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On Madhavan of Sangamagrama

A while back, I wrote on Kerala Astronomers and Eurocentrism. In that article, I wrote about the Kerala School of Mathematics as well and provided a number of references at the end. One of the books I referred was The Crest of the Peacock: Non-European Roots of Mathematics by Dr. George Gheverghese Joseph. The Telegraph had an interview with him in which he expanded on this topic and talks about Madhava in detail.

His works laid the foundations of the Kerala school of mathematics which flourished between AD 1,300 and 1,700. But he was only part of the wider Indian school founded by Aryabhata who wrote the masterpiece Aryabhateeyam in AD 499. There are still differences over Aryabhata’s birthplace, whether it was in the north or the south of the country. Madhava’s contribution was his work on the infinite series. Though Newton and Leibniz are credited with the discovery of calculus, the fact is one of its critical strands had been developed in Kerala more than two centuries before that. The West has now recognised this and accordingly renamed certain results relating to the trigonometric series, previously known as the Newton, Gregory and Leibniz series, as the Madhava-Newton, Madhava-Gregory and the Madhava-Leibniz series, respectively.

The irony is that we still don’t know much about Madhava, the man himself. An eminent mathematician from Oxford, Marcus Du Sautoy, recently made a series of television programmes on the history of mathematics. I was consulted on those programmes relating to the history of Indian mathematics, including the remarkable work in Kerala. He was particularly interested in finding the physical location of Madhava and his main disciples to add some footage of film. When he asked me I was clueless and somewhat embarrassed. But now I’m told that he hailed from Sangamagrama, a medieval town in present-day Irinjalakuda in Thrissur district. It is a shame that there is no memorial plaque at the place which would certainly attract maths tourists.[Restoring India’s calculus crown]

In a personal email, Michel Danino notes that Dr. George G. Joseph isn’t the only scholar to have worked on the Kerala School of mathematics; recent contributors to the field include the late Prof. K.V. Sarma, Dr. C.K. Raju, Dr. M.D. Srinivas, Dr. M.S. Sriram and Dr. K. Ramasubramanian, among others.

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Volcanoes: Mount Sinabung, Toba, Hasan Dağı, Pompeii


Mount Sinabung, Indonesia

Mount Sinabung, Indonesia

The above picture shows Mount Sinabung in  Indonesia’s North Sumatra province which has been erupting since last September. The Atlantic has 30 stunning photos of the January eruptions which show in detail the damage a volcano can cause and how it impacts human and animal life. Around 74,000 years back, there was a major volcanic explosion in Indonesia which caused a nuclear winter and a massive reduction in population. Though the destruction it caused was significant, people in Jwalapuram in Andhra Pradesh survived.

Though no one drew pictures of that eruption, one has been found of another one which happened in 6900 BCE, in the Hasan Dağı twin-peaks volcano located 130 km northeast of Çatalhöyük. A contemporary site to Mehrgarh, Çatalhöyük is one of the best preserved Neolithic settlements.

Rendering of a wall painting discovered at Shrine 14 during the original excavations of Çatalhöyük by British archaeologist James Mellaart in the 1960s and said to depict Hasan Dagi erupting. Image: John Swogger (Flickr, used under a CC BY-NC 3.0)

Though the interpretation that this was a depiction of a volcanic eruption was controversial, new studies have shown that the the painting was drawn during the time of the eruption and the artists may have witnessed the event.

Now if you want to experience a volcanic eruption in 3D, all you need is wait for the upcoming disaster-adventure movie, Pompeii

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Indian History Carnival–72: Linguistics, Yaadhum,Soubise, Ahmed Khan, Robert Smith

  1. Geo Currents has a post on the Vexatious History of Indo-European Studies. Part II of this post looks at how Indo-European linguistics was misused by various ideologues
    As “race science” gained strength in late 19th century Europe, it faced a major obstacle in Indo-European philology. European racial theorists maintained a stark separation between the so-called Caucasian[1] peoples of Europe and environs and the darker-skinned inhabitants of South Asia, yet the philologists argued that Europeans and northern Indians stemmed from the same stock. Some of the early efforts to mesh the new racial ideas with linguistic findings were rather strained. The popular American writer Charles Morris, for example, argued in 1888 that races are divided on the basis of both language and physical type, which generally but not always coincide; he further contended that “the Aryan is one of these linguistic races” (p. 5) that had lost its original physical essence. The general tendency was to emphasize ever more strongly this supposed loss of “purity,” and thus for physical type to trump linguistic commonality

