Thursday, February 20, 2014

HINDUISM DECODED---Learn from Maldieves ,how Hindu/Buddist were converted to islamist ,sunni muslim(worst fanatics) in 700 years.

 Hindu-Buddhist past erased in Maldives without a whisper from New Delhi-Maleban emerges in Indian ocean atoll.


 Image source-http://www.maldivesculture.com
Goddess Nidhi-lakshmi as represented on a 9th century coral block
While Maldivian President, Mohamammad Nasheed, who was elected through popular vote in the 2009 parliamentary elections, was forced on gun-point to resign on 7th February by the supporters of the opposition coalition being led by the Adhaalat (Justice Party), the Islamic fundamentalists attacked the National Museum of Maldives at Male and vandalized Hindu- Buddhist artifacts, erasing a monumental treasure from the Maldivian history. Though, Maldives is an Islamic state with 100% Sunni Muslim totaling 328,536 persons that inhabits 200 of its 1,192 islands, Islam came to the garland of atolls only in 1153A.D. Maldives has a Hindu-Buddhist past. Many of the atolls were also part of the Chola Empire and Buddhism is believed to have reached the islands during Ashoka’s time itself. Before Buddhism, Maldivians practiced Srauta tradition of Hinduism.

News report mention that around half a dozen of radical Muslim fanatics entered the museum and completely destroyed the collection of coral and lime figures, including the famous six-faced coral statue( Buddhist Tantric image) and famous Buddha’s head, Nearly 35 artifacts of Hindu and Buddhist tradition have been completely destroyed, some dating back to 6th century and most from 8-9th century. These were the main items of attraction since the time museum was opened on 26 July, 1952. The Chinese government had built the Museum as part of a UNESCO project . Museum Director has told media that 99 percent of the Maldives' pre-Islamic artifacts from before the 12th century, have been completely destroyed.
Six-faced coral-stone stele
                                                          Period: Circa 9th century CE ;
Place found: Ameeru Ahmad Magu, Henveiru, Male', early 1960s
 
 
 What is surprising is utter silence of Indian government on this vandalization of a tradition linked with India’s civilizational glory that too in a small state which is part of the SAARC &SAFTA. What further astonishes is the alacrity which the government showed in bestowing recognition to the coup d’etat within 24 hours and to add to the worse part, Indian Prime Minister made a phone call to congratulate the new President Mohammad Waheed Hassan Manik. Not a single whisper of condemnation came against the vandalism perpetrated by the Islamic fundamentalists of the Maldives, the Male-bans.
Coral stone head
Period: Circa 6th-7th centuries CE ;
Place found: Thoddoo island in North Ari atoll


Now, one can see the differential treatment meted by the government of India on two religious-cultural issues in the same month. When Jay Leno was joking about American Republican Party Presidential election contender ,Mitt Romney's wealth by pointing to a picture of the Golden temple and describing the GoldenTemple as Mitt Romney's summer home, the whole Indian establishment went into a tizzy. Indian government lodged a formal protest with the US government mentioning that it has offended Sikhs sentiments. MEA, Overseas Indian Affair Ministry, Indian Ambassador in the US all went into a huddle as if it was a national emergency. But, in the case of Malibanese erasure of Hindu-Buddhist past in the courtyard, what to say about the condemnation, the whole establishment is busy burying the incident under the Indian Ocean itself. One can also contrast the way the Rajya Sabha condemned the humiliation of Sikhs who were being forced to remove their turbans in the name of security at international airports, especially in Italy on 8th December, 2011. Italian Ambassador Giacomo Sanfelice di Monteforte was summoned in Delhi and protests lodged twice with the Italian government. Indian Foreign Minister called dishonor to Sikhs as “national insult”. One can also see the urgency on this very issue when Indian Prime Minister takes up the matter of Sikh turbans at important meeting of G-20 with the French President. It appears as if the whole establishment is so much engrossed in the issue of Sikh turbans that it is apt to call the administrative machinery as undergoing “turbanization”. But, the vandalization and erasure of a whole past rooted in the non-violence and compassion in the little island-state of Maldives is not even an issue to be condemned by the same bunch of people.
Tantric deity in coral stone

The double standard meted by the state vis-à-vis majority community and selected minority community is quite evident. There are people who drumbeat about secularism , but what they practice is utter devastative path of erasing the culture and creativity of the Indian civilization.
 
It is right time that India takes up a tough stand in its own backyard. India cannot afford to lose Maldives in the hands of Maleban who would turn it into a relay station for the Sea Ghazis, the Muslim fundamentalist pirates who now straddle Indian Ocean from the Strait of Hormuz to the Strait of Malacca and have emerged as the gravest threat to the safety of international navigations in the common waters.
 
Where Maldievians come from-READ MORE-LINK  Maldives culture-Hindu and Buddhist origin.
The Maldives people are a clear ethnic category, having a unique language derived from Sinhala but grafted on to an earlier Tamil base, and they have a homogeneous cultural tradition. In early medieval times they followed the Sri Lanka type of Buddhism, but in 1153 were converted to Islam by order of their ruler. There is another island located to the north of Maldives territory that belongs culturally to the Maldives, Minicoy (properly, Maliku), which because of events during the colonial period is now held by India as part of its Lakshadvip Island group. Most of the Maldives islands are tiny, less than a mile long, but Minicoy is the largest island populated by Divehi people. The Indian government does not allow foreigners to visit this island.


Historical Records
Early references to the Maldives are found in the Commentary on the Bharu Jataka and the Khuddapatha, early Buddhist texts, and the Dipavamsa, the earliest Sinhala epic (4th century BC), and the Mahavamsa (3rd century BC). The country was probably overrun from Kerala in the Sangam Period of South India (1-3 century AD). It is mentioned in the Greek text Periplus (1st century AD), by Pappas of Alexandria (4th century), and several fifth century Greek authors. The islands are mentioned by the Chinese travellers Fa Hsien (5th century) and Hsuan-Tsang (7th century), and in a document of the Tang Dynasty (8th century). The country was conquered by Tamil Pallavas from neighbouring Madras (late 7th century).

Islamic records start with an account by Sulaiman the merchant (c. 900 AD), and Al-Mas'udi (916), Abul Hassan the Persian (1026), Al Biruni (1039), and Al-Idrisi (c. 1100). In the meantime, the country was reconquered by the Tamils, namely by Rajaraja Cola (1017). Europeans are on a more familiar territory when they read the account of Marco Polo (1279- 92). Ibn Battuta made two visits and spent a year and a half in the Maldives as an Islamic legal advisor (1343-46).

Portuguese accounts begin from about 1500. In the brutal competition for control of ocean routes they invaded the Maldives in 1588, killed the sultan, and established Portuguese rule, but that only lasted for fifteen years. Most interesting is a lengthy three-volume account by François Pyrard of Laval, who was held captive in the Maldives (1602-07) and learned Divehi. It is a gold-mine of original Divehi history, customs, and language.

British interest dates from the early 1600s. The Divehis had always managed to remain essentially independent, except for the brief Portuguese occupation, but in 1887 the sultan formally accepted British suzerainty. The only sustained historical work of the Maldives done in the British period was that by H.C.P. Bell, a British antiquarian who studied the Buddhist remains, texts, and coins. The British did not leave an administrative or cultural stamp as they did in India, except for their base in Gan in the south. The Maldives became independent in 1965 and joined the United Nations.

