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Chapter 7

Calendar Reform and Eclipses: The Place of Edzná

HIGH NOON AMONG THE MAYA

Although both the 260-day sacred almanac and the 365-day
secular calendar predated the Maya by well over a millennium, and the
"principle" of using key calendar dates to define urban locations and
the Long Count itself had likewise been developed by the Olmecs
several centuries before the Maya emerged as a civilized society, it
was the latter who seized upon these intellectual tools and honed them
to the highest level of sophistication of any of the native peoples of
Mesoamerica. Ironically, they did so in one of the most difficult
environments in the entire region; yet, this same environment may
ultimately have been responsible for their failure to survive as an
advanced and vigorous culture until the arrival of the Europeans.

Having largely been displaced from their initial homeland
in the Gulf coastal plain of Mexico by the migration of the Zoques in
the thirteenth century B.C., most of the Mayan-speaking peoples ended
up moving toward the east. (It will be remembered that only one group
of Maya moved northward as a result of the Zoque advance, becoming in
the process the Huastecs.) The area into which the Maya moved can be
subdivided into three rather distinct geographic regions. The first of
these was the Petén region of northern Guatemala and southern Yucatán:
an area of relatively heavy precipitation mantled in dense tropical
rain forest, developed on a deeply weathered base of flat-lying
limestone, pocked with solution valleys -- many of which contain lakes
of some size -- and laced by numerous rivers. The second region was
the Yucatán Peninsula itself: an area of drier climate developed on a
low and almost featureless limestone plateau with no surface drainage
and supporting a vegetation cover of short, deciduous, tropical scrub
forest. And the third region comprised the highlands of Guatemala: an
area of subtropical to temperate mixed forest developed on a base of
folded limestone ridges in the north that give way to lofty volcanic
peaks in the south.

Figure 32.

The climatic station of Flores is located in the heart of the region
of Petén, now a part of northern Guatemala. It is representative of
Tikal and the core area of the so-called "Old Empire" of the Maya.
Although its water need (i.e., temperature) curve is somewhat more
variable than those of Soconusco or the Olmec region, its
precipitation curve demonstrates both a monsoonal peak during the
warmest months of the year and a very marked hurricane peak in early
autumn. Its warmth and moisture indices insure its classification as a
tropical humid climate, which supports a native vegetation of heavy
rain forest.

Figure 33.

Mérida, the capital and largest city of Yucatán, is located in the
northwestern quadrant of the peninsula, away from the trade winds
which blow in constantly from the Caribbean Sea. Its water budget
diagram is typical of the region which constituted the so-called "New
Empire" of the Maya, represented by such sites as Uxmal, Mayapán, and
Chichén Itzá. Its relatively uniform water need (i.e., temperature)
curve is unfortunately not matched by its precipitation curve, so much
of the year the area experiences a moisture deficit. Monsoonal rains
in the high-sun period seasonally provide enough moisture for a corn
harvest, and a small surplus is usually recorded with the passage of
an autumn hurricane. While the station's warmth index indicates that
it is clearly tropical, the fact that Mérida only receives about 60
percent of the moisture it actually needs means that the native
vegetation of the northern Yucatán is scrub forest. (Data from
Secretaría de Recursos Hidráulicos.)

As was pointed out earlier, the Maya seem to have founded their
earliest major ceremonial center in what has to have been the most
favored geographic setting in all of the Yucatán -- on the edge on the
largest aguada or alluvial depression, in the entire peninsula.
Located in what today is the interior of Campeche state, this vast
soil-filled depression provided the agricultural support system for
the incipient "city" we now know as Edzná. Dating to about 150 B.C.,
Edzná was a bustling urban node for more than 20,000 persons at the
peak of its existence in the early centuries of the Christian era.

Figure 34. The climatic station of Quezaltenango is located in the
western highlands of Guatemala, just over the Sierra Madre from
Soconusco. Its low latitude and high elevation combine to produce a
very even water need curve which in no month exceeds 75 mm (3 in.).
Although the station enjoys a 12-month growing season (delimited by
the straight line near the bottom of the graph),, an occasional frost
can pose a risk to crops. Its extreme precipitation curve, with a
low-sun deficit and a high-sun surplus, exemplifies a typical
monsoonal climate. However, with a warmth index of less than 4.0, it
qualifies as a warm-temperate humid climate which supports a native
vegetation of mixed broadleaf and coniferous forest.