  2. Baradwaj Rangan writes about Yaadhum, a documentary on the identity of Tamil Muslims.
    Yaadhum is some sort of road movie, and Anwar’s stops along the way illuminate various aspects of Islam in the South and even Goa. He goes to Chola country, establishing the presences of Muslims through an inscription that refers to “Ahmed the Turk.” He goes to Kayalpattinam, which belonged to the Pandyas, and finds an almost 1000-year-old mosque to which additions have been made at different times. He narrates the history of the Tamil Muslims of Pulicat, most of whom are boat builders. He goes to Calicut, home of the Mapilla Muslims. Prof. MGS Narayanan, Director General, Centre for Heritage Studies, Dept. of Cultural Affairs, Govt. of Kerala, talks about a law which is supposed to have been passed by the Zamorin that at least one member of the fishermen families in Calicut must get converted to Islam so that there will be enough people to support naval warfare against the Portuguese who wanted to conquer Malabar in the 16th century. (Hindus were generally reluctant to go to sea.)

  3. How does a slave from West Indies end up in West Bengal in 1777?  Carnival contributor Fëanor has that story
    He racked up large debts which the Duchess continued to pay off. He maintained a house in town, was a favourite of Garrick, and appeared at theatre vastly perfumed. ‘I smell Soubise!’ would go the cry amongst the punters when he appeared. He was caricatured in the popular press (one print by Austin showed him squaring off against the Duchess in a public fencing match), and even had portraits sketched by Gainsborough. In 1777, following an accusation of rape, he either escaped or was exiled to Bengal. As a skilled equestrian, he was able to found a riding school in Old Calcutta. He also taught fencing, and for a time sold books, possibly the first reported African British bookseller.

  4. Blake Smith writes about Ahmed Khan who was stuck in Marseilles on his way to London in 1792. He was off to London to sue British traders in Bombay for not paying back the loans.
    Ahmed did not speak French—yet—but he did speak Persian, then the language of diplomacy, poetry, and prestige throughout the Subcontinent. So did Pierre Ruffin, the French government’s official translator of ‘Oriental’ languages, which, at the time, meant Arabic and Persian. Ruffin, who had survived the fall of his former employers, had been in office for over a decade. His moment of glory had come in 1788, when an embassy from Tipu Sultan, ruler of the southern Indian state of Mysore, arrived in Paris to seal an alliance against Britain.

  5. Malini Roy has a post on Robert Smith, who was one of the British soldier artists who lived in India in the 19th century
    Smith’s view of Allahabad, for instance, focuses on a strange looking hybrid of a building, which is referred to by Lord Moira in his journal entry for 27 September 1814: ‘A mosque of rather elegant structure stands on the esplanade beyond the glacis. When we obtained possession of Allahabad, the proprietary right in the mosque was considered as transferred by the former Government to ours; and from some temporary exigency, the building was filled with stores. These being subsequently removed, much injury, through wantonness or neglect, was suffered by the edifice; and upon some crude suggestion, our Government had directed it to be pulled down. … The Moslems now implored that the building might be regarded as a monument of piety, and be spared. I have ordered that it shall be cleansed and repaired, and then delivered over to the petitioners’

The next carnival will be up on Jan 15th. Please leave your links as comments to this post or via e-mail.

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The Yogi who met Socrates

Death of Socrates by Jacques-Louis David (1748–1825)

Death of Socrates by Jacques-Louis David (1748–1825)

In the 5th century BCE, the contacts between India and Greece became sporadic. The reason for this was the defeat of the Persian army in two wars.  In 490 BCE, the Persian army, which included Indian cavalry, was defeated by the Athenians at the Battle of Marathon. The Persians were also defeated in 480 BCE at the Battle of Plataea which followed the Battle of Thermopylae (remember 300?).  Since the relation between the Persians and Greeks broke down, it in turn affected the Indo-Greek relations.

