How old are our mantras?

The Michael Wood documentary, The Story of India, which was telecast in six parts on PBS mentioned something interesting in the very first episode. Wood talked about the Out of Africa theory – the migration of humans 70,000 years back, from Africa along the shores of Arabian Sea into South India – and mentioned that all non-Africans in the world are descendents of these Indians. Nothing new in that.

Going in search of clues left by those ancient migrants in South India, he arrived at the house of a Kerala brahmin who is teaching his son mantras the way it has been done for millenia. Wood then shows the 2006 athirathram – a 12 day vedic ceremony – and mentions that certain sounds recited in this ceremony takes years to learn but have no meaning. When brahmins were asked for meaning, they did not know. They simply knew that it was handed down.
Since man is a speaking animal, we have always assumed that any word man says is in language, but some of those mantras are not in any known language. Hence these sounds, which are still recited today, are considered to have evolved before human speech.
Of Birds and Humans
Frits Staal of UC Berkeley  thought that the claim that mantras are older than language was “preposterous.” In 1975 he helped finance an athirathram, which had not been conducted since 1956 due to financial constraints. Analyzing the sounds he came to the conclusion that mantras could belong to a pre-language era since:

  • Mantras are language independent: Anything in language can be translated whereas mantras remain the same in all languages.
  • Mantras, even though they seem to be in a language like Sanskrit, are not used for their meaning.
  • Mantras follow patterns, like refrain, which is not seen in language.

The clincher for the pre-language theory came when the sound patterns were analyzed to find the nearest equivalent in nature. The technique followed was like this: He took a mantra like Jaimintya Gramageyagana (45.2.1) which goes:

vo no ha bu / idam idam pura ha bu / pra va pra
vas ia ia ha yi / nina ninava tarn u vo ha bu / stiisa vi
sakhtaia Ya ha vi / dramutalyayi / o vi la /

It was split into patterns like AB / CB / DE/.. where A = vo no and B = ha bu. Comparing it to bird songs, it was found that the patterns were similar and such patterns were not found any where else.
As a side effect, by comparing the patterns of mantras and certain birds, it is possible to find which birds influenced the mantras. There is research which found patterns in the composition of Igor Stravinsky and a bird usually found in the region where he worked. Thus some of the mantra sounds were found to be inspired by the songs of Blyth’s Reed Warbler and Whitethroat – two birds which migrate to India.
There are examples of bird-human interaction in Vedas and Upanishads. Some vedic chools have been named after birds — like kausika after the owl or taittiriya after the partridge. D. D. Kosambi believed that Vedic clans were totemic. Then there is the story of Satyakama Jabala in Chandogya Upanishad who:
Text not available
Critiques
Having established this similarity between bird song and mantra, the theory then takes off with a life of its own. There are vedic rituals for making rain and curing illness and similarly birds sing for building nests or attracting females; there are rituals and bird songs for various occasions. Then it was also found that bird sing – believe it or not – just for pleasure. So Staal extends the theory to say that, similar to skiing, dancing and music, mantras and rituals too are done for pleasure.
Between Staal’s athirathram in 1975 and Wood’s in 2006, one was held in 1990 near Thrissur which I attended  for a day. This athirathram, which was extensively covered in Malayalam newspapers, was highly respectful and the words I heard were not “playful” or “pleasurable.” I can understand singing for pleasure, but am yet to meet a priest who said, “it’s a weekend and raining outside, let’s do a ganapati homam for pleasure.”
Prof. Staal thinks that not just the sounds, but rituals too are meaningless. But Wood writes that mantras, “work on emotions, the physiology, and the nervous system.” According to Wood, these rituals are a away of achieving heightened mental and physical state. So I am not sure if this research is of the Ganesha phallus quality. If you have seen any paper or book by anyone else, please leave a comment.
Postscript: Kosambi’s concept that Vedic clans were named after animals was criticized inThe Early Brahmanical System of Gotra and Pravara (Purusottama Pandita, John Brough). They wrote that it is equivalent to saying an Englishman with the surname Fox belongs to a totemic clan of that animal.  Instead they suggest that the bird name could have come from the clan name.

Reference:
Michael Wood has a companion book to the program. More details can be found in Staal’s paper, Mantras and Bird Songs, in which one quoted sentence reads: “there are mechanisms in existence which reinforce economical perfection in motor skills independently of the attainment of the ultimate biological goal in whose pursuit the learned movement is developed.” Staal’s book on this topic is available in limited preview mode in Google Books.