Although the layout of Edzná mimicked that of Teotihuacán,
its contemporary on the Mexican plateau, by being oriented to the
setting sun on the "day the world began," the Maya priests were no
doubt quick to realize that August 13 was a date that had no real
meaning to the peasant farmers of the Yucatán. The priests were
certainly aware of the practice of using the zenithal passage of the
sun to herald the beginning of a new year, but at Edzná the sun passed
overhead at noon no less than 18 days earlier than the date that the
Olmecs had established as "the beginning of time." Obviously, while
the Maya couldn't change the facts of history, they could amend the
calendar to accord more closely with the realities of their own
physical setting.

Not only did the priests of Edzná appreciate the need for
such a calendar reform, but their reckoning also told them that an
auspicious time for such a change was drawing nigh. The Long Count was
nearing the completion of baktun 7, and baktun 8 was soon about to
begin. What more appropriate a time could they have contemplated for
"turning over a new leaf"?

Yet, as baktun 8 neared and the zenithal sun passed
overhead, it was as if the Maya's own auguries obliged them to
postpone the calendar reform. Forty-five days before the dawn of
baktun 8, they recorded the passage of the zenithal sun, which fell in
that year (A.D. 41) on the Maya date 3 Men 3 Uayeb. It was the latter
aspect of this date which must have given them pause, because the
"month" of Uayeb was the five-day unlucky period at the end of the
Maya year. During these five inauspicious days, the people were wont
to keep as low a profile as possible, engaging in only a minimum of
activities, as if hoping thereby to escape the wrath of the gods.
Certainly, not until the zenithal sun had cleared Uayeb could the
calendar reform be instituted safely and prudently. But because their
calendar did not take into account the extra quarter day in the length
of the solar year, this meant that a full 20 years were required to
advance the calendar by five days. Since the coincidence of the
zenithal sun with the "month" of Uayeb had begun in the equivalent of
the year A.D. 28 -- i.e., 13 years earlier -- there were still 7 years
to go before its passage would occur on 0 Pop, the first day of the
secular year. Thus, the very first time that the zenithal sun passed
overhead in the Maya area on 0 Pop occurred in the year A.D. 48 -- an
event which would have been recorded in the Long Count as 8.0.6.17.12
12 Eb 0 Pop.

In order to calibrate the zenithal sun passage, the Maya
priests had erected at the base of the Cinco Pisos pyramid in Edzná an
absolutely ingenious gnomon. (Remember that a gnomon can be any
upright pillar or post; its function is to not cast a shadow on the
days the sun is directly overhead.) The Edzná gnomon was a tapered
shaft of stone about half a meter (20 in.) in height surmounted by a
disk of stone which had the same diameter as the base of the shaft
(see Figure 29). Thus, on the days that the sun stood directly
overhead, the disk at the top of the shaft would envelop the entire
shaft in its own shadow, whereas on any other day a stripe of sunlight
would fall across the shaft. Hence, there was no question as to what
day would begin the new year.

There were also a couple of other things which the Maya
priests may have realized at the invocation of their reformed calendar
of which they may have been unaware earlier. They were well aware, of
course, that every time one of their "Vague Years" of 365 days was
completed, the date in the 260-day sacred almanac had advanced by
another 105 days. But, because the least common divisor between the
two counts was 5 and there were 20 day-names in the sacred almanac,
there would only be 4 day-names that would repeatedly coincide with
the beginning of the 365-day year. Thus, because their calendar reform
was initiated on a day called 12 Eb in the sacred almanac, in the
following year the Maya new year fell on 13 Caban (105 days later in
the sacred almanac). However, in the year after that -- because the
sacred almanac used only 13 numerals -- the new year fell on 1 Ik
(another advance of 105 days). And in the fourth year, the Maya new
year's day was celebrated on 2 Manik (105 days farther along in the
almanac). By the beginning of the fifth year, the cycle of 20
day-names started over, so that the following four years began on 3
Eb, 4 Caban, 5 Ik, and 6 Manik, respectively -- each year being
identified with the next higher numeral but always with one of the
same 4 day-names.