That said, there is evidence that Indian ascetics  traveled to Greece along a trade route that went through Oxus river, Caspian Sea, Kyros river and  Black Sea.  These ascetics influenced Diogenes of Sinope (412 – 323 BCE) who then introduced Indian ascetic practices into Greek traditions. But much before Diogenes, there is a mention of an Indian yogi who met Socrates and had a conversation.

According to Aristoxenus, a disciple of Aristotle, this Indian met Socrates in Athens and asked him what he studying. Socrates replied that he was studying human life. The Indian at this point laughed and asked him how could he study human life without studying the divine.  The quote is as follows

‘Now Aristoxenus the Musician says that this argument comes from the Indians: for a certain man of that nation fell in with Socrates at Athens, and presently asked him, what he was doing in philosophy: and when he said, that he was studying human life, the Indian laughed at him, and said that no one could comprehend things human, if he were ignorant of things divine [Eusebius of Caesarea: Praeparatio Evangelica (Preparation for the Gospel). Tr. E.H. Gifford (1903) — Book 11]

It is not sure if Socrates changed his mind, but his student Plato was influenced. Plato who previously argued that human and divine affairs were the same, started distinguishing between the two. According to Plato there was one kind of study concerning nature, another concerning humans and a third concerning dialectic.

‘But he maintained that we could not take a clear view of human affairs, unless the divine were previously discerned: for just as physicians, when treating any parts of the body, attend first to the state of the whole, so the man who is to take a clear view of things here on earth must first know the nature of the universe; and man, he said, was a part of the world; and good was of two kinds, our own good and that of the whole, and the good of the whole was the more important, because the other was for its sake.[Eusebius of Caesarea: Praeparatio Evangelica (Preparation for the Gospel). Tr. E.H. Gifford (1903) — Book 11]

Unfortunately, we don’t know the name of this Indian teacher and to what tradition he belongs to or any other detail.


    1. Mcevilley, Thomas C. The Shape of Ancient Thought: Comparative Studies in Greek and Indian Philosophies. 1st ed. Allworth Press, 2001.
    2. Caesarea, Eusebius of. Eusebius of Caesarea: Praeparatio Evangelica, 2010.
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Preserving Vedic Chanting

(Photo via Ujjwol Lamichhane)

If you have played the party game called “Pass the Secret”, you will know that by the time the message reaches back to you, it would have been distorted beyond recognition.  But for many millennia, the Vedic hymns were memorized and handed down by word of mouth and the contents were preserved intact. The actual wording, intonation and pronounciation had to be perfect and for this the Vedic seers created a system to prevent alteration.

At Huffington Post, Suhag Shukla explains this system

To ensure that the Vedas remained unchanged in content, intonation, and inflection, a number of techniques of recitation with increasing complexity and difficulty were developed, including Jatapata.

The first is Samhita, the simplest form of recitation that approaches the mantra as it is, for example,”the sky is blue” (abcd). Next is Padha, where each word is broken down, as in, “the/sky/is/blue” (a/b/c/d). Krama, the third technique, adds the first real level of difficulty into the recitation through a pattern of “the sky/sky is/is blue” (ab/bc/cd). Jatapata, the first of the more challenging, alternates between a repetitious interposing and transposing of words to create a pattern of “the sky sky the the sky/sky is is sky sky is/is blue blue is is blue” (abbaab/bccbbc/cddccd). Between Jatapata and the last technique are six other techniques (called Mala, Shikha, Rekha, Dvaja, Danda and Ratha) that again are built-in combinations and permutations that have ensured that the order and words of the Vedas remain unchanged. The ultimate and most complex technique is called Ghanam. Its mind-boggling backwards and forwards pattern is, “the sky sky the the sky is is sky the the sky is/sky is is sky sky is blue blue is sky is blue” (abbaabccbaabc/bccbbcddcbcd).[Peeling Back the Layers of Sanskrit and Vedic Chanting]

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