Thursday, December 29, 2011

Understanding ancient Indian mathematics

This topic lies at the intersection of DD Kosambi's twin interests in ancient Indian history and mathematics.


It is high time we studied our mathematical heritage with diligence and objectivity


A portion of a dedication tablet in a rock-cut Vishnu temple in Gwalior built in 876 AD. The number 270 seen in the inscription features the oldest extant zero in India.

Caption: A portion of a dedication tablet in a rock-cut Vishnu temple in Gwalior built in 876 AD. The number 270 seen in the inscription features the oldest extant zero in India.

Quite often I find that conversations, with people from various walks of life, on ancient Indian mathematics slide to “Vedic mathematics” of the “16 sutras” fame, which is supposed to endow one with magical powers of calculation. Actually, the “16 sutras” were introduced by Bharati Krishna Tirthaji, who was the Sankaracharya of Puri from 1925 until he passed away in 1960, associating with them procedures for certain arithmetical or algebraic computations. Thus, this so-called “Vedic mathematics (VM)” is essentially a 20th century phenomenon.

Neither the “sutras” nor the procedures that they are supposed to yield, or correspond to, have anything to do with either the Vedas, or even with any post-Vedic mathematical tradition of yore in India. The image that it may conjure up of ancient rishis engaged in such arithmetical exercises as are taught to the children in the name of VM, and representing the solutions through word-strings of a few words in modern styled Sanskrit, with hardly any sentence structure or grammar, is just too far from the realm of the plausible. It would have amounted to a joke, but for the aura it has acquired on account of various factors, including the general ignorance about the knowledge in ancient times. It is a pity that a long tradition of over 3,000 years of learning and pursuit of mathematical ideas has come to be perceived by a large section of the populace through the prism of something so mundane and so lacking in substance from a mathematical point of view, apart from not being genuine.

Tall claims

The colossal neglect involved is not for want of pride about the achievements of our ancients; on the contrary, there is a lot of writing on the topic, popular as well as technical, that is full of unsubstantiated claims conveying an almost supreme knowledge our forefathers are supposed to have possessed. But there is very little understanding or appreciation, on an intellectual plane, of the specics of their knowledge or achievements in real terms.

In the colonial era this variety of discourse emerged as an antithesis to the bias that was manifest in the works of some Western scholars. Due to the urgency to respond to the adverse propaganda on the one hand and the lack of resources in addressing the issues at a more profound level on the other, recourse was often taken to short-cuts, which involved more assertiveness than substance. There were indeed some Indian scholars, like Sudhakar Dvivedi, who adhered to a more intellectual approach, but they were a minority. Unfortunately, the old discourse has continued long after the colonial context is well past, and long after the world community has begun to view the Indian achievements with considerable objective curiosity and interest. It is high time that we switch to a mode betting a sovereign and intellectually self-reliant society, focussing on an objective study and critical assessment, without the reference frame of “what they say” and how “we must assert ourselves.”

Ancient India has indeed contributed a great deal to the world's mathematical heritage. The country also witnessed steady mathematical developments over most part of the last 3,000 years, throwing up many interesting mathematical ideas well ahead of their appearance elsewhere in the world, though at times they lagged behind, especially in the recent centuries. Here are some episodes from the fascinating story that forms a rich fabric of the sustained intellectual endeavour.

Vedic knowledge

The mathematical tradition in India goes back at least to the Vedas. For compositions with a broad scope covering all aspects of life, spiritual as well as secular, the Vedas show a great fascination for large numbers. As the transmission of the knowledge was oral, the numbers were not written, but expressed as combinations of powers of 10. It would be reasonable to believe that when the decimal place value system for written numbers came into being it owed a great deal to the way numbers were discussed in the older compositions.

The decimal place value system of writing numbers, together with the use of ‘0,' is known to have blossomed in India in the early centuries AD, and spread to the West through the intermediacy of the Persians and the Arabs. There were actually precursors to the system, and various components of it are found in other ancient cultures such as the Babylonian, Chinese, and Mayan. From the decimal representation of the natural numbers, the system was to evolve further into the form that is now commonplace and crucial in various walks of life, with decimal fractions becoming part of the number system in 16th century Europe, though this again has some intermediate history involving the Arabs. The evolution of the number system represents a major phase in the development of mathematical ideas, and arguably contributed greatly to the overall advance of science and technology. The cumulative history of the number system holds a lesson that progress of ideas is an inclusive phenomenon, and while contributing to the process should be a matter of joy and pride to those with allegiance to the respective contributors, the role of others also ought to be appreciated.

