COMPARING CHINESE AND MESOAMERICAN 

CALENDAR DATES

David B. Kelley, Ph.D.

Academic Studies Department,

International Campus Boston,

Showa Women’s University (of Tokyo),

Boston, MA 02130

Abstract.  For centuries, scholars have noted similarities in the names designating specific days within the traditional calendar systems of China and pre-Columbian Mesoamerica.  Yet no one seems to have attempted a day-by-day comparison of such names within a specific sequence of days.  Here, I show one method for achieving such a comparison, covering any 60-day sequence.  Use of the method correlates both Chinese and Mesoamerican dates to specific, proleptic Gregorian calendar dates, as well as to specific Julian Day numbers.  I attempt to demonstrate that, in any 60-day period, six consecutive series of 10 Chinese Heavenly Stems (with each series denoting the five metaphysical elements doubled: Wood-1, Wood-2, Fire-1, Fire-2, Earth-1, Earth-2, Metal-1, Metal-2, Water-1, and Water-2) can be compared to three consecutive series of 20 Mesoamerican Day Names.  Likewise, in any 60-Day period five consecutive series of 12 Chinese Earthly Branches (with each series denoting 12 zodiacal animals: Rat, Ox, Tiger, Rabbit, Dragon, Snake, Horse, Sheep, Monkey, Chicken, Dog, and Pig) can be compared with the same three consecutive series of 20 Mesoamerican Day Names.  This is possible because the 20 Mesoamerican Day Names (the Tzolk’in) include both metaphysical elements and animals.  This study initially employs the most favored of the correlation constants used to correlate the Mayan calendar and the poleptic Gregorian calendar but then employs another correlation constant (differing by only four days), that maximizes the number of correspondences (30) between the two calendar systems.

INTRODUCTION

In 1990, just before leaving the United States to take up a teaching position in Japan, I bought a large poster.  I had wanted something interesting to hang on my office wall, so I chose an image of the famous Aztec Calendar/Sun Stone entitled The Aztec Cosmos, which had been traced by Tomas J. Filsinger and published by Celestial Arts.  The 35.5 by 35.5 inch poster came with Filsinger’s 31-page guide to the poster, and it provided my first glimpse of the elements of the famous stone, including the 20 day names used in ancient Mesoamerica, in three languages: Aztec, Mayan, and Zapotec (all with English translations).¹  Upon reaching Japan, I immediately hung the poster on one wall of my new office and so came to look at it, casually, almost every day.  After some period of time (probably quite a bit longer after starting to view the poster than one might imagine), it struck me that the animal images representing the 20 Aztec days that circle around the central images included quite a few animals that were similar to the twelve Chinese zodiacal animals—Aztec animals such as the Lizard, the Snake, the Deer, the Rabbit, the Dog, the Monkey, the Jaguar, and the Eagle/Vulture that reminded me of such Chinese animals as the Dragon, the Snake, the Horse, the Rabbit, the Dog, the Monkey, the Tiger, and the Chicken.

Because of my previous, informal 20-year study of the Chinese calendar (see D. B. Kelley 1995a, 1995b), I also noticed some other similarities.  The Chinese, in denoting days, months, and years in their traditional calendar system, used not only a sequence of 12 zodiacal animals (which they call the “12 Earthly Branches”), but also five metaphysical elements, doubled up so as to form a sequence of 10 (which the Chinese call the “10 Heavenly Stems”), together forming an interlocking 60-day sequence of compound names, each of which involved one animal and one metaphysical element.  What I noticed was that the sequence of 20 Mesoamerican day names and glyphs (i.e., the Aztec, Mayan, and Zapotec versions, noted in the guide to the poster) included images that seemed to represent the metaphysical elements Fire, Water, and Earth, which were, intriguingly, the same as three of the Chinese metaphysical elements of which I was aware: Fire, Water, and Earth.  The combination of these similarities was the initial impetus for the comparative research that I present in this paper.

HUMBOLDT AND OTHERS WHO NOTICED

The thirty-four-year-old explorer Baron Friedrich Heinrich Alexander von Humboldt landed in New Spain in 1803, a few years after the rediscovery of the Calendar/Sun Stone, which had been buried beneath the Plaza Mayor of Mexico City for over 250 years.  After Humboldt had viewed that huge stone and perhaps other related artifacts, he became one of the first to note some of the same similarities that I found almost 190 years later, involving the various animals mentioned above (Tompkins 1976).  David H. Kelley and other researchers mentioned by Kelley in his numerous writings (e.g., D. H. Kelley 1974, 1980, 1983) have also speculated on certain similarities in Asian and Mesoamerican calendar systems.  And yet, to the present day and in spite of all the writings on the topic by myself, by David H. Kelley, and by others, I know of no comparative study of the 20 Mesoamerican day names and the Chinese combined 12 Earthly Branch and 10 Heavenly Stem day, month, and year designations that involve actual calendar sequences from both Mesoamerica and China.  Perhaps no one has attempted such a study because there were, heretofore, no tools available to accomplish it.  This paper attempts to demonstrate that such a comparison is not only possible but also of potential interest to scholars interested in ancient Mesoamerica and in China, because suitable tools are now widely available.