From this realization, the Maya developed the notion that
these four days of the sacred almanac -- Eb, Caban, Ik, and Manik --
were "the bearers of the years"; that is, they "carried" the year
along until it was passed on to the next "bearer," much as athletes
run a relay race. This idea of "year bearers" gives us an insight into
how the Maya envisioned time; each day was a "burden" to be carried by
the deity who presided over it until his leg of the relay was
complete, at which time he transferred it to the next deity, and so it
went.

Reassuring as the notion of regular "year bearers" must
have been to the Maya, they were still troubled by the fact that the
beginning of their new year soon failed to coincide with the zenithal
passage of the vertical sun. Naturally, this was because their "Vague
Year" was 365 days long, rather than 365 days plus a fraction, so that
in four years their secular calendar slipped a full day. Thus, when
the zenithal sun passed over Edzná for the fifth time, it did so on 1
Pop rather than 0 Pop; by the ninth time, new year's day fell on 2
Pop; by the thirteenth time, its passage took place on 3 Pop, and so
forth. Ironically, by measuring the passage of the zenithal sun over
Edzná so precisely, the Maya priests came to realize as never before
how imprecise their time-count really was. (In this same connection,
it is interesting to note that Bishop Landa records that the Maya had,
by the sixteenth century, shifted over to using the days Kan, Muluc,
Ix, and Cauac as their year bearers.)

On the other hand, the decision by the priests of Edzná to
make the beginning of their year accord with the zenithal passage of
the sun over their city -- an event which occurs on July 26 in our own
calendar -- left a lasting mark on Maya timekeeping. As it turned out,
the parallel of 19ş.5 N latitude on which Edzná is located neatly
bisects the Yucatán Peninsula, which means that throughout the Maya
heartland the zenithal passage of the sun was an event that had
meaning and relevance to everyone. It appears, therefore, that Edzná,
through the combined "accidents" of geography and history came to
serve as the "Greenwich of the Maya," for nowhere else within the
region they occupied could the July 26 zenithal passage be calibrated
except there. In other words, no other ceremonial center within the
Maya area is situated at precisely this latitude, so only at Edzná
could the new year's date be pinpointed. In fact, writing about Edzná,
Thompson observes that its priests seem to have exercised something
akin to a "veto power" in calendrical matters, for he mentions a
possible one-day correction to the calendar having been made there in
the year 671, after which all the other Maya ceremonial centers appear
to have fallen into line (Thompson, 1950).

Figure 35.

One of the early Spanish prelates of the Yucatán, Bishop Landa,
reported that the Maya marked the beginning of their new year with the
zenithal passage of the sun on the equivalent of July 26 in our
calendar. Such an event takes place along the parallel of 19ş.5 N, a
line which neatly bisects the peninsula but intersects only one major
site in doing so -- Edzná. Because the first day of the Maya new year,
0 Pop, initially coincided with July 26 around the year A.D. 48, this
would appear to mark the beginning of their "reformed" calendar.

Some researchers have assumed that each Maya ceremonial
center had its own calendar, but the observation by Thompson cited
above suggests otherwise. So, too, does the historical record, because
Bishop Diego de Landa, the third Spanish prelate of the Yucatán,
specifically records that the Maya began their new year with the
passage of the zenithal sun, and that the day this occurred was the
equivalent of July 26 in the Gregorian calendar. It is of further
interest to note that in the interval between the time the Maya
priests undertook the calendar reform in the year A.D. 48 and the time
that Landa wrote, one entire Sothic cycle of 1460 years had passed,
and astronomical events which were in phase in the year 48 were again
in phase in the year 1508. (The word Sothic comes from the Egyptian
name for the star Sirius. Because the ancient Egyptian calendar also
had 365 days, rather than 365.25 days, the rising of Sirius, which
marked the Egyptian new year, was likewise found to get out of phase
with the movements of the sun. However, by careful measurement the
Egyptians found that after 1460 full solar years had passed -- the
equivalent of 1461 of their "imperfect" years -- the sun and the stars
would once more be back in harmony with each other.) Thus, the
zenithal sun passage once again coincided with the day 0 Pop in the
Maya secular calendar in that year and during the three following
years.

