Early Indian MS evidence for "zero"

Early Indian document with ref. to zero

The Bakhsālī manuscript was unearthed by a peasant in 1881 in the village of Bakhshālī about eighty kilometers north-east of Peshawar. The scribe wrote it in the Śāradā script on birch-bark using a pen with a flat, rectangular tip. The most recent research shows that this is the earliest Śāradā manuscript ever discovered, and suggests that it may be datable to as early as AD 700, although a date of 1200 has been proposed in the past. The mathematical work recorded in the manuscript is probably from the seventh century, and appears to have been composed in the Gandhāra
district. The manuscript describes the foundations of arithmetic, including approximations of square roots, rules of inversion and proportion, the rule of three, various forms of equations, and a series of example problems on fiscal, taxation, travel, and geometrical topics (Hayashi 1995). It also uses a dot to symbolize zero, possibly making it the earliest written occurrence of this sign in India.

---
T Hayashi, The Bakhshali manuscript : An ancient Indian mathematical treatise (Groningen, 1995).

TeXWorks for linux

TeXworks is a nice editor with an emphasis on multilingual use, simplicity and rapid document preview. It is from Jonathan Kew, author of XeTeX.

Binary downloads for Mac and Windows are available from the TeXworks home page. For Ubuntu Linux, there's a PPA here.

The Origins of Zero

In 1998, I wrote the following letter to the editor of the New Scientist magazine, in response to an article that appeared on 25 April 1998 by Ian Stewart, entitled Zero, Zilch and Zip.

---------- cut -------------

From ucgadkw@link-1.ts.bcc.ac.uk Sun May 3 15:28:53 1998
Date: Sun, 3 May 1998 15:28:52 +0100 (BST)
From: Dominik Wujastyk
To: letters@newscientist.com
Subject: Ian Stewart: Zero, Zilch and Zip

Dear Sir,

Ian Stewart writes engagingly about the origin of the mathematical zero and place-value notation ("Zero, zilch and zip", 25 April, p 41), but he suggests that these two concepts are connected, when they are in fact both logically and historically separate. You can count reasonably successfully with place-value notation but no explicit zero, and vice versa.

Ian Stewart is also quite wrong in saying that "place notation was born probably in India, maybe with Arab help, not too long after AD 200".

Three key elements -- a decimal base, place-value, and zero (I abbreviate this to "DPZ") -- occurred separately at earlier times both in India and in other parts of the ancient world. In particular, the Babylonians were using a place-value system, with a space for the null value, in the second millennium BC, but their base for counting was sixty, not ten. By the time of Alexander the Great, they were even using a special symbol for this null value. From perhaps as early as the third century AD the Mayans also used place-value and zero, but with the base twenty. But it does indeed seem to have been the Indians who first combined these key elements together to form the basis of the arithmetic system that has come down to the modern world.

The Arabs did not have anything to do with the invention, and indeed Arabs only arrived in India about five hundred years later than Stewart suggests. The Arabs (or rather, the Muslims of the Middle East) certainly did transmit knowledge about zero and the place-value notation to Europe, but they learned it all from the Indians. We call our numerals "Arabic", it is true, but Arabic writers called them "Hindu", meaning "Indian".

The Indian numerals are first mentioned outside India in the year 662, when the Syrian bishop Severus Sebokt, annoyed by the intellectual arrogance of immigrant Greek scholars, reminded them pointedly that other nations were also very learned, such as the Hindus with their admirable systems of astronomy and arithmetic, including calculating with nine symbols.

Indian works on arithmetic, translated from the original Sanskrit in to Arabic (perhaps through Persian or Syriac), began to reach the Islamic world in about the eighth century. The first book known to us from outside India that demonstrates Indian methods of calculating with nine digits and zero was composed in the ninth century, probably in Baghdad, by al-Khwarizmi (whose name, through the medieval Latin and Old French, gives us "algorism" and "algorithm"). From about AD 950 on, many Arabic works demonstrating these new Indian methods of working out arithmetical problems, including fractions, were circulated under the name "al-Hisab al-Hindi', or "Indian calculation". After 1100, Latin translations of Al-Khwarizmi's work spread throughout the centres of medieval learning in Europe, which is how the the Indian DZP system ultimately reached us today.