THE TOOL I USE FOR DETERMINING DATES

In 1998, I downloaded a copy of the computer program InterCal, developed by Denis Elliott, an astronomer at the Jet Propulsion Laboratory (Caltech).  I contacted Elliott about this program, to thank him for having created such a useful tool for determining exact Mesoamerican (Mayan) and Chinese dates.  Eventually, I assisted him in a small way to improve the Chinese calendar component of InterCal (my perhaps rather selfish aim being easier comparisons of Mesoamerican and Chinese dates).  Elliott employed algorithms which were found in Calendrical Calculations: The Millennium Edition, by Nachum Dershowitz and Edward M. Reingold (2001).  The InterCal program has the capability of determining the correct designations for Chinese years, months, and days, as well as Mayan Long Count Haab and Tzolk’in designations.  InterCal also provides Julian Day (JD) numbers, often employed by astronomers such as Elliott and also by Mayanists who wish to denote a correlation constant that specifies a particular starting point for the Mayan calendar system.

LINEAR SEQUENCES OF DAYS

My curiosity concerning the similarities mentioned above caused me to delve ever deeper into the intricacies of the systems that contained the similarities.  What I learned was that both areas of the world employed cyclic calendars, in which various calendrical elements repeatedly appeared.  In both parts of the world, those cycles, often interlocked, served civil, religious, and astronomic purposes.  Some of the cycles were clearly tied to the passage of “natural” periods of time, and some were not.  The Mesoamericans also developed a linear progression of numbers, to mark a progression of days, starting with a day “0” and proceeding day by day, to keep track of the number of days accrued.  This so-called Long Count is itself sometimes considered to be cyclic in nature, but I tend to consider it to be non-cyclic—after all, the number of days can just continue to accumulate, by adding higher and higher orders of magnitude.  However, just as is so in the case of the modern Christian calendar, a starting point in time had to be selected, and in the case of the Long Count that point has been a matter of much debate.

In their discussions about this starting point, modern scholars employ another linear system to pinpoint certain days—the Julian Day system, developed by Joseph Scaliger in 1583, at the time of the Gregorian calendar reform.  He proposed a starting point for his system of 12:00 noon, 24 November 4714 B.C., in the proleptic Gregorian calendar.  Astronomers have since informally modified this system so that the starting point begins at midnight, twelve hours earlier.  Thus, to astronomers (and in the InterCal program) a Julian Day (JD) number of 584282.5 represents the midnight starting point of a specific day, but non-astronomers commonly use JD 584283 to represent that same day, even though that day number technically represents a time of 12:00 noon.  Astronomers began to use the noon starting point of each day because most of their work is done at night, and decimal fractions for periods during one specific night are more convenient than fractions spread over two separate days. 

The starting point of Scaliger’s system can be specified by a proleptic Gregorian calendar date, which means that, if one wishes to continue back into the past, the algorithms currently used to determine Gregorian calendar dates, one would reach 24 November 4714 B.C. as Scaliger’s starting point.  So, “proleptic” means only that calendrical rules are applied to dates that occurred prior to the development of the rules.  Likewise, if one wished to employ the rules that applied to the older Julian calendar system (i.e., the calendar implemented under Julius Caesar), one would reach 1 January 4713 B.C. as Scaliger’s starting point.  In this paper, I use proleptic Gregorian calendar dates exclusively, because the Gregorian calendar generates dates that are familiar to most of us, including the approximate dates of occurrence of the equinoxes and solstices.  Thus, a Gregorian date helps to give us a good perspective on the various key points in a solar year.   

The Mayan Long Count thus presaged Joseph Scaliger’s later creation.  Both the Maya and Scaliger created a system for counting a progressively increasing number of days.  And considering that many scholars believe (they do not know for certain) that the evidence points to a starting point for the Mayan Long Count of 11 August 3114 B.C. (a proleptic Gregorian date), or JD 584383, both the Maya and Scaliger chose starting points that were quite far in the past—indeed, enough so that all known historical events occurred well within the range of both systems.  But there was another reason why someone (or a group) would create such a linear system—it was useful in keeping track of, and fine-tuning, the cyclic components in calendar systems.  In this paper, I employ Scaliger’s system to pinpoint Mesoamerican, Chinese, and even proleptic Gregorian calendar dates.