All attempts to understand Maya civilization have been
made immensely more difficult because Bishop Landa, in his religious
zeal, managed to consign all but a handful of the Maya's books and
records to his bonfires. The rather straightforward description of the
astronomical importance of Edzná which I have sketched out above was
by no means as direct and uncomplicated as it might sound. But it did
begin with the two clues which Landa bequeathed to us -- namely, that
the Maya new year coincided with the passage of the zenithal sun and
that this event occurred on the equivalent of July 26 in our present
calendar.

Working from these clues, I reasoned that, if Landa's
information was correct, I should be able to zero in on the geographic
location where the Maya had devised their version of the calendar. A
solar ephemeris revealed that on July 26 the noonday sun passes
overhead at 19ş.5 N latitude, so armed with this knowledge, I next
turned to a detailed map of archaeological sites in the Yucatán
(National Geographic's "Archaeological Map of Middle America,"
published in 1968). The latter showed only one ceremonial center of
any significance at this latitude, its name being rendered as "Etzná";
to one side, there was a vignette describing it as a "Late Classic
site [having a] temple atop a pyramid faced with four stories of
rooms." A subsequent search of the literature turned up only a couple
of references to Edzná, including the one attributed to Thompson which
I cited above. Therefore, all I really knew about the place was that
its construction had been dated to the period A.D. 600-900 and that it
seemed to have had some "clout" when it came to resolving calendrical
issues.

In the winter of 1976 as I was devising my computer
program to run the "Maya" calendars back to the dates on which they
had been initiated, I put in a "flag" to have the program alert me as
to when the Maya day 0 Pop coincided with our day July 26. Employing
Goodman's correlation as my starting point -- namely, that the Long
Count date of 11.16.0.0.0 13 Ahau 8 Xul = November 4, 1539, 1 set the
program in motion and only seconds later I was informed that the
coincidence I was looking for had occurred most recently during the
years 1508-1511. Thereafter, the computer churned away until an entire
Sothic cycle had passed and we were back in the period A.D. 48-51.

In view of the antiquity of this date as opposed to the
relative "lateness" of Edzná's supposed founding, in my 1978 article
reporting the findings of my computer study I decided to make no
mention of the "Maya calendar reform" which I had hypothesized had
taken place there. (The deductions which had led me to Izapa had
embroiled me in enough conflict with the archaeologists, I felt.)
Ironically, as my article was going to press in the winter of 1978, 1
chanced to meet Prof. Matheny, who had recently excavated Edzná, in
the field. When I cautiously mentioned to him how my deductions had
suggested a calendar reform having taken place there "about 600 years
before the place was founded," he laughed and replied, "Well, Cinco
Pisos may have been a Late Classic construction but our radiocarbon
data show us that Edzná itself was a thriving concern already about
150 B.C." Encouraged by both my computer findings and Prof Matheny, I
then went on to Edzná to make the further discoveries reported in
these pages.

MAKING SENSE OF THE MOON

Pinning down the movement of the sun, irregular as it was
with respect to the Long Count, was like child's play for the Maya
compared to their struggle to understand the movements of the moon.
Once again their failure to recognize the concept of fractions obliged
them to undertake lengthy counts of cycles in the hope of eventually
finding two periods which coincided in nice, whole integers. A case in
point is the length of a lunation, the period of time between two
successive new moons. The Maya obviously realized that it was not 29
days, but it also was not 30 days. Attempting to describe a time
period which was actually 29 days, 12 hours, 44 minutes, and 2.8
seconds in length was for them a philosophical impossibility. Yet,
after they had counted 149 "moons" in a row they realized that exactly
12 tuns and 4 uinals had elapsed, or a total of 4400 days; they were
then confident that the cycle would begin over again, with the moon
occupying the same position it had had relative to the sun when the
cycle began. That they could do so with reasonable assurance is
demonstrated by the fact that 4400 days divided by 149 lunations
yields an average of 29.5302 days per lunation -- a value less than
0.0004 at variance with that used by modern astronomers!

