Indiana University

Maya Cosmology and Philosophy of Science

*DRAFT*

October 6, 1997

By

Charles R. Twardy

130 Goodbody Hall, IU

Bloomington, IN 47401

812/330-8618
TABLE OF CONTENTS

INTRODUCTION 1

MAYA ASTRONOMY AND COSMOLOGY 4

Written Record: the Dresden Codex 4

The Venus Table 5

The Lunar and Eclipse Almanacs 7

Ethnographic and Epigraphic Sources 8

Architectural Alignments 10

Solstice and equinox alignments 10

Venus alignments 12

The Pecked Cross and the 17̊ family 12

Summary 14

BUT IS IT SCIENCE? 16

Definitions in the archaeoastronomy literature 16

A Historian's View 21

Kuhnian Science 23

Applying Kuhn 25

On Beyond Kuhn 27

If not science, then what? 30

IMPLICATIONS FOR PHILOSOPHY OF SCIENCE 33

WORKS CITED 36
INTRODUCTION

Part of our fascination with the Maya can be attributed to the fact that they were literate . . . that is, the Classic Maya possessed a visible language that consisted of letters and a grammar, and one of the products of their literacy was the book. (Aveni 1992b, p.3)

That the Maya learned so much about the sky is interesting, but not entirely unusual for an established agricultural society.  Other ancient societies such as Babylonia, Egypt, China, India, and of course Greece accomplished similar feats, but the Maya were separated from the old world and its skywatching traditions by two oceans, and so present a fortuitous natural experiment in the development of knowledge. The  independent creation of an apparently scientific tradition reveals some commonalities in astronomical understanding, but also outlines the historical contingency of the forms in which good theories about celestial phenomena may come.

The Maya were not on the road to modern astronomy, and Maya astronomy could not be considered scientific now.  However, historians of science argue persuasively for the contingency of our own scientific theories, so the current borders of science are not a useful way of demarcating scientific from nonscientific past theories.  Phrenology was not non-science in the nineteenth century; it was just wrong science.  Taking account of this, a different task for philosophers of science is to articulate a broader definition of science which is useful to the historian or anthropologist.  Twenty or thirty years ago it was possible to see Newton lying dormant in every megalith, but now it is generally acknowledged that other cultures were not irrevocably on the road to a Scientific Revolution, and that we were wrong to have expected such.

The question is, what were the skywatching Maya doing, and in what ways was that scientific.  For this we need a definition, and too many authors-perhaps reacting to early archaeoastronomical enthusiasm-have been too quick to retreat to a modernist or Hellenocentric definition.  Accordingly, Mayanist Floyd Lounsbury (1978) writing a synopsis of Maya astronomy for the Dictionary of Scientific Biography said it clearly was not science.  Another Mesoamerican scholar, Michael Coe (1993:173) admires the “considerable body of empirically derived information about the natural world,” but cautions that “science in the modern sense was not present.”  Well, of course not, but was science in some other sense present?  The central figure in Mesoamerican astronomy is Anthony Aveni, who has repeatedly raised but not quite answered this question, asserting only that the Maya were not doing modern astronomy but something more ritualistic, which nevertheless should not be discounted as not-science merely because it does not fit our expectations of science(see for example, 1980:220, 319-320 and ,1989 #414).

Stephen McCluskey (1987) noted and deplored this field-wide reluctance to apply the label of  “science” to non-western or “primitive” astronomies.  He thought this reluctance stemmed from the obvious (to us) lack of separation between traditional astronomies and their associated cultures and religions.  Using Kuhn (1970), Hanson (1958), and Shapin (1982), he argued that this demarcation between science and non-science was based on a false model of science, and was therefore an inadequate reason to demarcate traditional astronomies from our own.

McCluskey offered a methodological solution to overcome this cultural barrier: start by assuming that traditional people were practicing science and analyze their practices as such.  This approach has its merits in counteracting a too-facile separation of “traditional” and “modern” merely because it is easier to see another culture's rituals than our own.  However, it leaves the basic outline of science undefined.  More recently he has offered a nuanced definition which attempts to characterize science as a culturally-seated attempt to understand those parts of the world which are significant for that culture.  I will suggest a small modification of this definition which is more readily applicable to our modern demarcations, and which makes explicit both systematicity and explanation, which I suspect were implicit in McCluskey's “intelligible.”

The reason for this work is not the modification of McCluskey's definition.  The point is show why we need this kind of a broad definition of science.  The one I construct serves well to outline what we are missing in our understanding of the scientific nature of Maya cosmology, and what kinds of questions anthropologists and historians need to consider when evaluating other non-modern or non-Greek knowledge.  It also shows that this distinction is still possible in a relativized framework.  At issue are the sometimes conflicting ideas of science as systematized knowledge, skeptical inquiry, public exchange, observational practice, methodology, and technical proficiency or expertise.  In the spirit of McCluskey's papers I hope to have shown why fixating on one of these is precisely the wrong way to go about answering the question.  The only right way is to attempt to become anthropologists of intellectual history and see how the knowledge system we are reconstructing served in the society in which it developed.  Anything else merely declares in complicated ways the obvious fact that ancient cultures did not have the same view of the world that we now do.
MAYA ASTRONOMY AND COSMOLOGY

 

While we have more Babylonian clay tablets than scholars have had time to read, we have only four Maya hieroglyphic codices, and some few texts transcribed after the Conquest.  Archaeological and ethnographic studies provide much of what we know.  All of these sources introduce their own problems of interpretation, and it seems that scholars have of necessity been guided by a consilience of inductions between the different lines of evidence.  Such a consilience does not guarantee truth, but if the skeptical tradition is alive and well it is our best chance.  Keeping this difficulties in mind, we review the highlights of contributions from each field.

Written Record: the Dresden Codex

The Dresden Codex is the most famous of the surviving Maya hieroglyphic books, and by far the most thoroughly studied.  The other principal codices are the Paris and Madrid codices, likewise named for the cities in which they were rediscovered long after the conquistadores had destroyed any extant copies in the New World.  The codices consist of many tables which appear to be something like illustrated almanacs.  An exemplary table is the Venus almanac in the Dresden Codex.  Scholars originally associated this set of six pages with Venus because of repeated appearances of that planet's synodic period, 584 days.  Further work has made this association almost certain.

