The Ciphers Of The Monks: A Forgotten Number Notation Of The Middle Ages

255 Pages·2000·24.273 MB·English

by  David A. King

ADDENDA AND CORRIGENDA TO KING, CIPHERS OF THE MONKS:
Addenda:
pp. 168-171: see next note.
p. 274, note to the third sentence - “I have a strong suspicion that there are... even
some other material objects on which our ciphers were used, hidden in museums
or in as yet unexcavated archaeological sites.” In an article by Siebo Heinken,
“Die Suche nach den Koggen der Ostsee”, National Geographic Deutschland
(Hamburg), July, 2001, pp. 54-61, (not in the American edition), there is illustrated
(p. 58) a wooden liquor bottle from the 14th or 15th century recovered from
excavations in the city of Rostock. Engraved on this are four marks, all of which
could be interpreted as numerical ciphers; my first reaction is that they should not
be, but who knows? The bottle belongs to the Landesmuseum Mecklenburg-Vor­
pommern, and is currently (summer, 2001) on display in the Museum fur Hambur-
gische Geschichte in Hamburg.
p. 277, line 5, and the bibliography - Reference should have been made to an
important new book: Steven C. McCluskey, Astronomies and Cultures in Early
Medieval Europe, Cambridge, etc.: Cambridge University Press, 1998.
p. 364, end of n. 3 from p. 363 - Add: See further King, “The Universal Horary
Quadrant”, to appear in Journal for the History of Astronomy in 2002.
p. 396, unnumbered footnote, and the bibliography - Reference should have been
made to Poulle, “U Astrolabe medieval”,which deals with manuscripts of astrolabe
texts of French provenance.
Corrigenda:
p. 267, end of page - instead of “for the” read “for the original texts”.
p. 362, 3-4 lines from bottom of n. 3 - for “numerous European quadrants” read
“numerous European astrolabes”.
p. 370, line 2 - for “show” read “shows”.
p. 468 - delete last two lines.
DAVID A. KING
THE CIPHERS OF THE MONKS
BOETHIUS THE CIPHERS
TEXTE UND ABHANDLUNGEN ZUR
GESCHICHTE DER MATHEMATIK
OF THE MONKS
UND DER NATURWISSENSCHAFTEN
BEGRUNDET VON JOSEPH EHRENFRIED HOFMANN
FRIEDRICH KLEMM UND BERNHARD STICKER
HERAUSGEGEBEN VON MENSO FOLKERTS
A FORGOTTEN NUMBER-NOTATION
OF THE MIDDLE AGES
BAND 44
BY
DAVID A. KING
FRANZ STEINER VERLAG STUTTGART FRANZ STEINER VERLAG STUTTGART
2001
2001
For Patricia,
Maximilian and Adrian
Die Deutsche Bibliothek - CIP-Einheitsaufnahme
King, David A.:
The ciphers of the monks : a forgotten number-notation of the Middle
Ages / by David A. King. - Stuttgart: Steiner, 2001
(Boethius; Bd. 44)
ISBN 3-515-07640-9
ISO 9706
Jede Verwertung des Werkes auBerhalb der Grenzen des Urhabe^htsgesetos Ut
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filmung oder vergleichbare Verfahren sowie fur die Speic e'"ung* ,af. @2001
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by Franz Steiner Verlag Wiesbaden GmbH, Sitz Stuttg
alterungsbestandigem Papier. Druck: Druckerei Proff, uras urg
Printed in Germany
TABLE OF CONTENTS
Preface ............................................................................................................... 15
Acknowledgements............................................................................................ 21
I Introduction................................................................................................. 27
1 The ciphers - some historiographical considerations........................... 27
2 The main varieties of ciphers............................................................... 32
3 The cultural context of the new number-notation................................ 40
II The English ciphers..................................................................................... 49
1 Introduction........................................................................................... 49
2 The ciphers of John of Basingstoke..................................................... 51
2.1 The Cambridge manuscript........................................................... 56
3 On the Greek origin of the Basingstoke ciphers.................................. 57
3.1 A Greek shorthand from the 4th century B.C. as attested on
a tablet found on the Acropolis..................................................... 58
3.2 The Tironian notes........................................................................ 61
3.3 Are the Basingstoke ciphers really of Greek origin?.................... 63
3.4 The Basingstoke ciphers and the runes.......................................... 65
4 The ciphers as letters of the alphabet - the late-12th-century English
ars notaria............................................................................................. 66
5 Ciphers similar to the Basingstoke ciphers in medieval Arabic
treatises.................................................................................................. 72
6 The Basingstoke ciphers at the hands of the Cistercians...................... 82
6.1 The Lambeth manuscript.............................................................. 82
7 The demise of the Basingstoke ciphers................................................ 89
III The horizontal ciphers of the Cistercians................................................... 91
1 Introduction........................................................................................... 91
1.1 The Cistercians............................................................................. 93
2 Two types of Cistercian ciphers........................................................... 94
3 The Cistercian ciphers as used in early manuscripts of mainly
religious content.................................................................................... 95
3.1 The Brussels manuscript............................................................... 95
3.2 The Laon manuscript.................................................................... 100
3.3 The Oxford Lyell manuscript....................................................... 102
3.4 The Liineburg manuscript............................................................. 103