The earlier history of this number system in India is not perfectly clear, but the Indian astronomer Aryabhata, born in 473, was the first to describe the decimal place-value system explicitly, in a chapter of a work in which he also discusses algebra, geometry, and trigonometry. Before him, the third-century author Sphujidhvaja seems to be the first author to describe the use a symbol for zero in the decimal place-value system.

It is often claimed that the adoption of the DPZ system was a great epistemological change heralding the opening of vast new mathematical horizons, and a leap forward in knowledge generally. I do not see why a notational change of this type should be seen as so important, and there
is little actual historical evidence of such an effect. The counting system that has become second nature to us may seem consummate, but surely that is only a matter of what we are used to, what we have been taught from childhood. The Babylonians, using a non-DZP system, constructed vast tables of astronomical and arithmetical parameters which required extraordinary amounts of calculation, but we see no evidence that they were hampered by having a sexagesimal (60-based) and not a decimal system. Early Greek arithmetic was decimal, but was conducted without recourse to the use of zero. Sometimes a non-DZP notation can be positively helpful: to add ten and ten in Roman (X + X = XX) does not even require knowledge of another symbol, nor any notational manipulation beyond writing the symbols more closely together. What could be easier? That quintessence of modernity, the digital computer, abandons the internal use of decimals entirely, using only binary digits, or bits. The feeling that the DZP combination is in some way "better" than any other system is surely no
different in principle from any other chauvinistic belief, such as that that one's own mother language -- whatever it may be -- is the easiest, best, and most expressive language in the world.

In areas where sexagesimal (60-based) counting still lurks in our own mathematics, such as in the 360 degrees in a circle, we suffer no epistemological harm. That a right angle has ninety degrees has not held our civilization back in any obvious way, though measurement in radians is of course routine in higher maths.

If some future government, politically desperate for a "British Sausage" issue, decides to go for total, all-out decimalization and legislates that a circle shall have ten degrees, there may be a leap in learning, but it may in a direction of five degrees.

Yours faithfully,

Dominik Wujastyk

--
Dr Dominik Wujastyk, FAX/voice: +44 171 611 8545/8467
Wellcome Institute for URL: http://www.ucl.ac.uk/~ucgadkw/
the History of Medicine, Email: d.wujastyk@ucl.ac.uk
Wellcome Trust, 183 Euston Road, Trust URL: http://www.wellcome.ac.uk
London NW1 2BE, England.

First Rule of History:
History doesn't repeat itself -- historians merely repeat each other.

JabRef

Good! The new beta of JabRef, 2.6b3, now has a properly-working interface to JSTOR. One can search by keyword for JSTOR entries, and JabRef lists the hits and lets you import whatever you want to your bibtex database. JabRef even helpfully marks possible duplicates. Very nice indeed, especially for us humanists.

Get your JabRef here: http://jabref.sourceforge.net/

At the moment, JabRef and Mendeley seem to be moving forward fast. They approach the problem of bibliography management slightly differently, and offer different feature-sets. However, both are emerging as seriously useful tools.

Just discovered http://www.textualscholarship.org/
as well as the website of Birmingham's ITSEE: http://www.itsee.bham.ac.uk/index.htm

Ztree under Ubuntu with Wine

The Gnome launcher for Ztree command line is
wineconsole --backend=user /path/to/Ztree/ZTW.EXE

Up The Junction

Under Windows, Dropbox wants everything it backs up to live in its own directory on your hard drive. Not soft/sym-links, but actual files.

However, if you're running Windows and have an NTFS drive, then you can in fact make "hard" soft links to your Dropbox directory without having to actually copy everything physically into the that directory. The tool is Junction, which handles hard links under NTFS. NTFS supports this natively, but MS in their wisdom never distributed a public tool to handle this feature.