CYCLES

In the Middle East and the West, one of the oldest surviving cycles is that of the seven days of the week, which has continued, uninterrupted, for thousands of years, in spite of the various calendar reforms that have been implemented over the millennia.  It is interesting to note that, in China, the calendrical use of the 28 Lunar Mansions (in an astronomical context, the names of 28 small constellations) to denote specific days, has also been in use for thousands of years, with the 4th, 11th, 18th, and 25th Mansions invariably occurring on a Western calendar Sunday.  We can only speculate on the actual, historical starting point of the system of weekdays and that of the Lunar Mansions.

Likewise, we do not know when the 60-day cycle of 12 Earthly Branches and 10 Heavenly Stems in China began, nor do we know when the interlocking 260-day cycle of 13 number prefixes and 20 day names in Mesoamerica (often referred to as the Sacred Year, but also by the Mayan term Tzolk’in or the Aztec term Tonalpohualli) began.

The Mesoamerican 260-day Sacred Year noted above, consisting of 20 thirteen-day and 13 twenty-day sets represents an interlocking cycle that very likely predates another interlocking Mesoamerican cycle, consisting of 20 number prefixes (beginning with zero) and 19 “months,” eighteen of which may be preceded by the full 20 number prefixes, and one of which (Wayeb) is preceded by only the first five number prefixes (starting with “zero”).  Together, they form the 365-day (Mayan) Haab, or (Aztec) Xiupohualli.  The two interlocking cycles of 260 days (the Sacred Year, or Tzolk’in) and 365 days (the Haab) may then be joined together to form a larger cycle, consisting of 18,980 days, often referred to as one Calendar Round.  In one Mesoamerican Calendar Round, any particular combination of (1-13) number prefix plus (1-20) day name and (0-19) number prefix plus (1-19) month name occurs only once every 18,980 days (approximately 52 solar years).

In China, we see that in one 60-day cycle, a particular combination of 10 Heavenly Stems and 12 Earthly Branches occurs only once during that period.  The set of 60 combinations has been called the Sexagenary Cycle. The Chinese also began to use the same 60 combinations to denote minutes, days, and, especially, luni-solar months (each beginning on the date of a new moon, with the first month always being Tiger).  They also came to denote the names of specific years (beginning with the combination Wood-1 Rat) within a cycle of 60 years.  According to modern calculations, on 18 February 2007 the 24th year of the 79th 60-year cycle began, marking the start of the Chinese year 4704, or the year Wood-2 Pig, the month Water-2 Tiger, and the day Water-2 Sheep.  The Chinese year 4704 is obtained when we assume that the start of the Chinese calendar began on Day 1 of Year 1 in Cycle 1.

Table 1 below shows the names and meanings/associations of those components of the Mayan and Chinese cycles discussed so far.   Note that the 10 Heavenly Stems also served as numbers, at least for a set of any ten items, including calendar dates.  Also, because there are 10 Chinese Heavenly Stems and 20 day names employed in the Mesoamerican 260-day cycle, in any type of comparison of actual day sequences the Heavenly Stem series occurs exactly twice with any full series of Mesoamerican day names.  Interestingly, the first Heavenly Stem corresponds to the final (units) position, and to the number 1 in that position, in any unfractionated Julian Day number marking that day.  So, for example, JD 584283 ends in a 3, so that implies that the Heavenly Stem for that day is the third one: Fire-1 (Bing).

Table 1.  Names and meanings/associations of the components of the Mayan and Chinese cycles discussed above.  

