I shall refer to these as, (1) the Mathematical Elements, (2) the Pictorial Elements, and (3) the Graphic Elements of the Mayan hieroglyphic writing.
II. The Mathematical Elements.
1. The Codices as Time-Counts.
In another work I have explained the numeral system in vogue among the ancient Mayas, as well as the etymology of the terms they employed.[[14]] It will be sufficient, therefore, to say here that their system was vigesimal, proceeding by multiples of twenty up to very large sums. In the same work I have quoted from original sources the information that the fives up to fifteen were represented by single straight lines and the intermediate numbers by dots. This has also been discovered independently by several students of the manuscripts.
The frequency and prominence of these elementary numerals in nearly every relic of Mayan writing, whether on paper, stone, or pottery, constitute a striking feature of such remains, and forcibly suggest that by far the majority of them have one and the same purpose, that is, counting; and when we find with almost equal frequency the signs for days and months associated with these numerals, we become certain that in these records we have before us time-counts—some sort of ephemerides or almanacs. This is true of all the Codices, and of nine out of ten of the inscriptions. Here, therefore, is a first and most important step gained toward the solution of the puzzle before us.
But did this incessant time-counting refer to the past or to the future? Was it history or was it prophecy? Or, passing beyond this world, was it astronomy? Was it mythology or ritual, the epochs and the eons of the gods? Perhaps the disposition, sequence, and values of the numbers themselves, once comprehended, will answer these vital questions.
2. The Mayan Numeral System.
Unfortunately, the old writers, either Spanish or native, tell us little about Maya mathematics. They say the computation ran thus:—
| 20 units | = one kal, 20. |
| 20 kal | = one bak, 400. |
| 20 bak | = one pic, 8000. |
| 20 pic | = one calab, 160,000. |
| 20 calab | = one kinchil or tzotzceh, 3,200,000. |
| 20 kinchil | = one alau, 64,000,000. |
The Tzental system was the same, though the terms differed somewhat: 20 units = one tab (cord or net-ful); 20 tabs = one bac; 20 bacs = one bac-baquetic (bundle of bacs); 20 bac-baquetics = one mam (grandfather); 20 mams = one mechun (grandmother); 20 mechuns = one mucul mam (great-grandfather), 64,000,000.[[15]]