It is well-known that Geometry was pursued in India in the context of construction of vedis for the yajnas of the Vedic period. The Sulvasutrascontain elaborate descriptions of construction of vedis and enunciate various geometric principles. These were composed in the rst millennium BC, the earliest Baudhayana Sulvasutra dating back to about 800 BC. Sulvasutra geometry did not go very far in comparison to the Euclidean geometry developed by the Greeks, who appeared on the scene a little later, in the seventh century BC. It was, however, an important stage of development in India too. The Sulvasutra geometers were aware, among other things, of what is now called the Pythagoras theorem, over 200 years before Pythagoras (all the four major Sulvasutras contain an explicit statement of the theorem), addressed (within the framework of their geometry) issues such as nding a circle with the same area as a square and vice versa, and worked out a very good approximation to the square root of two, in the course of their studies.

Though it is generally not recognised, the Sulvasutra geometry was itself evolving. This is seen, in particular, from the differences in the contents of the four major extant Sulvasutras. Certain revisions are especially striking. For instance, in the early Sulvasutra period the ratio of the circumference to the diameter was, as in other ancient cultures, thought to be three, as seen in a sutra of Baudhayana, but in the Manava Sulvasutra, a new value was proposed, as three-and-one-fth. Interestingly, the sutra describing it ends with an exultation “not a hair-breadth remains,” and though we see that it is still substantially off the mark, it is a gratifying instance of an advance made. In the Manava Sulvasutra one also nds an improvement over the method described by Baudhayana for nding the circle with the same area as that of a given square.

The Jain tradition has also been very important in the development of mathematics in the country. Unlike for the Vedic people, for Jain scholars the motivation for mathematics came not from ritual practices, which indeed were anathema to them, but from the contemplation of the cosmos. Jains had an elaborate cosmography in which mathematics played an integral role, and even largely philosophical Jain works are seen to incorporate mathematical discussions. Notable among the topics in the early Jain works, from about the fifth century BC to the second century AD, one may mention geometry of the circle, arithmetic of numbers with large powers of 10, permutations and combinations, and categorisations of innities (whose plurality had been recognised).

As in the Sulvasutra tradition, the Jains also recognised, around the middle of the rst millennium BC, that the ratio of the circumference of the circle to its diameter is not three. In “Suryaprajnapti,” a Jain text believed to be from the fourth century BC, after recalling the “traditional” value three for it, the author discards that in favour the square root of 10. This value for the ratio, which is reasonably close to the actual value, was prevalent in India over a long period and is often referred as the Jain value. It continued to be used long after Aryabhata introduced the well-known value 3.1416 for the ratio. The Jain texts also contain rather unique formulae for lengths of circular arcs in terms of the length of the corresponding chord and the bow (height) over the chord, and also for the area of regions subtended by circular arcs together with their chords. The means for the accurate determination of these quantities became available only after the advent of Calculus. How the ancient Jain scholars arrived at these formulae, which are close approximations, remains to be understood.

Jain tradition

After a lull of a few centuries in the early part of the rst millennium, pronounced mathematical activity is seen again in the Jain tradition from the 8th century until the middle of the 14th century. Ganitasarasangraha of Mahavira, written in 850, is one of the well-known and inuential works. Virasena (8th century), Sridhara (between 850 and 950), Nemicandra (around 980 CE), Thakkura Pheru (14th century) are some more names that may be mentioned. By the 13th and 14th centuries, Islamic architecture had taken root in India and inGanitasarakaumudi of Thakkura Pheru, who served as treasurer in the court of the Khilji Sultans in Delhi, one sees a combination of the native Jain tradition with Indo-Persian literature, including work on the calculation of areas and volumes involved in the construction of domes, arches, and tents used for residential purposes.

Mathematical astronomy or the Siddhanta tradition has been the dominant and enduring mathematical tradition in India. It ourished almost continuously for over seven centuries, starting with Aryabhata (476-550) who is regarded as the founder of scientic astronomy in India, and extending to Bhaskara II (1114-1185) and beyond. The essential continuity of the tradition can be seen from the long list of prominent names that follow Aryabhata, spread over centuries: Varahamihira in the sixth century, Bhaskara I and Brahmagupta in the seventh century, Govindaswami and Sankaranarayana in the ninth century, Aryabhata II and Vijayanandi in the 10th century, Sripati in the 11th century, Brahmadeva and Bhaskara II in the 12th century, and Narayana Pandit and Ganesa from the 14th and 16th centuries respectively.

Aryabhatiya, written in 499, is basic to the tradition, and even to the later works of the Kerala school of Madhava (more on that later). It consists of 121 verses divided into four chapters — Gitikapada, Ganitapada, Kalakriyapada and Golapada. The rst, which sets out the cosmology, contains also a verse describing a table of 24 sine differences at intervals of 225 minutes of arc. The second chapter, as the name suggests, is devoted to mathematics per se, and includes in particular procedures to nd square roots and cube roots, an approximate expression for ‘pi' (amounting to 3.1416 and specied to be approximate), formulae for areas and volumes of various geometric gures, and shadows, formulae for sums of consecutive integers, sums of squares, sums of cubes and computation of interest. The other two chapters are concerned with astronomy, dealing with distances and relative motions of planets, eclipses and so on.