Tamils, Sinhalas, and Arabs
Where did the Divehis come from? Generally, ordinary Divehis mostly know only that their islands were settled from Sri Lanka, that before Islam they were Buddhist, and that their language suggests the same origin. Because of the long dominance of Islamic tradition, they tend to stress Arabic and Muslim cultural influences and overemphasize Arab ancestors. Scholars came from the Islamic centres of learning in Egypt, and the Divehis accepted the Shafi school of Islamic law. They rationalize Divehi culture and behaviour in terms of traits in Arab culture mentioned earlier in old Islamic texts. But for all that, and despite eight centuries of official status, the Islamic tradition is something of a cultural overlay.
The Divehi kinship system is partly of Dravidian origin, and bears evidence of some matriliny, like the Nayar and other matrilineal groups of Kerala.

FUTURE- WILL SINK IN 100 YEARS AS WATER LEVEL RISES.

Wednesday, February 19, 2014

HINDUISM DECODED--Decimal Number System #DECODING #HINDUISM


Stick Counting Marks

Numbers in Early India
Lokavibhaga and zero
HOW WEST STOLE BHARAT AND TURNED IT TO INDIA-
In India, emphasis was not on military organization but in finding enlightenment. Indians, as early as 500 BCE, devised a system of different symbols for every number from one to nine, a system that came to be called Arabic numerals, because they spread first to Islamic countries before reaching Europe centuries later.

What is historically known goes back to the days of the Harappan civilization (2,600-3,000 BCE). Since this Indian civilization delved into commerce and cultural activities, it was only natural that they devise systems of weights and measurements. For example a bronze rod marked in units of 0.367 inches was discovered and points to the degree of accuracy they demanded. Evidently,such accuracy was required for town planning and construction projects.Weights corresponding to units of 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 200 and 500 have been discovered and they obviously played important parts in the development of trade and commerce.

It seems clear from the early Sanskrit works on mathematics that the insistent demand of the times was there, for these books are full of problems of trade and social relationships involving complicated calculations. There are problems dealing with taxation, debt and interest, problems of partnership, barter and exchange, and the calculation of the fineness of gold. The complexities of society, government operations and extensive trade required simpler methods of calculation.

Earliest Indian Literary and Archaeological References

When we discuss the numerals of today’s decimal number system we usually refer to them as “Arabian numbers.” Their origin, however, is in India, where they were first published in the Lokavibhaga on the 28th of August 458 AD.This Jain astronomical work, Lokavibhaga or “Parts of the Universe,” is the earliest document clearly exhibiting familiarity with the decimal system. One section of this same work gives detailed astronomical observations that confirm to modern scholars that this was written on the date it claimed to be written: 25 August 458 CE (Julian calendar). As Ifrah2 points out, this information not only allows us to date the document with precision, but also proves its authenticity. Should anyone doubt this astronomical information, it should be pointed out that to falsify such data requires a much greater understanding and skill than it does to make the original calculations.

The origin of the modern decimal-based place value system is ascribed to the Indian mathematician Aryabhata I, 498 CE. Using Sanskrit numeral words for the digits, Aryabhata stated “Sthanam sthanam dasa gunam” or “place to place is ten times in value.”The oldest record of this value place assignment is in a document recorded in 594 CE, a donation charter of Dadda III of Sankheda in the Bharukachcha region.

The earliest recorded inscription of decimal digits to include the symbol for the digit zero, a small circle, was found at the Chaturbhuja Temple at Gwalior, India, dated 876 CE.This Sanskrit inscription states that a garden was planted to produce flowers for temple worship and calculations were needed to assure they had enough flowers. Fifty garlands are mentioned (line 20), here 50 and 270 are written with zero. It is accepted as the undisputed proof of the first use of zero.

The usage of zero along with the other nine digits opened up a whole new world of science for the Indians. Indeed Indian astronomers were centuries ahead of the Christian world.The Indian scientists discovered that the earth spins on its axis and moves around the sun, a fact that Copernicus in Europe didn’t understand until a thousand years later—a discovery that he would have been persecuted for, had he lived longer.

From these and other sources there can be no doubt that our modern system of arithmetic—differing only in variations on the symbols used for the digits and minor details of computational schemes—originated in India at least by 510 CE and quite possibly by 458 CE.

The first sign that the Indian numerals were moving west comes from a source which predates the rise of the Arab nations. In 662 AD Severus Sebokht, a Nestorian bishop who lived in Keneshra on the Euphrates river, wrote regarding the Indian system of calculation with decimal numerals:

“ ... more ingenious than those of the Greeks and the Babylonians, and of their valuable methods of calculation which surpass description...” 3

This passage clearly indicates that knowledge of the Indian number system was known in lands soon to become part of the Arab world as early as the seventh century. The passage itself, of course, would certainly suggest that few people in that part of the world knew anything of the system. Severus Sebokht as a Christian bishop would have been interested in calculating the date of Easter (a problem to Christian churches for many hundreds of years). This may have encouraged him to find out about the astronomy works of the Indians and in these, of course, he would find the arithmetic of the nine symbols. The Decimal Number System

The Indian numerals are elements of Sanskrit and existed in several variants well before their formal publication during the late Gupta Period (c. 320-540 CE). In contrast to all earlier number systems, the Indian numerals did not relate to fingers, pebbles, sticks or other physical objects.


Arabic Indian Decimal Numerals

The development of this system hinged on three key abstract (and certainly non-intuitive) principles: (a) The idea of attaching to each basic figure graphical signs which were removed from all intuitive associations, and did not visually evoke the units they represented; (b) The idea of adopting the principle according to which the basic figures have a value which depends on the position they occupy in the representation of a number; and (c) The idea of a fully operational zero, filling the empty spaces of missing units and at the same time having the meaning of a null number. 4

The great intellectual achievement of the Indian number system can be appreciated when it is recognized what it means to abandon the representation of numbers through physical objects. It indicates that Indian priest-scientists thought of numbers as an intellectual concept, something abstract rather than concrete. This is a prerequisite for progress in mathematics and science in general, because the introduction of irrational numbers such as “pi,” the number needed to calculate the area inside a circle, or the use of imaginary numbers is impossible unless the link between numbers and physical objects is broken.

The Indian number system is exclusively a base 10 system, in contrast to the Babylonian (modern-day Iraq) system, which was base 60; for example, the calculation of time in seconds, minutes and hours. By the middle of the 2nd millennium BC, the Babylonian mathematics had a sophisticated sexagesimal positional numeral system (based on 60, not 10). Despite the invention of zero as a placeholder, the Babylonians never quite discovered zero as a number.

The lack of a positional value (or zero) was indicated by a space between sexagesimal numerals.They added the “space” symbol for the zero in about 400 BC. However, this effort to save the first place-value number system did not overcome its other problems and the rise of Alexandria spelled the end of the Babylonian number system and its cuneiform (hieroglyphic like) numbers.

It is remarkable that the rise of a civilization as advanced as Alexandria also meant the end of a place-value number system in Europe for nearly 2,000 years. Neither Egypt nor Greece nor Rome had a place-value number system, and throughout medieval times Europe used the absolute value number system of Rome (Roman Numerals). This held back the development of mathematics in Europe and meant that before the period of Enlightenment of the 17th century, the great mathematical discoveries were made elsewhere in East Asia and in Central America.

The Mayans in Central America independently invented zero in the fourth century CE.Their priest-astronomers used a snail-shell-like symbol to fill gaps in the (almost) base-20 positional ‘long-count’ system they used to calculate their calendar. They were highly skilled mathematicians, astronomers, artists and architects. However, they failed to make other key discoveries and inventions that might have helped their culture survive. The Mayan culture collapsed mysteriously around 900 CE. Both the Babylonians and the Mayans found zero the symbol, yet missed zero the number. Although China independently invented place value, they didn’t make the leap to zero until it was introduced to them by a Buddhist astronomer from India in 718 CE.