The Venus Table

Mechanically, the almanac functions as a Venus calendar.  The first page gives periodic corrections and entry points for the table proper, which continues on the left half of each of the next five pages.  Each half-page (four columns) is one complete Venus cycle, betrayed by the totals at the bottom (rows 26 and 19).  Starting at 0 and reading across, alternating between these two rows, the simple arithmetic reads:  

  0 + 236 = 236; + 90 = 326; + 250 = 576; + 8 = 584,  

which is Venus' synodic period.  If we look up to the first row, we find that, if we had started our day 0 on 1 Ahau, then we would now be on 13 K'an.  Moving to the next page, we repeat:  

584 + 236 = 820; + 90 = 910; + 250 = 1160; + 8 = 1168,  

putting us on the date 12 Lamat.  The process is continued through the fifth page, for a total of 2,920 days, or exactly 8 years of 365 days.  Also, since 2,920 is divisible by 20, the number of named days in the ritual calendar of 260 days, we return to the same day with which we began (in this case, Cib).  This allows us to re-enter the table on line two.  This continues through line thirteen which, after 2,92013 = 37,960 days = 146 cycles of 260 = 104 cycles of 365 = 65 Venus years, returns to 1 Ahau, allowing us to begin the table once more, after referring to the first page to apply the appropriate correction.

These corrections are required to counter a small drift introduced by the 584-day approximation (the actual average period is 583.92 days).  They are applied in such a way as to keep the predictions aligned with the appropriate days in the ritual calendar.  In particular, the Maya kept the heliacal risings of Venus on 1 Ahau dates.  This is similar to leap-year intercalations, and is on average an effective way to align the calendar with one of the cycles it mimics.

There remain some uncorrected discrepancies.  Any particular Venus year might not be closest to 584 days.

The synodic period varies annually, but has the same integer approximation every fifth year; the five-year cycle of Venus years repeats in a symmetrical sequence, 587, 583, 580, 583, 587. Thus, each of the [five] pages could have been assigned a Venus year of 580, 583, or 587 days and thereby accurately reflected the variations in the Venus cycle. (Justeson 1989)

Additionally, within the Maya four-phase division of this cycle, only the 8-day disappearance is close to reality.  In particular, Venus is actually visible for equal periods (263 days) as morning and evening star, and its “first” disappearance averages 50 days.  The overall accuracy is much better than this,  so researchers have assumed the errors were intentional.  It seems that they were introduced to keep Venus in phase with the 260-day calendar and perhaps also with the lunar cycles, and there is evidence which suggests their efficiency in so doing (Aveni 1980:89; 1992a).  What we should note in passing is that this means the Maya who wrote the Dresden codex had developed theoretical knowledge which went beyond their empirical observations.

Having such a calendar, the Maya could predict future planetary events, and indeed the almanacs appear to have provided for prognostications and divinations as well.  Aveni (Aveni 1980:184), following Thompson, thought the Venus almanac likely was constructed “to serve as a warning table for the apparitions of Venus,” so that ritually appropriate prophylactic or evasive measures could be initiated to mitigate the detrimental effects. This of course has strong parallels with the Babylonian tradition, and is also supported by various ethnohistorical accounts testifying to the unlucky nature of Venus' heliacal risings (see excerpts in Aveni 1980:186; Thompson 1972:64-71 and).

The Lunar and Eclipse Almanacs

Immediately following the Venus table is a lunar eclipse table, which functions in a similar manner.  Justeson (Justeson 1989) showed that “the recovery of good eclipse cycles was imposed on the Maya astrologer” as soon as he commensurated the 260-day calendar with the lunar cycle.   In particular, “the eclipse cycle of 405 lunar months in the Dresden Codex emerges as the shortest to rationalize the lunar synodic month with the sacred round to within less than a day.”  A better fit required almost twelve times longer.

This system apparently dates back to Palenque inscriptions, whose system interleaved 43 thirty-day months with 38 twenty-nine-day months (yielding an average of 29.53086 days per lunation, versus the modern value of 23.53059).  By stacking five such blocks of 81 months together they found that 405 months equaled 11,960 days, or 46 calendar rounds, providing the necessary commensuration.  This interval also appears in the Venus tables, and the Maya may have used Venus to help predict eclipses, or vice versa (Aveni 1992a).  A similar cycle at Copan cycle used 79 thirty-day months to 70 twenty-nine-day months, slightly less accurate than the Palenque formula but still very useful for predicting eclipse intervals (again, see Justeson 1989).

Another table in the Codex appears to be linked to eclipses as well.  Analyzing pages 61-69, Bricker and Bricker (1989) found evidence that the Maya also tracked eclipses with a tropical calendar.  This table needed far more frequent correction in order to prevent drift, but these corrections seem to have shown similar concern for maintaining relations in the ritual calendar.  At the same conference, Michael Closs (1989) augmented these arithmetical analyses with linguistic and ethnographic studies to try to understand how eclipses were perceived by the ancient Maya.

Ethnographic and Epigraphic Sources

In several Conquest-era documents Europeans wrote that the Maya considered eclipses to be caused by animals eating the sun or moon (Closs 1989).  The animals were jaguars in some accounts; in others they were versions of the sizable ants feared for their crop destruction.  According to these sources, eclipses were dreaded, for “should the sun or moon fail to reappear, then all the furniture and other objects with which people are surrounded would be changed into devils or beasts that would devour all living things,” an account reminiscent of the demise of the third creation in the Popol Vuh.  Those observed made a great deal of noise, or shot weapons at the heavenly body in question, presumably in order to defend it from the attacking animal or animals.  According to Closs, some Yucatec Maya phrases for “eclipse” translate literally as “‛to be bitten the moon [or sun].'”  The phrase itself might be only an apt metaphor, but the ethnohistorical documents indicate that some Maya at least interpreted it more literally.

Closs thought these stories were similar enough to indicate a common origin, and argued that originally Venus was the eclipse agent.  Re-analyzing the Dresden Codex and some carved glyphs, he found similarities between the Venus “diving god” glyph and the stories of animals descending to the earth during eclipses to devour humanity, as well as some other parallels.  According to Closs, Venus played the role of a devouring celestial serpent, and lord of the underworld.  The mapping is not certain, and we shall see next that the celestial serpent has also been identified with the ecliptic, but there is some reason to believe that there were ties between the Venus and eclipse cycles, and Closs has at least helped to establish a central role for Venus in Maya cosmology.

