[INDOLOGY] Once again on the origin of zero: the date of the Bakhshali manuscript (or manuscripts?)

Sat Sep 16 15:53:24 UTC 2017

Dear Agathe,

Thank you for specifying the content aspect of folio 16v and 17r. I have to say however that in cases like this the fact that there is a relationship in content of the text does not always mean that the two folios were produced at the same time. In my modest experience as a cataloguer, it can be quite tricky to establish the correct stratigraphy of composite manuscripts. In fact, if I understand correctly the edition and translation by Hayashi (many thanks, your work is masterpiece of textual scholarship and it saved me during the last months!), the first example for sutra 27 finishes on folio 16v, and on folio 17r a new verification begins, followed by another example. In my modest opinion, this is not so conclusive as it might look at a first glance, as we could always argue that the verification and the second example (which is not marked as such in the manuscript, if I understand correctly the editorial practice, the use of the brackets, and if I read correctly the manuscript) were added in a second moment to verify and explain the sutra further. I'm afraid that we don't have a smoking gun, so to say, to be totally sure that the two folios are contiguous, although it is obviously that it is most probable that they are indeed contiguous. This doesn't necessarily mean however that they were written at the same time, since the upper part of folio 17 is missing and therefore we cannot be sure that the text was continuous between the two folios. All we can know is that on folio 17r there is a verification for the sutra on folio 16v and a second example, but we cannot know for sure whether they were added later or not. Still, I'm not doubting the order of the folios here, only that we cannot be sure that they were written at the same time.

As to the analysis of the ink, I know of the laboratory at the CSMC in Hamburg, as I used to work in the predecessor of the CSMC. I am not sure though how far it could help us to know about the composition of the ink in solving the conundrum of the date. When I was in Cambridge we analysed the inks used in miniatures of a Pancaraksa manuscript, but all we could get to know was the composition of the ink, surely not the date. I'm not totally sure, but if I remember correctly, if the ink was produced also with mineral substances, then the radiocarbon dating wouldn't be totally reliable. All we would know from the analysis of the ink would be whether they used the same type of ink or not on the two folios. Surely this would help us a bit more, but again it wouldn't be totally conclusive.

Finally, I have given a lot of thought before introducing in my report the statement about the function of the Bakhshali manuscript(s). I understand fully and totally agree with you that "many of the general procedures and problems found in the BM have echoes in problems and procedures found in the highbrow scholarly mathematical chapters of later sanskrit siddhāntas. As any historian of mathematics could tell you, apparently “practical” problems are sometimes pretexts for theoretical considerations…" Indeed this is natural (didn't it happen in late medieval Europe as well? I'm thinking of the rising trade and merchant corporations). I'm not saying that merchants wrote the texts in the Bakhshali, what I am saying is that it makes a hell of a lot of sense that precisely this type of practical problems–and not, for instance, an overwhelming number of astrological calculations–are found in this manuscript (or manuscripts?). Also, the style of the texts obviously points to a scholarly context, but we have to bear in mind that the language per se is not Paninian Sanskrit, it is rather a sort of Buddhist Hybrid Sanskrit. I kindly have to ask you however to wait until I finish to write the article, if you don't mind.

Best wishes,

Camillo

________________________________
From: Agathe Keller [kelleragathe600 at gmail.com]
Sent: Saturday, September 16, 2017 1:01 PM
To: Camillo Formigatti; Takao Hayashi
Cc: Indology List
Subject: Re: [INDOLOGY] Once again on the origin of zero: the date of the Bakhshali manuscript (or manuscripts?)

Dear Camillio, Dear all,

Thank you indeed for telling us a bit more of the context of your work and the general decision to go public about it.

Just to specify things, contents wise, since there is a textual continuity between the recto and verso of folio 16, and since there is a mathematical continuity between the verso of folio 16 and the recto of folio 17 (the resolution and then verification of the result of an example), there are indeed two possibilities: either folio 17 is a copy of an older folio that had deteriorated, either somebody used an older birch bark (folio 16) and a new one (folio 17) while writing this part of the text.
So i concur with everybody either paleography, or a technique to analyze the ink on both folios will help us clear what is in all cases a very fascinating spotlight on how the Bakhṣālī manuscript was made. I might be wrong but in Hamburg, at the center for Manuscript Studies, I recall that they had a kind of unobstrutive infra-red reading technique that could reveal the contents of ink pigments… so such techniques exist and could tell us more about the BM as well.

