Academic journal article Proceedings of the American Philosophical Society

Maya Concepts of Zero

Academic journal article Proceedings of the American Philosophical Society

Maya Concepts of Zero

Article excerpt

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 used, in addition to the partially visible quatrefoil * (T173), a shell-in-hand * (T17:713a), a head variant * (T1085), and a full-figure form (figs. 2-8). In the bark-paper screenfold manuscripts (extant in four Precolumbian codices) the Maya drew zero in the form of a stylized image of an oliva seashell * (fig. 9). This range of visual expression for a single number or word is standard within the Maya hieroglyphic corpus made by scribes who delighted to form their written language out of syllables, words, and numerical signs that intertwine and change like the animate elements of the tropical, mountainous, and coastal region in which they lived.


Maya Use of Zero in Long Count Inscriptions

As early as the first century BC Preclassic civilizations of Mesoamerica began to record historical time from a chosen starting point that has been correlated to 3114 BC. This count of days, known as the Long Count, consists of five periods identified by epigraphers2 as

bak'tun 144,000 days [20 k'atun ]

k'atun 7,200 days [20 tun]

tun 360 days [18 winal]

winal 20 days [20 k'in]

k'in 1 day

As a count of days it is a base-twenty system with each step equal to twenty times the previous step, with the constant exception of the third step, which was calculated as times eighteen.

In addition to the Long Count the Maya used several other calendars that were day counts. One of these is a 260-day almanac that consists of 20 named-days and numbers 1-13. This almanac is the oldest of the Mesoamerican day counts adopted by the ancient Maya; it is still counted and used by Maya priests today (Tedlock 1982, 89; Earle 2008, 69). Another calendar of days that the ancient Maya counted is a solar year of 365 days that consists of 18 "months" of 20 days with a residue period of 5 days. …

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