Tag Archives: Traditions

Shubha Sankranthi (2017)

makar-sankranti-odia

Shubha Makara Sankranthi to all our readers!

Whether you call it Makara Sankranthi, Lohri, Magh Bihu, Ghughuti, Pongal, Sakraat, Khicheri, Saaji, Suggi, Tirmoori, Uttarayan or “the transition of the sun into the constellation capricorn“, we wish you all a very Happy Harvest Festival!

Part of celebrating what unites us is understanding the beauty of the variety. Sanskrit is the language that unites us and Devanagari the most accessible to us, yet greetings come in many languages and many scripts. This year’s is written in the superfun script of the Odias of Odisha (ancient Kalinga, Utkala, & Oddra). To know how they celebrate today, here is a must follow handle or two for all things Odia, including ICP’s own @Itssitu, who was featured last year with her article on Odisha Fashion.

Pongal-greetings-tamilFrom Odisha we go to Tamil Nadu and a particularly emotive Pongal, where the great tradition of Jallikattu is presently prohibited. One need not participate or even be a fan of a tradition that is important to a different socio-economic group (in this case rural), but it’s important to respect all traditions, particularly when the animal is not harmed and is in fact treated as part of the family. Jallikattu is neither Spanish Bullfighting nor Cowboy Rodeo. The animal is safe, well-treated, and it is the unarmed players who are taking the risk given the powerful bull horns and hooves. It may be more martial than most may handle, but when the animal is treated well, it’s yet another part of festival fun.

JALLIKKATTU - PONGAL FESTIVAL'S SPECIAL BRAVE ART EVENT OF TAMIL PEOPLE - Art by Anikartick,Chennai,TamilNadu,India
Art by Anikartick

For some, Makara Sankranthi is about flying kites, for others it is about drawing Kolam(Rangoli) or playing Jallikattu, and for still others, it is a brilliant bonfire, symbolising a fresh start and personal cleansing.

Punjabi-lohri-graphic

Punjab’s  Lohri (like Bhogi in Andhra’s 4 day Sankranthi) is a great utsav of aag. It is celebrated by Punjabis the world over, and symbolises that spirit in a different way. And yet, the same voices who show no concern for say trees on Christmas, suddenly do when it comes to Lohri (leave aside New Years Eve vs Crackerless Diwali).

Do what you can to preserve the tradition and petition and protest peaceably. Use facts, logic, and calm patience to make the case and point out double standards. Some connect to their culture through intellectual endeavours, others through philosophical inquiry, but most through their traditions and festivals (and the delicious cuisine that goes with them).

sankranthinepal

Makara Sankranthi is not just a Pan-Indian, but a Pan-Indic festival, and is celebrated with great gusto by our brothers in Nepal.

So whether you say Sankranthi Shubhkamnayein, Shubheccha, or Shubhakaankshaalu, from all of us at ICP, we wish you the very best!

makar-sankranti-sun-blessing

Historical Literature of India

PKVCmottoWith the Real Sheet-Anchor of Indian History established, the time has come to move forward with an exegesis on Bharatiya Itihasas. After all, if foreign sources and foreign histories have been prioritised in order to impose a false chronology and false history on India, then the reassertion of the native Historical Literature of India becomes critical.

History is Itihasa (pronounced Ithihaasa), meaning “So indeed it happened”. Historical illiterates may pretend the term only applied to the epics, but it did not. There are a number of traditional histories in regional languages like Hindi, that use the term Itihasa. Charitra often translated to history, refers to Chronicles and Vamsavalis refers to Vamsa-avalis (Family Lineages or Geneologies).

At present, the modus operandi of our sepoy historians and fraudacharyas has been to prioritise colonial Christian chronologies, foreign histories, and inscriptions. We have already discussed the issues with the previous two. But in case the reader might wonder why epigraphy and numismatics offer problems, here is the logic:

ProbWithInscriptions
[1,24]
After all, data manipulation, even by much worshipped scientists is not unheard of–why should British colonialists who back-stabbed their way to colonising India, be free from suspicion when their descendants are not? When modern academics and greedy corporations can be credibly accused of this, why are greedy Imperialists (medieval or colonial) being absolved by Post-modernists? The fact remains that expedience, rather than consistency and character, has been the by word of science-celebrities and scientism advocates. That is the importance of tradition. It actually communicates the historical memory of a people. Science can’t construct historical memory…it can only validate it.

For all the glories sung of Herodotus, forget what Indian sepoys have to sing; here is what his fellow Europeans themselves wrote about him:

AulusGellius[9, 17]

Manetho, Egyptian Historian and High Priest of the Temple of Isis ate Sebennytus, about 300 B.C.), whose works are unfortunately [or conveniently?] lost, is said to have written a book on purpose to correct the errors of Herodotus, and by Greek and Roman authors alike the titles of ‘fabler’ and ‘legend-writer’ have been freely applied to ‘the father of history’.” [10, xxv] Woods, Henry George. Herodotus. Oxford.1873.p.xxv

G.F.Abbot: “Herodotus has been called the ‘Father of History’; in truth he is only the father of story-telling; the first and most lively of our special correspondents…21: his celebrated Logoi…further vitiated by careless inaccuracy, love of exaggeration, addiction to entertaining anecdote, and indiscriminate acceptance of ancient lore—all of which properly belongs to a rudimentary age” [10,2]

So lore is ok in History when the Greeks do it, but not so much when Indians do it. This is the much-vaunted “Father of History” in the west whose sources we must place unquestioned “scientific” faith in. The real question of course is whether he is the father of history or father of hearsay.

This is not to denigrate historical sources other than our own; but rather to show what it’s like to apply the same standards foreigners apply to Indic Civilization. Scientism advocates and sepoys, of course, have double-standards.

So Homer wrote of a Cyclops and a Scylla, Herodotus of the Sun God’s intervention in the life of the Croesus, but the Mahabharata’s history of a royal family, succession crisis, and war, must be balanced by Pollockian chicken droppings, because “Science”.  No wonder this same set became chelas of self-proclaimed cultural Christian Richard Dawkins. They too are almost there…culturally. Enough. Those with unjustifiable egos and sepoy sensibilities are welcome to wallow in their own ignorance, but those with more logical inclinations can understand why the same videshis who dictated false history cannot be credibly expected to construct another. Fool me once shame on you…

As such, upon what historical materials can sincere students of history and cultured members of Indic society rely?

SourcesHistoryChelamPlot
[3,xiv]
Therefore, per Historian of Indian Civilization (knowledgeable in World history) and Traditional Brahmin Pandit Kota Venkatalachalam, this is our…

Traditional Historical Literature of India (in order of importance).

1. Puranas

2. Itihasas & Charitras

3. Vamsavalis

4. Textual & Literary Historical references (in non-historical works such as literature & math)

Other sources

5. Tamrapatras, Prasastis, and other inscriptions/epigraphy

6. Coins (and other physical evidence)

7. Foreign Histories and Travelogues

Even an orthodox Brahmin Pandit like Kota Venkatachalam was willing to accept credible and well-written histories like the Chachnama, which, due to the terrible destruction inflicted on Sindh, fills the gap left in native records. But he mentions this only after critical analysis, rather than abject intellectual slavery to all records foreign.

StrayRefs
[6,6]
He (and we) have necessarily placed foreign sources at the lower end of importance (and after careful scrutiny) for reasons he had described.

What’s more, the famous and fantastical accounts of Dog-faced men who barked [all very scientific you see] from the “[Western] father of history” are proof of why in this topsy turvy Kali Yuga, we must take their order of precedence and turn it on its head. Foreign sources and foreign opinions are of the least important to us. The accounts, texts, and traditions of our traditional scholars are the most important.

People from all jatis (castes) should have access to our Itihasa-Purana, as they are our own people, and can be trained as traditional and “modern” scholars alike. Foreigners, necessarily, should no longer have such unlimited access or unlimited importance to our primary sources and primary texts given the havoc they have wreaked on Bharat from De Nobili and  William Jones down to Doniger and Sheldon Pollock. Only fools trust foreigners more than their own people (just as only casteists support AIT — as they are eager to be adopted by foreigners…).

SelfInterestHistory
[6,7]
There may be many good-hearted non-Indians, some even who are sincere…but the sins of others necessitate our need for reducing access at this time. This does not mean being rude or disrespectful to non-Indians…only being prudent and showing discretion. That is the real reason why we study Niti and the Panchatantra. And Niti is one of the main reasons we study Itihasa (History).

Sepoys, on the otherhand, have no time for Niti. They exist only to do their masters’ will so as to retain their (undeserved) emoluments.

AITSepoys
[6,12]
The time to consign such termites, catamites, and dust mites to the dustbin has come. These intellectual equivalents of dung beetles have spewed enough foreign manure. We must reconstruct our real history, our own history, on our own sources.

NativeLiteratureHistory
[4, 12-13]
As we scrap the foreign imposed history and restore our own, it becomes necessary to study the Native Sources of History. The Historical Literature of [Greater] India.

1. Puranas
Bhagavatapurana picture
Bhagavatha Purana

The Puranas may strike one as a surprising choice for an historical source, but there is a solid, logical basis for this. The Puranas consist of more than just “legendary” and “divine” aspects. There are in fact a number of distinguishing features (lakshanas) to them.

PuranaLakshanam
[5, APP 31]
There are 18 Mahapuranas (major) and 18 Upapuranas (minor). While not all of these are sources of history, many of them, such as the Vishnu Purana and the Bhavishya Purana provide credible historical accounts, with minor reference to the fantastical. Some may wonder what the reason is for this format. In contrast to the West, which sees the Secular and Sacred in conflict, the Indic tradition recognises the harmony of the material and spiritual. After recognising the limitations of the former, we understand the transcendental nature of the latter . Only limited minds cannot see this.

PurapiNavah-hhi57

Puranas, therefore, are highly useful not just for learning history, but understanding Niti contained in it.

2. Itihasas & Charitras

RajataranginiIssues

There are numerous histories and charitras composed by our ancients. For far too often, our modernists have insisted that only literature following foreign strictures can be classified as a “history”. But this is preposterous. Different civilizations evolve different styles and philosophies. Due to the dogmatic nature of some traditions, they require a violent separation of church and state to curtail further violence. For others, adherence to the truth was so strong, that no such separation was or is required to apprehend true history.

 

TrustNativeHistorians
[6,18]
Desh drohis promoting AIT may devalue the accounts of Kalhana as mere Poetry, but the author of the Rajatarangini is an historian par excellence. Funny how the same voices who take inspiration from the name of the Rajatarangini don’t seem to have properly read it.  Following the traditional asisha/mangala (benediction) in the beginning is the convention in Sanskrit Kavya. But that never stopped Kalhana from implementing the historical method in his work.

KalhanaMotive

For this reason, although Kalhana’s magnum opus is often classified as a Chronicle, it should not be reduced to the rank of its grecian and anglo-saxon counterparts. The Rajatarangini is a proper Itihasa of Kashmir.

Kalhana discusses his methodology, expresses hesitance at describing supernatural events, and presents his topic in an informative and poetic manner.  Works of history, which frequently analyse events and their significance, are Itihasas. Works that merely collect and present annals are chronicles, which are better referred to as Charitras. The word Charita, as seen in the Buddhacharita and the Harshacharita, is naturally related to Charitra. Jain and Buddhist literature (such as Ashvagosha’s work mentioned above) naturally take their place here as well. Charitras merely describe deeds in chronological order; Itihasas analyse their significance to teach Niti and Dharma.

3. Vamsavalis

NepalVamsavali

Vamsavalis are the Dynastic King lists. These are the Royal Chronologies of Provincial Histories. Nepal is a famous example. Other Provincial Royal Chronologies also exist..

Vamsavalis-hhii

As Pandit Chelam notes, there are Manuscript copies of various dynasties that are available to this day. These involve the traditional names of the ancient provinces (janapadas/desas) of Bharatavarsha, such as Kasi, Panchala, Kalinga, Sindhu, Ujjain, etc. Some are, true to name, dedicated purely to established families of note. The Velugoti Vamsavali in the Telugu region is one such example.

Nevertheless, the historical value of these genealogies are significant. Historical material and detail is available, but must be collected and disseminated.

Another important set of historical sources comes from the records of Traditional Mathas and Agraharas. While not traditional vamsavalis in the strict sense, they are useful to supplement King lists due the repository of information regarding the guru-sishya paramparas in Mathas and families that populated agraharas and their interactions with political authority. Every head of main mathas (and Buddhist/Jain monestaries as seen in the Jaina Pattavalis which record pontiffs) of India is recorded. These lineages are as reliable as king lists and provide a means of authenticating and verifying which king ruled when based on the corresponding spiritual leader.

4. Textual & Literary Evidence

*(historical references in non-historical works such as literature & math)

TraditionHistory
[6,40]
Textual & Literary evidence refers to non-historical sources that offer historical details. Examples include discussions or references to various kings or personalities, as the Mudrarakshasa by Visakhadatta famously does. Despite being a play, it is nevertheless based on the history of the Maurya Dynasty and its famed Chancellor Chanakya.

Others can be various treatises and texts such as Kalidasa’s Jyotirvidabharana.

Nevertheless, these four categories compose the essential historical literature of India. Foreign sources have already been discussed in detail, and the nature of prasastis and tamrasasanassilpasasanas, and numistmatics is better discussed elsewhere.

The main purpose was to establish that there were and are serious historical literatures within the Indic tradition that can be relied upon. Foreign sources can be used merely to supplement. But it should be obvious to all thinking persons that Bharatiyas need not wax eloquent over Herodotus and Thucydides, when they have ample historians of their own.

In fact, the much-celebrated Thucydides has himself been criticised over the years. First on grounds of style. It seems drab prose tends not to appeal to all scholars of history, which puts to favour Herodotus, and ironically, Kalhana as well. But more importantly, on other grounds as well:

his style is often very compressed and difficult to understand, so that any translation is necessarily an interpretation.”

There are big implications here for our modern admiration of Thucydides as a historian. First, the “good” translations of his History (those that are fluent and easy to read) give a very bad idea of the linguistic character of the original Greek. The “better” they are, the less likely they are to reflect the flavor of what Thucydides wrote—rather like Finnegans Wake rewritten in the clear idiom of Jane Austen. Second, many of our favorite “quotations” from Thucydides, those slogans that are taken to reveal his distinctive approach to history, bear a tenuous relationship to his original text. As a general rule, the catchier the slogans sound, the more likely they are to be largely the product of the translator rather than of Thucydides himself. He simply did not write many of the bons mots attributed to him.

But however we choose to excuse Thucydides, the fact remains that his History is sometimes made almost incomprehensible by neologisms, awkward abstractions, and linguistic idiosyncrasies of all kinds. These are not only a problem for the modern reader. They infuriated some ancient readers too. In the first century BC, in a long essay devoted to Thucydides’ work, Dionysius of Halicarnassus, a literary critic and historian himself, complained—with ample supporting quotations—of the “forced expressions,” “non sequiturs,” “artificialities,” and “riddling obscurity.”

Real historians understand that they have a duty to communicate clearly and logically, and educate their audiences effectively, elite and mass alike. Historians engaging in non-sequiturs and abstractions are hucksters, more often than not . But then again as they say, if you cannot dazzle them with brilliance, the baffle them with…

Judging by bloviating blog ramblings popular on social media among some who think and seem like they’re smart, but not really , it is not surprising why some self-important sections think Thucydides is superior to Kalhana. No wonder they count Ayn Rand fans among their ranks…After all, these are the self-same cognitive defectives who think Indra is superior to Vishnu and believe AIT is the traditional view in India…poor souls.

The truth of the matter is, Kalhana managed to accomplish the best of both Herodotus and Thucydides. He wrote in an engaging and appealing literary style that respected tradition (like Herodotus) but also analysed history carefully using methodology (like Thucydides). He carefully reviewed the scholars that preceded him (Nilamuni, Helaraja, and Padmamihira, with 12 Kashmiri chroniclers in total), truthfully researched and recounted the history of Kashmir’s kings and queens,  and engagingly provided his analysis and useful niti for readers in a literary manner.

The Truly Learned write not to amuse themselves and dazzle and baffle their sycophants, but to educate people on the lessons of life and history. That is the true measure of an Acharya.

So let read what a real one had to say.

Here is what Bharata Charitra Bhaskara, Pandit Sri Kota Venkatachalam wrote on the matter [Emphasis and Proofing ours]

The following Post was originally published at True Indian History on August 15, 2009


Historical Literature of India

1. A.Stein writes in his introduction to Rajatarangini Westminister edition Vol. I. P. 3:— “It has often been said of the india of the_Hindus that it possessed no history. The remark is true if we apply it to history as a science and art, such as classical culture in its noblest prose-works has bequeathed it to us. But it is manifestly wrong if by history is meant either historical development or the materials for studying it. India has never known, amongst its Sastras, the study of history such as Greece and Rome cultivated or as modern Europe understands it. Yet the materials for such study are equally at our disposal in India. They are contained not only in such original sources of information as Inscriptions, Coins and Antiquarian remains, generally, advancing research has also proved that written records of events or of traditions concerning them have by no means been wanting in ancient India.”

2. H. Wilson in his admirable introduction to his translation of the Visnu Purana, while dealing with the contents of the Third book observes that a very large portion of the contents of the Itihasas and Puranas is genuine and old and writes:

“The arrangement of the Vedas and other writings considered by the Hindus–being, in fact, the authorities of their religious rites and beliefs–which is described in the beginning of the Third Book, is of much importance to the history of the Hindu Literature and of the Hindu religion. The sage Vyasa is here represented not as the author but the arranger or the compiler of the Vedas, the Itihasas and the Puranas. His name denotes his character meaning the ‘arranger’ or ‘distributor’; and the recurrence of many Vyasas, many individuals who remodelled the Hindu scriptures, has nothing in it, that is improbable. except the fabulous intervals by which the if labours are separated. The rearranging, the re-fashioning, of old materials is nothing more than the progress of time would be likely to render necessary. The last recognised compilation is that of Krishna Dvaipayana, assisted by Brahmans, who were already conversant with the subjects respectively assigned to them. They were the members of the college or school supposed by the Hindus to have flourished in a period more remote, no doubt, than the truth, but not at all unlikely to have been instituted at some time prior to the accounts of India which we owe to Greek writers and in which we see enough of the system to justify our inferring that it w as then entire.

That there have been other Vyasas and other schools since that date, that Brahmans unknown to fame have remodelled some of the Hindu scriptures, and especially the Puranas, cannot reasonably be counted, after dispassionately weighing the strong internal evidence, which all of them afford, of their intermixture of unauthorized and comparatively modern ingredients. But the same internal testimony furnishes proof equally decisive, of the anterior existence of ancient materials; and it is, therefore, as idle as it is irrational, to dispute the antiquity or the authenticity of the contents of the Puranas, in the face of abundant positive and circumstantial evidence of the prevalence of the doctrines, which they teach, the currency of the legends which they narrate, and the integrity of the institutions which they describe at least three centuries before the Christian Era. But the origin and development of their doctrines, traditions and institutions were not the work of a day; and the testimony that establishes their existence three centuries before Christianity, carries it back to a much more remote antiquity, to an antiquity, that is, probably, not surpassed by any of the prevailing fictions, institutions or beliefs of the ancient world.” (Willson’s Vishnu Purana, London Ed. P.P.LXII and LXIII.)

Again in dealing with the contents of the Fourth Amsa of the Visnu Purana, the Professor remarks:-
The Fourth Book contains all that the Hindus have of their ancient History. It is a tolerably comprehensive list Of dynasties and individuals; it is a barren record of events. It can scarcely be doubted, however, that much of it is a genuine chronicle of persons, if not of occurrences. That it is discredited by palpable absurdities in regard to the longevity of the princes of the earlier dynasties, must be granted; and the particulars preserved of some of them are trivial and fabulous. Still there is an artificial simplicity and consistency in the succession of persons, and a possibility and probability in some of the transactions, which give to these traditions the semblance of authenticity, and render it likely that these are      not altogether without foundation. At any rate,in the absence of all other sources of information the record, such as it is, deserves not to be altogether set aside. It is not essential to its celebrity or its usefulness, that any exact chronological adjustment of the different reigns should be attempted. Their distribution amongst the several Yugas, undertaken by Sir William Jones, or his Pandits, finds no countenance from the original texts, rather than an identical notice of the age in which a particular monarch ruled or the general fact that the dynasties prior to Krishna precede the time of the Great War and the beginning of the Kali Age, both which events are placed five thousand years ago…….This, may or may not, be too remote but it is sufficient, in a subject where precision is impossible, to be satisfied with the general impression, that, in the dynasties of Kings detailed in Puranas, we have a record, which, although it cannot fail to have suffered detriment from age, and may have been injured by careless or injudicious compilation, preserves an account not wholly undeserving of confidence, of the establishment and succession of regular monarchies, amongst the Hindus, from as early an era and for as continuous a duration, as any in the credible annals of mankind.” (Do. Book LXIV, LXV)

MahabharataManuscript
And lastly, in discussing the general nature of the Puranas , and of their values as historical records, he_says:-
“After the date of the Great War, the Vishnu Purana, in common with other Puranas, which contain similar lists, specifies Kings and Dynasties with greater precision; and offers political and chronological particulars to which, on the score of probability there is nothing to obiect. In truth, their general accuracy has been incontrovertibly established. Inscriptions on columns of stone, on rocks, on coins deciphered only of late years through the extraordinary ingenuity and perseverence of Mr. James Princep, have verified the names of races and titles of princes – the Gupta and the Andhra Rajas mentioned in the Puranas.” (Wilson’s Vishnu Purana Page LXX.)

3. In his Rajasthan. Col. Tod says :-

“Those who expect from a people like the Hindus a species of composition of precisely the same character as the historical works of Greece and Rome, commit the very egregious error of overlooking the peculiarities which distinguish the natives of india from all other races, and which strongly discriminate their intellectual productions of every kind from those of the West. Their philosophy, their poetry, their architecture are marked with traits of originality; and the same may be expected to pervade their history, which, like the arts enumerated, took a character from its intimate association with the religion of the people.

ln the absence of regular and legitimate historical records there are, however, other native works, (they may, indeed, be said to abound) which in the hands of a skilful and patient investigator, would afford no despicable materials for the history of India. The first of these are the Puranas and genealogical legends, of the princes which, obscured as they are by the mythological details, allegory, and improbable circumstances, contain, many facts that serve as beacons to direct, the research of the historian.”

“Another species of historical records is found in the accounts given by the Brahmins of the endowments of the temples their dilapidation and repairs which furnish occasions for the introduction of historical and chronological details In the legends respecting places of pilgrimage and religious resort, profane events are blended with superstitious rites and ordinances local ceremonies and customs. The controversies of the Jains furnish, also, much historical information, especially with reference to Guzerat and Nehrwala during the Chaulac Dynasty. From a close and attentive examination of the Jain records, which embody all that those ancient sectarians knew of science, many chasms in Hindu history might be filled up.”

Every MATHA or religious college of any importance preserves the succession of its heads. Among the Jains, we have the PATTAVALIS or successions of pontiffs, for a full and lucid notice of some of which we are indebted to Dr. Hoernle:  they purport to run back to even the death of the last TIRTHAMKARA Vardhamana-Mahavira.”(528 B. C.)

“The preservation of pedigrees and successions have evidently been a national characteristic for very many centuries. And we cannot doubt that considerable attention was paid to the matter in connection with the royal families and that Vamsavalis or Rajavalis, lists of the lineal successions of kings, were compiled and kept from very early times. We distinctly recognise the use of such VAMSAVALIS, giving the relationships and successions of kings, but no chronological details beyond the record of the total duration of each reign with occasionally a coronation date recorded in an era, in the copper-plate records. We trace them, for instance in the introductory passages, of the grants of the Eastern Chalukya Series ( See SII, I 35; EI, V. 131) which from the period A.D. 918 to 925 onwards, name the successive kings beginning with the founder of the line, who reigned three centuries before that time, but do not put forward more than the length of the reign of each of them; and, from certain differences in the figures for some of the reigns, we recognise that there were varying versions of those VAMSAVALIS. We trace the use of the VAMSAVALIS again in the similar records of the, Eastern Gangas of Kalinga, which, from A.D. 1058 onwards (EI, IV, 183), give the same deta ils about the kings of that line with effect from about A.D. 99O and one of which, issued A.D. 1296 ( JASB, L XV 229), includes a coronation date of A.D. 1141 or 1142. There has been brought to light from Nepal a long Vamsavali (by Pandit Bhagavan Lal Indraji P.H.D. Hon. and M.R.A.S.) which purports to give an_unbroken list of the rulers of that country, with the lengths of their reigns and an occasional landmark in the shape of the date of an accession stated in an era, back from A.D. 1768 to even so fabulous an antiquity as six or seven centuries before the commencement of the Kali age in B.C. 3102.”
(Quoted By M. Krishnamachariar in his History of Classical Sanskrit Literature, Introduction 38 ff.)

4. In his Rajatarangini KALHANA mentions certain previous writers.—”Suvrata, whose work, he says, was made difficult by misplaced learning; Kshemendra who drew up a list of kings, of which, however, he says, no part is free from mistakes; Nilamuni, who wrote the NILAMATAPURANA, Helaraja, who composed a list of kings in twelve thousand verses; and Srimihira or Padmamihira and the author SRI CHCHAVILLAKARA. His own work, he tells us, was based on eleven collections of RAJAKATHAS or stories about kings and on the work of Nilamuni.

