The Bower Manuscript – Navanitika, the Ancient Medical Book of Bharat discovered in 19th century in Central Asia!

The Bower Manuscript – Navanitika, the Ancient Medical Book of Bharat discovered in 19^th century in Central Asia!

Bower to Waterhouse to Rudolf Hoernle: Next to the Bakhshali manuscript, the Bower manuscript attracts Indian researchers of Science and Technology in India. Actually, it is “Navanitika,” an ancient medical book, recovered partially. However, it is named after Hamilton Bower – a British Lieutenant, who bought the manuscript in March, 1890 while on a mission to chase an assassin charged with hacking a Scotsman to death. Just like “Periyar planetarium,” [who has nothing to do anything with astronomy], the Medical manuscript of the book has been named after the purchaser of the book, instead of the author. The story of the purchase goes in this way – On the night of 2^nd or 3^rd March 1890, a man came to his tent and offered to sell him old manuscripts and artefacts that his treasure hunters had found. Bower bought them. This proves that the European explorers, army officers, members of the Society of Jesus and others had been in the vigorous searchers and purchasers of Indian manuscripts[1]. James Waterhouse, the then President of the Asiatic Society of Bengal. Waterhouse mentioned that the Bower manuscript had 56 leaves (the edition now preserved at Bodleian Library has 51 leaves). That is five pages / leaves were missing from the recovered collection. He reported that the Bower manuscript was bound with two wooden boards on either end and a string running through a hole. The fragmentary manuscript was analyzed, edited, translated and published by Rudolf Hoernle in 1897 in instalments,[2] but, not completed.

The Manuscript book was meddled with: Immediately after his return to India in February 1891, Hoernle began to study the manuscript. He found that the manuscript leaves were jumbled out of sequence, but had the page numbers marked on the left. They were obviously written in three or four styles[3], thus by three / four persons or three / four different periods. After re-arranging them, he concluded that it was an abridged collection of several different treatises[4]. “On examining more closely the several leaves, I noticed that they were evidently mixed up. The leaves written in the different hands followed one another without any order. But I also noticed that many of the leaves were marked with numbers on their left hand margin…..It further seemed that the three varieties of writing distinguished three different works…………The work is a compendium of medicine, is named the Navanitika, and consists of sixteen chapters (adhydya). That it was written by a Buddhist, is seen from the initiatory salutation of the “Tathagatas” or Buddhas……based on the excellent system of the Maharishis as composed by them in olden times……..Now as to the age of the MS., I believe it to be very old and written not later than the end of the 5th century A. D. The style of writing is exactly like that which we meet with in the early Gupta inscriptions[5], between 450 and 550 A. D..,” He presented the first decipherment two months later, at the meeting of the Society in April 1891, with evidence that it was “the oldest Indian written book that is known to exist”.The Bower Manuscript, sometimes referred to as the Yashomitra Manuscript, is preserved in the collections of the Bodleian Library in Oxford.

The facts that could be derived from the analysis of the Bower Manuscript: The following facts could be listed as the facts derived from the analysis of the manuscript:

1. The Indian medical system and books travelled with the Buddhist monks going to Central Asia, China etc.
2. Sanskrit was the language used, but it was written in different scripts. Here, it was written in the Gupta Brajmi, as the British noted.
3. The writers, composers and practitioners of medicinal works acknowledged the source to “….the excellent system of the Maharishis as composed by them in olden times……”
4. In other words, the Buddhists acknowledged that they derived such knowledge from the earlier Rishis, the Hindus.
5. Thus, there had been an established medical system in the ancient India.
6. The collectors, sellers and buyers of the manuscripts used to mix-up the manuscripts without knowing the contents and significance.
7. During the 19^th-20^th centuries, the dating of the manuscripts was done relatively. Comparing the style of the script with that of the style of scripts used in the rock inscriptions.
8. As the rock inscriptions have been dated after the invasion of Alexander’s invasion and Asoka was reportedly copied the “Brahmi script” from the Greeks, they were dated to c. 3d cent.BCE.
9. Thus, the historical period of India started with c.326 BCE and all other incidences were placed in the pre-historic period.

