Medieval Europe’s satanic ciphers: on the genesis of a modern myth

Abstract

The purpose of this article is to investigate the genesis and growth of a historical canard that can be encountered in numerous popular as well as some scholarly publications devoted to the history of mathematics. According to one of the core elements of this story, the number or symbol for zero was the cause of much anxiety in medieval Europe, as its unusual properties caused it to be associated with the Devil or with black magic. This anxiety is supposed to have extended to the entire system of Hindu-Arabic numerals, such that the use of these numerals was banned by the Church or by other powerful institutions. I shall argue that this narrative is false or unsubstantiated at nearly every level of analysis. Some elements arose from an unwarranted interpretation of medieval sources, while others are based on the unbridled imagination of certain modern authors.

Acknowledgements

I should like to thank Joshua Bennett, Charles Burnett, and David Juste for offering helpful comments and advice.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Notes

1 Pernoud 1977; Harris and Grigsby 2008; Weill-Parot and Sales 2017. See also the relevant chapters in Numbers 2009.

2 This sort of reconstructive work has been carried out with particular thoroughness for the myth of medieval belief in a flat Earth. See, for example, Russell 1991; Wolf 2004; Reinhardt 2007; Roland 2013. See also Classen 2007, for the myth of the medieval chastity belt.

3 Wallin’s article is based on the books by Kaplan (1999) and Seife (2000), which will be discussed in section 3.3 of this article.

4 For general orientation, see Lemay 1977; 1982; Allard 1990; Folkerts 2001a; Berggren 2002; Kunitzsch 2005; Burnett 2006; Ambrosetti 2008; Schärlig 2010; Wedell 2015; Folkerts and Hughes 2016, and the articles assembled in Burnett 2010.

5 See MS El Escorial, Real Bibliotheca de San Lorenzo, d.I.2, fol. 12^v. The numerals on this page were copied into MS El Escorial, Real Biblioteca de San Lorenzo, d.I.1, fol. 9^v (from San Millán de la Cogolla), which dates from 994. For transcriptions and facsimiles, see Smith and Karpinski (1911, 138) and Burnam (1912–25, 89–96). On the dating of these codices, see Gómez Pallarès (1987, 29–32).

6 MS El Escorial, Real Bibliotheca de San Lorenzo, d.I.2, fol. 12^v, ‘Scire debemus in Indos subtilissimum ingenium habere et ceteras gentes eis in arithmetica et geometrica et ceteris liberalibus disciplinis concedere’. I here follow the translation in Burnett (2006, 17).

7 On the Gerbertian abacus, see Beaujouan 1948; 1996; Evans 1977a; 1979; Gibson and Newton 1995; Folkerts 1996; 2000; 2001b; Burnett 2002c; Otisk 2015.

8 The evidence is discussed by Burnett (1996, 228–229; 2002c, 106–107; 2003, 94; 2006, 25–27) and Folkerts (2000, 219–221).

9 The text was lasted edited by Folkerts (1997).

10 These three texts were last edited by Allard (1992). See also the overviews in Allard (1991) and Ambrosetti (2008, 197–212). For the so-called ‘second book’ of the Liber Alchorismi, see Burnett, Zhao and Lampe (2007).

11 See also Herreman 2001.

12 John of Sacrobosco’s work was last edited by Pedersen (1983, 174–201). See also Pedersen (1985, 182–183, 195–201). On the Carmen de algorismo, see Ambrosetti (2016), who counts 161 manuscripts. On the topic of thirteenth-century algorithmic writing, see also the texts edited and discussed in Busard (2000) and Burnett (2002b).

13 On the nomenclature of zero in early algorithms, see Lemay (1977, 451–453); Evans (1977b, 117); Allard (1990, 154); Burnett (1996, 236–237); Ambrosetti (2016, 80). On the relationship between cifra and words in various European vernaculars, see Tropfke (1921, 8–14).

14 See, for example, the Liber Algorismi (ed. Folkerts 1997, 32–34). For an unconvincing attempt to trace the circular sign for zero back to a ninth-century Carolingian origin, see Stevens (2013–14), whose account is replete with inaccuracies.

15 In Arabic manuscripts prior to 1200, the use of HAN is mostly limited to texts on arithmetic, whereas in astronomical sources the abjad system of notation was preferred. HAN are rarely encountered in texts of a non-scientific nature. See Lemay (1982, 383–384); Kunitzsch (2005, 9–14, 28).

16 See on this plurality Burnett (2000; 2006, 20–21, 28–29); Berggren (2002, 351–354); King (2001); Kunitzsch (2005, 24–27).

17 See the edition, translation, and discussion of this text by Burnett (1996).

18 Some early examples of this are provided by Burnett (2002a).

19 See Reinher of Paderborn, Compotus emendatus, praef. (ed. Lohr 2015, 3, ll. 20–22): ‘In designatione numerorum figuris plerumque utimur aliis quam Latinis propter scribendi et computandi compendium’.

20 See also the quote from this passage in Cunnington (1904, 42).

21 Article no. 102 (Quod nullus de arte scribat in suo libro per abbacum) was lasted edited in Camerani Marri (1955, 72–73). For the appearance of the same article in the revised statutes of 1300, 1313, and 1316, see the comparative table at the end of Camerani Marri (1955, not paginated). For the English translation cited here, see Struik (1968, 292). The passage is translated differently in Murray (1978, 170–171). See the discussion in Lüneburg (2008, 106–110), which offers a valuable criticism of some of the previous literature. On the interpretation of the phrase ‘openly and in full by way of letters’ (aperte et extense scribere per literam), see Nagl (1889, 162–167).