A STARTING POINT FOR THE MAYAN CALENDAR

The designation for the starting point of the Mayan calendar, including the Long Count, can be obtained from the preceding table, by combining the numeral 4 and the day name Ahaw from the sections under “260-Day Cycle (Tzolk’in)” with the numeral 8 and the month name Kumk’u from the sections under “365-Day Cycle (Haab),” thus obtaining the famous (to Mayanists, at least) Mayan date 4 Ahaw 8 Kumk’u.  Accompanying this cyclically-based name can also be found the Long Count number: 0.0.0.0.0, which represents, by modern scholarly convention, in descending order of magnitude: 0 Baktun, 0 Katun, 0 Tun, 0 Winal, and 0 Kin, with 1 Baktun = 144,000 days, 1 Katun = 7,200 days, 1 Tun = 360 days, 1 Winal = 20 days, and 1 Kin = 1 day.  Since the Maya employed a vegesimal (i.e., base-20), place-value system of numeration, one would expect all magnitudes of order to increase by units of 20; yet, for calendrical purposes (only), the system was modified in the case of the Winal order of magnitude, so while we see that 20 Kin = 1 Winal, only 18 (not 20) Winal = 1 Tun.  The higher orders of magnitude above the Winal consistently increase by units of twenty, even beyond the Baktun, so that 20 Baktun = 1 Pictun = 2,880,000 days, 20 Pictun = 1 Calabtun = 57,600,000 days, etc.  Higher orders were used by the Maya, including the Kinchiltun and the Analtun, and so my earlier assumption that the Long Count is non-cyclical has been validated, which means that a Long Count of 14.0.0.0.0, denoting a date in the distant future, is perfectly reasonable.  However, exactly what Western calendar date, or better still, what Julian Day number, is equivalent to the (proleptic) Mayan date 4 Ahaw 8 Kumk’u 0.0.0.0.0 remains unknown, although there have been numerous attempts to pinpoint the exact date.

One of the favored dates is JD 584283 proleptic Gregorian calendar date, or 11 August 3114 B.C., and at least for the 260-day cycle (Tzolk’in), there is some validation of this date, since at least one group of highland Maya people has continued to maintain their Tzolk’in series to this day, and this series agrees with the JD 584283 figure.  There is other evidence available that favors the JD 584283 number, but since the 260-day cycle repeats itself every 260 days, we are sometimes left with controversial astronomical and archeological means to demonstrate a case.  One unique (and no doubt controversial) quality of this paper is that it applies—for the first time, as far as I am aware—a completely different line of evidence to the question of the Mesoamerican calendar system.  It introduces a calendar system from outside the Americas, and attempts to compare specific sequences of dates that seem to show marked similarities in their naming and use.  My purpose is to show that other calendar systems may provide insights into the workings of the Mesoamerican systems, and thereby help to focus upon features that may elucidate the nature of the Mesoamerican calendar systems.

A STARTING POINT FOR THE CHINESE CALENDAR

According to legend, in 2697 B.C. Huang Di ascended the throne of the kingdom of Yin, located in what is now China, and appointed the court scholar, Da Nao, the task of creating the Sexegenary Cycle, which is sometimes referred to by the combined names of the first Heavenly Stem and first Earthly Branch in the series of 60, Jia Zi.  Table 2 presents the complete series:

Table 2.  Ancient Chinese Sexegenary Cycle.

The Chinese did not develop or employ a non-cyclical, linear system of numeration such as the Mayan Long Count, the Western calendar series of years, or the Julian Day series.  Instead, they attached the formal name of the reign of each emperor (much as the Japanese do today) to one of 60 combinations of Heavenly Stems and Earthy Branches.  Since the Chinese maintained a carefully ordered list of the emperors, including some—especially from the distant past—who may or may not have existed, this method was normally sufficient to denote specific years.  In more modern times, unknown Chinese scholars attempted to calculate both the duration and period in time of the past emperors, and developed the present non-cyclical system of “Chinese” years, most likely under Western influence.  As noted earlier in this paper, the result is that on 18 February 2007 the 24th year of the 79th 60-year cycle began, marking the start of the Chinese year 4704.  It is no accident that the first day of the first year of the first 60-year cycle would fall, according to calculations made using the current Chinese year number, in the year of the accession of Huang Di, or 2697 B.C.

Using a computer program such as InterCal, it is possible to apply currently known algorithms to the task of pinpointing the date of the first day of the first year of the first 60-year cycle, which happens to fall on JD 736413, or the proleptic Gregorian calendar date of 17 February 2697 B.C.  At least, this is the date yielded by the InterCal program.  The InterCal creator, the astronomer Denis Elliott, cautions that, “the accuracy of the InterCal version of the Chinese calendar is not guaranteed.”  And, further, that, “No matter how accurate the equations are today, they will lose accuracy as you calculate further and further into the past or future.”  The reason for this situation is that, “The equations do not give the positions of the sun and moon in closed form.  Such closed-form solutions do not exist because there are more than two bodies in the solar system.  Instead, the equations consist of time series expansions centered on the present, which lose accuracy as the time difference from the present grows” (Elliott 1998).  This is an especially important point because, unlike the Mayan calendar system, the Chinese system is tied to the actual movements of the sun and moon, about which the Chinese maintained tables for calendrical use, and still do.  This means that the above-mentioned date of 17 February 2697 B.C. represents the date of the occurrence of a New Moon, since all Chinese months attempt to mark the actual passage of the moon through one lunar period, ranging from 29 to 30 days.  By contrast, the Mayan calendar required the use of a Supplemental Series (which, by the way, tends to support the JD 584283 starting point) to note the movements of the moon.   

