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ABSTRACT
Slates from the Visigothic era that have appeared in certain areas of the Iberian Peninsula have aroused considerable academic interest. One of the liveliest and still open debates concerns the significance of a series of signs engraved on these slates. Their identification with the Roman numbering system is currently the most widely accepted hypothesis, to the extent that it has become more or less taken for granted and has shaped theories about the function and dating of numeral slates. The present study questions the validity of this premise by undertaking a comparative diachronic analysis of the signs I, X, and V on the slates relative to those used in Roman numbering. I propose a new reading of these signs as not straightforwardly Roman, but rather as the result of local innovations relating to the cultural and economic needs of the communities in which this numerical system is present.
Disclosure statement
No potential conflict of interest was reported by the authors.
Acknowledgements
I am extremely grateful to my supervisor Santiago Castellanos García and to Antonella Liuzzo Scorpo for reading the original manuscript and improving it with their advice. The feedback I was given by the anonymous reviewers was also highly useful, and I offer particular thanks to Stephen Chrisomalis, who asked that his name be revealed to me after my article had been accepted for publication. I also appreciate the suggestions that I received during my PhD research from Isabel Velázquez Soriano, Pablo de la Cruz Díaz Martinez, Iñaki Martín Viso, Jamie Wood, Andrew Elliot, Graham Barret, Robert Portass, and David Natal Villazala. Finally, I would like to thank the staff of the Salamanca Provincial Museum, especially Alberto Bescós Corral, Sonsoles Grande Tomé, and Rosario Pérez Martín for all their support during research of some of the Visigothic slates that appear in this study.
Notes on Contributor
Nerea Fernández Cadenas is a PhD student at the University of León in Spain. Having obtained an honours degree, she is currently working on a doctoral thesis on the topic of numerical and illustrated slates and their possible relationship to rural contexts in the Visigothic period. Her research is funded by a national fellowship from the Spanish Ministry of Education and Vocational Training. She has undertaken research stays at the University of Lincoln in the United Kingdom and University of Salamanca in Spain. Among the prizes she has won is the 2020 Simon Barton Conference Prize of the Society for the Medieval Mediterranean.
Notes
*This work was supported by the Spanish Ministry of Education, Culture and Sport during my predoctoral fellowship FPU 16/06932, and by the Spanish Ministry of the Economy and Competitiveness within the project “Local Spaces and Social Complexity. The Medieval Roots of a 21st-Century Problem” (PI Santiago Castellanos García, HAR2016-76094-C4-1-R).
1 A good overview of the places where number slates have appeared is provided by Martín Viso, who also subdivides these deposits into hill forts (or castella), urban contexts, production centres, villas and peasant villages: Martín Viso, “Huellas del poder,” and Martín Viso, “The ‘Visigothic’ Slates.”
2 Velázquez Soriano, Las pizarras visigodas: edición crítica, 70.
3 Velázquez Soriano, Las pizarras visigodas: edición crítica, 73–74, documents twelve slates with references to the reigns of named kings: numbers 8, 39, 41, 121, and 128 mention Reccared; number 9 alludes to the reigns of Recceswinth and Chindaswinth; number 43 mentions Recceswinth; numbers 18 and 92 speak of Chindaswinth; on number 19 it is possible to make out “Sise,” so it may refer either to Sisebut or Sisenand; number 26 names Egica; and on number 44 Wamba can be read.
4 At the San Pelayo site a numerical slate was documented in a tip that seems to have been abandoned in the fifth century, giving a late Roman date limit for the item: Dahí Elena, “Un contexto cerámico.”
5 Martín Viso, “The ‘Visigothic’ Slates,” 17.
6 Balañà i Abadía, “Eduardo Saavedra Moragas,” 447.
7 Paredes Guillén, Origen del nombre, 82–83.
8 Gómez-Moreno and García Blanco, “El Unamuno de 1901 a 1903,” 30.
9 Hübner, Monumenta Linguae, 207, included this particular slate in the section of falsae vel suspectae, in other words among the false or dubious entries, which suggests that the characteristics of the signs made him doubt whether they could be unequivocally identified with the Iberian language.