Influential work

Brahmagupta's Brahmasphutasiddhanta is a voluminous work, especially for its time, on Siddhanta astronomy, in which there are two chapters, Chapter 12 and Chapter 18, devoted to general mathematics. Incidentally, Chapter 11 is a critique on earlier works including Aryabhatiya; as in other healthy scientific communities this tradition also had many, and often bitter, controversies. Chapter 12 is well-known for its systematic treatment of arithmetic operations, including with negative numbers; the notion of negative numbers had eluded Europe until the middle of the second millennium. The chapter also contains geometry, including in particular his famous formula for the area of a quadrilateral (stated without the condition of cyclicity of the quadrilateral that is needed for its validity — a point criticised by later mathematicians in the tradition). Chapter 18 is devoted to the kuttaka and other methods, including for solving second-degree indeterminate equations. An identity described in the work features also in some current studies where it is referred as the Brahmagupta identity. Apart from this, Chapter 21 has verses dealing with trigonometry. Brahmasphutasiddhanta considerably influenced mathematics in the Arab world, and in turn the later developments in Europe. Bhaskara II is the author of the famous mathematical texts Lilavati and Bijaganita. Apart from being an accomplished mathematician he was a great teacher and populariser of mathematics. Lilavati, which literally means ‘one who is playful,' presents mathematics in a playful way, with several verses directly addressing a pretty young woman, and examples presented through reference to various animals, trees, ornaments, and so on. (Legend has it that the book is named after his daughter after her wedding failed to materialise on account of an accident with the clock, but there is no historical evidence to that effect.) The book presents, apart from various introductory aspects of arithmetic, geometry of triangles and quadrilaterals, examples of applications of the Pythagoras theorem, trirasika, kuttaka methods, problems on permutations and combinations, etc. The Bijaganita is an advanced-level treatise on Algebra, the first independent work of its kind in Indian tradition. Operations with unknowns, kuttaka and chakravala methods for solutions of indeterminate equations are some of the topics discussed, together with examples. Bhaskara's work on astronomy, Siddhantasiromani and Karana kutuhala, contain several important results in trigonometry, and also some ideas of Calculus.

The works in the Siddhanta tradition have been edited on a substantial scale and there are various commentaries available, including many from the earlier centuries, and works by European authors such as Colebrook, and many Indian authors including Sudhakara Dvivedi, Kuppanna Sastri and K.V. Sarma. The two-volume book of Datta and Singh and the book of Saraswati Amma serve as convenient references for many results known in this tradition. Various details have been described, with a comprehensive discussion, in the recent book by Kim Plofker. The Bakhshali manuscript, which consists of 70 folios of bhurjapatra (birch bark), is another work of signicance in the study of ancient Indian mathematics, with many open issues around it. The manuscript was found buried in a eld near Peshawar, by a farmer, in 1881. It was acquired by the Indologist A.F.R. Hoernle, who studied it and published a short account on it. He later presented the manuscript to the Bodleian Library at Oxford, where it has been since then. Facsimile copies of all the folios were brought out by Kaye in 1927, which have since then been the source material for the subsequent studies. The date of the manuscript has been a subject of much controversy since the early years, with the estimated dates ranging from the early centuries of CE to the 12th century.

Takao Hayashi, who produced what is perhaps the most authoritative account so far, concludes that the manuscript may be assigned sometime between the eighth century and the 12th century, while the mathematical work in it may most probably be from the seventh century. Carbon dating of the manuscript could settle the issue, but efforts towards this have not materialised so far.

A formula for extraction of square-roots of non-square numbers found in the manuscript has attracted much attention. Another interesting feature of theBakhshali manuscript is that it involves calculations with large numbers (in decimal representation).

Kerala school

Let me nally come to what is called the Kerala School. In the 1830s, Charles Whish, an English civil servant in the Madras establishment of the East India Company, brought to light a collection of manuscripts from a mathematical school that ourished in the north-central part of Kerala, between what are now Kozhikode and Kochi. The school, with a long teacher-student lineage, lasted for over 200 years from the late 14th century well into the 17th century. It is seen to have originated with Madhava, who has been attributed by his successors many results presented in their texts. Apart from Madhava, Nilakantha Somayaji was another leading personality from the school. There are no extant works of Madhava on mathematics (though some works on astronomy are known). Nilakantha authored a book called Tantrasangraha (in Sanskrit) in 1500 AD. There have also been expositions and commentaries by many other exponents from the school, notable among them being Yuktidipikaand Kriyakramakari by Sankara, and Ganitayuktibhasha by Jyeshthadeva which is in Malayalam. Since the middle of the 20th century, various Indian scholars have researched on these manuscripts and the contents of most of the manuscripts have been looked into. An edited translation of the latter was produced by K.V. Sarma and it has recently been published with explanatory notes by K. Ramasubramanian, M.D. Srinivas and M.S. Sriram. An edited translation of Tantrasangraha has been brought out more recently by K. Ramasubramanian and M.S. Sriram.

