Mayan Numerical system
By Justin Burk
One aspect of Mayan culture that is well known today is their intricate numerical writing system. This system is composed of shells, dots, and lines to make up the numerals. In this article, I will introduce you to the Mayan numerals, teach you how to write out each numeral, and then explain how they were used for math in Mayan times.
The first thing you must know about Mayan numbers is how they are formatted. In the system, each number is made up of a combination of three symbols, each of which represent different things. The first one you'll notice is the shell, represented by an oval with many curved lines on it. This shell represents nothing, or in modern terms the number zero. This is incredibly important, because the Mayans invented the concept of zero independently from any other civilization, though they were not the first to invent it on Earth.
The second symbol you will notice is the dot. This represents one. These dots can be combined to create larger numbers. For example, two dots is two, three dots is three, and four dots is four. Five is where the lines come into play. Five dots make a line, so every line represents five. After five, the dots appear above the line for six and so on.
The Mayans may have used stones, sticks, and shells to represent these numbers physically.
This can be compared to the somewhat similar Roman numerals, where the numeral I is comparable to the dot and numeral V is comparable to the line. One thing to keep in mind, though, is that the Mayan system of numbers is base 20.
In modern times, we are used to base 10 counting, though in ancient times, many cultures used different bases, such as the Sumerians using base 60. But what is a base? The base is how many unique numbers there are in your counting system before it repeats. For example, our base 10 unit has 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, then it repeats with 1 and 0. Another example is hexadecimal, which is base 16 and include 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F, then repeats to 1 and 0.
Mayan numerals work in a similar way, but base 20. So after 19 (four dots with three lines), the next number would be written with a dot in the first space and a shell in the space below it (being a 1 and 0). To find out how much each dot is worth, you can do 20 to the power of how many rows it is high. So the second position (1 up) would be 20 to the first power, thus making each dot worth twenty. The third position (2 up) would be 20 the second power, meaning each dot is worth 400.
Adding in Mayan numerals is as easy as putting the two numbers together and reformatting them to fit with the format.
In this example, we have to add 27 and 58. The numbers have been separated into two sections for clarity sake. Our first number 27 is represented with a dot at the top representing 20 and two dots and a line on the bottom representing 7. Our second number has two dots on the top representing 40 and three lines and three dots on the bottom representing 18. Putting them together, we get three dots on the top and four lines and 5 dots on the bottom. We then reformat the four dots into a dot in the top position, because four lines equal twenty, thus carrying them over to another dot on the top. We then convert the five dots on the bottom into a line, because a line represents five. We then get our answer: four dots, each equaling 20 meaning 80, and a line on the bottom, which is 5. Our answer is 85.
In conclusion, Mayan numerals were a very innovative number system for their time, making them one of the greatest accomplishments of the Mayan civilization. Learning about these numerals gives us a look into the incredible culture of the Mayans. Below I will include images of Mayan numerals as they were used by the Mayans.
Portion of the Dresden codex
Portion of the Paris Codex
Portion of the Madrid codex