10 Ballesteros, Estudio histórico de Ávila, 48.
11 The variety of the signs and their limited frequency of repetition led to the conclusion that this was an alphabet: Morán Bardón, Investigaciones, Plate XVI. Concerning Bars, Morán Bardón, 113, states only that he had a considerable acquaintance with ancient languages without offering further details.
12 Cabré Aguiló, “Ídolo de Ciudad Rodrigo,” 163.
13 Gómez-Moreno, Discursos, 17.
14 Morán Bardón, “Pizarra de Salamanca,” 263. It is striking that no reference is made to the number hypothesis previously put forward by Paredes Guillén, Unamuno, or Gómez-Moreno: Paredes Guillén, Origen del nombre, 82–83; Gómez-Moreno and García Blanco, “El Unamuno de 1901-1903,” 30–31; Gómez-Moreno, Discursos, 17. It appears that Morán Bardón was not aware of this work and came to the same conclusion independently.
15 Morán Bardón, “Pizarra de Salamanca,” 262.
16 Morán Bardón, “Pizarra de Salamanca,” 261.
17 Morán Bardón, Reseña histórico-artística, 61.
18 Gómez-Moreno, Documentación goda en pizarra, 27. The same opinion was later also held by Isabel Velázquez, Las pizarras visigodas: edición crítica, 32.
19 Gómez-Moreno, Documentación goda en pizarra, 27. This means that no combinations duplicating V are found, such as VV. However, the opposite is true for the other signs, for instance XX or IIII. Indeed, some examples have recently been found in which the upright line unit is repeated more than four times: Jiménez Pardo and Gabaldón Martínez, “Tres nuevas pizarras,” 452–53.
20 Gómez-Moreno, Documentación goda en pizarra, 27.
21 Velázquez Soriano, Las pizarras visigodas, 291-92, described the existence of carbon copies (“calcos de pizarras numéricas”) of original slates, in which signs were written in reverse, such as , combinations that are in many cases impossible because it would be acceptable to have a sequence like IV but not IIIV, yet this was how the text ran. To solve this question, she proposed two possibilities: either a mould was employed to make the copy of the slates, or these slates were written from right to left. My research, however, has uncovered original numerical slates, not copies, that show combinations such as those mentioned by Velázquez Soriano. These include Museo Provincial de Salamanca, 1983/2/492; Universidad de Salamanca, 2019/USAL/13 (see Figure 6a) and 2019/USAL/15. Whereas in the rest of the numerical slates analysed the signs that are covered by a horizontal line are always ordered from highest to lowest value, these examples show such combinations as “IXV” (see Figure 6a). I would argue that, rather than using a mould, these are the result of writing from right to left on some slates.
22 Díaz y Díaz, “Sobre la posible data,” 236.
23 This O symbol had already been commented on by Gómez-Moreno, Documentación goda en pizarra, 27, who argued that it was a deformation of a V when this was inscribed on the slate. The same view was initially held by Velázquez Soriano, Las pizarras visigodas: edición crítica, 33. However, she later stated that on a very few pieces on which the total of the figures is not identical, a clear V sign and a circular O shape can be found on the same slate and even in the same line: Velázquez Soriano, Las pizarras visigodas, 291. The question, as she saw it, was whether this O sign should be interpreted as having the same value as V or something completely different.
24 Díaz y Díaz, “Sobre la posible data,” 237.
25 Her PhD thesis, “El latín de las pizarras visigóticas (edición y estudio),” had been defended the previous year at the Universidad Complutense de Madrid.
26 Velázquez Soriano, Las pizarras visigodas, 33.
27 Díaz Martínez and Martín Viso, “Una contabilidad esquiva,” 237.
28 This idea was first put forward in Arce, Castellanos, Escalona Monge, Martín Viso, and Velázquez Soriano, “Las pizarras visigodas,” 145. Slates found in numbers in hill settlements are interpreted as an indication of the existence of taxes controlled and managed by the elite. Number slates recorded in villas, on the other hand, are seen as related to payments, whether tithes or other tributes made by serfs to the dominus of the villa: see Martín Viso, “The ‘Visigothic’ Slates,” 149.
29 Díaz Martínez and Martín Viso, “Una contabilidad esquiva,” 228. The hypothesis that the use of this system required a combination of arithmetical knowledge and writing abilities was defended once again in 2012 by Cordero Ruíz and Martín Viso, “Sobre los usos,” 260–61, and by Martín Viso, “The ‘Vigothic’ Slates,” 162–63.