A more predominantly ethnographic account is found in (Sosa 1986) who tried to map the current beliefs of the Maya of Chamula onto the ancient written sources.  He admits that the evidence for a continuity of tradition in Chamula is “neither conclusive nor extensive”-a standard difficulty for ethnographies-but he thinks their layered-domes cosmology is more likely than a flat-layers concept, and perhaps the account is useful as a possible cosmological scheme in which to set the Dresden almanacs.  The Chamula consider the earth to be “an island and the middle of three sections. The sky and the Underworld make up the remainder. Chamula is considered the center of this entire cosmological system and of the island earth as well.”  The sky itself is made of three concentric domes; humans see only the first.  This dome shows projections of the occupants in the upper layers, the celestial objects which are associated with deities, now mostly Christianized.

Sosa reported that the “Chamula solar path is conceived of as a celestial band, which is created by solar motion,” a notion he said was supported by a myth where Venus is a (Chamula) servant girl who “sweeps the sun's path.”  Returning to ethnohistoric sources, Sosa reminded us that in the Chilam Balam of Mani, the several planets “are described as existing in six particular ‛canopies of heaven.'”

Sosa also identified the sky serpent, which has a mouth on each horizon, with the ecliptic.  The serpent eats planets in the east and disgorges them in the west.  The path they travel is the body of the serpent, and Sosa noted that  “among the Chorti, such monsters are known as Chicchan. Both the Chol chan and the Yucatec caan share the meanings of sky and serpent.”

More recent work (Freidel, et al. 1993; Tedlock and Tedlock 1993), has attempted to unify Maya cosmology using the Popol Vuh, the inscriptions especially at Palenque and Copan, the codices, and modern daykeeping practices among highland Maya communities.  The Tedlocks have suggested that the main players in the Popol Vuh are constellations or planets, and have correlated the names and course of events in the Popol Vuh with dates of planetary phenomena.  Freidel and Schele continued this work to show further correspondences between scenes in inscriptions and codices with the yearly celestial movements of the Milky Way through the sky.  The upshot of this work has been to find that sky lore is closely intertwined with much of the surviving written record, and to begin to show the metaphors and images used to describe celestial phenomena.

Architectural Alignments

Building alignments are not by themselves conclusive evidence of celestial knowledge or interest.  It is too easy to see alignments where there are none, or to misinterpret those alignments we know.  One can also measure incorrectly.  Repeated alignments, large-scale alignments, and alignments to an object or event independently known to be significant are more trustworthy.  We must be guided by converging evidence (Aveni and Hotaling 1994).

Solstice and equinox alignments

General east-west alignments abound in modern and ancient civilizations.  Alignments which pick out particular horizon-based events like a solstice or an equinox are still common, but less so.  Such events are important agricultural and calendrical markers, and may have more significance in some cultures.  The most famous Maya examples of equinoctial alignments include the Toltec-influenced Castillo at Chichen-Itza, and those arrangements like Group E at Uaxactun.  Aveni and Hartung (Aveni and Hartung 1989) reexamined the namesake group and similar setups found throughout the Maya region.  Based on a 1978 survey they concluded that the group at Uaxactun was a “functioning (though not precise) solstice observatory,” but declined to say it was an equinoctial one because of the “ruined state of the buildings.”

This Group E structure consists of three temples in a row on a North-South mound, and a fourth temple or structure due West from this line of temples.  At Uaxactun Aveni and Hortung found that from a likely observation point on the Western temple's staircase the three temples on the Eastern mound aligned to within one solar diameter of the June solstice, the equinox, and the December solstice respectively.  The basic form of the group E Structures appears at several other Mayan sites, but the authors thought that most of the other structures were not aligned well enough to have also functioned as solar observatories.  This led them to suggest that perhaps, “most E-complexes might have been non-functioning copies of the astronomically operational archetype at Uaxactun,” a possible but not compelling interpretation.  “Functional” operates in a strange sense here.  In order to build the temples, the inhabitants already knew where the solstices were, and presumably when.  So the good alignments indicate to us that this was known, but not how; even the best aligned structures need not have been an “observatory” so much as a “participatory.”

Aveni and Hartung themselves concluded that at many of the complexes, “More attention had been given to ritual and ceremony and less care had been paid to the rigid and rigorous sort of calendric concern derived from the orientation scheme we find at Uaxactun.” My point is that such calendrics may indeed have been present at all sites regardless of the possibly “ceremonial” architecture, or indeed, at none of them.  It is probably true however, that “the widespread occurrence of the group E style in the Peten may be taken as a general indication of social cohesion in that area and the (probably) earlier Cenote Group E variance may signal the onset of that reunification process....”  At the time there was no solid chronology of the Group E-type complexes (Aveni and Hartung 1989), and although (Weaver 1993) agreed that the complexes at Tikal and Cenote probably predated that at Uaxactun, I am unaware of further developments.

Venus alignments

Knowing that Venus played an important role in Maya cosmology, alignments to this planet in particular are among the more persuasive candidates for planned astronomical alignment.  Aveni's definitive, and overly-thorough analysis of the Caracol at Chichen Itza (repeated in1980) makes a strong case.  The Caracol has three levels, constructed at different times.  All three levels, which are not aligned to each other, have features with a common 27½̊ alignment, which matches the northernmost setting position of the planet Venus on its eight-year cycle.   One of these is a window in the upper level.  Another window points to the southerly extreme of this cycle.

Built about the same time as the Caracol, the rectangular Palace of the Governor at Uxmal is decorated with the glyphs generally thought to represent Venus.  A line perpendicular to the face through a platform in the courtyard intersects the principal pyramid at Cetzuk on the horizon several kilometers away.  This line of sight also corresponded to the southernmost rising position of Venus in its eight-year cycle. In addition, Temple 22 at Copan which has been called a Venus temple because of some of its decorative glyphs, may also show Venus alignments, although this is less certain.