Tamrasasana, or ‘Copper chapters‘ consist sometimes of a single plate but mare usually of_several plates strung together on a large signet—ring_ which bears generally the seal of the authority who issued the particular chapter. The stone records usually describe themselves by the name of Silasasana or ‘Stone-chapters’, Sila-lekha or ‘Stone-writings’,or Prasasti or “Eulogies’. They are found on rocks, on religious columns such as those which bear some of the edicts( inscription recording grants, chiefly of grants and allowances engrossed on copper plates) of Priyadasi and others which were set up in front of temples as “flagstaffs” of the Gods; on battle-columns of victory such as the two at Mandasor, on the walls and beams, sand pillars of caves and temples, on the pedestals of images, and on slabs built into the walls of temples or set up in the courtyards of temples or in conspicuous places in village sites or fields. And they are often accompanied by sculptures which give the seal of authority issuing the. record, or mark its sectarian nature, or illustrate some scene referred to in it.
_ The Chronology of Classical Sanskrit Literature starts with Mahabharata war and Kaliyuga. Kaliyuga commenced on 20th February 3102 B.C., just on the day on which Sri Krishna departed to his divine abode. The Kuru-Pandava war was fought 37 years before Kali, that is in 3139 B.C. Onwards from the commencement of Kaliyuga, Puranas contain accounts of various kingdoms that flourished from time to time and successive dynasties that ruled and fell during the course of about 35 centuries. To an impartial observer the tenor of these accounts warrants their accuracy and to the mind of the Hindu– the Hindus of those bygone ages when scepticism had not called tradition superstition—-life here is evanescent and life’s endeavour must be the attainment of beatitude eternal. Ancient sages (Rishis perceived the divine hymns of the Vedas and passed them on for the edification of posterity. Since the advent of Kali, a prospective crop of vice and folly was predicted and to wean the erring world from such sin and misery, Vyasa formulated Puranas with the object of Vedopabrinha, that is, supplemented the exposition of Vedic teachings, and that in the garb of a language and narrative that would be easily assimilated by the masses. To such philosophical minds, the rise and fall of kings and kingdoms was not worth remembrance, save as another realistic means of illustrating the tenets of philosophy, e.g., the truth of the divine essence, Brahman, the unreality at sensual pleasures, the liberation of individual soul and the attainment of eternity in beatitude or oneness with the Spirit Divine and above all the inevitable occurrence of God’s mandates shortly termed Destiny or otherwise called Kaala or Niyati.
If this is the object of Puranic literature, it is a sacrilege to charge the author or authors of them, whoever it was, with having fabricated scriptural testimony for attributing an antiquity to Indian literature and Indian civilization, which it did not possess; for even if they had been, as many orientalists have said, made up late after the Christian era, the authors would not have anticipated this method of political history of the 18th and 19th centuries A. D. The Puranic lists of dynasties of kings and kingdoms furnish details of dates to an extent that even in days of historical records may be surprising, for they mention even months and days in their computation. Whatever those ancient authors did or wrote, they did it with sincerity and accuracy, ‘truth’ being the basis of accuracy. Our educational institutions are saturated with the teachings of modern scholars on the untruth of these Puranic accounts, but it is still hoped that time will come when truth will triumph and display a real orientation of ancient Indian History.
(P. P. XXXVIII — XLIV History of Classical Sanskrit Lit. By_M,· Krishnnmachariar) (38 to -44 pages)
( F, E. Pargiter has given an admirable summary of Early Indian Traditional History, as recorded in Puranas in JRAS (1914) 267 et seq.) _


NoForeignHistory
[7,20]
It is unsurprising that the pedantic but puerile would think to give priority to the videshi on everything from civilizational origin to empiricism. This is why verbosity and complexity is not the measure of intelligence, but rather clear logic with actionable solutions. This is why pedantic parrots do not offer any of the latter.

Just at the time when Bharatiyas are reasserting ownership of their own heritage, this band of do-nothing dimwits proceeds to emphasise the need for foreign sources to make ours more “scientific”, which is code for secular. Funny how the same cabal  of casteists is quick to drop their gotras to assert authority, while doing everything possible to undermine the historical tradition maintained by real brahmanas like Pandit Chelam.

If science is the new religion, and every culture is considered “more scientific” than your own by sepoys and gyaanis,  is it any wonder that misguided youth seek to convert to every civilization but your own? Science cannot be religion. Science does not replace tradition.

Contrary to fraudacharyas who seek to undercut and supersede astika Brahmin Pandits like Kota Venkatachalam, traditional Bharat did have “real history”. But history is not science. How could it be?  The data is imperfect. Other than some epigragraphy and numismatics, it is not verifiable (unless you have a time-machine). And the results are never the same, but as Mark Twain asserted, they do “rhyme”.

HistoryNotScience
[3,xxi]
That is the danger of scientism. It seeks to impose the ramblings of scientifically credentialed propagandists, imagining credential in one area as credential to speak in another (Vedic tradition). It seeks to use the credibility of the profession of science to force eminently unscientific conclusions, as the Christian Historians who pushed the Biblical Chronology and the Hearsay using Herodotus’ fantastical views of India (dog-faced men who bark). And for all the glorification of Persian chroniclers of Turk invaders, the propaganda and fallacies of Ferishta et al are well known to those who actual analyse what they read…rather than read and regurgitate like parrots.

NoForeignHistory

Pandit Chelam himself criticised many of the conclusions of Hieun-tsang as unreliable and poorly informed. As such, foreign histories and observations of travel writers are useful to provide other perspectives and to fill in gaps. But the notion of using them to “balance” our own tradition is absurd as the theories these ahankari-shikandis push (“ait”, “Indra superior to Vishnu”, “Ramana maharishi had mental problems”). Like the vesya of yore, these academics-vaisya sold out to the highest bidder; all they have are sinecures, “sybaritic” nonsense, and (questionable) gotras to salve their egos. Real Brahmanas know better, and recognise the logic of actual Historian Pandit Chelam’s conclusions.

The time for rejecting the colonial histories and their sepoy enforced foreign sources has come. The time to reassert the primary and predominant place of our native historical sources is here.  It is time to prove worthy of our inheritance.

samudrahorse


References:

  1. True Indian History. [Various Blog Bosts]
  2. Kota, Venkatachalam Paakayaji (Pandit). The Age of the Mahabharata War. Vijayawada: Tirumala.1988 (posthumously)
  3. Kota, Venkatachalam Paakayaji (Pandit). The Plot in Indian Chronology.Vijayawada: Arya Vijnana. 1953
  4. Kota, Venkatachalam Paakayaji (Pandit). Chronology of Ancient Hindu History Part I. Vijayawada:AVG
  5. Kota, Venkatachalam Paakayaji (Pandit). The Age of Buddha, Milinda, and Amtiyoko. Guntur: Sri Ajanta Printers.1956
  6. Kota, Venkatachalam Paakayaji (Pandit). Chronology of Kashmir History Reconstructed. Guntur: Sri Ajanta. 1955
  7. Kota, Venkatachalam Paakayaji (Pandit). Chronology of Nepal History Reconstructed.Vijayawada: SahiniPress. 1953
  8. Kota, Venkatachalam Paakayaji (Pandit). Chronology of Ancient Hindu History Part II. Vijayawada:AVG
  9. Aulus Gellius: Young, Arthur Milton. Echoes of Two Cultures. University of Pittsburgh.1964.p.17
  10. Foster, Edith & Donald Lateiner. Thucydides and Herodotus. Oxford. 2012. p.2
  11. Dawkins: I’m a cultural Christian. http://news.bbc.co.uk/2/hi/uk_news/politics/7136682.stm
Acknowledgment: Our sincere thanks to Sri G.D. Prasad garu, grandson of Pandit Kota Venkatachalam for his kind permission to reprint these articles and excerpts.

Indic Sports: Culture of Kreeda

KrishnaVsChanoora

Amid all the discussion on one of India’s worst ever showings at the Olympics, a question arises about the Indic proclivity for Sports. As one foreign commentator recently asked, “Why is India so bad at the Olympics”. While we should not forget the legitimate point that the Olympics is no stranger to skullduggery, as the entire Russian Olympic Team and poor Narendra Yadav can attest to (his case should be reviewed again by an independent commission of concerned citizens), self-reflection is also critical.

Our own people have made attempts to understand. Others, to analyse. Interestingly enough, the Chinese have already conducted an analysis. And if it is authentic, it seems fairly spot on—after all, no one knows you better than your own shatrus, declared or undeclared.

Of course, by now, we’re all familiar with Indian twitter’s flooding of fading C-list celebrity Piers Morgan’s TL.

The more embarrassing aspect, of course, wasn’t Piers Morgan (unceremoniously fired from his pathetic hosting at CNN ) and his blunderbuss badinage. Rather it was that Indiots still clamber after the 2 pence opinions of a brit  “nobody-cares” after 70 years of Independence. See what nationality brought it to this professional troll’s attention in the first place.

Why do we care whether they care? Why do we care what they think? Rather than be upset about what they said, do something about what they see…next time. It’s not his place (or any foreigner’s place) to tell us, but he is right…be embarrassed. All praise to not only the two medalists Sakshi and Sindhu, but all the fourth placers like Abhinav Bindra (former gold medalist) and hardscrabble athletes who fought against all odds (Dipa Karmakar). But while giving them credit, criticise yourself. You are to blame.

If you only obsess about one sport and don’t give viewership or patronage to others…you are to blame. If at 36 years of age you still divine over the chicken droppings of yester-year celebrities of a certain sport, yes you are to blame. And if you still obsess over genetics rather than training, yes you are to blame. All these things breed and re-emphasise inferiority complexes, because only being good at one thing and useless at everything else, makes for good poodles, but incompetent individuals.

The root of this, frankly, comes from continuing to prize colonial culture (English—see the undistinguished Germanic dialect in which I must write this article, literature, and of course, cricket) long after those with self-respect have stopped caring. The root of the Indian lack of self-respect comes from lack of leadership. And the root of the lack of leadership comes from lack of team spirit and team sports. Even if the other team is better than you, it is only the Indiot who publicly accepts it and publicly self-flagellates about it, instead of privately doing something about it. It is not the size of the dog in the fight, it is the size of the fight in the dog. All the more so if he works as pack.

In any event, the obsession with the colonial game of cricket aside, it does lead to a natural question—have Indians been traditionally averse to Sports? The answer is an obvious NO (even the traditional 64 Arts mentions “Skill in youthful sports” as one of them). For social media gyaanis on public journeys of self-discovery: there have been entire books written on this matter. Nevertheless, this rather ridiculous question is primarily due to the modern tendency in the knowledge-based economy to only focus on two aspects of traditional societal Dharma. That physicality and team collaboration are required by the other two are well-known, and in all likelihood, explain the current decline for internal collaboration and penchant for external cooperation. Until the concept of “win as a team” is beaten soundly back into the heads of headstrong, overly-proud know-it-all yet “under-informed” Indians, such embarrassing showings are all but predictable. The repeated failure of Leander Paes and Mahesh Bhupathi to work together for national honour is one such example.

That is why culture is so central to the problem Indic Civilization faces. The same hypocritical hindus who whine day in day out about why medieval Indian kings didn’t work together, are the least likely to do the same today. But as we covered in our previous article on the Dharma of Collaboration, it is not some single “delicate genius” who diffuses victory through sheer, incomprehensible levels of self-proclaimed “IQ”, but a competent society dedicated to team success. In fact, we specifically used the example of the American Olympic Men’s Basketball team in our Post on Collaboration above.

Individually brilliant people who don’t work together, will, time and again, be defeated by average people who work together very well. Not just the players, not just the organization, but society and civilization as a whole should serve as secondary and tertiary support structures. The problem is while stuffing their face with hakka noodles, most Indians would in fact rather watch and play “kircket”, a near individual sport, with tennis, an actual individual sport, filling the remaining void.

Genius and Genetics (and TFR) provide a baseline (pun intended). These keep you in the game and provide a reservoir of potential. But unless there is training,dedication, and above all, (internal) collaboration, this potential energy, cannot be turned into kinetic energy, let alone kinetic action. Feckless, penny-packet, eleventh hour-last minute efforts are no more advisable than an all-nighter before the JEE or the EAMCET. That is why the spirit of Kreeda, true Kreeda, team Kreeda, must be re-ingrained in the modern Indian.

The renowned Chinese travellers Hieun Tsang and Fa Hien wrote of a plethora of sporting activities. Swimming, sword – fighting ( fencing, as we know it today ), running, wrestling and ball games were immensely popular among the students of Nalanda and Taxila. In the 16th century, a Portuguese ambassador who visited Krishnanagar was impressed by the range of sports activity, and the many sports venues, in the city. The king, Raja Krishnadev was an ace wrestler and horseman, himself. [1]

Kreeda, of course, is most famous to us due to the infamous dyut kreeda from the Mahabharata. But Kreeda is more than just mere gambling or pass-time amusement. It in fact covers a range of activities, some mental, some physical, some recreational, and some martial. I am deliberately leaving out “kircket” because that colonial game is really an individual sport masquerading as a team one—and it is also one of the twin causes for the catastrophic decline in Indic competence…the other being mass masala films. However, I will purposefully add a non-native game, field hockey, because it is one of the sports that for a variety of reasons, must be emphasised, invested in, and encouraged today.

I should also note that full credit goes to our teammates over at Tamizh Cultural Portal for presciently recognising the importance of this and doing something about it long before we did. While we will build upon the foundation they laid, we recommend first a full read of their excellent section here.

For our purposes however, what are the various aspects of the traditional Indic culture of Kreeda? This list is by no means exhaustive and is meant to serve as a preliminary structure upon which we can continue to build.

  • Martial Arts
  • Sports
  • Games
  • Personalities
Martial Arts

Kalaripayattu_weapons

Kreeda literally means “Sport” or “Play”. Yet despite including the harmless and the childhood amusement, it also extends to the violent and martial. While these may have had applications on ancient battlefields, or for self-defence, they can also be engaged in harmlessly by responsible adults, for recreation.

It is unsurprising that martial arts would be so closely related to sport in general. Just as neuroscientists assert that dreams help us simulate and deal with difficult scenarios in the future, so too do sports help us deal with the martial and security scenarios of life. One look at the Afghan game of buzkashi alone shows the type of tactics used by Central Asian horsemen on medieval battlefieds. Karate and Kung Fu are, naturally, more famous and more obvious in their applications. Lesser known, and more important, is that Classical Martial Art of India from Kerala.

Kalaripayattu

kalaripayattu-martial-art-of-kerala-500x500

The famed martial art of Kerala, Kalaripayattu has become the de facto classical Martial Art of India. Rooted in Dhanurveda and Ayurveda respectively, it demonstrates the Indic origin of the concept of vital points (marmas), showcased in a certain hollywood movie. Indeed, it is considered the origin of the great spiritual East Asian martial arts traditions, such as Kung Fu and Karate. Tradition holds that the Buddhist monks taught it to the Chinese at the Shaolin Monastery. This is considered by many to have led to the development of Kung Fu and the martial arts tradition of the East. [8]

kalari_lock

Kalaripayattu is practiced to this day in its home state. Beyond the energetic and acrobatic armed and unarmed combat, it features both men and women practitioners hailing from different jatis, nationalities, and even age groups.

kalarilady

But why simply read about what you can see. Here is a well-known video of an elderly women trained in Kalari, fighting against a man half her age!

Malla Yuddha

20130125175804-malla-yuddha

Malla Yuddha forever has a place in the hearts of the Hindus for the great wrestling bouts not only between Krishna and Chanoora and Bheema and Jarasandha, but even today. While the Olympics predictably favours greco-roman style, there are many wrestlers in India, both male and female, folk and entertainment.

200px-Khali_cropped
The Great Khali of the WWE

There are some who might add pehlwaan, but it is about as Indic as qawwali. Malla Yuddha is our traditional name, and should be the terminology. There are none, however, who are more famous or beloved than the man who played Hanuman in Ramanand Sagar’s Ramayan.

Dara_Singh_with_Wrestling_Cupdharas012hanuman

Wrestling historically takes place in Akharas, and there are many such even today.

Mushti Yuddha

With descriptions dating back to the ancient period, and texts such as the Manasollasa, Mushti-Yuddha is the traditional Indic art of Boxing. The Portuguese visitor Nunez was astonished at how ferocious the style of boxing was in the Great City of Vijayanagara. [2]

Boxers could routinely end up with broken teeth or battered eyes. While the modern era demands a bit more consideration for the health and safety of boxers, perhaps it is time to look to the past to take inspiration for our future.

Gadha Yuddha

Archery may be the most iconic and most common, but quite possibly no martial art remains as dear to the Indian imagination as Gadha Yuddha. Whether it is Balarama, Bheema, Duryodhana, or Lord Vishnu himself with his famous Kaumodhaki, the mace has a celebrated place in the hearts of Hindus. The rules for Gada Yuddha are simple…no hitting below the belt. But the rules for Dharma Yuddha demand the destruction of dushtas like Duryodhana, who himself cheated at Dice and committed injustice against Draupadi.

Gatka

The Armory of Gatka Practitioners

Like Kalariyapattu, Gatka (the great martial art of the Sikhs) is less for spectators and more for warriors. Nevertheless, the need for self-defence aside, it offers a number of potential competitive aspects beyond the obvious fencing. The Charkha (chakra) throwing aspects alone offer potential for competitive sport.

Officially dating back to the venerable Guru Hargobind Singh ji,  “Gatka can be practiced either as a sport (khel) or ritual (rasmi).” It features aspects of armed and unarmed combat, as can be seen above. It is practiced to this day.

More importantly however, again like its Southern counterpart, Gatka is a direct connection to the ancient Indic warrior ethos. It is an outgrowth of traditional Sastra-Vidya, which in Punjabi is called Shastar Vidya ਸ਼ਸਤਰ ਵਿਦਿਆ, but has become a tradition in its own right. Sikh Dharma may be centuries old, but it draws from and is part of a millennia old Dharmic Civilization. Whether for sport or for safety, preserving and passing on its proud traditions remains important for Sikh, Citizen, and Soldier alike.

Dhanurvidya

arjuna-draupadi-swayamvar-mahabharata

From Rama Dasarathi to the modern Limba Ram, archery has long been considered the crest-jewel of Indic Kreeda. Equally valuable on the pre-modern battlefield as it was before a bullseye (or as above, below a fish eye), prowess with a bow was prized by men and women alike. Draupadi may have rejected Karna despite his skills with a dhanush, but Arjuna still had to prove himself to her in order to win her hand.

Boxing and wrestling are often referred to, but were not generally the hobbies of respectable young men…who performed for the amusement of an audience. The archery contest, however, was a much-loved amusement of the warrior class, and vivid descriptions of such contests occur in the Epics.”[2, 209]

Even Bhagavan Shri Ram had to demonstrate his power, by stringing the great bow of Lord Shiva. Such is the central place of Dhanurkrida, Dhanurvidya, and Dhanurveda in our culture.

Traditional Sports

Beyond martial arts, there are many traditional Sports that owe their origin to the Indian Subcontinent. Some are popular, some are regional, but all are part of the panoply of Bharatiya Kreeda.

Kabaddi

Part-game, part-sport, all excitement, Kabaddi is instantly recognisable to the average Indian, and an increasingly profitable business venture. Well-known to children and adults of all ages, it is now on track towards becoming a spectator sport in India, and perhaps even, other counties.

Not only national leagues in India, but many among the diaspora are making their mark.

Kabaddi is a high intensity contact sport, with seven players on each side; played for a period of 40 minutes with a 5 – minute break (20-5-20). The core idea of the game is to score points by raiding into the opponent’s court and touching as many defense players as possible without getting caught; in a single breath. One player, chanting Kabaddi!! Kabaddi!! Kabaddi!! Charges into the opponent court and tries to touch the opponent closest to him, while the seven opponents maneuver to catch the attacker.

Jallikattu

Banned by the Supreme Court on controversial and discriminatory grounds, Jallikattu is the traditional game of Bull-taming of Tamizh Nadu. While there are variants in other parts of the country, unlike Spanish bull-fighting, the animal is left alive and unharmed. It is only the players, who play voluntarily, who may be under any risk. Such is their veertha (warrior spirit).

Mallakhamba

Malkhamb_team_of_the_Bombay_Sappers

This legendary sport was revived by the Chhatrapatis for the purposes of the Maratha Navy and its multi-masted ships, but Mallakhamba is the ancient art of pole gymnastics. It is conservatively dated to the medieval period, but in all likelihood, is much more ancient.

Mallakhamb dates back to the 12th century and finds reference in the classic Manasollasa (1135 AD) by Somesvara Chalukya. [9]

It is still done today by the Bombay Sappers of the Indian Army. There is a push to make it a more popular sport.

Games

The distinction between Sports and Games is often very difficult to discern. There are many Sports with limited physical exertion (Golf) and many games with a surfeit of Physical Exertion, Kho-Kho. Which is which is a matter of subjectivity, but board games, card games, and school yard games, all fit the bill more for game than for sport.

Chess

ChessSet

Traditional and especially Ancient India had many games of which to boast, but the king of them all was the game of kings: Chess.

Foreign deniers may be a plenty (with Europeans, Chinese, and even the Persians attempting to claim it), but there is no denying Chess originated in India. Bharatavarsha can boast of not only the ancestor to Chess (Chaturanga), which featured as many as four players and used dice,  but the precursor to the modern version that “had developed into a game of some complexity, with a king-piece, and pieces of four other types, cor-responding to the corps of the ancient Indian army–an elephant, a horse, a chariot or ship, and four footmen. “[2, 208]

Radha-Krishna_chess

The earliest reference to Chaturanga is found in the Harshacharita of Banabhatta, dated to the 6th century.  It is said to have spread to China and was the ancestor of many strategic games there as well.

In the 6th century the game was learnt by the Persians and when Persia was conquered by the Arabs it quickly spread all over the Middle East, under the name shatranj, the Persian corruption of caturanga.” [2, 208]

While many have attempted to claim it, in whatever form, it is an Indian original, with the only distinction that matters being between the Indian version and modern Chess. The irony, of course, is that while Indians have produced Grandmasters and champions like Viswanathan Anand and Koneru Humpy, they continue to succeed at Chess yet fail at strategy. Perhaps it is time to view Kreeda as a way to win at life.

Dyut Kreeda

dyutkrida
The Infamous Dice game, and the Chaupad board

The Infamous Game of Dice naturally makes its place in the rankings. Gambling was obviously popular in ancient India. “Six-sided dice have been found in the Indus cities, and the ‘Gamester’s Lament’ of the Rg Veda testifies to the popularity of gambling among the early Aaryans“. [2,207]

The word aksa in the context of gambling is generally roughly translated ‘dice’, but the aksas in the earliest gambling games were not dice, but small hard nuts called vibheesaka or vibheedaka; apparently players drew a handful of these from a bowl and scored if the number was a multiple of four.” [2, 207]

Played on the chaupad board, it was a popular recreation not only between rival kings, but those other famed competitors in life: husband and wife.

Dice may have been popular in Ancient India, but it remains relevant even in the modern Era.

Mokshapatam

We all may be familiar with the childhood game of Snakes and Ladders. Less familiar, however, is how it originated in India.

Even the traditional game of snakes and ladders had a traditional name “Mokshapatam”. The roles of the devas are likened to it, as fulfillment of one’s role results in promotion up the ladder of creation. It was, therefore, based upon the principle of Karma. The Jain version was called Gyan Chaupar.

Gyan_chaupar

Kreedapatram

Often called Ganjifa, Kreedapatram is the ancient name for Indian card games, of which there were many. Traditional Indian cards were round, but the variety of games were plentiful, and it is still a popular pass time to this day. Here one effort to revive one.

Kho Kho

The game of kho kho is very simple and can be played by all ages. It is thought to have originated in Maharashtra, and it is considered one of India’s most popular traditional games. It is described as a “modified form of run and chase“. [1]

Each team consists of twelve players, but only nine players take the field for a contest. A match consists of two innings. An innings consists of chasing and running turns of 7 minutes each. Eight members of the chasing team sit in their eight squares on the central lane, alternately facing the opposite direction, while the ninth member is an active chaser, and stands at either of the posts, ready to begin the pursuit. Members of the chasing team have to put their opponent out, touching them with their palms, but without committing a foul. All the action in Kho-Kho is provided by the defenders, who try to play out the 7 minutes time, and the chasers who try to dismiss them. A defender can be dismissed in three ways: 1) if he is touched by an active chaser with his palm without committing a foul, 2) if he goes out of the limits on his own, 3) if he enters the limit late. [1]

Gilli-danda

Well known to children in school yard throughout India, Gilli-danda is a game of sticks.”The bigger one is called “danda” and the smaller one is called “gilli“. The player then uses the danda to hit the gilli at the raised end, which flips it into the air. While it is in the air, the player strikes the gilli, hitting it as far as possible. Having struck the gilli, the player is required to run and touch a pre-agreed point outside the circle before the gilli is retrieved by an opponent.” [10]

It may not have applications to stadium spectator sport, but Gilli-danda remains another Iconic game of Indic Civilization.