30 The majority of these slates are held by the Museo Provincial de Salamanca and classified in the folowing documents: 1952/1 (Morán collection); 1983/2 (Cortinal de San Juan); 1983/12, 1984/23, and 1990/14 (Cuarto de las Hoyas); 1983/10 (El Hornacino); 1990/14 (Galindo y Perahuy); 1990/17 (Huerta); 1996/6 (Cinco Villas); 1999/2 (Martín Pérez); 1999/6 (El Cenizal); 1999/8 (Casaretones); 2006/7 and 2008/60 (Monte EL Alcaide); 20026/9, 2007/19; 2008/48 and 2019/7 (La Legoriza); 2013/3 (La Genestosa). The collection of numerical slates at the University of Salamanca (2019/ Usal) has been analysed.
31 Such an approach had already been hinted at by Urbina Álvarez, who stated that the meaning of these figures and their use in late Antiquity might better be sought outside a purely accounting context or a single region: Urbina Álvarez, “Hallazgo de dos pizarras,” 144.
32 The different types of writing surfaces include ordinary ones that were created with the purpose of receiving writing, such as papyrus, parchment, or paper; and extraordinary ones which were not originally intended for writing, such as wood and slate.
33 This discipline investigates the manner in which the brain processes information, taking into account features such as perception, concept formation, learning, and memory: Chrisomalis, Numerical Notation, 14.
34 An exception concerns those above which a horizontal line is drawn, as discussed below.
35 Chrisomalis, Numerical Notation, 111.
36 Regarding the absence of subtraction-based values, according to Velázquez Soriano, Las pizarras visigodas, 291, it was something to be expected during the period in question. For example, the Puteanus, which is a manuscript dated in the fifth century, shows examples in which forty was written without subtraction: Shipley, “Numeral Corruptions,” 51. Despite exceptions like this, the use of subtraction is common from the Roman Republic onwards, and so the lack of this technique in the number slates is still intriguing.
37 The oldest archaeological context where a numerical slate was found was a rubbish tip dating between the last quarter of the fourth century and the first half of the fifth: Dahí Elena, “Un contexto cerámico.” 93. On the chronology of numerical slates and their archaeological contexts, see Cordero Ruíz and Martín Viso, “Sobre los usos,” 262–63.
38 Chrisomalis, Numerical Notation, 109.
39 Museo Provincial de Salamanca, nos. 1983/2/468, 1983/2/474, and 2005/14/LE201/BU.
40 For instance, Velázquez, Las pizarras visigodas, 32, states that it is understandable that in general the only numerals found are I, V, and X, if it is kept in mind that quantities were being noted down progressively, two at a time, fifteen at a time, and so forth. In her view, the purpose of these annotations, whatever it may have been, did not lead to, or record, sets of fifty for example, which would have been expressed using L.
41 The slate with a “C” was found at El Cortinal de San Juan in Salamanca Province and has the accession number 1982/2/596. The origin of the slate with an “M” is unknown, because it was found among the holdings of the University of Salamanca as part of a batch of 16 slate fragments. It was given the accession number: 2019/USAL/13.
42 While it is true that there are some Roman inscriptions with the symbol “M,” according to Chrisomalis, Numerical Notation, 111, this sign is not so much a numeral as an abbreviation of the word mille.
43 Museo Provincial de Salamanca, nos. 1983/2/460; 1983/2/466; 1983/2/500; 1983/2/521; 1983/2/592; 1983/2/716; 1983/2/718; 1996/6/5; 2006/7/473; 2006/7/468; 2006/9/ST27/212; 2019/USAL/14.
44 See above note 21. Museo Provincial de Salamanca, no. 1983/2/492; Universidad de Salamanca, nos. 2019/USAL/13 (see Figure 6a); 2019/USAL/15.
