Behind Astronomical Patterns


Kan B’ahlam as warrior, depicted on the Palenque Temple XVII Tablet

by Gerardo Aldana

One of the real challenges facing the interpretation of ancient astronomies—from non-academic ‘2012’ prophecies to the most traditional scholarship on the Dresden Codex Venus Table—is that presented by ‘patterns in randomness.’ In my opinion, the best explanation of the type of challenge historians of astronomy confront comes from the Ramsey Theory within the field of Combinatorial Mathematics. The problem arises from the relationship between the amount of data available, and the constraints imposed on it for a given interpretation. The example of Figure 1 shows that a large enough data set, with a fixed number of constraints, generates verifiable patterns whether they are intentional or not. In history of astronomy terms, if I have a large enough set of historical dates, some of them will correspond to astronomical events even though they weren’t so planned originally.

The famed Mayanist J. Eric S. Thompson (the villain in Michael Coe’s Breaking the Maya Code) confronted this situation in 1935 when reviewing the work of Hans Ludendorff for his early consideration of the calendar correlation question. Ludendorff pooled together a set of dates from Classic period hieroglyphic inscriptions, and then found a number of astronomical periods within them. Thompson, however, checked his math and found that many of Ludendorff’s dates were reconstructed incorrectly. Thompson’s further analysis showed that there were more “relevant” astronomical patterns among the incorrectly reconstructed dates, than among those that were accurately reconstructed. The point being that Ludendorff generated a large data set that was essentially random, relative to the patterns he found interesting. The constraints were sufficiently few (looking for celestial events) that patterns were generated simply resulting from Ramsey Theory, not because Mayan scribes did intentionally build them into these hieroglyphic inscriptions.

I have suggested in the past that this may be a more pervasive problem in modern interpretations of Mayan astronomy than most are willing to admit. So this was a major issue for me as I undertook the research behind The Apotheosis of Janaab’ Pakal: Science, History, and Religion at Classic Maya Palenque. I had become familiar with Thompson’s caveat relatively early, but I also ran into the issue head-on in my attempt to complete an essay assignment in graduate school. When I found planetary periods, therefore, built into intervals separating recorded historical events within a set of hieroglyphic texts from Palenque, I was very skeptical that they might be relevant. Had I simply stumbled upon a very elaborate pattern in randomness?

House C of the Palace at Palenque

Working within the History of Science, my nascent methodological instincts were to unpack the historical context of this apparent application of scientific knowledge. The result turned into a deep historical investigation into the ‘who, what, when, where, why and how’ behind the astronomical patterns—in other words, I chose to circumvent the purely mathematical question of whether the pattern existed or not for a concerted investigation into the people who purportedly created it.

The book is unique, then, as the first to go through each of these important factors with astronomy as its motivating question. The ‘who’ pointed to Kan B’ahlam, prince until assuming the throne of Palenque in his mid-fifties. As the son of a very successful ruler, he also found a very pointed interest in commemorating the magnitude of his father’s accomplishments. By multiple accounts, he was a cosmopolitan figure, probably visiting many of the major Classic Mayan cities (allies) of his day. The ‘who’ therefore pointed to a figure exposed to the various regional artistic and scientific expressions of his contemporaries, and one with the time to develop them according to his own interests before having to take over the duties of the throne from his elderly father.

The ‘where’ was straightforwardly important: Palenque sat close to the Usumacinta River, which was the major trade route for elite goods between the Maya region and Central Mexico (i.e. Teotihuacan and Monte Alban). Control over the river was tremendously important to all of Classic Mayan politics, putting Palenque in a critical position throughout its history. The ‘when’ not only correlated to a reasonable timeframe for this type of activity within Classic Mayan astronomical interests, but also a time of significant political pressure on Kan B’ahlam. The city of Palenque had suffered a massive military defeat shortly before Kan B’ahlam’s father, Janaab’ Pakal was enthroned. Janaab’ Pakal brought the city back to a position of prominence, but the city’s allies were still weak. Kan B’ahlam, therefore, had to demonstrate his leadership and his ability to maintain the position of prominence that his father had achieved. Part of this involved the construction project that housed the inscriptions carrying the astronomy in question.

Janaab’ Pakal on the Palenque Temple XXI Panel

The ‘what’ was a bit more complicated. My investigation showed that the presence of planetary periods within ‘mythistorical’ texts was made possible by the invention of a calendric tool by the eventual members of Kan B’ahlam’s royal court. Called the 819-Day Count by modern scholars, this mathematical convenience facilitated computations over vast periods of time into the past or future, relating them to the synodic periods of the visible planets. Kan B’ahlam and his scribes used the tool to place otherwise ambiguously dated mythological events into historical time. (Not unlike Johannes Kepler’s attempts to fix the birth of Christ using both calendric and astronomical evidence.) The resulting narrative connecting mythological figures to historical members of the Palenque dynasty was parsed into three texts, which were carved into stone tablets and hung in the three temples of the Cross Group.