The Spirit of Kreeda, more than anything else, is one rooted in Team spirit. What is the Indic word for team?—perhaps therein lies the problem as most of our gyaanis seem to have forgotten it (if they ever knew it). Various words such as dal, vahni, and prayuj have been used. Due to a combination of semantic politics and narrative aesthetics, the last one is likely best suited for our times.

There are many, many, many more sports and games such as Boat racing, Polo, and various ball games which could be discussed here (and are discussed elsewhere). But either their origins still remain uncertain, or concision demands we focus only on a few here. Nevertheless, it is easy enough to see here that there has long been a tradition of Sport, a culture of Kreeda, throughout Bharatavarsha. The issue before us is not only whether we can revive them, but whether we can take inspiration from them to reinvigorate our approach to Modern Sports.

Modern Sports

Field Hockey

dhyanchand

From Dhyan Chand to the recently deceased Mohd. Shaheed, India’s field hockey heroes are perennially over-shadowed and under-appreciated it. It is time we did them justice. Naysayers may argue that football should be the priority non-native sport stressed by Indians, but I disagree. Indians already have a strong traditional track record in Field Hockey. To see short term results, Field Hockey will give us the best ROI, and boost in national sports morale.

Football (also known as Soccer)

Quite possibly one of the most simple and most easily recognisable of games, Football is an international phenomenon. It does not carry weight because a nation of a billion people, and some former colonies and their erstwhile coloniser play it, but because the entire world plays it. Kick the ball into the goal, pass to your teammates, defend your territory. It is the simplest most elegant expression of team collaboration. Everything a certain wicket-based sport is not.

Football must be an important long-term investment for the Indian public not only because Baichung Bhutia was popular with the ladies (ok that’s a private reason for gents), but because it remains the uncontested “Global Sport”. To see much smaller countries and even non-South American/non-European/non-African countries be ranked and notable teams should be a national insult for India. This is the cost of cricket.

Non-native sport though it is, it is the unofficial game of humanity (at least at present) and even if a World Cup is unthinkable and a distant dream, it should begin to at least be an aspiration. Even if you can’t play, start watching these games, start forming football leagues, and start joining your kids in a sport that will actually help them in life, even if they can’t become the next Ronaldo.

Personalities

Along with remembering our traditional sports and games, and the culture that drove them, it is also important to remember and honour the great personalities who contributed to our Sports culture. Such lists are usually subjective, but certain names tend to crop up, and thus, are mentionable either for merit or for fame. In any event, they should be remembered nonetheless:

Women

Kunjarani Devi

Karnam Malleshwari

India’s first female olympic individual medalist, Malleshwari Karnam hails from Andhra.

P.T. Usha

Mithali Raj

Anju Bobby George

Saina Nehwal

P.V.Sindhu

Sania Mirza

Sakshi Malik

Anushka Sharma may have played a wrestler, but young Sakshi Malik is the real deal. Champion wrestler and Olympic Bronze medalist, she deserves our respect (and a healthy fear for her strength…) for what she accomplished. She is proof again that the Bharatiya Naari may be seen as a pretty package, but packs a powerful Shakti too.

Mary Kom

Dipa Kalmakar

Dipa Kalmakar represents not only the potential reservoir of talent in India, but of simply how much of a difference a culture of training and support (institutional or societal) makes. That she was able to place fourth despite being the first Indian woman to even compete in Olympic gymnastics, speaks volumes about the greatness of her spirit, and why India citizens need to stop talking and start putting their money where their mouth is to support such athletes.

Men

Dhyan Chand

Ravi Shastri

Dara Singh

Dara Singh ji may be most famous for playing Lord Hanuman, but he was a great strong-man in his own right, in his own day. He may have been a champion Pehlwaani, but Dara Singh would have been right at home in traditional Malla Yuddha.

Limba Ram

Viswanathan Anand

Vijay Amritraj

India’s greatest tennis player who never won a Grand Slam. Perennial top ten threat, international celebrity, and one of India’s most recognisable sports figures, Vijay Amritraj of Tamizh Nadu represents Indian Sports almost to the T. Full of talent, with many missed opportunities, and the potential to dominate, only if he trained like the Borgs and Connors and Mcenroe’s of the world.

Mohd.Shaheed

Dhanraj Pillai

Sachin Tendulkar

Saurav Ganguly

Kapil Dev

Sunil Gavaskar

Harbhajan Singh

Navjot Singh Sidhu

Pullela Gopichand

Mahendra Singh Dhoni

Abhinav Bindra

Leander Paes

Baichung Bhutia

Considered India’s greatest football player, Baichung Bhutia should be a household name simply for the effort he has put in to popularise the sport and give support to young talent. This now retired “Sikkimese Sniper” started a football school in Delhi.

Vijender Singh

Olympic and now up-and-coming Professional Boxer, Vijender Singh is an athlete to watch for. He hails from Haryana. With a current W-L ratio of 7-0, he is a true Mushti-Yoddha in the making.

Most of these personalities are well-known enough that they do not require description. All of them, for the sake of brevity, are from India. But over time, we hope to add on to this and describe in greater detail.

Conclusion

winasateam

India is not a sports averse culture. India does not lack a sports culture. India lacks a team sports culture. That is the problem today. The cure for its millions upon millions of middle class, mummy’s boy, spoiled brats, does not lie in Sachin Tendulkar, but in Dhyan Chand, who played a true team sport. It does not lie in importing yet another foreign coach (or foreign saviour), but in building in-house talent through team thinking.

Kircket” is not a team sport. It is effectively an individual sport played by a team, with very little equipe-wide coordination. But between fire-teams and the entire army, there are intermediate levels of multi-person units (company, battalion, division, etc). The problem with Indians is that they forever vacillate between tyranny and sycophancy. “Kick the person who licks, and lick the person who kicks”. This is the “team” motto of our iq obsessed, barely genetically male gyaanis. How about doing neither? How about respecting authority and treating subordinates with respect? Even the Indian Army’s officers could learn this simple principle.

The concept of the loyal lieutenant is utterly lacking. Rather than a first among equals, it is “I must either oppress or be oppressed”—how is unity, team spirit, and coordination possible in such a toxic atmosphere?

kreedagames

Kreeda also has been able  to create awareness by documenting information on traditional games. “We can get a lead for a game from anywhere, even the most unlikely places. The history of some games are unknown and some have many versions, but we do everything to find and get to the bottom of it. I can give you the history, origin and rules of any game!” she beams. [5]

There are many efforts to revive not only traditional sports but traditional games today. Instead of just playing whatever Star TV tells you is “fashionable”, support these efforts and revive these games. Instead of snakes and ladders, play moksha-patam. Instead of playing hide-and-seek, tell your kids to play kho kho.

For all his obsolete lameness, Piers Morgan was right about one thing: Indians need training (just as he and his fellow brits need therapy). Even more pathetic than the 2 medals (Indian men, be ashamed of yourselves), is the fact that Indians not only don’t know how to conduct themselves, they don’t care to learn. “Absolute subservience. Or Unrestricted freedom of action and pontification”. No wonder Indians can’t get anything done unless it’s for a foreign MNC or for a paycheck or for punya…For anything else, it’s “Either I or my caste-brother is team captain, or I don’t play!

This is why for all the gyaani obsession over “merit” (i.e. ability to read and regurgitate for marks), the focus for positions must be “competence”. Are you competent to do the job? Are you competent to contribute to the organization? Despite your knowledge, are you competent to work in teams? When it’s an idiot Indian movie and the theme is “me against the world” the concept of team disappears. When you are forced to work and win as a team, however, then questions of competence (rather than marks and parrot pedantry) come up. See, incompetence. The national slogan should be Work Hard, Play Hard. Not the present one: Work only if I have to, Play only if the mood strikes, and Eat & Drink always.

It is time to get rid of this recipe for incompetence. It is time to throw away the bipolar monkey of the past century and rebuild the national character. Bharatiya Kreeda is one way to do it. Pick a team sport (a real sport, kircket doesn’t count) or team game, and begin today.

Being a single-line sports country has made obstacles for development of other sports in the country. You might be able to name the whole team that represented the country at the 2011 Cricket World Cup, but most of you would not know who PD Chaugule was. Chaugule was the first Indian who represented the country at the 1920 Summer Olympics in Belgium and took that same oath: “For the honour of my country, and glory of my sport. [7]

Many of you may still wonder, why despite all insistence on the Indic, we have given pride of place to a non-native sport like Field Hockey. Beyond just ROI, beyond even national sports morale, it offers the potential for something else. Something that, amid all the religious wars, and caste wars, and petty feuds, gives a vision of greater possibilities. If divide et impera was the motto for foreign imperialists & native sepoys, then the one for all true patriots and rooted Indians should be simple….

I am no SRK fan, kintuChak De India.

References:
  1. Traditional Indian Sports. http://sports.indiapress.org/ancient_indian_games.php
  2. Basham, A.L. The Wonder that was India. New Delhi: Rupa.1999
  3. http://www.ranker.com/list/famous-female-athletes-from-india/reference
  4. http://indiatoday.intoday.in/education/story/games-in-india/1/475954.html
  5. http://www.newindianexpress.com/cities/chennai/The-tradition-of-playing-long-forgotten-games/2016/08/17/article3582674.ece
  6. http://indianexpress.com/article/lifestyle/books/the-plays-the-thing-a-history-of-sport-in-india/
  7. http://www.sportskeeda.com/cricket/sports-fanaticism-in-india-history-and-where-are-we-today
  8. Sreenivasan, Rajeev. The Buddhist Connection: Sabarimala and the Tibetans.http://www.rediff.com/news/dec/31rajeev.htm
  9. http://www.telegraphindia.com/1111103/jsp/orissa/story_14698853.jsp
  10. http://www.thebetterindia.com/10492/lesser-known-traditional-games-sports-india/
  11. http://www.newsgram.com/ganjifa-an-indian-card-game-is-revived-by-sunish-chabba-of-sydney-australia/
  12. http://www.hindustantimes.com/punjab/gatka-a-traditional-martial-art-associated-with-sikhism-now-a-national-sport/story-RTMaURkzAMlaRPtb5jMlDN.html

Shubha Krishna Janmashtami (2016)

krishnashtami2016From all of us at ICP, Happy Sri Krishna Janmashtami! Shubha Janmashtami! Janmashtami shubhkamnaye!

For those of us who know he was no mere myth, but left this Earth in 3102 BCE, this day is especially sacred, as a reminder of the validity of the Mahabharata’s message.

sri_krishna_janmashtami146-309x250

Struggles against Adharma are there now more than ever. Even our traditions stemming from Krishna’s life are not being spared. What do the people do?

Dahi_Handi

It is why the time has come for people to not just sing “Hare Krishna”, but to take a page out of the Karma yogi’s book and do their karma. Between aggressive and passive is assertive. Learn from Sri Krishna and understand how to work together to effectively and legally preserve your interests, traditions, culture, and above all, preserve Dharma.

And remember, whatever the odds against you, Yatho Krishna tatho Dharma. Yatho Dharma, tatho Jayaha! Jai Shri Krishna!

 

tkrishna2

The Real Sheet Anchor of Indian History

File:Mahabharata BharatVarsh.jpg

From the mists of legend to the waters of memory called history, it is a long process, and to some, may indeed appear to be a long leap. But let it be stated upfront that history is indeed history. Just as Science requires reproducibility and verifiability, so too does history require evidence and documented proof, and above all adherence to the truth.

ChelamHistoricalDeterminePandit Kota Venkatachalam [2, 11]

As we have demonstrated through this Series of Posts…

  1. An appeal to Young Indologists
  2. Aryan Invasion Theory Violates Vedic Tradition
  3. Who were the Yavanas?
  4. Personalities: Sagara
  5. Vedic Cosmology—The Dharmic View of Time

…Indian history has been subjected to much intellectual violence, and the case of evidence such as the Kumbhalgarh inscription, outright physical violence. Selective interpretation, foreign racial glorification, colonial expedience, document fabrication, and evidence forgery have been the tools of the trade of history’s most dishonest cabal of “historians”.

The most skilled propagandists are not those who claim obvious falsehoods, but rather, state selective and half truths. What is credible and plausible is often the most incorrigible…of falsehoods. Unlike the True Brahmanas of yore who preserved and passed on our Tradition and History, these Racist-Imperialists have no religious injunction to speak the truth (or to feel shame…). Indeed, contrary to their self-apotheosis and perennial self-lionising, the British were able to take control of India not through some Gandhian described physical or martial superiority, or even technological marvelry, but rather, through deception.

As the Oxford Military History of the World would credit, it was British mastery of subcontinental politics (a.k.a. deception and back-stabbing) that ensured their control of 200 hundred million souls. It is also an abject lesson of what happens when you only consider “Rajniti” rather than Niti and Dharma. This parampara of foreign ‘intellectuals’ committed intellectual violence against our texts, tradition, and history. Their tradition continues today in its “post-modern” incarnation, wherein even the Ramayana date from the Colonial era has been brought down from BCE to CE, all by the supposedly secular poco-pomo gang. Even Chanakya-Kautilya has not been spared, and is now being denied, not on the basis of new evidence, but on the basis of new “interpretations” of evidence and ostensible tampering of evidence. Enough benefits of the doubt.

This is why Indian history, Indian culture, and Indian civilization must be logically and truthfully re-constructed from Indians, by Indians, and for Indians…real Indians rooted in the land and its tradition and culture. Others tamper with it in the name of expedience (previously British Empire, now Breaking India), real Indians tell it in the name of the truth. Therefore, if the colonial history we have been taught is not simply in need of correction, but root-and-branch re-construction, it becomes imperative to start at the beginning.

Students of history would already be familiar with that much bally-hooed “Sheet-anchor of History” (as so named by Max Muller and concocted by William Jones, et al) based Alexander’s Invasion of India in 326 B.C., and Chandra-gupta Maurya’s coronation at Pataliputra in 321 B.C.E. However, as seen, and as soon will be seen, Pandit Kota Venkatachalam, through painstaking and disciplined historical research—rather than the navel-gazing our gyaanis are notorious for—demonstrated why the former was an unimportant event and the latter, an utter falsehood.  If the wrong Chandra-Gupta were purposefully identified as the ruler of Magadha in 321 B.C.E (It was actually Chandra Gupta I), then what in fact is our true benchmark for asserting verifiable and recorded “history” from mere legend?

TrueAnchorSheetpng
[1, 183]
The Real Sheet Anchor of Indian History is the Mahabharata War of 3138 B.C.E. This is based not just upon astronomical calculation, but also hard historical evidence, via archaeologically-relevant inscriptions, documented chronologies, recorded Royal Lineages, and a Tradition of referencing dates beginning with the Kali Yuga (3102 B.C.E ) present even in the Rajatarangini, which is accepted by all parties (colonial, sepoy, or otherwise) as real history. This is no mere “hindutva history” hypothesis, but a legitimate and logical assertion conducted by Sri Kota Venkatachalam, who was uniquely qualified in having both a traditional and a Western Education. Unlike the fake “acharyas” in our midst today, he was an actual Acharya, as well, with the competence to understand our Vedic tradition and Puranic History, while providing responses to Western standards for documented proof, evidence, and “rationality”.

Furthermore, acceptance and assertion of this position as genuine History, is supported by our own independent study of history over decades. Many of the charges and allegations originally made by Pandit Chelam, were independently observed by us in a number of different topics under Indian history, routinely and repeatedly. Only, we do not claim the authority of an Acharya, which Pandit Chelam is most deserving of and eminently qualified as. The sole purpose of this point is to note that 3138 B.C.E was not cavalierly arrived at, nor do we treat Pandit Chelam’s word as the “gospel” (pardon the expression). The Itihaas of the Mahabharata is not merely the legend from an epic, but the Chronologically concrete Historical Past of the Indian Subcontinent & the true Sheet anchor of its History.

PKVCthePIIC

It was Sri Venkatachalam’s own exemplification of historical methodology, logical investigation, scholarly subject-matter-expertise, but above all, scrupulous adherence to the Truth throughout his publications on History, that established the credibility of this dating. It was only after properly surveying his original reference sources that we have put our weight behind this, and recognise not only the possibility or plausibility, but also the near-certainty that this is in fact the correct Sheet Anchor for Indian History.  Those who wish to contest this claim on whatever grounds, are advised to refer to not only our previous articles listed above, which establish the credibility of this historical foundation, but Pandit Chelam’s own large selection of works in English.

The next natural objection, of course, is whether Mahabharata Epic, which features not only weaponry beyond scientific verification (Divine missiles called astras), but also the supernatural or paranormal (Divine Beings, Incarnations of God, and even Demons) could be treated as History? The answer, of course, is that if both Homer and Herodotus (“Father of History” for Europeans), who both feature the Sun God and other divine beings (even a Cyclops), as part of their works can be considered “Sources of Authentic History”, then there is no reason the Mahabharata cannot be. Vyasa’s Epic may feature “mythological” aspects that are not believable in our own time, but if Homer and Herodotus’ Divine involvement in historical events can be explained away as “allegory/metaphor ” or “poetic license”, then there is no reason this same standard cannot be applied to the Mahabharata. Let these non-scientifically verifiable aspects be treated as allegory or atisayokti by our atheist friends, but let the basic sequence of events be treated as History: Dynasty, Succession Crisis, Subcontinetal War, Coronation.

And as for the age of many of the characters (between 120-200 years), well if Methusaleh (Grandsire of Noah) at ( 969 years) could have been accepted by William Jones’ and his Christian Chronology, which serves as the basis for the present “Post-Modern” Chronology, can be glossed over, then so can this.

WillyJChronos

When a real history by a real historian such as Kalhana can accept the historicity of the Kurukshetra War, than there is no reason we lesser mortals cannot.

ChronosConclusionThe Time has come to reclaim our True History of Bharatavarsha. Let there be no more confusion!

Here is what Bharata Charitra Bhaskara, Pandit Sri Kota Venkatachalam wrote on the matter [Emphasis and Proofing ours].

KRVChronosPandit Kota Venkatachalam [3, 39]

The following Post was originally published at True Indian History on June 26, 2009


The following Post was originally published at True Indian History on June 27, 2009


The following Post was originally published at True Indian History on June 28, 2009



battlefield-of-kurukshetra

The following Post was originally published at True Indian History on August 16, 2009


Gift Deed of Janamejaya — An Early Inscription of Kali Era

According to the Mahabharata (2nd Aswasa of Adiparva) Parikshit ruled for 60 years from the first year of the Kali (3101 B. C.) Era and died stricken by the curse of a Rishi(3041 B. C), when the coronation of Janamejaya his son, took place in Kali 61,(3041 B. C.).
An inscription (plate) of a gift deed by Emperor Janemejaya. (Indian Antiquary P. P. 333-334) runs thus:-This is the first inscription known which used the Jayabhyudaya Yudhistira Saka, which had its origin in Kali first year; (Both the Eras started in the same cycle year Pramadhi. This gift deed refers to a gift of land for the worship of Sri Sita and Rama on the bank of the Thungabhadra River, by Janamejaya (son of Parikshit) in the 89th year of Jayabhyudaya Yudhistira Saka i. e. Kali 89 i. e. B. C. 3012. The year Plavanga mentioned in the inscription tallies with the 89th year of Kali. Kali Era starts in the year 3102 B. C., the 20th Feb. at 2-27’-30″ hours. i.e. in the cycle year of Pramadhi the 1st day of the bright half of the month of Chaitram at 2-27-30 hours. Similar gift by the same Emperor Janamejaya was made on the same day to Sri Goswamy Anandalinga Jangama of Ushamutt through his disciple Jnanalinga Jangama for the worship of God Kedaranath in Kedara Kshetra situated in north Himalaya. The Inscription (plate) of the above gift which is preserved in the mutt even to this day runs thus:
……and so on.

In those times sacrifices were much in vogue and the Aswamedha and Sarpayaga performed by Janamejaya have become famous. Satanika, the eldest of the five sons of Janamejaya succeeded him to the throne. In his time in Naimisaranya the Satrayaga was performed by Saunaka and other Rishis, which is supposed to take one thousand years. The kings of this dynasty ruled till Kali 1468 (or 1634 B.C.), and in their time the Vedic religion was patronised and protected. In the several Yagnas performed in those days many animals were sacrificed and the common men were disgusted with the sacrifices of animals. Then in Kali 1215 or 1887 B.C. Buddha was born, to Suddhodana, the 23rd king of the Ikshvaku Royal dynasty of Kosala and preached a new religion in opposition to and in disregard of the Vedas.


There is no prominent event in the history of the Ikshvaku Royal dynasty except for the birth of Buddha in 1887 B.C. In Kali 1468(B.C. 1634) Kshemaka, the last Emperor of the royal dynasty of Hastinapura and Sumitra, the last king of the royal Ikshvaku dynasty of Kosala Kingdom both died childless. So the king of Magadha became Emperor and founder of the Imperial dynasty of Magadha.(Capital of Magadha was ‘Girivraja’)

The following Post was originally published at True Indian History on July 1, 2009


Pandit Kota Venkata Chelam wrote:

As researches progress this date (1887-1807 B. C.) of Buddha is bound to be accepted by scholars, if the scholars have not so far arrived at this date, it was because there was a common notion among them that the last word on the subject had been already said. If they had realised that the question was open for further investigation atleast some of them would certainly pursue enquiry in this direction and arrived at the date fixed by me.

It is highly refreshing to note that there is at least one scholar who could not superstitiously believe the existing theory about Buddha’s date, but thought it worthwhile to investigate into the question with an open mind. I refer to Sri V. Thiruvenkatachariyar M.A., L.T., (Formerly Head of Department of Mathematics, Govt. Arts College., Rajahmundry.) who arrived at the same date as myself (1807 B. C.) as the year of Buddha’s death and has fixed the actual day of the week and the month also. (Tuesday, Vaishakha Purnima).

His way of approach to the subject was astronomical. The fact that the same date 1807 B. C. was arrived at by two different ways of approach may induce the scholars to pause and try to revise the existing fictitious date of Buddha Nirvana. (483 B. C.). Having arrived at the same date independently we had occasion to compare notes at a stage when the present volume(1) was completely printed and was awaiting binding. I thought it worthwhile to incorporate the learned professor’s thesis in this volume. He has kindly permitted this and has sent a typed copy of his thesis, (on 18-1-55) which is herein incorporated. I am thankful to the professor for thus helping the cause of the true historical research which both of us have at heart.

(1) Age of Buddha,Milinda & Amtiyoka and Yuga-Purana by Pandit Kota Venkata Chelam (1956)


WillJsMisrepPandit Kota Venkatachalam [3, 29]

All this makes Rajiv Malhotra’s Battle for Sanskrit so relevant for our times. For if foreigners claim a monopoly not only on interpretation of our traditional texts (we have seen how self-serving and expedient they have been with shifting dates to serve changing needs), but on even training future scholars of Sanskrit in foreign universities, who will be left who understands the real value of our text and tradition?

Apropos for the times, a Sanskritist almost a century ago made the same complaint about foreign malfeasance with our texts for the purpose of their political expedience.

SanskritistonChelamJatavallabula Purushottam. Sanskrit Lecturer S.R.R., and C.V.R College Vijayawada (Andhra Pradesh) [3, xvii]

Many of you may ask “Have they no shame?”, but the question is, don’t we? The same social media whiners who carp and cavil about kings of yore failing to do the right thing, are now doing the same. Some have sold out, others are too scared, but some are simply spoiled, rotten brats who have no integrity to do the right thing and come together for a common cause. Unjustifiably arrogant, they, as Pandit Chelam complained of Rai Bahadurs past, simply hold on to the history they have been taught because it is comfortable and convenient for them. They are no different than the petty princelings who complained to Yashwant Holkar about what could have been…He replied contemptuously noting there was no point day-dreaming now. If only they had done their duty, their little part, when they had the chance…

It is not enough to merely claim the mantle of “Science and Reason”, but to actually test these “scientific” claims against empirical analysis and logic. The history we have been taught is wrong. Time to set it right. Not in the name of ego. Not in the name of self-glorification. But in the name of the truth…the real Truth.

Satyameva Jayate

Emblem_of_India.svg


References:

  1. True Indian History. [Various Blog Bosts]
  2. Kota, Venkatachalam Paakayaji (Pandit). The Mahabharata War. Vijayawada: Tirumala.1988 (posthumously)
  3. Kota, Venkatachalam Paakayaji (Pandit). The Plot in Indian Chronology.Vijayawada: Arya Vijnana. 1953
  4. Kota, Venkatachalam Paakayaji (Pandit). Chronology of Ancient Hindu History Part I. Vijayawada:AVG
  5. Kota, Venkatachalam Paakayaji (Pandit). The Age of Buddha, Milinda, and Amtiyoko. Guntur: Sri Ajanta Printers.1956
Acknowledgment: Our sincere thanks to Sri G.D. Prasad garu, grandson of Pandit Kota Venkatachalam for his kind permission to reprint these articles and excerpts.