The Kerala works contain mathematics at a considerably advanced level than earlier works from anywhere in the world. They include a series expansion for ‘pi' and the arc-tangent series, and the series for sine and cosine functions that were obtained in Europe by Gregory, Leibnitz and Newton, respectively, over 200 years later. Some numerical values for ‘pi' that are accurate to 11 decimals are a highlight of the work. In many ways, the work of the Kerala mathematicians anticipated calculus as it developed in Europe later, and in particular involves manipulations with indenitely small quantities (in the determination of circumference of the circle and so on) analogous to the innitesimals in calculus; it has also been argued by some authors that the work is indeed calculus already.

Honouring the tradition

A lot needs to be done to honour this rich mathematical heritage. The extant manuscripts need to be cared for to prevent deterioration, catalogued properly with due updates and, most important, they need to be studied diligently and the ndings placed in proper context on the broad canvass of the world of mathematics, from an objective standpoint. Let the occasion of the 125th birth anniversary of the genius of Srinivasa Ramanujan, a global mathematician to the core, inspire us as a nation, to apply ourselves to this task.

(The author is Distinguished Professor, School of Mathematics, Tata Institute of Fundamental Research, Mumbai.)

Thursday, December 8, 2011

The Many Careers of DD Kosambi- pdf version

Thanks to the good folks at Leftword, the publisher of the book The Many Careers of DD Kosambi, a pdf version of the book is now available for download.

Do purchase the paper copy of the book from Leftword, and help their efforts in publication of studies on DD Kosambi.

Download the pdf version.

Tuesday, December 6, 2011

The Many Careers of DD Kosambi

Thanks to the truly indefatigable Arvind Gupta, the latest collection of critical essays edited by the historian DN Jha is now available for download. Most of these essays have appeared in EPW earlier and are available on this blog. However, this book contains all essays in one place, along with a couple of newer ones.  

Download the book

Friday, July 22, 2011

The Agenda of the Gita

Cross posted from my personal blog

Left liberals are likely to denounce the BJP’s support for the Karnataka government’s introduction of Gita classes in schools as an attempt at stifling minority rights and invoke on the separation of the state and the church. The BJP’s agenda, however, goes far beyond just a communal agenda. To decipher that, one has to trace the agenda behind the Gita itself.

The Gita has, in popular belief, symbolized the rejuvenation of Hinduism after a thousand years of Buddhist domination. It was the book that apparently struck the last nail on Buddhist thought by a thirty-something Adi Sankracharya. Sankara advocated the advaita--in other words, a form of subjective idealism. In simple words, what it means is that there is only one entity in the universe, the Brahma. The rest is an illusion. Thus, he reconciled all the contradictions in the world by proclaiming that everything is an illusion, or Maya. A person needs to realize this supposed unity and unless one is able to do so, one remains entangled in the web of illusions, or mayajaal.

The Gita attempted to do the same--reconcile contradictions. It attempted to justify violence in the name of morality. It ordained the caste system, and showed women “their place.” In other words, The Gita is the chariot of Brahmanism and what can be called the ideology of racism ensconced within Brahmanism.

Monday, June 13, 2011

Prof DD Kosambi- some reminiscences by Dr. BV Sreekantan

Source- RESONANCE June 2011 599
Professor D D Kosambi – Some Reminiscences
It is with distinct pleasure that I recall my very pleasant informal and peripheral association with Prof. D D Kosambi for a period of 14 years from 1948 to 1962. This came about in a rather unusual way. I had applied in the summer of 1948 for admission to the Tata Institute of Fundamental Research as a research student. In the application form, in answer to the query about my research interests, I had written Theoretical/Experimental physics. I was called for an interview on the 6th of August. First I was interviewed by the experimental committee, with Bhabha as theChairman. I was called for a second time the same day and this time the committee consisted of Dr Bhabha, Prof. Kosambi and Prof. Levy. Dr Bhabha told themthat he had already examined my knowledge of physics and asked them to question me in mathematics. Prof. Levy asked me some questions about matrices and then Prof. Kosambi asked some question in statistics. He also asked me whether I know the Iyengars in the Mathematics department of Central College. A little later, I was called for a third time to Dr Bhabha’s room. As I entered, Dr Bhabha said “Sreekantan, we have decided to admit you. Tell us whether you want to dotheory or experimental research”. I replied “Sir, you have interviewed me. I go by your advice”. Dr Bhabha said “young man, if you join experimental group then perhaps you may also be able to do theoretical work. The other way is doubtful. Moreover, you have some experience in electronics which very few have in this country. If I were you, I will choose to do experimental work”. I joined the Cosmic Ray group of the Institute on the 12th August 1948.

