The Ciphers of the Monks –
A forgotten number notation of the Middle Ages
Stuttgart: Steiner, 2001
This book contains the first history of a remarkable number-notation from the Middle Ages that is unknown to most specialists in both Medieval Studies and the History of Mathematics.
The basic forms involve nine appendages to a vertical stem for the units, tens, hundreds and thousands. These are then combined on a single stem to form a cipher representing any number up to 9999:~
This ‘forgotten’ number-notation was developed in the late 13th century by Cistercian monks in what is now the border region between France and Belgium (particularly Aulne-sur-Sambre in the diocese of Liège and Vaucelles in the diocese of Cambrai). It was used by the Cistercians – admittedly by only a few but nevertheless all over Europe – for at least two centuries thereafter, as an alternative to the well-known Roman numerals and the less-well-known, ‘new’ Hindu-Arabic numerals (whose introduction into Europe took five centuries). The monks used it for numbering pages of manuscripts and items in lists, for writing for representing year-numbers in dates, and for numbering staves of music. The two dozen surviving manuscripts featuring ciphers are from localities between England and Normandy to Italy and between Spain and Sweden.
This numerical notation was also used outside the scriptoria of the monasteries, for we find it used on a remarkable medieval astronomical instrument – an astrolabe, that is, a two-dimensional model of the universe that one can hold in one’s hands – made in Picardy in the 14th century, in a treatise on arithmetic from Normandy ca. 1400, and in some astronomical tables compiled in Salamanca in the late 15th century. In Flanders from the 15th to the 18th century wine-gaugers used this notation for marking volumes on wine-barrels and divisions on the scales of their gauging-rods.
The Cistercian monks developed this notation from a simpler one in which any number up to 99 is represented by a single cipher. This simpler notation was brought by the monk John of Basingstoke to England from Athens in the early 13th century, and owes its inspiration to an ancient Greek shorthand, described in an inscription on a stone discovered in the late 19th century on the Acropolis.
The monastic ciphers in both their manifestations – numerical and alphabetical – were influential in the development of Renaissance shorthands and secret codes. From the 16th to the 19th century they were featured in various works on numerical notations. They were adopted by the Freemasons in Paris in 1780 and they are featured in 20th-century nationalistic writings on German folklore. However, it was not before the reappearance of the astrolabe with ciphers at Christie’s of London in 1991 that any attempt was made to ascertain their origin, to investigate the way in which they were used in the Middle Ages, and to document their eventual demise as a result of the difficulties associated with printing them.
