The Mayan System of Numbers
The first striking thing about the Mayan counting system is the fact that the Maya counted in twenties, rather than tens. This number base differs from the Arabic numbers of the decimal system used worldwide today, which uses base ten. A simple way of thinking about this is that instead of using their fingers to count to ten, the Maya used their fingers and toes to count to twenty. This is base twenty or the vigesimal system.
In the decimal system, the more zeros that follow a number the more times it is multiplied by a factor of ten. For example, the base ten or decimal number 786 can also be written like this:
6 × 1 (6) + 8 × 10 (80) + 7 × 100 (700) = 786
Here's another example. The decimal number 3,440 can be written:
0 × 1 (0) + 4 × 10 (40) + 4 × 100 (400) + 3 × 1,000 (3,000) = 3,440
Each extra column adds a factor of ten: increasing from ones to tens, then hundreds, thousands, tens of thousands, hundreds of thousands, and millions. This is something so familiar that it may come as a surprise that there are other equally valid ways of doing it.
For the Maya, each position in a number raises the number by a factor of twenty, rather than ten. The Maya use columns of glyphs to represent the position of their numbers, rather than numerals. The higher up the column the glyph is placed, the higher the multiple of the number. Representing these vigesimal numbers in Arabic numerals looks something like this:
In base twenty, the vigesimal number 786 looks like this:
6 × 1 (6) + 8 × 20 (160) + 7 × 400 (2,800) = 2,966 in base ten
In base twenty, if we were to write the number 3,440, it would look like this:
0 × 1 (0) + 4 × 20 (80) + 4 × 400 (1,600) + 3 × 8,000 (24,000) = 25,680 in base ten
Instead of ones, tens, hundreds, thousands, and tens of thousands, the Mayan number system went from ones to twenties, four hundreds, eight thousands, and one hundred and sixty thousands. By the time the fifth position of a number is reached, the factor of that number is sixteen times bigger than it would be in the base ten. Numbers get much bigger much more quickly than in the decimal system. There are some definite advantages to this: This way of counting gave the Maya the ability to be easily able to conceptualize very big numbers and to add and subtract from them very quickly.
The Concept of Zero
The Maya were sophisticated mathematicians and had a concept and symbol for zero, something the Romans never had. Zero didn't exist in the west until the Arabic numbering system was adopted around
The Mayan symbol for one is a simple dot. For the number two, just add another dot. Add more dots for three and four. The number five is represented as a bar. Six is simply another dot placed above the bar and further dots are added in the same way for seven, eight, and nine. Ten consists of two bars. Eleven adds another dot above those two bars and so on, all the way up to nineteen, which is written as three bars with four dots above it. Nineteen, like nine in Arabic numbers, is the highest number that can occupy any position. Twenty is represented by introducing another position. In the Maya's case, it was by adding another column of glyphs.
Mayan numbers from zero to nineteen
This is actually a very elegant number system. Having just three symbols makes it one of the simplest ever devised mathematically. There is the shell symbol for zero. The dot represents one and the bar stands for five. It's capable of representing big numbers very easily and it doesn't require the learning and memorization that the abstract symbols of the Arabic numerals from one to nine do.
Numbers Make a Difference
In his book Outliers, social psychologist and author Malcolm Gladwell suggests that one of the most important factors that makes Asian children generally better at mathematics is the fact that the words for numbers in Asian languages are generally shorter and more logical than those in western languages. This seemingly small advantage translates into quite a large effect over time. What Gladwell shows is that these tiny differences in the speed of computation add up cumulatively to a significant general advantage. It seems that the Mayan vigesimal system may have had even greater advantages because of its inherent simplicity and logic. This idea shows that mathematical ability may be more of a culturally determined trait than it is an inherent talent, so the Maya would have been able to compute larger numbers and dates faster and more easily than we can today. Effectively, what this means is that the Maya were probably better at math than we are.