More difficult yet, however, was trying to find some
regular pattern in the moon's seemingly erratic bouncing around the
sky. Unlike the sun, which moves progressively farther north or south
each day until it finally reaches its "stopping place" and then turns
around, the moon rises and sets at such different times of the day or
night in such widely differing places along the horizon that it might
seem "illogical," "crazy," or "drunken" in its behavior. Indeed, if it
were not for the fact that on occasion the moon suddenly became dark,
or, even worse, that the sun itself was sometimes "devoured" by
darkness without warning, perhaps there would have been no real reason
to try to make sense out of the moon's motions. Initially, the priests
may have shared the layman's terror of the disappearing sun or moon,
but not too many eclipses would have occurred before they may have
suspected some functional relationship between the orderly path of the
sun and the seemingly disorderly path of the moon. Yet, not until the
"crazy" ricocheting of the latter could be understood would they be
able to predict the occurrence of eclipses, and only after they had
mastered that skill would they be in a position to exercise the full
power of that knowledge over their untutored subjects.

Figure 36.

Stela C from Tres Zapotes now reposes in the National Museum of
Anthropology and History in Mexico City. The missing baktun value of
its Long Count inscription was found in 1969, confirming the carving's
32 B.C. date. The lower edge of the stela is ruptured through the
middle of the glyphs that give the number and name of the day in the
sacred calendar.

The preoccupation of the early Mesoamericans with this
matter of eclipses can probably be detected in one of the oldest Long
Count inscriptions yet discovered, namely, Stela C from Tres Zapotes
found by Matthew Stirling in 1939. Although the controversy over
whether its missing baktun value was a "7" or an "8" was conclusively
settled with the discovery of the detached fragment in 1969, no real
attempt has been made to ascertain what its date actually recorded.
Its inscription reads "7.16.6.16.18" in the Long Count, which may be
transcribed into the Julian date of September 5, -31, or 32 B.C., if
we use the Goodman-Martínez-Thompson correlation value of 584,285. (Of
course, if we were to employ Thompson's "revised" value of 584,283
from 1935, the date would equate to September 3 instead.)

In an earlier paper (Malmström, 1992a), I advanced the
notion that, although Stela C was only discovered in 1939, the meaning
of its inscription may well be found in a monumental work of European
science first published in 1877. Known as Canon der Finsternisse, or
"Table of Eclipses," the volume is the work of Theodor von Oppolzer,
an Austrian count, and a team of his assistants, and constitutes a
catalog of over 8000 solar and 5200 lunar eclipses ranging in date
from 1208 B.C. to A.D. 2161. Although his 376 pages of calculations
and 160 maps charting the central paths of the solar eclipses were all
carried out by hand, their accuracy has only recently been reconfirmed
by modern researchers using computers (Meeus and Mucke, 1979).

Listed as event no. 2803 in Oppolzer's list of solar
eclipses is one whose path of centrality passed right over the Olmec
ceremonial center of Tres Zapotes at dawn on the morning of August 31,
32 B.C. A more frightening celestial event can scarcely be imagined,
for the sun rose out of the Gulf of Mexico totally black except for a
ring of light around its outer edges. Oppolzer described it as an
annular, or ringlike, eclipse, and subsequent calculations at the U.S.
Naval Observatory have revealed that the disk of the sun was 93
percent obscured (personal communication). Surely, a "day without a
sunrise" is not likely to have gone unrecorded by the Olmecs!

But, if this eclipse really is the same event as that
described by Oppolzer, why does its date not coincide with that which
he records? A number of possible explanations suggest themselves: (1)
perhaps the Olmecs waited either three or five days to record it,
depending on which correlation value of Thompson's one uses; (2)
perhaps the stone carver who engraved the stela made an error of
either three or five days in inscribing the date; or (3) perhaps the
Goodman-Martínez-Thompson correlation value is incorrect by three to
five days. Of course, there is also a fourth possibility -- namely,
that it had nothing whatsoever to do with the eclipse recorded by
Oppolzer, and that it was merely a strikingly close coincidence of
both geography and history.

The first hypothesis has no merit whatsoever, for if the
Olmecs consciously chose to put off recording the date, they would
certainly have no means for measuring eclipse cycles with any
precision. Any basis they might have had for maintaining accurate
records would thus largely have been vitiated.

The second hypothesis is credible; after all, "to err is
human." If this is the case, the inscription on Stela C is more likely
the result of an illiterate stone carver's mistake, however, than of a
priest's miscalculation. But, if so, which is the "easier" mistake to
make: to carve an extra three dots in the final, or kin, position --
equivalent to a three-day error -- or to carve an extra bar in the kin
position -- equivalent to a five-day error? Clearly, the mistaken
addition of one symbol -- the bar -- would have been more likely than
the mistaken addition of three symbols, so the discrepancy between
Oppolzer and the Olmecs would appear to have been a matter of five
days rather than three.