The BM is unique in the history of mathematics in South Asia because it was unearthed and not found and preserved in a library collection. So it would be fascinating if it, itself testifies to a process of continuous copy! Of course we would all love to be able to contextualise the texts we work on: who used them, who made them, etc. Even more so for a text that is in itself a historical artifact and not a late copy of an older text. For this reason, I would really like to know on what basis you think that :

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.

because actually many of the general procedures and problems found in the BM have echoes in problems and procedures found in the highbrow scholarly mathematical chapters of later sanskrit siddhāntas. As any historian of mathematics could tell you, apparently “practical” problems are sometimes pretexts for theoretical considerations…and much of the features of the BM such as the use of “verifications/proofs” points to this. Further wouldn’t the language used in the BM precisely point rather to a scholarly context?
But i confess my ignorance on the milieus of buddhist merchants on the silk road, (the Dunhuang manuscripts I know of all have mathematical texts in chineese), and would be happy for any lights on this topic!

All this said, I do find shocking the Bodleian’s choice of a press release before the publication of a peer reviewed article…

yours

Agathe Keller
CNRS-Université Paris Diderot

On 16 Sep 2017, at 11:58, Camillo Formigatti via INDOLOGY <indology at list.indology.info<mailto:indology at list.indology.info>> wrote:

Dear Oliver,

I had heard rumors about this enterprise of yours and I was almost losing hope to see it, this is simply great news!

Will there be the possibility to enlarge the corpus? May I supply you with akṣaras of Nepalese and Central Asian manuscripts I'm currently working on for projects unrelated to the Bakhshali?

It would be great to have a broader basis of manuscripts for INDOSKRIPT, above all since I have access to ten of thousands of images of folios from the Cambridge collections.

Best wishes,

Camillo

________________________________
From: hellwig7 at gmx.de<mailto:hellwig7 at gmx.de> [hellwig7 at gmx.de<mailto:hellwig7 at gmx.de>]
Sent: Saturday, September 16, 2017 10:31 AM
To: Walter Slaje; Camillo Formigatti
Cc: Andrea Acri; Indology List
Subject: Re: [INDOLOGY] Once again on the origin of zero: the date of the Bakhshali manuscript (or manuscripts?)

Dear Camillo,

I would not try too hard to get the executable of Indoskript to work. We (H. Falk and I) are currently preparing an web version of Indoskript, which will go online in the next months.

Best, Oliver

---
Oliver Hellwig, SFB 991, Universität Düsseldorf

From: Walter Slaje<mailto:slaje at kabelmail.de>
Sent: Saturday, September 16, 2017 11:03 AM
To: Camillo Formigatti<mailto:camillo.formigatti at bodleian.ox.ac.uk>
Cc: Andrea Acri<mailto:andrea.acri at ephe.sorbonne.fr> ; Indology List<mailto:indology at list.indology.info> ; Oliver Hellwig<mailto:hellwig7 at gmx.de>
Subject: Re: [INDOLOGY] Once again on the origin of zero: the date of the Bakhshali manuscript (or manuscripts?)

Dear Dr Formigatti,

thank you for your detailed and indeed very welcome elucidation!
I think, however, there is a need to dispel a possible misunderstanding: The only umbrage I was taking at was the scientist’s zero discovery claim and the lack of any Indological expertise in this sensationalist broadcast, which would
perhaps have 
be
en
justified for the radiocarbon dating. It is reassuring to learn about the actual background of the whole undertaking, for which the research team deserves unreserved congratulations, and I would
be 
the last person not to applaud
 to their efforts
.

What you say about “the reason why Hayashi is not mentioned in the Guardian article–nor is any of us from the team (...) is that this is an article (...) written for the broader public”, invites one to think why a broader public and Indological knowledge should be seen as mutually exclusive?

The technical problems with INDOSKRIPT you have pointed out, the advantage of which are its sets of paleographically comparable data, could only be satisfactorily answered by Oliver Hellwig, the programming mastermind behind INDOSKRIPT.

A final remark on layers of birch-bark manuscripts: I have documented MSS, where damaged leaves of a text had been supplemented materially by single leaf layers of the same text taken from intact leaves of other MSS (see, e.g., my catalogue of the Viennese MSS collection, 1990, no. 42 (p. 91), no. 53 (p. 103), no. 60 (p. 11)). Such widespread practice would result in a complete text, however with textual overlapping from possibly different strands of transmission (!). While the material layering is still visually recognizable in the first generation of conflated texts of that kind, this would no longer be the case in the copies made by one scribal hand from this exemplar. If the process was carried on for centuries, only a philological analysis could uncover what lies beneath
an apparently homogeneous surface.