What the Bower Manuscript or “Navanitika” deals with?: The writers salute the Tathagatas with the claim that they are going to write an approved compendium of medicine called the Navanitaka, based on the excellent system of the Maharishis as composed by them in olden times. Useful medicinal details are given for the cure of diseases of women and children. The work is commended to those physicians whose minds delight in conciseness, but on account of the multiplicity of its prescriptions.

1. The first chapter will give prescriptions of powders ;
2. the second of clarified butter;
3. the third will be concerned with oils.
4. The fourth will be about the mixtures which are used in the treatment of various diseases.
5. The fifth will give prescriptions of clysters,
6. the sixth rules about elixirs.
7. The seventh will be about gruels,
8. the eighth about aphrodisiacs,
9. the ninth about eyewashes,
10. the tenth about hair-dyes.
11. The eleventh will be concerned with applications of the yellow myrobalan.
12. The twelfth will be about bitumen,
13. the thirteenth about castor-oil.
14. The fourteenth will be concerned with the treatment of children;
15. the fifteenth will deal with the treatment of barren women.
16. Lastly the sixteenth will be about the treatment of women who have children.

 These sixteen chapters will constitute the Navanitaka.

Rudolf Hoernle on Indian Oesteology[6]: After the Bakhshali and Bower manuscripts, what made Rudolf Hoernle to take interest in “Indian Oesteology” is not known. He compared the number of bones mentioned in the medical works of the Greeks and the Indians. theory of the Ancient Indians regarding the skeleton, or the bony frame of the human body, has been transmitted to us m three different systems These are the systems of Atreya, Susruta, and Vagbhata. Pointing out that Ktesias[7] [400 BCE] came to India[8], he placed Charaka and Sushruta in the 6^th cent.BCE period. He also discussed about the two versions of the origin of medicine – one from Indra to Bharadwaja to Atreya to others and two from Indra to Dhanvantri (also called as Divadoshs, Kasiraja) to others. Rudolf Hoernle who proposed date of 600 BCE to Susruta uses a calibrating data point of Satapatha Brahmana to 500 BCE. Here, he gives 1000 BCE  to Satapatha Brahmana. Thus, he would have come across different manuscripts, birch-bark books on Indian medicine and hence his relative dates given to Indian works change. That the Indian civilization had/has been continuing for many thousands of years, whereas, the much talked, publicized and praised civilizations lie Assyrian, Babylonian, Egyptian, Roman, Greek and other civilizations had disappeared. Therefore, without proper healthcare etc., the Indians could not have lived to produce population. This implies the existence of doctors, hospitals etc., from the earlier period. The Mehrgarh evidences prove that dental surgery was practised at least 7500 YBP. The evidences of Trepanation also go back to c.4300 YBP or 2300 BCE[9]. The Chola inscription of the medieval period recorded about the existence of a full-fledged hospital with a surgeon. That so many battles and wars were fought also prove the existence of doctors, hospitals, surgeons and medicines. Therefore, putting all evidences together, the literary evidences could match with the historical and protohistorical evidences to link the prehistoric with historical period.

Rhinoplasty – From Susruta to Dinnanath Kangharia: Vaidya Bhagwan Dash in his introduction gives the following details[10]:

“Unfortunately, Lord Buddha himself succumbed to death after an operation by an Ayurvedic surgeon, and thereafter, surgery was considered as a form of violence against which his followers stood very firm and prohibited the various surgical measures by people, including surgeons of the country. The knowledge of surgery including anatomy gradually declined and looks on these subjects subsequently disappeared”.

Rhinoplasty was also practised in India, but, banned by the British government[11].

The rhinoplasty / (rhino = nose + plastiokos = shaping of) / shaping of the nose by plastic surgery practised in India up to 18^th century CE also proves the tradition of Sushruta. K. S. Goleria[12], S. C. Almast[13], Tribhovandas Shah[14], J. L. Gupta[15] and others[16] have pointed out such cases. The rhinoplasty has been practised by certain families e.g, Marattas of Kumar near Pune, Nepal, Kangharias of Kangra, and Himachal Pradesh. Dr. S. C. Almast reports that Sri. Dinanath Kangaria at Kangra and his family has been practising since 1440 CE. In fact, they claim that it was followed since the Mahabharat War, which took place around 3100 BCE. Taking the Trepanation evidences, as discussed below, it may not be brushed aside as boasted claim. Tribhovandas Motichand Shah was the then Chief Medical Officer at Junagadh in 1889 and he has recorded over a hundred cases of rhinoplasty conducted over four years describing the minute operative details and discussed the advantages of forehead rhinoplasty. Thus, it is evident that the tradition of rhinoplasty has been followed without a break.

