Rarely have scholars considered methods the Maya may have used in computing their complicated calendrics and in counting more mundane things, such as articles of commerce. In 1941 the Mayanist, J. Eric Thompson, published a method that he devised for calculating Mayan dates, which appears to be similar to that suggested in the tables of the Dresden Codex; in 1947 Linton Satterthwaite, Jr., also published on Mayan calendrical arithmetic.
The author of the small book herein reviewed presents still another method of applying Mayan numerals arithmetically. Although Sanchez states that the ancient Mayan arithmetical methods are unknown, he submits that the dot-and-bar numerals can be easily used to add, subtract, multiply, and divide. With rather complicated examples the author illustrates his method using the Mayan dot-and-bar symbols, the concept of zero, and place-value notation based on the vigesimal system. He first illustrates arithmetical problems using the pure vigesimal system as might have been employed for counting objects of trade, such as cacao beans; he then proceeds to solve problems involving time calculations with the modified tun place value (360 instead of 400). Underlying his entire procedure is the idea that the Maya used counters, possibly grains of maize and beans and small stones as mnemonic devices. His idea is reinforced by Diego de Landa’s sixteenth-century statement that the Maya counted on the ground or on a flat surface, and by the fact that the use of counters has been reported for present-day Indian groups in the Guatemala Highlands. That the Maya may have devised a kind of abacus for calculation is conjectural, although Thompson and others have supported this idea.
Doubtless many ways could be devised for using Mayan numerals arithmetically. But there is still no way of knowing precisely how the ancient Maya made their calculations.