3.5 The Uppsala manuscript............................................................... 104
3.6 The Basle manuscript................................................................... 106
3.7 The Turin manuscript................................................................... 108
4 Ciphers in musical notation.................................................................. 112
4.1 The Turin manuscript again......................................................... 112
8 Table of Contents Table of Contents 9
5 The horizontal ciphers in marginalia.................................................... 115 7 The ciphers as letters of the alphabet in two magical texts................... 178
5.1 The Wolfenbiittel manuscript....................................................... 115 7.1 The Uppsala manuscript again..................................................... 179
5.2 A manuscript formerly belonging to W. W. Greg....................... 116 7.2 The Heidelberg manuscript........................................................... 180
5.3 The Erfurt manuscript................................................................... 117 8 The doodles of a monk - different representations of the Cross by
5.4 The Munich (I) manuscript........................................................... 119 means of ciphers................................................................................... 182
6 Ciphers featured in marginalia in manuscripts of non-religious 8.1 The Paris (III) manuscript............................................................. 182
content.................................................................................................. 120 9 The early evidence on ciphers reviewed.............................................. 185
6.1 The Gottingen manuscript............................................................ 120 9.1 How many manuscripts originally featured ciphers?................... 187
7 The horizontal ciphers developed into an alphabetic code.................. 121
The fate of the monastic ciphers in the Renaissance and thereafter......... 189
7.1 The Munich (II) manuscript.......................................................... 121
1 Introductory remarks............................................................................ 189
8 An anomalous set of ciphers................................................................ 124
2 The ciphers as presented by Agrippa of Nettesheim............................ 190
8.1 The Lyons manuscript.................................................................. 124
2.1 The Chaldean connection.............................................................. 194
9 Two other sets of basic ciphers in manuscripts of scientific content... 126
2.2 The Leiden manuscript................................................................. 197
9.1 The Munich (III) manuscript........................................................ 126
2.3 The manuscript from The Hague.................................................. 197
9.2 The Oxford Tanner manuscript..................................................... 129
2.4 Francis Barrett and Agrippa’s ciphers.......................................... 200
IV The astrolabe of Berselius.......................................................................... 131 3 Tb^ ciphers in the French translation of Trithemius’ Poly graphics...... 202
1 Introduction.......................................................................................... 131 4 The ciphers as developed by Cardano.................................................. 206
2 A medieval astrolabe engraved with monastic ciphers....................... 131 5 The ciphers in other early printed works on the history of numerical
3 The Picard connection.......................................................................... 138 notations................................................................................................ 210
3.1 The names of the months on the astrolabe.................................... 138 5.1 Johannes Noviomagus.................................................................. 211
3.2 Medieval Picardy and its dialect................................................... 140 5.2 The Dutch treatise Die maniere (without ciphers)........................ 214
3.3 Who made the Picard astrolabe?................................................... 141 5.3 Matthaeus Hostus.......................................................................... 215
4 Paschasius Berselius, the donor in 1522, and Hadrianus Amerotius, 5.4 Georg Henisch.............................................................................. 215
the recipient.......................................................................................... 141 5.5 Valerianus Bolzanius.................................................................... 219
4.1 The dedication on the astrolabe.................................................... 141 5.6 Alphonse Costadau....................................................................... 220
4.2 Paschasius Berselius..................................................................... 143 5.7 Johann Christoph Heilbronner et al............................................... 221
4.3 Hadrianus Amerotius.................................................................... 147 6 Some shorthand scripts and codes from the early Renaissance based
4.4 Some remaining questions............................................................ 149 on the ciphers........................................................................................ 226
*
6.1 Timothy Bright............................................................................. 227
V The French vertical ciphers in manuscript sources.................................... 152
6.2 Daniel Schwenter.......................................................................... 228
1 Introduction.......................................................................................... 152