Vienna University AKH on a bright Autumn morning

The Institute for South Asian, Tibetan and Buddhist Studies is straight ahead, through an archway and to the right.

... and now iBus

The latest release of Ubuntu, 9.10 Karmic Koala, has just come out and has replaced SCIM altogether with another system called iBus. However, everything seems to work almost identically from the user's point of view, and the tricks I mentioned earlier still make everything work. m17n also works with iBus.

LaTeX, Unicode, Kile, TeXmaker, Ubuntu Gnome, and SCIM /SKIM

I run Ubuntu GNU/Linux, with the Gnome windows manager. Kile is the most sophisticated LaTeX editor under Linux at present, and TeXmaker is also very good and has the added advantage of being cross-platform.

TeXmaker installs easily with aptitude, but Kile asks for the whole TeXlive distribution to be downloaded as dependencies. This is fine, as far as it goes. But the TeXlive distributed through aptitude is terribly out of date (2007). So it's quite reasonable to get a more recent TeXlive from TUG and install that. But then Kile still wants to install the old 2007 one through aptitude, and everything gets mess. Luckily, it's possible to fool aptitude into thinking that it's TeXlive is already installed. So now you've got Kile and and up-to-date TeXlive. Great, you think.

Until you start trying to type Unicode (you are using XeLaTeX, aren't you?).

Under GNU/Linux, you can use SCIM and the m17n input method, especially the excellent sa-translit and sa-devnag keyboard handlers to enter Unicode roman transliteration or Devanagari very quickly and easily, rapidly swapping keyboards with ctrl-space. It's great.

But Kile and TeXmaker are written using the QT toolkit, like many applications that are written for the KDE environment rather than Gnome. This means that SCIM doesn't immediately work with them. Blast.

Okay, it's deeply buried on the net, but there is an answer to this too, and it works. It's here.

Hooray! Kile, TeXmaker, TeX Live 2008, Ubuntu 9.04, Gnome, SCIM, m17n, all working fine.

I have to say, though, this should all be much easier, and should be done through aptitude.

Footnote:
After installing or uninstalling other language-related stuff in Ubuntu, sometimes iBus stops working. This can be fixed by going to System/Administration/Language Support and making sure keyboard input method is set to "ibus". Sometimes this tool also installs parts of the language support that are missing.

Also, if your writing area still give the ibus message "no input window", it can be aanecessary to right-click your mouse, select "input methods" and set "ibus".

Radio 4 broadcast

Episode 1 of "The Test of Time", on Suśruta's surgery:click here.

Academia.edu

I'm exploring the use of the new Academia website. My area is here.

Ballantyne's 1855 edition of the Mahābhāṣya

I'm glad to have found Ballantyne's edition of the Mahābhāṣya with Kaiyaṭa and Nāgeśa's commentaries, in the Digital Library of India collection. The edition is from Mirzapore, 1855 (bibliographical details).

Here are some representative pages from it:

Title page:

Mahābhāṣyam

bhāṣyapradīpena vivaraṇena ca sahitaṃ

kāśyāṃ rājakīyapāṭhālaye śrīmadvālaṇṭainnāmaka-

tadadhyakṣaprestais tatratyaiḥ

***

śrīnārāyaṇaśāstridevadatta-

durgodattaśarmabhirvyākaraṇapaṇḍitaiḥ

śrīmaccaturvedahīrānandaśarmabhir

alaṅkārapaṇḍitaiś ca saṃśodhitaṃ

sāṃkhyaśāstrādhyāpakaśrīmatkāśīnāthaśāstribhir

nidhyātaṃ

***

mirjāpurapattane trivedidurbaliśarmaṇā saṃśodhya mudrākṣariar upanibaddhaṃ

bhāratavarṣīya-

paścimottarapradeśādhyakṣaniyogān mudritam

// san 1855 īsvī //

So now we know that Ballantyne was aided by Nārāyaṇaśāstrī [and?] Devadattadurgodattaśarmā, specialist(s) in vyākaraṇa, and with Caturveda Hīrānandaśarmā, an alaṅkāra paṇḍit. These pandits

edited the text. The sāṃkhya professor Kāśīnāthaśāstrī reflected upon the

text (nidhyātaṃ), which presumably means that he edited the text for content.