The Pecked Cross and the 17̊ family

Aveni, Hartung, and Buckingham (1978) studied 29 pecked-cross petroglyphs found predominantly around Teotihuacan but also in and near the Early Classic Maya site of Uaxactun.  The petroglyph they measured at Uaxactun had an alignment of 17.5̊, which aligns with a 17̊ axis from Teotihuacan's central pecked-cross to another cross visible on a rock outcropping 7 km. to the northeast.  This latter axis is also within ½̊ of perpendicular to the east-west axis of Teotihuacan.  Aveni and Hortung also claimed the petroglyph aligned with the Uaxactun grid, though this is unclear.  These two sites are examples of what Aveni has called the “17̊ family of orientations,” a cluster of about 20 sites (out of 90 surveyed) whose principal alignments fall between 15̊ and 20̊ east of north(Aveni 1980, p.237).  The 1978 article suggests that other crosses stem from Teotihuacan and “must be related to the propagation of the grid plan of that city.”  In this paper's later development as a chapter in Skywatchers, Aveni presented a convincing case for an alignment to the setting point of the Pleides around the time of construction.  However, because of precession the Pleides would not have worked for later sites, leading Aveni to suggest that, “the axes of Tula and other members of the 17̊ group [were] nonfunctional imitations following the tradition established by Teotihuacan architects and astronomers,” a familiar but again uncompelling argument.

Peeler and Winter (1988) disagreed with that argument strategy and sought to explain the proliferation of the 17̊ family and another cluster of alignments near 8̊ west of north, suggesting both were manifestations of a “November 10 orientation,” sometimes solar, sometimes stellar, which had been established long before Teotihuacan.   

To summarize then: in the Olmec heartland at 1000 B.C. the November 10/11 date is: a) that of the rising and setting opposite the sun of the star Alnilam, which set along one standard architectural alignment; b) the day the sun rose at 108.5̊, another standard architectural alignment; c) the day (±3 days) transits of Venus could occur; d) the end of a 260-day count permitting more accurate prediction of the timing of these transits; and e) the day the sun passes directly overhead.  At other latitudes, only the day of the solar zenith passage would differ.

 

The authors then presented iconographic evidence to support their alignment hypothesis.  A symbol they read as the belt of Orion seems to have been associated with the rainy season, and perhaps Venus as well.  Part of their argument was to establish “the existence among the Olmec and their contemporaries of an already complex calendar very similar to that found later throughout Mesoamerica,” but it also establishes plausible alignments and motivations for those alignments at non-Teotihuacan sites (and much earlier ones at that).  On their argument, it remains to be shown why November 10 was such a significant date, and how well it was maintained into the Early Classic period.

Summary

The ancient Maya had a keen awareness of the celestial cycles and manifested care in tracking them and maintaining this knowledge.  Like the Babylonians, they seem to have used this knowledge for planning seasonal events and for divination.  Unlike Babylonia, we do not have full records indicating what the rulers were to do to avoid a forecast disaster, or what each kind of planetary event meant, although there is evidence that these sorts of concerns were relevant. Maya creation stories seem to encode celestial knowledge and to weave it together with their calendar, which was the primary tool for understanding the rhythms of the heavens.  The Maya were very attentive to commensurations of planetary cycles with the 260-day sacred round, and with each other.  The correction procedures in the codices keep important events falling on the same kind of days in the calendar, deliberately allowing observations to drift from theory until such an appropriate correction could be made.

Ethnohistorical and ethnographic accounts at least partially corroborate our interpretations of the remaining written sources, but the Conquest-era accounts of fearful and late reactions to eclipses hint that if some Classic Maya priests could predict eclipses, that practice may not have been preserved.  Of course, foreknowledge does not necessarily remove fear, knowledge possessed by elites is not necessarily transferred to commoners, and the European missionaries were not objective observers, but it remains possible that either this astronomical knowledge had not survived entirely intact, or we have misinterpreted its use and intent.  We should also remember that what was known in some regions may not have been known or valued everywhere.

BUT IS IT SCIENCE?

Definitions in the archaeoastronomy literature

In Skywatchers (219-221) Aveni noted that both ancient and modern astronomy “seek to attain a predictive advantage over nature which affords a measure of control over the environment,” or presumably, control over human behavior in anticipation of the environment.  This similarity in goals does not however, constitute a similarity in methods or thought.  The Maya employed a much simpler technology and a vastly different cosmology.  Aveni, an astronomer by training, wrote:

The scientists' notion of explanation through prediction, their scientific curiosity, and their will to harness the forces of nature possess no analogs in native American systems of thought.  Our study of their way teaches us that the Maya no more cared about what the moon was made of than we care about the planting of our crops to coincide with the heliacal rising of the Pleides (Aveni 1980, p.320).

Yet for those “compelled to give an answer to the scientific question,” he stated,

the Maya could have developed their astronomical warning tables in the codices only through naked-eye observational techniques, oft encoded in the architecture and passing through successive stages of refinement over long periods of time.  We must view their calendar as a predictive device, the accuracy of which improves with time as better observations are made.  In this sense one may accommodate Aaboe's definition of scientific astronomy....( p.320)

Historian of astronomy A. Aaboe had written, “a scientific astronomical theory is then a mathematical description of celestial phenomena capable of yielding numerical predictions that can be tested against observations.” Although Aaboe considered Maya astronomy an example of advanced prescientific astronomy, the various almanacs in the Dresden codex clearly fit his definition, but this is because it is a nonspecific definition that completely ignores cultural context.

In World Archaeoastronomy, Aveni noted that, “curiously, this quality of being scientific is rarely defined in discussions regarding cultural contrast....”  Nine years after Skywatchers, he bluntly called Aaboe's model, “ethnocentric.”  He also invoked a paper by Stephen McCluskey which surveyed the usual reasons for separating scientific and “primitive” astronomy.  (Aaboe 1974; Aveni 1989; McCluskey 1987)  McCluskey wrote that some of these reasons were:

[the] static or unchanging nature of primitive astronomy, its lack of openness to theoretical alternatives, the absence of any notion of progress, the absence of a separation of primitive astronomy from its social context and the failure of a given culture to pursue knowledge for its own sake.

He considered these to be too ethnocentric, and, following Kuhn, Hanson, and Shapin, he argued that these criteria were a poor description of science in the first place.