45 Chrisomalis, Numerical Notation, 111.
46 Museo Provincial de Salamanca, nos. 1983/2/453; 1983/2/526; 1983/2/545; 2006/7/449; 2006/7/456.
47 There are some exceptions to this rule: for example, graffiti in Pompeii show combinations of more than four identical “I” or “X" signs, such as XXXXX or IIIIIII. These graffiti are written in charcoal on the walls of the Taverna vasaria (Della Corte, “Pompei,” 98 –99), in some houses like the home of Maius Castricius (Benefield, “Ancient Graffiti in Pompei,” 81–85), and in the house of the Four Styles (Benefield, “Dialogues of Ancient Graffiti,” 37–38). This exception is a function of combinations like “IIIIIIIIII” to keep a running count, for example, of the number of visitors or clients coming to the house: Benefield, “Dialogues of Ancient Graffiti,” 37. However, when the numbers “I”, “V,” and “X” are mixed in the same combinations they show substraction and are ordered in greater to lesser value. For example, we can see the following combination “XXXXIVI” (Della Corte, “Pompei,” 99), but never VXIXXIX as on the Visigothic slates. That is, the Pompeii graffiti are still following the basic rules of standard Roman numeration, but it seems to be different because of their application to daily needs.
48 Gómez-Moreno, Documentación goda, 15; Martín Viso, “The ‘Visigothic’ Slates,” 15.
49 Albertini, “Documents époque vandale,” 301–03.
50 Martín Viso, “The ‘Visigothic’ Slates,” 19, held that “this is the same system that is documented on the Iberian numerical slates. The accounting system of the slates thus seems to have been common in the late antique Western Mediterranean, to be connected with literate social analysis.”
51 Courtois et al., Tablettes Albertini, 12–14.
52 Some of these documents show the specific date of the transaction: the oldest is dated 489 and the most recent is dated 496, which coincide with the reign of the Vandal king Ghuntamund (484–496): Courtois et al., Tablettes Albertini, 11–15.
53 Albertini, “Actes de vente du Ve siècle,” 23.
54 Albertini, “Actes de vente du Ve siècle,” 23.
55 Courtois et al., Tablettes Albertini, 10.
56 Triptychs IV, V, and XVIII: Courtois et al., Tablettes Albertini, 9 .
57 Courtois et al., Tablettes Albertini, 10.
58 Courtois et al., Tablettes Albertini, 9.
59 To my mind, it seems more plausible that the accounting antedates the act of sale because thirteen documents related to the sale of parcels, such as the one that appears in this triptych, have been located (Courtois et al., Tablettes Albertini, 9). This suggests that there was an intention to save and conserve them. It would seem to indicate that the accounting was done prior to 496, the date of the sale on the triptych. However, this hypothesis cannot be verified, since the tablets were not found in a scientific excavation but by members of the tribe of Sidi-Asid, who used similar writing tools to those used on the wooden tablets, as Carcorpino, “Les Tablettes Albertini,” 148, has already observed. These were a reed quill and an ink made of burnt wool and dried carob.
60 There is another material difference: the signs on the slates are engraved with a stylus whereas the Albertini tablet is written with a quill and ink.
61 This is the position sustained by Martín Viso, “The ‘Visigothic’ Slates,” 19.
62 Židov, Tally Sticks, 96.
63 The British Exchequer tallies from the thirteenth century are an example of tally sticks that became an official government record: Menninger, Number Words, 236–40. Another much older example are the split tally sticks of the Achaemenid Bactrian Empire from the fourteenth–thirteenth century BCE, for which Henkelman and Folmer, “Wooden Credit Records,” 177, propose an institutional character because of the unity of their format, related to some kind of credit situation.
64 Examples have been found dating from the seventeenth through the twentieth century. It is probable that they existed long before, but were not preserved because they were made of perishable materials: Židov, Tally Sticks, 91. With regard to their geographical distribution, tally sticks have been documented in a number of regions throughout Europe, such as Switzerland, Italy, Germany, and Romania, but also in America: Židov, Tally Sticks, 93–95.
65 Menninger, Number Words, 240.
66 Menninger, Number Words, 240.
67 Menninger, Number Words, 241: “Now let us ask the same question the other way around: Are the Roman numerals, at least I, V, and X, actually forms of notches cut into tally sticks? I believe that further facts will confirm that this is so, apart from mere similarity of form and the fact that such notches are very easy to carve.”
68 Židov, Tally Sticks, 100.
69 Židov, Tally Sticks, 49.