Vedic Cosmology — The Dharmic View of Time

dhwanidotcom

“History became Legend, Legend became Myth”. This most famous of lines from a modern movie is emblematic of human attitudes towards civilizational memory. When timescales become incredulous, the story is called “Legend”, when they become mind-boggling the story is called “Myth”. Perhaps that is why since the time of William Jones to his brown successors, every effort has been made to reduce the antiquity of Indian history and Indic Civilization.

Most Hindus are naturally very (over) accommodative and in their (self-defeating) gullibility, assume all people must be on a similar journey of self-discovery of the Truth. Perhaps that is why Hindus are notorious for their stupidity in routinely anointing foreign or foreign-trained individuals as “saviours”–social media being exhibit A. The reality, however, is that expedience has been the byword of these ‘saviours’, and as even Kissinger remarked in his at least nominal analysis of the Arthasastra, even Cultural/Historical traditions can be subject to manipulation in order to exert political control and dominance [What’s sadder is that Indiots again need an outsider to remind them of this, but then again if only universities from phoreign can be good, same with experts]. But when your m.o. for “merit” is read and regurgitate for marks, no wonder you can’t apply theory in reality. Ironically, Chanakya himself has now become targeted by these self-same “breaking India” forces, with a most ridiculous time period suggestion and even arguing that Chanakya is not the same as Kautilya—in utter contradiction of our tradition. As such, the time has arrived for a concerted, and uncompromising pushback.

Much like the William Jones of yester-year, these modern Western Universalists (and their sub rosa cooperators) are attempting to force-fit Indian history and culture into their Christian or now “Post-Modern” chronology–which invariably suits their “narrative”.

manavadamchronosThe Ramayana has gone from a time-honoured tale of Righteousness, Nobility, and Self-Sacrifice to a political instrument for medieval use. Such is the insolence of this ilk. In light of that, since the hypocrisy of these “Ivory Tower Intellectuals” has been exposed, the time has come to assert certain realities: Let Science be Science and let Tradition be Tradition.

Perhaps that is why those in the realm of Western Humanities live in perpetual fear of the Hard Science empirical experts. As Shivoham has argued, their “closed logic” assumption based, selectively rational constructs fall apart in the face of close scrutiny and examination.

Therefore, let Science be Science, and be taught as Science,  let Tradition be Tradition, and be taught as Tradition, and let the prying hands of post-modern, aspiring “acharyas” of the sherry-swilling variety be kept out of the realm of tradition, where only true astika and adhyatmika Acharyas belong. One such realm is Cosmology.

vedicosmology

In our previous article, we recounted the life and achievement of the great Emperor,  Sagara of the Solar Dynasty. He was one such “legendary” king, and his relevance was not only due to the kingly example of sternness he demonstrated in the face of adversity, but also on account of how it disproves the Colonial and poco-pomo purposeful misinterpretation of the word “yavana” to mean Greek. How could a king from the Satya Yuga be fighting Greeks who did not exist till the first millennium BCE in the Kali Yuga?  If you do not know the difference between a Kalpa, a Manvantara, and a Yuga, and that we are in the 5118th year of the Kali Yuga, of the 28th Chatur Yuga, of the Vaivasvata Manvantara, of the Sveta Varaha Kalpa, what business do you have in interpreting and playing interpreter of our philosophical and historical texts?

Manvantare

That is why it is not enough to merely assert a “nationalist narrative” within the conventional history, but to tear down this Colonial Era Christian Cosmology-derived Chronology of 4004 BCE (courtesy William Jones) and actually assert what our Vedic Cosmology actually says. If any buffoon with a Sanskrit certificate from Sheldon Pollock University can cherry pick some words to posit an asinine theory, then the traditional understanding built on guardianship of truth will be lost. That was the traditional reason for varna vyavastha, because the truth would be passed down from father to son, with any deviation from the truth bringing shame on the family. Western “Indologists” have no such need for shame. Without properly understanding that Yavana did not mean Greek or that the Satya Yuga comes long before the present Kali Yuga, our children (and sickular seniors with the maturity of children…) will remain utterly clueless on the internal logic of our tradition and traditional systems. History is most assuredly history, but as the recent findings regarding the Xia Dynasty of China demonstrate, what foreigners derisively called “legend” is often found to be genuine history.

What’s more, there is a cliquish band of idiots that is forever navel-gazing over the alleged superiority of Indra over Vishnu. But this only demonstrates their ignorance of not only the Puranas but the Veda itself [Vishnu himself takes up the position of Indra in the first Manvantara as Yajna/Shatakratu. The present Indra is Purandara (in this current Shraddhadeva/Vaivasvata Manvantara). The next Indra is Bali, of Vamana avatara fame]. This is the danger of deconstruction of systems—you can learn more and more, about less and less. All this is why proper understanding of Vedic Cosmology and the traditional Dharmic method of time-keeping  is required.  However, for graduates of Witzel academy (and its rw acolytes), such a thought even becomes a question as they do not understand (or refuse to understand) the proper hermeneutics involved in interpreting our traditional texts—and they have the audacity to assert a monopoly over it. What a sad world we live in that degree-holders from phoreign are considered more credible interpreters of our sacred texts than our actual traditionally trained, spiritual Acharyas.

RigVedaBrahmaKalpaTherefore, whether in fact our “Legends” are Scientifically and Archaeologically confirmed “History” is for Scientists and Archaeologists, in particular, to verify. But the tradition is the tradition, and for traditional Acharyas alone to assert. Foreign and foreign-trained “academics” and “intellectuals” have no more credibility in this regard and only fools grant them this. Let there be no more confusion.

Per our previous remarks, we will remain true to our word and merely repeat what an actual Acharya, Pandit Sri Kota Venkatachalam wrote of our traditional Dharmic View of Time and our Traditional Vedic Cosmology. Here is what here wrote [Emphasis and Proofing ours].

8.1brahmakalpa

The following Post was originally published at True Indian History on June 23, 2009


The Age of the Present Creation

According to the Smritis,
18 winks of the eye= 1 Kastha
30 kastas………..=1 Kala
30 kalas ………..=1 Muhurta
30 muhurtas………=1 Day and night.(This Ahoratree is the human day.)

According to Jyotisha.
6 respirations………….= 1 Vighati
60 Vighatikas ………….= 1 Ghatika
60 Ghatikas ……………= 1 Day and night(This Ahoratree is the human day.)

15 days………..= 1 Paksha
2 pakshas………= 1 human month

1 human month = 1 day and night: of the Pitris(Manes),the Sukla Paksha being their day and the Krishna Paksha being their night.

12 Human months or one year = 1 The Ahoratree of the Devas

6 Human months = 1 Ayana, ( From Pushya to Jyesta is day of the Devas, from
Ashadha to Margasira is night of the Devatas.

30 human years = 1 Month of the Devatas.
360 human years or 12 Daiva months = 1 Year of the Devatas

12000 Daiva years or 43,20,000 Years = One Daiva yuga or ordinary Mahayuga

0.4 Mahayuga = 4800 Daiva years = 17,28,000 years = Kritayuga with yugasandi and Sandhyamsa.
0.3 Mahayuga = 3600 Daiva Years = 12,96,000 years = Tretayuga
0.2 Mahayuga = 2400 Daiva Years = 8,64,000 years = Dwaparayuga
0.1 Mahayuga = 1200 Daiva Years = 4,32,000 years = Kaliyuga

1 Mahayuga = Kritayuga + Tretayuga + Dwaparayuga + Kaliyuga

1000 Daiva Yugas or ordinary Maha Yugas or 432 crores of ordinary years = One day time for Brahma. This is Udayakalpa. = 30 Ghaticas for Brahma.

Another 1000 Daiva Yugas or 432 crores of ordinary years = Night for Brahma or Kshaya kalpa

2000 Daiva Yugas or ordinary Maha yugas i. e., 864 crores of ordinary years = One Ahoratree of Brahma.

30 Ahoratrees of Brahma or 6,000 ordinary Mahayugas= One Month of Brahma
12 such Brahma months = One Brahma year.
100 Brahmaic years = Life period of Brahma.

During the day time of Brahma(1000 Mahayugas) , 14 Manus look after this world. Each Manu reigns 71 Mahayugas . In the first day of the fifty first year of Brahma have rolled away the following periods:-
6 Manus = 6 x 71 = 426 Mahayugas = 184,03,20,000
27 Mahayugas of the period of Vivasvata, the seventh Manu = 11,66,40,000
The Kritayuga of the 28th Mahayuga = 0.4 Mahayuga = 17,28,000
The Tretayuga = 00.3 Mahayuga = 12,96,000
The Dwapara = 0.2 Mahayuga = 8,64,000
The Kaliyuga till (Kali 5056 or 1955 A. D.,) = 5,056
__________________
Total.= 426+27+0.9 Mahayugas + 5056 years = 196,08,53,056 years
___________________

Seven Jalapralayas each of duration of a Kritayuga
= 7*0.4 Mahayugas =2.8 Mahayugas = 7 * 17,28,000 = 1,20,96,000
_________________
Total. 197,29,49,056 years
_________________

and this is the time since Brahma
woke up on the first day of his
fifty first year and to get at the
age of this creation, DEDUCT from
this, 1,70,64,000 years being the
time of Brahma’s Dhyana or
contemplation before beginning to
issue life. .. … … … 1,70,64,000
_______________
Time since creation began upto 1955 A. D , —- … 195,58,85,056
________________
The time that has passed by in the
period of the present Manu (the 7th)
Vivasvata … … … 12,05,33,056
The Period of a Manu … … 30,67,20,000
This Manu will continue for … … 18,61,86,944

Thus we arrive at this conclusion :- Brahma has completed his fiftieth year; and in the first day of his fifty first year of life have gone by thirteen (Brahma)ghatikas, and forty-two vighatikas i. e., 195,58,85,056 years upto 1955 A. D. This is recorded in our Panchangas year by year.

This is Genuine Historical Data of the Vedas.
In conformity of the above Vedic Historical Data for the modern history of Bharat, we can safely adopt the Puranic data commencing from the Mahabharata war of 3138 B. C. or 36 years before the beginning of Kali Yuga 3102 B. C., or 62 years before the Saptarshi era of 3076 B.C.

Brahma

The following Post was originally published at True Indian History on May 22, 2009


Time and place always noted carefully by Orthodox Hindus

 

It is admitted on all hands nowadays that in the entire range of world’s literature the Vedas of the Hindus are the most ancient. And the Vedas form the basis for the various daily activities prescribed for and performed by the Bharatiyas from the time of their rising from bed…in the morning to the time of their going to bed in the night. From the procedure of brushing the teeth all the daily physical and intellectual activities of the human being are laid down in the form of sacred duties in the Vedas. Even to this day the conduct of the orthodox among the Indians is regulated by the Vedic injunctions.

For the due performance of these Vedic rites time and place are of importance and have to be carefully fixed and noted. The prescribed rites have to be performed at the times prescribed exactly without any discrepancy even to the very minute and second. Time is fixed accurately with reference to the movements and relative positions of the Sun, Moon, the Planets and Stars and the activities of the orthodox Hindus, who observe the traditional ritual are still regulated by the time thus determined, even to this day.

Almanacs are prepared every year for the purpose, on the basis of their highly developed and perfected astronomical science and these are available to the common people. It is the custom of the country to keep the almanac in every Hindu household. With its help every one knows the date (the phase of Moon), the day of the weeks, the star associated with the Moon, Yoga and karana and is enabled to perform the rites prescribed for him, his religious injunctions. Besides, these contain details of the movements of the different planets and their positions from time to time. the fixing of the present time in the flow of time from the beginning of the month. the year, the yuga, the Manvanthara, the kalpa, the beginning of creation itself. According to these almanacs, which show a remarkable uniformity in these matters from time to time and province to province throughout the country
1. the present time 1952 A.D. is the year 5053 of the kali Yuga.
2. the time elapsed since the beginning of the Manvanthara of Vaivaswatha Manu the seventh Manu is 12,05,33,053 years.
3. The time elapsed since the beginning of the 28th Mahayuga is 38,93,053 years,
4. In the 28th Mahayuga. of the present kaliyuga the time elapsed is 5053 years.

So 1952 A.D is equivalent to kali 5053. Hence the first year of the Kali Era comes in 3101 B. C. Even the scholars of the west (the orientalists) of modern times all recognise that the kali Era of the Hindu system of reckoning time began at 2-27’-30″ hours on the 20th of February 3102 B.C., the first year of the kali Era is 3101 B.C., that in the year Kali 26 on the first day of the year,i.e. in 3076 B.C., the victors in the Mahabharata war, the Pandavas, Yudhishtira and his brothers ascended to heaven. that on that day the constellation of stars familiarly known as Saptarshi Mandala left the region of Magha and entered the region of the next star and from that time commenced the Saptarshi Era or the Yudhishtira kala Era. This Era is known in Kashmir as the Kashmirabda even to this day and it figures in their almanacs from year to year, even according to Dr. Buhler. (Vide indian Eras ‘in English’ by this author(Pandit Kota Venkata Chelam) ).


brahmavishnulakshmi

The following Post was originally published at True Indian History on May 12, 2009


Max Muller-On relative reliability and regard for truth of oriental scholars

 

Of the relative reliability and regard for truth, so essential a qualification for purposes of history, of oriental scholars, the writers of our Puranas and ancient books, on
one hand and the western scholars engaged in historical research and controversy on the other hand, a fair estimate is available to us in the words of Prof. Max Muller, himself,
a well-known western scholar who interested himself in the ancient literature and religion of our country.

Prof. “Max Muller” in his book “‘India; what can it teach us” P. 63 writes thus:—

During the last twenty years however, I have had some excellent opportunities of watching a number of native scholars under circumstances where it is not difficult to detect a man‘s character, I mean in literary work, and, more particularly, in literary controversy. I have watched them carrying on such controversies both among themselves and with certain European scholars, and I feel bound to say that, with hardly one exception they have displayed a far greater respect for truth, and a far more manly and generous spirit than we are accustomed to even in Europe and America. They have shown strength, but no rudeness; nay, I know that nothing has surprised them as much as the coarse invective to which certain sanskrit scholars have condescended, rudeness of speech being, according to their view of human nature, a safe sign not only of bad breeding but of want of knowledge. When they were wrong they have readily admitted their mistake; when they were right they have never sneered at their European adversaries. There has been, with few exceptions, no quibbling, no special pleading, no untruthfulness on their part, and certainly none of that low cunning of the scholar who writes down and publishes what he knows perfectly well to be false, and snaps his fingers at those who still value truth and self respect more highly than victory or applause at any price,”
Let me add that I have been repeatedly told by English merchants that commercial honour stands higher in India than in any other country, and that a dishonoured bill is hardly known there.


 


As we can see, for all the criticism of our Traditional Pandits and our traditional concepts of Jyotisha and Itihasa, it is eminently clear that we were scrupulously in marking the date and time. Jyotisha is more than mere astrology, but is in fact, the study of time-keeping, with astronomical calculation intimitaley connected with daily passage of time. This has proven to be a far more accurate method due to Indic Perspective to Mathematics. Rather than creating an artificial “order” based on human models impervious to outside scrutiny, it attempts to accurately determine time based on the reality we perceive.

vishnugarbha

Moreover, there is a traditional mandate to tell the truth among our traditional astika acharyas, which even foreigners recognised. Whether this Vedic Cosmology, this Dharmic View of Time, this conception of time is scientifically validated or not, a number of scientists have already spoken on the similarity of these Hindu timescales to modern astronomy. Here is what one of the famous western astronomers of the last century is recorded to have said [and we will end with that].

The Hindu religion is the only one of the world’s great faiths dedicated to the idea that the Cosmos itself undergoes an immense, indeed an infinite, number of deaths and rebirths. It is the only religion in which the time scales correspond to those of modern scientific cosmology. Its cycles run from our ordinary day and night to a day and night of Brahma, 8.64 billion years long. Longer than the age of the Earth or the Sun and about half the time since the Big Bang.”

shivacern

References:

  1. True Indian History. [Various Blog Posts]
  2. Kota, Venkatachalam Paakayaji (Pandit). The Age of Buddha, Milinda, and Amtiyoko. Guntur: Sri Ajanta Printers.1956
  3. Varaha Purana. http://gita-society.com/section3/HinduPuranas16.htm

Acknowledgment: Our sincere thanks to Sri G.D. Prasad garu, grandson of Pandit Kota Venkatachalam for his kind permission to reprint these articles and excerpts.

An Indic Perspective to Mathematics — 3

mahaviracharya

(This is the concluding part of the sequel to ‘Introduction to Ganita’)

Part 1 (Introduction) 

Part 2 (Ganita – Math Encounters)

Part 3 (below): Ganita prevailed over Math in their encounters, but what did it really win? While Ganita’s results were absorbed into Mathematics, the underlying pramana and upapattis were rejected. We explain why this happened, and its implications.

Digestion Of Ganita, the Needham Question, and the Road Ahead
Nothing in life is to be feared, it is only to be understood. Now is the time to understand more, so that we may fear less - Marie Curie.
The Digestion of Ganita

It appears the ancient Babylonians had something in common with the Indians: they were pattern-seekers. As far as trying to understand how the world around us works, Richard Feynman rejected (Greek) Mathematics in favor of what he recognized as a Babylonian method, as discussed in this lecture below. Despite this endorsement, it is the Greek approach that drives Mathematics today, while the Babylonian culture can be found only in famous museums today. Why?

It would not be a problem for any civilization to view and benefit from imported knowledge by employing a native lens, without denigrating and destroying the external source tradition, and based on mutual respect. However, when knowledge from another culture is deliberately cannibalized and appropriated as a predator, it is a serious problem. It turns into a process known as’digestion‘. We now describe how Ganita was digested into Mathematics after their encounters.

The Digestion of Ganita into Mathematics

This process of digestion has been laid out by Rajiv Malhotra in [4]. We apply this description step-by-step to see how Ganita was digested into Mathematics.

Step 1.The less powerful culture is assimilated into the dominant one in such a way that: the dominant civilization dismembers the weaker one into parts from which it picks and chooses which pieces it wants to appropriate“.  During their encounter, all the important results of Ganita, starting from the place value system with zero, to algebra, trigonometry, algorithms, combinatorics, … to calculus were accepted by Europe to obtain real-life benefits. However, the underlying epistemology and approach of Ganita that has worked so well for 2000+ years, and could be used to generate such astonishing results in the future were amputated from Ganita. Only the results were retained within Mathematics.

Step 2.appropriated elements get mapped onto the language and social structures of the dominant civilization’s own history and paradigms, leaving little if any trace of the links to the source tradition“. The formal Math rooted in the Greek tradition was enhanced and expanded so that the Ganita results could be systematically re-derived and reinterpreted in a compatible manner. Later, the beneficial features of the native Encuvati system of pedagogy was appropriated into the British teaching approach, and ‘undesirable’ features were deleted to ensure compatibility with ‘Christian values’ [15]. Once this process was complete, the source tradition of Ganita was expendable.

Step 3.the civilization that was thus mined gets depleted of its cultural and social capital because the appropriated elements are modified to fit the dominant civilization’s own history, and these elements are shown to be disconnected from, and even in conflict with, the source civilization“.

A. The credit for a re-engineered calculus was given to Newton/Leibniz and not Madhava and the Kerala School. We are taught the Pythagoras theorem and proof, not Baudhayana’s result and validation procedure. Fibonacci numbers, not Gopala-Hemachandra series. The IEEE journals recognize Arab numerals, not Hindu numbers, and so on. The list is long. In almost all these cases, the standard reason is that the Indians had not proved their results using the formal system devised by the west, even though each of these results were generated first by Ganita and also satisfactorily validated within the source tradition, often centuries earlier. The Ganita tradition was erased from the history of Mathematics.

B. On the other hand, the following types of claims are created:

  • Vedanga Jyotisha was full of astrology and religious mumbo-jumbo
  • Ganita was some kind of elite “Vedic Mathematics”
  • Hindu tradition was backward, caste-ridden, superstitious and incapable of producing such advanced scientific results.

Whereas, the exact opposite is true.

  • Vedanga Jyotisha is the science of time-keeping, and “the entire Jyotisa does not have a single sentence relating to astrology or prophecy” [1], whereas the main goal of European calendar reform was to advance the cause of organized religion [1]
  • Ganita was pragmatic and accessible to ordinary Indians including vegetable vendors who taught the greatest Arab scholar of their time [14], while today’s formal Mathematics is indeed the preserve of an elite few [1].
  • Hinduphobia is rampant in the Humanities departments of Western universities, which is subsequently exported to Indian universities, even as the digestion of Hindu science and technology results continues unabated [16].

Step 4. The final result is catastrophic for the source civilization: “the depleted civilization enters the proverbial museum as yet another dead culture, ceasing to pose a threat to the dominant one. After being digested, what is left of a civilization is waste material to be removed and destroyed.”  A mathematical monoculture was imposed on India during the colonial era after uprooting the ‘beautiful tree‘, India’s indigenous decentralized education system whose Ganita curriculum was sensitive to local requirements. Few students and teachers in Indian schools and universities today are aware of the source Ganita tradition. Among those who recognize the word,  few realize it is not an Indian neologism for Mathematics. Is this not an instance of cultural genocide?

How can we protect and revive the authentic and practical Ganita tradition that was the head of all the Indian sciences? To do this, we must identify the nature of the civilizational ‘Poison Pills’ within Ganita.

Civilizational Poison Pills

Rajiv Malhotra introduced the idea of civilizational poison pills from an Indian perspective in ‘Indra’s Net’. [13]. “Poison pills are those elements or tenets that cannot be digested into the DNA of a predator, because consuming them would lead to the destruction of the predator’s constitution. If a predator absorbs such an element, it will mutate so profoundly that it will lose its original identity and qualities.”  We now try to identify the poison pill in Ganita that needs to be preserved.

Ganita’s Poison Pill

The Indians achieved a smart reduction in uncertainty in calculations to a contextually admissible level, instead of beating themselves up trying to attain complete certainty. Ganita and Vedic thought recognizes that human understanding of the cosmos is never fully complete. In [4], the Indian and western mindset is compared thus: “Indians indeed find it natural to engage in non-linear thinking, juxtaposing opposites and tackling complexities that cannot be reduced to simple concepts or terms. They may be said even to thrive on ambiguity, doubt, uncertainty, multitasking, and in the absence of centralized authority and normative codes. Westerners, by contrast, tend by and large to be fearful of unpredictable or decentralized situations. They regard these situations as problems to be fixed. As we shall see, there is in fact some scholarly evidence that demonstrates this view of Western attitudes.” For a mindset that revels in perfection, this element of uncertainty that was acceptable within Ganita is a poison pill. This anxiety was evident in all stakeholders in Europe during the Ganita-Math encounters.

Western Fear of Uncertainty

Practically every Western point of view from the ultra-secular, to the religious during the Ganita-Math encounters was in conflict with Ganita’s poison pill:

  • In the abacus-algorismus battle, Ganita’s idea of ‘one manifesting as many’ in its place value system and the way it managed non-representability was suspect, given the scope for ‘chaos’ and ‘fraud’.
  • For a reasoning mind like Descartes, measuring the ratio of curved to straight lines involved an irreducible uncertainty, an understanding of which was beyond the human mind. This gave rise to the term ‘irrational numbers’ [1]. Not surprisingly, he rejected the idea of infinitesimals too.
  • Philosopher Thomas Hobbes was no friend of the Jesuits. But he too found the absolute, perfect order found in Euclidean geometry was its most appealing aspect and reflected his own perspective. As noted in [12] “in their deep structure, the Jesuit papal kingdom and the Hobbesian commonwealth are strikingly similar. Both are hierarchical, absolutist states where the will of the ruler, whether Pope or Leviathan, is the law.”
  • The Jesuits, Protestants, Eastern Orthodoxy, Anglicans, and a vast majority of Christian sects may have disagreed on some theological points, but all subscribed to the history-centric truth claims of the Nicene Creed [4]. At least three aspects of Mathematics would’ve appealed to them:
    • Calendar and time-keeping helped preserve history centric dogma and reestablish the importance of clergy.
    • The top-down, hierarchical perfect Eucliean order.
    • Proving theorems without need for empirical demonstration. History-centric Christianity treats the body as a vessel of original sin. Embodied knowing is problematic for this mindset.
  • Pioneer Jesuat monk Cavalieri underwent an inner struggle [12] after ingesting this poison pill, and all but disowned his Ganita-based idea of ‘indivisibles’.
  • Scientists who championed the cause of the infinitesimals, and their successors could never come to grips either. The Tagore-Einstein conversation is a good example. As mentioned in [4] “Not even Einstein was able to reconcile himself to the uncertainty inherent in quantum mechanics, prompting him to remark: ‘God does not play dice with the universe.’ But Shiva and Parvati, the Hindu cosmic couple, do happily play dice. Indian philosophy is receptive to the uncertainty theories of physics.

See Article 

However this poison pill does not negatively impact the Indian mindset. Why? Our Ganita Post discusses in detail, but we briefly summarize here for the sake of completion.

Ganita’s Comfort in Dealing with Uncertainty

The Indians were comfortable working with contextually accurate estimates for non-quantities like √2 and π, recognizing that the result could be improved upon.  Hindu society has no central authority that could ban innovation or the exploration of the realms of uncertainty. Its decentralized structure produced independent thinkers and innovators in every era. Dharma systems have built-in safeguards against Hobbesian/Church absolutism. As Rajiv Malhotra explains in [4] “Chaos is entrenched in the Vedas, the Puranas and Hinduism in general for a reason: its role is to counterbalance and dilute any absolutist tendencies as well as provide creative dynamism through ambiguity and uncertainty.” Ganita inherits all these features, and must retain all these properties for best results.