A few weeks later, Dr Bhabha called me and said that I will be working on the Cosmic Ray Mumeson Decay problem. I should read up all the necessary literature and present a colloquium on the subject in about six weeks time. On the day of my first colloquium, I was surprised and shocked to find that right in front row of the small lecture hall were sitting Dr Bhabha, Prof. Kosambi, Prof. Levy and Prof. Masani. Behind them experimentalists AS Rao, Sahian, Thattar and others. There were no facilities for slide projector or for overhead projector system. Everything had to be written on the black board with chalk piece.

I had drawn on the black board, some of the experimental arrangements that had been adopted by others for the study of meson decay and started explaining them one by one. Dr Bhabha interrupted me, came to the black board and suggested what modifications should be made in our experimental arrangements for the experiment. Immediately after that Prof. Kosambi came to the black board and suggested some more changes. Then there ensured a discussion on the pros and cons of the modified arrangements. The net result was that my colloquium which was to be for one hour stretched to three successive Wednesday colloquia, at the end of which, I knew what exactly was the ideal experimental set-up, what precautions I had to take and what kind of statistics I had to gather and how I should go about the analysis – enough work for two years to follow.

Towards the end of 1948, Dr Bhabha invited us for a Tea Party at his Malabar Hills house next to the Hanging Gardens and overlooking the Arabian Sea. The party was to felicitate Prof. Kosambi who had been invited by the Harvard University as a Visiting Professor. In September 1949, the new premises of TIFR at Appollo Pier, near Gateway of India became ready and we moved there. The Yacht club building had a large Dance Hall in the first floor which was converted to the Library, Laboratory for Cosmic Ray Research by the High Altitude Studies group and at one end two special air conditioned rooms were made; one for Prof. Kosambi and the other for Prof. Bernard Peters who had joined TIFR. Our Cloud Chamber laboratory was in the ground floor. Prof. Kosambi used to come to our laboratories frequently for two different reasons. One was that he was a great consumer of chacolates which he used to get from abroad and these had to be stored in an air conditioned room. Since our cloud chamber rooms had to have twenty four hour air conditioning, he used to store his stock in one of these rooms. The second reason was that Dr Kosambi had a great interest in photography. He had a Cannon Reflex Camera with which he used to take photographs. Occasionally he would give it to me to take photographs. We had all the facilities in the cloud chamber section for developing films and also do enlargements of prints. He also had expertise in Sepia toning of the prints. After moving to Yacht Club, Prof. Kosambi gave a course of lectures on statistical treatment of data. In fact in my very first paper from TIFR, on the ‘Life time of mu-meson’ I have thanked Prof. Kosambi for helping me with the statistical analysis of the data.

In 1954, after my PhD thesis, Dr Bhabha deputed me to MIT, Cambridge, to work with Prof Bruno Rossi for a year or so. When I went to tell Prof. Kosambi about this, he said that it is a good idea to have post doctoral research experience abroad and told me that his sisters’ son Arun Prasad was studying at MIT in the Aeronautics Department. He would give me a small packet which I should give it to Arun which I gladly did after going there. I did not meet Arun again for a long time. I was happy to see him in the lecture hall at NIAS, after 56 years when Prof. Kosambi’s daughter Prof. Meera Kosambi gave a lecture in November 2010.

Prof. Kosambi lived in Poona and used to come to Bombay everyday by Deccan Queen which during those days would have only first and second class carriages and some were reserved for season- ticket holders. It used to be said that one particular window seat in the train was always reserved for Prof. Kosambi. Hewas a voracious reader of fiction. He would buy new books, read them on the train and give them away to our small library in the lounge next to the dinning hall at Yacht Club.

In 1962, we moved to the new building of TIFR at Navy Nagar. Prof. Kosambi moved away from TIFR. I did not have the fortune of meeting him after this.

B V Sreekantan, National Institute of Advanced Studies, Bangalore 560 012, India.

Tuesday, May 3, 2011

When did early humans reach India?

When did early humans reach India? | Down To Earth
When did early humans reach India?
Author(s): Tiasa Adhya
Issue: May 15, 2011

Stone tools suggest a million years ago, previous assumption was 0.5 million years ago

imagePappu and her research team started studying the site in Tamil Nadu in 1999 (Courtesy: Shanti Pappu)EARLY humans arrived in India from Africa more than a million years ago, indicate newly discovered stone tools. The discovery overturns the earlier assumption that our ancestors reached India about half a million years ago.