[serialposts]

Layoff Patterns

In Saudi Arabia

In a move that may affect hundreds of expatriates, including Indians, Saudi Arabia has asked all companies in the kingdom to fire foreigners first, if they have to layoff staff. “Labour offices are instructing companies to start with foreigners first, if they have to sack staff,” the ‘Saudi Gazette’ quoted Muhammad Al-Hamdan, head of the labour office in the eastern province, as saying. [Sack expats first, then locals: Saudi govt to cos- The Economic Times]

In United States

A perennially contentious issue, the H-1B visa has drawn fire in recent weeks as layoffs have multiplied. Sen. Charles Grassley, R-Iowa, told Microsoft it should lay off guest workers before “similarly qualified American employees.” Grassley has co-sponsored legislation to give priority in hiring to American workers.[Layoffs mean more than lost wages for H-1B visa holders – San Jose Mercury News]

Battle of the Ten Kings

The Dasharajnya War or “war of 10 kings” was a turning point in the history of India because it firmly re-established the dominance of the Puru-Bharata Dynasty over smaller royal dynasties and tribal chieftans over the Sapta-Sindhu region going west towards present-day Afghanistan/Persia and east towards Uttar Pradesh. This Puru-Bharata Dynasty provided the continuity of leadership which is documented in the ancient scriptures of Sanathana Dharma (Hinduism) — particularly the Rigveda. The fact that this great story, which I believe must be raised to the standard of ‘epic’ in all fairness, is relatively unknown and forgotten is surprising and raises questions. When did this war occur? Where did this all happen? Why is it important and why should it be raised to the level of India’s two existing epics, namely the Ramayana and the Mahabharata?[Hindu Council UK (email from Rajeev Srinivasan)]


Niraj Mohanka
has a long article on the Battle of the Ten Kings and dates it to 2900 BCE. One line in the article — the gifts given by Sudas to his priest Vasishta (2 chariots, 4 horses with gold trappings) — will make you wonder if there were horses at that time? Didn’t Aryans bring horses to India.? To find answers it is worth reading The Horse and the Aryan Debate by Michel Danino along with this.

[serialposts]

The Kerala School and Lord of Guruvayoor

All Malayalees know Melpathur Narayana Bhattithiri (1559-1632 ) and his famous composition — Narayaneeyam — still sung in Guruvayoor temple. The immediate story that comes to mind is his tiff with his contemporary Poonthanam, whose judge turned out to be Guruvayoorappan
While Melpathur was composing Narayaneeyam in Sanskrit, Poonthanam was writing Jnanapana in Malayalam. This was a time when Malayalam was considered inferior to Sanskrit. When Poonthanam went to show his poem to Melpathur, he refused to see it; treating him like a groundling, Melpathur asked Poonthanam to learn Sanskrit.
The next day, Melpathur came to sing ten slokas of Narayaneeyam before Guruvayoorappan and he met a boy who found many mistakes in his composition. The boy vanished and a celestial voice announced, “Poonthanam’s bhakthi (devotion) is more pleasing to me than Melpathur’s vibhakthi (learning or knowledge in Sanskrit grammar)”.
So goes the legend.
Is there any truth to this story or is it something which which was written to show that Malayalam was as good as Sanskrit? Would a Sanskrit scholar like Melpathur make mistakes in his composition.? What we know is two pieces of information about Melpathur from which we will have to deduce information.
While Narayaneeyam is Melpathur’s most famous composition, he also wrote sreepaada saptati in praise of Bhagavathi, Manameyodayam on Mimamsa, and Kriyakramam on nambudiri rituals. Less known is the fact that Melpathur was connected to the Kerala school of mathematics. Melpathur was the student of Achyuta Pisharati (c. 1550-1621) who was the student of Jyestadeva, the author of yuktibhasha. Melpathur is not know for astronomical models or mathematical proofs but, according to Wikipedia, for Prkriya-sarvawom, which sets forth an axiomatic system elaborating on the classical system of Panini. This is believed to be written in sixty days[1].