The inevitability of uncertainty was no cause for panic. It even opened up a degree of freedom for (dharmic, ethical) optimization using Yukti.  This comfort with uncertainty is visible right through Ganita’s storied history from Paanini‘s Ashtadhyayi before the common era, to the Aryabhatiya in the 5th century C.E, within the calculus results of Madhava in the 14th century, to Ramanujan in the 20th century. This perspective placed the Indian creation of all its algorithms, interpolations, calculus, etc. on solid epistemological ground. Let’s look at the Aryabhatiya, as an example.

Aryabhata‘s R-sine difference table shown below required an algorithmic package that managed uncertainty every step of the way in a transparent manner: one method for estimating square-roots, another for interpolation, and yet another non-mechanical exception step to generate an optimal final estimate for each value in the table. The Kerala Ganita experts extended such prior work to infinite series, including their own innovative exception terms [1].

Source: Indian lecture series on Mathematics [14]

Western mathematicians who reviewed Ramanujan’s notes found that he often used the terms “nearly” and “very nearly”[10]. Ramanujan came up with clever, non-mechanical approximations for specific quantities like π. Some of his approximations eventually lead to exact results. His exact infinite series for π triggered the most dramatic leap in accuracy since Madhava [14]. Some examples of his approximations are shown below [10].

ramanujan-1

ramanujan-1

The Indian approach seeks balance between chaos and order [4] and represents a dharmic optimization under uncertainty.

Eliminating uncertainty and deleting Yukti, Upapatti, and Pramana from Ganita to digest it, drains it of key features that make it a powerful and reliable approach for solving real-life problems. Furthermore, lack of Pramana can lead to pseudo-science and fraud, as we will see shortly. Preserving these features within an Indian approach to Mathematics has the twin benefits of recovering pragmatism and making the subject understandable and usable by everyone. It protects against further digestion and denigration of the source tradition.

Finally, How can Ganita preserve this poison pill while continuing to retain its open architecture [13] and confidently exchange knowledge with other cultures?

The need of the hour is a thorough and systematic purva paksha of Mathematics and Modern Science, employing an Indian lens.

We don’t have to be a Manjul Bhargava to experience some differences between Ganita and Math.  We can simply try out the basic instruments employed within each subject.

Indian Rope vs Euclidean Geometry Box

One of C.K. Raju’s most important contributions is his cogent argument for a fundamental change in the way math is taught in Indian schools and colleges.

Source: fastudent.com

The rope is a key entity in Ganita and the Darshanas. A fundamental feature of the rope is its flexibility, reflecting the idea of ‘one manifesting as many’. The night-time confusion between a rope and a snake is an example that has been used Dharmic seekers to communicate the deep ideas about the nature of ultimate reality.

Source: Library of Congress

The knotted rope is a critical component of the ancient Indian navigational instrument known as the rapalagai  or kamal [1]. The ‘Sulba’ in the Sulba Sutras means ‘cord/string/rope’, and the rope served as a measuring tool since ancient times. Consequently, as C.K. Raju notes, the circumference can be the independent quantity measured quite naturally using a rope, with the straight line radius derived from this. A mathematical mind measures the straight line (Euclidean distance) first. A geometry box consists of an assortment of rigid straight-edged tools, and each one is used for a specific operation.

source: Indian Mathematics Lecture Series [14]
A knotted string can measured curved lines. When it is stretched taut between pins, it becomes a straight line, and with one of the pins freed, it behaves like a compass. This strings-and-pins set can be used to construct squares, rectangles, circles, etc, i.e., its flexibility reproduces the functionality of an expensive geometry box at a fraction of the cost. It unlocks the creativity of Ganita and is available even to the poorest student.

Indian Nyaya versus Aristotelian Logic

From the Indian point of view, two-valued (Aristotelian) logic can play a supporting role (e.g. like tarka [22]) but does not enable a person to attain a higher level of consciousness [4]. Note that such reductive logic is different from the holistic logic of Nyaya, which accepts multiple pramanas. In fact, no major school of Indian thought directly mentions deductive logic as pramana [22]. On the other hand, all major Indian schools of thought accept pratyaksha pramana, which in rejected by Mathematics [1]. Misusing two-valued logic (that has no place for uncertainty) as pramana negates Ganita’s poison pill.

Mathematics in India Today

The  current approach to teaching mathematics in India appears to be a stressful  and boring mixture of bits-and-pieces of Ganita mashed up with partially understood formal Mathematics imported from the west. This digested teaching approach has been successful in confounding multiple generations of Indian students. The modern rote/mechanical mode is a distortion of the original approach of recollective memory, which was a distinct mode of learning that cultivated the amazing computational (Ganita) abilities of the Indians [15].

Repeat after me:

“An acre is the area of a rectangle

whose length is one furlong

and whose width is one chain” – Pink Floyd, The Wall.

The 2016 Hindi movie ‘Nil Battey Sannata’ (~ 0/0) dramatizes this state of confusion. The movie claims that Math is a natural enemy of girls (“Ladkiyon ko Maths se purani dushmani hain“). While this may or may not be true,  the daughters of Lilavati  should not experience any difficulty with Ganita. For the great Shakuntala Devi, Ganita was a bandhu, not an enemy. The sophisticated Ganita within Kolam designs attests to the embodied learning capability within women. Let us also not forget the women engineers of ISRO who mastered the Ganita of rockets and spacecraft (yes, Ganita’s calculus without limits can do this well [1]).

ISRO staff celebrating ‘Mangalyaan’ success. credit: www.aniruddhafriend-samirsinh.com

The intrepid mother in the movie tells her daughter that “maths yaad karne ki nahi, samajne ki cheez hai“, while the maths-savvy classmate advises: “ek baar maths se dosti karke dekho, usse majhedaar aur kuch nahi“. A key scene in the movie shows everyday, familiar objects from real life being used to convey this ‘samaj’ – clearly a Ganita rather than an Euclidean solution to an Indian problem [15].

In formal math, even something as simple as a point (Bindu) gets hairy. (Euclid: A point is that which has no part, then graduate to this).  A blind import of western approaches into the Indian classroom without subjecting it to a thorough purva paksha,  is a folly not just restricted to Ganita, but one that been repeated in different areas of study including social sciences, economics, religion, art, etc. The net result is years of misery for most Indian students followed by a trip to the west to get it straight from the horse’s mouth. S. Gurumurthy has repeatedly noted the negative impact and the poor track record of such a reductive mathematics in solving practical problems in the Indian economic context.  We close with a discussion on contemporary mathematics and the way forward.

The Needham Question
"With the appearance on the scene of intensive studies of mathematics, science,  technology and medicine in the great non-European civilisations, debate is likely to sharpen, for the failure of China and India to give rise to distinctively modern science while being ahead of Europe for fourteen previous centuries is going to take some explaining” - Joseph Needham.

Many Indian scholars have attempted to answer this complex question. However, virtually all of these responses that try to provide social/religious explanations offer little insight due to a shallow understanding of dharma and Ganita traditions, and the inability to do a systematic Purva Paksha of the western approach using an Indian lens. We quickly summarize three perspectives below noting that we are only scratching the surface here.

A. Several centuries of foreign occupation

This occupation of India ranked among the worst and longest-running genocides in history and was characterized by violence that specifically the Indian intellectuals. Such a strategy is likely to have taken a heavy toll on Indian R&D output and institutions. When there was a sustained break from this violence, e.g., the time period of  the Vijayanagara empire,  we observe that Ganita, Ayurveda, astronomy, and other sciences achieved significant progress.

B. Civilizational inertia: complacency or weariness?

The sharpest debates in India occurred internally, between the various darshanas, which may have shifted the focus away from the study of external cultures entering India. There appears to be no evidence of a thorough study of the axiomatic approach from a native perspective. The Indians may have identified the lack of integral unity in the western approach and rejected it without any further examination of possible useful features.  CK Raju notes in [1] that it was only in the 18th century that India got the Elements translated from Persian into Sanskrit (by Jai Singh). This lack of a systematic Purva Paksha is not limited to Ganita alone but is also seen in many other areas, as pointed out by Rajiv Malhotra [16], suggesting an overly inward focus, careless disunity against an external threat, and a lack of strategic thinking.

C. The Unreasonable Effectiveness of Mathematics

Roddam Narasimha’s analysis examines a question complementary to Needham’s: what are the reasons for a sudden European resurgence after 1400+ years of backwardness in science and technology? He cites a key reason for their resurgence in the 17th century: the mathematization of science. Galileo is his study of the motion of falling bodies, used the calculus (via Cavalieri) to came up with the ‘law of the parabolic fall’. This is considered the first ever quantitative representation of motion using mathematical equations [12].  Scientists thereafter began to develop effective quantitative models relating different physical quantities like velocity, momentum, etc. using abstract models and calculus.Newton titled his famous scientific work as ‘Principia Mathematica‘. These mathematical models, however ‘wrong’ they may be, helped in new discoveries.

Indian Ganita experts too may not have anticipated this unreasonable effectiveness of mathematics when they rejected it for centuries. Narasimha summarizes this in [17]:  “Modern science seems to have acquired, perhaps by fortunate accident, the property that the great Buddhist philosopher Nagarjuna called prapakatva: i.e., it delivers what it promises; it may not be the Truth, but it is honest“.

The Road Ahead

Ganita, in the more recent interactions with modern science and math has made positive contributions, e.g., Satyendranath Bose and Narendra Karmarkar. The Bose-Einstein statistics comes out of counting exercise and is a significant contribution to Quantum Mechanics[17]. Karmarkar is famous for inventing the first practically effective algorithm for solving linear programs that is also theoretically efficient. Karmarkar’s proof of convergence demonstrates Yukti in gradually reducing the level of uncertainty in the solution quality in way that is both practically viable, and theoretically rigorous (a teeny bit of uncertainty remains in the end but it can be safely ignored).  Clearly, interacting with and exchanging ideas with other cultures can be beneficial, provided it is done with eyes wide open.  Scientists and applied mathematicians today employ a variety of different methods, including deduction, induction, inference, etc., along with empirical validation, etc., to come up with new findings and inventions.

Per Roddam Narasimha, the Indians paid a price for rejecting the axiomatic approach, but their stance was vindicated later by the 20th century developments in Quantum/Classical Mechanics and Logic [17].  Furthermore, modern science is being increasingly plagued by a variety of harmful ‘viruses’ that would not affect a ‘Ganita OS’.

Unreasonable expectations from Mathematics

The mathematization of science has succeeded, but only when the order it brings is honestly balanced by the reality check of an unpredictable nature.  The unbalanced mathematization of economics has resulted in a series of spectacular failures when applied in real life. Indian thinkers like S. Gurumurthy have studied these economic models in depth, and opted for a balanced Ganita-like method, bringing in empirical validation and Yukti to determine practical solutions anchored in Indian reality. Western social science, which mimics the axiomatic approach is degenerating into a self-serving pseudo-science that offers little insight. A sizable proportion of results published in modern scientific journals are not reproducibleThis highly cited 2005 article discusses the implications.  And then there is the issue of fraud that is peculiar to the western modeling approach based on Aristotelian logic.

Falling for Supermodels
Without+photoshop+_305e904f954ae7c6b82bd7893278408d
Source: funnyjunk.com

Supermodels sell an advertising pitch, not reality. Yet the temptation of falling for the perfection of abstract math models and ignoring the uncertainty of the real world can be too strong. As [17] notes: “The history of Western science is shot through with the idea of theories and models and of fraud. Ptolemy himself has been accused of fraud; so in more recent times have Galileo, Newton, Mendel, Millikan and a great variety of other less well-known figures. I believe the reason for this can be traced to faith in two-valued logic.” All models approximate reality. When this gap gets too wide, it makes sense to reject that model. However, it is tempting to reject reality in favor of a pet model or preferred hypothesis by cherry-picking data, fudging results, or tweaking the model in ‘creative’ ways to ‘make’ it work (e.g. some ‘AIT’ models in the Indian context).

Ganita does not suffer from this issue. Why? As noted in [17] that when “observation is the starting point and one has no great faith in any particular physical model, which was the prevailing norm of Indian scientific thought, the question of fraud does not arise. Indian scientists, even classical ones, do not appear to have accused each other of fraud. This could not have been mere politeness, as they did make charges of ignorance or even stupidity against each other (as Brahmagupta did on Aryabhata, for example). We could say that fraud is the besetting sin of a model-making scientific culture“.

Synthetic unity has its advantages and has revolutionized modern science, but progress based on Integral unity is more sustainable.

Some western scientists and mathematicians may have sensed this lack of Pramana. Poincare explored the role of intuition and inference in his candid 1905 essay [18]. We even get a hint of integral unity here. Albert Einstein was aware of the limitations of Math when he noted “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.” Contemporary mathematician Terrence Tao recognizes that there is more to mathematics than just rigor and proof [19]. Thus, we see a limited move by Math toward the Ganita position while remaining firmly grounded in its native western tradition. Ganita can reciprocate in mutual respect, anchored in its own epistemology. We conclude with an informal discussion on emerging technologies.

Digestion by Machine: Math versus Ganita

Ganita is well-suited for this era of decentralized internet, analytics, big data, and digital computing which is algorithm driven. The emerging world of Artificial Intelligence is also very interesting. We touched upon AI citing an important observation of Subhash Kak [20] in our post on Ganita. As AI becomes highly sophisticated, it will be able to automate many human capabilities. It may eventually master the axiomatic approach and digest the Euclidean mathematician.

On the other hand the Indian approach to knowledge is rooted in the correspondence principle of Bandhu. Potential fallibility is acknowledged. Machines cannot replicate embodied knowing since they lack Bandhus, and they will not have the ability to attain a higher state of consciousness. For example, machines cannot chant mantras. Next, this ‘Euclidean’ robot will be able to master scriptures, and emulate all text-prescribed functionality of a cleric. It can function as a virtual holy establishment by delivering impeccable discourses. It will become an expert of theology by encoding history-centric truth claims as axioms and applying two-valued logic. However, it cannot become a Yogi.  Learning Ganita and internalizing the Dharmic worldview offers job security in the world of robots!  India can lead the way forward by carefully reintegrating useful features of modern science and math into its Vedic framework [21].

References:
  1. Cultural foundations of mathematics: the nature of mathematical proof and the transmission of the calculus from India to Europe in the 16th c. CE, C. K. Raju. Pearson Longman, 2007.
  2. Plato on Mathematics. MacTutor History of Mathematics archive. 2007.
  3. Plato’s Theory of Recollection. Uploaded by Lorenzo Colombani. Academia.edu. 2013.
  4. Being Different: An Indian Challenge to Western Universalism. Rajiv Malhotra. Harper Collins. 2011.
  5. Axiomatism and Computational Positivism: Two Mathematical Cultures in Pursuit of Exact Sciences. Roddam Narasimha. Reprinted from Economic and Political Weekly, 2003.
  6. Use and Misues of Logic. Donald Simanek. 1997.
  7. Computers, mathematics education, and the alternative epistemology of the calculus in the Yuktibhasa. C. K. Raju. 2001.
  8.  American Veda: From Emerson and the Beatles to Yoga and Meditation How Indian Spirituality Changed the West. Phil Goldberg. Random House LLC. 2010.
  9. Logic in Indian Thought. Subhash Kak.
  10. Ramanujan’s Notebooks. Bruce Berndt. Mathematics Magazine (51). 1978.
  11. C. K. Raju. Teaching mathematics with a different philosophy. Part 2: Calculus without Limits. 2013.
  12. Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World. Amir Alexander. Farrar, Straus and Giroux reprint / Scientific American. 2014.
  13. Indra’s Net: Defending Hinduism’s Philosophical Unity. Rajiv Malhotra. Harper Collins. 2011
  14. Mathematics in India – From Vedic Period to Modern Times: Video Lecture Series, by M. D. Srinivas. K. Ramasubramaniam, M. S. Sriram. 2013.
  15. Mathematics Education in India: Status and Outlook. Editors: R. Ramanujam, K. Subramaniam. Homi Bhabha Centre for Science Education, TIFR. 2012.
  16. The Battle For Sanskrit. Rajiv Malhotra. Harper Collins. 2016.
  17. Some thoughts on the Indian half of Needham question: Axioms, models and algorithms. Roddam Narasimha. Infinity Foundation. 2002.
  18. Intuition and Logic in Mathematics. English Translation of Essay by Henri Poincaré. 1905.
  19. The Pragnya Sutra: Aphorisms of Intuition. Subhash Kak. Baton Rouge, 2006.
  20. There’s more to mathematics than rigour and proofs. Terence Tao. 2009.
  21. Vedic Framework And Modern Science. Rajiv Malhotra. Swarajya Magazine. 2015.
  22. Epistemology and Language in Indian Astronomy and Mathematics. Roddam Narasimha. Journal of Indian Philosophy, 2007.
  23. The Math Page. Plane Geometry: An Adventure in Language and Logic based on
    Euclid’s Elements. Lawrence Spector, 2016.
  24. Continuity and Infinitesimals. Stanford Encyclopedia of Philosophy. 2005, substantive revision 2013.
  25. The Indian Origins of the Calculus and its Transmission to Europe Prior to Newton and Leibniz. Part II: Lessons for Mathematics Education. C. K. Raju, 2005.
  26. Why Write: Legos, Power, and Control.  F. D. Poston. Johns Hopkins School of Education.
  27. Indo-Portuguese Encounters: Journeys in Science, Technology, and Culture. Edited by Lokita Varadarajan. Indian National Science Academy. 2006.
  28. The Kerala School, European Mathematics and Navigation. D. P. Agarwal. Infinity Foundation Mandala website.
Acknowledgments: I'm deeply grateful to the ICP blogger and editor for their constructive comments, review, and feedback.

An Indic Perspective to Mathematics — 2

This is the Second in a Set of Posts as a follow up to our ‘Introduction to Ganita’.


AlgorithmGanita
Source: IIT Lecture Series on Indian Mathematics [14]
This Set of Posts on the Indic Perspective to Mathematics is the third installment of our continuing Series on Ganita.  Our first article in the Series celebrated Srinivasa Ramanujan. The Second provided an Introduction to Ganita. Emphases within quotes are ours.

Topic Outline

Part 1: (Introduction) 

In Part 1 of this Set of Posts on the Indic Perspective to Mathematics, we provided a background on the historical paradigms that drive the engines of Ganita and Western Mathematics respectively.

Part 2: (below) Ganita-Math Encounters. Ganita and Math came face-to-face when Indian Algorithms and Calculus traveled to Europe to help solve two critical problems: calculating with big numbers and managing the infinitely small. In a tense battle, Ganita’s balance of order and chaos prevails over the top-down Euclidean order backed by the church. We become aware of the massive contribution of the Vijayanagara empire to modern science.

Part 3: We adopt an Indic civilizational perspective of the Math-Ganita encounters. This gives rise to  interesting questions like ‘What was lost when Mathematics digested Ganita?’. We also look ahead, exploring the importance of Ganita and its Indian approach in a futuristic world.

Ganita-Mathematics Encounters
Experts have their expert fun
ex cathedra 
telling one 
just how nothing can be done. - Piet Hein.

In the Introduction to this Set of Posts, we studied the Greek origins of ‘Mathematics’. The abstract nature of Mathematics resulted in a drastically reduced practical output and Europe plunged into a 1000+ year dark era. During this period, Ganita contributions from Dharma thought systems helped keep math practically relevant in other parts of the world, right up to the 17-18th century CE. In particular, this injection of Ganita helped resolve two Math crises in Europe [1]. For the purpose of this post, we oversimplify and classify these problems as the ‘big’, and ‘small’ number’ crises. By helping resolve these crises, Ganita played a leading role in the birth and progress of modern science.

Big Number Crisis (Abacus vs Algorismus)

Here is example of a 10-digit Hindu number and its Roman numeral representation.

large numbers
credit: http://forbrains.co.uk/free_online_tools/convert_to_roman_numerals

There are several such websites that allow us to perform this conversion and three aspects stand out. First is the reference to ‘Arab numbers‘ in many sites. Second, is a maximum limit on the input. Third, ‘0’ or negative numbers are not valid input. The idea of ‘Arab numbers’ is of course, deep-rooted in the western STEM community to this day (IEEE journal publication guidelines still refer erroneously to ‘Arabic numerals’) since a large body of Ganita knowledge made it to the west via Arab translations of Sanskrit works. As can be gauged from the conversion tool, the Roman system is cumbersome for doing actual calculations. Its representation is additive in nature and there is no place value for zero, and the idea that placing a ‘0’ after a number would increase its value was befuddling. The west relied on the abacus / counting board, which was adequate for simple arithmetic calculations (the Indians did most of their routine arithmetic mentally). The introduction of ‘algorismus’ from India via Arab sources  around the 11th-12th century CE provided the merchants of Florence with an incredibly advanced way of quickly and accurately performing all kinds of numerical calculations [1].

Although traders found it to be practically useful, resistance to the alien method was stiff and it was several centuries (16th century) before the Hindu system gained unanimous acceptance. Well, almost. The British treasury preferred to place their money in the ‘secure’ hands of the abacus and held out until the 17th century [1].  By that time, the second math crisis in Europe was well underway.

Source: wikimedia.org.

Smiling Boetius‘ works with Hindu numerals to prevail over his opponent, Pythagoras, who is sadly stuck with a counting board abacus. This depiction of the victory of ‘algorismus’ is on the cover of Gregor Reisch’s Margarita Philosophica (1508) [1].

Aside from the suspicion of an Arab source in a crusading world, a technical reason for the distrust appears to be Ganita’s approximation techniques combined with the fear of zeroes being added to make sums bigger. To a mind accustomed to the perfection of Euclidean math, not even the tiniest quantity could be discarded. Such unacceptable imperfections could open the door to fraud and chaos [1]. The Indian approach, since the Sulba Sutras, recognized the non-representability of certain quantities (e.g. √2) and employed pragmatic and epistemologically secure approximation methods without anxiety, in order to reduce uncertainty (round-off error) to within an acceptable level [1]. ‘Algorismus’ was absorbed into European practice in order to resolve real-life calculations, but not the underlying pramana and empirical rationale (e.g. upapatti).  Why?

Small Number crisis (Infinitesimals and the Indian Origin of Calculus)

The Indian Background Story

Source: HaindavaKeralam| Zenith of Vijayanagara Empire
Brothers Harihara and Bukka, with the blessings of Rishi Vidyaranya, laid the foundation for one of the most important empires in Indian and world history in 1336 CE. In particular, the global scientific community owes the Vijayanagara empire a debt of gratitude.

While most regions of 14th century India reeled from the attack of fundamentalist invaders who had already destroyed India’s top universities and institutions, the Vijayanagara Empire became an oasis that protected and nurtured the Dharma. In particular, a school of Ganita was etablished in Kerala thanks to the prosperity and security enjoyed by the region during the Vijayanagara period, between the 14th and 16th century CE. An important member of this Ganita tradition was Madhava of Sangamagrama (~1350-1425 CE). This school produced a illustrious line of scholars who were the genuine adhyatmic and intellectual successors of Aryabhata, Bhaskara, and other great seekers. A major part of the foundation for modern science was laid by the Kerala school and the Ganita tradition they carried forward.

Recall that Aryabhata had already come up with finite difference equations for interpolation by 499 CE to generate fine-grained sine values. His practical approach essentially translates into Euler’s  18th century method for solving ordinary differential equations (ODEs). These results were subsequently improved upon by Brahmagupta (his second order interpolation result is known as ‘Stirling’s Interpolation Formula‘ today),  Bhaskara-2, and others [1]. Today, Indians are familiar with the phrase ‘Tatkal booking’ of train tickets. The ancient Ganita experts had developed algorithms  to calculate the Tatkalika gati of planets, their instantaneous velocity (an important quantity in Newtonian physics), as shown below.

Source: Lecture Series on Indian Mathematics [14]

We can observe a continual progress in India toward calculus, right from Aryabhata [1]. For all practical purposes, the Ganita school in Kerala during the Vijayanagara period can rightfully claim to be the developers of Calculus (from a formal mathematics perspective, western historians credit them for ‘pre calculus’). C.K. Raju has demonstrated the all-around practical viability of this epistemologically secure calculus without the use of ‘limits’ [11].

Madhava gave the world some beautiful and important results in infinite series by 1375 CE, centuries before Newton/Leibniz/Gregory/Taylor/McLaurin & Co.

madhava_collage
Source: Indian Mathematics, An Overview (https://youtu.be/p2WankcGP3Q)

In the derivation of these calculus results we can observe a smart management of the non-representability of infinitesimals based on order counting, along with a judiciously chosen exceptional / end-correction term (right side of the picture above). This is a really cool and important innovation that serves twin purposes, as explained by C. K. Raju below [1].

correction_term

There are many other novel ideas and instances of such Yukti within the Indian approach.  The interested reader can refer to [1] for a detailed description of the techniques employed.