Brahmi script exposed the forgeries and frauds of the British researchers: As the European researchers were searching for antiquities with the help of local people, they slowly understood the requirements of the Europeans. As they themselves were making profits by selling the antiquities, the guides in connivance with the locals started manufacturing copies of the antiquities, so that they could be sold to different explorers. It was in this competitive environment that Islam Akhun emerged. In 1895 he approached the British Consul in Kashgar, Sir George Macartney, with a number of manuscripts on paper. Ibrahim Mullah, Islam Akhun’s partner, was also selling similar items to the Russian consul Nikolai Petrovsky. He sent them to St. Petersburg to be translated. Ibrahim Mullah had some knowledge of Cyrillic scripts, and so he incorporated Cyrillic characters, which proved very confusing for those scholars tasked with their translation. Some were in a script similar to Brahmi and the documents were in several different formats, many bound with copper ties. Macartney purchased the documents and sent them to India in the hope that Augustus Rudolf Hoernlé, a prominent scholar of Indo-Aryan languages, would be able to decipher them. In April 1901 Stein tracked down Islam Akhun in Khotan and questioned him over the course of two days. Initially, Islam Akhun claimed innocence, insisting he had only been an agent for Macartney, and had himself purchased the documents from other parties, knowing how much the English desired them.  On his return to England, Stein met with Hoernle in his house in Oxford in July 1901 and informed the position[17].

Hoernle works destroyed or not – the background: Hoernle hoped that his own report could be destroyed but this was not possible as it had already been published. However, he was able to edit the second part before it went to print. Many of the forgeries remain in the collections of the British Library and the Institute of Oriental Manuscripts, St. Petersburg. Interestingly, in the case of A.A. fuhrer, the same thing happened in bringing a casket that reportedly containing the ashes of Buddha, on which, Asokan Brahmi was inscribed[18]. Buhler deciphered the script in both cases. Vincent Smith intervened and decided. The publications of both Hoernle and Fuhrer were suspended or stopped or suppressed. Only par ts-II to VII are available. I have dealt with Fuhrer in detail in my paper[19]. The Asokan Brahmi has been placed to c.3^rd cent.BCE, but, Brahmi inscriptions are found on the monuments of Jain and Buddhist periods. Then, its dating should go to 7^th-6^th cent.BCE. When the dating of the perishable documents could go back to first centuries BCE-CE period, the scripts found on the inscriptions could not have been restricted to c.3^rd cent.BCE based on the Alexander invasion. Therefore, the dating of the Brahmi script has to be reassessed.

© K. V. Ramakrishna Rao

29-04-2020

[1]  In another paper, I have shown how the Indian manuscripts were taken away by these groups to Europe and later to USA and supplying to Scientists, researchers, libraries and museums.

 K.V.Ramakrishna Rao, The Transmission of Medical Knowledge from Tamizhagam to Europe (15^th to 20^th centuries), sent for the seminar held at Los Angeles from November 17^th to 19^th 2006.

[2] A. F. Rudolf Hoernle, The Bower Manuscript, Parts III to VII, Archaeology of Survey of India, Calcutta, 1897.

[3]  The first point that strikes one on looking through the MS. is, that it appears to be written in three, if not four, different styles. This point has been already noticed in the November account.

Rudolf Hoernle, Birch Bark Manuscript, From the Proceedings, Asiatic Society of Bengal, for April, 1891, p.1.

[4] Rudolf Hoernle, Birch Bark Manuscript, From the Proceedings, Asiatic Society of Bengal, for April, 1891. Issued as a 20-page booklet.

