• 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
The Indic Mathematical Tradition 6000 BCE To ?
Some interesting links:



[url="http://www.lifepositive.com/mind/culture/indology/ancientindia.asp"]How advanced were we?[/url]



Mathematics and the Spiritual Dimension

I remember the time my father pulled me aside and said, "Son, you can explain everything with math." He was a rationalist, and for him God existed only in the sentiments of the uneducated. At the time I believed him, and I think his advice had a lot to do with my decision to pursue a degree in physics. Somewhere along the way, however, in 1969, something happened (something many people are still trying to figure out) which drew me away from the spirit of that fatherly advice and subsequently my once promising career.

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.

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 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.

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.

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.

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).

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.

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 /X = ." 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 to any number of decimal places (since arctan 1 = /4). Whether he accomplished this by inventing a system as good as calculus or without the aid of calculus; either way it is astonishing.

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.

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 insert 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, Êapa, 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.

[Reprinted with permission

from Saranagati OnLine Magazine]

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.

Ancient Sanskrit scholars "hid" many things behind normal

shlokas. One key to uncover the hidden meaning goes like:

kaadinava Taadinava paadipanchakam

yaadyashhtakah kshha shunyam

Now, apply this key to the following shloka:





What one obtains is the value of p / 10 correct to 31 places after the decimal point !

0.31415926 53589793 23846264 3383279

The implications of the above are mindboggling. Whereas the ancient Egyptians had a value of 3 for pi, the much later Greeks too did not go beyond the first two decimal places. But, they might be excused because they did not follow the decimal system. However, to know the value to 31 places Surely, the composer then knew about the concepts of irrational numbers... surely, the mathematician saw in pi something beyond its merely being the ratio of the circumference to the diameter of a circle.. and how on earth does one compute the value of pi to 30+ places? The tragedy is that such masterpieces were hidden, requiring geniuses of like order to appreciate them. Were the ancient greats such egotists that they deemed it improper to educate simpler people? How long can such knowledge be sustained, if it is to be propagated only through rote repetition of "Holy" texts? No wonder, that a climate conducive to a pure quest for knowledge was never fostered ...
Vedic Science & Mathematics
<!--QuoteBegin-acharya+Nov 11 2003, 05:50 AM-->QUOTE(acharya @ Nov 11 2003, 05:50 AM)<!--QuoteEBegin--> http://www.pa.uky.edu/~ameya/pi.html

Ancient Sanskrit scholars "hid" many things behind normal
shlokas. One key to uncover the hidden meaning goes like:

kaadinava Taadinava paadipanchakam
yaadyashhtakah kshha shunyam

Now, apply this key to the following shloka:


What one obtains is the value of p / 10 correct to 31 places after the decimal point !

0.31415926  53589793  23846264  3383279

The implications of the above are mindboggling. Whereas the ancient Egyptians had a value of 3 for pi, the much later Greeks too  did not go beyond the first two decimal places. But, they might be excused because they did not follow the decimal system. However, to know the value to 31 places Surely, the composer then knew about the concepts of irrational numbers... surely, the  mathematician saw in pi something beyond its merely being the ratio of the circumference to the diameter of a circle.. and how on earth  does one compute the value of pi to 30+ places? The tragedy is that such masterpieces were hidden, requiring geniuses of like order to appreciate them. Were the ancient greats such egotists that they deemed it improper to educate simpler people?  How long can such knowledge be sustained, if it is to be propagated only through rote repetition of "Holy" texts? No wonder, that a  climate conducive to a pure quest for knowledge was never fostered ... <!--QuoteEnd--><!--QuoteEEnd-->
Hi Acharya,

I applied the key and what I get doesn't look like an expansion for pi/10 !!

pi/10= 0.31415926 53589793 23846264 3383279

What I get is:

3143158426 523...

It seems to be incorrect in the fourth place itself. What is going on?
My first post i think !

Anyway are here any members who have some knowledge about indian astrology,i suppose it has a very strong relation with astronomy and mathematics ?
<!--QuoteBegin-amarnath+Jan 23 2004, 05:19 AM-->QUOTE(amarnath @ Jan 23 2004, 05:19 AM)<!--QuoteEBegin--> Anyway are here any members who have some knowledge about indian astrology,i suppose it has a very strong relation with astronomy and mathematics ? <!--QuoteEnd--><!--QuoteEEnd-->
amarnath: I do have interest in this area too, but zero knowledge. Some friends I know who are 'experts' in this are not forum members - yet.