70 Menninger, Number Words, 235.
71 Ninni, Sui segni prealfabetici, 11.
72 Židov, Tally Sticks, 135. The surviving tallies are from the nineteenth century; Židov suggests that they may well have been used from the Middle Ages onward but that they have not been preserved due to the perishable nature of wood.
73 Židov, Tally Sticks, 102, 170.
74 Ifrah, Historia Universal, 176.
75 Škarpa, “Raboš u Dalmaciji,” 174.
76 Ifrah, Historia Universal, 476, argued that, independently of place, the creative imagination of graphic symbols is limited by the same cultural conditions. As discussed below, these universal conditions are the limited capacity for subitizing, preventing more than four units from being counted at a single glance; the shape of the hand; and the hardness of some writing surfaces.
77 According to Chrisomalis, Numerical Notation, 436, this principle may be defined as “the association of a collection of discrete set of identical marks with a set of objects of the same quantity.”
78 Ifrah, Historia Universal, 476.
79 The practice of notching bones is recorded from the Aurignacian era (43,000-26,000 BCE) onward: Ifrah, Historia Universal, 169.
80 Chrisomalis, Numerical Notation, 15.
81 The term makes reference to the Latin past participle subitus, in the sense of “sudden:” Kaufman et al., “Discrimination of Visual Number,” 520.
82 One of the first experiments on numbers cognition took place in 1886. James McKeen Cattell carried out a trial with nine people who had to describe a set of letters, pictures, or colours. The time needed for a correct response grew considerably once there were more than four units involved: Cattel, “The Time It Takes,” 64. In 1945 psychological researchers at Mount Holyoke College in Massachusetts came to the same conclusion as Cattell. Essentially, the human ability to perceive immediately the value of signs in a series begins to fall off sharply as more than four elements emerge. To establish the total when quantities are greater than four it is necessary to count: Kaufman et al., “Discrimination of Visual Number,” 520.
83 Mandler and Sebo, “Subitizing,” 5.
84 Having in common the division of a series into group of three to five elements; Chrisomalis, Numerical Notation, 368, called this regularity the Rule of Four.
85 Chrisomalis, Numerical Notation, 93–132.
86 Overmann, “Numerosity Structures,” 645, explains the concept of discretization as “an emergent property of the interaction of numerosity with material structures (both the physical body and cultural artefacts) … Material structures provide affordances such as tangibility and manipulability that help to scaffold quantities beyond the subitizing range by enabling their identification as distinct tactile and visual entities.”
87 Menninger, Number Words, 240.
88 According to Menninger, Number Words, 36, this is a natural grouping: “Whereas the custom of assigning number values to pebbles or to parts of the body yields only a continuous, undifferentiated supplementary quantity, the quantity derived from the fingers and toes is already classified and grouped by nature: 5 fingers mark a hand, 10 is represented by two hands, 20 by hands and feet.”
89 Keyser, “The Origin of Latin Numerals,” 535. This theory was at its height in the seventeenth and eighteenth centuries. It was also later put forward by Mommsen in his study of Italian dialects. For Mommsen, Die unteritalischen Dialekte, 19–20 and 33–34, the symbols I, X, and V were pre-alphabetic and had their origin in a pictographic system, whilst the remainder were derived from the Chalcidian alphabet.
90 Keyser, “The Origin of Latin Numerals,” 536.
91 Cushing, “Manual Concepts,” 294.
92 In experiments it was also noted that if the two hands were separated when indicating ten, the gesture was not understood. The hands had necessarily to be joined together. Cushing, “Manual Concepts,” 313.
93 Cushing, “Manual Concepts,” 296.
94 Henkelman and Folmer, “Wooden Credit Records,” 177.
95 Menninger, Number Words, 249. Other researchers, like Ifrah, Historia Universal, 173, define this system as the book-keeping of the illiterate.
96 Martín Viso, “Huellas del poder,” 290.
97 Martín Viso, “Tributación y escenarios locales,” 287–88; Díaz Martínez and Martín Viso, “Una contabilidad esquiva,” 236–38; Martín Viso, “Pizarras numerales de época posromana,” 1.
98 Fernández Cadenas, “Pizarras numerales en contexto,” 37.
99 As is the case of the archaeological sites of La Legoriza and Monte El Alcaide: Fernández Cadenas, “Pizarras numerales en contexto,” 37.