Zero becomes a real number
The concept of zero as a number and not merely a symbol for separation is attributed to India where by the 9th century CE practical calculations were carried out using zero, which was treated like any other number, even in the case of division.
The story of zero is actually a story of two zeroes: zero as a symbol to represent nothing and zero as a number that can be used in calculations and has its own mathematical properties.
It has been commented that in India, the concept of nothing is important in its early religion and philosophy and so it was much more natural to have a symbol for it than for the Latin (Roman) and Greek systems. The rules for the use of zero were written down first by Brahmagupta, in his book “Brahmasphutha Siddhanta” (The Opening of the Universe) in the year 628 CE. Here Brahmagupta considers not only zero, but negative numbers, and the algebraic rules for the elementary operations of arithmetic with such numbers.
“The importance of the creation of the zero mark can never be exaggerated.This giving to airy nothing, not merely a local habitation and a name, a picture, a symbol, but helpful power, is the characteristic of the Hindu race from whence it sprang. It is like coining the Nirvana into dynamos. No single mathematical creation has been more potent for the general on-go of intelligence and power.” - G. B. Halsted 5
A very important distinction for the Indian symbol for zero, is that, unlike the Babylonian and Mayan zero, the Indian zero symbol came to be understood as meaning nothing.
As the Indian decimal zero and its new mathematics spread from the Arab world to Europe in the Middle Ages, words derived from sifr and zephyrus came to refer to calculation, as well as to privileged knowledge and secret codes. Records show that the ancient Greeks seemed unsure about the status of zero as a number.They asked themselves,“How can nothing be something?” This lead to philosophical and, by the Medieval period, religious arguments about the nature and existence of zero and the vacuum.
The word “zero” came via the French word zéro, and cipher came from the Arabic word safira which means “it was empty.” Also sifr, meaning “zero” or “nothing,” was the translation for the Sanskrit word sunya, which means void or empty.
The number zero was especially regarded with suspicion in Europe, so much so that the word cipher for zero became a word for secret code in modern usage. It is very likely a linguistic memory of the time when using decimal arithmetic was deemed evidence of dabbling in the occult, which was potentially punishable by the all-powerful Catholic Church with death
Glorification of the Decimal Number System
The Indian numerals and the positional number system were introduced to the Islamic civilization by Al-Khwarizmi, the founder of several branches and basic concepts of mathematics. Al-Khwarizmi's book on arithmetic synthesized Greek and Indian knowledge and also contained his own fundamental contribution to mathematics and science including an explanation of the use of zero. It was only centuries later, in the 12th century, that the Indian numeral system was introduced to the Western world through Latin translations of his arithmetic.
Michel de Montaigne, Mayor of Bordeaux (France) and one of the most learned men of his day, confessed in 1588 (prior to the widespread adoption of decimal arithmetic in Europe), that in spite of his great education and erudition, "I cannot yet cast account either with penne or counters." That is, he could not do basic arithmetic.6
Dantzig notes in regards to the discovery of the positional decimal arithmetic, "… it assumes the proportions of a world-event… without it no progress in arithmetic was possible."7
Pierre-Simon Laplace, the famous 19th century mathematician, explained: "The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged from India. The idea seems so simple nowadays that it's significance and profound importance is no longer appreciated. It's simplicity lies in the way it facilitated calculation and places arithmetic foremost amongst useful inventions. The importance of this invention is more readily appreciated when one considers that it was beyond the two greatest men of Antiquity, Archimedes and Apollonius." 8
Ifrah describes the significance of this discovery in these terms: "Now that we can stand back from the story, the birth of our modern number-system seems a colossal event in the history of humanity, as momentous as the mastery of fire, the development of agriculture, or the invention of writing, of the wheel, or of the steam engine." 9
Indian mathematicians used their revolutionary number system to advance human knowledge at great speed. The Sthananga Sutra, an Indian religious work from the second century AD, contains detailed operations that involve logarithms to the base 2. Modern texts credit the discovery of logarithms to the Scottish mathematician John Napier, who published his discovery in 1614. Indian knowledge of logarithms thus precedes Napier's discovery by more than 1,000 years.
Panini's Systematization of Sanskrit & The Binary Number System
Panini's precise systematization of the Sanskrit language in the 4th or 7th century BCE is widely considered as a forerunner of the Backus Normal Form (discovered by John Backus in 1959), which forms the basis of the current computer language. Panini is recognized as one of the foremost geniuses of ancient India and is credited with the systematization of Sanskrit as a language. Panini's work was so thorough that no one in the past 2,000 years has been able to improve on it. He codified every aspect of spoken communication, including pronunciation, tones and gestures. NASA scientist Rick Briggs, as part of his NASA research, showed that Sanskrit is the most perfectly suited, unambiguous, language for programming Artificial Intelligence.10
Gayatri Sanskrit
Jain mathematicians (6th-7th century BCE) have the distinction of being a bridge between the Vedic Period in mathematics to the so-called Classical Period. They are also credited with extricating mathematics from religious rituals. The Jains' fascination with large numbers directly led them to defining infinity into several types.
Pingala (300 to 200 BCE), a well-recognized Jain mathematician, although not strictly a mathematician but a musical theorist, is credited with first using the Binary numeral system in the form of short and long syllables, making it similar to Morse code. He and his contemporary Indian scholars used the Sanskrit word sunya to refer to zero or void. He is also credited with discovering the "Pascal triangle" and the binominal coefficient. Basic concepts of the Fibonacci numbers have also been described by Pingala.
Fibinacci Numbers
The Binary Number System Discovered in Europe 2,000 Years Later
Two thousand years later in 1679, the prominent mathematician Gottfried Wilhelm von Leibniz, prompted by such huge mistakes as Columbus finding the West Indies in the Americas when in fact he thought he was in Japan, decided to stop human error with a better numerical system. In the process he invented the binary number system which allowed the representation of all numbers with only ones and zeros.
A simple diagram illustrates this easily. Our habit is to think in tens, hundreds, thousands, etc. However, the number nine written in binary is 1001. The first column (from the right) counts how many ones, the second, how many twos, then how many fours, eights etc. Thus nine in binary is one eight, no fours, no twos and one one [1001].
Binary Numbers Example
This system provides the most efficient way of adding and subtracting numbers and is ideally suited for the computer, although von Leibniz never built the binary machine that he designed at that time. It wasn't until 1944 in the midst of World War II, that the world's first binary computer, Colossus, was developed in Bletchley Park, England utilizing the simple system of electrical currents being either off or on as representing zero or one. In this binary format millions of rapid calculations were made, allowing the Allies to crack the German coded messages with such skill that they often knew the contents of these messages even before Hitler did.
The Decimal Number System Spreads to Muslim Countries
Usage of the decimal number system spread to Muslim countries where scholars were amazed by it's usage and simplicity. By 776 AD the Arab empire was beginning to take shape. The Arabic world, in comparison to Europe, was much more accepting of the Indian system — in fact, the West owes it's knowledge of the scheme to Arab scholars. Arabian scholars were always prepared to give Indian scientists credit for their number system. An early Arabian work states that,
"We also inherited a treatise on calculation with numbers from the sciences of India, which Abu Djafar Mohammed Ibn Musa al-Charismi developed further. It is the most comprehensive, most practical, and requires the least effort to learn; it testifies for the thorough intellect of the Indians, their creative talent, their superior ability to discriminate and their inventiveness." 11
On the other hand, the Europeans response to the extraordinary cultural and scientific achievements of India during the British occupation of India, was to postulate the Aryan Invasion Theory — that India's wondrous heritage came from Europe. Although this theory remains a controversial issue, more recent archaeological, linguistic, genetic and other evidence has effectively shown that there is no substantiation for this Aryan Invasion Theory. The earliest known use of the Indian decimal number system in Europe is in a Sicilian coin of 1134; in Britain the first use is in 1490.
Around the middle of the tenth century, Al-Uqlidisi wrote Kitab al-fusul fi al-hisab al-Hindi, which is the earliest surviving book that presents the Indian system. In it Al-Uqlidisi argues that this system is of practical value: "Most arithmeticians are obliged to use it in their work: since it is easy and immediate, requires little memorization, provides quick answers, and demands little thought ... " 12
In the fourth part of this book Al-Uqlidisi showed how to modify the methods of calculating with Indian symbols, which had required a dust board, to methods which could be carried out with pen and paper. This requirement of a dust board had been an obstacle to the Indian system's acceptance. For example As-Suli, after praising the Indian system for it's great simplicity, wrote in the first half of the tenth century: "Official scribes nevertheless avoid using [the Indian system] because it requires equipment [like a dust board] and they consider that a system that requires nothing but the members of the body is more secure and more fitting to the dignity of a leader." Al-Uqlidisi's work is therefore important in attempting to remove one of the obstacles to acceptance of the Indian nine symbols. It is also historically important as it is the earliest known text offering a direct treatment of decimal fractions.
Another reference to the transmission of Indian numerals is found in the work of Al-Qifti's Chronology of the Scholars written around the end of the 12th century. This publication quotes much earlier sources.13
It was not simply that the Arabs took over the Indian number system. Rather different number systems were used simultaneously in the Arabic world over a long period of time. For example there were at least three different types of arithmetic used in Arab countries in the eleventh century:
1 - A system derived from counting on the fingers with the numerals written entirely in words—this finger-reckoning arithmetic was the system used by the business community
2 - The sexagesimal system with numerals denoted by letters of the Arabic alphabet
3 - The arithmetic of the Indian numerals and fractions with the decimal place-value system.
Decimal Numbers