It is worth comparing the meaningful Sanskrit non-translatable abhiyukti (expressing, or translating one’s Yukti in action) to its nearest English counterpart ‘algorithm’. The latter from the Latin ‘algorismus’, which in turn came from Al-khwarizmi who had translated Sanskrit texts of Ganita (see the picture at the top of this post). Jyesthadeva published the Ganita Yuktibhasa around 1530 CE in Malayalam, which provides the detailed mathematical rationale validating the Calculus results[1].

Why was Calculus Important to India?

Madhava’s infinite series with end-correction terms, allowed him to quickly calculate estimates for trigonometric values and π (pi) to very high levels of accuracy. For example, Madhava was able to calculate π to 11 decimal places, which represents both a quantitative, and methodological leap over prior brute-force type approaches (the next such dramatic leap was also due to Ganita, via Ramanujan) [14].  A natural follow-up question is: why were precise trigonometric values useful? Isn’t calculating π to many decimal places purely an academic exercise?  We summarize the reasons below, referring the interested reader to [1] for a detailed description.

Agriculture and Trade were key contributors to an Indian economy that played a dominant role on the world stage from 0 CE (and earlier) through 1750 CE.

Agriculture
  1. Krishi was and is a dominant component of the Indian economy. It was (and still is) dependent on a successful rainy season, which means that accurately calculating the arrival time of monsoons is important. A couple of weeks ago, the Indian government announced a $60M supercomputer project to better predict monsoons.
  2. Vedanga Jyotisha is primarily a science of time keeping that has numerous applications and has been recognized by researchers as a key source of knowledge in the ancient world [1]. It enabled the Indians to maintain an accurate calendar. Thus, from a Krishi perspective, the Ganita of Jyotisha acted as a decision support system for planning and scheduling key agricultural activities.
  3. The Indian calendar date and time was calculated with respect to the prime meridian at Ujjain (long before Greenwich), which was then re-calibrated to obtain local times at locations all over Bharatvarsha that covered a vast area (ancient India was united by time too!). This local re-calibration:
    • ⇒ required the calculation of the local latitude and longitude (lat-long)
    • ⇒ which (in the Indian approach) used the size of Earth as input
    • ⇒ this required a value for π
    • ⇒ trigonometric values were also needed for lat-long calculations
    • Precise numerical values were required since tiny errors get magnified after multiplication by big numbers (in the order of the Earth’s radius). Thanks to the Ganita tradition, the Indians had access to good estimates that were continuously improved upon.
ujjainmeridian
Source: builtheritageconservation| The Ujjain Meridian
Overseas Trade

India has a culture of calculation and embodied knowing that goes back thousands of years. Many ordinary Indians even today take pride in their ability to think and calculate on their feet, or pull off some Jugaad without the aid of electronic devices. The pattern-seeking Indian nature is visible in their traditional approach to navigation, reflecting an ability to discover sufficient order even within an ocean of chaos. The metaphor of the Samudra Manthana truly comes alive here.

  1. India, thanks to its manufacturing and technological prowess, had established lucrative trading relationships as a net exporter with several countries, from ancient Rome to the far east. Much was this was done through open sea routes, and not just sailing close to the coast [1].
  2. Prior to the 11th century CE, accumulated navigational knowledge included seasonal wind patterns (‘wind lore’), nature of ocean currents (‘current lore’), etc., and the empirical wisdom of sea-craft. The ancient Tamizh seafarers made use of the Saptharishi mandalam (Ursa Majorin the southern hemisphere. This database of seafaring wisdom and best practices were preserved, improved upon, and transmitted from generation to generation via the oral traditions of the seafaring Jatis [27].
  3. Thus, the Indian sailors had already established a tradition of navigation and deep sea voyage without written charts (they rejected the method of dead reckoning‘ in order to stay alive). Their approach included an empirical understanding of ocean patterns, Ganita, and instrumentation like the rapalagai (kamal) for celestial observations. Tamizh navigators deciphered currents using a simple device known as mitappu palagai [27].
  4. Such historical data further debunks the theory that oral traditions were ‘pre-rational’ and the sole preserve of Vedic scholars. Hinduphobic Indologists like Sheldon Pollock are dismissive of such priceless oral traditions [16]. The western universal idea of history begins with written text and it is tough for this mindset to imagine open-sea navigation without written charts.
  5. Accurately determining the local lat-long using celestial observations (solar altitude at noon, pole star at night, etc.) was part of this approach.
  6. More reliable navigation in the open seas is possible if the 3L: latitude, longitude, and loxodrome can be accurately obtained for any given location. These were indeed calculated in multiple ways by the Indians using trigonometric values [1].
chola sea route pic
Source: Indo-Portuguese Encounters [27] | Chola Sea Route
Continual Progress in Calculating Accurate Trigonometric Values
  1. Aryabhata’s astounding publication of his R-sine difference table along with an interpolation method stepped away from the geometrical approach that was employed until then [1]. The Aryabhatiya was a prized intellectual property of its time. It significantly improved the accuracy of trigonometric values (given the sine value of an angle, one can use elementary identities to calculate all other trig values).
  2. Aryabhata’s work paved the way for Calculus. Over the next 1000 years, the Indians steadily improved upon prior estimates.
  3. Calculus was a natural outcome of this process of deriving ever more accurate trigonometric values. The Kerala school’s calculus extended the finite series based trigonometric results to a highly accurate infinite series based approach.

We refer the reader to this essay [28] by D.P. Agarwal for his summary of the Kerala School, European Mathematics, and Navigation. It is highly likely that this Ganita knowledge traveled to Europe via European missionaries in Kerala and played a key part in revolutionizing physics and mechanics via Newton’s Principia Mathematica and other works.  This story serves as background for the question: why did the idea of ‘infinitesimals’ which was a non-issue in the Ganita world, spark a crisis in Europe?

The European Background Story

Ancient Greek math hit a roadblock after encountering paradoxes tied to infinitely small quantities. Mathematics could not deal with the irritating uncertainty around infinitesimals and the problem of non-representability: For example, an infinite number of threads of minuscule but nonzero length, joined end-to-end should yield an infinitely long thread. On the other hand, combining even an infinite number of threads of ‘zero’ length would only yield zero. Aristotle believed that continuum could be divided endlessly and could not be made up of ‘indivisibles’.

A famous paradox (which used to be popular among those preparing for engineering school entrance exams in India) is that of Achilles and the Tortoise. Around 500 BCE,  Zeno of Elea came up with several such paradoxes that exposed the gaps in a seemingly perfect mathematics and two-valued logic. Unable to satisfactorily resolve such contradictions and deal with non-representability of certain quantities (a fundamental requirement for numerical calculations), Greek progress halted. The dark ages robbed the west of native expertise and appears to have hurt them in key areas including, but not limited to [1, 27]:

  • Astronomy, Navigation, Instrumentation
  • Calendrical Systems, Ship Building
  • Medicine and Botany

After more than a thousand years, between the 12th-16th century, we can observe the emergence of a new kind of Mathematics in Europe, which was fundamentally different in its epistemology from the Euclidean approach. This knowledge first arrived via Arab/Persian translations of Ganita works in Sanskrit, and later through Missionaries who had direct access to Ganita’s latest results in Sanskrit and local Indian languages. We kick off this discussion using the European calendar as a case study.

Trick question: What came after Thursday, October 4th, 1582 in Europe?

The answer is Friday, October 15th. The European (Julian) calendar was slow by about 11  minutes per year for about 1200 years across their dark age. Church and Biblical dogma reigned supreme from the time the Nicene creed was formalized in 325 CE. This dogma can be best understood as an instance of history-centrism [4], and a key to preserving the credibility of this ‘history’ of unique divine intervention is proper time keeping and dating of these events. This was a key motivation behind the European quest for a better calendar.

The Indians had maintained accurate calendars since ancient times thanks to Vedanga Jyotisha for use within multiple applications, and Buddhists even helped with calendars in China [1] (helping the Chinese is an old Indian habit…). The Roman Church realized in 1582 that their calendar was trailing the correct date by 11 whole days. This key project of calendar reform was taken up by Christopher Clavius (1538-1612 CE), a Jesuit priest. Thanks to his painstaking work, Pope Gregory was able to press the fast-forward button on the calendar (thereafter named after him), recommend a leap year correction, and the rest is history.

Milanese artist Camillo Rusconi’s sclupture, 18th century. Pope Gregory is on top of an urn depicting the 1582 promulgation of the Gregorian calendar. Source: http://vminko.org/ under GNU Free Documentation License 1.3.

C.K. Raju has uncovered the Indian source of this calendar bug fix [24, 1]: “Jesuits, like Matteo Ricci, who trained in mathematics and astronomy, under Clavius’ new syllabus [Ricci also visited Coimbra and learnt navigation], were sent to India. In a 1581 letter, Ricci explicitly acknowledged that he was trying to understand local methods of timekeeping from “an intelligent Brahmin or an honest Moor”, in the vicinity of Cochin, which was, then, the key centre for mathematics and astronomy, since the Vijaynagar empire had sheltered it from the continuous onslaughts of raiders from the north. Language was hardly a problem, for the Jesuits had established a substantial presence in India, had a college in Cochin, and had even started  printing presses in local languages, like Malayalam and Tamil by the 1570’s.“. The Jesuits have continued to exercise their influence on the Indian education system to this day. They also played a key role in the second Math-Ganita tussle.

Jesuit (Euclidean) Order versus Indian (Ganita) Chaos

The Jesuits are members of the Society of Jesus, an organization founded by St. Ignatius of Loyola (1491-1556) and rooted in Roman Catholicism. Per [12] “In the broadest sense, imposing order on chaos was the Society’s core mission, both in its internal arrangements and in its engagement with the world.

Sir Peter Paul’s ‘The Miracles of Saint Ignatius of Loyola’ (Source: wikimedia.org)

This painting of Ignatius of Loyola is richly symbolic. It depicts the victory of a perfect top-down hierarchical order over chaos. Loyola and his back-robed Jesuits are in the middle, watched over by angels at the top. Loyola is calmly performing an exorcism, expelling the chaotic evil spirits possessing the bodies of terrified people at the bottom of the picture. [12] provides an insightful description of this picture, noting the role of the black robed Jesuits of Loyola’s Society of Jesus: “They are Ignatius’s army, there to learn from their master, follow his directions, and ultimately take over his mission of turning chaos into order and bringing peace to the afflicted. For that was indeed the “miracle” of St. Ignatius and his followers. Like no one else, they managed to restore peace and order in a land torn apart by the challenge of the Reformation.“.

The Church gained immensely via this decisive mathematical triumph of calendar reform, and Clavius who played an instrumental role, realized the benefits obtainable by investing in mathematics. This was a time period characterized by fissures and dissent in Christianity, with several alternatives and reformations (e.g., led by Calvin) cropping up that challenged the exclusive authority of the catholic church. In this climate, Clavius felt that the top-down hierarchical perfection within Euclidean geometry would be a great fit for the Jesuit curriculum, and in sync with the primary goal of their founder St. Ignatius of Loyola.

As mentioned in [12] “It was clear to Clavius that Euclid’s method had succeeded in doing precisely what the Jesuits were struggling so hard to accomplish: imposing a true, eternal, and unchallengeable order upon a seemingly chaotic reality. Just as Ganita was recognized as the foremost of the sciences in India since ancient times, Euclidean Mathematics became a most important subject in Europe after the calendar reform. The Society of Jesus embraced Math and all was well for a while. The focus had shifted to other pressing topics. For example, navigational challenges had to be overcome in order to ‘discover‘ reliable sea routes to new lands.

The Indivisibles

Calculus created a rather sudden splash into Europe within 50 years of the calendar reform [1]. By that time, the calculus, which was rooted in Indian epistemology had already been developed and studied for two centuries.  Bonaventura Cavilieri (1598-1647), a Milanese Jesuat monk and a student of Galileo was an early adopter. While the Jesuits were more like a MNC, the Jesuats were a local group of Italian monks lower in the pecking order. However, Galileo’s endorsement boosted Cavalieri’s profile significantly. Cavalieri introduced the ‘method of indivisibles’, in which “planes and solids had an indeterminate number of indivisibles” and authored the book Geometria indivisibilibus (Geometry by Way of Indivisibles) in 1635 [12].

While the idea of indivisibles was embraced by the Galileans, the Jesuits were not as welcoming. Those who worked with infinitesimal quantities did so for its practical value in generating realistic new results and could not really establish any logical consistency needed to prove infallible theorems. Unlike Euclid’s Elements which used top-down deductive logic to prove specific theorems from axioms, the use of infinitesimals required the ground-up Ganita approach: to start from physical reality and work toward generalized results, which could lead to innovation and potentially unpredictable discoveries. Clearly, Yukti was not welcomed by the church whereas Galileo’s methods were more compatible with Ganita.

Galileo Galilei (1564 – 1642 CE)

Galileo had become a formidable opponent by that time. He had earlier discovered the moons around Jupiter, and as a prashasthi [16] to a rich grand duke who ruled Florence, named the moons after him and his family. In return, he was rewarded with benefits that included the post of ‘Chief Mathematician’ to the Duke in 1611, which also freed him up to pursue his work as an independent researcher. As [12] notes, “The Galileans also sought truth, but their approach was the reverse of that of the Jesuits: instead of imposing a unified order upon the world, they attempted to study the world as given, and to find the order within.” This started a conflict between the Galileans and the Jesuits.

For the church, the idea that matter could be broken down into infinitely small indivisible atoms was unacceptable. The archives of the Society of Jesus in Rome records for posterity the ruling of their leaders in 1632 on infinitesimals [12]:” Judgment on the Composition of the Continuum by Indivisibles”. …The permanent continuum can be constituted of only physical indivisibles or atomic corpuscles having mathematical parts identified with them. Therefore the said corpuscles can be actually distinguished from each other.” The church basically ducked the question of non-representability and banned the idea and the mathematical study of ‘indivisibles’.

Among the critics of these indivisibles was Thomas Hobbes, the philosopher author of the Leviathan, who deeply influenced Western thought. Hobbes was also an excellent mathematician and a devotee of the Euclidean approach. He was bitterly opposed in this battle of the infinitesimals by John Wallis of England, one of the founders of the Royal Society, the new science academy [12]. Wallis had little time for eternal proofs, and was firmly rooted in what we can unmistakably recognize as the pragmatic Ganita approach for solving real-life problems. Hobbes had tried in vain for several years to prove that he could ‘square the circle‘, and each attempt in this futile exercise was eagerly demolished by Wallis and exploited to the hilt in their public feud [12]. Eventually, Wallis’ team ‘won’ the contest (possibly in terms of cultural and scientific acceptance) and Newton came up with his famous work Principia Mathematica that relies heavily on calculus. Interested readers can refer to [12, 1] for a detailed discussion.

The Ghosts of Departed Quantities

It is worth noting some logical inconsistencies in the positions of both sides in this battle. The church was fighting to save their dogmatic belief in an infallible and orderly Euclidean math against a group injecting a practically useful but poorly-understood imported concept into this math. Every researcher seemed to have his own pet model showing how the math of the infinitely small worked.  In an important and devastating piece of satirical writing, Anglican church bishop Berkeley ridiculed the questionable fluxions of Newton, and Leibniz’s ‘infinitesimal change’ as “the ghosts of departed quantities”. CK Raju concludes (as do others) that this calculus was not on firm epistemological ground.

The European approach appeared to be mechanical and did not, for example, employ the end-correction terms that had helped keep Indian derivation transparent and anchored in a valid pramana [1]. Mathematicians could not accept, understand, or were unaware of the Ganita rationale behind the amazing calculus results derived by the Kerala School. For example, it is known that “Newton later became discontented with the undeniable presence of infinitesimals in his calculus, and dissatisfied with the dubious procedure of “neglecting” them” [24].  Mathematics was enhanced so that calculus was eventually placed on a firm formal foundation in the 20th century [1].

Transmission of Calculus from India to Europe

The etymology of ‘calculus‘ (17th century CE, Latin) relates to ‘reckoning’ and ‘accounting’. This focus is entirely empirical and on calculation, far away from the Euclidean world of theorems and proofs. On the other hand, it is directly corresponds in meaning, intent, and usage to Ganita. So far, research has uncovered three kinds of evidence linking Indian Calculus transmission to Europe: documentary, circumstantial, and epistemological. The interested reader is referred to [24, 1] for details. A primary, initial motivation for appropriating Ganita’s calculus results appears to be the practical problem of navigation: to obtain accurate trigonometric values required to calculate the 3L mentioned earlier [1].

A note in [24] on the circumstantial evidence is worth stating: “Unlike India, where the series expansions developed over a thousand-year period 499-1501 CE, they appear suddenly in fully developed form in a Europe still adjusting to grasp arithmetic and decimal fractions“. The 1400+ year discontinuity in the study of infinitesimals  in Europe was followed by a sudden upsurge in results in the 16th-17th century [12], right after Ganita’s documented achievements in Kerala and the establishment of European missions along the west coast. In fact, this was also a period when results from Ayurveda and Siddha began traveling to Europe giving birth to modern Botany, and similarly revolutionizing western medicine, health-care, and sanitation.

Epistemological Evidence

The epistemological evidence is fascinating to read [1]. A barrier in the western mindset as far as dealing with uncertainty manifests itself clearly in both the first and second math crises. As noted in [24]: “The European difficulty with zero did not concern merely the numeral zero, but related also to the process of discarding or zeroing a “non-representable” during the course of a calculation—similar to the process of rounding. Though the Indian method of summing the infinite series constituted valid pramana, it was not understood in Europe; the earlier difficulty with non-representables zeroed during a calculation reappeared in a new form. This was now seen as a new difficulty—the problem of discarding infinitesimals… In both cases of algorismus and calculus, Europeans were unable to reject the new mathematical techniques because of the tremendous practical value for calculations (required for commerce, navigation etc.), and unable also to accept them because they did not fit in the metaphysical frame of what Europeans then regarded as valid“.

Another instructive story (see page 3 of this essay), highlighting the outcome and unintentional humor caused by a borrow-copy-paste of Ganita without fully understanding its epistemology, is about how ‘sine’ and ‘cosine’ entered Europe. These mistranslated terms destroy the insight behind the original Sanskrit terms jya and kojya [1], baffling generations of Indian students studying Trigonometry.

To this day, neither organized religion and its theology, nor secular mathematicians, have been able to fully embrace the epistemology and validation procedure of Ganita. Why is this? And examining this question from the other direction, why did the Indians not take Euclidean math seriously for two thousand years? What is the future of Ganita? We study these civilizational perspectives in the third and concluding Post of this Set.

Selected References
  1. Cultural foundations of mathematics: the nature of mathematical proof and the transmission of the calculus from India to Europe in the 16th c. CE, C. K. Raju. Pearson Longman, 2007.
  2. Plato on Mathematics. MacTutor History of Mathematics archive. 2007.
  3. Plato’s Theory of Recollection. Uploaded by Lorenzo Colombani. Academia.edu. 2013.
  4. Being Different: An Indian Challenge to Western Universalism. Rajiv Malhotra. Harper Collins. 2011.
  5. Axiomatism and Computational Positivism: Two Mathematical Cultures in Pursuit of Exact Sciences. Roddam Narasimha. Reprinted from Economic and Political Weekly, 2003.
  6. Use and Misues of Logic. Donald Simanek. 1997.
  7. Computers, mathematics education, and the alternative epistemology of the calculus in the Yuktibhasa. C. K. Raju. 2001.
  8.  American Veda: From Emerson and the Beatles to Yoga and Meditation How Indian Spirituality Changed the West. Phil Goldberg. Random House LLC. 2010.
  9. Logic in Indian Thought. Subhash Kak.
  10. Ramanujan’s Notebooks. Bruce Berndt. Mathematics Magazine (51). 1978.
  11. C. K. Raju. Teaching mathematics with a different philosophy. Part 2: Calculus without Limits. 2013.
  12. Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World. Amir Alexander. Farrar, Straus and Giroux reprint / Scientific American. 2014.
  13. Indra’s Net: Defending Hinduism’s Philosophical Unity. Rajiv Malhotra. Harper Collins. 2011
  14. Mathematics in India – From Vedic Period to Modern Times: Video Lecture Series, by M. D. Srinivas. K. Ramasubramaniam, M. S. Sriram. 2013.
  15. Mathematics Education in India: Status and Outlook. Editors: R. Ramanujam, K. Subramaniam. Homi Bhabha Centre for Science Education, TIFR. 2012.
  16. The Battle For Sanskrit. Rajiv Malhotra. Harper Collins. 2016.

(A full list of references will be published along with Part-3).

Acknowledgment: Big thanks to the ICP blogger and the editor for their constructive feedback, patience, and comments that helped shape and improve this post.

An Indic Perspective to Mathematics — 1

This is the first of a 3-part set of Posts that follows our ‘Introduction to Ganita’


baudhayanatheorem
Pythagorean or Baudhayana Theorem? (from Bhaskara’s Lilavati)
Topic Outline

This Post studies from an Indic perspective, the path taken by Mathematics from ancient Greece to reach its present form. We compare and contrast Math with Ganita (introduced in our previous post) and in this process, also gain a better appreciation for Ganita. In some places, oversimplifications are employed for ease of understanding, and to bring into focus certain latent aspects of the discourse. All emphases within quotes are ours.

For convenience, this Post has been divided into a set of three, to be published consecutively. The first part is presented today, but the entire set is previewed below:

Part 1: We study the origins and motivations of Math and the pivotal roles of Plato, Aristotle, and Euclid (via Elements) in shaping the initial course of Mathematics. We compare the Indian and Greek logic, noting the non-universality of logic. To each civilization and culture, their own: Pramana versus Proof. A fundamentally different understanding of the nature of ultimate reality guides the Math and Ganita approaches: The integral unity underlying Ganita versus a synthetic unity in which Math lives as a separately independent component.

Part 2: We observe and learn what happens when Ganita encountered Math. Sparks fly in a tussle between order and chaos when two sharply different approaches clash.

Part 3: We adopt an Indic civilizational perspective of the Math-Ganita encounters. This gives rise to  interesting questions like ‘What was lost when Mathematics digested Ganita?’. We also look ahead, exploring the importance of Ganita and its Indian approach in a futuristic world.

Part 1:Introduction
Dolores Umbridge: It is the view of the Ministry that a theoretical knowledge will be sufficient to get you through your examinations, which after all, is what school is all about.

Harry Potter: And how is theory supposed to prepare us for what's out there?

(Harry Potter and the Order of the Phoenix, by J. K. Rowling).

Mathematics is the ‘science of learning’ that originated in ancient Greece, and comes from the Greek root mathesiz, or learning [1]. Plato’s Republic (~375 BCE) mentions the five specific disciplines of mathematics as: Arithmetic, Astronomy, Plane and Solid Geometry, and Harmonics [2]. Plato founded the Academy in Athens and gave Western (Greek) philosophy to the world.  ‘Learning’ had a specific meaning in this philosophy. His ‘theory of recollection’ indicates that ‘mathesiz’ is all about a soul recollecting the knowledge it has forgotten. We cannot learn anything new, and only recall what we forgot [3]. His teacher was Socrates, and Aristotle was his famous pupil.  Plato took as ideal that which was perfect, unchanging, abstract, even spiritual, and regarded the phenomenal world riddled with uncertainty as inferior. He favored the rational over the empirical, and the goal of uplifting the soul as superior to the task of performing mundane calculations. For example, when it came to arithmetic, his views as the narrator in the Republic were pretty clear [2]:

I must add how charming the science of arithmetic is! and in how many ways it is a subtle and useful tool to achieve our purposes, if pursued in the spirit of a philosopher, and not of a shopkeeper!’

‘How do you mean?’, he asked.

‘I mean, as I was saying, that arithmetic has a very great and elevating effect, compelling the mind to reason about abstract number, and rebelling against the introduction of visible or tangible objects into the argument.”

Several elegant results came out this Greek approach which can be broadly viewed as a sequence of axiom/model followed by the use of deductive logic to prove an infallible theorem [5]. The exemplar for this approach is Elements, the treatise on geometry attributed to Euclid (~300 BCE), and this ancient work played a very powerful role in shaping the course of Mathematics. The impact of Euclidean geometry is visible to this day. However, progress in the realm of practical application and calculation was curtailed by the downgrading or even the elimination of the empirical.  While logic and deductive reasoning are indispensable in detecting inconsistencies in arguments and help in viewing existing ideas more clearly, scholars have recognized the limitations of logic when it comes to understanding the nature of ultimate reality:

  1. Logic can be misused when it is employed to find Truth. About Aristotle [6]: “it was, for him, a tool for finding truth, but it didn’t keep him from making the most profound errors of thought. Nearly every argument and conclusion he made about physical science was wrong and misguided. Any tool can be misused, and in these pre-scientific days logic was misused repeatedly“.
  2. Deductive reasoning can help us analyze existing ideas better and lead us to a different way of tackling a problem, but in itself cannot lead us to new knowledge.  “deduced conclusions are just restatements and repackaging of the content contained in the premises. The conclusions may look new to us, because we hadn’t thought through the logic, but they contain no more than the information contained in the premises. They are just cast in new form, a form that may seem to give us new insight and suggest new applications, but in fact no new information or truths are generated. This is especially noticeable in mathematics…“[6].