6.3 Giovanni Battista Porta................................................................. 232
2 The vertical ciphers at the University of Paris..................................... 153
6.4 John Wilkins................................................................................. 235
2.1 The Vatican manuscript............................................................... 153
6.5 William Oughtred......................................................................... 236
3 The ciphers in a treatise on arithmetic from Normandy...................... 155
7 The ciphers from Wroclaw to Uppsala and Rome in the
3.1 The Paris (I) manuscript............................................................... 155
17th century........................................................................................... 237
4 Ciphers in astronomical and astrological tables................................... 160
8 The ciphers still in use for wine-gauging in Bruges in 1720 ............... 239
4.1 The Segovia manuscript............................................................... 160
8.1 The Bruges (II) manuscript........................................................... 239
5 Ciphers for marking volumes on wine-barrels..................................... 164
8.2 JanVaerman................................................................................. 241
5.1 The Damme manuscript................................................................ 165
9 The ciphers as used by Parisian Freemasons ca. 1780......................... 243
5.2 The Bruges (I) manuscript............................................................ 166
10 The ciphers and early optical telegraphy?............................................ 248
5.3 Wine-barrels marked with monastic ciphers?............................... 168
11 The ciphers in early-20th-century German fantasy............................. 251
6 Vertical ciphers used as letters of the alphabet.................................... 171
6.1 The Los Angeles manuscript........................................................ 172
6.2 The London Sloane manuscript.................................................... 173
6.3 An associated musical notation.................................................... 176
6.4 Some secret codes in the Papal Archives...................................... 177
10 Table of Contents Table of Contents 11
VII The ciphers falling between the cracks of modern scholarship and 3 The textual tradition....................................................... 396
emerging therefrom..................................................................................... 262 4 Jean Fusoris and his workshop............................................................. 397
1 The history of the ciphers in modem scholarship................................ 262 5 Three astronomical instruments related to the Picard astrolabe with
2 Conclusion............................................................................................. 271 ciphers................................................................................................... 398
L - The Picard astrolabe with monastic ciphers............................................... 406
Appendix A - General bibliographical notes.................................................... 275
1 The throne............................................................................................. 406
1 The Middle Ages................................................................................... 275
2 The design of the rete........................................................................... 406
2 Medieval manuscripts.......................................................................... 276
3 The stars on the rete............................................................................. 408
3 Science in the Middle Ages.................................................................. 276
4 The names of the zodiacal signs and the months................................. 410
4 Historical shorthands............................................................................ 278
5 The plates and the latitudes they serve................................................. 411
5 Studies of the ciphers........................................................................... 279
6 The calendrical scale............................................................................ 416
B - The survival of the Roman numerals in medieval Europe......................... 281 7 The shadow squares............................................................................. 416
8 Construction marks.............................................................................. 416
C - Ancient Greek and medieval alphanumerical notations............................ 290
9 The alidade, radial rule and nut and bolt.............................................. 419
1 Greek alphanumerical notation............................................................ 290
2 Islamic alphanumerical notation.......................................................... 295 M - The Virgin of Berselius.............................................................................. 420
3 The alphanumerical notation on the earliest known European
N - Non-historical reflections on the ciphers................................................... 427
astrolabe................................................................................................ 302
1 The ciphers as a viable number-notation.............................................. 427
4 Miscellaneous........................................................................................ 304
2 On the morphology and aesthetics of the ciphers................................. 428
5 A Cistercian alphanumerical notation.................................................. 305
3 Ciphers to bases other than 10.............................................................. 429