The third hypothesis -- that the GMT itself may be off by
three to five days -- is hardly likely, but the merits of the second
hypothesis are now reflected in the accuracy of the original Thompson
correlation value of 584,285. If that value is used, then the five-day
discrepancy between Oppolzer and the Olmecs is substantiated; if, on
the other hand, we use Thompson's "revised" value of 584,283, then the
lack of a correspondence between the two dates can no longer be
explained as an error, and we would probably have to abandon any
thought that the Olmecs were recording the eclipse after all. That, in
turn, would mean discarding both the close historical "coincidence"
between the two dates and the geographic "coincidence" of the passing
of the eclipse's central path directly over Tres Zapotes. In effect,
therefore, the inscription of Stela C, erroneous though it seems to
be, appears to confirm the accuracy of the original Thompson
correlation value between the Olmec calendar and our own.

In all fairness, however, it should be noted that there is
one further complication in this interpretation of Stela C's date. The
bottom edge of the inscription is broken just at the point where the
number and name of the day in the sacred almanac is recorded. If the
Long Count inscription itself is accurate, the day-number and -name
should be 6 Eznab, and this is the way the fragmentary glyph at the
bottom of the inscription is translated by most scholars. If the
numeral is indeed rendered by a dot and a bar, then there is no
question of its being a "6," but in keeping with my hypothesis that a
second bar had been mistakenly added to the inscription. Obviously, my
argument is not destroyed by such a reading but it is substantially
weakened, for to be consistent with my hypothesis, the day -number
should have been a " 1 " instead.

Of course, if the inscription is accurate as it stands, it
would then reopen the whole issue of what it was that the Olmecs were
actually recording on that intriguing occasion. If the blackened sun
at dawn was not noteworthy enough to take cognizance of, what other
event could have been so much more spectacular or important to them
that they took notice of it instead? Was it the occultation of Mars by
the sun that coincided very closely with the eclipse? Or might it have
been the occultation of the bright star Regulus (magnitude 1.35) by
the planet Venus that occurred during the following couple of nights?
Neither of these seem very likely, for surely both of these
astronomical events literally pale into insignificance when compared
to a total solar eclipse. Thus, we are left with the very real
possibility that nothing of note astronomically had prompted the
carving of the inscription of Stela C but that something even more
earthshaking had taken place in and around Tres Zapotes shortly after
the ominous eclipse had occurred. Thanks to its location in the
foothills of a volcanic region like the Tuxtlas, the most obvious
possibilities become either a monstrous earthquake or a devastating
eruption.

The point of this digression has been simply to illustrate
that, about the time that Edzná was coming into being, the
Mesoamericans appear to have begun recording eclipse data on their
stelae, possibly in the hope that through accurate timekeeping they
would eventually solve the puzzle of when these fearsome events would
recur. In the intellectual community of the Maya, therefore, this
problem must have been near the top of the agenda as Edzná was being
founded.

In the flat and featureless landscape of Yucatán, it had
been a rather simple matter to lay out a new city oriented to the
sunset on "the day the world began" because the "summer solstice + 52
days" formula had already been developed. Nonetheless, in a region
where the local topography presented no opportunities for calibration
against a natural landmark, the "gun-sight" alignment from the
courtyard of Cinco Pisos through the notch in the artificial horizon
to the top of the small pyramid constituted an ingenious solution to
the problem of the city's orientation. In the same way, the erection
of the tapered shaft surmounted by the stone disk had been an
ingenious solution to calibrating the passage of the zenithal sun. The
problem now at hand required some means of marking the moon's rising
and setting position along the circumference of the monotonously
uniform horizon that stretched out from Edzná in all directions.

Figure 37.

View of the western horizon as seen from the top of Cinco Pisos at
Edzná. The elongated mound across the plaza served as an artificial
horizon for a priest standing in the doorway of the courtyard,
allowing him to sight through the notch in the middle of the mound to
the summit of the pyramid immediately behind it to calibrate the
sunset on August 13 -- an azimuth of 285ş.5. The pyramid which
intersects the true horizon farther to the right, or northwest, is "La
Vieja," whose azimuth marks the northernmost stillstand of the moon
(i.e., 300ş).