22 See, for example, Smith and Ginsburg (1937, 17); Neill Wright (1952, 126); Menninger (1969, 426–427); Tucci (1989, 556); Burton (2011, 280); King (2001, 315); Cherubini (2006, 332); Chrisomalis (2010, 123). According to Gazalé (2000, 48) the guild ‘ruled that the old figures could not be as easily falsified as the new ones, which could be turned into different figures without difficulty.’ It should be emphasized that no such comment appears in the source text.

23 According to Struik (1968, 292–293) the ordinance reflects a power struggle between merchant guilds in the context of the ongoing conflict between Guelphs and Ghibellines in Florence.

24 As already noticed by Crossley (2013, 92n42), who gives the example of Chrisomalis (2010, 123–124) citing Berggren (2002, 361), who cites Pullan (1968, 34). To give but two additional ones: Caianiello (2014, 229n61) cites Cherubini (2006, 331–332n55), who cites Tabarroni (1983, 148n5) citing Horn d’Arturo (1925, 211), who refers to Taylor (1883, 263), whose sources are unknown. Also, Ambrosetti (2008, 247) cites Pellegrini (1972, 27), who in turn cites Pareja (1951, 693), who fails to provide a source, as do many others, including Haskins (1904, 154–155) and King (2001, 316).

25 See the edition by Denifle (1892, 453, ll. 25–28): ‘Ponat eciam in libro venali extrinsecus et in evidenti loco et claris litteris non [per] zyphras nomen venditoris cum ipsius congnomine [sic] et precium libri, sub pena viginti solidorum Universitati solvenda et per rectoris exigenda’. Murray (1978, 171), for unclear reasons, dates these statutes to 1305.

26 Statuta dominorum artistarum Achademiae Patauinae, [sine loc.]: Pasquino di Roma, [after 1500], fol. 34^v (lib. III, c. 24). These statutes were already cited by Kirchhoff (1853, 30).

27 For biographical details, see Lebsanft 1989.

28 Some results of this article are summarized in Jordan (1906, 64–68).

29 Jordan’s idea of two opposing camps of calculators was to have a remarkably long afterlife, as seen from the popular articles by Stone (1972) and Reynolds (1993). As recently as 2010 a serious history of mathematics (Chrisomalis 2010, 123) declared that Leonardo of Pisa’s Liber abbaci ‘sparked an important debate between two camps, the abacists, those who preferred computation with the medieval abacus, and the algorithmists, who preferred pen-and-paper calculations using the Western ciphered-positional numerals. The history of this debate is well documented, as it involved many important commercial families, renowned mathematicians and clergymen, and even state authorities (Menninger 1969, 422–445; Evans 1977b; Murray 1978, 163–175)’. None of the studies cited here provide robust documentation of an actual debate between two factions. See also Caianiello (2014, 229).

30 William of Malmesbury, Gesta regum Anglorum, 2.167.3, ed. Mynors (1998, 280): ‘Abacum certe primum a Saracenis rapiens, regulas dedit quae a sudantibus abacistis uix intelliguntur’. For the English translation see ibid., 281.

31 The notion that William regarded Gerbert’s mathematics as ‘dangerous Saracen magic’ was introduced into the literature by Cochrane (1994, 7, 43), who masked her incorrect interpretation of the text as a quote taken from it. From Cochrane’s book, the fake quote passed into Lyons (2012, 86) and Kaplan (1999, 66, 75), who repeated it in an appearance on BBC Radio 4’s In Our Time (13 May 2004).

32 On the ‘black legend’ surrounding Gerbert of Aurillac, see Truitt 2012; Ricklin 2015.

33 William of Malmesbury, Gesta regum Anglorum, 2.167.5, ed. Mynors 1998, 282, ‘Sed haec uulgariter ficta crediderit aliquis, quod soleat populus litteratorum famam ledere, dicens illum loqui cum demone quem in aliquo uiderint excellentem opere’. English translation ibid., 283.

34 Alain de Lille, Anticlaudianus, 2.436–438 (ed. Bossuat 1955, 85); Alain de Lille, De planctu naturae, 2.192–193 (ed. Häring 1978, 816).

35 Gautier de Coinci, Miracles de Nostre Dame, II Mir 32, ll. 224–227 (ed. Koenig 1970, 426–427).

36 Compare, for example, the Modern Hebrew slang term dapar efes or the German insult Du Null! Gazalé (2000, 46) notes that ‘[i]n contemporary Egypt, an individual despised by his or her peers, is metaphorically referred to as sifr ‘ala al-yassaar, literally meaning “zero on the left-hand side”, or as we would say today, “nonsignificant zero”’.

37 The questionable value of this argument becomes clear once one considers that that Alexandre de Villedieu authored (or is believed to have authored) equally popular didactic poems on the ecclesiastical calendar (Massa compoti) and grammar (Doctrinale puerorum). Would anyone claim that their verse form was indicative of a ‘popular disinclination’ towards these subjects?

38 Morrison and Morrison (1999, 546), even saw fit to include it among ‘100 or so books that shaped a century of science’.

39 Asked to corroborate the reference in an email exchange of 1 June 2019, Kaplan responded to me with the following: ‘Rather than misquoting me, let’s say [Teresi] well exercised his considerable powers of summing up’.