D - The introduction of the “Hindu-Arabic” numerals in Europe.................... 309 4 Arithmetic with ciphers........................................................................ 432
E - Sundry numeral notations and symbols in medieval and later sources..... 318
Manuscripts cited................................................................................................ 435
1 Potential numeral notations in Runic cryptography............................. 318
Astronomical instruments cited......................................................................... 438
2 ‘Calendrical numerals’......................................................................... 321
Bibliography and bibliographical abbreviations................................................ 442
3 Stone-masons’marks in the German-speaking world.......................... 324
Indexes................................................................................................................ 502
4 Numerical symbols for marking volumes on wine-barrels.................. 335
Index of topics............................................................................................. 502
5 Numerical notations used by millers in Flanders................................. 340
Index of modem authors............................................................................ 505
6 The numerical notation used by French foresters................................ 343
7 ‘Antler-numbers’from Austria for representing ages.......................... 343
8 The alphabetical and numeral systems of the Freemasons................... 344
9 Miscellaneous markings for weights and measures............................. 350
F - Aspects of medieval astronomy................................................................. 355
1 The basics.............................................................................................. 355
2 An advanced astronomical-astrological excursus................................ 357
G - The principle and use of the astrolabe....................................................... 359
H - On medieval European astronomical instruments..................................... 364
1 The rewards of cataloguing instruments.............................................. 364
2 Some early European astrolabes.......................................................... 369
J - The quatrefoil on medieval astrolabe retes................................................ 380
K - Astronomical instrumentation in Northern France in the 14th century.... 391
1 A 14th-century astrolabe for Paris....................................................... 391
2 Other astrolabes from Northern France................................................ 391
SUMMARY
This is the first comprehensive study of an ingenious number-notation from the
Middle Ages that was devised and mainly used by monks. The notation is not un­
known to the scholarly literature, but only recently have its historical context, as
well as its monastic connection and its ultimate origin been investigated. As a result
of the fact that the notation belongs as much to the history of monasticism as to the
history of mathematics, it has fallen between the cracks of modern scholarship and
is generally unknown to medievalists and historians of mathematics alike.
The notation appears in its first manifestation in early-13th-century England:
any number up to 99 can be represented by a single cipher. This simple notation is
somehow related to an ancient Greek shorthand-notation that was discovered on a
stone tablet on the Acropolis a century ago. These ciphers were brought from Ath­
ens to England by the monk John of Basingstoke (d. 1252) and were used by Cister­
cian monks in England in the second half of that century. A second, more useful
version is first attested in the late 13th century in what is today the border country
between Belgium and France: now any number up to 9999 can be represented by a
single cipher. This manifestation of the ciphers is due to Cistercian monks, who
were amongst the first to prepare indexes and concordances of books and whose
other activity in developing aids to scholarship is already well-known. The ciphers
were used in the Middle Ages in monastic scriptoria - for the foliation of manu­
scripts, for writing year-numbers, preparing indexes and concordances, numbering
sermons and the like, and outside the scriptoria - for marking the scales on an astro­
nomical instrument, writing year-numbers in astronomical tables, and for incising
volumes on wine-barrels. Related notations were used in medieval and Renaissance
shorthands and coded scripts.
This richly-illustrated book enables the reader to survey the medieval manu­
scripts and Renaissance books in which the ciphers occur, and to take a close look at
an intriguing medieval astrolabe marked with ciphers. The reader is offered occa­
sional excursions into the history of shorthand, magical recipes, musical notation,
masons’ marks, masonic alphabets, astronomy and astrology, religious art, and the
wine-trade. It becomes clear how several generations of scholars have sought in
vain to understand this notation and its origins, and how the ciphers - the third
numerical notation of medieval Europe after the Roman and Hindu-Arabic numer­
als - could remain for so long essentially forgotten.
PREFACE - INVITATION TO A JOURNEY THROUGH
THE MIDDLE AGES
“The attraction of the Middle Ages has been altogether less coherent
{than the pull of the ancient world on modern sensibilities}. It is more
like the lure of a fabulous island for visitors, all of whom are capable of
finding something to please their fancy and return with different ac­
counts of all they saw ... .To touch on the history of Europe for more
than a thousand years is still to rake over a storehouse of treasures in
the hope of a fabulous find. The idea of hidden secrets and wonderful
mysteries remains an inescapable part of what is expected of the Mid­
dle Ages.” D. Matthew, Atlas (1983), p. 15.