No doubt the first task was to provide the priests with a
vantage point which allowed them a complete and unencumbered view of
the entire 360ş circuit of the horizon -- hence the need to erect what
was perhaps the highest pyramid yet constructed in Mesoamerica. When
completed, the aptly named Cinco Pisos ("Five Stories") towered more
than 40 m (130 ft) above the rocky platform on which it was sited,
becoming in the process a true landmark visible from 40-50 km (20-30
mi) away. Although Cinco Pisos is a Late Classic structure (i.e.,
built between A.D. 600 and 900), its situation at a focal point for
the ceremonial center's canal system (which dates to the Late
Preclassic period  -- 300 B.C. to A.D. 300) makes it seem likely that
an earlier structure previously occupied this critical position. In
fact, Matheny suggests that "perhaps the remains of the Late
Preclassic structure still exist within Cinco Pisos" (1983, 81). In
any case, from the top of this key structure one could look out in any
direction in a clear sight-line to the far horizon.

The real problem was to keep track of the places along the
horizon where the moon either rose or set. That Cinco Pisos faced
slightly to the northwest to begin with -- having been oriented along
with the rest of Edzná to an azimuth of 285ş.5 -- meant that the
moon's setting position was the one the priests chose to calibrate.
But with a horizon so distant and so featureless, one is tempted to
conclude that most of the initial record keeping may have been done by
marking lines in the appropriate directions on the top platform of
Cinco Pisos itself. Only after the observations had narrowed in on a
distinct enough point to erect some structure against the horizon at
the required azimuth would that have been done.

Conceptually, the Maya already had the model of the sun's
behavior on which to predicate their observations. Its northernmost
stopping point marked the summer solstice, which in turn established
the beginning date for the 52-day count which fixed "the day the world
began" -- i.e., August 13. If they could locate a similar position for
the moon -- its northernmost setting point -- perhaps that would allow
them to begin the count which would eventually reveal the secrets of
the eclipse cycle.

Deciding what the northernmost setting point of the moon
really was must have been a tedious and frequently altered judgment in
itself. Each time the moon reached what appeared to be an even more
extreme setting position, the count for the eclipse cycle would have
to be started again. One can well imagine that sometimes years of
patient counting and record keeping might have gone on before the moon
unexpectedly pushed its setting position even farther north along the
horizon and literally wiped out the whole exhaustive tally in one fell
swoop.

When this process actually began and how long it took to
yield any kind of meaningful results has to be pure conjecture. It is
probably safe to say that the idea for launching the count may already
have been formulated shortly after Edzná was founded, and may well
have been under way when the calendar reform fixing the new new year's
day was adopted. What we do know for certain is that the first time
that mention is made of the phase of the moon corresponding to a given
Long Count date is in an inscription dating from A.D . 357 (Coe, 1980,
159). This does not mean, of course, that the problem had been solved
by then, but only that from that time forward this seemingly important
fact was now to be regularly recorded along with the date itself.
Indeed, this may be evidence that the lunar cycle had not yet been
worked out, and that the priests felt the additional bit of
information regarding the phase of the moon might actually be useful
in finally establishing the cycle -- once they could examine the
records in retrospect.

This is not to say that the eclipse cycle could not have
been worked out within the first half century that the quest was
initiated. What the Maya were ultimately to learn was that the cycle
required a full 6797 days, or 18.61 years, to complete, so if they had
actually recognized the moon's northernmost stillstand on one
occasion, they would have had to count that long to find the moon once
more back at the same setting position. Of course, to confirm the
accuracy of their count would require the completion of at least one
more full cycle, so by this time more than 37 years would have
elapsed. Thus, to postulate even the minimum time span necessary for
such an achievement makes one appreciate the care and continuity which
the Maya priests exercised in keeping a constant, running tally over
the equivalent of more than an entire generation.

Although less than a half dozen of the original Maya
manuscripts appear to have escaped the flames of the fanatic
Spaniards, one of those that did survive is the so-called Dresden
Codex, which has subsequently been recognized as an elaborate eclipse
warning table. Thompson, among other scholars, assigns a
twelfth-century origin to it, but concedes that its three base dates
go back to the middle of the eighth century. (My suggestion that the
Stela C inscription may have involved a five-day error owing to a
stone carver's failure to understand the date he was carving finds an
ironic parallel in the Dresden Codex. Thompson's study of the
manuscript revealed that no fewer than 92 errors of transcription have
been made in recording its dates [1972, 115-116], but no one, least of
all Thompson, has ever suggested discounting the validity of the
tables on that account.)