A research team led by Shanti Pappu of non-profit Sharma Centre for Heritage Education in Chennai discovered 3,528 stone tools at a prehistoric site in Attirampakkam in the Kortallayar river basin of Tamil Nadu. The tools fall into a class of artefacts called Acheulian tools that scientists believe were first created by Homo erectus— ancestors of modern humans—in Africa more than 1.6 million years ago. The Acheulian tools largely include handaxes and cleavers.

The conclusion of Pappu’s study was earlier voiced by Robin Dennell of University of Sheffield in England in a commentary published in 2005 in the journal Nature.

The Old Stone Age, or Palaeolithic Age, is divided into three periods— Lower Palaeolithic, Middle Palaeolithic and Upper Palaeolithic. Each period is characterised by typical stone tool assemblages. The Acheulian is a phase within the Lower Palaeolithic, characterised by a stone tool assemblage consisting largely of handaxes and cleavers.

Acheulian populations were primarily hunters and gatherers, skilled at adapting to different environments. “We know this from fossil remains found at sites in India and world over,” says Pappu. The Acheulian tools were probably used to butcher and skin animals and to exploit plant resources like roots and tubers, she adds.

imageAcheulian handaxeDating, for the first time The archaeologists found the artefacts at a depth of one to nine metres in thick layers of clay.

To date the tools, the research team analysed traces of certain elements embedded in them and by correlating the archaeological layers excavated at the site with changes in the earth’s magnetic field. Many such artefacts have been found in south India, but this is the first study that has dated the tools.

The team used two dating methods, palaeomagnetic dating of the sediments that covered the Acheulian tools and cosmogenic nuclide burial dating of the stone tools. The former is based on the principle of periodic reversal of the earth’s magnetic fields over geological time periods. The palaeomagnetic measurements showed a reversed polarity, meaning the sediment samples predate the period after the last reversal of the earth’s magnetic field.

“The sediments date to more than 1.07 million years,” says Pappu. The burial dating technique measures isotopes of two earth metals, aluminium and beryllium, which gives the age of burial of the tool.

The finding “is one of the finest in Indian archaeology”, says V N Misra, retired professor of anthropology at Deccan College in Pune. “It proves, for the first time, that early humans migrated from Africa to Tropical Asia and Europe. They did not go to the Himalayan side of India because of the colder climate,” he adds. It proves that early humans were present in Asia much earlier than in Europe, he concludes.

The study, published in the March issue of Science, is part of an ongoing research project of Sharma Centre for Heritage Education. The research aims to understand prehistoric stone tool technology and changes in patterns of adaptation of Homo erectus to changing environments at Attirampakkam.

“We examine what type of development (agriculture and infrastructure development) is destroying prehistoric sites. This will help pave the way for methods that could be adopted to conserve the sites,” says Pappu.
Tags: Science & Technology, Africa, History, India, Life Science, Tamil Nadu

Sunday, May 1, 2011

Remnants of Mauryan-era stupas found in Girnar forest

The Hindu : States / Other States : Remnants of Mauryan-era stupas found in Girnar forest
Union Environment and Forests Minister Jairam Ramesh has asked Gujarat Chief Minister Narendra Modi to undertake a thorough archaeological survey of the Girnar reserve forest and the Gir sanctuary in Junagadh district in the Saurashtra region of the State.

In a letter dated April 21, Mr. Ramesh said he was giving the advice on the suggestion of a noted historian from Delhi University Nayanjot Lahiri, who recently visited the reserve forest and found the remnants of two “stupas” which she believed could be of the Mauryan dynasty.

Mr. Ramesh said Dr. Lahiri located one of the stupas, locally known as Lakha Medi, near the Bhordevi temple inside the forest.

The historian reckoned that the stupa must have been about 50 feet high. Its core was of solid bricks, similar to the “Sanchi Stupa – I” (Madhya Pradesh) and the “Stupa at Piprahwa” (Uttar Pradesh), believed to be of the Mauryan era.

She had also found many loose bricks around indicating there could have been other stupas in the vicinity. But what was more alarming was that the bricks from the stupas were being taken away by the locals for renovating the temple.

“Therefore, it is urgent, that there is a complete survey of the stupa with accurate line drawings and photographs followed by careful archaeological conservation,” Mr. Ramesh said.
Better stupa

The historian located another “stupa,” locally called “Rathakot,” near another temple known as “Jina Baba ki Madi,” beyond Hasnapur dam in the Girnar reserve forest. This stupa was found to be in a much better condition.

