The medieval fear for the number zero

Indo-Arabic numerals are ubiquitous and recognizable throughout the world. Their application with positional notation spread throughout Europe in the Middle Ages thanks to the Arabs and the Liber abbaci of Leonardo of Pisa in the 12th century. However, the church did not like the idea of zero and, by extension, Arabic numerals...or, at least, that is what it usually tells.

Not an encouraging idea...

It is usually told that zero represented nothingness, a concept that seemed to conflict with the soul and spirituality. Nothingness would have been associated with the work of Satan, so zero would be his symbol. Therefore, this figure was a heresy. Supposedly, it was the governments and/or the church that would have forbidden the zero as heretical and not belonging to the Christian world.

The zero would come from the Sanskrit shunya (void), which would arrive in Arabic as sifr (صفر). In Spanish, this word would produce the term "cifra", but it is also said that in Portuguese it is the origin of chifre, "horn", being more associated with Satanism. Writing with ciphers was unintelligible to those who did not know them, so it was associated with the occult. In other words, the ciphers were a code or secret key, as one of the meanings in the RAE (Royal Spanish Academy) states. Meanwhile, governments would have banned their use because accountants could easily switch between a negative and positive symbol. Despite the justifications, their usefulness, especially among merchants and accountants, would have prevailed.

...that repetition does not make true

Expansion of Indo-Arabic numerals

This numbering spread from India to the Middle East around the 7th century AD. Before the zero, the numbers 1 to 9 appeared in a manuscript of the monastery of San Martín de Albeda, La Rioja, in 976, where it indicates its Indian origin. Gerbert of Aurillac, future Pope Sylvester II, who studied in Catalonia from 967-970, attested, never better said, to the presence of these numbers in the apices that were used together with the abacuses. Contemporary texts showed the apices with the 9 digits and, occasionally, a placeholder known as sipos, represented with a circle or a wheel.

Arithmetic written with these numbers reached Europe in the early 12th century with a now lost work written by Al-Juarismi in 825, which came in Latin as Dixit Algorizmi, separated into the manuscripts Liber Ysagogarum Alchorismi, Liber Alchorismi and Liber Pulveris. Around the beginning of the 13th century, the Ars algorismi and Salem algorismus offer religious interpretations of arithmetical calculations. Shortly thereafter, two works became part of the university curriculum: Algorismus vulgaris by Johannes de Sacrobosco and Carmen de algorismus, attributed to Alexandre de Villedieu. In addition, the Liber abbaci of Leonardo of Pisa, known as Fibonacci, had a great influence on the treatises on commercial arithmetic. His use of the abacus, not as an instrument, but as the art of calculating itself caused the schools of commercial arithmetic to be called scuole or botteghe d'abbaco.

Coexistence

Arabic numerals coexisted with Roman numerals throughout the medieval period. These centuries saw experimentation with alphanumeric notations or with unrelated symbols, such as Cistercian notation.

Although there was no persecution, it was difficult to learn a new system when the traditional one offered no problem. Proof of this is that there were works, such as the algorithmic treatise of H. Ocreatus, where it was preferred to teach positional notation with Roman numerals. Because of this, some areas of knowledge were more receptive to these changes. Writers on astronomy and astrology were among the pioneers in this regard. Students of computus, who calculated ecclesiastical dates, were also early adopters. Even the 12th century mathematician Reinher von Paderborn advocated the simplicity and economy of these numbers, which he used in his Compotus emendatus. Robert Grosseteste, who was to become bishop of Lincoln, also did the same in his Compotus.

Prohibition

One of the prohibitions occurred in the Florentine guild of money changers in 1299, which did not allow its members to write debits and credits in the account books with the "abacus letters", but with legible text. Although there is speculation that this could be because the different forms of Arabic numerals could lead to speculation, it is neither confirmed nor is it the only possible reason.

