Distance Numbers

On Maya inscriptions there are often several dates. The Maya frequently used phrases that were structured like this: On this date, this event happened. Then, after this many days, we reach this date, where this event happened. Distance Numbers are the way that the Maya recorded the number of days between events.

Often the Maya would only record one Long Count date on a monument, then use distance numbers from that Long Count to reach another date, which they would abbreviate with a Calendar Round date. The Calendar Round date, by itself can be in any 52 year period, but using the previous Long Count as an anchor and the Distance Number, the new date is also anchored in the Long Count.

Distance Numbers can move either forward or backwards in time. The Maya had special glyphs to indicate which direction in time the Distance Number is intended to move.

Distance Numbers are distinguished from Long Counts in the inscriptions by the fact that they usually start with the lowest unit, the k'ins, and record as many larger units as it takes to show the entire distance number. So a glyph block showing 4 k'ins, 8 winals, and 9 tuns is a distance number, since it starts with the k'ins and gets progressively larger. The Maya also frequently combined the k'in and winal counts into one glyph block, with one number on the left side of the block and the other on the top. The number that extends into the upper left corner of the glyph block is the count of k'ins.

Shown below is an example of the kind of arithmetic that the Maya used. The inscription is from Stela 3 at Piedras Negras. The Long Counts in parentheses are implied; only the Calendar Round dates appear on the stela. The Maya often did a series of dates separated by Distance Numbers like this. To simplify addition, the distance numbers below have been reversed from the order on the stela to have the largest unit appear first.

 9.12. 2. 0.16  5 Kib 14 Yaxk'in
      12.10. 0  count forward to
(9.12.14.10.16) 1 Kib 14 K'ank'in
    1. 1.11.10  count forward to
(9.13.16. 4. 6) 4 Kimi 14 Wo
       3. 8.15  count forward to
(9.13.19.13. 1) 11 Imix 14 Yax
          4.19  count forward to
(9.14. 0. 0. 0) 6 Ahaw 13 Muwan