Mr. Ramesh said Dr. Lahiri believed that if a proper survey was carried out, the reserve forest and the sanctuary could become famous for not only being the only abode of the Asiatic Lions, but also of the country's “historic heritage.”

The survey would require close cooperation between the State Forest Department and the Department of Archaeology.
‘Coral Atlas'

Meanwhile, a first comprehensive “Coral Atlas” of the State — giving not only the figures and extent of the coral reefs across the State's coastline, but also the details of the habitat scenario in each of the reefs — has been released by the State government. The Atlas was prepared by the State-owned Gujarat Ecology Commission with technical assistance from the Bhashkaracharya Institute of Space Applications and Geo-Informatics.

According to Principal Secretary of the State Environment and Forests Department S.K. Nanda, the Atlas would serve as an important baseline in the preparation of the Integrated Coastal Zone Management Plan for Gujarat initiated by the Union Environment Ministry. “It is also a contribution to the State's earnest efforts towards sustainable development,” he said.
Website launched

Along with the Atlas, a dedicated website on Integrated Coastal Zone Management Project was also launched by the State government. The Atlas was the second publication of the GEC after the “Mangrove Atlas of Gujarat” last year featuring thematic maps of mangrove distribution along the State's coastline.

“The initiative by GEC is an attempt to come out with the baseline documentation on the natural heritage in order to ensure effective management of the coastal zone in line with the rising developmental activities on the coastal belt,” GEC member-secretary E. Belaguruswamy said.

Keywords: Jairam Ramesh, Girnar forest, Mauryan-era

Sunday, March 13, 2011

Tamil-Brahmi script found at Pattanam in Kerala

The Hindu : News / National : Tamil-Brahmi script found at Pattanam in Kerala
A Tamil-Brahmi script on a pot rim, reading “a ma na”, meaning a Jaina, has been found at Pattanam in Ernakulam district, Kerala, establishing that Jainism was prevalent on the west coast at least from second century CE (Common Era). The script can be dated to circa second century CE. The three Tamil-Brahmi letters are followed by two symbols generally called Megalithic graffiti and these two symbols could not be identified. This is the third Tamil-Brahmi script to be found in the Pattanam excavations.

The Kerala Council for Historical Research (KCHR) has been conducting excavations at Pattanam since 2007, with the approval of the Archaeological Survey of India. The pot-rim was found during the sixth season of the excavation currently under way. Pattanam is now identified as the thriving port called Muziris by the Romans. Tamil Sangam literature celebrates it as Muciri.

P.J. Cherian, Director of the Pattanam excavations, said: “The discovery, in the Kerala context, has a great significance because of the dearth of evidence so far of the pre-Brahminical past of Kerala, especially in relation to the socio-cultural and religious life of the people. We have direct evidence from Pattanam now with the Brahmi script which mentions “a ma na” [Jaina] and so we have evidence that Jainism and Buddhism were extensively practised in Kerala.”

Iravatham Mahadevan, a scholar in Indus and Tamil-Brahmi scripts, said the discovery showed that “there was Jainism on the west coast at least from second century CE. The importance of the finding is that it stratigraphically corroborates the earlier datings given to the Tamil-Brahmi cave inscriptions in Tamil Nadu on palaeographic evidence. I will date this sherd, on palaeographic evidence, to circa second century CE.”

The Tamil word “a ma na” meaning a Jaina was derived from Sanskrit Sramana via Prakrit Samana and Tamil Camana, said Mr. Mahadevan. The two megalithic graffiti, following the three Tamil-Brahmi letters, could not be identified. “But we know from similar finds in Tamil Nadu, especially at Kodumanal, that Tamil-Brahmi letters and megalithic graffiti symbols occur side by side,” he said. Mr. Mahadevan was sure that “many more exciting finds will be made at Muciri [Pattanam] which was a flourishing port on the west coast during the Sangam age in Tamil Nadu, which coincided with the classical period in the West.”

Mr. Cherian, who is also Director of KCHR, said the discovery “excites me as an excavator because it was for the first time we are getting direct evidence relating to a religious system or faith in Kerala.” The pot might have belonged to a Jaina monk. The broken rim with the script was found at a depth of two metres in trench 29 in the early historical layer which “by our stratigraphic understanding could belong to third-second CE period,” he said. The associated finds included amphora sherds, iron nails, and beads among others.

In a trial trench laid earlier at Pattanam by Professor V. Selvakumar, Assistant Professor, Department of Archaeology and Epigraphy, Tamil University, Thanjavur and K.P. Shajan of KCHR, a pot-sherd with the Tamil-Brahmi letters reading “ur pa ve o” was found. Later, another Tamil-Brahmi script with the letters “ca ta [n]” was found. Mr. Mahadevan praised the Pattanam excavations as “the best conducted excavations in south India.” He said it was “a potentially important site and excavations are being done in a competent way by Mr. Cherian and his team from the KCHR and they have involved experts from around the world.”