The text was edited and typeset in Mirjāpurapattana by Durbaliśarmā.

And here are the first two and the last pages of the text:

Yet again on Goldstücker's Mahābhāṣya editions

A few weeks ago I went into Cambridge University Library and had a look at Goldstücker's editions of the Mahābhāṣya. The entry by Haas in the BL catalogue (see previous blog post) gives no sense of the sheer physical size of these publications. These are seriously big volumes. They filled all the shelves of a delivery trolley. They gave me a sense of some quixotic mission in Goldstücker's mind, that somehow reproducing these raw, unprocessed mss in London, at enormous cost, could achieve a socio-political end, could establish in Europe a renewed respect for India's intellectual traditions.

There are three publications here, each being an unadorned photocopy (in modern terms) of a Sanskrit manuscript in Devanāgarī script:

1. Mbh. 1 vol.
   
2. Mbh with Kaiyyaṭa. 3 vols.
   
3. Mbh with Kaiyyaṭa and Nāgeśa. 2 vols.
   

Here are some notes:

1. Patanjali's Mahābhāshya. Reproduced ... samvat, 1751. In one volume.

The first 20 ff. of this ms. (pp. 2-41) are from a different ms. than the remainder. Ends: iti ata parāṇivo yathānyāsam iti kaścātra ... ukāraśca na tau staḥ yad iha tau syātāṃ//

p.43, scribe's fol. 8r,: tāv evāyam upadiśet nanu

It's a lovely Jaina ms, magnificently written.
Ends, v.2, p.697: saṃvat 1751 varṣe poṣaśukla trayodaśyāṃ tithau vudhāvasare śrīsarasāmadhye likhitā pratiriyaṃ ṣrī kharataragacche śrīśrī ṣagaracaṃdrasūrisāṣāyāṃ vācanācārya śrīsukhani?dhāna?gaṇīnāṃ tacchiṣyavācanācārya ... āṇaṃdadhīra likhitaṃ ... ṣrījinadattasūri jnnakuśalasūriprasādāt/

2. Title page:

Patanjali's Mahābhāshya with Kaiyyaṭa's Bhāshyapradīpa ... from an undated manuscript. In three volumes.

Vol.3, p.2218 has post-colophon:
kāṣyāṃ gṛhītaṃ makarasthe gurau saṃvat// iti mahābhāṣye aṣṭamo dhyāyaḥ// ṣrī rāhakaṣṇāya namostu// rāmamahābhāṣyasya pustakam idam āhnika 7

3. Title page:

Nāgojibhaṭṭa's Bhāṣyapradīpoddyota on Kaiyyaṭa's Bhāshyapradīpa. Reproduced by photo-lithography under supervision of Professor T. H. Goldstücker from a manuscript dated samvat, 1871. In two volumes. London: India Museum 1874. (Camb. UL. S833.a.87.6)

This is a ms. of saṃ 1811, sāke 1676 [AD 1754] vakratuṇḍasamīpe, manikarṇikāghāt, kāśī, copied by Udaigaja kāyastha.

Therefore, it looks as if G. may have misread 1811 as 1871. Or perhaps the printers who prepared the t.p. (after G. had died) made the mistake.

Dānasāgara fo Ballālasena on text criticism.

The Dānasāgara of Ballālasena (ca. 1200) includes a number of interesting and important remarks on the nature of Sanskrit scholarship, methods of teaching and learning, the creation of manuscripts and their donation to temples, etc. The displayed passage describes textual criticism (ed. B. Bhattacharya, 1953, Bibliotheca Indica 274, pp.४८०-८१).