McCluskey there proposed the broad but contextual definition, “astronomy is the means by which societies seek to make their observations of the heavens intelligible.”  Western astronomy did not develop in the absence of social and historical events any more than Hopi or Maya astronomy did, and this definition would include much more of the actual context which surrounded Greco-Babylonian skywatching, to say nothing of Renaissance astrology.  This banishes the simplistic view that “high precision is equated with scientific and low precision with ritualistic behavior,” but it hangs a great deal of weight on the undefined terms “observations” and “intelligible.”  Unless those terms are in some way restricted, the definition appears completely unable to separate speculation which is based on or leads to knowledge of the natural world, and that which is not.  In particular, the absence of prediction and mathematical formulations seem a strong weakness, since evidence of these is what has led us to recognize apparently astronomical inscriptions as such.

Historian of ancient science David Pingree has lashed out against a distortion he has dubbed “Hellenophilia,” an intoxication with Greek culture which leads historians to define science as Greek science to the exclusion of all else (Pingree 1983).  He argued that “astral omens, astrology, magic, medicine, and law . . . were or are sciences within the contexts of the cultures in which they once flourished or now are practiced.”  What then is the proper definition of science “for the historian of science?”  For Pingree, “science is a systematic explanation of perceived or imaginary phenomena, or else is based on such an explanation.”  This rightly rejects standards of truthfulness, which would in time likely exclude everything, and it also avoids privileging current methodology.  And although it usefully separates science into actions and bodies of knowledge, its inclusion of “imaginary phenomena,” though well-motivated, removes any requirement for interobserver consensus.  More seriously, the definition is not contextual enough.  As broad as it is, it ought to include our own culture, but while both religion and astrology offer such systematic explanations, they are not both counted as science by canonical sources.  This is a major failing, but we take from Pingree's account his persuasive and well-supported argument that alternative methodologies have also given good results, and the corollary that a definition of science ought to include more than Greek science.

In a forthcoming piece, McCluskey attempts a stricter, more explicitly social definition.  For him science is:

(1) Any attempt by the members of a community to establish a framework that makes their observations of nature intelligible. (2) a body of socially accepted knowledge about nature, including both accepted observations of nature and the frameworks used to make those observations intelligible. (3) a body of exemplary practices and techniques for observing nature and interpreting such observations.

If we map McCluskey's intelligible frameworks onto Pingree's explanations, then McCluskey has divided science into, (1) an act which tries to produce a body of knowledge, (2) a body of possibly explanatory knowledge resulting from the act, and (3) a methodology for acting.  But part (1) is even broader than Pingree's definition, no longer requiring systematicity, and it would still fail for our society, since not all such attempts count as science.  Somehow (1) must be more strongly tied to (2) and (3).  Perhaps this is more along the lines we need:

science: (a) a systematic body of socially accepted knowledge about nature necessarily including both accepted observations and explanations of those observations, (b) a set of exemplary (and therefore socially-accepted) practices and techniques for observing nature and interpreting such observations, and (c) the action of following b in order to produce and test a.

On this account, science is both reliable knowledge about the world, and the accepted methods for finding it.  It is relativized to particular cultures, so that Babylonian astrology-astronomy is included, but modern astrology is not because it is not accepted by its society, although we could find a subculture in which astrology is science.  This definition also leaves open the possibility that any given practice, approach, or methodology could in the future cross the line of demarcation in either direction, in accordance with what historians and sociologists have observed.  Philosopher Richard Rorty has argued that such a socially-based definition is the best that can be hoped for, because science itself is not a “natural kind” {Rorty, 1990?}.

Aveni <forthcoming> has recently agreed with this point of view: “to a considerable degree science can be thought of . . . as a social construct rather than a self contained entity that has evolved independent of societal influence.”  This view motivates McCluskey's suggestion that anthropologists and archaeologists start with the assumption that other astronomies are also science.  This way, he contended, we might learn that ritual was an important way to pass on knowledge about the world, rather than an obstruction to its development.  Indeed, ritual is an ideal candidate for the preservation of crucial knowledge, and McCluskey's use of Kuhnian exemplars points to a parallel in the transmission of modern scientific know-how, if not knowledge.  In earlier works Aveni at least implicitly endorsed the idea of indigenous science.  When he was not directly addressing the question, he spoke of improving our “understanding of Maya science,” or declared, “our study has sought to explore the nature of Maya exact science....”  (Aveni and Hotaling 1994) More explicitly, in the introduction to The Sky in Mayan Literature (Aveni 1992b), he concluded:

When we penetrate the cosmological meaning of the codices, we learn that here were people quite like ourselves who believed in a universe that could be conceived and described in mathematical terms.... Though the ends served by such predictions were founded upon religious and astrological beliefs, certain elements of the whole process begin to sound very much like what we read in the history of science in Western culture.  But then, if we are willing to look back a few centuries, we discover that our own inquiry into nature possessed a similar foundation.

The early archaeoastronomers saw the roots of modern astronomy everywhere they looked, often ignoring an anthropological point of view.  Now we have a richer history of science which, partly informed by anthropology, sees some of the nonmodern aspects of old world science and astronomy.   Nevertheless, there are valid objections the whole project of looking for science outside its usual history.

A Historian's View

Historian of astronomy Owen Gingerich stated the conservative position in his paper in World Archaeoastronomy:

Modern science is a uniquely Western phenomenon that has arisen only once on our planet.   As a historian of Renaissance astronomy, I find that one of the most fascinating questions is: to what extent has this flowering of modern, predictive science been inevitable? (Gingerich 1986, p.38)

Gingerich argued for the historical contingency of science, and against the scientistic determinism which characterized earlier megalith-measurers who were too eager to see nascent physics everywhere.  Seen historically,

we begin to recognize the Principia as a unique creative achievement; not only would [the] words and ordering be otherwise if another scientist had attacked the problems of mechanics, but even the physical concepts would have differed.

As Hamiltonian mechanics demonstrated, force and inertia are not necessary for physics.  It follows that all science need not look quite like a particular portion of the history of Western science, since that was just as contingent as other history.  In fact Western science may have been too contingent, an unstable region of idea space we should expect no others to have traveled.  Yet even if this is true, as I think likely, it does not imply that other cultures were not scientific in the senses explored in the previous section.  Rather, it tempers our expectations of what that kind of science entails.