The three base dates of the Dresden Codex occur in the
latter part of the year 755 and define two 15-day intervals. For this
reason, Maud Makemson suggested, in 1943, that they most likely
represent two solar eclipses bracketing a lunar eclipse (Makemson,
1943). While not disputing such an interpretation, Floyd Lounsbury,
writing in 1978, argues that if this is correct, then these dates must
have been arrived at by calculation rather than through observation,
because no such celestial events took place in Yucatán in that year
(Lounsbury, 1978, 816).

The three dates in question would equate to November 8,
November 23, and December 8, 755, if the original correlation value of
Thompson (namely, 584,285) is employed. (Naturally, if his "revised"
version is used, it would put each of these dates two days earlier.)
When the first of these dates was checked against a planetarium
programmed to duplicate celestial events as seen from Edzná on that
day, it was found that the sun and moon did in fact rise just eight
minutes apart on that morning over the Yucatán, with an angular
separation of less than 2ş.5. In other words, there had been a "near
miss" to a solar eclipse visible in the Maya area on that date.

For the second date, we once again employ the calculations
of Oppolzer (1887). Fifteen days after the near solar eclipse over the
Yucatán -- i.e., on November 23 -- he records a total lunar eclipse as
having taken place, but ironically, his data demonstrate that it was
visible only in the half of the world centered on the Indian
subcontinent. On the third date, again using Oppolzer as our source,
we find that a partial solar eclipse did indeed take place on December
8, 755, but its central path lay over the ocean between South Africa
and Antarctica, where probably not a single human being witnessed it.

From this data we can draw two very important conclusions.
First, by the year 755 the Maya had apparently worked out the motions
of the moon with such precision that they knew when an eclipse should
occur, but they still could not be sure if it actually would occur, in
the sense of being visible to them. Second, the original Thompson
correlation value of 584,285 is clearly the correct one, for an
acknowledged eclipse warning table such as the Dresden Codex could
certainly not have been based upon a foundation two days out of phase
with the realities of the celestial sphere.

Figure 38.

In this map view of Edzná, we see the features shown photographically
in Figure 37. The astronomical importance of Edzná may be gauged from
these facts: (1) only at its specific latitude could the beginning of
the Maya new year be calibrated, here with the assistance of a
remarkable gnomon; (2) the "day the world began" was commemorated in
the "gun-sight" orientation between the doorway of Cinco Pisos and the
small pyramid across the plaza; and (3) lunar cycles were measured by
using the line of sight between Cinco Pisos and "La Vieja" on the
northwestern horizon.

Although we cannot be certain when the Maya finally
succeeded in working out the lunar eclipse cycle, it would seem that
most of the basic "research" on the problem was carried out at Edzná.
Located some 300 m (1000 ft) to the northwest of Cinco Pisos is the
ruin of a lofty pyramid which Matheny has termed "La Vieja," or the
"Old One." The "La Vieja" complex appears to date to the Late Classic
period as well, but has not experienced the "urban renewal" from which
Cinco Pisos subsequently benefited (Matheny, 1983, 109). Even in its
dilapidated condition it is still high enough to intersect the horizon
as seen from the top of Cinco Pisos; indeed, it is the only manmade
construction which does so. This fact immediately prompted me to
measure its azimuth as seen from Edzná's commanding edifice, and the
value I obtained was 300ş. This means that the summit of the pyramid
lies exactly 5ş beyond the sun's northernmost setting position at the
summer solstice. Because the moon's orbit is just a hair over 5ş off
that of the sun, it seems very likely that the Northwest Pyramid, or
"La Vieja," had been erected as a horizon marker to commemorate the
moon's northernmost stillstand. Not only is "La Vieja" an eloquent
testimonial to the patience and accuracy of Maya "science," but
because of its specialized function, it is also probably worthy of
being designated as the oldest lunar observatory in the New World.
(Indeed, if Matheny's dating of "La Vieja" is accurate, then it is
apparent that the Maya had succeeded in measuring the interval between
lunar stillstand maxima at least by A.D. 300.)

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