Persian author Mohammed ibn Musa al-Khwarizmi wrote a book, often claimed to be the first Arabic text written including the rules of arithmetic for the decimal number system, called Kitab al Jabr wa'l-Muqabala (Rules of Restoring and Equating) dating from about 825 AD.14
Although the original Arabic text is lost, a twelfth century Latin translation, Algoritmi de numero Indorum (in English Al-Khwarizmi on the Hindu Art of Reckoning), gave rise to the word 'algorithm' deriving from his name in the title. Furthermore, from the Arabic title of the original book, Kitab al Jabr w'al-Muqabala, we derive our modern word 'algebra.' 15
"The imam and emir of the believers, al-Ma'mun, encouraged me to write a concise work on the calculations al-jabr and al-muqabala, confined to a pleasant and interesting art of calculation, which people constantly have need of for their inheritances, their wills, their judgements and their transactions, and in all the things they have to do together, notably, the measurement of land, the digging of canals, geometry and other things of that kind." 16
Al-Khwarizmi developed this numerical system further with quadratic equations, algebra, etc. — enabling science, mathematics and astronomy in Islamic countries to develop dramatically. However, on the other side of the Mediterranean, Christian Europe doggedly continued with the awkward Roman numerals for centuries.
The Pope & Fibonacci Try to Introduce the Indian Decimal Number System into Europe
It is astonishing how many years passed before the Indian numeral system finally gained full acceptance in the rest of the world. There are indications that it reached southern Europe perhaps as early as 500 CE, but with Europe mired in the Dark Ages, few paid any attention. The first surviving example of the Indian numerals in document form in Europe was, however, long before the time of al-Banna in the fourteenth century. The Indian numerals appear in the Codex Vigilanus copied by a monk in Spain in 976.17
Significantly, the main part of Europe was not ready at that time to accept new ideas of any kind. Acceptance was slow, even as late as the fifteenth century when European mathematics began it's rapid development, which continues today.
During this time counting tables were used by "bankers" in medieval Italian cities for exchanging currencies. If they cheated their table would be broken and this banker was then know as rukta or broken (banka-rukta), an early version of the modern word 'bankrupt.'
That the European monks depicted Indian numerals in a variety of orientations is clear evidence that they did not understand the usefulness of place-value number systems. Calculations in Europe were still made on calculation boards. Among the first uses of the Indian system in Europe was the introduction of Indian numerals for checker board calculations by Gerbert d'Aurillac, who became Pope Sylvester II in 999. When he encountered Indian numerals in Arabic manuscripts held in a Spanish monastery, he introduced round tokens with Indian numerals to his calculation board.
Pope Sylvester
However, this system encountered stiff resistance in part from accountants who did not want their craft rendered obsolete and to clerics who were aghast to hear that the Pope had traveled to Islamic lands to study this foreign method. Because of this Islamic connection it was widely rumored that he was a sorcerer, and that he had sold his soul to Lucifer during his travels. This accusation persisted until 1648, when papal authorities reopened Sylvester's tomb to make sure that his body had not been infested by Satanic forces.18
The early Christian world view was largely a product of Aristotelian conceptions, where the Earth was the center of the universe, set in motion by an "unmoved mover," or God. Because there was no place for a void in this cosmology it followed that the concept of zero and everything associated with it was a godless concept. Eastern philosophies however, rooted in ideas of eternal cycles of creation and destruction, had no such qualms.
Leonardo of Pisa, also known as Fibonacci, the young son of an Italian diplomat, who is now regarded as one of the greatest mathematicians of all time, discovered the "Arabic numerals" in the port of Bijaya, Algeria. The Indo-Arabic system was re-introduced to Europe by Fibonacci, in his 1202 CE book, Liber Abaci (Book of the Abacus or Book of Calculating), which was a showcase for the Indian numerals, with emphasis on it's usage by merchants.19
Although this work persuaded many European mathematicians of the day to use this "new" system, usage of the ten digit positional system remained limited for many years, in part because the scheme continued to be considered "diabolical," due to the mistaken impression that it originated in the Arab world, in spite of Fibonacci's clear descriptions of the "nine Indian figures" plus zero.20
Fibonacci
Decimal arithmetic began to be widely used by scientists beginning in the 1400s, and was employed, for instance, by Copernicus, Galileo, Kepler and Newton, but it was not universally used in European commerce until after the French Revolution in 1793.21
Nicolas Copernicus, said to be the founder of modern astronomy, in his great work De Revolutionibus, published not long before his death in 1543, presented his "heretical" idea that the earth rotated on it's axis and traveled around the sun once yearly. This went against the philosophical and religious beliefs that the Catholic Church and all of Europe had held during medieval times.22
Copernicus
Copernicus never knew the great stir his work caused, but two other renowned Italian scientists, Galileo Galilei and Giordano Bruno, wholeheartedly supported Copernicus' system and suffered greatly at the hands of the Church's inquisitors for daring to oppose the Church's views and stultifying authority.
Both were tortured extensively, Bruno for daring to go even beyond Copernicus to claim that space was boundless and that the sun and it's planets were but one of any number of similar systems. Bruno, after eight years in chains, was burned at the stake—his life a testimony to the drive for knowledge and truth that marked the incredible period of the Renaissance.
The old and frail Galileo was put in prison for the duration of his life. Nearly four hundred years later the Catholic Church grudgingly admitted that Galileo was right.
The usage of this streamlined decimal number system of counting was not easily accepted in the rest Christian dominated Europe either. Florence, Italy, banned the usage of this new number system in 1299 CE. Such attitudes forced the continued universal usage of the awkward and difficult Roman numerals.
However, use of the calculation board and of the abacus coexisted with the Indian number system for centuries. Because most people in medieval Europe were illiterate (in addition to superstitious) and the Indian calculation method required the writing down of numbers, the abacus remained the preferred tool in commerce and administration. Science, on the other hand, adopted the Indian place-value number system early.
Abacus
Despite many scholars finding calculating with Indian symbols helpful in their work, the business community continued to use their finger arithmetic throughout the tenth century. Abu'l-Wafa, who was himself an expert in the use of Indian numerals, nevertheless wrote a text on how to use finger-reckoning arithmetic since this was the system used by the business community and teaching material aimed at these people had to be written using the appropriate system.23
The parallel use of competing systems for calculation and measurement is not an unusual occurrence. The use of the Fahrenheit temperature scale by the public of the USA and the Celsius temperature scale by the scientists of the USA is another current example. Scientists like Copernicus, Brahe and Kepler understood the superiority of the Indian number system over the Roman numbers and used it for their detailed observations and calculations. Medieval publications demonstrate the use of the Indian method parallel to the use of the abacus and calculation boards during their time.
When James Cook in 1776 planned the voyage that brought him to Australia, the financial commitment was comparable to the commitment made by the USA and the USSR to get a man to the moon. Yet the Colonial Office prepared his budget with tokens on a checker board.
The use of the abacus or calculation board for administrative purposes continued in Europe until 1791, when the French National Assembly, which was set up through the French Revolution two years earlier, adopted the Indian calculation method for France and banned the use of the abacus from schools and government offices. Government offices in England continued to calculate taxes on calculation boards for another decade.
The Catholic Church had always regarded charging interest on loans as sinful but with the Reformation in the late Middle Ages, the Church became business friendly, dropping it's rejection of capitalism. With this new interest in capitalism and the necessity of calculating interest and compound interest, the old Roman numeral system failed badly and the new system was finally accepted. This also allowed European ships to sail afield once they were able to calculate their position consistently and easily.
Finally, the Copernican revolution shook European mathematics free from the shackles of Aristotelian cosmology. René Descartes in the 17th century invented his cartesian coordinate system of positive and negative numbers with zero at it's center. This combined algebra and geometry and led the way to calculus and a complete acceptance of the decimal number system in the western world. 24
Other Scientific Contributions of India
Subsequent phases of developments in mathematics are found, along with ritual practices, in Vedic texts and in the Puranas. Calculations for the precise building of ritual altars were important, for obvious reasons. Arithmetical principles such as addition, subtraction, multiplication, fractions, cubes, squares and roots were developed during these periods, they are referred to in the Narad Vishnu Purana (1000 BCE). Geometric principles are found in the Sulva Sutras, authored by Baudhayana (800 BCE) and Apasthamba (600 BCE).
In 510 CE, the Indian mathematician Aryabhata explicitly described schemes for various arithmetic operations, even including square roots and cube roots — schemes likely known in India earlier than this date. Aryabhata's actual algorithm for computing square roots is described in greater detail in a 628 CE manuscript by a faithful disciple named Bhaskara I. Additionally, Aryabhata gave a decimal value of pi = 3.1416. Ifrah further confirms that Aryabhata's works would have been impossible without the usage of zero and the place-value system.25
Aryabhata
One of India's greatest gifts to the world is in the field of mathematics. The adoption of zero and the decimal place-value system in India unbarred the gates of the mind to rapid progress in arithmetic and algebra.
India pioneered almost every field of mathematics, from the numeral system and arithmetical principles of addition, subtraction, multiplication and division, to the invention of zero and the notion of infinity, to the power and place value and decimal systems, geometry and many of the theorems traditionally attributed and named after the Greeks or other Europeans.
Infinity
Algebra, trigonometry and even significant parts of calculus, were all developed by Indians to a significant degree of finesse, long before any country or individual that the Europeans have credited.
This author has taken the liberty of directly quoting from some of the references given here, such as the quotations by some scholars or historians and, when necessary actual descriptions of the mathematical notations (rather than paraphrasing them). I am indebted to the original authors for their scholarly writings, without which justice could not have been done in narrating the contributions of Indians in Mathematics through history.