Gingerich saw two parts to science, the predictive and the explanatory-understanding.  Early societies did not suffer in explanation or understanding, but they did in prediction.

Yet what seems different about the modern scientific world view is the sheer complexity of the connections between its explanative and predictive aspects, as well as the continual reforming of the theoretical structure in the light of observation and experiment.  It is these aspects that characterize modern science and set it qualitatively apart from the rudimentary systems of archaeo- and ethnoastronomy.

If this is not yet clear enough, he added, “paradoxically, archaeoastronomy may have more to say about the non-origin of science than about its origins, and that to look for the origins of science here may lead to misleading or anachronistic conclusions.”  Accurate calendars abound in many cultures, but need not imply accurate nor frequent observations.  They do require some numeracy, but “this does not mean that the typical member of the group has much appreciation of its numerical or observational basis.”  Indeed, as we have seen, the users of the Dresden codex need not have known how to extend the system, just as moderns can use ephemerides, almanacs and calendars without being able to precess star positions, derive planetary orbits, or find the solstices.

According to Gingerich, then, we should not go in expecting to find something recognizable as science, but whatever we do find will add “grist for the mill” of history, because “the differences and even the lack of change may help clarify why changes happened in far different contexts.”    Archaeoastronomy “transcends the history of science, because it studies not only the roots of science but also how people have coped with the natural world in ways that do not necessarily lead to science.”(Gingerich 1986)

Gingerich's thesis uses a rather narrow definition of science as a practice resembling Greek or later European science, and within that definition it makes a good argument.  It is good to remind us of the contingency of intellectual history, and the implication that similar conceptual systems are unlikely to emerge independently.  But that is not the question McCluskey and other anthropologists have asked.  Rather, knowing from philosophy of science that a modernist, positivist account of science fails, they conclude the definition of science itself must (a) broaden, and (b) relativize to culture, at least somewhat.  Therefore, the unique, contingent, and very different practices of the Maya may nevertheless meet a broader definition of science.

Kuhnian Science

The Standard View as advanced by Robert Merton was an idealistic view of science.  Roughly, true science proceeds, or ought to proceed, in the manner described in science textbooks: the scientist, with impartial skepticism, reserves all judgment and theorizing until facts, through judicious experimentation, determine the outcome.  Although individual scientists may fall short of this ideal due to human limitations, science advances to the degree that its “norms” are followed.  Where it makes mistakes, these can be explained by showing how the scientist deviated from the norms.

Historian of science Thomas Kuhn noted that many of the advances in science have been unjustifiable according to these norms, vindicated only in retrospect.  If scientists were to attempt strictly to follow Merton's norms, it seemed science would look nothing like it presently does, and would become useless as a description of the world.  Although stated imprecisely enough to allow accusations of a “mob-psychology” view of science, Kuhn's thesis, as clarified by later writing, was more sedate.  Science, according to Kuhn, advances by the necessarily premature assumption of a certain system or paradigm, and then attempts to make that paradigm successfully describe the data.  Scientists do not, in practice, wait until all of the data are in before deciding.  Often the decision is made based on an as-yet-unproven insight, and then the work is done.  In short, “What the tradition sees as eliminable imperfections in its rules of choice I take to be in part responses to the essential nature of science.”(Kuhn 1987 p.202)  A completely objective science, accepting nothing until proven, would remain indecisive and stagnant.  Science “advances” (changes to a new paradigm) not by skepticism, but by what seems to be an unjustifiable faith in a system that has not yet been fully articulated.

In support of this stance, Kuhn recounted that in the pre-paradigmatic era before Benjamin Franklin postulated his fluid theory of electricity, there was much controversy about but little progress in understanding electrical phenomena.  Once Franklin's general model emerged as a standard, however, scientists began to take certain metaphysical components-such as the nature of electrons-for granted and focus experimentation on the physical manifestations of this metaphysical framework.  Without the framework, there was no basis for asking the questions which led to so-called crucial experiments.  Most new theories, like Franklin's, are accepted before the final jury is in.  In a sense, they have to be, or there could never arise the amount of work necessary to test the full capacities of the model.  Thus a research program is born.  Kuhn noted that there may be many competing programs (paradigms), but “an individual's transfer of allegiance from theory to theory is often better described as conversion than as choice,” (p.207) because for the events Kuhn was describing, the choice was not yet clear except in retrospect.

Kuhnian science has two distinct modes of operation.  Normal science, the vast majority of science, improves the accuracy and scope of the existing system.  Revolutionary science scraps all or part of the existing system in favor of another.  After most scientists have adopted the new model, it is seen clearly to have been the better choice, and those still refusing to accept the new model (e.g., Einstein after the enshrinement of quantum mechanics) appear somewhat atavistic.  From this new point of view, Whiggish intellectual history is very tempting.

Applying Kuhn

To my complete surprise . . . exposure to out-of-date scientific theory and practice radically undermined some of my basic conceptions about the nature of science and the reasons for its special success....  If these out-of-date beliefs are to be called myths, then myths can be produced by the same sorts of methods and held for the same sorts of reasons that now lead to scientific knowledge.  (Kuhn, 1962, pp.vii & 2)

Scientific theories ebb and flow, but the enterprise of science as a whole has continued to increase its explanatory power through these shifts in understanding, and more strongly, because of them.  That there are shifts is, according to Kuhn (1970), a defining characteristic of the Western scientific tradition, and on first glance it seems that this is precisely where Maya science differed.  This merits a closer look.

Normal science is dogmatic: it assumes a particular paradigm and strives to reconcile existing theories, schemas, and observations under this general world view and methodology.  Revolutionary science occurs when the (relevant) scientific community finally decides that there are too many anomalies, and switches to a new paradigm.  But in retrospect it is easy to see that Kuhn's analysis was too coarse; even a small field of science will not at any time be in one state or the other.  Revolutionary and normal science generally coexist.  Science is a large enterprise, and parts of it are always under construction (and demolition), even if at any one time, most of the structure is relatively stable.

