Article suitable for older students

‘Codex Corner’: Aztec zero

18th Jul 2023

Codex Vergara fol. 37 showing zero glyph

We all know the ancient Maya invented and used zero - it can be found in codices and stela inscriptions (follow link below to learn more...) Indeed, they employed several glyphs (including a portrait head) to depict zero. But what about the Aztecs? Scholars agree that they too shared a concept of zero, but where and when did they use it, and what symbol did they use for it? (Compiled by Ian Mursell/Mexicolore)

It would seem inconceivable that the Mexica - the last in a long line of high cultures in Mexico, stretching back thousands of years - did not learn from the Maya the use of zero as a ‘placeholder’ and notational symbol. Yes, their writing system was less sophisticated, as was their knowledge of time and mathematical calculations. Yet ‘it is well known that the Aztecs possessed a complex system of counting, which was expressed in hieroglyphic writing by numerous symbols. Furthermore, our recent decipherment of two early post-conquest census-cadastral documents [surveys to establish land boundaries - pic 1] from the Valley of Mexico demonstrates that Texcocan-Aztecs used a positional notation system... heretofore only attributed to the Maya...
’In addition to picture symbols, Texcocan-Aztecs used a positional line-and-dot system that had the advantage of writing efficiency, since it employed only four symbols that were easy to draw - a vertical line, a bundle of five lines linked at the top, a dot, a corn glyph (cintli) - with position indicating the value of the symbols’ (Harvey & Williams, 1980:499).

It is the ‘corn glyph’ that scholars now think was used by Nahua scribes in the mid-16th century to represent zero. Before analysing it, we should point out that the vast majority of number symbols used by the Mexica featured in their tribute manuscripts, where having to note receipts consisting of ‘zero’ would have been decidedly unappealing! However in the context of land measurements - at the centre of myriad disputes with Spanish encomenderos after the invasion - zero would appear quite frequently. In contrast with decidedly imprecise Spanish attempts to measure units of land at the time, native Mexicans were not only adept, ‘central Mexican Indians were measuring their lands very exactly, down to the yard in both dimensions, using quite sophisticated and individual terminology. At that time Spaniards in Mexico were still transferring land by the league, with no other description than the names of nearby owners or outstanding geographical features’ (Anderson, Berdan & Lockhart, 1976:5). This suggests strongly that the Nahua were continuing with pre-invasion practices rather than adapting to anything European - ie, that the zero symbol was in no way an import.

Shown in picture 2 is a household’s single field, its area noted, by means of numbers occurring in three ‘registers’ (indicated in red) - these record the area of the field in square quahuitl (3 Spanish varas or 2.5 metres). The corn glyph, cintli at the top of the rectangle, indicates zero in the third register (Harvey & Williams, 1986:243). To grasp the full scope of the (quite complex) positional line-and-dot notation, read the research by Harvey and Williams, listed below.
The maize glyph in fact depicts a shelled - ie, empty - ear of corn (pic 3), significant as it hints at the reason for choosing this glyph to represent zero: a maize cob left with none of its life-giving, sacred kernels.

Sources/references:-
• Anderson, Arthur J.O., Berdan, Frances & Lockhart, James (trans and eds.) (1976) Beyond the Codices: the Nahua View of Colonial Mexico, University of California Press, Berkeley
• Closs, Michael P. (2001) ‘Numerical Notation’, in The Oxford Encylopedia of Mesoamerican Cultures vol. 2, General Editor Davíd Carrasco, OUP
• Harvey, Herbert R. & Williams, Barbara J. (1986) ‘Decipherment and Some Implications of Aztec Numerical Glyphs’, in Native American Mathematics, ed. Michael P. Closs, University of Texas Press, Austin
• ------- (1980) ‘Aztec Arithmetic: Positional Notation and Area Calculation’, Science, vol. 210, 31 October, 499-505.

Image sources:-
• Main, pic 1 (R) & pic 2: images downloaded from US Library of Congress - https://www.loc.gov/item/2021668120/
• Pic 1 (L): image downloaded from http://news.bbc.co.uk/hi/spanish/science/newsid_7328000/7328605.stm
• Pic 3 (L): drawing by and courtesy of Graciela Sánchez
• Pic 3 (R): photo by Feng Yu / Alamy Stock Photo.