References Decimal Numbers NASA Article on Sanskrit & Knowledge RepresentationAl-Qifti-Chronology of the StarsReferences Decimal Numbers

Sanskrit & Artificial Intelligence — NASA article.#DECODING #HINDUISM

Sanskrit Artificial Intelligence

Sanskrit & Artificial Intelligence — NASA-by
Rick Briggs Roacs, NASA Ames Research Center, Moffet Field, California.

Abstract


NASA AstronautIn the past twenty years, much time, effort, and money has been expended on designing an unambiguous representation of natural languages to make them accessible to computer processing. These efforts have centered around creating schemata designed to parallel logical relations with relations expressed by the syntax and semantics of natural languages, which are clearly cumbersome and ambiguous in their function as vehicles for the transmission of logical data. Understandably, there is a widespread belief that natural languages are unsuitable for the transmission of many ideas that artificial languages can render with great precision and mathematical rigor.

But this dichotomy, which has served as a premise underlying much work in the areas of linguistics and artificial intelligence, is a false one. There is at least one language, Sanskrit, which for the duration of almost 1,000 years was a living spoken language with a considerable literature of its own. Besides works of literary value, there was a long philosophical and grammatical tradition that has continued to exist with undiminished vigor until the present century. Among the accomplishments of the grammarians can be reckoned a method for paraphrasing Sanskrit in a manner that is identical not only in essence but in form with current work in Artificial Intelligence. This article demonstrates that a natural language can serve as an artificial language also, and that much work in AI has been reinventing a wheel millenia old.

Sanskrit - XML Generator

First, a typical Knowledge Representation Scheme (using Semantic Nets) will be laid out, followed by an outline of the method used by the ancient Indian Grammarians to analyze sentences unambiguously. Finally, the clear parallelism between the two will be demonstrated, and the theoretical implications of this equivalence will be given.


Semantic Nets
For the sake of comparison, a brief overview of semantic nets will be given, and examples will be included that will be compared to the Indian approach. After early attempts at machine translation (which were based to a large extent on simple dictionary look-up) failed in their effort to teach a computer to understand natural language, work in AI turned to Knowledge Representation.

Since translation is not simply a map from lexical item to lexical item, and since ambiguity is inherent in a large number of utterances, some means is required to encode what the actual meaning of a sentence is. Clearly, there must be a representation of meaning independent of words used. Another problem is the interference of syntax. In some sentences (for example active/passive) syntax is, for all intents and purposes, independent of meaning. Here one would like to eliminate considerations of syntax. In other sentences the syntax contributes to the meaning and here one wishes to extract it.

Sanskrit Semantic Net System

I will consider a "prototypical" semantic net system similar to that of Lindsay, Norman, and Rumelhart in the hopes that it is fairly representative of basic semantic net theory. Taking a simple example first, one would represent "John gave the ball to Mary" as in Figure 1. Here five nodes connected by four labeled arcs capture the entire meaning of the sentence. This information can be stored as a series of "triples":

give, agent, John

give, object, ball

give, recipient, Mary

give, time, past.

Note that grammatical information has been transformed into an arc and a node (past tense). A more complicated example will illustrate embedded sentences and changes of state:

John Mary

book past

Figure 1.

"John told Mary that the train moved out of the station at 3 o'clock."