Take a look at this site:

I've used the software for some basic calculations and seemed correct when cross-checked by others. As you might know, there's the science and math aspect which can be confirmend for accuracy and then there's this subjective aspect of interpreting the results where people have the differences.

There are some forums where these guys hang out - will see if I can get more on this.
<!--QuoteBegin-amarnath+Jan 23 2004, 02:49 PM-->QUOTE(amarnath @ Jan 23 2004, 02:49 PM)<!--QuoteEBegin--> My first post i think !

Anyway are here any members who have some knowledge about indian astrology,i suppose it has a very strong relation with astronomy and mathematics ? <!--QuoteEnd--><!--QuoteEEnd-->

<b>amarnath :</b>

The Indian Astrology System is more accurate than the Western System. One of the main reasons is that the Indian System allows for “Ayana”- Precession- where as the Western System doesn’t.

Thus per the Western System the Sun enters Capricon on 23 Decemeber and as per the Indian System it enters on 13th January (Makar Sankrant)

<b>Ancient India -Mathematics</b>

<b>Ancient India - Science & Medicine</b>

<b>Ancient India - Ship Building & Navigation</b>

<b>Ancient India - Sports & Games</b>

<b>Ancient India - Astronomy</b>

<b>maize in ancient India:</b>
The Washington Post
December 13, 1994, Tuesday, Final Edition


LENGTH: 1025 words

HEADLINE: Altered Images;
<b>Plastic Surgery's Earliest Cases Date to Ancient Egypt, India </b>
SERIES: Occasional

BYLINE: Thomas V. DiBacco, Special to The Washington Post

Plastic surgery, the reshaping of body tissues for reconstructive or cosmetic
purposes, dates back to antiquity. Derived from the Greek plastikos and the
Latin plasticere, both meaning to mold, the surgery was employed in instances of
battle wounds or animal attacks.

Egyptians performed plastic surgery as early as 3400 B.C., <b>but it was in
India, sometime between the sixth century B.C. and the sixth century A.D. when
the Hindu medical chronicle Susruta Samhita was written, that the skill evolved</b>.

Indian surgeons devised what came to be known as the attached-flap method of
plastic surgery as a solution for the punishment for adultery -- the cutting off
of the nose. In the procedure, skin transplanted to the nose area was kept ali
by remaining attached to healthy tissue. As the Susruta Samhita explained:

"When a man's nose has been cut off or destroyed, the physician takes the
leaf of a plant which is the size of the destroyed parts. He places it on the
patient's cheek and cuts out of this cheek a piece of skin of the same size (but
in such a manner that the skin at one end remains attached to the cheek). Then
he freshens with his scalpel the edges of the stump of the nose and wraps the
piece of skin from the cheek carefully all around it, and sews it at the edges.
"Then he places two thin pipes in the nose where the nostrils should go, to
facilitate breathing and to prevent the sewn skin from collapsing. There after
he strews powder of sapan wood, licorice-root and barberry on it and covers with
cotton. As soon as the skin has grown together with the nose, he cuts through
the connection with the cheek."

The Greek physician Galen (130-201 A.D.) performed reconstruction of the
nose, ears and mouth, but plastic surgery fell into disuse in Europe for the
next thousand years. During the Middle (or Dark) Ages. it became the target of
the Catholic Church because surgery ran the risk of inflicting death upon
patients. What's more, the spilling of blood by a surgeon and the power that he
held over a patient's body were suggestive of sorcery.

The procedure would not be revived in Europe until around the time
Christopher Columbus set sail in 1492, when Italian surgeons used skin from both
the cheek and arm to replace noses. In 1597, Gasparo Tagliacozzi, professor of
surgery at Bologna, employed upper-arm skin grafts on individuals whose noses
had been destroyed by syphilis. The graft at one end remained attached to the
arm, to be nourished by the body's blood.

<b>Not until the 18th century, when British surgeons in India saw the
attached-flap surgery performed, did the procedure make headway in northern
Europe. A century later, free-tissue grafts were initiated in which tissue was
completely cut away from original sites.</b>

Plastic surgery came to America in the 19th century. It was the hallmark of
itinerant, untrained surgeons who promised far more than they could deliver in
correcting various deformities. Their patients often were left with
complications and ugly scars, giving the practice a bad name.

