Many thanks for your enthusiasm about this discovery!
I will try and reply to each point you raise, but allow me to quote at the outset a very telling passage written by Cecil Bendall in 1882, in his article On European Collections of Sanskrit Manuscripts from Nepal: Their Antiquity and Bearing on Chronology, History and Literature. When I was first told about the results of the radiocarbon dating of the Bakhshali manuscript, I did not believe it, in fact my very first thought was that they must had done something wrong at the Oxford Radiocarbon Accelerator Unit. My second thought then was precisely that the scribe (or scribes) must had used old birch-bark sheets to write parts of the manuscript in later centuries. However, at that moment I was also working on an article on the history of the Cambridge collections of Sanskrit manuscripts and this quote by Cecil Bendall helped me to keep an open mind:
"The early dates of some of these MSS. have been, indeed, received in some quarters with certain incredulity; but for myself, I must testify that, after about two years study, both of the great Cambridge collection, of which I have been during this time engaged in preparing a catalogue, and of various Buddhistic MSS. in other libraries, the truthfulness and genuineness of the colophons is placed in almost every case beyond a doubt by evidence both varied and conclusive." (Bendall 1882, 190).
I think this is a very telling passage in which our attitude towards this type of discoveries is very aptly described. Apparently, we haven't changed much in the last one-hundred years. In the 19th century, some of our esteemed colleagues didn't even believe that the colophons of old Nepalese palm-leaf manuscripts were authentic. Surely, as we all know, there are cases of colophons of old antigraphs copied together with the main text into more recent apographs, but can we honestly say that they are the great majority of colophons of South Asian manuscripts?
Let me now reply to your points.
"If the manuscript (however fragmentary it may be) is thought to contain a single, unitary text, then the date of its copying (and/or composition?) must be the 9th-10th century. I fail to see what is so sensational about this apart from the fact that it shows how writing supports that were centuries older might have been (re)utilized."
On my part, I fail to see why you think more plausible that somebody reused 700-years old birch-bark sheets to write on it, when they could have used contemporary birch-bark sheet, which would have surely been less fragile. I rather think that we are dealing with a composite manuscript consisting of at least three distinct codicological units. Actually, what seems more plausible to me is exactly the reverse, that somebody supplemented the damaged parts of an old manuscript by copying them on new birch bark, as often is the case in old North Indian and Nepalese palm-leaf manuscripts with damaged folios (as for instance happened with this 11th century Nepalese palm-leaf manuscript: https://cudl.lib.cam.ac.uk/view/MS-ADD-01643/1). If you however think that your hypothesis is more plausible, then I have to say that I disagree with you.
"(By the way: is an analysis of the ink technically possible?)."
It’s not as simple as you might think. It is something we are considering though, as this would be the only way to ascertain what really happened, whether the scribe (or scribes) used old birch-bark sheets to write a new text in the 10th century or if they replaced old and damaged sheets with new birch-bark sheets on which they copied the text of the damaged folios.
"The earliest attestation of the written zero would still be the 8th-century Southeast Asian inscriptions (and not the Gwalior temple, as incorrectly reported in the article)."