But there is for Kuhn an “essential tension” (see also Kuhn 1977) between universally extending the current paradigm and casting away old theories to proceed to a better view of the world.  In the twentieth century, the naïve view of science focusses on the revolutionary progress from system to system, and introductions to the history of science proceed from revolution to revolution.  Kuhn threw in a measure of salt when he noted that while progress has clear meaning within normal science, it becomes much more soupy during a revolution.  After the fact, the Copernican revolution looks like progress, because it helped get us to where we are now (and that's good, right?).  But as the first investigators embraced Copernicanism, they had to throw out a great deal, with no replacement available. Copernicanism implied, among other things, that contemporary physics was wrong.  The switch to this new system required a belief that the remaining problems could be worked out, and involved a step in a direction that could not unabashedly be called progressive.

There is another edge to Kuhn's argument, and here he follows Karl Popper.  Popper said that science was a game, and that one of the rules was continually to question existing theories and to try to show them false.  Failure to do so meant that one had retired from the game; the assumption is that ultimate success is never possible, so inspired questions will show any theory to be false.  Add the assumption that humans have the ingenuity to create a new system, and we conclude that a healthy scientific tradition should involve revolutions.

The discarding of previous theories in favor of newer, apparently better ones, is a telltale sign of a healthy scientific enterprise, and demarcates science from say, religion.  It does not separate science from enterprises like art, which also have paradigm shifts.  Fortunately, Kuhn added the principle that in science, only one paradigm is right.  In this sense, paradigm shifts are more than changes in taste.  But even if the Maya had this kind of monism, they do not appear to have had revolutions.  The Maya, then, seem to have been masters of normal science, but devoid of such revolutionary science which defined the Western tradition's conception of itself from the Scientific Revolution forward.

On Beyond Kuhn

There are two problems with this simple point of view.  First, one could argue that physics from Newton to Einstein (three centuries) was a poor example of science because the essential model of nature remained fixed.  This is intriguing, but it is absurd if we want to account for science as practiced.   This shows a problem with Kuhn's account.  It is too idealistic to suppose that all of science, or indeed even a whole field of science is either in normal or revolutionary science.  In short, it suffers from a false dichotomy between revolution and evolution. They are not, in fact, mutually exclusive.  I construe them as follows:   

Revolution: a substantial change in the function & structure of the subject at hand. In particular:

a) weak notion: a change great enough that an actor from setting A would be significantly unable to function if transplanted into setting B.

b) strong notion: a change great enough that an actor from A would be unable to adapt enough to function passably in B.   

Evolution: a continuous change of the subject of interest over time, or an approximation of continuous change such that there are no nonremovable discontinuities.

There are four possibilities: (1) Zero change = (degenerate) evolution without revolution.  (2) Small change = evolution without revolution. (3) Large, continuous change = evolution with revolution. (4) Large, discontinuous change = revolution without evolution.

Only the last category is “purely” revolutionary.  The point is that while a revolution is a large change between measured points, this change might nevertheless have been continuous and evolutionary between those points.  The long Newtonian era was not void of substantial changes, and a comparison between Hamiltonian/LaGrangian and Newtonian formulations of dynamics betrays a large conceptual difference, but since we can trace the progression, we know they are also evolutionary.  It is indeed the fact that we know there were these continuous innovations that forces us to doubt the earlier conclusion that the Newtonian era was unscientific, and to reject that part of Kuhn's analysis.  The questioning tradition was still alive and well, even if the fundamental cosmology was not thrown out in the intervening period.  The apparent paradox reveals itself as a scale problem.

The Maya present a reverse scale problem.  We have little or no evidence for this kind of internal revision, and so when presented with a case which looks like extended single-paradigm dominance, we have concluded that there was in fact no science going on, perhaps because we lack the evidence to see changes at a less-than-global level.  Major conceptual revolutions are a good indicator for a scientific tradition, but neither their presence nor their absence is diagnostic, and they may be failing us here.  Not all revolutions change the entire cultural cosmology, and indeed we could argue that some of the really fundamental elements of Western cosmology have not changed since Greece.

We have the Dresden Codex, which appears to be some kind of divinatory table, almanac, or ephemeris.  Completely missing is how to produce such a document.  If observing a new celestial body, how does one go about building an accurate predictive device?  Archaeologists have made various guesses, but basically we do not know.  We do know that the Dresden Codex is a Post Classic (15th-century) version of  a Late Classic (10th-century) document (Coe 1993:173,188), which may imply that no significant conceptual changes had occurred during the intervening centuries.  Even if this is so, we still have to reckon with the rise of astronomical knowledge in the Classic period.

We have at least one case of a revision in astronomical knowledge during this time.  The Copan moon formula (149 moons = 4,400 days) began to be used during the 7th century, and spread to other Maya centers thereafter (Coe 1993:187)  This in turn appears to have been replaced in the next two centuries since the Dresden Codex used the Palenque formula (405 moons = 11,960 days).  These notes indicate that during the Classic period at least, both observation and interpretation continued, and that revisions were made in order to improve predictive capacity.  The best candidate for the transition from preparadigmatic to paradigmatic skywatching would have been the adoption of the systems of calendrical correlation.  Existing evidence traces parts of the calendrical system back to the Olmec, so this kind of  “revolution” would almost certainly seem evolutionary at a finer scale.

So there are aspects of Mayan astronomy which are compatible with our revised Kuhnian account of science as well as with our revised version of McCluskey's definition.  The practice of calendrical commensuration was a well-established methodology by the end of the Classic period.  It constituted a Kuhnian paradigm, and thereby served as the socially-accepted practice by which to generate reliable knowledge.  The knowledge was useful in agriculture.  Within the broader explanatory framework of Maya cosmology, Maya astronomy was used in politics, warfare, and community life.  Still better, it was precise enough to test and to revise if necessary.  Might it still have been something other than science?

If not science, then what?

The observational, calendrical, and predictive aspects of Maya skywatching are well- established, but how did they come together within an explanatory framework?  Do we see the interplay which Gingerich thought especially characteristic of modern science?  Or do we have an advanced example of some kind of atheoretic technology?  On our definition, the absence of a systematic explanatory framework would make a body of natural knowledge less scientific, or not scientific at all, despite its predictive success.  It is difficult to imagine proficient knowledge about the natural world in the absence of some sort of explanatory system, and the Maya did have a general cosmology, some of which is recorded in Conquest documents, some inferred from the archaeological context, and still more is gathered from contemporary Maya communities in the hope that some of the original traditions have survived in some form.  The question is whether this knowledge was systematic.  