This Mathematics lived in an abstract infallible world divorced from reality.  One cannot also overemphasize the impact of Aristotle’s ‘law of the excluded middle’ on western thought – a law that leaves no room for uncertainty. The intellectual ideas of Greece were eventually digested [4] into Christianity via the so-called ‘Hellenic-Hebraic’ synthesis. This should come as no surprise given the motivation for the studying mathematics included ideas of absolute perfection and ‘uplifting of the soul’. Mathematics thus became intertwined with the theology of an organized religion. A comparative study of the Indian and the Greek approach bring out the sharp differences between the Ganita and the Mathesiz approaches. Ganita, the integral science of computing, is not the same as mathematics. Unlike the five categories of Mathematics laid out by Plato, Ganita is all pervasive.

via @Calvinn_Hobbes

In [4], Rajiv Malhotra comments on the influence of Aristotle on western thought: “The Law of the Excluded Middle dictates that the principle ‘P or not-P’ separates one thing from another in an absolute sense. All physical and logical entities are invariant units, mutually exclusive of each other. This is not just a pragmatic criterion for distinguishing one thing from another; it is the very nature of reality in both concrete and abstract realms. The law eliminates the possibility of things being mutually dependent, interrelated and interpenetrated. It is diametrically opposed to the intertwined and fluid relationships characteristic of integral unity…”.

There appears to have existed a state of tension between the fallible-and-real and the infallible-and-perfect domain in the western thought since the time of Plato, which manifests itself today as the anxiety-filled binary of ‘religion versus science’. Since this gap was never breached, only a synthetic unity was ever possible [4], and the resultant western approach is reductionist. The independent parts have to be subsequently synthesized to achieve unity. For example, we read in  [25] that “much of Western civilization is based on separating the parts. One date is separate from another, history separate from math which is separate from biology. It’s a world view we inherited from Newton and Descartes, so useful in many ways and disastrous in others. However, there has always been an alternative view of the universe as a single, totally interconnected system. You’ll find that in Eastern traditions.“. To this day, Mathematics and Science are treated and taught as two different school subjects. A key tussle here is between the ‘lower’ empirical world we can experience, and the ‘higher’ abstract-theoretical domain, with the latter being considered superior. This western view is even being taken as the universal approach to knowledge.

Western Universalism

Today, we can observe the promotion of the notion of a western universalism that traces its origin to the intellectual tradition of ancient Europe. For example, the choice of the logo for UNESCO, a world body, reflects a desire to preserve the memory of Parthenon in ancient Greece, which was damaged in wars eons ago. Key buildings in several prominent universities in the United States are designed to remind viewers of the glory of ancient Rome and Greece.

The UNESCO logo (Credit: wikimedia.org)

The belief in the dominance of Euclidean Mathematics is reflected in the argument between the ancient Greeks and Epicureans.

The Epicurean Ass

The Epicureans opposed the followers of Euclid who, from their perspective, appeared to be proving obvious results. For example, consider the following proposition in Elements as discussed in [23]:

Any two sides of a triangle are together greater than the remaining side.

In other words, a straight line is the shortest distance between two points!

If anyone wanted to ridicule mathematics for its insistence on the axiomatic method of orderly proof, this theorem offers a wide target. In fact, the Epicureans (those Athenian free-thinkers, who defined philosophy as the art of making life happy) did exactly that. They said that this theorem required no proof, and was known even to an ass. For if hay were placed at one vertex, they argued, and an ass at another, the poor dumb animal would not travel two sides of the triangle to get his food, but only the one side which separated them.”

C. K. Raju explains both sides of the argument [7]: “Proclus replied that the ass only knew that the theorem was true, he did not know why it was true. The Epicurean response to Proclus has, unfortunately, not been well documented. The Epicureans presumably objected that mathematics could not hope to explain why the theorem was true, since mathematics was ignorant of its own principles..” In the end, the Greek response cites the authority of Plato that mathematics “takes its principles from the highest sciences and, holding them without demonstration, demonstrates their consequences. [7].

Let us now introduce an Indic perspective.

In contrast with this Greek view, all Indian schools of thought accept empirical means of verification (e.g., pratyaksha pramana [1, 22]) while acknowledging the potential fallibility. All darshanas would reject any axiomatic approach that lacked valid pramana. The use of empirical rationale has existed in India since ancient times, including the Sulba Sutras (800 BCE or earlier) and is different from the axiom-theorem approach. C. K. Raju puts this in perspective: “Because no proof was stated it does not, of course, follow that the authors of the sulba sutras did not know why the result was true. But the method of proof that convinced them may well have  differed from the current definition of proof. Thus, it is incorrect to assert that the constructional methods used in the sulba-sutras implicitly lead to a proof in a formalistic sense. It is incorrect because the rationale for the formula for a right-angled triangle, from the constructional methods of the sulba-sutras right down to the 16th century Yuktibhasa, explicitly appeals to the empirical“. [7]

The Epicurean Ass argument has been kept alive in some form or the other to this day in a western worldview. From an Indian point of view, a Ganita expert like Srinivasa Ramanujan too was deemed a ‘wizard’ [14, Lecture 1] who did not know why his results were true, despite his point that he employed his own valid method, which produced so many astounding new and true results. He had to move from Kumbakonam to work in the U.K. to prove his results to the satisfaction of the formal math community in order to gain acceptance.

Indian Gurus, Yogis, Siddhas, and Tantriks who, through years of practice and sadhana, demonstrated amazing results in transcendental meditation, mind sciences, and medical sciences are sometimes labeled pre-rational Indian ‘mystics’ [4] as opposed to western ‘scientists’ who came up with sophisticated instrumentation that subsequently confirmed these results. Universities like Harvard periodically comes out with a research report ‘proving‘ prior findings in Yoga and Ayurveda from the Dharma traditions, which have been practically employed for centuries.

Public intellectuals like Rajiv Malhotra also ask: How often are these Hindu and Buddhist monks, who are the primary producers of this knowledge, credited as co-authors in the journal papers? This bias is propagated subtly by western scholars who study Hinduism. For example, Phil Goldberg who teaches at Loyola Marmount University, an institution rooted in the Jesuit Catholic tradition, compares ‘Indian philosophy and Western science’ in [8]. He also endorses the rejection of the ‘orange’ [saffron] robe of Dharma in favor of the authoritative western scientific garb of a ‘white lab coat’ in order to increase the credibility of Yoga and meditation techniques in the minds of westerners. Note the approach is one of extracting the benefits, and then rejecting/denigrating the Dharma source. Such biased attitudes have also helped feed an increasing Hinduphobia within western academia.

Two-valued logic is not universal. India had not one but several different schools of thought that also studied logic [22], including Nyaya and Navya Nyaya, as well the Buddhist Catuskoti, and Jaina Syadavada. In fact, the Buddhist understanding of integral unity as encapsulated in Nagarjuna’s brilliant arguments has been recognized as nothing short of a “death-blow to all synthetic unities that start with different essences and then look for unity” [4].

Indian Logic vs Greek Logic

There are several papers available that discuss the Indian approach to logic. For example see this work of Subhash Kak [9] and this discussion of Indian and Greek logic. In the popular textbook example for Indian syllogism versus that of Aristotelian logic, the first thing we notice are the ‘five steps’ in the Indian approach versus three in the Greek template [22]. The steps in the Indian rules of inference are not redundant and serve as a reality-check based on the correspondence principle of Bandhu [9], whereas the Greek argument is restricted to the infallible abstract domain. As Roddam Narasimha notes in [5] where he compares Greek Axiomatism and Indian Computational Positivism, the Indian distrust of deduction-based logic “appears to have been based on the conviction that the process of finding good axioms was a dubious enterprise. Note that logic in itself was not something that was shunned in India; without going into a detailed discussion of Indian systems of logic, it is enough to note here that time and again Indians use deductive logic to demonstrate inconsistencies or to refute the positions of an adversary in debate, rather than to derive what western cultures have long sought through that method – namely, certain truth.“.

The intellectual prowess of the ‘deductive logician’ has been promoted in popular western culture. For example, Sherlock Holmes is recognized foremost for his superb deductive reasoning, and is considered the most portrayed literary human character in history. However, an analysis of his stories show that Holmes relied a lot on anumana (inference) including the so-called abductive and inductive methods, and Conan Doyle did consider Holmes’ methods to be fallible, which resembles a Ganita approach to sleuthing!

Sherlock Holmes Portrait Paget.jpg
‘Sherlock Holmes’ By Sidney Paget (1860-1908) , Public Domain. Credit: Wiki Commons

CK Raju [1] calls out some flaws in the claim to universality of two-valued logic. First, the Hindu darshanas, Buddhist Catuskoti, and Jaina Syadavada offer solid alternatives from a different culture. These alternatives have always been compatible with the latest developments in science at every point in time, including Quantum Mechanics. We do not find any serious ‘religion vs science’ problem in India [4]. Even the materialist Charvaka school would reject this reductive logic for not accepting a Pratyaksha Pramana [1, 22]. Finally, it is tough to justify two-valued logic citing empirical evidence if its claim to dominance lies in its empiricism-free perfection [1].

A remaining argument in favor of a universality of two-valued logic and axiomatism is the endorsement by ‘higher authority’, representing a distorted version of Sabda pramana [22]. Indeed some proofs published in journals today are so abstract and technical that they can only be decoded by top formal mathematicians. The remainder of the global math community take it as truth based on the verbal authority of an elite few.

Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true - Bertrand Russell.
Vignette: Demotion of a Theorem

In middle school geometry, we learn about the congruence of triangles and come across the side-angle-side (SAS) postulate [23]:

“The fundamental condition for congruence is that two sides and the included angle of one triangle be equal to two sides and the included angle of the other.”

This result can be easily verified using empirical rationale (proof-by-superposition, as Euclid himself did), and would be perfectly acceptable in Ganita, but not in mathematics. This is because superposition involves moving one triangle and placing it on top of the other, which is considered a ‘fallible’ process. The SAS result is difficult to prove using logic alone and thus the SAS theorem was demoted to the status of an unproven postulate.

We conclude Part 1 by delineating a key, irreconcilable difference between Ganita and Mathematics. This difference also manifests in virtually every other field of study.

Summary: Fundamental Difference between Ganita & Mathematics

The ancient Indians recognized Nyaya (logic) and employed Tarka (reasoning) and even mastered it, but did not put it on a pedestal because of certain limitations. Results in Ganita, like all other Indian disciplines, are tied to a valid Pramana and rooted in reality, rather than an axiom-based proof operating in a separate abstract domain. The empirical approach can elevate the practitioner to a higher state of consciousness (The Bhagavad Gita recognizes it as a valid way to transcendental knowledge [4]).

Subhash Kak summarizes the Indian approach to acquiring knowledge based on bandhus [9]: “The universe is viewed as three regions of earth, space, and sky which in the human being are mirrored in the physical body, the breath, and mind. The processes in the sky, on earth, and within the mind are taken to be connected. The  universe is mirrored in the cognitive system, leading to the idea that introspection can yield knowledge“.  It is worth repeating what has been said before: In nature, the western civilization is intellectual, the Chinese civilization is philosophical, and the Indian civilization is spiritual (adhyatmic).

Ganita is rooted in an integral unity whereas Mathematics exists as a separately independent part of a synthetic unity.

This integral approach produced some of the most important contributions, from Hindu numerals, place value system with zero, to symbolic language for managing equations [5]  and calculus. On the other hand, the abstract nature of Mathematics resulted in a drastically reduced practical output while Europe drifted into a 1000+ year Dark Age. During this entire period, Ganita contributions from all Dharma thought systems proved to be crucial in keeping mathematics practically relevant in other parts of the world, up to the 17-18th century CE. We discuss these Ganita-Math encounters in the upcoming second part of this set of Posts.

Selected References
  1. Cultural foundations of mathematics: the nature of mathematical proof and the transmission of the calculus from India to Europe in the 16th c. CE, C. K. Raju. Pearson Longman, 2007.
  2. Plato on Mathematics. MacTutor History of Mathematics archive. 2007.
  3. Plato’s Theory of Recollection. Uploaded by Lorenzo Colombani. Academia.edu. 2013.
  4. Being Different: An Indian Challenge to Western Universalism. Rajiv Malhotra. Harper Collins. 2011.
  5. Axiomatism and Computational Positivism: Two Mathematical Cultures in Pursuit of Exact Sciences. Roddam Narasimha. Reprinted from Economic and Political Weekly, 2003.
  6. Use and Misues of Logic. Donald Simanek. 1997.
  7. Computers, mathematics education, and the alternative epistemology of the calculus in the Yuktibhasa. C. K. Raju. 2001.
  8.  American Veda: From Emerson and the Beatles to Yoga and Meditation How Indian Spirituality Changed the West. Phil Goldberg. Random House LLC. 2010.
  9. Logic in Indian Thought. Subhash Kak.

(The complete list of references will be published along with part 3).

Acknowledgments: I would like to thank the ICP bloggers for their constructive feedback and the editor for his incisive comments and ideas.

Introduction to Ganita

Lilavati1Bhaskara2
Lilavati by Bhaskaracharya 2

This introductory blog provides the background for an upcoming Ganita series here at ICP. All emphasis within quotes is by this author.

Losing one glove is certainly painful,

but nothing compared to the pain,

of losing one, throwing away the other,

and finding the first one again. 

—Piet Hein, Danish Mathematician

Introduction

Though often compared with the field of Mathematics, Ganita is best defined as the science and art of computation that originated in India. This is based on the definition offered by Ganesha Daivajna in his commentary (1540CE) on the classic Ganita treatise Lilavati of Bhaskara-2 [1]. Other descriptions of Ganita include ‘computing science’, ‘reckoning’, ‘science of counting’, ‘science of calculation’, etc. Although Ganita is related to Mathematics, they are not the same. The practice of Ganita cuts across multiple areas including Mathematics, Computing, Science, Logic, Analytics, etc. The term Mathematical Sciencesmay be closer to Ganita There is no exact English equivalent for the Sanskrit word Ganita, and it is better to use ‘Ganita’ as is.  

An ancient extant work of Ganita is the Sulvasutras (Sulbasutras), which are the oldest texts of geometry dating back to 800 BCE or earlier [1]. A verse in the Vedanga Jyotisha (1100 BCE or earlier) attests to the pride of place occupied by Ganita in ancient India.

Like the crest on the peacock’s head,
Like the gem in the cobra’s hood,
So stands Ganita*,
At the head of all the sciences.

The Ganita Culture of India

Indians are famous for their Ganita prowess. The greatest Persian scholar of his time, Ibn Sina (aka Avicenna, 10-11th CE) found that an Indian vegetable vendor’s calculating skills were superior to anything he knew [1].  European visitors during colonial times were astounded and remarked that “the natives of India are remarkable for the facility with which they acquire the mathematics; and indeed they excel in anything in which figures or numbers are concerned”.  The East India Company promised a reward of twenty pounds to its soldiers if they could learn arithmetic from the Indians [2]. It is well known that the word ‘algorithm’ comes from Algorismus, the latinization of ‘Al-Khwarizmi’, the person who translated several Sanskrit texts of Ganita (e.g. those of Brahmagupta) into Arabic. Thus, an algorithm implies the Indian method of computation, i.e., ‘Ganita’.  Much of Ganita and its methods made its way to Europe, first through Arab translators, and later through Jesuit priests stationed in India [3].

The Ganita curriculum in Indian schools prior to European colonization was functional, pragmatic, autonomous, and also guided by, and customized to local needs. The method of teaching Ganita in schools was ahead of its time. Researchers attribute this success to: “a culture of pedagogy grounded in a form of memory very different from the modern associations of memory with rote or mechanical mode. This could be characterized as recollective memory where memory practices constituted a distinct mode of learning and not merely aids to learning”[2]. 

To this day, the Ganita prowess, ability to recall, and the computing literacy of Indians is second to none. It is no coincidence that Indians excel in STEM disciplines. Understanding how Ganita works and what lies at its core is useful and interesting. Ganita can be a refreshing complement to the dull and dry Math taught in schools today. Training young minds to apply the Ganita approach to problem solving can offer them a competitive advantage. Manjul Bhargava, Fields Medal winner, is an example of a contemporary scholar who scaled the peak of Mathematics and is also well versed in Ganita and aware of its Indian tradition.

Above all, Ganita is a precious part of India’s heritage and culture. It is inevitable that India will regain its lost political and economic freedom. But this can and must be achieved without selling out or forgetting its traditions and indigenous knowledge systems like Ganita, Yoga, and Ayurveda. The trauma of a civilization that realizes that it squandered away its priceless cultural treasures will be unbearable.

The Scope of Ganita

This introductory video of an excellent IIT lecture series on Indian contributions to mathematics provides a good overview of Ganita. It was recognized that Ganita’s applications span the secular and sacred domains without any artificial distinction between the two. This integral nature of Ganita was embraced by all the great Buddhist, Jaina, and Hindu scientists and astronomers since ancient times.

pervasiveness ganithasarasangraha mahaviracharya 2
source: IIT lecture series on Ganita [1]
India’s Rishis and Ganita experts attributed their astonishing insights to a sacred source. The practice of Ganita offered a valid means of attaining this infinite, transcendental knowledge, and through this process, skilled practitioners also came up with ingenious practical solutions to a variety of problems.

Sacred Source of Ganita

Panini (BCE)

The Siva Sutras in Panini’s Ashtadhyayi, which one can consider as an early example of the Indian approach to science, were revealed to Panini (pronounced: Paanini) via the sacred sounds from Shiva’s Damru. In fact, some scholars consider the Indian approach to math and science to be the ‘Paninian approach’ [1]. Indian kids traditionally start their exam papers with a small notation above the top of the page as an invocation to Ganesha (e.g. Tamil kids draw a tiny ‘Pillayaar Chuzhi’). This is an ancient practice of a tradition that reveres wisdom and learning, and one that is worth preserving. From Panini to Ramanujan, we see a great line of Ganita scholars beginning their works with an explicit tribute to a divine deity and their sacred cosmology.

Aryabhata (499 CE)

In his Aryabhatiya, the great astronomer Aryabhata who’s statue today adorns UNESCO, begins by paying obeisance to Brahma who is recognized as “the god who is the one and the many” [5]. This is a pertinent point from a Ganita perspective which we shall see later. We learn the following from the commentaries on Aryabhatiya:

  • Bhaskara I : “It is said : ‘(Aryabhata) who exactly followed into the footsteps of (Vyasa) the son of Parasara, the ornament among men, who, by virtue of penance, acquired the knowledge of the subjects beyond the reach of the senses and the poetic eye capable of doing good to others’.” 
  • “Aryabhata’s devotion to Brahma was indeed of a high order. For, in his view, the end of learning was the attainment of the Supreme Brahman and this could be easily achieved by the study of astronomy”.
  • Aryabhata is obtaining new results by navigating through an existing ocean of knowledge: “Having taken a deep plunge into the entire ocean of the Aryabhata-sastra with the boat of intellect, I have acquired this jewel, the Karana-ratna, adorned by the rays of all the planets.

Nilakantha Somayaji (1444-1544 CE)

He was a great Ganita expert and astronomer from the Kerala School (who can be viewed as Aryabhata’s intellectual successors). Nilakantha was also recognized for his mastery of all six darshanas of Hinduism [6]. His great work Tantrasamgraha begins with an invocation to Vishnu. Commentators on this work note that the invocations recognize Vishnu as both the material and the efficient cause of the universe [7].

Srinivasa Ramanujan (1877 – 1920)

srinivasaramanujan

Ramanujan attributed his amazing results to Goddess Namagiri. His statements reveal a firm belief and appreciation of Hinduism and its understanding of ultimate reality. The source of his knowledge was beyond anything cognizable by ordinary senses. Thanks to his biography [8], there’s a lot of material describing, from a western perspective, Ramanujan’s amazing ability, and the following samples provide clues about his methods. Ramanujan is a role model for aspiring young Indian mathematicians and scientists, and this was acknowledged by the Nobel Laureate Astrophysicist, S. Chandrashekar.

  • Ramanujan’s belief in hidden forces and the powers of the supernatural
    was never, at least back in India, something about which he felt the need
    to apologize or keep quiet
  • Ramanujan “had grown up on the Indian gods and the relaxed fluidity of Hindu belief. In him, the natural and the supernatural, Jacobi and Namagiri, Number
    and God, found a common home, stood in something like an easy intimacy.
  • “…the mystical streak in him sat side by side, apparently at perfect ease, with raw mathematical ability may testify to a peculiar flexibility of mind, a special receptivity to loose conceptual linkages and tenuous associations.
  • his openness to supernatural influences hinted at a mind endowed with slippery, flexible, and elastic notions of cause and effect that left him receptive to what those equipped with more purely logical gifts could not see; that found union in what
    others saw as unrelated; that embraced before prematurely dismissing

Each of these independent Indian thinkers freely moves between the transactional and the sacred domains without anxiety. Their work was firmly anchored in Dharma, and serving this integrated unity. The deities invoked include the celestial Hindu trinity and the Devi. Dharma is not the same as religion [10], and this is not theology or missionary zeal working overtime to fudge mathematical models in order to make it compatible with religious scripture, prophecy, and God. Rather, Ganita’s findings arise from a seeker’s quest to learn the truth about the nature of ultimate reality. The Bhagavad Gita (verses 9.4, 3.40-41) recognizes the empirical to be rooted as well as culminating in the transcendental [13]. Ganita is a sacred and valid path to reach the transcendent, and the continuity in the views of four great scholars from different time periods in Indian history drives home this point. Given the importance attached to this sacred source by its foremost practitioners, it is more accurate to view Ganita as the integral science of computing.  Attempts to equate Ganita to a purely pragmatic and secular science or math is inaccurate and reductionist.

The creation stories in the Vedas lend themselves to a rich interpretation that trace out a fundamental Ganita template which was adopted by all these great practitioners. Toward this, we start with an algorithmic interpretation of Prajapati’s efforts to create a stable, self-organized universe [9].

Prajapati’s Algorithm

Prajapati employs an algorithm to create the cosmos. An iteration in this algorithm consists of an experimental trial, followed by an observation of the output data, which triggers a review and validation phase, followed by an adjustment of ‘design parameters’ and re-trial, if necessary. This process converges to Prajapati’s satisfaction within three iterations. However, no attempt is made to prove or claim with absolute certainty that among all possible universes, his is the most perfect and infallible. Since time is cyclical, such universes are dissolved and recreated with no beginning or end. The Rig Veda explicitly recognizes the inherent uncertainty associated with any answer to such questions [10].

  1. The first empirical trial produces a cosmos which is observed to be full of entities too similar in nature and they simply merge into each other, so that there is practically nothing to unite.  This is a homogeneous and ‘over-ordered’ universe where there is nothing left to know, and this system quickly becomes unmanageable. From a statistical perspective, there is little or no variance in this first universe.
  2. Prajapati increases variability in his second try but the output shifts to the other extreme. The world is now way too heterogeneous and there is no commonality between beings to relate to, and to unite. Nothing is certain and can be known, and chaos reigns.
  3. Learning from the first two attempts, Prajapati is able to achieve a good balance in his third version that overcomes prior problems, and the algorithm terminates with a stable universe.

How does Prajapati accomplish this task? In his book ‘Being Different’, Rajiv Malhotra says “Prajapati recognizes that all life should be situated between these opposing excesses of too much identity difference and too much homogeneity. Ultimately, he succeeds in producing just such a universe. He does so through the power of resemblance, known as ‘bandhuta’ or bandhu, which was discussed in Chapter 3. The Vedas abound in attempts at finding connections among the numerous planes of reality. This serves as a cardinal principle of all Vedic thought and moral discourse”.

Every entity created is unique, while also bearing some form of resemblance to each other.  Some resemblances may be more easily spotted, while others may be subtle and identifiable only after considerable effort. These Bandhus are the ‘conceptual linkages and tenuous associations’ revealed to Ramanujan after intense tapasya, and he is able to find “union in what others saw as unrelated” because the cognizable world is mirrored and mapped into the transcendental world, and vice versa via these Bandhus [11]. These strands of resemblances intertwine the elements of the universe into an integral unity, where every individual element’s identity is real but provisional, while always being rooted in the independent whole. There are no separately independent realities for individual elements and the methods of Ganita mirror Prajapati’s algorithm.

Bandhu
"The bandhus represent the laws that hold the universe together (Vishnu), paroksha is the dance of consciousness that is ever changing (Shiva), and Yajna is the process of
 change (Devi)" - Subhash Kak, Pragnya Sutra [PS, 12].

The idea of ‘resemblance’ is fundamental to the acquisition of knowledge that is required to make ‘risky’ and useful predictions about the future with a measure of confidence. This concept can be illustrated using the analogy of a modern business forecasting system. Suppose a company launches a brand-new product in the market and needs to know now how many units it is likely to sell in the next 6-12 months. Since no prior sales data about this product is available, no statistical method cannot be employed to directly calculate this number. To overcome this limitation, the new product A is mapped in terms of its selling attributes to that pre-existing product B which it resembles most. B’s data is borrowed to generate an initial sales forecast for A. Machine learning and AI techniques can be used to learn such recursive patterns, even deep ones, from unstructured data.