More on early editions of the Mahābhāṣya

The 1876 Catalogue of Sanskrit and Pali Books in the British Museum, by Haas, p.100, contains the entries on the right for Mahābhāṣya editions:

Thus, there was the beginning of an edition by Ballantyne in 1855-1856, which is very early. Although this is only a small part of the whole text, the Navāhnika is a seminally important part of the work.  It is interesting to see that even in this very early edition, the commentary of Kaiyaṭa and the subcommentary of Nāgeśa are included. Ballantyne usually worked in close collaboration with paṇḍits, whom he was generous in acknowledging. I will be interesting to know with whom he produced this edition.

Then there's an edition fifteen years later, in Varanasi in 1870. This looks like a real "paṇḍit's" edition, also with the important commentary of Kaiyaṭa but with only notes from the editors and from Nāgeśa and by the paṇḍits themselves. Its production, just over a century after Nāgeśa Bhaṭṭa's death, and in his home town, is likely to embody at least to some extent a direct lineage of the interpretation of the text from the great Varanasi grammarians of earlier times, including Vaidyanātha Payaguṇḍa, Nāgeśa and Bhaṭṭoji Dikṣita.

And then the 1876 Haas catalogue gives the entry on the left, which refers to the lithograph discussed in my post of October 16, 2007, about the lithographer William Griggs and the shockingly expensive lithograph he produced. Haas has identified or corrected the date of the manuscript (saṃ 1751 = AD 1808/9). I have not seen the edition yet, but I would hazard that the manuscript is part of the old IOLR collection in the BL. This lithograph was published in London in 1874, in a limited edition of 50 copies. There's this copy in the British Library, and I would expect to find copies in Oxford and Cambridge at least.

So now we know that the impulse behind this old lithographic edition came from Theodore Goldstücker (1821-1872), who was at that time a professor at University College London, having been invited to move from Germany to England by H. H. Wilson in 1850. Goldstücker was a "Forty-Eighter" in the sense of being a refugee from the German Revolution of 1848-1849. This lithograph edition of the Mahābhāṣya was published posthumously.

It would seem, though, that even at the time of its publication, the London edition has already been partially superseded by the Varanasi edition of four years earlier. However, the London edition provided the whole of Nāgeśa's subcommentary, where the Varanasi edition only gave extracted notes, so it certainly pushed the boundary of knowledge forward.

Goldstücker had earlier written a book about Pāṇinian grammar that was important and impressively penetrating for its time. The title of the 1861 edition of the book in the BL online catalogue is Panini, his place in Sanscrit Literature ... A separate impression of the preface to the Fac-Simile of MS. No. 17 in the Library of Her Majesty’s Home Government for India, etc. (BL classmark 14092.cc.4.). The text had first appeared as a preface to his edition of the Mānava-kalpa-sūtra, and was only published as a separate book in 1861. It was reprinted in Allahabad in 1914, Benares 1965, and may still be reprinted occasionally in India.

The excellent entry on Goldstücker in the DNB written by Nick Allen (doi:10.1093/ref:odnb/10925) throws valuable light on the interaction between Goldstücker's personality and his scholarship. He had a private income, and never drew a full salary from any university. Goldstücker functioned on the pattern of an eighteenth-century enlightenment gentleman scholar, in Steve Shapin's sense (A Social History of Truth), free from the prejudicial taint of employment and thus able to pursue truth impartially. He was very clever, very talented, and very hard-working. But his ambitions for scholarly achievement were so high that he judged much of his own writing to be unready for actual publication. Although kind and friendly on a personal level, he engaged in severe, even savage, criticism of other published Western scholars, but published little of his own work. Several of his books, including the Mahābhāṣya edition, were in fact facsimile or typeset reproductions of Indian scholastic manuscripts. In his introduction to one such edition, of the Jaiminīyanyāyamālāvistara by Mādhava, Goldstücker lays out his intention to publish a European equivalent of the famous Bibliotheca Indica series, with a special mission of publishing the manuscripts of the Colebrooke collection in the British Museum and, if possible, manuscripts from the Sarasvati Mahal library in Thanjavur that would be brought from Thanjavur to London by His Serene Highness Prince Frederic of Schleswig-Holstein, who was a Sanskritist.