Approximately a third of plastic surgery today deals with beautification,
although the line between its two main branches, reconstructive and cosmetic,
has been blurred.

Equally offensive were hack inventors who took advantage of the public's
gullibility for miracle cures, as for example a "nose-improver" that was hawked
on the streets of the nation's capital in the 1880s. Consisting of a two-part
metal shell connected by a hinge, the device was to be affixed over the nose
only at night, with the manufacturer claiming results in a mere eight weeks.

"The inventor boasts," read one contemporary account, "that it will keep its
shape until the owner grows tired of it, when he may buy an improver with a
different mold, and appear with another equally beautiful nose."

Physicians in the early 20th century such as Jacques Joseph (1865-1934) in
Berlin and Sir Harold Gillies (1882-1960) in England began to publish scholarly
articles and textbooks on plastic surgery that described advances they had made.
These publications came as the ravages of World War I made reconstructive
surgery a necessity. Still, this specialized field of medicine was slow to
develop in America. Not until 1937 was the American Board of Plastic and
Reconstructive Surgery founded to establish standards for practitioners. The
high casualty rates of World War II spurred improvements in plastic surgery
procedures for wounds and burns.

In recent decades, plastic surgeons have used a variety of skin flaps as well
as cartilage, bone and nerve grafts.

Use of artificial limbs (prostheses) and fixation plates and wires to hold
tissue, and the repositioning and suturing of displaced tissue fragments, are
sophisticated techniques used to treat trauma patients and those with congenital

And microsurgery has permitted the rejoining of microscopic nerves and blood
vessels, extending the application of plastic surgery.

By the 1990s, silicone breast implants aroused controversy because the
device sometimes ruptured into surrounding tissue. In response, the Food and
Drug Administration in 1992 restricted such implants to women needing
reconstructive surgery after breast cancer treatment.

Approximately a third of plastic surgery today involves beautification,
although the line between reconstructive and cosmetic surgery has been blurred
by the argument that improved form enhances a person's ability to function.

The distinction is made by insurance companies in denying benefits for
"cosmetic surgery or other services primarily intended to change or improve

Thomas V. DiBacco is a historian at American University.

CAPTIONTongueanels from Tagliacozzi's 16th century text show four stages in the
rebuilding of a nose. 1. Skin flap is partly cut from arm of noseless patient,
upper left. 2. Other end is grafted onto face while patient wears a rigid
harness for 14 days so blood from arm can nourish skin for the new nose, upper
right. 3. Flap is severed from arm, lower left. 4. Skin graft is bandaged, lower
right, for two more weeks before it can be molded into a new nose.

If any of you DISH Network subscribers has access to LinkTV, check this 2 hour documentary on Ayurveda: The Art of Being

<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->The documentary reveals how the revitalized holistic discipline, based on the most ancient of techniques, can be applied in this age of nuclear power, the internet and instant everything<!--QuoteEnd--><!--QuoteEEnd-->

It's really amazing to see and hear about people being treated with herbs from our ancient texts in matter of days without any side effects.
<b>Sanskritising the IITs</b>
Along with probability theory, calculus, courses in mechanical, chemical or civil engineering, students of the Indian Institute of Technology, Delhi, will soon have a new subject to pore over: Sanskrit.

For the last three years, IIT Delhi has been working on a plan to introduce two courses in Sanskrit for undergraduate students. These courses are expected to give the students a glimpse into the information contained in ancient Sanskrit texts.

The idea is to 'bring the students and teachers to the orders of thinking that are available in Sanskrit without any mediation by the contemporary demands of what constitutes an intellectual discourse'. In other words, the course aims at broadening students' thinking.

But the move is also the result of a nudge from Union Minister for Human Resources Development Murli Manohar Joshi.

In July 2000, the HRD ministry sent out notices to around 40 educational institutions, including the IITs and the Indian Institute of Science, asking them to consider the idea of introducing Sanskrit courses. Over the last three-and-a-half years, a group of nine IIT professors along with an advisory committee comprising Sanskrit experts drew up the curriculum for the courses.