Kerala School of Mathematics(teachers and students)

So would a person, who understood Panini, be sloppy with his work? Maybe. Sreedhara Menon, in his Survey of Kerala History, writes about Revathi Pattathanam, an annual assembly of scholars held in Calicut. Those who displayed exceptional knowledge in debates were awarded the title Bhatta. Melpathur was denied the Bhatta title six times before he won it eventually[1].
There is little information about Poonthanam’s later life, but much more about Melpathur and his royal patrons. But we don’t know anything Melpathur’s first drafts of Narayaneeyam and so it is hard to pin down the narrative historically.
Though Poonthanam’s Jnanappana too is still sung in houses in Kerala, the title of father of Malayalam goes to Thunchatthu Ezhutachan — a contemporary of Poonthanam and Melpathur — who translated Ramayana, and Mahabharata and standardized the Malayalam alphabet [2].
References:
[1] A Sreedhara Menon, A Survey of Kerala History
[2] S. Ramanath Aiyar, A Brief Sketch of Travancore, the Model State of India

A Conference on the Sindhu-Sarasvati Valley Civilization

A conference titled “International Conference on the Sindhu-Sarasvati Valley Civilization: A Reappraisal” is being held in Los Angeles on Feb. 21 and 22, 2009.

The aim of the conference is to discuss, reconsider and reconstruct a shared identity of the Sindhu (Indus) and Saraswati cultures, using archaeological and other scientific evidence as well as Vedic literature. For two days eminent archaeologists, linguists, anthropologists, historians, religious studies specialists and geneticists will present and discuss their findings on the salient issues of the Sindhu-Saraswati civilization and assess its contribution to Indian culture.  The conference hopes to inform the general educated public about the contribution of these early South Asian cultures to world civilization, and about the issues and problems of interpretation related to them.

The title of the conference itself will cause alarm among one section of historians who believe that Indus Civilization and Vedic culture have nothing in common. Now the ritual will start with the precision of the south west monsoon and words will start pouring – Hindutva, Gujarat, rich NRIs, minorities, oort cloud etc. This is despite the fact that some of the participants — Jonathan Mark Kenoyer (University of Wisconsin), Jim G. Shaffer (Case Western Reserve University), Carl C. Lamberg-Karlovsky (Harvard University), Edwin Bryant (Rutgers University), Maurizio Tosi (University of Bologna, Italy) and Nicholas Kazanas (Omilos Meleton Cultural Institute, Athens) —- are not even Hindus.

These conferences, whether ideology driven or not, are happening regularly in India and United States. Also the rivalry between the AIT camp and the opponents has resulted in a great debate which would have been one sided otherwise. For a historian who is not bound by dogma, these discourses are educational, since it brings out data, which would have remained buried.
Note: The conference is free for public.

