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INSCRIBED IN STONE on the Hieroglyphic Stairway at Copan is a description of Ruler 13, Waxaklahun Ub'aah K'awil, dying on 3 May AD 738 with k'a'ay u-?-sak-ik', "his breath expired in war" (Stuart 2005, 385). After this evocation of the ruler's last breath, the inscription continues as a poetic lament in the form of a triplet: mi'temple', m/'-'altar', mi-kab'-ch'e'n? translated as "no pyramid, no altar, no earth/cave" (Hull 2003, 464) (fig. 1). The "no" in these clauses was written by the Maya scribe with the partially visible quatrefoil glyph * (T173).1 In the Classic Maya inscriptions scribes also used this same glyph * (Tl 73) along with several other variants to write a sign that functioned as zero in their calendrics and mathematical calculations (fig. 2). How to read this mi - "no" - and other Maya signs for zero is the topic of this essay.
From the third to the fifteenth century, in stone inscriptions and bark-paper screenfold manuscripts, the Maya calculated and represented extraordinarily vast expanses of time, from the past through the present and into the future. In multiple parallel calculations they followed and recorded historical events and the movements of the sun, moon, Venus, and several other bodies in the sky. To record these complex calculations, they adopted and devised different written calendars and almanacs, several of which are written in a base-twenty place-value notation system that includes a visualized symbol for zero. With precision and clarity, this zero was used as a placeholder in a system that allowed the Maya to grow their numbers exponentially.
In the West, the decimal place-value system, with its ten numerals 0-9, came from India via Arab mathematicians beginning in the tenth century (Hill 1915, 29; Chrisomalis 2010, 219). In their vigesimal system the Maya counted with only three numerals, a dot * for one, a bar - for five, and a diverse group of symbols and glyphs made up of iconic components for zero. The Maya adopted the dot and bar from earlier Mesoamerican numerical systems dating back to 1000 BC (Coe 1965, 756; Marcus 1976, 36; Justeson 1986, 440). To the dot and bar, the Classic Maya added an explicitly visualized zero. To represent this zero in the stone inscriptions, the Maya...