As Allen notes, "For so learned a scholar Goldstücker's output was disappointing, and exercised only limited influence." Several of his main research projects ballooned in size and detail out of all proportion, becoming entirely unwieldy and impossible to complete or to publish. Thus he left a trail of unfinished works behind him. Two volumes of his minor articles and lectures were published posthumously in London in 1879. His papers were deposited in the British Museum, with a stipulation that they would not be published until after 1920, but by that time the Great War and subsequent scholarly progress and shifts in perspective meant that his works would no longer be viewed as worth the labour of editing and publication. As Allen further noted, "Critics have also said that, for all his zeal and fastidiousness, he lacked sound judgement, and was insufficiently critical of native Indian scholarly tradition." Golstücker held enormous admiration for the tradition of Sanskrit scholarship in India, and believed that Indian culture and society would gain immeasurably through the recovery of its ancient intellectual achievements, and that this was most appropriately achieved through a synthesis of Indian and European scholarly effort. Yet his own efforts to achieve his goals and to advance Sanskrit scholarship were, finally, Quixotic: grandiose, severe, and ultimately vain when compared with his undoubted talents.

Critical edition typesetting

Some years ago, John Lavagnino and I wrote the EDMAC
software for typesetting critical editions. EDMAC was an application for use with plain TeX. Later, adaptations were made to allow EDMAC to work with LaTeX etc. More recently, the ConTeXt package, also based on TeX, has been developing methods for handling critical edition typesetting.

Idris Hamid, Colorado State University, recently gave this talk at the TUG 2007 conference, San Diego, about doing critical editions using ConTeXt.

Ayurvedic Man

The famous "Ayurvedic Man" image (Wellcome Library Iconographic Collection 574912i) that has appeared on several book covers and in several publications, is owned by the Wellcome Library, London, and a low-res version can be viewed on their website. I wrote a small article referring to the image recently, in the journal Medical History.


As a result of a recent query about the texts that surround the image, I can now report that the texts are citations from the Bhāvaprakāśa of Bhāvamiśra, the 16th century physician who lived in North India, perhaps Varanasi. For more information on Bhāvamiśra, see G. J. Meulenbeld, Indian Medical Literature, IIa: 239--46.

The Bhāvaprakāśa texts cited in this painting almost all come from BhP 1.1. prakaraṇa 3 (garbhaprakaraṇa).

Earliest edition of the Mahābhāṣya?

William Griggs (1832–1911) was the inventor of a photolithographic process. The DNB entry on him has the following extraordinary information:

Griggs was as successful in bringing down the price of reproducing old manuscripts and letterpress texts as he had been in reducing costs in chromolithography. His production of fifty copies of the Mahabhasya (the standard authority on Sanskrit grammar), consisting of 4674 pages (1871), was carried out for £6000 less than the estimate for a tracing of the original manuscript by hand, an enormous sum at the time. More widely known were his Shakespeare quartos, with critical introductions by Frederick James Furnivall and others, in forty-three volumes (1881–91); hand-traced facsimiles of the same works by E. W. Ashbee, superintended by James Orchard Halliwell-Phillipps, had been sold at more than eight times the price.

I was unaware of this piece of printing history, and it would be interesting to find out who commissioned this particular work, and to see copies of the photolithograph. It seems implausible that it would have cost much more than £6000 to commission scribes to copy out the Mahābhāṣya in the late 19 century. Griggs worked in London, in close association with the India Office.

... on the history of Indian food

Oh, on the subject of the history of Indian food, one mustn't forget the rather wonderful publications of K. T. Achaya.