In fact, housing them in these temples made it possible for Kan B’ahlam to construct the “same” message to various audiences at Palenque, private to public, educated to uneducated. The overall apotheosis of Janaab’ Pakal as the Maize God, and the three temples as houses of the dynasty’s patron deities were messages represented in architectural monuments, in sculpture and paintings outside and within those monuments, in hieroglyphic texts housed within those temples, and in an esoteric calendric language based on the 819-Day Count and embedded within those texts.

The overall historical case, then, argues against a pattern-in-randomness, rather the astronomical patterns were artifacts of a concerted intellectual effort with relevance to the city as a whole.

On the other hand, this did not completely erase my concerns with Ramsey Theory here. Instead, in reflecting upon Kan B’ahlam’s (and his successors’) use of this esoteric language, it seemed that the place of patterns in randomness had simply been shifted. When we consider the mythological events of interest to Kan B’ahlam’s court, for instance, we recognize that they did not necessarily have physical correlates to which an accuracy of reconstruction could be measured. When Kan B’ahlam was trying to place the birth date of one of his patron deities, he may simply have been appealing to pattern in randomness. In other words, the utility of his placement of that mythological event did not depend on its accuracy in the capturing of physical phenomena. As long as he was convinced that the pattern was viable, Kan B’ahlam could take it as such.

Now, we might very cynically write this off as ‘religion’, and let the whole matter go as an example of how far modern society has progressed since we no longer base our government on “astronumerology” or really anything like it. But I am not so sure that this is a viable stance to take.

Specifically, it occurs to me that Kan B’ahlam was not interested in creating history out of mythology for the sake of pure intellectual curiosity. This esoteric scientific endeavor was at the core of an economic intervention in his local kingdom (and quite possibly neighboring ones as well). To build the temples, carve the monuments, and decorate them, Kan B’ahlam would have been putting a large labor force to work. Moreover, the completion of these structures and their maintenance would have required feasting and festivals, which in turn meant more labor, more trade, more economic stimulus. We may want to dismiss Kan B’ahlam’s “astrology” as primitive religion and based on patterns in randomness, but we cannot dismiss the tangible and quantifiable impacts it had on the city.

Temple of the Cross, seen from the Palace at Palenque

On the one hand, this would seem to provide an opportunity to better appreciate Classic Mayan civilization. If we recognize and begin to excavate these relationships between religion and economic effect, we can better appreciate the complexity of the society they lived in. (Certainly it would be a welcome departure from, for example, depictions of mass hysteria at the sight of an eclipse.) On the other hand, it would seem disingenuous to not see some kind of correlate in modern society. And in fact, Donald MacKenzie has pointed at a similar issue when taking a Science Studies approach to modern economics.

In An Engine Not a Camera, MacKenzie argues that the role of economics as a science is not necessarily to provide accurate representations of what it calls economic activity. The importance of economic models is not in their accuracy, but in their ability to generate expectations that lead to changes in behavior, which are intended to have real material outcomes. Indeed, the recent credit-default-swaps economic modeling seems just as esoteric as Kan B’ahlam’s 819-Day Count. Statistician Dr. David Li came up with a way to capture in a formula an otherwise ambiguously defined risk. But that formula allowed others to apply it in their own ways to find quantitative justification for wild financial speculation. When it was all over, everyone wondered why people were buying Li’s solution in the first place… especially when he himself didn’t believe in it. A reasonable hypothesis is that they were interested in MacKenzie’s economic engine, and not in economics as a camera.

In the end, then, I wonder if this doesn’t amount to a “we might not be so different after all” story. Economists have long recognized the absurdity of some of the assumptions that are critical to the models that they develop, and so the patterns that they suggest are relevant. If indeed human economic activity (actual activity in the mall, on the street, at the local ATM machine) is simply too great a data set, and the constraints we impose are too few, then Ramsey Theory suggests that multiple patterns will result, and that many of them will be spurious. In this case, the utility of economics in modern society is not in its accuracy as a science, but in its production of authorities. Because certain economists or groups of economists utilize math and statistics in ways that produce provocative patterns, and because members of society are willing to believe that these patterns are meaningful, they will react accordingly—and self-fulfilling prophecies will increase the authority of those leading economists. Oddly enough, this strikes me as little different from the role of the ajk’uhuuntaak of Kan B’ahlam’s court.

All photographs are by the author.

About the Author:

Gerardo Aldana is an associate professor in the Department of Chicano Studies at the University of California, Santa Barbara. He is the author of Tying Headbands or Venus Appearing: New translations of k’al, the Dresden Codex Venus Pages and Classic period royal binding rituals (British Archaeological Reports International Series, in press) and The Maya Calendar Correlation Problem (in Calendars and Years II: Astronomy and Time in the Ancient and Medieval World Oxbow Books, Oxford, 2010). The Apotheosis of Janaab’ Pakal: Science, History, and Religion at Classic Maya Palenque was first published in 2007 (University Press of Colorado) and then released in paperback in 2010.

Gerardo’s research takes a history of science approach to the hieroglyphic and architectural records of astronomy in Precontact Mayan civilizations. Currently his focus is on the Dresden Codex Venus Table and its relationship to K’ak’ U Pakal K’awiil, a hieroglyphically documented ruler of Chich’en Itza.