COMPARING STARTING POINTS

Neither the Mayan nor the Chinese starting date is known.  The favored JD 584283 (proleptic Greogorian calendar date 11 August 3114 B.C.) figure for the Mayan calendar start, suggested by carbon-14 dating of archeological material, seems to fall within the range of possibility, but such a range may be extended to more than 200 years (plus or minus), irrespective of disagreement with present highland Maya use of the 260-day cycle.  The same is true of attempts to appraise possible Julian Day figures, based on the occurrences of lunations and lunar and solar eclipses – we presently lack the ability to precisely (enough) determine the exact dates of such physical phenomena (as mentioned in the section above).  This would require the existence of perfectly accurate tables, dating back to the general period in question.  In the end, we are left with any possible 4 Ahaw 8 Kumk’u occurrence within that 200-year or so range, as a possible starting point for the Mayan calendar.

Unfortunately, the same is true of the true starting point of the Chinese calendar.  We don’t know with absolute certainty when the first Wood Rat year occurred.  We can assume that the proleptic Mayan and Chinese starting dates were created for reasons that are still unclear, yet what remains are the systems, cyclic or non-cyclic in nature.  And, we can compare the two systems.  Perhaps by performing such comparisons, some light can be shed that will elucidate those elusive starting points; that, in fact, is the primary purpose of this paper.

Using the figure of JD 584283 for 4 Ahaw 8 Kumk’u, and the figure JD 736413 for the possible day on which the first year of the first Chinese cycle began, we are left with a difference of exactly 151,130 days (i.e., the mathematical difference between the two Julian Day numbers).  Using these Julian Day numbers, I calculated the occurrences of the Mayan day named 4 Ahaw 8 Kumk’u, and the occurrences of the first day of the first year (Wood Rat) of each 60-year Chinese Sexagenary cycle, from the respective starting dates mentioned above through to modern times, using the InterCal program.  In the case of the Mayan cycles, this means that, counting the first occurrence of 4 Ahaw 8 Kumk’u as being in Cycle 1, and each cycle being of 18,980 day’s duration, the most recent, and 99th cycle of 18,980 days began on 20 March 1980 (i.e., JD 2444319).  In the case of the Chinese 60-year cycles, this means that, counting the first occurrence of the year Wood Rat as being in Cycle 1, and each cycle being close to a multiple of 60 of the tropical year, the most recent, and 79th cycle began on 2 February 1984.  

This amounts to comparing cycles of 52 years with cycles of 60 years, with the 60-year cycles approaching physical reality more closely, since the Mayan 52-year cycles differ from the actual multiple of 52 tropical years by about 13 days.  The two cycles, of about 52 years and 60 years each, come closest in their respective occurrences of 4 Ahaw 8 Kumk’u and the start of a Wood Rat year, roughly, every 284,882 days (almost exactly 800 solar years), or every 15th Mayan cycle of 52 years, or every 13th Chinese cycle of 60 years.  Table 3 shows the results of such calculations:  

Table 3.  A Comparison of Mayan 52-year and Chinese 60-year cycles and their starting points.

Note that I used the point at which the first Mayan day of 4 Ahaw 8 Kumk’u occurred closest to the day on which the first Wood Rat year began, as the start of those 800-year points of convergence, just mentioned.  Interestingly, the first such point of convergence involved Mayan and Chinese dates that were separated by a mere 290 days, with the 4 Ahaw 8 Kumk’u date occurring on proleptic Gregorian 29 April 2698 B.C., and the Chinese Wood Rat first Wood Rat year occurring on proleptic Gregorian 17 February 2697 B.C.  This means that, theoretically, the Mayan calendar could have begun eight 52-year cycles before the theoretical start of the Chinese calendar system, i.e., on 11 August 3114 B.C.

Using the Mayan Long Count numbers to denote these preceding eight occurrences of 4 Ahaw 8 Kumk’u, the following sequence occurs:  (first occurrence) 0.0.0.0.0, (second occurrence) 02.12.13.0, (third occurrence) 0.5.5.8.0, (fourth occurrence) 0.17.18.3.0, (fifth occurrence) 0.10.10.16.0, (sixth occurrence) 0.13.3.11.0, (seventh occurrence) 0.15.16.6.0, (eighth occurrence) 0.18.9.1.0, and the day of closest convergence on (ninth occurrence) 1.11.1.14.0.  So, at about the point at which the order of magnitude of the Baktun changed from 0 to 1, we meet the first point of convergence between the theoretical Mayan and Chinese calendar systems.  This is interesting, although perhaps of no great importance (that remains to be seen).  In fact, the preceding discussion on “Starting Points” has served only to prepare the reader for the major comparisons presented in this paper.

