Earliest Maya calendar fragment found in Guatemala

Archaeologists have discovered the earliest confirmed example of Maya calendar notation on two fragments of plaster at the Maya site of San Bartolo, Guatemala. The paint-on-lime-plaster fragments feature a dot and a horizontal line over the head of a deer. This is “7 deer,” one of the days of the Maya calendar. Radiocarbon dating of charcoal found next to the plaster returned a date range of 300-200 B.C.

“The Maya had a solar calendar, like us, but they also had a ritual one,” says Hurst. “We also have one, as Easter is part of that sequence of rituals throughout the year,” she adds. It was associated with a creation myth and also to mark the celebrations that accompanied the Haab, the 360-day calendar. The remaining five days, although they were counted, were disastrous and people avoided leaving their homes. Surrounding both was the Calendar Round, which completed its cycle every 52 years. The complex way that the Maya had to organize time was completed with the Long Count, a vigesimal system (base 20) of counting the days linearly. It is with the latter that it has been possible to find equivalencies between the Maya calendar and the Gregorian calendar.

San Bartolo made global news in 2001 when archaeologists discovered vividly painted murals from the Late Preclassic period (400 B.C. to 200 A.D.) in its central stepped pyramid, dubbed Las Pinturas after the colorful wall paintings. Ceramic artifacts dated them to around 100 B.C., the penultimate of seven construction phases of the pyramid. The calendar hieroglyphics date to the third phase.

Previous discoveries of hieroglyphic inscriptions at San Bartolo proved that writing systems had developed in the Central Maya Lowlands area far earlier than previously realized. The earliest examples of Maya hieroglyphic writing, found in Oaxaca, Mexico, date to around 400 B.C. The earliest examples in San Bartolo date to around 300 B.C., a significant movement in a short time considering San Bartolo is more than 500 miles southeast of Oaxaca.

During the third phase of construction, the central pyramid was smaller. When it was expanded, walls had to be knocked down. Archaeologists discovered more than 7,000 pieces of plaster, remnants of the destroyed walls. They were disposed of carefully, not simply thrown away as construction debris. The former walls were deliberately deposited inside the newly-enlarged chamber, a sort of symbolic burial of the sacred imagery and text.

The study of the find has been published in the journal Science Advances and can be read in its entirety here.

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  1. According to Gauss’s Easter algorithm, the number of the year is denoted by Y, while mod denotes the remainder of integer division (e.g., 13 mod 5 ≡ 3). Calculate first a, b, and c:

    a = Y mod 19; 2022 mod 19 = 8
    b = Y mod 4; 2022 mod 4 = 2
    c = Y mod 7; 2022 mod 7 = 6

    For the Julian calendar (used in Eastern churches), M = 15 and N = 6, and for the Gregorian calendar (used in Western churches), M and N are (for Y >= 1900 and <= 2099) M = 24 and N = 5.

    d = (19 * a + M ) mod 30; (19 * 8 + 24 ) mod 30 = 26
    e = (2 ∗ b + 4 ∗ c + 6 ∗ d + N ) mod 7; (2 * 2 + 4 * 6 + 6 * 26 + 5 ) mod 7 = 0

    If d + e 10, Easter is on 18th of April.

    Hence, (d + e − 9)th of April, i.e. 26+0-9, April 17th is Easter Sunday in 2022.


    At the Council of Nicaea in 325AD (after the introduction of the Julian solar calendar) it was established that Easter is the first Sunday after the first full moon in spring.

    In the Julian calendar, an Easter cycle has a period duration of 532 years. After that, the series of 532 Easter dates starts all over again. This number is the least common multiple of the lunar cycle period (19 full moon dates), the 7-day week (regular annual shift of weekdays by one day), and the leap period (shift of weekdays by two days every four years): 19 × 7 × 4 = 532.

    The Gregorian calendar reform in 1582 not only better aligned the calendar with the solar year (365.2425 days, not the less accurate 365.2468 days from the Jewish calendar), but also corrected the small error in the equation underlying the lunar cycle (235 lunar months = 6939.75 days).

    The Easter cycle has grown to 5,700,000 years in the Gregorian calendar, but this has only theoretical significance, because after such a long time, even the Easter dates determined with the more accurate rules of the Gregorian calendar will have moved completely away from astronomical realities.

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