Monday, February 7, 2011

DD Kosambi Festival 2011 is On

Oheraldo Goa's complete online news edition :: Star-studded-line-up-for-D-D-Kosambi-Festival-of-Ideas
Star-studded line-up for D D Kosambi Festival of Ideas


Panjim, Feb 4: Chief Minister Digambar Kamat will inaugurate the D D Kosambi Festival of Ideas on Saturday at Kala Academy, Panjim, to be followed by a lecture delivered by eminent scientist Dr Raghunath Mashelkar. This is the fourth edition of this lecture series, and will be held from February 5 to 10 at Kala Academy, Panjim.

Other speakers will include another great scientist and former President of India Dr A P J Abdul Kalam, Tibetan leader and Buddhist luminary His Holiness the Dalai Lama, Indian-born British economist and intellectual Lord Meghnad Desai, Human Rights activist and former Judge of South Africa’s Constitutional Court Justice Albie Sachs and Rajya Sabha MP, Hindu leader and President of the Indian Council for Cultural Relations (ICCR) Dr Karan Singh.
Saturday’s talk will have Dr Raghunath Mashelkar speaking about ‘Making the Impossible, Possible’, from 5 pm to 7.30 pm. Dr Mashelkar is the former Director General of the Council for Scientific and Industrial Research (CSIR), a chain of 38 government research and development (R&D) institutions employing 20,000 scientists, which includes the National Institute of Oceanography (NIO), located in Goa.

A son of Goa, Dr Mashelkar was born on January 1, 1943 in Mashel, Tiswadi, in a modest family. He went to school barefoot and almost had to give up studies owing to his family’s strained economic circumstances. Nevertheless, he was a rank holder in the matriculation examination.

An apocryphal story says that his school principal and science teacher, Bhave, once concentrated the rays of the sun through a magnifying lens on a paper till it burned and told him, “This lens is you. If you concentrate on your studies, one day you will reach the sky.” Though his mother could not support his college education, Dr Mashelkar managed to become a chemical engineer, won a Tata scholarship, went overseas and got his PhD degree.
He did ground-breaking work in polymer science and engineering, going on to become the head of the National Chemical Laboratory (NCL). He was then named Director General of the CSIR. Under his leadership, the CSIR was first in the World Intellectual Property Organisation’s (WIPO’s) Patent Cooperation Treaty (PCT) filings among developing nations in 2002. CSIR still has a 30-40 per cent share of all US patents granted to Indians in India during the last three years.

His personal experience of reaching the very top of his profession from the most dire of circumstances has convinced him that India is fated to become one of the world’s greatest intellectual and economic engines. He has been responsible for creating an unprecedented national awareness in India on Intellectual Property Rights (IPR).
He led the challenge to successfully revoke the US patent on the wound-healing properties of Turmeric. He also chaired the technical committee that successfully challenged and revoked US patents on Basmati Rice. This set in motion a movement for the protection of traditional knowledge in the entire developing world.
Two Sundays ago, Dr Mashelkar and former Atomic Energy Commission chief Dr Anil Kakodkar sat and listened to the dreams, hopes and aspirations of young people from across Goa at the youth convention for the Vision Document for Goa-2035 – to prepare a roadmap for the development of Goa – at Ravindra Bhavan, Margao. He remarked, after listening to the ideas of dozens of young Goan men and women that it was possibly among the finest three hours of his life.

Mashelkar is presently the president of the Global Research Alliance, a network of publicly funded research and development institutes from the Asia-Pacific region, South Africa, Europe and the USA with over 60,000 scientists. He is also the President of India’s National Innovation Foundation.

Other topics and timings:

Sun Feb 6: Dr A P J Abdul Kalam, ‘Imagination Leads to Creativity’, 5 pm to 6 pm.
Mon Feb 7: Dalai Lama, ‘Ethics for the New Millennium’, 2.30 pm to 4.30 pm.
Tue Feb 8: Lord Meghnad Desai, ‘Kosambi, Modernity and the Question of Social Inclusion’, 5 pm to 7.30 pm.
Wed Feb 9: Justice Albie Sachs, ‘Light on a Hill’, 5 pm to 7.30 pm.
Thu Feb 10: Dr Karan Singh, ‘The relevance of Vedanta in today’s context’, 5pm to 7.30 pm.

An interaction session between the public and the speaker is held subsequent to the talk.
The Directorate of Art & Culture initiated the D D Kosambi Festival of Ideas to commemorate the birth centenary of Damodar Dharmanand Kosambi, Indian mathematician, statistician, physicist, historian and polymath, and a great son of Goa. This festival is the only one of its kind in the country.