Fig. 42. Bar and Dot Numerals of the Mayas.
The straight vigesimal system was doubtless used by the Mayas in ordinary counting, but in counting time a very important change was introduced in the third position. Also the names were modified: hun was called kin which means sun or day. In the second position kal was called uinal which means month and 18 of these were taken to form a tun, stone, which was the third unit. The tun then had a value of 18 × 20 = 360 days, making a conventional year about five and a quarter days less than a true year. Twenty tuns made a kaltun or katun and above this period the numeral system proceeded as before and in the ascending values the names already given were merely combined with tun, if Gates is right in his clever suggestion. For years it has been customary to speak of the fifth period as cycle for want of a native term: this will now be called baktun. One hablatun, the highest period with a name, has the astonishing value of 460,800,000,000 days. However, the highest numbers fall considerably short of this potential limit.
In our decimal system the number 347,981, for instance, is really:—
| 3 × | 100000 |
| 4 × | 10000 |
| 7 × | 1000 |
| 9 × | 100 |
| 8 × | 10 |
| 1 × | 1 |
When written out in a horizontal line each “position” has a value ten times that of the “position” to the right of it. It is understood that a digit which stands in a “position” is to be multiplied by 1, 10, 100, 1000, etc., as the case may be. The Mayas, using the principle of position, ordinarily write their bar and dot numerals in columns. But we can partially transcribe a Mayan number in imitation of our own system by putting dots or dashes between the positions or periods. The number in five positions given below is transcribed as 9.12.16.7.8.
| 9 × | 144000 | 1,296,000 |
| 12 × | 7200 | 86,400 |
| 16 × | 360 | 5,760 |
| 7 × | 20 | 140 |
| 8 × | 1 | 8 |
| 1,388,308 |
We read this date: 9 baktuns, 12 katuns, 16 tuns, 7 uinals, and 8 kins. It is convenient to remember that a tun is a little less than a year, a katun a little less than 20 years and a baktun a little less than 400 years. But the count is really of days, not years.
Fig. 43. Face Numerals found in Mayan Inscriptions. In most cases these are the faces of gods. Reading from left to right: the values are 1, 3, 4, 5, 6, 9, 10.