[5] “The whole manuscript is written in what Mr. Fleet (in his Gupta Inscriptions in Volume III of the Corpus Inscription urn Indicorum, p. 3) distinguishes as the Northern class of the Nagari alphabet, which is characterized by the peculiar form of them. Of this class, however, three varieties are observable in the MS” – Rudolf Hoernle.

[6]  A. F. Rudolf Hoernle, Studies in the Medicine of Ancient India – Oesteology or the Bones of Human Body, Part-I, Oxford at the Clarendon Press, 1907.

[7] Ktesias also known as Ctesias the Cnidian or Ctesias of Cnidus, was a Greek physician and historian from the town of Cnidus in Caria, when Caria was part of the Achaemenid Empire flourished during the 5th century BCE.

[8] A. F. Rudolf Hoernle, Studies in the Medicine of Ancient India – Oesteology or the Bones of Human Body, preface, two Greek physicians, Ktesias, about 400 BCE , and Magasthenes about 300 BCE, visited, or resided in Northern India,

[9] K. V. Ramakrishna Rao, The position of Surgery Before and After Buddha, Swadeshi Science Movement, Bangalore, Sastratrayi,  pp.187-198.

[10] Vaidya Bhagwan Dash, in his introduction to the Hoernle’s book, pp.xix-xx.

1984. F. Rudolf Hoernle, Studies in the Medicine of Ancient India (Osteology or the Bones of the Human Body), Concept Publishing Company, New Delhi, 1984.

[11] Nasal reconstructions had been practised as a relatively routine procedure in India for centuries. This was driven by the common use of nasal mutilation in India as a means of punishment or private vengeance for various forms of immorality. The procedures are described in two well-known early Indian medical works, the Suśruta Saṃhitā, thought to date to the middle of the first millennium BCE, and the Aṣṭāṅgahṛdayasaṃhitā, believed to date from the sixth century CE.  By the nineteenth century the technique had been handed down through separate families in three different parts of India.

https://blogs.bl.uk/science/2016/10/britains-first-nose-job.html

[12] K. S. Goleria, Pedicie Flaps – A Historical Review, Indian Journal of Surgery, 1966, Vol.28, pp.247-254.

[13] S. C. Almast, History and Evolution of the Indian method of Rhinoplasty, Transactions of Fourth Internation Congress, Rome, Oct.1967, pp.19-25.

[14] Tribhuvandas, Rhinoplasty – A Short Description of One Hundred Cases, The Source Book of Plastic Surgery, 1977, pp.121-127.

[15] J. L. Gupta, Past, Present and Future of Plastic Surgery in India, Indian Journal of Plastic Surgery, 1991, Vol.24, pp.1-9.

[16] Keegan, Rhinoplastic Operations with Description of Recent Improvements in the Indian method, Bailliere, Tindall and Cox, London, 1900.

[17] What Stein wrote to Hoernle, “Islam Akhun is a very clever rascal, with a good deal of humour and brains quite above the level of his compatriots. His memory as to the articles he supplied was surprising. When he was once on the road to a full confession, it was easy to see how well his avowals agreed with the stories he had told M. and which your Report reproduces. I appreciate brains even in a scoundrel, and I wonder whether I. A. is not too dangerous a fellow to let loose on an innocent Khotan. … I do not know which documents you consider to be written in a kind of debased Nāgarī, and must reserve my opinion until you have shown them to me. But from what I have indicated above, you will realize why I fear that this reading will not prove more justified than my own supposition of Pahlavi characters in some of I. A.’s fabrications. Questions of this kind ought to be examined after a reliable knowledge of local facts has been secured, and I have spared no trouble to obtain this. You and others will be put by my report in full possession of these dates, and will then be able to judge for yourself whether it is worthwhile to continue the study of those documents in “unknown” characters”.

[18] JRASB, The Piprdhwd Stitpa, containing relics of Buddha. By WILLIAM CLAXTON PEPPE, Esq. Communicated, with a Note, by VINCENT A. SMITH, I.C.S., M.R.A.S. With two Plates. Pp.573-588

[19] K. V. Ramakrishna Rao, Salvaging, redeeming and Saving Archaeology and Managing Heritage in the Indian Context, A paper presented at the National Seminar, “Salvaging Archaeology and Heritage Management” held at Meenakshi College, Chennai on November 29th and 30th 2016.