Table of contents:~
I Introduction
1 The ciphers – some historiographical considerations
2 The main varieties of ciphers
3 The need for a new number-notation
II The English ciphers
1 Introduction
2 The ciphers of John of Basingstoke
2.1 The Cambridge manuscript
3 On the Greek origin of the Basingstoke ciphers
3.1 A Greek shorthand from the 4th century B.C. as attested on a tablet found on the Acropolis
3.2 The Tironian notes
3.3 Are the Basingstoke ciphers really of Greek origin?
3.4 The Basingstoke ciphers and the runes
4 The ciphers as letters of the alphabet – the late-12th-century English ars notaria
5 Ciphers similar to the Basingstoke ciphers in medieval Arabic treatises
6 The Basingstoke ciphers at the hands of the Cistercians
6.1 The Lambeth manuscript
III The horizontal ciphers of the Cistercians
1 Introduction
1.1 The Cistercians
2 Two types of Cistercian ciphers
3 The Cistercian ciphers as used in early manuscripts of mainly religious content
3.1 The Brussels manuscript
3.2 The Laon manuscript
3.3 The Oxford Lyell manuscript
3.4 The Lüneburg manuscript
3.5 The Uppsala manuscript
3.6 The Basle manuscript
3.7 The Turin manuscript
4 Ciphers in musical notation
4.1 The Turin manuscript again
5 The horizontal ciphers in marginalia
5.1 The Wolfenbüttel manuscript
5.2 A manuscript formerly belonging to W. W. Greg
5.3 The Erfurt manuscript
5.4 The Munich (I) manuscript
6 Ciphers featured in marginalia in manuscripts of non-religious content
6.1 The Göttingen manuscript
7 The horizontal ciphers developed into an alphabetic code
7.1 The Munich (II) manuscript
8 An anomalous set of ciphers
8.1 The Lyons manuscript
9 Two other sets of basic ciphers in manuscripts of scientific content
9.1 The Munich (III) manuscript
9.2 The Oxford Tanner manuscript
IV The astrolabe of Berselius
1 Introduction
2 A medieval astrolabe engraved with monastic ciphers
3 The Picard connection
3.1 The names of the months on the astrolabe
3.2 Medieval Picardy and its dialect
3.3 Who made the Picard astrolabe?
4 Paschasius Berselius, the donor in 1522, and Hadrianus Amerotius, the recipient
4.1 The dedication on the astrolabe
4.2 Paschasius Berselius
4.3 Hadrianus Amerotius
4.4 Some remaining questions
V The French vertical ciphers in manuscript sources
1 Introduction
2 The vertical ciphers at the University of Paris
2.1 The Vatican manuscript
3 The ciphers in a treatise on arithmetic from Normandy
3.1 The Paris (I) manuscript
4 Ciphers in astronomical and astrological tables
4.1 The Segovia manuscript
5 Ciphers for marking volumes on wine-barrels
5.1 The Damme manuscript
5.2 The Bruges (I) manuscript
5.3 Wine-barrels marked with monastic ciphers?
6 Vertical ciphers used as letters of the alphabet
6.1 The Los Angeles manuscript
6.2 The London Sloane manuscript
6.3 An associated musical notation
7 The ciphers as letters of the alphabet in two magical texts
7.1 The Uppsala manuscript again
7.2 The Heidelberg manuscript
8 The doodles of a monk – different representations of the Cross by means of ciphers
8.1 The Paris (III) manuscript
9 The early evidence on ciphers reviewed
9.1 How many manuscripts originally featured ciphers?
VI The fate of the monastic ciphers in the Renaissance and thereafter
1 Introductory remarks
2 The ciphers as presented by Agrippa of Nettesheim
2.1 The Chaldean connection
2.2 The manuscript from The Hague
2.3 Francis Barrett and Agrippa’s ciphers
3 The ciphers in the French translation of Trithemius’ Polygraphiæ
4 The ciphers as developed by Cardano
5 The ciphers in other early printed works on the history of numerical notations
5.1 Johannes Noviomagus
5.2 The Dutch treatise Die maniere
5.3 Matthæus Hostus
5.4 Georg Henisch
5.4 Valerianus Bolzanius
5.5 Alphonse Costadau
5.6 Johann Christoph Heilbronner et al.
6 Some shorthand scripts and codes from the early Renaissance based on the ciphers
6.1 Timothy Bright
6.2 Daniel Schwenter
6.3 Johannes Baptista Porta
6.4 John Wilkins
6.5 William Oughtred
7 The ciphers from Wroclaw to Uppsala and Rome in the 17th century
8 The ciphers still in use for wine-gauging in Bruges in 1720
8.1 The Bruges (II) manuscript
8.2 Jan Vaerman
9 The ciphers as used by Parisian Freemasons ca. 1780
10 The ciphers and early optical telegraphy?
11 The ciphers in early-20th-century German fantasy
VII The ciphers falling between the cracks of modern scholarship and emerging therefrom
1 The history of the ciphers in modern scholarship
2 Conclusion
Appendix A: General bibliographical notes
1 The Middle Ages
2 Medieval manuscripts
3 Science in the Middle Ages
4 Historical shorthands
5 Studies of the ciphers
Appendix B: The survival of the Roman numerals in medieval Europe
Appendix C: Ancient Greek and medieval alphanumerical notations
1 Greek alphanumerical notation
2 Islamic alphanumerical notation
3 The alphanumerical notation on the earliest known European astrolabe
4 Miscellaneous
5 A Cistercian alphanumerical notation
Appendix D: The introduction of the “Hindu-Arabic” numerals in Europe
Appendix E: Unusual numeral forms and symbols in medieval and later sources
1 Potential numeral systems in Runic cryptography
2 ‘Calendrical numerals’
3 Stone-masons’ marks in the German-speaking world
4 Numerical symbols for marking volumes on wine-barrels
5 Numerical notations used by millers in Flanders
6 The numerical notation used by French foresters
7 ‘Antler-numbers’ for counting ages
8 The alphabetical and numeral systems of the Freemasons
Appendix F: Aspects of medieval astronomy
1 The basics
2 An astronomical-astrological excursus
Appendix G: The principle and use of the astrolabe
Appendix H: On medieval European astronomical instruments
1 The delights of cataloguing
2 Some early European astrolabes
Appendix J: The quatrefoil on medieval astrolabe retes
Appendix K: Astronomical instrumentation in Northern France in the 14th century
1 A 14th-century astrolabe for Paris
2 Other astrolabes from Northern France
3 The textual tradition
4 Jean Fusoris and his workshop
5 Three astronomical instruments related to the Picard astrolabe with ciphers
Appendix L: The Picard astrolabe with monastic ciphers
1 The throne
2 The design of the rete
3 The stars on the rete
4 The names of the zodiacal signs and the months
5 The plates and the latitudes they serve
6 The calendrical scale
7 The shadow squares
8 Construction marks
9 The alidade, radial rule and nut and bolt
Appendix M: The Virgin of Berselius
Appendix N: Non-historical reflections on the ciphers
1 The ciphers as a viable number-notation
2 On the morphology and aesthetics of the ciphers
3 Ciphers to bases other than 10
4 Arithmetic with ciphers
Manuscripts cited
Astronomical instruments cited
Bibliography and bibliographical abbreviations
Acknowledgments