A 60-DAY SEQUENCE OF CHINESE AND MESOAMERICAN DATES

The 260-day cycle (Tzolk’in) was widely employed in pre-Conquest Mesoamerica, used by the Zapotec, Mixtec, Maya, Aztec, and other groups, and is, to this day, employed by highland Mayas and others.  The 365-day cycle was not employed as widely, and even our understanding of the month names used in the 365-day cycle is also limited, so for the comparative purposes of this paper I wish to focus upon the 260-day cycle.  Further, I would like to focus on the 20 day names associated with the 260-day cycle, because they seem to have associates that are comparable to both the 10 Heavenly Stem and 12 Earthly Branch cycles of the combined Chinese Sexagenary cycle.  Another reason is that three cycles of 20 Mesoamerican day names can more easily be compared to the Chinese Sexagenary cycle, since three cycles of 20 Mesoamerican occur within the same 60-day period as six Heavenly Stem and five Earthly Branch cycles that can be used to specify Chinese day names.

This approach should not imply that I find the overall 260-day cycle lacking in interest or importance, in either a Mesoamerican or Chinese context.  I have written before, and no doubt will write again, about that period of time.  After all, as noted by the astronomer Denis Elliott, “The fact that the Tzolkin cycle existed and had so much religious significance says a lot about the importance of the planet Venus to the Maya.  They followed its motions closely, and knew the average length of time Venus spends as the “Evening Star” is 260 days. Similarly, the average time spent as the “Morning Star” is 260 days (Elliott 1998).

In a Chinese context, in 1995 I noted that 13 August marks the midpoint of a 260-day Chinese period running from 5 April (Ching Ming) to 21 December (winter solstice), with the festival of Ching Ming being the second-most important spring festival, after Li Chun (which marks the start of spring and the start of the Chinese solar year, on 5 February).  I wrote that, “Prior to certain calendar reforms before 1 B.C. (perhaps around 400 B.C.) the Chinese solar year began with the Winter Solstice, which explains why the first zodiacal element, Rat, is associated with the Winter Solstice.  After the calendar reforms, the third zodiacal element, Tiger, became associated with the new solar year.  It is interesting to note that the first Mayan month is associated with the Jaguar” (D. B. Kelley 1995b:).  The Maya connected the meaning of their first month Mat with an authority figure, just as the Jaguar is so associated.  Even in the current luni-solar system of months, which are variable and tied to the motions of the moon, and in the current Chinese solar calendar (which is tied to the movements of the sun), the first month of the year is named Tiger, and although the Heavenly Stem component of the Sexagenary designation for the luni-solar month may differ from year to year, the Earthly Branch component is always Tiger.  In China, the Tiger is often metaphysically associated with Wind and is female, just as the Dragon is metaphysically associated with Water and is male, and so are the two main Feng-Shui animals.

Now we approach the matter of an actual sequence of 60 day’s duration.  Any 60-day period may be compared, but since the Julian Day (JD) number 584283 is so prominent I elected to begin by using that correlation constant for the Mayan calendar data.  “Correlation constant” is the term used to describe the starting point of the Mayan calendar system, which was named 4 Ahaw 8 Kumk’u.  All correlations of Mayan dates with Western calendar dates follow from its use.  Mayanists have employed quite a few different proposed correlation constants and have published the results of their research in favor of one or another.  I am employing the JD 584283 correlation constant first, because it is the most common in the literature and happens to agree with the known dating system still employed by certain highland Maya groups.  As for the matter of correlating Chinese and Western calendar dates, there is no such difficulty in correlation—the algorithms are well known, and were employed in the development of the InterCal computer program that I used to obtain the data in this paper.  As it turns out, JD 584283 (11 August 3114 B.C.) is equivalent to the Chinese day named Fire Dragon.  The original Mayan data presented in Table 4, below, were obtained using InterCal (which can produce data for any correlation constant) and are arranged in three columns, with the data for JD 584283 being found in the third line of the column farthest to the left, as indicated by an arrow.  It is found on the third line because, starting with the 18th day name, each column presents a set of data in each column that is more consistent, throughout the three columns.  

Table 4.  A 60-day sequence of Chinese and Mesoamerican calendar day names, set side by side.