Bakhshali manuscript and Ramanujam: Mathematical manuscripts from Bodleian Library of Oxford to Cambridge!

Bakhshali manuscript and Ramanujam: Mathematical manuscripts from Bodleian Library of Oxford to Cambridge!

Hard work and esoteric wisdom: Srinivasa Ramanujan claimed that he got such amazing mathematical wisdom from “Namagiri Devi,”[1] just like Kalidasa getting knowledge from Kali. According to Ramanujan, she appeared to him in visions, proposing mathematical formulas and he would have taken down. One such event was described by him as follows:

“While asleep, I had an unusual experience. There was a red screen formed by flowing blood, as it were. I was observing it. Suddenly a hand began to write on the screen. I became all attention. That hand wrote a number of elliptic integrals. They stuck to my mind. As soon as I woke up, I committed them to writing“.

 Or it could be taken down in this way also – as he always used to think about such theorems, formulae etc., a sudden spark would have helped him to get the result. Of course, for such intuition, a divine blessing is required. Furthermore, Ramanujan’s mother received permission from Namagiri Thayar for Ramanujan to go to England in a dream. Ramanujam like any other devout Hindu student would have always attributed his knowledge, timely recollection at the time of examination, thereby writing examinations well, getting high marks, etc., only to his favourite God or Goddess. However, his hard work plays a key role always. Thus, definitely, their knowledge was tremendous, stupendous and great only. Such mathematical knowledge was preserved in India historically. Actually, it was not known how many pages the manuscript bound contained, how many recovered, left at the site itself, damaged and cured for research, and kept at the Bodleian library now. Thus, the oldest mathematical manuscript is now known as “Bakhshali manuscript”  contained the Indian mathematical past historically.

Bakhshali manuscript – the notebook/workbook of an Ancient Indian Student: The “Bakhshali manuscript” is nothing but, a notebook or workbook of an ancient Indian student containing many pages, but, only 70 were reportedly recovered in a mutilated condition found between stones, when a peasant living enclosure was dug. In May 1881, near a village called Bakhshali, lying in the Yusufzai district of the Peshawer division, at the extreme Northwestern frontier of India. About its nature also, different versions are available.

The letter dated 5th of July 1881, from the Assistant Commissioner of  Mardan states[2], “According to the finder’s statement the greater part of the manuscript had been destroyed in taking it up from the place where it lay between stones. The remains, when brought to me, were like dry tinder, and there may be about fifty pages left some of which would be certainly legible to anyone who knew the characters. The letters on some of the pages are very clear and look like some kind of Prakrit, but it is most difficult to separate the pages without injuring them. I had intended to forward the manuscript to the Lahore Museum in the hope that it might be sent on thence to some scholar, but I was unable to have a proper tin box made for it before I left Mardan. I will see to this on my return from leave. The papyrus will require very tender manipulation. The result will be interesting, if it enables us to judge the age of the ruins where the manuscript was found.”

Rudolf Hoernle noted, “Unfortunately, probably through the careless handling of the finder, it is now in an excessively mutilated condition, both with regard to the size and the number of the leaves. Their present size, as you observe (see Plate I), is about 6 by 3 ½ inches; their original size, however, must have been about 7 by 8 ¼ inches. This might have been presumed from the well-known fact that the old birch-bark manuscripts were always written on leaves of a squarish size. But I was enabled to determine the point by a curious fact.”

Its size varies from 13×7 to 18×21 cms size. In other words, the sizes of the notebook pages were thus equivalent to A4 to a bigger size. Professor Buhler, who had read of the discovery in the Bombay Gazette communicated the announcement to Professor Weber, who brought it to the notice of the fifth International Congress of Orientalists then assembled in Berlin. In Buhler’s letter to Weber it was stated that the manuscript had been found, “..carefully enclosed in a stone chamber……,” however, the 70 leaves recovered showed that they were damaged severely, while removing. As noted, the “Bakshali manuscript” was nothing but, a student mathematical book cum workbook containing many pages. It has many interesting problems, but, difficult to solve. The manuscript is written in Sharada character of a rather ancient type, in Sanskrit and on the leaves of birch-bark which from age have become dry like tinder and extremely fragile[3].