“To the modern mind the very concept of the Middle Ages implies a
state of transition or a cultural and historical interspace between the
demise of the Classical Age and its eventual rebirth or Renaissance. It
need hardly be said that the people of the Middle Ages did not see
themselves as a mere filling in a cultural sandwich. They both lived for
the day and built for eternity, though the imminent end of their world
was ever a matter of fear and foreboding.” M. Jenner, Medieval Eng­
land (1991), p. 15.
“A few histories of the middle ages mention mathematics, and a few
histories of mathematics mention the middle ages. But with rare and
distinguished exceptions these two streams of research start from points
too distant to fructify the common ground between them.” A. Murray,
Reason and Society in the Middle Ages (1978/91), p. 142.
“There is a sense in which it is fair to say that a historian is primarily a
manipulator of data. This is of course an incomplete and perhaps some­
what misleading description of the historian’s task, but it is not entirely
untrue. After all, his job consists mostly of gathering information from
other documents and sources, culling out the significant details, and
rearranging them in a meaningful pattern.” W. Van Egmond, “Com­
puter Catalog Descriptions of Scientific Manuscripts” (1990), p. 109.
“One of the perpetual delights, as well as one of the continual hazards,
of following wherever the books lead, is the fact that we are forever
being dropped without warning into new topics where we are total inno­
cents, and we must attempt to become Instant Experts............The re­
peated scramble to master a historical framework new to us is at the
same time exhilarating and terrifying.” M. A. and R. H. Rouse, Authen­
tic Witnesses (1991), p. 10. (Their sentiments are shared by this au­
thor!)
“Everything is more complicated than it looks.” Murphy (eternal).
As a specialist in the history of medieval Islamic science who has spent the past 30
years working on Islamic scientific manuscripts and astronomical instruments I feel
very much like a visitor to the European Middle Ages and early Renaissance. In my
account of a forgotten number-notation used by monks in the Middle Ages, I take
16 Preface Preface 17
the reader on a European journey from the 13th century to the 16th, with occasional ing from the 13th, 14th and 15th centuries. I should not like to be accused of claim­
excursions to the 4th century B.C. and to the 20th century A.D. The journey starts in ing that all monks, or even all Cistercians, used ciphers. Obviously only a very few
Athens, thence to England and Belgium but then all over Europe from Spain to did, in scattered locations and at different times.
Sweden. I offer a kind of guided tour of the available materials for the history of the Unfortunately for the reputation of the ciphers they were mislabelled in the ear­
ciphers, with optional excursions for the reader into realms into which I myself have ly 16th century as a result of contemporaneous misreadings of an encyclopaedia of
not ventured very far, but to which I at least offer some approaches through copious the occult sciences by Agrippa of Nettesheim, who had seen the ciphers in some
bibliographical references.1 astrological and magical manuscripts. He treated them in his text after numeral forms
This journey of mine through medieval and Renaissance history was made pos­ which he labelled “Chaldean”; thus, his readers simply labelled them “Chaldean”.
sible by generations of scholars of widely different national and academic back­ This label and Agrippa’s association of them with astrology and magic have persist­
grounds whose writings, mainly published in obscure books and journals, I have ed to the present day. My own appellation ‘ciphers’ has no medieval foundation
been able to consult. Some of these writings I have extracted in the form of direct whatsoever, but I can think of no better term.
quotes, intended to give the reader a feeling for the scope of previous investigations Although I have pursued various leads in the documented history of short-hand
and the insights of their authors, and in a very few cases, for the limitations of their scripts and their ancient predecessors, I cannot claim to have resolved the problems
authors.2 surrounding the origin of the numerical ciphers. It is clear that the simpler version of
The ciphers were originally developed as a viable alternative and supplement to the ciphers is of ancient Greek origin, although it is unknown to Classical Studies. I
the cumbersome Roman numerals, then only slowly being replaced in Europe by the can nevertheless indicate some of the parallels between the occurrence of runes in
Hindu-Arabic numerals.3 Numerals perform two functions: one representational (to early medieval manuscripts and ciphers in later medieval manuscripts. These paral­
look at) and the other operational (to compute with). Roman numerals are represen­ lels actually continue through the age of printing into modern scholarship (and fan­
tational; one can compute with them, but the process is tedious. The new alternative, tasy).