However, a machine has its limits. Computer Scientist and Sanskrit scholar Prof. Subhash Kak notes [12] “… knowledge emerges from a familiarization with its inner space and it may be seen to be a consequence of the bandhus (bonds) that exist between the outer and inner worlds. If there were no such bandhu, it would be impossible to make sense of the world. Machines only follow predefined rules and they don’t have bandhus, which is why they cannot be conscious. The bandhus are the ground that make awareness possible“.

Bandhus can be in the form of numbers, biological rhythms, sounds, lights, touch, etc.[11]. Or via Meghadutam? A study of the applications and motivation of ancient Indian geometry reveals the traditional Hindu approach of coexisting in harmony and synchronizing with nature by recognizing certain auspicious and sacred ratios and numbers (e.g. 108).  Two examples are stated below, which also bring to light the continuity and commonality in thought between the Harappan and Vedic time periods. We will discuss this in depth later in our series.

  1. The ratios and measurements used in Harappan architecture at Dholavira (2500 BCE or earlier)
  2. The dimensions and numbers of bricks used in Vedic fire altars.

Two of the three key notions of dharmic cosmology are recursion and paradox [11]. The former, via the principle of resemblance, injects a sense of order and certainty into our view of the transactional world, whereas the latter preserves the mystery and uncertainty about the true nature of ultimate reality. It is convenient in the Ganita context to understand this recursion using the Vedic metaphor of Indra’s net.

Self Organizing Patterns: Vedic Metaphor of Indra’s Net
"The Vedic deity Indra is said to have an infinite net consisting of a jewel in each node, arranged so that every jewel reflects all the other jewels; there is no separate self-existence of any jewel. Each is unique in its reflection of all others. Indra's Net symbolizes a universe with infinite dependencies and relations interwoven among all its members, none of which exists apart from but only in the context of this collective reality."  - Rajiv Malhotra, Indra's Net.

The links in this self-organized network are precisely the Bandhus. Since the ultimate reality is like Indra’s Net, Prajapati’s world allows order and information to emerge from what appears to be nothing but chaos and uncertainty (even soccer matches!). Such an Indra’s Net becomes a limitless source of useful ideas for Ganita. We provide three examples from Mathematics to illustrate this.

  • The ‘Rule of Five’ [14] states that: “There is a 93.75% chance that the median of a population is between the smallest and largest values in any random sample of five from that population.” Just five random samples are enough in nature, with no preconception about its probability distribution, to achieve a significant reduction in uncertainty – from being totally unsure, to knowing a lot about any group’s median behavior. This order has been hiding all along in plain sight.
  • The world around us is full of (approximately) normal distributions or bell curves, allowing a certain statistical order to emerge out of seemingly disorganized groups.
    source: usablestats.com

    Of course, not everything in nature is normally distributed. There are plenty of exceptions [14]. In [15], Lyon tries to understand how such normal distributions come about in nature. He argues that it is not because of the central limit theorem. He uses inference (which Indian logicians recognize as anumana) to understand how these patterns are generated in nature. By using the idea of ‘entropy’ to denote the degree of chaos (or disorder), we learn: “A further fact, which serves to ’explain’ why it is that this ’order generated out of chaos’ often has the appearance of a normal distribution, is that out of all distributions having the same variance the normal has maximum entropy (i.e. the minimum amount of information).” The balance between order and chaos in nature produces approximate bell curves, whose statistical properties can be gainfully employed to better understand this world. Sometimes, this Indra’s Net manifests itself as spectacular visuals.

  • In the brief video below, we can observe fireflies synchronizing. Thousands of fireflies light up at the same instant by simply doing their Dharma of flashing ‘strobes’ and sending out a visual signal, and in turn appropriately responding to incoming signals [16]. This was first noticed by western researchers in the jungles of Thailand. After the first sync-up, they remain synced. Self-organization is quite natural in the Vedic universe, and now we are beginning to see rigorous mathematical proofs reaffirming this reality. Inference and intuition was used by mathematicians in tandem with logical reasoning to understand the process of ‘sync’ and prove that synchronization is guaranteed in nature under certain conditions. Strogatz notes in [16] “The implication is that in a population of fireflies or brain cells, the oscillators have to be similar enough or nobody will synchronize at all.”  A certain balance between order and chaos is required for sync, and evidently, this is not uncommon in nature. After all, the dance of the universe is synced to the dance of Nataraja. Out of these self-organization principles emerge the beautiful equations and results of Ganita.

The Ganita of self-organization shows up prominently in Hinduism and in India. This decentralized ‘sync’ by insects could be quite naturally viewed by Hindus as a firefly Kumbh Mela. Pre-colonial India was largely decentralized. Self-organization reduces transactional costs and is environment friendly. Hinduism’s resilience and even a degree of ‘antifragility’ are due to built-in error-correcting mechanisms and the ability to constructively balance order and chaos [10]. The fidelity of Vedic chants has been orally preserved over several thousand years via embedded  layers of data redundancy that resemble ideas within modern methods of information transmission over a noisy communication channel. In the video below, Manjul Bhargava provides an example of Ganita in Sanskrit Kavya, which embeds an error-correcting code.

Several notoriously hard-to-solve mathematical problems (see example picture below) recognized in computational complexity theory are routinely managed in practice. Problem instances that actually manifest in nature appear to have certain data patterns and organization that allow them to be solved fairly quickly to the level of accuracy required by the practical application.

The Best ‘Bottleneck’ Traveling Salesman Route across USA (source: akira.ruc.dk)

Along with resemblances and patterns in nature comes paradox. Per Subhash Kak [11], “paradox is the recognition that the bandhu must lie outside of rational system, leading to the distinction between the “higher” science of consciousness and the “lower,” rational objective science“.  How does Ganita deal with paradox and uncertainty?

Ganita: At Ease With Uncertainty

A bit beyond perception’s reach

I sometimes believe I see

that Life is two locked boxes, each

containing the other’s key. 

—Piet Hein

(and in the words of Clint Eastwood, “If you want a guarantee, buy a toaster“).

In the Vedic period, there used to be enigmatic exchanges between scholars, known as Brahmodya, where a riddle about the nature of ultimate reality (Brahman, in Hinduism) was posed. The respondent remained silent if they could not decipher it, or countered with a deeper riddle if the hidden Bandhu was recognized [17]. (An entertaining version of this contest is the silent exchange via hand-gestures between Kalidasa and the scholar-princess Vidyottama). Dharma traditions recognize that our understanding of reality is likely to be incomplete. For example, Rajiv Malhotra notes in [10]: “There is equivalence in the relationship between sunya (emptiness) and purna (completeness or integral wholeness), the paradox being that the void has within it the whole“. With new knowledge and its associated benefits invariably comes uncertainty and ‘side effects’. There is no ‘free lunch’. Consequently, man-made algorithms are not infallible and dharma systems explicitly factor this in.

It is well known that Smritis have to be updated periodically while always serving  the unchanging Shruti.  Similarly, Ganita practitioners come up with increasingly better Siddhantas that progressively improve our understanding of natural phenomena. What is also important to remember is that the Indian approach to any field, including Ganita, is one of shraddha that is grounded in the sacred. We can be transformed by this experience and attain higher levels of consciousness that bring us ever closer to experiencing the ultimate reality.  This view is apparent in Aryabhatiya [5]: “the end of learning was the attainment of the Supreme Brahman and this could be easily achieved by the study of astronomy. In the closing stanza of the Dasagitikasutra, he says: “Knowing this Dasagitikasutra, the motion of the Earth and the planets, on the celestial sphere, one attains the Supreme Brahman after piercing through the orbits of the planets and the stars“.

The Integral versus the Synthetic Approach

We briefly compare two alternative approaches to dealing with paradox and uncertainty:

  1. Integral approach
    • Recognize reality with all its inherent diversity as is, as the ideal, and treat knowledge acquisition as a systematic process of reducing uncertainty.
    • Inference and intuition is useful in gaining new knowledge, and ingenuity is prized in such a tradition. Such knowledge is fallible, and new and improved methods are continually developed to reduce error to an acceptable level. Pragmatism rules, and the layman is familiar with the Ganita required for his/her own profession [2].
    • The validity of a method is demonstrated via Upapattis [1] that are rooted in reality.  From a logic perspective, the validity of knowledge is tied to the specific Pramanas it relies on, which may not be universally acceptable.
  2. Synthetic approach [10, 3]
    • Reject chaos as undesirable and consider ‘perfect order’ to be the ideal, and reality as subservient to this ideal ‘model’.
    • This binary mindset prefers to view reality as a bunch of separately independent systems where knowledge acquisition is preferably beyond doubt and free of empiricism.
    • Every new result is proven conclusively and universally using logic, starting from a minimal number of ‘self-evident’ axioms.

This distinction does not automatically imply that Ganita (example of integral approach) and modern science/math (largely synthetic approach) are in a state of irreconcilable conflict. As Roddam Narasimha notes [24]: “Modern science seems to have acquired, perhaps by fortunate accident, the property that the great Buddhist philosopher Nagarjuna called prapakatva: i.e., it delivers what it promises; it may not be the Truth, but it is honest“. What is undeniable and supported by fact is that by the 16th century CE, Ganita results had already laid the foundations for many crucial developments in modern science and mathematics [3].  Ramanujan is an example of an Indian who practiced the integral approach, and found a way to work constructively with western mathematicians so that his results could benefit the world.

It is interesting to see how Mathematician Hardy and Ramanujan reacted to each other’s approach as noted in [8].

  1. When Hardy asked for proof, we excerpt Ramanujan’s response: “…. I dilate on this simply to convince you that you will not be able to follow my methods of proof if I indicate the lines on which I proceed in a single letter. You may ask how you can accept results based upon wrong premises. What I tell you is this: Verify the results I give and if they agree with your results, got by treading on the groove in which the present day mathematicians move, you should at least grant that there may be some truths in my fundamental basis.
  2. Professor Hardy’s description of Ramanujan’s approach: “It was his insight into algebraic formulae, transformations of infinite series and so forth, that was most amazing. On this side most certainly I have never met his equal, and I can compare him only with Euler or Jacobi. He worked far more than the majority of modern mathematicians, by induction from numerical examples; all his congruence properties of partitions, for example, were discovered in this way. But with his memory, his patience and his power of calculation, he combined a power of generalisation, a feeling for form, a capacity for rapid modification of his hypothesis, that were often really startling, and made him, in his own peculiar field, without a rival in his day.”.  Prof. Hardy was careful not to tamper with Ramanujan’s mysterious ability, which was rooted in Ganita.
  3. On Ramanujan’s approach to the partition problem: “… the uncanny accuracy of their results attested to the power of the approximating technique they had used to get them ..So subtle and inspired were the approximations it permitted that it went beyond approximation to promise exactitude. …. Selberg, in fact, argues that Hardy’s insistence on certain methods of classical analysis actually impeded their efforts; and that lacking faith in Ramanujan’s intuition he discouraged a search for the kind of exact solution Rademacher produced twenty years later.”

Commentators have often termed this integral Indian approach as ‘Paninian’. We try to better understand what they mean by that.

The Real is the Ideal, and the Perfect is its Approximation

If the west has Euclid as the pioneer and exemplar for mathematics, India follows Panini. In [18], Dr. J. J. Bajaj explains this statement by using the commentary of Patanjali on Panini’s work: “In providing this characterisation of the science of grammar Patanjali laid his finger on perhaps the most essential feature of the Indian scientific effort. Science in India seems to start with the assumption that truth resides in the real world with all its diversity and complexity… As Patanjali emphasises, valid utterances are not manufactured by the Linguist, but are already established by the practice in the world. Nobody goes to a linguist asking for valid utterances, the way one goes to a potter asking for pots. Linguist do make generalisations about the language as spoken in the world. But these generalisations are not the truth behind or above the reality. These are not the idealisation according to which reality is to be tailored. On the other hand what is ideal is the real, and some part of the real always escapes our idealisation of it. There are always exceptions. It is the business of the scientist to formulate these generalisations, but also at the same time to be always attuned to the reality, to always to conscious of the exceptional nature of each specific instance. This attitude, as we shall have occasion to see, seems to permeate all Indian science and makes it an exercise quite different from the scientific enterprise of the West.

This discussion tells us that Panini’s is an integral approach rooted in the ultimate reality. On the other hand, the synthetic approach mentioned is popular in the west. Advances in modern science have been attributed to this approach. However, this approach can allow false assumptions to creep if the reality-check step is missing. There is an interesting story about the US Air Force set in the 1950s when they discovered that many of their pilots were losing control of their planes and crashing at an alarming rate.

source: thestar.com

The investigation eventually narrowed down the cause to the design of the cockpit, which was precisely engineered to a precise standard in the 1920s for the average American pilot. The USAF theory was that the average pilot had gotten bigger in the prior three decades and so the cockpit dimensions need to be re-sized upward. More than 4000 pilots were measured across 140 dimensions to compute a new standardized design. During this process, an analyst who was sifting through this data discovered that the total number of pilots who were average or near-average across these dimensions was exactly zero.  The ideal pilot simply did not exist.

A similar survey was conducted a few years earlier to find a lady in Cleveland who would closely match the ideal normal figure (‘Norma’). Among the nearly 4000 contestants, there was not one lady in the survey who matched Norma’s perfect vital statistics. Assuming that reality will conform to a non-existent ideal model is a recipe for disaster. USAF quickly realized that it was far better to design and periodically update designs based on the observed reality by explicitly taking uncertainty into account. This is exactly what the USAF did thereafter and switched their cockpit design philosophy to ‘individual fit’. It was a pragmatic response to an important problem that was jeopardizing pilot safety and costing millions of dollars. From an Indian perspective, the USAF chose the Ganita approach. Every US military branch embraced this idea soon after. A similar revolution is ongoing in healthcare, with allopathic medicine representing the synthetic alternative, and Ayurveda being the integral method. This integral approach to computing produced amazing results such as the decimal place value system and Algebra.

Integral Unity of Indian Place Value System

The Indian decimal place value system that is now used all over the world is startlingly simple and elegant. It arises from the sacred idea of ‘the One that manifests as many’ that exists in all Dharma thought systems (and Aryabhatiya paid obeisance to). Just like Panini was able to encode the infinite possibilities of pre-existing and all future utterances using a small number of rules, the Indian place value system too can represent all previously used and yet-to-be-used numbers in the universe using just a few symbols and rules.  Every digit in an N-digit number is denoted by its symbol that has a provisional reality, and through an established place value, it acquires a manifested form that unites into the whole number. As shown in the picture below,  some two thousand years ago, Rishis explain that the same symbol ‘1’ can realize different values, e.g. in the unit, tens, and hundreds place just as a lady can be a daughter, sister, mother, etc.

decimal pv system analogy to a lady3
source: Module 1 of IIT lecture series [1]
Algebra and Sanskrit

The place value system is essentially algebraic in nature. Bijaganita (Algebra via Arabic Al-Jabr) is a natural extension of this idea that arose independently in India (early algebraic results can be found in the Sulvasutras[1]). Here a single symbol like ‘x’ represents an unmanifest quantity that can potentially take one of many values. It eventually takes a fixed numerical value that is feasible to the equations representing the reality which it is part of. In [10], we find this algebraic concept mirrored in Sanskrit [10]: “When a word with a contextually determined meaning is reduced to only one of its many meanings, it is akin to assigning a specific constant value to an algebraic variable, thereby eliminating its usefulness as a variable.”

These context-sensitive meanings in Sanskrit, and the Contextual and Universal Dharma ethics are other well-known concepts that resemble this idea. For example, the word ‘Lingam’ which means symbol or icon has multiple contextual meanings [10]. The idea of equations and the introduction of a symbolic processing language to manage such equations also existed in India. The Bakshali manuscript provides evidence of this [6]. Aside from the decimal system, there were also the Katapayadi, Bhutasamkhya, and the Aryabhata notation that encoded numerical data in exquisite sacred verse [1]. Here are some bewitching examples.

This Paninian approach naturally motivates the generation of permutations and combinations while are fundamental to the idea of mathematical ‘probability and chance’, and finds application in Sanskrit Kavya [3]. The infinite-series results achieved by Madhava of the Kerala school long before McLaurin/Taylor/Leibniz, etc. also resemble this generating principle. The game of chess (Chaturanga), and snakes and ladders (Moksha Pata, Vaikuntapalli), etc. also have a similar structure and not surprisingly, originated in India. German Sanskritist Paul Thieme noted that a civilization that produced Paninian grammar could easily have produced also the game of chess, which it did [4].  The potential chaos that can arise from permitting multiplicity is ingeniously managed via the guiding principles of Dharma to produce harmonious order. All these discussions raise an obvious question – why are Indians so ‘tuned in’ to this integral approach?

Forest Civilization’s Pattern Seekers and Algorizers

The multiplicity of numbers, cascading permutations, infinitesimals running amok, and the never ending decimals of irrationals seemingly paralyzed the binary mindset at one point in time. On the other hand, this chaotic prospect caused little anxiety among the ancient Indians who were grounded in Dharmic view where such diversity are but natural forms of the One. In general, the practice of Ganita is appealing to those who seek recurring patterns and inter-connections in nature.

India is a forest civilization [10]. A significant portion of the narrative in two of its major works of Itihasa, the Ramayana and the Mahabharata, occur in the forest, which is a complex ecosystem where the inter-dependency of its members is Omnipresent.  It is but natural that the Indians are attracted to the infinitely repeating patterns that abound in nature and draw inspiration and inferences from them. On the left is a picture of the tessellations drawn by ancient Indians on rocks [19] several thousands of years ago (possibly upper Paleolithic period. This may remind some of Kolams). On the right is a visualization of the theta function [20] that Ramanujan may have studied while coming up with his equations for the ‘mock theta’ functions that he made famous.

tessellations in ancient Indian rock art theta functions

Based on an intuition and deep contemplation about certain connections and resemblances observed in nature, a Ganita expert comes up with a sequence of calculations. Scientist Roddam Narasimha describes this Indian approach [24] as that of pattern seekers and algorisers and that the Indian astronomer (like Aryabhata) can “discern patterns in planetary motion and make computations, and proceeds to devise clever algorithms to carry out such calculations“. He describes the Indian approach via the following sequence: observation →  algorithm → validated conclusion. Several Sanskrit keywords are used within this approach, for which no exact English equivalent word exists. We briefly summarize these keywords based on the discussion in [6].

Key Ganita Non-Translatables

Pramana – correct cognition, a means of acquiring valid knowledge. Pratyaksha and Anumana are two important Pramanas in Ganita.

Anumana – inference, the key reasoning component in Indian logic. This is not the same as deduction, but is a derived conclusion from the observation of patterns.

Pariksha – careful comprehensive observation. e.g. yantra pariksha:  observation using instruments. An extension of Pratyaksha (direct observation and perception), the oldest and most universal Pramana among darshanas.

Drg-Ganita –  ‘seeing and computing’. This is an important method introduced by Parameshwara of the Kerala school, which looks for agreement between what was computed and what is observed.

Siddhanta – a validated conclusion, or a validated algorithmic package. What happens when there is a clash between Siddhantas? In [6], “Nilakantha recommends that under such  conditions more observations need to be taken with instruments and compared with calculation, and that the numerical parameters should be changed (or the algorithms tuned) so as to improve agreement. In other words a new siddhanta has to be created. Siddhantas are thus human creations, and the best at any time may not remain
so for long—it is valid only for some finite periods of time.”

Yukti – skilful and ingenious practice. Ganita gives the pride of place to Yukti, sometimes overruling the primacy of the Agamas. Verse (2.5) from the Bhagavad Gita says “yogah: karmasu kausalam“, yoga is skill in action [6].  It appears that the Ganita tradition had little time for ‘pure’ theorists who lacked the Yukti or intent to deliver realizable results.

Anveshana – ‘wild goose chase’. In general usage, this word has a positive connotation but in the context of Ganita it represents a futile exploration.

Upapatti – a rigorous validation of results to the satisfaction of peer experts. Yukti is employed to constructively demonstrate how a result can be correctly reproduced by anyone else. This is not the same as the synthetic notion of abstract proof [1]. An important book in this regard is the Ganita Yukti Bhasa of Jyeshtadeva hailing from the Kerala school. It is a myth that Indian mathematicians provided no proof of their results. One has to read the accompanying commentaries on the results stated in Sutra form in order to understand all aspects of a Ganita result, including the validation step. The tradition of providing Upapattis is an old and well established one [22].

We conclude this introductory post by excerpting some passages from an essay on Mathematics by Henry Poincaré. In this essay, we get to read his independent views on the nature of reality. He also provides a balanced discussion of the pros and cons of different approaches that can be employed to generate new results. It is worth comparing his views with the ancient Indian perspective. This discussion also sets the stage for the next blog in this series.

Poincaré on ‘what is reality?’

We excerpt a couple of paragraphs from a 1905 essay [21] by the great French mathematician Henri Poincaré. From a Dharma and Ganita perspective, Poincare alludes to the integral unity of reality rather than a synthetic ‘artificial assemblage’. He also talks about the need for a ‘direct sense’ of the internal unity of a piece of reasoning in order to possess the ‘entire reality’. He also uses the principle of resemblance to explain his ideas.

The physiologists tell us that organisms are formed of cells; the chemists add that cells themselves are formed of atoms. Does this mean that these atoms or these cells constitute reality, or rather the sole reality? The way in which these cells are arranged and from which results the unity of the individual, is not it also a reality much more interesting than that of the isolated elements…?

Well, there is something analogous to this in mathematics. The logician cuts up, so to speak, each demonstration into a very great number of elementary operations; when we have examined these operations one after the other and ascertained that each is correct, are we to think we have grasped the real meaning of the demonstration? …. Evidently not; we shall not yet possess the entire reality; that I know not what which makes the unity of the demonstration will completely elude us.

“…often a very uncommon penetration is necessary for their discovery. The analysts, not to let these hidden analogies escape them, that is, in order to be inventors, must, without the aid of the senses and imagination, have a direct sense of what constitutes the unity of a piece of reasoning, of what makes, so to speak, its soul and inmost life. When one talked with M Hermite, he never evoked a sensuous image, and yet you soon perceived that the most abstract entities were for him like living beings. He did not see them, but he perceived that they are not an artificial assemblage, and that they have some principle of internal unity.


What we don’t know about India’s Ganita heritage is much more than what we currently know. Only a minuscule fraction of primary source texts of Ganita have been studied and interpreted so far. We have to thank researchers like the late K. V. Sarma for their tireless work in this regard.

"Our youth are hungry for a sensible knowledge of our past, but are denied an opportunity to acquire it by a marvellous educational system that shuns history in science curricula, and by the paucity of attractive but reliable accounts of the fascinating history of Indic ideas. Our academies, universities, museums and other institutions need to make such a project a national mission. Anything less would be irrational blindness to a unique legacy." - Roddam Narasimha [23].
Acknowledgment: I thank the ICP editor and bloggers for their constructive feedback and corrections.
* Indic epistemology traditionally places Ganita under Jyotisha. The original quote in Vedanga Jyotisha refers to Jyotisha in its enlarged meaning, hence the popular direct translation today of that word as referring to 'Math', used above as Ganita.

References
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  3. Cultural Foundations of Mathematics: The Nature of Mathematical Proof and the Transmission of the Calculus from India to Europe in the 16th c. CE., C. K. Raju, Pearson India. 2009.
  4. Vilasamanimanjari: a 19th century chess manual in Sanskrit. Shrinivas Tilak. 2011.
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    Kripa Shankar Shukla, in collaboration with K. V. Sarma. 1976.
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  11. Art and Cosmology in India. Subhash Kak. Patanjali Lecture given at Center for Indic Studies, University of Massachusetts, 2006.
  12. The Pragnya Sutra: Aphorisms of Intuition. Subhash Kak. Baton Rouge, 2006.
  13. Indra’s Net: Defending Hinduism’s Philosophical Unity. Rajiv Malhotra. Harper Collins. 2011.
  14. How to Measure Anything: Finding the Value of Intangibles in Business. 3rd Edition. Douglas W. Hubbard. Wiley. 2014.
  15. Why are Normal Distributions Normal? Aidan Lyon. British Journal of the Philosophy of Science. 2013.
  16. Sync: How Order Emerges from Chaos In the Universe, Nature, and Daily Life. Steven H. Strogatz,Hachette Books. 2012.
  17. Abhinavagupta’s Conception of Humor, svabhinava.org.  Sunthar Visuvalingam.
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  19. Computing Science in Ancient India. T. R. N. Rao and Subhash Kak. Center for Advanced Computer Studies. University of SW Louisiana. 1998.
  20. Ramanujan’s Mock Modular Forms: Indian Mathematician’s Dream Conjecture Finally Proven. Huffington Post Science 2012.
  21. Intuition and Logic in Mathematics. English Translation of Essay by Henri Poincaré. 1905.
  22. Ganita Yukti Bhasa: Rationales in Mathematical Astronomy of Jyeshtadeva. Vol 1. Malalayalam text critically edited with English translation by K. V. Sarma. 2008
  23. The ‘historic’ storm at the Mumbai Science Congress. Roddam Narasimha. Guest Editorial, Current Science, Vol 108 (4), 2015.
  24. Some thoughts on the Indian half of Needham question: Axioms, models and algorithms. Roddam Narasimha. 2002.
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