As shown in Figure 2, there was a change in state in which the train moved to some unspecified location from the station. It went to the former at 3:00 and from the latter at 3:O0. Now one can routinely convert the net to triples as before.

The verb is given central significance in this scheme and is considered the focus and distinguishing aspect of the sentence. However, there are other sentence types which differ fundamentally from the above examples. Figure 3 illustrates a sentence that is one of "state" rather than of "event ." Other nets could represent statements of time, location or more complicated structures.

A verb, say, "give," has been taken as primitive, but what is the meaning of "give" itself? Is it only definable in terms of the structure it generates? Clearly two verbs can generate the same structure. One can take a set-theoretic approach and a particular give as an element of "giving events" itself a subset of ALL-EVENTS. An example of this approach is given in Figure 4 ("John, a programmer living at Maple St., gives a book to Mary, who is a lawyer"). If one were to "read" this semantic net, one would have a very long text of awkward English: "There is a John" who is an element of the "Persons" set and who is the person who lives at ADRI, where ADRI is a subset of ADDRESS-EVENTS, itself a subset of 'ALL EVENTS', and has location '37 Maple St.', an element of Addresses; and who is a "worker" of 'occupation 1'. . .etc."

The degree to which a semantic net (or any unambiguous, nonsyntactic representation) is cumbersome and odd-sounding in a natural language is the degree to which that language is "natural" and deviates from the precise or "artificial." As we shall see, there was a language spoken among an ancient scientific community that has a deviation of zero.

The hierarchical structure of the above net and the explicit descriptions of set-relations are essential to really capture the meaning of the sentence and to facilitate inference. It is believed by most in the AI and general linguistic community that natural languages do not make such seemingly trivial hierarchies explicit. Below is a description of a natural language, Shastric Sanskrit, where for the past millenia successful attempts have been made to encode such information.

Shastric Sanskrit

The sentence:

(1) "Caitra goes to the village." (graamam gacchati caitra)

receives in the analysis given by an eighteenth-century Sanskrit Grammarian from Maharashtra, India, the following paraphrase:

(2) "There is an activity which leads to a connection-activity which has as Agent no one other than Caitra, specified by singularity, [which] is taking place in the present and which has as Object something not different from 'village'."

The author, Nagesha, is one of a group of three or four prominent theoreticians who stand at the end of a long tradition of investigation. Its beginnings date to the middle of the first millennium B.C. when the morphology and phonological structure of the language, as well as the framework for its syntactic description were codified by Panini. His successors elucidated the brief, algebraic formulations that he had used as grammatical rules and where possible tried to improve upon them. A great deal of fervent grammatical research took place between the fourth century B.C and the fourth century A.D. and culminated in the seminal work, the Vaiakyapadiya by Bhartrhari. Little was done subsequently to advance the study of syntax, until the so-called "New Grammarian" school appeared in the early part of the sixteenth century with the publication of Bhattoji Dikshita's Vaiyakarana-bhusanasara and its commentary by his relative Kaundabhatta, who worked from Benares. Nagesha (1730-1810) was responsible for a major work, the Vaiyakaranasiddhantamanjusa, or Treasury of dejinitive statements of grammarians, which was condensed later into the earlier described work. These books have not yet been translated.

The reasoning of these authors is couched in a style of language that had been developed especially to formulate logical relations with scientific precision. It is a terse, very condensed form of Sanskrit, which paradoxically at times becomes so abstruse that a commentary is necessary to clarify it.

One of the main differences between the Indian approach to language analysis and that of most of the current linguistic theories is that the analysis of the sentence was not based on a noun-phrase model with its attending binary parsing technique but instead on a conception that viewed the sentence as springing from the semantic message that the speaker wished to convey. In its origins, sentence description was phrased in terms of a generative model: From a number of primitive syntactic categories (verbal action, agents, object, etc.) the structure of the sentence was derived so that every word of a sentence could be referred back to the syntactic input categories. Secondarily and at a later period in history, the model was reversed to establish a method for analytical descriptions. In the analysis of the Indian grammarians, every sentence expresses an action that is conveyed both by the verb and by a set of "auxiliaries." The verbal action (Icriyu- "action" or sadhyu-"that which is to be accomplished,") is represented by the verbal root of the verb form; the "auxiliary activities" by the nominals (nouns, adjectives, indeclinables) and their case endings (one of six).

The meaning of the verb is said to be both vyapara (action, activity, cause), and phulu (fruit, result, effect). Syntactically, its meaning is invariably linked with the meaning of the verb "to do". Therefore, in order to discover the meaning of any verb it is sufficient to answer the question: "What does he do?" The answer would yield a phrase in which the meaning of the direct object corresponds to the verbal meaning. For example, "he goes" would yield the paraphrase: "He performs an act of going"; "he drinks": "he performs an act of drinking," etc. This procedure allows us to rephrase the sentence in terms of the verb "to do" or one of its synonyms, and an object formed from the verbal root which expresses the verbal action as an action noun. It still leaves us with a verb form ("he does," "he performs"), which contains unanalyzed semantic information This information in Sanskrit is indicated by the fact that there is an agent who is engaged in an act of going, or drinking, and that the action is taking place in the present time.

Rather that allow the agent to relate to the syntax in this complex, unsystematic fashion, the agent is viewed as a one-time representative, or instantiation of a larger category of "Agency," which is operative in Sanskrit sentences. In turn, "Agency" is a member of a larger class of "auxiliary activities," which will be discussed presently. Thus Caitra is some Caitral or instance of Caitras, and agency is hierarchically related to the auxiliary activities. The fact that in this specific instance the agent is a third person-singular is solved as follows: The number category (singular, dual, or plural) is regarded as a quality of the Agent and the person category (first, second, or third) as a grammatical category to be retrieved from a search list, where its place is determined by the singularity of the agent.

The next step in the process of isolating the verbal meaning is to rephrase the description in such a way that the agent and number categories appear as qualities of the verbal action. This procedure leaves us with an accurate, but quite abstract formulation of the scntcnce: (3) "Caitra is going" (gacchati caitra) - "An act of going is taking place in the present of which the agent is no one other than Caitra qualified by singularity." (atraikatvaavacchinnacaitraabinnakartrko vartamaanakaa- liko gamanaanukuulo vyaapaarah:) (Double vowels indicate length.)

If the sentence contains, besides an agent, a direct object, an indirect object and/or other nominals that are dependent on the principal action of the verb, then in the Indian system these nominals are in turn viewed as representations of actions that contribute to the complete meaning of the sentence. However, it is not sufficient to state, for instance, that a word with a dative case represents the "recipient" of the verbal action, for the relation between the recipient and the verbal action itself requires more exact specification if we are to center the sentence description around the notion of the verbal action. To that end, the action described by the sentence is not regarded as an indivisible unit, but one that allows further subdivisions. Hence a sentence such as: (4) "John gave the ball to Mary" involves the verb Yo give," which is viewed as a verbal action composed of a number of auxiliary activities. Among these would be John's holding the ball in his hand, the movement of the hand holding the ball from John as a starting point toward Mary's hand as the goal, the seizing of the ball by Mary's hand, etc. It is a fundamental notion that actions themselves cannot be perceived, but the result of the action is observable, viz. the movement of the hand. In this instance we can infer that at least two actions have taken place:

(a) An act of movement starting from the direction of John and taking place in the direction of Mary's hand. Its Agent is "the ball" and its result is a union with Mary's hand.

(b) An act of receiving, which consists of an act of grasping whose agent is Mary's hand.