Please note that I have simplified the Mayan glyphs slightly—I have removed the day symbols from the calendrical cartouches they are normally enclosed in, on monuments.  I have also removed the crescent-shaped “fillers” that are often found in monumental inscriptions of the dot (and bar) Mayan numbers for ‘one’ and ‘two,’ for the sake of simplicity and clarity of representation.

Table 5, below, presents the very same data, but translated into English.  It also includes certain frequent associations that color the common meanings of both the Mesoamerican and Chinese data.  The meanings and associations are presented for each of the data points, i.e., each of the 60 successive days.  To the far left of each of the three columns of twenty days each is found a separate running count of the sixty days (i.e., 1-60).

Table 5.  English meanings of day names in 60-day sequences from Chinese and Mesoamerican calendars.

In Table 6, below, I summarize the specific points of commonality that appear to be evident between the Mesoamerican and Chinese data sets.  Please remember that any similarities that become evident in this particular 60-day period will also be evident in any 60-day period that one might choose, given the same correlation constant, which in this case is JD 584283.  Please note that all commonalities appear exclusively in the range 21-40, or the middle section of the table.  Further, all commonalities here involve Chinese Earthly Branches, or their associations.  No Chinese Heavenly Stems (involving the five Chinese metaphysical elements of Wood, Fire, Earth, Metal, or Water) appear in the summary.

Table 6.  Matchings between Chinese and Mesoamerican day names in a 60-day sequence, using a JD 584283 correlation constant.

All of my Aztec and Mayan data have been checked for accuracy by Mesoamerican Studies specialists, including David H. Kelley, although I alone am responsible for any errors found in this presentation.  I think all Mesoamerican data in the above table can be easily understood.  However, the reader may require some explanation of the Chinese data.  The Chinese character (or glyph, if you like) used to represent the Earthly Branch Dog does not really mean ‘Dog’; the Chinese use another character for that.  The same is true of all twelve characters used in the Earthly Branch series.  Yet, in a series, they are used to denote just those twelve animals:  Rat, Ox, Tiger, Rabbit, Dragon, Snake, Horse, Sheep, Monkey, Chicken, Dog, and Pig.  In the case of the Chinese character for Dog, its earliest known form was that of a broadax, or battleaxe (Hinata 1973)—a weapon of war, which is why I compared it to Aztec and Mayan Knife.  Likewise, the Chinese character used to represent the first Earthly Branch and Rat, does not actually mean ‘Rat’; the Chinese use another character for that.  As in the case of the character for the Earthly Branch Dog, that for Rat has various meanings; but among these is ‘Master’, which is found as well in the proper name Gung Zi, better known in the West as Confucius, or Master Gung, since his family name was Gung.  It is also a rank of Chinese aristocracy, equivalent to the fourth grade of nobility (Mayers 1968).

The Chinese characters used for the second and third Earthly Branches are more problematic, but I include them because, in the case of the third Tiger, that animal is so often associated with the wind.  Yet, the original meaning of the character was not associated with the wind.  Likewise, the original form of the second character was not associated with any sort of reptilian creature.  I include it because of my research comparing the 20 Mesoamerican day names and the 28 Chinese Lunar Mansion animals, which represents twelve sets of animals, sometimes with three related (in the minds of the Chinese) animals in one set, and sometimes only two related animals.  Among the 28 Lunar Mansion animals and within the set in which we find Ox, we also find another “earth” animal, the mythical, four-legged, reptilian Xie Zhi (Mathews 1943), which was indeed comparable to the Aztec Crocodile (Caiman), or according to some Mayanists, Mayan ‘Earth Monster’.

A FOUR-DAY CHANGE IN THE JD 584283 CORRELATION CONSTANT

I was initially excited to find that, by using the JD 584283 correlation constant to obtain Mesoamerican data, at least one Mesoamerican Snake, Dog, and Jaguar day-name designation matched one Chinese Snake, Dog, and Tiger day-name designation, in any 60-day period.  Yet, it bothered me that the Mesoamerican day names denoting metaphysical elements such as Wind, Fire, Earth, and Water, never occurred on the same day as one of the Chinese metaphysical elements; therefore, I began to change the correlation constant.  I found that the correlation constant closest to the JD 584283 figure which would yield matches between Mesoamerican day names and Chinese Heavenly Stems and the same Earthly Branches discussed above, is JD 584279.  Application of that correlation constant yields the following data:

Table 7.  Matchings of Chinese and Mesoamerican day names in a 60-day sequence, using a JD 584279 correlation constant.