"Modern scientific concepts are not more than 300 years old. <b>Students must know what constituted science in India during the last 1,000 years. Today, science and technology are decided within the Western framework. It is important to know India's legacy in these subjects," says Wagesh Shukla, professor of mathematics at IIT Delhi and c</b>onvener of the committee that decided the curriculum.

Ancient India has been credited with many discoveries in mathematics, astronomy, medicine and architecture and most of the discoveries in that age have been chronicled in Sanskrit.

Sanskrit, which developed in around 1500 BC, is regarded as the Asian equivalent of Latin because of its role in chronicling India's religious and historical literature. More Sanskrit documents are estimated to have been preserved than documents in Latin and Greek combined.

However, Sanskrit as a spoken language died out centuries ago; today, it is only spoken by scholars and others who have been trained in the language. As a result, the entire knowledge codified in the ancient texts has been lost as well, say the IIT Delhi professors.

"India's contribution to the field of science and technology has been noteworthy. Take, for instance, the concept of shunya [zero]. This has been chronicled in the Sanskrit texts but, because people do not know the language, there is no widespread access to the information," says Dr M Jagadesh Kumar, associate professor at the department of electrical engineering, IIT Delhi, who now heads the committee overseeing the introduction of the courses.

To re-introduce some of the ancient ideas to students, IIT Delhi has planned two courses: Building Science, which will deal with engineering knowledge drawn from the ancient texts, and Study of Scientific Systems in ancient India, which will present scientific ideas from Sanskrit texts.

"The basic idea is not as much to present specific examples from Sanskrit texts as to introduce students to what constituted the body of scientific work in ancient India. We are not looking in the text for examples of what we see today in modern science. We are looking for what functioned as science and how it was used," says Professor Shukla.

<b>Students who opt for Study of Scientific Systems will learn what 'proof,' 'observation,' 'rule' and other scientific definitions meant to the thinkers of the past. They will also learn different kinds of logical reasoning systems with examples drawn from various Sanskrit texts</b>.

<b>The key text that will be taught will be the Astadhyayi, the grammar of Sanskrit. "It is responsible for modern linguistic sciences and is supposed to be the forerunner of artificial intelligence," says Professor Shukla</b>.

IIT Delhi plans to prepare course material based on Sanskrit texts for use by students both in the IITs and in other colleges. It also plans to produce research monographs which "debate, employ or reject the practicality of the paradigms of investigation that are available in Sanskrit for taking up the problems of science and technology of the new century," says Professor Kumar.

The Sanskrit courses will, however, be taught in English, the medium of instruction at the IITs. But their introduction has been stymied for a while now due to the unavailability of qualified teachers.

Since IIT Delhi is keen on introducing its students to ideas drawn from ancient Sanskrit texts rather than teaching them the language, finding someone who fits the bill has been difficult.

"We are not just teaching the language, we are looking at the science and technology part of it. Most Sanskrit teachers are language experts. We need people who are conversant with both the language and the scientific knowledge written in the language. We want to expose students to both aspects," says Professor Kumar, who has volunteered to teach the courses till the Institute is able to find new teachers.

The Sanskrit courses will be offered as electives to students, which means they will retain the ultimate choice on whether they want to study it or not.

"Students already have a very heavy curriculum. We cannot add more courses. But we will offer these are electives so they can take it if they are interested," says Professor Kumar.

Every student in the undergraduate engineering course at IIT Delhi has to take at least one humanities course. Currently, students have subjects like psychology, literature, philosophy and sociology to choose from.

Most students are unaware of the plans to introduce Sanskrit courses.

"I haven't heard about this. But if we were given the option to take these courses, I don't see any problem. It certainly sounds interesting. After all, Sanskrit is something we all have heard about though we never got a chance to study it," says Kalpana Singh, an undergraduate student in textiles engineering and general secretary of the students.

Other students say a lot will depend on how the course is structured and marketed.

<b>"It sounds interesting if the course talks of ancient scientific ideas and concepts. I feel it is better than studying sociology or psychology and would not mind taking it.</b> It depends on how the course is presented. If it is about learning the language, I don't know if I will go for it, but if it is about ancient concepts, why not?" asks Vikas Mittal, a second year student of chemical engineering.

IIT Delhi says it did not plan to introduce these courses because of any pressure from the HRD ministry. Rather, it is an attempt to "expose students to the best of everything."