It is obvious that the act of receiving can be interpreted as an action involving a union with Mary's hand, an enveloping of the ball by Mary's hand, etc., so that in theory it might be difficult to decide where to stop this process of splitting meanings, or what the semantic primitives are. That the Indians were aware of the problem is evident from the following passage: "The name 'action' cannot be applied to the solitary point reached by extreme subdivision."

The set of actions described in (a) and (b) can be viewed as actions that contribute to the meaning of the total sentence, vix. the fact that the ball is transferred from John to Mary. In this sense they are "auxiliary actions" (Sanskrit kuruku-literally "that which brings about") that may be isolated as complete actions in their own right for possible further subdivision, but in this particular context are subordinate to the total action of "giving." These "auxiliary activities" when they become thus subordinated to the main sentence meaning, are represented by case endings affixed to nominals corresponding to the agents of the original auxiliary activity. The Sanskrit language has seven case endings (excluding the vocative), and six of these are definable representations of specific "auxiliary activities." The seventh, the genitive, represents a set of auxiliary activities that are not defined by the other six. The auxiliary actions are listed as a group of six: Agent, Object, Instrument, Recipient, Point of Departure, Locality. They are the semantic correspondents of the syntactic case endings: nominative, accusative, instrumental, dative, ablative and locative, but these are not in exact equivalence since the same syntactic structure can represent different semantic messages, as will be discussed below. There is a good deal of overlap between the karakas and the case endings, and a few of them, such as Point of Departure, also are used for syntactic information, in this case "because of". In many instances the relation is best characterized as that of the allo-eme variety.

To illustrate the operation of this model of description, a sentence involving an act of cooking rice is often quoted: (5) "Out of friendship, Maitra cooks rice for Devadatta in a pot, over a fire."

Here the total process of cooking is rendered by the verb form "cooks" as well as a number of auxiliary actions:

1. An Agent represented by the person Maitra

2. An Object by the "rice"

3. An Instrument by the "fire"

4. A Recipient by the person Devadatta

5. A Point of Departure (which includes the causal relationship) by the "friendship" (which is between Maitra and Devadatta)

6. The Locality by the "pot"

So the total meaning of the sentence is not complete without the intercession of six auxiliary actions. The action itself can be inferred from a change of the condition of the grains of rice, which started out being hard and ended up being soft.

Again, it would be possible to atomize the meaning expressed by the phrase: "to cook rice": It is an operation that is not a unitary "process", but a combination of processes, such as "to place a pot on the fire, to add fuel to the fire, to fan", etc. These processes, moreover, are not taking place in the abstract, but they are tied to, or "resting on" agencies that are associated with the processes. The word used for "tied to" is a form of the verbal root a-sri, which means to lie on, have recourse to, be situated on." Hence it is possible and usually necessary to paraphrase a sentence such as "he gives" as: "an act of giving residing in him." Hence the paraphrase of sentence (5) will be: (6) "There is an activity conducive to a softening which is a change residing in something not different from rice, and which takes place in the present, and resides in an agent not different from Maitra, who is specified by singularity and has a Recipient not different from Devadatta, an Instrument not different from.. .," etc.

It should be pointed out that these Sanskrit Grammatical Scientists actually wrote and talked this way. The domain for this type of language was the equivalent of today's technical journals. In their ancient journals and in verbal communication with each other they used this specific, unambiguous form of Sanskrit in a remarkably concise way.

Besides the verbal root, all verbs have certain suffixes that express the tense and/or mode, the person (s) engaged in the "action" and the number of persons or items so engaged. For example, the use of passive voice would necessitate using an Agent with an instrumental suffix, whereas the nonpassive voice implies that the agent of the sentence, if represented by a noun or pronoun, will be marked by a nominative singular suffix.

Word order in Sanskrit has usually no more than stylistic significance, and the Sanskrit theoreticians paid no more than scant attention to it. The language is then very suited to an approach that eliminates syntax and produces basically a list of semantic messages associated with the karakas.

An example of the operation of this model on an intransitive sentence is the following:

(7) Because of the wind, a leaf falls from a tree to the ground."

Here the wind is instrumental in bringing about an operation that results in a leaf being disunited from a tree and being united with the ground. By virtue of functioning as instrument of the operation, the term "wind" qualifies as a representative of the auxiliary activity "Instrument"; by virtue of functioning as the place from which the operation commences, the "tree" qualifies to be called "The Point of Departure"; by virtue of the fact that it is the place where the leaf ends up, the "ground" receives the designation "Locality". In the example, the word "leaf" serves only to further specify the agent that is already specified by the nonpassive verb in the form of a personal suffix. In the language it is rendered as a nominative case suffix. In passive sentences other statements have to be made. One may argue that the above phrase does not differ in meaning from "The wind blows a leaf from the tree," in which the "wind" appears in the Agent slot, the "leaf" in the Object slot. The truth is that this phrase is transitive, whereas the earlier one is intransitive. "Transitivity" can be viewed as an additional feature added to the verb. In Sanskrit this process is often accomplished by a suffix, the causative suffix, which when added to the verbal root would change the meaning as follows: "The wind causes the leaf to fall from the tree," and since English has the word "blows" as the equivalent of "causes to fall" in the case of an Instrument "wind," the relation is not quite transparent. Therefore, the analysis of the sentence presented earlier, in spite of its manifest awkwardness, enabled the Indian theoreticians to introduce a clarity into their speculations on language that was theretofore un- available. Structures that appeared radically different at first sight become transparent transforms of a basic set of elementary semantic categories.

It is by no means the case that these analyses have been exhausted, or that their potential has been exploited to the full. On the contrary, it would seem that detailed analyses of sentences and discourse units had just received a great impetus from Nagesha, when history intervened: The British conquered India and brought with them new and apparently effective means for studying and analyzing languages. The subsequent introduction of Western methods of language analysis, including such areas of research as historical and structural linguistics, and lately generative linguistics, has for a long time acted as an impediment to further research along the traditional ways. Lately, however, serious and responsible research into Indian semantics has been resumed, especially at the University of Poona, India. The surprising equivalence of the Indian analysis to the techniques used in applications of Artificial Intelligence will be discussed in the next section.

Equivalence


A comparison of the theories discussed in the first section with the Indian theories of sentence analysis in the second section shows at once a few striking similarities. Both theories take extreme care to define minute details with which a language describes the relations between events in the natural world. In both instances, the analysis itself is a map of the relations between events in the universe described. In the case of the computer-oriented analysis, this mapping is a necessary prerequisite for making the speaker's natural language digestible for the artificial processor; in the case of Sanskrit, the motivation is more elusive and probably has to do with an age-old Indo-Aryan preoccupation to discover the nature of the reality behind the the impressions we human beings receive through the operation of our sense organs. Be it as it may, it is a matter of surprise to discover that the outcome of both trends of thinking-so removed in time, space, and culture-have arrived at a representation of linguistic events that is not only theoretically equivalent but close in form as well. The one superficial difference is that the Indian tradition was on the whole, unfamiliar with the facility of diagrammatic representation, and attempted instead to formulate all abstract notions in grammatical sentences. In the following paragraphs a number of the parallellisms of the two analyses will be pointed out to illustrate the equivalence of the two systems.

Consider the sentence: "John is going." The Sanskrit paraphrase would be

"An Act of going is taking place in which the Agent is 'John' specified by singularity and masculinity."

If we now turn to the analysis in semantic nets, the event portrayed by a set of triples is the following:

1. "going events, instance, go (this specific going event)"

2. "go, agent, John"

3. "go, time, present."