Well, if you are convinced that the results of the radiocarbon dating of the Bakhshali manuscript are wrong, then you are right and the zero in 8th century Southeast Asian inscriptions would be the oldest attestation of a symbol for a placeholder in a decimal positional notation system (and strictly speaking, not of a symbol for zero, as I try to explain below). As I said above, I was prepared for the scepticism of colleagues, since my first reaction too was that these dates are impossible. On the other hand, I have to say that I don’t see why we can accept without blinking the radiocarbon dating of the Gāndhārī material or of early Sanskrit manuscripts such as the Spitzer manuscript or of other Buddhist manuscripts from Turfan and other Silk Road sites (all listed in the article by Allon, Jacobsen, Zoppi, and Salomon in the third volume of the Buddhist Schoyen manuscripts, 2006), while in the case of the Bakhshali manuscript we ought not to accept them. I don't know, maybe I’m too naïve to understand the arguments, but what it seems to me is that we are all sceptical because it is difficult to explain these results, since they go against several assumptions we take for granted. I believe that what is puzzling you is the fact that we have three different dates. Imagine if we would have chosen to radiocarbon date only one fragment and not three, or if I would have chosen the three fragments only from the part denoted as M by Kaye in his editio princeps. In the first case, we would have had one single date as result (either the oldest, the middle, or the latest one), and in the second case we might probably have had three similar results with only one later date, which would have convinced us that we are all correct in our assumptions about the development of North Indian scripts, particularly of the Śāradā, as we would have thought "Hey, this is great, a 10th-century (proto-)Śāradā manuscript! After the inscriptions in (proto-)Śāradā, we finally have the oldest dated manuscript against which we can date other Śāradā inscriptions and manuscripts." Alas, I chose instead three fragments from parts of the manuscript (or manuscripts?) which according to Kaye were written in two (or even three) different hands, precisely because we all wanted to be sure to have a sound approach—and I wanted to verify Kaye's palaeographical analysis and understand whether the two (or three scribes) wrote in different periods or not. This is the reason why we have now these three different results. (Honestly, I didn't expect this huge difference in the dates of the three fragments, above all because I thought that the results would have ranged between the 10th and the 12th century; incidentally, Hayashi did not fully believe in the correctness of Kaye's palaeographical assessment and for this reason his reconstruction of the order of the folios differs from Kaye's.) Maybe we ought to reassess our assumptions a bit, instead of blaming the results—but again, I am probably too naïve, or ignorant, or not knowledgeable enough and my hypothesis are all wrong (above all my assessment of the position of the script of folio 16 in the development of the Gilgit-Bamiyan scripts, which I will describe in the article I mentioned, but about which I am not totally sure myself, as often is the case in palaeographical studies).
(By the way, the Guardian article doesn’t mention the Gwalior inscription, which is actually mentioned in the video, and it is not totally incorrect what Prof. du Sautoy says, because he doesn’t say anything about the Gwalior inscription as being the oldest attestation of a written zero, he simply mentions it as an old attestation of this symbol. Anyway, I have always stressed to all other colleagues involved in the project at various levels that the oldest attestations of a place-holder symbol in the form of a zero are from Southeast Asia and not in the Gwalior inscription, as they sometimes said—as you can imagine, I have closely followed the recent discussion about this topic here on Indology, but I kept my mouth shut because I couldn’t reveal our results due to an embargo from the Bodleian Libraries Communication office. If you read anything in which somebody from the University of Oxford says that the place-holder symbol in the Gwalior inscription is the oldest attestation of the symbol for zero, well evidently they haven’t listened to me.)
"But in your message, when you speak about different stratas and tables of ak.saras, you clearly imply that this/these manuscript(s) contain(s) a composite/heterogeneous text indeed, and that part of it might date back to the 3rd-4th century. May I ask you to anticipate/synthesize some of your key findings here, or at least clarify this point? And, what is the relationship between folios 16 and 17?"
At this moment, I am in no position to say with certainty whether we are dealing simply with a composite manuscript consisting of three codicological units (a kernel and two or more dependent codicological units) and at the same time containing only one single sūtra + commentary textual unit, or rather with a composite and multi-text manuscript, consisting of three (or even more) independent codicological units (possibly even without a clear kernel!) and at the same time containing two or more different sūtra + commentary textual units. I have to specify that with sūtra + commentary textual unit I mean the group of [(sūtra + udāharaṇa) and (commentary + nyāsa (sthāpana or nyāsasthāpana), karaṇa and one or more pratyayas)], which I consider as a single text (although I might be totally wrong). So as you can see, to a certain extent we could already say that this is a multi-text manuscript. I do believe though that we have to keep an open mind, start our research from scratch and possibly rethink the grouping of the folios. For this reason again I am in no position to say anything more about the relationship of folio 16 and 17, as I don't know anything of Indian mathematics (and very very very little of mathematics in general). Our intention has been from the very start of this project simply to verify the date of the Bakhshali manuscript with the only means that we thought would clarify the one-century old debate about the antiquity of this manuscript and its implication for the history of mathematics, since the palaeographical and textual means employed so far provided a wide range of dates. We would have then left the results in the hand of the real experts, like Takao Hayashi and Agathe Keller, with whom we were already in contact before starting the project. Unfortunately—or luckily—we complicated the picture even more, and here I am replying to your questions.