The tradition of Birch-bark manuscripts of North India spreading from Central Asia to China: The Birch-bark manuscripts are documents written on pieces of the inner layer of birch bark (of tree), which was commonly used for writing in ancient India. The evidence of birch bark for writing goes back many centuries and in various cultures. The oldest dated birch bark manuscripts are numerous Gandhāran Buddhist texts from approximately the 1^st century BCE to CE, which are believed to have created in Gandhara part of Bharat (now Afghanistan), likely by the Dharmaguptaka sect of Buddhists. That the Buddhism was existed till the medieval period above Bharat from Central Asia to China and of course down to South East Asia is well known. In other words, just like the tradition of “Talapatra” of south India, the north Indians used “Bhiojpatra.” Moreover, the writing was there, during the first centuries with an established educational system. As these manuscripts withstood time, there could have been more, but, unless, the Europeans reveal, Indian researchers are not in a position to proceed further. Now coming to numbers and zero, as this Bakshali manuscript contained zeros, it would have been more interesting, had the manuscript was shown to Ramanujam by his British friends of the Cambridge.

The number “0”, decimal numbers etc: According to the westerners / the European experts, the origin of the symbol zero has long been one of the world’s greatest mathematical mysteries. However, The Rigveda Mandala X has the concepts of 0 and 1, giving examples of the concept of “non-existence” and “existence”. Pingala[4] has been credited with the inventor of Binary Mathematics[5]. Here, the Bakshali manuscript contains many zeros mentioned specifically. Though, many consider the symbol noted as dot, big dot etc., it appears as circle only[6]. Therefore, it’s dating from the first centuries was disputed and taken to the 4^th century CE. In 2017, the Bakhshali manuscript, was subjected to radiocarbon dating conducted. Various dates have been obtained ranging from the 3^rd or 4^th century CE to 12^th century. In fact, composed of material from at least three different periods, as per the C-14 dating.

Table[7] Laboratory codes, radiocarbon determinations, stable carbon isotope composition and calibrated ages for the birch bark from the Bakhshali manuscript. Presented uncertainties in the radiocarbon determination are one standard deviation.

Sample	ORAU laboratory code	Radiocarbon determination / BP	δ / ‰	Calibrated age, 95.4% Confidence interval / cal AD
Bakhshali folio 16	OxA-35,405	1751 ± 29	-27.3	224 – 383
Bakhshali folio 17	OxA-35,406	1247 ± 27	-27.0	680 – 868
Bakhshali folio 33	OxA-35,407	1108 ± 26	-24.6	885 – 993

If that is the case, no student or scholar would keep his book, notebook or textbook with such mixed manuscripts. Such mix-up must have done by the discoverer of or the person recovered the manuscripts. Probably, they could have recovered three such manuscripts at different levels. As Dakshasila University was nearby and it was destroyed by the Mohammedans, all these books could have been found scattered. Or the “enclosed” place, where, the manuscript was found, could have been a school that was destroyed. The most elaborate and authoritative academic study on the manuscript, conducted by Japanese scholar Dr Hayashi Takao[8], asserted that it probably dated from between the 8^th and the 12^th century, based on factors such as the style of writing and the literary and mathematical content. Another researcher has noted some astronomical details also[9]. Thus, the earlier dating of the manuscript goes before the 9th-century inscription of zero found on the wall of a temple in Gwalior, Madhya Pradesh, which was previously considered to be the oldest recorded example of a zero used as a placeholder in India.

The zero symbol could have been evolved from a dot that was used in ancient India and can be seen throughout the Bakhshali manuscript. The dot was originally used as a ‘placeholder’, meaning it was used to indicate orders of magnitude in a number system – for example, denoting 10s, 100s and 1000s. In fact, in the Bakhshali Mss, it is clearly written as 0 instead of a big dot.  The “Number system” that was reportedly used by the Egyptian, Babylonian, Mayan and Roman are compared with that of the Indian for comparison. While the use of zero as a placeholder was seen in several different ancient cultures, such as among the ancient Mayans and Babylonians, the symbol in the Bakhshali manuscript is particularly significant for two reasons. Firstly, it is this dot that evolved to have a hollow centre and became the symbol that we use as zero today. Secondly, it was only in India that this zero developed into a number in its own right, hence creating the concept and the number zero that we understand today – this happened in 628 CE, just a few centuries after the Bakhshali manuscript was produced, when the Indian astronomer and mathematician Brahmagupta wrote a text called Brahmasphutasiddhanta, which is the first document to discuss zero and its operations.

