured during attacks on other countries resulting in so much women that 4 women per divine Arab male was allowed by Ala-mighty himself.. ...don't forget wonderful contibution to the science of Genetics by inbreeding/marrying within the family and multiplying rapidly without which the study of genetic disease would not have gone so far..........last but not the least is scientific application of female circum....!!!!!!!!!!!

http://middleeastinfo.org/article2580.html <!--emo&:flush--><img src='style_emoticons/<#EMO_DIR#>/Flush.gif' border='0' style='vertical-align:middle' alt='Flush.gif' /><!--endemo-->

[agnivayu]

<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->It is not just Science, Mathematics have been plagiarized but the very civilization of Arabs stands on the Hindu blood, money and brain power.

A bunch of blood thirsty thugs' aka Ghazni/Ghauri/Turks' only contribution to this world is 'Taqaiiya' or deceit during ambush and redistribution of women folks captured during attacks on other countries resulting in so much women that 4 women per divine Arab male was allowed by Ala-mighty himself.. ...don't forget wonderful contibution to the science of Genetics by inbreeding/marrying within the family and multiplying rapidly without which the study of genetic disease would not have gone so far..........last but not the least is scientific application of female circum....!!!!!!!!!!!

http://middleeastinfo.org/article2580.html <!--emo&:flush--><img src='style_emoticons/<#EMO_DIR#>/Flush.gif' border='0' style='vertical-align:middle' alt='Flush.gif' /><!--endemo-->
[right][snapback]50448[/snapback][/right]
<!--QuoteEnd--><!--QuoteEEnd-->

Arabs and muslims are the most decadent bunch of people in the world. Their outward extreme conservatism is just a facade.

[Guest]

"Arab Sciences"
Since when ???

[Sunder]

<!--QuoteBegin-Mudy+Apr 30 2006, 06:15 AM-->QUOTE(Mudy @ Apr 30 2006, 06:15 AM)<!--QuoteEBegin-->"Arab Sciences"
Since when ???
[right][snapback]50469[/snapback][/right]
<!--QuoteEnd--><!--QuoteEEnd-->
Not a single alphabet in Sciences contains A, R, A, or B.

It is quite important for India and Indians to counter this propaganda and ensure that the contributions of Science and mathematics are reclaimed and properly ackknowledged to be Hindu contributions (like we did for Swastika.)

If this propoganda continues and takes root, then world history will sadly be a distorted one.

[Guest]

Well, not so fast. The basic statement that the Arabs (not really Arab but for the most part they came from conquered Iranian/Central asian territories) copied from india has a lot of truth in it. But there are a couple of things they did better than the europeans.

1.They invariably give credit to the Indics for the use of their results. When they used to refer to Sind Hind, they meant the Siddhantas (the Surya siddhanta authored by Brahmagupta) and the Panch siddhanta by Varahamihira which is itself a summary of 5 older siddhantas. Except for the instances in the middle ages mentioned in my paper on Vedic Mathematicians
the west has completely ignored Indic contributions and we have now internalized it and believe that the Indic contribution was minimal.

Both al-Khwaresmi and al-Biruni - both from Khwaresm and spoke a dialect of Farsi gave full credit to indic scientists and specifically mention Aryabhatta among others. Saad al Andalusi from Moorish Spain in 1100 ce in Tabaqat al Umam pays a handsome tribute to indics also. so the respect of the Arabs for al-Hind was very high at least among the scientific community.

The Arabs did make a contributions in the area of medicine and in astronomy ( a lot of the stars in the sky are named after arabic names)

But the arab effort was not sustainable and it came to an end with the sack of Baghdad by Hulagu.

[Guest]

<b>Vedic Mathematicians in Ancient India (Part I)</b>
By Kaushal Vepa