# “The Mayan Computer”

**By Scott Hamilton**

I came across an article this week about the ancient Mayan number system, and it shocked me how close it comes to a modern number system. The binary number system used by every computer in production today is very similar in nature to the ancient Mayan number system…at least the number system used by the “common” people.

The modern binary number system is a base-2 system, meaning that it only has two symbols and the position of the symbols determine their values. I will start by explaining the standard number system you are all familiar with, the base-10 number system. The base-10 number system has ten symbols (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9); in order to write a number greater than nine you write two digits. The digits from right to left get multiplied by a factor of ten, the base of the number system. So each place value is a multiple of ten, (10, 100, 1000 etc.)

The binary system used by every computer developed today uses a base-2 number system, which means in this case each place value is a multiple of two, (2, 4, 8, 16, 32, etc). This is where things got interesting to me when it came to the Mayan number system. The Mayan number system is a base-20 number system, meaning that each place value in the Mayan system is a multiple of 20. (20,; 400, 8000, 160,000, 3,200,000, etc.) I noticed that it had a very similar structure to the binary system, but with extra powers of 10.

Most archaeologists believe this number system was developed based on the number of fingers and toes a person could use to count. Each place value was equal to the maximum number of things a person could count on their fingers and toes. The simplicity of their number system and the ease with which modern computers can work with base-20 numbers made me wonder if there was in fact a different reason behind the system. They were able to represent very large numbers with a simple set of only three symbols. A special symbol to represent zero, a dot for a value of one and a line for a value of five. Their maximum single digit of 19 consisted of four dots and four lines.

Another interesting thing about the Mayan number system was the fact that they were the first culture to have a symbol to represent zero, that could also be used as a placeholder in a number; just like we can add zeros to the end of a number to multiply by 10, the Mayans could add a zero to the top of a number to multiply the number by twenty.

These two facts make the Mayan number system very simple to utilize, especially with addition and subtraction problems, as you simply had to stack the two numbers and combine the dots and lines. The complexity of Mayan architecture, art and science suggests that they were doing much more complex calculations than simple addition and subtraction. They developed some of the oldest and most accurate star charts. They even calculated the length of a year to be 365.242 days, which is nearly as precise as we use on the modern Gregorian calendar, 365.2425. They also came within less than 2 hours of difference in calculating the lunar month (29.5308 days vs 29.53059 days).

It makes me wonder if they had some type of computer using a similar number system to our modern computers. If so, it was likely a mechanical device that manipulated sticks (lines) and stones (dots). Our first computers were mechanical in nature, so it’s not a far-fetched idea, and their number system seems to fit the necessary simplicity.

Until next week, stay safe and learn something new.

*Scott Hamilton is an Expert in Emerging Technologies at ATOS and can be reached with questions and comments via email to sh*******@te**********.org or through his website at https://www.techshepherd.org.*