Perhaps the Bakshāli, too, is itself a product,
 at the beginning or
somewhere 
in the middle
,
of
a 
repeated process of material layer conflations

.

Kindly regarding,
WS

2017-09-16 1:39 GMT+02:00 Camillo Formigatti <camillo.formigatti at bodleian.ox.ac.uk<mailto:camillo.formigatti at bodleian.ox.ac.uk>>:
Dear Prof. Slaje,

Many thanks for your reply to my message on the radiocarbon dating of the Bakhshali manuscript, I was hoping to read your comments and opinions on the results. I feel that I have to clarify some points and I hope that this reply will help you at least a little bit to dissipate some of your legitimate doubts. I also hope that you will forgive me if I might sound a bit on the defensive, but I have spent the last months doubting myself the results of the radiocarbon dating, only to have to slowly revise my opinions and be more open to possibilities.

I have greatly profited from your wonderful 1993 book on the Śāradā script when I was still a PhD student working on Kashmirian manuscripts, then when I was I cataloguing the Śāradā manuscripts in the Cambridge collections, and more recently when I was completing a survey of the birch-bark manuscripts in the Bodleian collections to assess their conditions (I was surprised to find five uncatalogued birch-bark manuscripts belonging to what I call the Leitner collection, which are actually mentioned in the introduction of the catalogue by Winternitz and Keith, but that had escaped my attention so far; anyway, this is yet another story). I am fully aware that I am a beginner in the field of the paleography of the Śāradā script. Moreover, I know very well that I am certainly not the most qualified scholar who could assess the implications of these results for the palaeography of North Indian scripts, and certainly not at all for the history of Indian mathematics. Nevertheless, I have been asked to assist during the whole project of radiocarbon dating the Bakhshali manuscript in my role as the curator of the Sanskrit manuscripts in the Bodleian Libraries. I have tried to do my best and to do my homework properly, so to say, if you allow me this rather prosaic simile with the job of school students. I have taken care of all Indological aspects and implications of this project very closely since its outset. In our team we are all well aware of Takao Hayashi's work on the Bakhshali, in fact we have been in contact with him and Agathe Keller before the start of the project, and the only reason why we haven't communicated the results to them in advance and before the press release is because of decisions coming from higher above us in the food chain (if you allow me again a prosaic metaphor). In fact, I have read and used Hayashi's 1995 edition very intensively in the last few months, alongside Kaye's first edition, Hoernle's article, and several other articles and books on the topic of zero and the history of mathematics in India (many thanks to Kim Plofker, without her wonderful contributions to the history of Indian mathematics I would have been lost), as well as Lore Sander's palaeographical studies, your own 1993 book, and several other publications on the palaeography of Indian scripts (obviously starting with the one by our great forefather Georg Buehler). The reason why Hayashi is not mentioned in the Guardian article–nor is any of us from the team, by the way, except for Prof. du Sautoy–is that this is an article in a newspaper and hence written for the broader public. As one of my Bodleian colleagues pointed out to me today when I wrote to him that I was disappointed that none of us from the team was even mentioned in the Guardian article (above all because two of us are EU citizens, and I believe I don't need to say more): we cannot control what the press chooses to do and publish. The Guardian was allowed the exclusive on this news (together with the BBC) and provided with the names of all members of the team that I mentioned in my first message. They chose to interview and quote only Prof. du Sautoy and the Bodley's Librarian Richard Ovenden, who both have a high profile and an own Wikipedia page. If this is what Bodleian Communications thinks it's better to do to have a wider impact on the broader public, well I can't certainly influence their decision. I surely agree with you that it would have made a hell of a lot more sense to interview Takao Hayashi and ask him his opinion, but we all know how these things go, don't we?