Below I have pasted an extract from the part I have prepared for the Bodleian’s official ‘Bakhshali Research Statement&Background’ document (the full document can be found at this link: http://www.sciencemag.org/sites/default/files/Bakhshali%20Research%20Statement_13%209%2017_FINAL.pdf). Please bear in mind that this report is written for non-specialists, so some parts of what I wrote might sound very generic and not totally exact or sufficiently supported by scholarly evidence in the eyes of Indologists. In my article I will obviously try and underpin with textual and palaeographical evidence some of the hypothetical statements (and I stress hypothetical!) that I make in these very short report. I hope however that it provisionally answers some of your questions.
"Do all these folios contain the 0?"
All folios contain the symbol 0 used either as a placeholder or as a symbol for an unknown, but not as a zero in its own rights (as I try to explain below).
"Further: I'm not steeped in mathematics either, so I fail to grasp the full implications of this statement (especially the second sentence): "In the fragile document, zero does not yet feature as a number in its own right, but as a placeholder in a number system, just as the “0” in “101” indicates no tens. It features a problem to which the answer is zero, but here the answer is left blank"."
As to the question of what is a zero, what Prof. du Sautoy means is that one thing is to have any symbol (in our case, the dot that will evolve into the hollow symbol 0) as a placeholder to denote the absence of units, tens, hundreds, etc. in a positional notation system (be it decimal, as in the Indian system, or sexagesimal, as in the Babylonian system). This fact is per se not so exciting, as it is clearly explained even in the Guardian article: ‘Several ancient cultures independently came up with similar placeholder symbols. The Babylonians used a double wedge for nothing as part of cuneiform symbols dating back 5,000 years, while the Mayans used a shell to denote absence in their complex calendar system.’ What is more exciting in the Bakhshali manuscript is another function of the dot, i.e. precisely the fact that it represents an unknown (for instance in equations). However, as I understand it (but my knowledge and understanding of mathematics is very poor), this is again different than thinking of having as result of an operation zero, i.e. nothing, from something. I hope my explanation is clear, as it took me sometime to understand why Prof. du Sautoy was desperately looking for what we laymen called a ‘mathematical’ zero, when we all thought that the Bakhshali was already full of them!
The carbon dating has revealed that the Bakhshali manuscript is a composite document and consists of at least three different parts with different ages. Due to the fragmentary nature of the manuscript, it is difficult to reconstruct the original order of the folios and consequently of the extant texts. Until now, the manuscript has been studied as if it were one single item. The first editor of the manuscript, G. R. Kaye, employed the following criteria to establish the order of the folios:
(1) Logical sequence of contents.
(2) The ‘find order.’
(3) Physical appearance such as the size, shape, degree of damage, and knots in the birch bark.
(4) The script and language.
(5) Numbered sūtras.
In the most recent complete study of the manuscript (1995), Takao Hayashi does not deem the fourth criterion reliable enough for the reconstruction of the order of the folios. This approach is again based on the assumption that all extant parts of the manuscript were written at the same time – an assertion now overturned by the new carbon dating results.
The early date of folio 16 fits well into the cultural milieu in which this part of the manuscript was probably produced and circulated. The content of the Bakhshali manuscript is similar to the type of texts that Buddhist merchants would have needed to study (and possibly use as reference) for their daily trading activities. It includes very practical mathematical examples and equations, such as how to compute the loss in weight of a quantity of impure metal in the process of refining it, etc.
The manuscript was recovered in the village of Bakhshali in Pakistan, in an area that belongs to the historical Gandhāra region. It is a region in which major cities such as Peshawar (Skt. Puruṣapura) and Taxila (Skt. Takṣaśilā) were important commercial and cultural hubs. This area belonged to the Indian, Persian, and Greek cultural spheres of influence and had contacts with Chinese culture through the Silk Road. The oldest Buddhist and South Asian manuscripts extant were also found in the Greater Gandhāra region and their dates range from the first century BCE to the fourth century CE – so a similar time period to that of folio 16 of the Bakhshali manuscript. Although written in a different script and a different language than the Bakhshali manuscript, these Buddhist manuscripts are also written on birch-bark.