Ramanujam and zero: The concept and evolution of 0 and ∞ haven challenging for all civilizations, but, the ancient Indians were dealing with them, philosophically and mathematically with clear-cut logic. Of course, there was no difference between philosophy and mathematics till medieval periods. Ramanujam asked his teacher what would happen if zero was divided by zero. They did not use 0 till 12^th century and ∞ 17^th century[10]. The westerners did not recognize them till the medieval / modern period. If any number is divided by itself, 1 is obtained, then, zero divided by zero would give 1 as result. It is not known as to Ramanujan would have read “Bija ganita” of Bhaskaracharya or not. However, it is evident that he had taken much interest in zero and other numbers. Thus, had Ramanujan seen the Bakashali manuscript, many riddles of the manuscript would have been solved. After all, the distance between Cambridge and Oxford is about 100 kms and it would take two hours to reach. It is not known who prevented him not to see the Bakhshali manuscript.

© K. V. Ramakrishna Rao

27-04-2020

[1] Ramanujan prayed to the goddess Namagiri by sitting in the center of a four pillared mandapam facing the goddess, in the Narasimha swamy Temple. It is said that they stayed in the precincts of the temple for three days, and Ramanujan got the permission of the goddess to go to England, in a dream when he was asleep. He woke Narayana Iyer and told him that his mission of getting the permission of the goddess to go to England was accomplished.

[2] G. R. Kaye, The Bakhshali Manuscript – A Study in Medieal Mathematics, Vol.I, in Indian Historical researches, Royal Asiatic Society, Calcutta, 1933,  p.1

[3] Birch-bark is an outer bark of the Silver Birch (Betula utilis, Betula bhojpaltra, or the Bhurja tree, as it is vai’iously called) which flourishes in the Himalayas from Kashmir to Sikkim. It grows on all the higher ranges of the Kashmiri- hills from a height of about 6,000 feet to 12,000 foot. The forests in the (Gurais district supply most of the bhojpatra that is sold in Srinagar. The bark is used chiefly for the roofing of houses, for wrapping up things, for lining baskets, etc., and the villagers still use it as a writing material.

1. R. Kaye, Vol.I, p.4

[4] Pingala (c.3rd / 2nd century BCE) was an ancient mathematician, famous for his work, the Chandas shastra (chandas-śāstra, also Chandas sutra chandas-sūtra), a Sanskrit treatise on prosody considered one of the Vedanga. Pingala is identified as the younger brother of Panini, the great grammarian of c. 5^th century BCE. Other traditions identify him with Patanjali, the author of the Mahabhashya.

[5] K. V. Ramakrishna Rao, Date of Pingala – The Origin of Binary Computation in India, VYOMA, Bangalore, 2004, pp.356-362.

[6] R.N. Mukherjee; Zero, Encyclopaedia of Classical Indian Sciences, H. Selin, R. Narasimha (edt.), Universities Press, (2007) pp. 441-444.

[7] David Howell, Carbon dating reveals Bakhshali manuscript is centuries older than scholars believed and is formed of multiple leaves nearly 500 years different in age, By David Howell, Head of Heritage Science at the Bodleian Libraries, 3 July 2017

[8] Hayashi Takao, The Bakhshali Manuscript – an ancient mathematical tratise, Egbert Forsten, Groningen, Netherlands,1995.

[9] Syshma Zadoo, Critical study of the Bakhshali Manuscript, PhD thesis, University of Kashmir, 1992, pp.141-142.

[10] K. V. Ramakrishna Rao, From Zero to Infinity, in “Vigyan Bharati Pradeepika”, Bharatiya Vigyan Sammelan, – Proceedings, Vol.8, No.1, April 13, 2002,  pp. 45-54.