Linda Schele has been piecing together evidence from inscriptions, paintings, codices, and myths in order to expand archaeologists' understanding of Maya cosmology.  In Maya Cosmos (Freidel, et al. 1993) she documented her path to discovering her current theory.  According to Schele, the often-depicted World Tree, the Crocodile or Sky Serpent, and the Canoe all refer to the Milky Way in different orientations in the sky, either throughout the year or during the course of a particular night.  She also made a case for a Maya zodiac (different from others which have been proposed, such as Brotherston (1986)), and posited other correlations between mythic elements and regions of the sky.  The underlying thesis is that much of the Maya mythology is an allegory for the changing night sky and its effects upon humanity.  Dennis Tedlock (Tedlock 1985; Tedlock and Tedlock 1993) also champions this thesis, and has interpreted the Popol Vuh creation myth as a narration of the dance of the constellations, and the appearance of Venus as the morning star announcing the birth of the sun.

It is not clear how to answer our question.  These stories flesh out the almanacs, and reunite the tables of numbers with the illustrations they surround; they provide a cosmology and a worldview.  If Schele, Freidel, and the Tedlocks are right and the divine stories are a pervasive and cohesive allegory for the sky, why should we think them explanatory at all, rather than a set of good memory aids?  If, rather, the stories are taken at face value, as religious stories about gods who might appear to be celestial objects, then they are of course explanatory as most religious beliefs are, although in some ways less systematic.  There is potentially a tradeoff between systematicity and explanatory power.  If, as Schele believes, Maya cosmology is less mysterious than we used to think, and more of an allegory for the sky, this may make it more systematic, but at the same time may mean it was more of a description and less of an explanation.

What was systematic was the use of the 260-day calendar and the pursuit of commensurable cycles between this and celestial events.  Conversely, we could also say that the use of celestial events to aid the observation and perhaps construction of the calendar was systematic, as well as the construction of certain buildings with deliberate alignments.  These pieces are in place, but without an underlying cosmology they are not explanatory.  On the other side, the people who tried to frighten off the animal eating the sun were reacting to an explanation, not a description.  It was a good explanation.  It was a physical explanation.  But was it part of a systematic style of explanation?  I think this is an important question, and eventually an answerable question, but it is a question for archaeologists and anthropologists who are in a better position to evaluate the cosmology.  Tedlock and Schele have provided us with a systematic explanation of Maya cosmology, but that is not the same thing as Maya cosmology providing the Maya with a systematic explanation of their astronomical observations.

IMPLICATIONS FOR PHILOSOPHY OF SCIENCE

If science is a body of exact, testable, theoretical knowledge about a part of the natural world, along the lines that Aaboe suggested, then contrary to his own evaluation, the Maya skywatching tradition which led to the Dresden Codex was science.  The Maya who compiled such codices had a good deal of knowledge about the sky, and had built an impressively exact calendrical theory which helped to systematize what they observed, though to what extent the system was both systematic and explanatory has been left unanswered.  We have also ignored Maya taxonomy and medicine, which may provide clearer answers to exactly those sorts of questions.  One of the goals of the paper has been to show that science is not just a body of exact, testable, theoretical knowledge.  Such definitions omit the processes by which such knowledge is obtained, and either impair our ability to conceive of a science which is not Greek sc ience, or disregard the distinction between what societies consider to be science and nonscience.

Central to the notion of science is the idea that there is a reliable, accepted method or set of methods for acquiring and testing claims about the natural world.  Precisely what that method involves has changed through time in the European tradition, and may be expected so to change from culture to culture.  There is no one scientific method, and as Rorty has argued, science is not a natural kind: its boundaries are obscure at best.  The failure to separate two separate projects in the philosophy of science has led to some well-deserved debate.

The first is the project of demarcation, which seeks to separate science from nonscience, in a particular culture, usually and most usefully current culture.  In this task philosophers of science should actively patrol the boundaries of science, seeking both to understand what makes something count as science and to define what counts as science, and why.  Here philosophers should question activities like Creation science and astrology which meet some but not all of our current requirements for science.  What historians and philosophers have found, however, is that part of the history of science is the history of what counts as science.  Methodologies change based on what has worked in the past and what has not, and part of the advance of science has been the understanding of failed inferences, an understanding which has been learned and which, like the subject matter and style of science, is historically contextual.

The realization of the changing nature of science leads to a second project, delineation.  Given that the nature of science has changed in our own history, and given our dissatisfaction with the temptation thereby to cast aside all bases for distinction, what is it that seems to be necessary, sufficient, or at least highly indicative of an enterprise we might call science?  In short, can we find a satisfactory relativized definition of science?  This paper has attempted to use what we know from Maya anthropology and archaeology to help formulate such a relativized definition.  There is still some demarcation here, but of a weaker sort.  If, following Pingree, we realize that not all science in this sense must be Greek science, we can not project our own historically-derived methodological biases into other cultures, however appropriate we know those to be for our own.

I have suggested a definition which incorporates two important aspects of science, the knowledge base and the observational methods, and sets these in the context of social acceptance.  Like Pingree and McCluskey's definitions, it allows astrology to be a science in the proper setting, and I think that the history of science justifies this consequence.  Unlike Pingree and McCluskey's definitions, the one offered here allows modern society as a whole to consider astrology a non-science.  Perhaps the definition fails on grounds not considered here, but any future definition offered for the project of delineation ought as well allow for definitions in the present project of demarcation.  

The humble conclusion for the Maya is that by some definitions, yes they were practicing science, by others no.  By the one advanced here, perhaps we do not yet know, but a look into some pieces of Maya culture has helped us to explore what we consider important about science, and confront the implications of different definitions.  No, the Maya were not on the road to modern astronomy, so far as we can tell.  The question is, what can we tell besides that?  Can we evaluate and study scientific traditions which are not on our own branch of the intellectual phylogeny?  Hopefully this paper has provided a clear analysis of various aspects of science which may be in mind when we ask whether Maya astronomy was scientific, and explored those features of Maya astronomy which have a bearing on the question.  

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