1. Thomas, 1904, pp. 282-90.
  2. Thompson, 1934, pp. 251-53
  3. Bowditch, 1910; Morley, 1915; Thompson, 1927; Palacios, 1933; Teeple, 1930.
  4. Landa, 1938, par. 24.  Ralph L. Roys in this connection writes:  “I don’t think Landa is here referring to any counting apparatus, but only notes that cacao counting was done on a flat surface, perhaps so that the buyer could inspect the kernels to see they were not shells stuffed with earth.”
  5. A few cases, notably that of the famous Tuxtla Statuette (but this is quite possibly Olmec) and that of a stela at Pestac, Chiapas, show that the presence of symbols for the orders was not essential even in ritualistic inscriptions.
  6. Among the numerous references to this type of divination might be cited examples for the Yucatec (Lopez de Cogolludo, 1867-1868, bk. 5, ch. 18), for the Lacandon Chol (Tozzer, 1913), for the Quiche (Popol Vuh, p. 177), and for the present-day highland Maya of Guatemala (LaFarge and Byers, 1931, pp. 154-55).
  7. Acosta, 1608, bk. 6, ch. 8.  Passage translated by J.E.S.T.  Mr. Ralph L. Roys suggests that a cord frame might have been employed by the Maya, although noting that there is no record of such a thing in literature.  He writes:  “Diego Chi in his explanation of the calendar, as given in Brinton, 1882, p. 47, remarks that his ancestors counted years up to the number four by means of the thun; but five and its multiples by the payche.”  These are, of course, our bars and dots. Thun is defined in the Motul dictionary as, among other things, a drop or splash. Payche is not translated in any dictionary.  Nevertheless among the meanings assigned to pay is to draw or pull along, while che means not only tree, but also stick.  The whole could therefore be translated ’pull-stick.’  Purely as a suggestion, might not this indicate the use of a perforated stick strung on an abacus cord to record the number five?  Jade beads (tun) might have been similarly strung to mark the numbers one to four, and a red shell bead for zero, since zero is represented by a red shell in the codices.  You could then arrange each section of your cord abacus with five cords.  On the top one would be strung five beads, on each of the next three cords a perforated stick for five, on the bottom one a red shell bead to represent zero. ¶“If a pod had once been used for five, might it not have a cacao pod?  In the Vienna dictionary we read ’cacao, la masorca mui pequena, ppizte.’  Since ppiz usually means to measure, and te tree and by extension, wood, we may have a hint as to the derivation of the payche.”  ¶Serious drawbacks to the use of cacao beans in this way would be their size and value.  The bean pod, since it contains approximately five beans, would have a mnemonic value, absent in the case of a cacao pod.  One gets the impression that cacao kernels were reserved for actual currency transactions.
  8. Wassen, n.d. ca. 1931.
  9. Bowditch, 1910, app. 7; Joyce, 1923, app.; Lizardi Ramos, 1937.
  10. Förstemann, 1906, p. 133; Spinden, 1924, p. 62.  Here the suggestion is made that the computing year may have been used in measuring sidereal time.
  11. Thomas, 1904, pp. 237-48; Beyer, 1933.  Förstemann, however, was the first to correct 16 Uo to 17 Uo.
  12. Ring Numbers, a term coined by Robert Willson (1924), are Secondary Series, one or more units of which are enclosed in a ring, and which, when subtracted from the base, 4 Ahau 8 Cumhu, reach the starting points of the Initial Series with which they are linked.  Their function was first ascertained by Förstemann (1904, pp. 411-12).
  13. Bowditch, 1903, p. 8; Morley, 1937-1938, 2: 541-46.  In the second citation, Dr. Pogo is credited with the belief that 8 Yax is an error of the computer, not of the sculptor.
  14. Beyer, 1932, pp. 115-16.
  15. Morley, 1920, p. 323.

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