"Sanskrit texts contain a lot of information about India's contribution to science and technology. Sadly, our students are not aware of it. We do not see any so-called 'saffronisation' agenda in making our students aware of India's history and contributions to science and technology," says Professor Kumar.

Eventually, IIT Delhi plans to integrate the Sanskrit courses into its system of teaching -- rather than just offering it as an elective -- and start awarding degree programmes in the subject. Almost all the material prepared will be put in a downloadable form on the IIT website. Instructional CDs and DVDs will also be created.

<b>"Such a course could add value to the students. We would probably take more interest in engineering if we know how old some concepts in it are and how it has helped our civilization in the past," says Mittal.</b>
<!--QuoteBegin-Mudy+Mar 10 2004, 01:21 AM-->QUOTE(Mudy @ Mar 10 2004, 01:21 AM)<!--QuoteEBegin--> <b>Sanskritising the IITs</b> <!--QuoteEnd--><!--QuoteEEnd-->
IIT Sanskrit: These are some sites I make regular visits to (probably a daily or weekly visits.)

Also check out the Yogasutra and brahmasutra links.. Excellent source of bhashyas if you know samskrit.
X-posting:Was posted by ramana in another thread:

<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->This webpage documents Aryabhatta I made significant contributions to Algebra.


More comprehensive description of Indina contributions is given here:


Another short history of Indian developments in Mathematics


Indian Mathematics: Redressing the balance
Ancient Jaina Mathematics: an Introduction by D.P. Agrawal
<span style='font-size:14pt;line-height:100%'>Did Bhaskar II discover calculus?</span>
<span style='font-size:14pt;line-height:100%'>Bhaskar II was born in Vijapur in the province of Karnataka in 1114 A.D. He wrote Siddhanta-Shiromani in 1150, which became a classical text in Mathematics and Astronomy. The book is divided in four parts: Lilavati deals with arithmetic, Bijaganita with algebra, Ganitadhyaya and Goladhyaya with astronomy</span>.

In Siddhanta Shiromani, Bhaskar II defines two kinds of planetary velocities: Sthula gati (average speed) and Sukshma or Tatkaliki gati (instantaneous velocity). The process of finding instantaneous velocity involves the use of differential calculus. There is definite proof that Bhaskar II carried out such calculations using the method of differentiation.

According to Hindu astronomy,

l = lmean ± r sina/R


l = true longitude

lmean = mean longitude

r = radius of the epicycle

a = anomaly


R = radius of the deferent cycle

Bhaskar II formulates the expression for the tatkaliki gati (instantaneous velocity) as follows:

"To find the instantaneous velocity (in longitude) of the planet, the kotiphala is to be multiplied by the time rate of change of anomaly and divided by the radius, and the quotient (thus obtained) is to be added to or subtracted from the velocity of the mean planet according as its position is in the six signs from the beginning of Cancer or Capricorn."

Expressed mathematically,

dl/dt = dlmean/dt ± (r cosa/R) da/dt


r cosa = kotiphala

This equation not only provides his familiarity with the notion of differentiation, but also shows his knowledge of the expression

d(sina)/da = cosa

After Bhaskar II, India went through a long hostile foreign rule, and could not produce any mathematician of his caliber for a long time to come.

Reference: D. M. Bose, S.N. Sen and B. V. Subbarayappa, "A Concise History of Science in India", Indian National Science Academy, 1971, p. 203

This website is maintained by Dr. Roy. If you wish, you can contact Dr. Roy by sending an e-mail to info@goldeneggpublishing.com.

<b>An overview of Indian mathematics</b>
Link: http://www.infinityfoundation.com/mandala/...r_raju_kala.htm

Title: "Kâla: Traditional Indian Time Beliefs in Relation to the Western and the Scientific"
by C. K. Raju, PhD

Link: http://www.atributetohinduism.com/calculus.pdf
Title : The Infinitesimal Calculus: How and Why it Was Imported into Europe

Link: http://www.ex.ac.uk/~PErnest/pome11/art18.htm
Title: Mathematics and Culture

link: http://www.indianscience.org/scope.shtml
Title: Book series on Indian science and technology - Project overview

Forum Jump:

Users browsing this thread: 1 Guest(s)