CHAPTER 11 LANGUAGE AND LANGUAGES OF MESOAMERICA 437for the syllable miwas used with period signs in these contexts to say, for example, “there were
no ha7b.”
The simple place-value notation continued in use in the working almanacs used by calen-
dar priests, judging from the screenfolds that survive from the Postclassic period, and the pho-
netic sign miwas used in the appropriate position. The contexts of use of long count dates in these
manuscripts was in arithmetic tables, especially astronomical tables, where dates and time spans
were generated by repeated additions of one number to another. Every other symbol in these
shorthand expressions was manipulated using numerical algorithms for place-value addition. The
misign would have been integrated into these algorithms. Given a numerical interpretation in
these contexts, this would be the first real zero known in the history of mathematics.
Two points deserve special notice here. First, contrary to popular belief, place-value nota-
tion did not develop after the invention of zero. Just the reverse is true: A numerical zero served
no practical purpose in ancient mathematics until place-value notation was in use. Second, in
this particular case, the numerical zero was in the first place a linguistic practice adopted for po-
etic purposes. It was the embedding of the notation for this poetic device in a mathematical con-
text that led to its reinterpretation as a numeral. The concept of zero, then, was discoveredby
Mayas; it was not “invented.”
Figure 11.4 The long count dates on Abaj
Takalik Stela 5. After John Justeson, “Pratiche
di calculo nell’antica Mesoamerica,” in
Anthony F. Aveni, ed., vol. II of Storia della
Scienza,pp. 976–990. Rome: Istituto della
Enciclopedia Italiana, Fondata da Giovanni
Treccani., 2001, p.988, fig.5. The long count
dates are 8.4.5.(0).17 (the seating of the year
in A.D. 125) and 8.3.2.(0).10; no digit is
recorded where, based on later texts, a zero
is expected. The second digit in the second
long count is reconstructed as having been a
3 by John Graham, based on its layout.