Moreover, the language used in the manuscript is not standard Sanskrit, and according to Hayashi it shows features of what is called Buddhist Hybrid Sanskrit, as well as of other Middle-Indo Aryan languages (Prakrit and Apabhraṃśa), and also of Old Kashmiri. This is yet another feature that can be explained by the fact that the manuscript in its present state is composed of at least three different manuscripts with different dates. The three dates would then correspond to different stages of linguistic development.
Dr Camillo A. Formigatti
John Clay Sanskrit Librarian
The Weston Library
Broad Street, Oxford
Tel. (office): 01865 (2)77208
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thank you for sharing this news, and especially for your (in)valuable work on this most important document. Let me point out at the very outset that all I know about this manuscript derives from the Guardian article and Wikipedia (disclaimer: I have no access to a library right now!), so please forgive me for being so naive.
If the manuscript (however fragmentary it may be) is thought to contain a single, unitary text, then the date of its copying (and/or composition?) must be the 9th-10th century. I fail to see what is so sensational about this apart from the fact that it shows how writing supports that were centuries older might have been (re)utilized. (By the way: is an analysis of the ink technically possible?). The earliest attestation of the written zero would still be the 8th-century Southeast Asian inscriptions (and not the Gwalior temple, as incorrectly reported in the article).
But in your message, when you speak about different stratas and tables of ak.saras, you clearly imply that this/these manuscript(s) contain(s) a composite/heterogeneous text indeed, and that part of it might date back to the 3rd-4th century. May I ask you to anticipate/synthesize some of your key findings here, or at least clarify this point? And, what is the relationship between folios 16 and 17? Do all these folios contain the 0?
Further: I'm not steeped in mathematics either, so I fail to grasp the full implications of this statement (especially the second sentence):
"In the fragile document, zero does not yet feature as a number in its own right, but as a placeholder in a number system, just as the “0” in “101” indicates no tens. It features a problem to which the answer is zero, but here the answer is left blank".
Hopefully some of our learned colleagues will be able to clarify this point.
Sent from my iPhone
On 14 Sep 2017, at 17:15, Camillo Formigatti via INDOLOGY <email@example.com> wrote:
I’m pleased to be finally able to share this exciting news with you:
I imagine that some of you might probably raise their eyebrows after reading this article. The results came as a big surprise to us too, and to me were literally jaw-dropping. I realize that these results have several implications not only for the history of mathematics, but also for our field of study, and I know that the article in The Guardian surely doesn’t answer the many questions you might be asking yourselves now. I will try to briefly anticipate some of them.
The decision and implementation of radiocarbon dating the Bakhshali manuscript took several months of preparation on the part of the team of colleagues with which I collaborated. The team included colleagues from the Bodleian Libraries and other University of Oxford departments: David Howell (Bodleian Libraries’ Head of Heritage Science), Dr Gillian Evison (Head of the Bodleian Libraries' Oriental Section & Indian Institute Librarian), Virginia M Lladó-Buisán (Bodleian Libraries’ Head of Conservation and Collection Care), Dr David Chivall (Chemistry Laboratory Manager at the School of Archaeology of the University of Oxford), and Prof. Marcus du Sautoy (Charles Simonyi Professor for the Public Understanding of Science and Professor of Mathematics at the Oxford University). We decided to take samples from three folios in order to be sure to have a sensible margin of certainty for the results. I chose folios 16, 17, and 33, and the analysis was conducted by Dr Chivall at the Oxford Radiocarbon Accelerator Unit. The results of the calibrated age (95.4% confidence interval / cal AD) are as follows:
Folio 16: 224 (95.4%) 383calAD
Folio 17: 680 (74.8%) 779calAD
790 (20.6%) 868calAD
Folio 33: 885 (95.4%) 993calAD
We did not expect such a big difference in the date range of the three folios. I am currently preparing an article in which I provide the background for the choice of these three specific folios, tables of all akṣaras from the three folios as an aid to assign the extant folios to the different strata of the manuscript (including selected aksaras of other dated and undated manuscripts in similar scripts for comparison), and a first palaeographical appraisal of the results.
Dr Camillo A. Formigatti
John Clay Sanskrit Librarian
The Weston Library
Broad Street, Oxford
Tel. (office): 01865 (2)77208
GROW YOUR MIND
in Oxford University’s
Gardens, Libraries and Museums