Op-Ed in Mail Today: Kerala Astronomers and Eurocentrism


(This op-ed was published in Jan 25, 2009 edition of Mail Today/ PDF)
To commemorate the International Year of Astronomy in 2009, P Govinda Pillai, a Communist Party of India (Marxist) ideologue, in an article in the Malayalam newspaper Mathruboomi, examined the legacy of Copernicus, Galileo and Kepler. He also bought out an important topic – Eurocentrism in history writing – due to which we know about the work done on telescopes by Galileo, Hans Lippershey and Roger Bacon, but almost nothing by the Arab scientist al-Hassan.
Mr. Pillai stopped there. He wrote nothing about the contributions of mathematicians and astronomers from his state, Kerala, in developing the heliocentric model and calculating planetary orbits. It is not Mr. Pillai alone who is at fault. This apathy, this ignorance, this refusal to acknowledge Indian contributions — all point to a deep malaise in our historical studies. For perspective on this issue, we need to understand the contributions of Indian astronomers and decide if we should be like Confucians during the time of the Ming dynasty or 21st century Peruvian archaeologists.
The Kerala School of Mathematics
In 1832, a paper, “On the Hindu quadrature of a circle”, was read at the Royal Asiatic Society. This paper by Charles M. Whish of the East Indian Company Civil Service described eight mathematical series quoting from a text called Tantra Sangraham (1500 CE) which he had discovered in Kerala. These series were also mentioned in Yukti Dipika by Sankara Variyar and Yukti-Bhasa by Jyestadevan; both those authors had learned mathematics and astronomy from Kellalur Nilakanta Somayaji, the author of Tantra Sangraham. Some of those series were linked to Madhavan of Sangramagramam (1340-1425 CE). These mathematicians who lived between the 14th and 16th centuries formed the Kerala School of Mathematics and were proof that Indian mathematics did not vanish after Bhaskaracharya.
The importance of the Kerala school can be appreciated only by understanding the Copernican revolution. The contribution of Copernicus was two fold: first he improved
the mathematics behind the Ptolemaic system and second, changed the model from geocentric to heliocentric. The heliocentric model was proposed as early as the third century BCE by the Greek astronomer Aristarchus of Samos and so it is the math that made the difference.
In his Tantra Sangraham, Nilakanta revised the Indian planetary model for the interior planets, Mercury and Venus and for this he formulated equations to find the center of the planets better than both Islamic and European traditions. He also described the planetary motion in which Mercury, Venus, Mars, Jupiter and Saturn moved in eccentric orbits around the Sun, which in turn went around the Earth. Till Nilakanta, the Indian planetary theory had different rules for calculating  latitudes for interior and exterior planets. Nilakanta provided a unified rule. The heliocentric model of Copernicus did not alter the computational scheme for interior planets; it would have to wait till Kepler (who wrote horoscopes to supplement his income).
In their propensity to solve astronomical problems, mathematicians of the Kerala school developed concepts like Gregory’s series and the Leibniz’s series. The hallmark of earlier texts, like those of Madhava, were instructions and results without proofs or explanations. It is believed that the proofs and explanations were passed orally and hence rarely recorded. Yuktibhasha, the text written by Jyesthadeva, contain proofs of the theorems and the derivations of the rules, making it a complete text of mathematical analysis and possibly the first calculus text.

Lessons from Peru
Our education system, based on content from Western textbooks, have rarely questioned Western accomplishments. But Peruvians thought differently. When Peruvian archaeologists revisited the history written by the victors they discovered that the romantic tales woven by the Conquistadors were – well, tales. According to the original story, Francisco Pizarro, a Spaniard arrived in Peru in 1532 with few hundred men. Few weeks after their arrival, in a surprise attack, they killed the Inca king Atahualpa and took Cusco, the Inca capital. Four years later the Inca rebellion attacked Cusco and the new city of Lima.
On August 10, 1536, while Copernicus and the Kerala school were revolutionizing the world of astronomy half a world away, Francisco Pizzaro watched as tens of thousands of Incas closed in on Lima. With just a few hundred troops, Pizzaro had to come up with a strategy for survival. The Spaniards lead a cavalry attack and first killed the Inca general and his captains. Devoid of leadership the Incas scattered and once again the Spaniards won.
Recent archaeological excavations found a different version of this story. Out of the many skeletons found in the grave near Lima, only three were found to be killed by Spanish weapons; the rest by Incas. A testimony by Incas who were present in the battle was found in the Archive of the Franciscans at the Convent of San Francisco de Lima, which mentioned that it was not a great battle, but just a few skirmishes. Pizzaro was helped by a large army of Indian allies and the battle was not between the Spaniards and Incas, but between two Inca groups. It was also found that size of rebels were not in tens of thousands, but in thousands and there was no cavalry charge.
Thanks to the work of native archaeologists dramatic accounts of a small band of heroic Europeans subduing the Incas has a new narrative.
Lessons from China
Instead of following such examples and popularizing the work of Indian mathematicians, we have been behaving like Confucians at the court of the 15th century Ming emperor Zhu Di who erased evidence of the large fleets that sailed as far as the Swahili coast. While the world knows about the accomplishments of Europeans like Vasco da Gama, Columbus, Magellan and Francis Drake, little is known about Zheng He who arrived in Calicut eighty years before da Gama commanding a fleet of three hundred ships carrying 28,000 men; Vasco da Gama arrived with three ships and less than two hundred men.
Between 1405 to 1433, Zheng He’s fleet made seven voyages —- three to India, one to Persian Gulf and three to the African coast — trading, transporting ambassadors, and establishing Chinese colonies. Following the death of the emperor who  commissioned these voyages, the Confucians at the court gained influence. Confucius thought that foreign travel interfered with family obligations and Confucians wanted to curtail the ambitious sailors and the prosperous merchants.
So ships were let to rot in the port and the logs books and maps were destroyed. The construction of any ship with more than two masts was considered a capital offense. A major attempt at erasing a proud chapter in their history was done by the natives themselves.
Appreciating our stars
The goal is not to diminish the accomplishments of Copernicus or Galileo but to note that no less important accomplishments were achieved by the Kerala school either before or around the same time. Interestingly in the West, Copernican revolution was considered a movement into science to which the Church, obstinate in religious dogma, would take umbrage. In India no one was burned at the stake or put under house arrest for proposing a heliocentric model.
Instead of accepting the astronomical concepts of the Church on faith, Galileo investigated them and found new truths. Extrapolating that to historical studies we need to critically examine the Eurocentric history like the Peruvians and popularize the work of our ancestors. In this International year of astronomy, if we do not inform everyone about our great astronomers, who will ?
Postscript: In the midst of all this Eurocentric history, as a surprising exception to the norm, the only educational institution where one can take an elective course in The Pre-History of Calculus and Celestial Mechanics in Medieval Kerala is Canisius College, New York.
References: This credit for this article goes to Ranjith, a reader of this blog. He alerted me to Govinda Pillai’s article and then sent various research papers and articles about the Kerala School. He made me read Modification of the earlier Indian planetary theory by the Kerala astronomers, 500 years of Tantrasangraha, Madhavan, the father of analysis, Whish’s showroom revisited and The Pre-History of Calculus and Celestial Mechanics in Medieval Kerala.
Dick Teresi’s book Lost Discoveries, which I first read in 2003, covers the ancient roots of modern science and has sections on Indian mathematicians and astronomers. I remember buying The Crest of the Peacock and lending it to a mathematician friend; the book is now inside a singularity. The Great Inca rebellion was covered in the excellent PBS documentary of the same name. References for Zheng He can be found in an earlier article. In 2000, the University of Madras organized a conference to celebrate the 500th anniversary of Tantrasangraha. The papers presented at this conference can be found in 500 Years of Tantrasangraha
Finally, Rajiv Malhotra on Eurocentrism of Hegel, Marx, Mueller, Monier Williams, Husserl.
(images via wikipedia and indiaclub)

