A New Interpretation of the Stone Rings of Zempoala

In the central plaza of Zempoala, just beneath the massive pyramids that frame its northeastern corner,
are three intriguing rings of stone, each fashioned of rounded beach cobbles cemented together to form
a series of small, stepped pillars. The largest of the rings contains 43 of the stepped pillars, the middle-
sized ring has 28 such features, and the smallest ring numbers 13 stepped pillars around its
circumference. It would appear that the three rings were used to calibrate different astronomical cycles,
possibly by moving a marker or an idol from one stepped pillar to the next with each passing day (in
somewhat the same way that has been suggested for recording the passage of time at the Pyramid of
the Niches at El Tajín).

The largest ring is the most enigmatic, for no cycle based on 43 is known from Mesoamerica.
However, the manner in which the ring is constructed differs from the two smaller rings in that it is
divided at the cardinal points into quarters -- on its north side by a door or gate opening into the circle,
and on the east, south, and west by a composite pillar having a step on each side of it. Thus, each of
the respective quarters contains 10 single-stepped pillars, all of whose steps face in the same direction
-- clockwise in the northeasterly and southwesterly quadrants and counter-clockwise in the
southeasterly and northwesterly quadrants. (To describe it in another way it may be said that all steps
in the southern half of the circle face north while all those in the northern half face south.) While it is
obvious that a conscious effort had been made to distinguish the four cardinal points or quadrants
through the architectural device of alternating the orientation of their steps, what is not so clear is
whether only the single-stepped pillars in each quadrant were meant to be counted -- yielding a total
of 40 -- or whether one or more of the three composite pillars marking the cardinal points were to
have been counted as well -- yielding a total of 43. (Naturally, if it were the steps which were being
counted, the total would be 46 instead, i.e., 40 pillars with single-steps and three with double-steps).
Lacking any indigenous explanation for how the circle was actually employed, we can only conclude
that its Totonac builders were attempting to calibrate some celestial cycle which lay in the range of
40 to 46 days, but what might this have been?

Of course, if it is argued that the three composite pillars, each with their double steps, served merely
as architectural markers which set off the cardinal points, then the number that was being reckoned
was 40 rather than either 43 or 46. However, no count of 40 days is known from Mesoamerica,
although it obviously could have served to define two cycles of 20. Naturally, if it had been used as
one component in defining a "year," then we might have expected to find some means of recording
nine full circuits of the ring -- i.e. 9 x 40 = 360 -- but no such "device" is present. If it had been used
in conjunction with the middle-sized ring, it would, of course, define an interval of 1120 days
(40 x 28), which bears no relationship to either the sacred or secular calendar. However, had it been
used together with the smallest ring of 13 pillars, it could have calibrated two full cycles of the sacred
almanac, or 40 x 13 = 520 days. The latter, known as a double tzolkin in Mayan terminology, equates
to three eclipse half-years, and thereby provides a useful interval in predicting eclipses. (An eclipse
year is the length of time it takes for the sun to move from one of its intersections with the path of the
moon, or node, until it returns to the same intersection, or node. It measures 346.62 days in length.
Hence, an eclipse half-year totals 173.31 days, and three eclipse half years add up to 519.93 days.
In Mesoamerican terms, this value would be rounded to 520 days, or the equivalent of two rounds
of the 260-day sacred almanac.)

If we are correct in suggesting a lunar association for the two smaller rings, namely 13 full moons
per year with approximately 28 days between each of them, then what observable movement of the
moon has a periodicity in the range of 40 to 46 days?. For anyone practicing a horizon-based
astronomy, as did the Mesoamericans, it would soon become apparent that the average interval
between extreme rising positions of the moon was about 13 days, although it varies in fact between
12 and 15 days. Were they to have defined the interval between two consecutive risings at either the
moon's northern or southern extreme positions, they would have found that it averaged between 27
and 28 days -- in other words, one sidereal month (27.32 days). But for a people with no appreciation
of fractions, neither of these cycles was accurate enough to pinpoint the possible occurrence of an
eclipse. On the other hand, a cycle which embraces an interval of one and a half sidereal months
(which is the length of time it would take the moon to move, for example, between two consecutive
risings at its northern extreme and its next rising at its southern extreme) averages out at almost
exactly 41 days (27.32 + 13.66 = 40.98). To have used such a cycle, of course, would have meant
ignoring two of the pillars in the ring -- most likely, I would imagine, the two composite pillars
marking the east and west extremes of the circle -- while counting only the southernmost one.

How might this cycle have been useful in warning of eclipses? Naturally, the 41-day cycle can be
tested anywhere in the world, but for this study an analysis was made of all the eclipses which were
visible at Zempoala during the years 1992 through 1997. Not too surprisingly, the most common
intervals between eclipses were found to be 162-163 days (3 occurrences), 177-178 days
(3 occurrences), and 191-192 days (3 occurrences), and/or combinations of these values.

To approximate the lowest of these values would obviously require four rounds of counting, perhaps
each round being calibrated by a mneomic device which designated one of the four quadrants of the
circle. Thus, as a given count neared the end of the fourth round of the ring, the priest would be
aware that an eclipse might take place, although he could never be entirely sure whether it actually
would take place (in the sense of being visible to him). If the fourth round was completed without an
eclipse being observed, i.e., taking him up through day 164, he would initiate both a second count
using the 13-pillar ring and a third count using the 28-pillar ring. If the second count likewise was
completed without an eclipse being observed, i.e., with day 177 having been passed, he had a
fall-back position by utilizing the 28-pillar ring to bring him up to day 192. Of course, if an eclipse
did take place near the end of a 13-day cycle, it was also quite possible that another eclipse would
occur by the time the 28-day cycle ended, in effect building an additional 15-day cycle into the
equation as well. On the other hand, if day 192 also came and went without an eclipse being
observed, he could quite confidently start his initial 41-day count over again.

It is, therefore, quite possible that by using the three rings in the manner described, the Totonac
priests were able to calibrate the movements of the moon closely enough so as to know when it
might next be "devoured" by the sun. In any event, there is every reason to believe that the three
stone rings of Zempoala afford yet another bit of evidence testifying to the intellectual curiosity and
architectural ingenuity of the early Mesoamericans.

(Note that references for this and the other papers are found on the 'home page' of this article.)

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