The first equivalence to be observed is that the basic framework for inference is the same. John must be a semantic primitive, or it must have a dictionary entry, or it must be further represented (i.e. "John, number, 1" etc.) if further processing requires more detail (e.g. "HOW many people are going?"). Similarly, in the Indian analysis, the detail required in one case is not necessarily required in another case, although it can be produced on demand (if needed). The point to be made is that in both systems, an extensive degree of specification is crucial in understanding the real meaning of the sentence to the extent that it will allow inferences to be made about the facts not explicitly stated in the sentence

Sanskrit Semantic Net System

The basic crux of the equivalence can be illustrated by a careful look at sentence (5) noted in Part II.

"Out of friendship, Maitra cooks rice for Devadatta in a pot over a fire "

The semantic net is supplied in Figure 5. The triples corresponding to the net are:

cause, event, friendship

friendship, objectl, Devadatta

friendship, object2, Maitra

cause, result cook

cook, agent, Maitra

cook, recipient, Devadatta

cook, instrument, fire

cook, object, rice

cook, on-lot, pot.

The sentence in the Indian analysis is rendered as follows:

The Agent is represented by Maitra, the Object by "rice," the Instrument by "fire," the Recipient by "Devadatta," the Point of Departure (or cause) by "friendship" (between Maitra and Devadatta), the Locality by "pot."

Since all of these syntactic structures represent actions auxiliary to the action "cook," let us write %ook" uext to each karakn and its sentence representat(ion:

cook, agent, Maitra

cook, object, rice

cook, instrument, fire

cook, recipient, Devadatta

cook, because-of, friendship

friendship, Maitra, Devadatta

cook, locality, pot.

The comparison of the analyses shows that the Sanskrit sentence when rendered into triples matches the analysis arrived at through the application of computer processing. That is surprising, because the form of the Sanskrit sentence is radically different from that of the English. For comparison, the Sanskrit sentence is given here: Maitrah: sauhardyat Devadattaya odanam ghate agnina pacati.

Here the stem forms of the nouns are: Muitra-sauhardya- "friendship," Devadatta -, odana- "gruel," ghatu- "pot," agni- "fire' and the verb stem is paca- "cook". The deviations of the stem forms occuring at the end of each word represent the change dictated by the word's semantic and syntactic position. It should also be noted that the Indian analysis calls for the specification of even a greater amount of grammatical and semantic detail: Maitra, Devadatta, the pot, and fire would all be said to be qualified by "singularity" and "masculinity" and the act of cooking can optionally be expanded into a number of successive perceivable activities. Also note that the phrase "over a fire" on the face of it sounds like a locative of the same form as "in a pot." However, the context indicates that the prepositional phrase describes the instrument through which the heating of the rice takes place and, therefore, is best regarded as an instrument semantically. cause

Of course, many versions of semantic nets have been proposed, some of which match the Indian system better than others do in terms of specific concepts and structure. The important point is that the same ideas are present in both traditions and that in the case of many proposed semantic net systems it is the Indian analysis which is more specific.

A third important similarity between the two treatments of the sentence is its focal point which in both cases is the verb. The Sanskrit here is more specific by rendering the activity as a "going-event", rather than "ongoing." This procedure introduces a new necessary level of abstraction, for in order to keep the analysis properly structured, the focal point ought to be phrased: "there is an event taking place which is one of cooking," rather than "there is cooking taking place", in order for the computer to distinguish between the levels of unspecified "doing" (vyapara) and the result of the doing (phala).

A further similarity between the two systems is the striving for unambiguity. Both Indian and AI schools en-code in a very clear, often apparently redundant way, in order to make the analysis accessible to inference. Thus, by using the distinction of phala and vyapara, individual processes are separated into components which in term are decomposable. For example, "to cook rice" was broken down as "placing a pot on the fire, adding fuel, fanning, etc." Cooking rice also implies a change of state, realized by the phala, which is the heated softened rice. Such specifications are necessary to make logical pathways, which otherwise would remain unclear. For example, take the following sentence:Rice Cooking

"Maitra cooked rice for Devadatta who burned his mouth while eating it."

The semantic nets used earlier do not give any information about the logical connection between the two clauses. In order to fully understand the sentence, one has to be able to make the inference that the cooking process involves the process of "heating" and the process of "making palatable." The Sanskrit grammarians bridged the logical gap by the employment of the phalu/ vyapara distinction. Semantic nets could accomplish the same in a variety of ways:

1. by mapping "cooking" as a change of state, which would involve an excessive amount of detail with too much compulsory inference;

2. by representing the whole statement as a cause (event-result), or

3. by including dictionary information about cooking. A further comparison between the Indian system and the theory of semantic nets points to another similarity: The passive and the active transforms of the same sentence are given the same analysis in both systems. In the Indian system the notion of the "intention of the speaker" (tatparya, vivaksa) is adduced as a cause for distinguishing the two transforms semantically. The passive construction is said to emphasize the object, the nonpassive emphasizes the agent. But the explicit triples are not different. This observation indicates that both systems extract the meaning from the syntax.

Finally, a point worth noting is the Indian analysis of the intransitive phrase (7) describing the leaf falling from the tree. The semantic net analysis resembles the Sanskrit analysis remarkably, but the latter has an interesting flavor. Instead of a change from one location to another, as the semantic net analysis prescribes, the Indian system views the process as a uniting and disuniting of an agent. This process is equivalent to the concept of addition to and deletion from sets. A leaf falling to the ground can be viewed as a leaf disuniting from the set of leaves still attached to the tree followed by a uniting with (addition to) the set of leaves already on the ground. This theory is very useful and necessary to formulate changes or statements of state, such as "The hill is in the valley."

In the Indian system, inference is very complete indeed. There is the notion that in an event of "moving", there is, at each instant, a disunion with a preceding point (the source, the initial state), and a union with the following point, toward the destination, the final state. This calculus-like concept fascillitates inference. If it is stated that a process occurred, then a language processor could answer queries about the state of the world at any point during the execution of the process.

As has been shown, the main point in which the two lines of thought have converged is that the decomposition of each prose sentence into karalca-representations of action and focal verbal-action, yields the same set of triples as those which result from the decomposition of a semantic net into nodes, arcs, and labels. It is interesting to speculate as to why the Indians found it worthwhile to pursue studies into unambiguous coding of natural language into semantic elements. It is tempting to think of them as computer scientists without the hardware, but a possible explanation is that a search for clear, unambigous understanding is inherent in the human being.

Let us not forget that among the great accomplishments of the Indian thinkers were the invention of zero, and of the binary number system a thousand years before the West re-invented them.

Zero Mathematical SymbolBinary Number System

Their analysis of language casts doubt on the humanistic distinction between natural and artificial intelligence, and may throw light on how research in AI may finally solve the natural language understanding and machine translation problems.

References
Bhatta, Nagesha (1963) Vaiyakarana-Siddhanta-Laghu-Manjusa, Benares (Chowkhamba Sanskrit Series Office).

Nilsson, Nils J. Principles of Artificial Intelligence. Palo Alto: Tioga Publishing Co

Bhatta, Nagesha (1974) Parama-Lalu-Manjusa Edited by Pandit Alakhadeva Sharma, Benares (Chowkhambha Sanskrit Series Office).

Rumelhart, D E. & D A. Norman (1973) Active Semantic Networks as a model of human memory. IJCAI.

Wang, William S-Y (1967) "Final Administrative Report to the National Science Foundation." Project for Machine Translation. University of California, Berkeley. (A biblzographical summary of work done in Berkeley on a program to translate Chinese.)

[THE AI MAGAZINE Spring, 1985 #39]