Why Humanities?

One of the casualities of a bad economy is humanities – philosophy, history, poetry and arts. Cash strapped universities have cut down on the study of “dead languages” and teach “useful skills.” As the debate about the value of humanities goes on David Tebaldi, executive director of Mass Humanities, explains why “a high civilization must not limit its efforts to science and technology alone.”

History teaches us how those who came before us have confronted the challenges of the past; literature provides insights into human needs, desires, and motivations; philosophy helps to clarify and illuminate what, in the end, is truly of value. Taken together, the humanities give us a fuller sense of what is possible, desirable, and right.[The lasting value of the humanities]

False Gods and Filthy Idols

Many pilgrims also put themselues vnder the chariot wheeles, to the end that their false god may go ouer them: and al they ouer whom the chariot runneth, are crushed in pieces, and diuided asunder in the midst, and slaine right out. Yea, and in doing this, they think themselues to die most holily and securely, in the seruice of their god. And by this meanes euery yere, there die vnder the said filthy idol, mo then 500.[Journal of Friar Odoric]

Those are the words of Friar Odoric, who traveled to India after 1316 CE. In writings by missionaries like him there is contempt for idol worship and polytheism; both are considered primitive.

So why is monotheism good and polytheism bad? The simple answer comes from these words in the Ten Commandments: “Do not have any other gods before me” and “You shall not make for yourself an idol, whether in the form of anything that is in heaven above, or that is on the earth beneath, or that is in the water under the earth.”

It was believed that there is a natural progression of religion from worshiping gods who are personifications of natural forces to a supreme God who is not limited by nature. Thus coming from a Europe which had abandoned Caananite religions tainted by polytheism and idol worship, the Friar was shocked to see people worshiping “a dead idole, which, from the nauel vpward, resembleth a man, and from the nauel downeward an oxe.”

In the 18th and 19th century, an evolutionary model of religion was put forward in which polytheism was considered primitive, monolatry an improvement and monotheism, the purest form. Instead of understanding them as two different ways, a value judgment was passed. It was during that time that Thomas Macaulay and his friends came to India. For them the task was clear: the primitive practices had to be stopped and the natives had to be uplifted to the purest form.