ciphers, was likewise representational; no-one appears to have tried to compute with The state of documentation of medieval European manuscripts leaves much to
them (no-one, that is, before myself). But, as we shall see, as used in the 13th, 14th be desired. Some catalogues devote but a line or two to each manuscript, so that, for
and 15th century mainly by Cistercian monks and scribes, the ciphers had several example, pagination in an unusual notation would not be mentioned. Other cata­
advantages. They are attested in only about two dozen manuscripts. This is a minus­ logues devote several pages to each manuscript, usually more to the text(s) it con­
cule fraction of the hundreds of thousands of Latin and vernacular manuscripts surviv­ tains (and especially to the miniatures) than to the manuscript itself. Catalogues
detailed enough that, for example, even such unusual features as marginalia fea­
turing ciphers are mentioned, are few indeed. These, though, are the catalogues which
1 For the reader who is unfamiliar with the basic literature on the Middle Ages I have included
can bring the manuscripts back to life. There may well be dozens of inadequately-
some bibliographical notes in Appendix A.
2 Thus, for example, E. H. Antonsen, “15th Rune” (1980), p. 1: catalogued manuscripts gathering dust in libraries all over Europe that could con­
“Every now and then it is useful to review the history of a discipline in order to gain insight tribute to our topic. I have thought it worthwhile to illustrate as many of the sources
into the origin of opinions prevailing in it. In doing so, one sometimes finds that extraneous as possible, not least because the vast majority has not been published previously by
factors played a significant role in the development of theories which have come to be anyone else but also because any description of a manuscript without an illustration
accepted as dogma and have been passed down unquestioned from generation to generation
will be deficient (there is, in fact, no substitute for actually examining the manu­
in the firm belief that these theories are grounded solely on ‘scientific’ considerations. A
script). In so doing I provide medievalists with a new corpus of paleographic mate­
case in point is provided by the history of views concerning the phonological value of the
rial.
15th rune in the Germanic fuj)ark, the so-called algiz-rune, Y.”
3 On the history of numeral forms some of the standard works are: Menninger, Zahlwort und A study of the manuscripts featuring ciphers at the level of R. Derolez’ investi­
Ziffer, Hartner, Zahlensysteme; Willers, Zahlzeicherv, Ifrah, Histoire universelle des chiffres; gation of the medieval manuscripts featuring runes (1954) would still be worth­
and also the pertinent comments in Neugebauer, The Exact Sciences in Antiquity, pp. 3-28. while.4 Yet the study of the earliest European manuscripts featuring Arabic nume-
There are numerous histories of number-systems for the general reader - for example, Loffler,
Ziffern und Ziffersysteme - none, however, in English, except for the translation Ifrah, Univer­
4 R. Derolez, Runica manuscripta, described his research procedures as follows (pp. lviii-lix):
sal History of Numbers. A curious publication, beautifully illustrated and with a text not with­
“For collecting this material I had three sources: (a) The older literature on the subject.
out merit, but alas not readily available, is Peignot & Adamoff, Chiffre\ this work also deals
Most items discussed here have been edited in one form or other before. Not all these
with the development of the alphabet and the use of numbers and letters in society. It was
editions have come to runologists’ notice in due time; they are scattered in older works and
published by Credit Lyonnais - if only we could get a French bank interested in medieval
periodicals, some of which are quite hard to reach ... .(b) Library catalogues enabled me to
French astrolabes or medieval French ciphers! Number symbolism in the Middle Ages, inevi­
unearth several new items, but on the whole the results of this rather tedious search were
tably only in the religious context, is the subject of Meyer & Surtrup, Lexikon derma. Zahlen-
out of proportion with the labour involved in it. ... In many cases librarians and authors of
bedeutungen. There is no survey of early printed works on historical number-systems. I have
catalogues are not to blame for having overlooked runes in their manuscripts. Runic items
included some surveys of various numeral notations in Appendixes B-E.
may be scribbled on pages which were originally left blank, in the margins, on fly-leaves