**Date**: 200**Owner**: Immanuel Giel**Source Type**: Images

This chart helps to simplify Mayan counting, the first step to deciphering the deep and manifold meanings found in Mayan writings. Although both head-variant numerals and full-figure glyphs were also used to represent numbers and days, this system was the basis for calculations and numerical charts, such as those found in the Dresden Codex, and probably predated more complicated counting schemes.

The Maya only had three symbols with which to express numeric value, the dot (=1), the bar (=5), and the zero glyph. This chart shows how these symbols could be combined to make the numbers 1-20, the basis of Mesoamerica's vigesimal system (just as the modern West uses a decimal system based on multiples of 10, indigenous Mesoamericans based counting on sets of twenties). Combinations of numbers 0-20 would be stacked vertically to create larger numbers. The bottom layer would have a number like those seen on this chart for which place value is already assigned. Each upper layer is then multiplied by place value factors of 20. Thus the second layer (consisting of a number 0-20) was multiplied by twenty, the first place factor in a vigesimal system. The third layer's number was then multiplied by 20 twice (or 400), the fourth layer by 20 to the third power (or 8000), etc. This system may seem overly complex, but it is no less natural or intuitive than modern counting systems and would have been easy to manipulate for those accustomed to it.

The number zero was most likely "invented" by the ancient Olmecs and is one of the most advanced mathematic concepts found anywhere in the pre-modern world. The graphic representation of the absence of numeric value is not intuitive, but inventing a way to hold place value was necessary for advanced mathematics or calculating large numbers (like the days of the Long Count). Thus Mayans could write the number "60" simply by placing 3 (three dots) in the second layer (3x20=60) and a zero in the bottom layer. The top and bottom layers are then added together to get the total sum: 60+0=60.

A description of how to read a more complex number might prove useful for better understanding Mayan counting. Let's say there is a glyph with 3 layers, the highest is 11 (2 bars and 1 dot), the second layer is 8 (1 bar and 3 dots), and the bottom layer is 7 (1 bar and 2 dots). The third layer, 11, must be multiplied by 20 twice (or, 400), which equals 4400. The second layer, 8, must be multiplied by 20 once, which equals 160. The bottom layer is not multiplied by anything, and thus remains 7. These 3 sums are then added together to calculate the total numerical value of the 3 layer symbol: 4400+160+7=4567. See if you can draw this and other numbers out in Mayan symbols.

Reference: Barsh, Russel Lawrence. Counting, Computation, and the Calendar in Mesoamerica. Brooklyn, NY: Brooklyn Children's Museum, 1965.

Leon-Portilla, Miguel. Time and Reality in the Thought of the Maya. Second ed. Norman: University of Oklahoma Press, 1988.

**CITATION**: Immanuel Giel 14:47, 21 December 2006 (UTC). Public Domain.

**DIGITAL ID**: 13083