Prof. Christine Hayes at Yale explains what happened next and how this evolutionary model of religion evolved into a r-evolutionary model. This is part of her course on Introduction to the Old Testament (Hebrew Bible) which explains how the Bible was in fact adapted from various Near East traditions. The course is no MMW4, but worth listening.

Draft Arun Shourie

Gaurav has started an effort to Draft Arun Shourie to be BJP’s candidate for prime minister.
I own few of Arun Shourie’s books and have learned a great deal from his meticulous research. His Eminent Historians prompted me to find the truth behind various blue pills I swallowed in school and Missionaries in India provided the references for the Macaulay series.
He would make a fine prime minister, but I doubt it will happen since he is not an Octogenarian. One possibility is him being a compromise candidate, a la Manmohan Singh, but then it depends on too many random variables.
There are debates going on about this topic, like if Shourie can win votes for the party or if he is too much of an intellectual to govern successfully. This debate is one of the side effects of Gaurav’s campaign.

Chinese Power in Indian Ocean (2/2)

Zheng He’s map (via Wikipedia)

Read Part 1

Turning Inward
After the death of Zhu Di, China turned against naval expeditions for which there are many reasons.

The simplest is that the Confucians prevailed. The imperial bureaucracy sought to contain the expansionary ambitions of its sailors and the increasing power of its merchant class: Confucian ideology venerates authority and agrarian ways, not innovation and trade. “Barbarian” nations were thought to offer little of value to China. [The Asian Voyage: In the Wake of the Admiral]

Confucius thought that foreign travel interfered with family obligations. In Analects he said “While his parents are alive, the son may not go abroad to a distance. If he does go abroad, he must have a fixed place to which he goes.” Since this was the moral code for the upper class, government service and farming were considered noble professions

Other factors contributed: the renovation of the north-south Grand Canal, for one, facilitated grain transportand other internal commerce in gentle inland waters, obviating the need for an ocean route. And the tax burden of maintaining a big fleet was severe. But the decision to scuttle the great ships was in large part political. With the death of Yongle, the Emperor who sent Zheng He on his voyages, the conservatives began their ascendancy. China suspended naval expeditions. By century’s end, construction of any ship with more than two masts was deemed a capital offense. [The Asian Voyage: In the Wake of the Admiral

Then things took a turn for the worse. The ships were let to rot in the port and the logs books and maps were destroyed. A major attempt at erasing history was done. Then as they say, life finds a way.

Unlike Agathocles, whose memory survived only through coins, Zheg He’s traces were scattered around for it to be erased quickly. In some countries he was worshipped as a god. The chronicles of Zheng He’s translators Ma Huan (Overall Survey of the Western Shores) and Fei Hsin (Overall Survey of the Star Fleet) survived. So did a few imperial decrees and some maps. Zheng He died in the seventh voyage and was probably buried at sea; his tomb contains his clothes.

Though Zheng He’s voyages were meant to be a peaceful projection of power, they often interfered in local politics and projected force. A Chinese pirate Chen Zuyi who was active in the Sumatra was captured in a battle in the Straits of Malaca and taken to Nanjing and executed. Michael Yamashita mentions that the Chinese put a new king – Manavikarma – on the throne of Calicut. The Sri Lankan king Alakeswara refused to be a tributary to the Chinese; he was captured and taken in chains to Zheng He’s boss.
If the Chinese were a naval power during the ascent of the European powers, the Arabian Sea and Indian Ocean would have seen a different geo-political equilibrium.
References: This article was motivated by the lecture on China by Prof. Matthew Herbst in MMW4 series. By then Maddy had posted his well researched article on Zheng He (Cheng Ho) in Calicut. Michael Yamashita got paid to travel along his path for a year resulting in the book Zheng He (Discovery) which has amazing photographs. I did not read Gavin Menzies’ book, but picked the PBS documentary 1421: The Year China Discovered America (PBS)? based on it. When China Ruled the Seas devotes few pages to what they did in Calicut. Maddy also has a comprehensive article covering the Chinese trade in Calicut.
Postscript: A British submarine commander, Gavin Menzies, in a best selling book 1421: The Year China Discovered America argued that Zheng He’s fleet reached America in 1421. A PBS documentary by the same name put Gavin Menzies on camera and contradicted most of his assumptions. Mr. Menzies agreed with the producers that most of his evidence is flimsy, but he still stood by his theory.