Finally, I am well aware of the existence of INDOSKRIPT and I have used this wonderful tool before, but I am sorry to say that at the moment I do not fully agree with the statement "The individual akṣaras of the Bakshāli MS can be consulted in their extracted forms and [...] compared to their paleographic environment most conveniently [italics mine] by using the tools of INDOSKRIPT." The reason why I do not agree is merely a technical one. I used to consult INDOSKRIPT regularly when I was running a PC with Windows XP. When I switched to Linux/Ubuntu I then installed a pirate copy of Windows XP on a Virtual Machine only to be able to use INDOSKRIPT (this was back in 2007). Soon it turned out to be too taxing for the RAM of my computer and also it was pretty cumbersome to switch from Ubuntu, on which I was running Emacs for my work, to the VM to consult the INDOSKRIPT database. When in 2011 in Cambridge I was given as project laptop a MacPro, again I tried to install INDOSKRIPT, this time using the Wine emulator program. Much to my dismay, this time INDOSKRIPT didn't start at all. I did not want to install again a VM and install on it a Windows system, because I did not have access to any pirate copy of Windows XP (probably I could have easily downloaded one, I know) and I did not want to buy Windows only to run INDOSKRIPT. I have just followed the link to the INDOSKRIPT webpage that you provide and I cannot find any further implementation of the INDOSKRIPT database to run it on a Linux or Mac OS X system. If I am missing it, I kindly ask you to point me to it, as I certainly do not want to reinvent the wheel and if I can easily install this wonderful database on my Mac OS X or my Lubuntu machine to comfortably compare the akṣaras of the Bakhshali manuscript, I will do it for sure, instead of slaving to extract and modify akṣaras from the pictures of the Bakhshali I have or from images of manuscripts I have downloaded from the IDP website.

(As a side note, I actually prefer to use the facsimile in Kaye's edition, since we are not allowed to photograph the Bakhshali anymore due to its poor condition and I have been told that when Hayashi asked permission to use in his own edition the reproductions used for Kaye's edition, it turned out that the original takes got lost, so the facsimile in Hayashi's edition is based on photographs of the printed version of Kaye's facsimile.)

Best wishes,

Camillo Formigatti

________________________________
From: Walter Slaje [slaje at kabelmail.de<mailto:slaje at kabelmail.de>]
Sent: Friday, September 15, 2017 8:01 AM
To: Andrea Acri
Cc: Indology List
Subject: Re: [INDOLOGY] Once again on the origin of zero: the date of the Bakhshali manuscript (or manuscripts?)

I fully concur with what Dr Acri has to say in this matter. Moreover, the initial statement of the interviewed mathematician „The most exciting thing is that we’ve identified a zero“ is presumptuous, as the „identification“ claimed here is actually decade-long common Indological knowledge easily traceable in the relevant literature on the subject. I wonder why no Indologist with a profound disciplinary knowledge was asked to give qualified statements.

A reproduction together with a transliteration of this famous manuscript was brought to the public in 1995:
Takao Hayashi, The Bakshali Manuscript. Groningen 1995.

The individual akṣaras of the Bakshāli MS can be consulted in their extracted forms and, in the possible attempt of a fresh dating, compared to their paleographic environment most conveniently by using the tools of INDOSKRIPT (http://userpage.fu-berlin.de/falk/):

[X]

Best regards,
WS

-----------------------------
Prof. Dr. Walter Slaje
Hermann-Löns-Str. 1
D-99425 Weimar
Deutschland

Ego ex animi mei sententia spondeo ac polliceor
studia humanitatis impigro labore culturum et provecturum
non sordidi lucri causa nec ad vanam captandam gloriam,
sed quo magis veritas propagetur et lux eius, qua salus
humani generis continetur, clarius effulgeat.
Vindobonae, die XXI. mensis Novembris MCMLXXXIII.

2017-09-15 2:41 GMT+02:00 Andrea Acri via INDOLOGY <indology at list.indology.info<mailto:indology at list.indology.info>>:
Dear Camillo

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.

Best regards
Andrea Acri

Sent from my iPhone

On 14 Sep 2017, at 17:15, Camillo Formigatti via INDOLOGY <indology at list.indology.info<mailto:indology at list.indology.info>> wrote:

Dear Colleagues,

I’m pleased to be finally able to share this exciting news with you:

https://www.theguardian.com/science/2017/sep/14/much-ado-about-nothing-ancient-indian-text-contains-earliest-zero-symbol

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.

Best wishes,

Camillo

________________________________

Dr Camillo A. Formigatti
John Clay Sanskrit Librarian

Bodleian Libraries
The Weston Library
Broad Street, Oxford
OX1 3BG

Email: camillo.formigatti at bodleian.ox.ac.uk<mailto:camillo.formigatti at bodleian.ox.ac.uk>
Tel. (office): 01865 (2)77208
www.bodleian.ox.ac.uk<http://www.bodleian.ox.ac.uk/>

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