Although the other prohibition is from the Paduan booksellers in 1348, there are no citations to the primary source to verify this. However, the University of Padua ordered in 1331 that book sellers should indicate their own name and the price of the merchandise clearly visible on the outer cover, with clear letters, not figures. The same happened at the University of Bologna in 1317, 1347 and 1432 and at the University of Florence in 1387. This prohibition only applied to the prices shown, not to the accounting records. This did occur in Trieste, where money changers and merchants were forbidden to keep their books with these figures. Moreover, in Frankfurt am Main, the city council in 1494 ordered its accountants to stop using these figures in their public books.

Countless names

It is true that the Arabs called zero sifr, which was transliterated as a cipher, but they also popularly called it da'ira saghir ("little circle"), which became known in Latin as circulus. A 12th-century English scribe wrote on the back of the front flyleaf of a book the names of the zero. These include cifra vel solfra vel nichit t. 0 cimera sipos.

The invention of the rejection of the authorities

This supposed ecclesiastical rejection of zero has its roots in the anti-Catholic views of John William Draper and Andrew Dickson White, who promoted the idea of terraplanism in the Middle Ages. Although Taylor Ball and Florian Cajori already mentioned the Paduan and Florentine prohibitions with some errors, it was Leo Jordan of the University of Munich, in the article Materialien
zur Geschichte der arabischen Zahlzeichen in Frankreich, who invented a conflict between the abachists and the followers of the algorithm. Moreover, he presented Gerbert of Aurillac as a monk who had escaped from the Saracens with a forbidden book thanks to the help of the devil. In fact, he devotes more lines to his exploits as a soothsayer and necromancer than to his mathematical work, pointing out that the devil had taught him his art. In the article, Jordan repeatedly misinterprets multiple works, speculates without showing the sources on which he relies, and portrays the Arabs in an Orientalist light, as magicians from distant lands.

Although a very flimsy article, it influenced the reputable The Hindu-Arabic Numerals (1911) by David Eugene Smith and Louis Charles Karpinski. From there, his assertions kept appearing in influential works, such as The Story of Reckoning in the Middle Ages (1926) by Florence A. Yeldham or the popular Mathematics for the Million (1936) by Lancelot Hogben, the latest edition of which dates from 1996.

Although for decades, the error was limited to spotty repetition of some of Jordan's assertions, Brian Rotman's Signifying Nothing (1987) and Georges Ifrah's From one to zero (1985) fed the lie. For Rotman, the rejection of zero involved Aristotelian horror vacui, which Augustine of Hippo related to the devil. His conclusions are based entirely on religious reasoning, without any historical basis for them. Initially, Ifrah was more restrained, but in Histoire universelle (1994) he starts from exaggerations that praise Islamic civilization and despises Christian Europe, where the advantages of the new system would not have been understood and mathematicians would have been burned on the pyre for using them. Subjectivity, lack of sources and misinterpretations are common in both, who seem more concerned with adding impact to their account than reflecting a true picture of reality. Robert Kaplan's The nothing that is (1999) and Dick Teresi's Lost discoveries (2002) also provide their own interpretations starting from the same ideas and making the same mistakes. Zero: Biography of a Dangerous Idea (2000) by Charles Seife takes the concept and makes it the main theme of the book, expanding that the fear of zero, that is, of nothingness and chaos, was common since ancient times. Ronald Green's Nothing Matters (2011) indicates that the church, without pointing to the inquisition or specifying further, was doing its best to persecute and execute those who used zero. In addition, he would know the Buddhist meaning of nothingness in India, which is why they would want to suppress the idea.

Summary

Although there were punctual prohibitions for specific causes, there was simply a slow adoption until the 15th century. The claims of persecution for the use of zero or Indo-Arabic numerals are unsubstantiated and are based on a very biased article.

Source

• Nothaft, C. P. E. (2020). Medieval Europe’s satanic ciphers: on the genesis of a modern myth. British Journal for the History of Mathematics, 35(2), 107-136.