The Mesoamerican data are virtually unchanged from the previous table, except that the third line represents the data obtained from the use of the new correlation constant: JD 584279.  What have substantially changed are the Chinese data, which have shifted backward in time by four days.  Table 8 summarizes the matchings that occur, using the new correlation constant:

Table 8.  Matches between Chinese and Mesoamerican day names in a 60-day sequence, using a JD584279 correlation constant.

Please note that the four-day shift in the correlation constant has resulted in a shift in the overall arrangement of the matches between the 20 Mesoamerican day names and the 12 Chinese Earthly Branches, from the range 21-40, in the middle section of the table shown previously (using JD 584283), to the range 1-20, in the left section of the table shown above.  Now it should become clear as to why I maintained the particular ordering of the Mesoamerican day names in the three columnar groups of data: i.e., 1-20, 21-40, and 41-60—such an arrangement more effectively highlights the shifts in the summarized data.

The four-day shift in the correlation constant dramatically increased the number of matches between the Mesoamerican and Chinese data.  From the previous nine matches, all involving Mesoamerican day names and Chinese Earthly Branches (i.e., animals and their associations), the number of matches has increased to 30, involving Mesoamerican day names and both Chinese Earthly Branches and Heavenly Stems (i.e., metaphysical elements and their associations), during any 60-day period.  David H. Kelley introduced me to the element of Fire as a substitute for the fourth Aztec day name, more commonly meaning ‘Lizard’ (Kelley 1980:S4, S5, S8, S44).  It is interesting  that this allows for a match between both Aztec day-name meanings and both the Chinese Heavenly Stem Fire-1 and Chinese Earthly Branch Dragon, on one single day.  And since the Mesoamerican day names are evenly divisible by ten (i.e., the number of Chinese Heavenly Stems), we find that a match occurs between Aztec Fire and Chinese Fire-1 three times within any sixty-day period.

The next match I would like to discuss involves Aztec/Mayan Wind and Aztec Twisted Grass and Reed.  In the Indo-Tibetan system, Wind is the equivalent of the Chinese metaphysical element Wood.  In fact, the Chinese element Wood is, itself, closely associated with Wind, just as the zodiacal animal Tiger is.  For that reason, I considered Aztec/Mayan Wind to be a match for the Chinese Heavenly Stem Wood-1.  On the other hand, Chinese metaphysical Wood is symbolized by a Tree, especially in the Sino-Tibetan system of iconography.  Since it seems to be associated with all forms of plant-life, I consider both Aztec Twisted Grass and Reed (as forms of plant-life) to be matches for both Chinese Heavenly Stem Wood-1 and Wood-2.  This “double” use of essentially one Chinese metaphysical element is not unique in the summary table.

The Chinese metaphysical element Metal is symbolized in the Sino-Tibetan system of iconography by a Sword.  On the other hand, the metaphysical element Metal is also closely associated with the planet Venus.  In fact, the Chinese name for the planet is ‘Metal Star’.  Both Chinese associations (i.e., Sword and Venus) considered both Aztec/Mayan Knife and Mayan Venus to be matches for Chinese Heavenly Stem Metal-1.

The Chinese metaphysical element Earth was perhaps the easiest match to make, as the Heavenly Stem Earth-2 occurs on the same days as Aztec/Mayan Earth(quake).  The only Chinese metaphysical element (of the five) that is still missing is Water.  Interestingly, though, the ninth Aztec/Mayan day name Water occurs only one day prior to the Chinese Heavenly Stem Water-1.  Likewise, the nineteenth Aztec/Mayan day name, which is closely associated with Rain/Storm, occurs only one day prior to the Chinese Heavenly Stem Water-1.  In spite of the lack of a solid match, the possibility of some sort of systematic relationship between certain Mesoamerican day names, and both the Chinese Heavenly Stems and Earthly Branches is tantalizing, to say the least.  

DISCUSSION

In 1995, David H. Kelley was kind enough to share with me an unpublished paper entitled “The Invention of the Mesoamerican Calendar.”  In it, he attempted to reconstruct the earliest form of the Mesoamerican calendar system, including the names, meanings, and sequence of the 20 day names (used in the Tzolk’in).  Kelley employed all data available to him, which were much more ample than those available to me.  The meanings varied widely, and in some cases so did the sequence of names, so the complexity of Kelley’s task was daunting (or would have been to me).  One of Kelley’s conclusions was that the Aztec varieties of the 20 day names appear to be among the most primitive, which is why I added the Aztec data to this paper.  In the end, he was left with exclusively Mesoamerican data from which to make his reconstruction.  One of my intentions in writing this paper was to show that supplementary information, from an “outside” source, may be pertinent.  The type of “matching” data presented in the last section is indicative of the ways by which Chinese-based data can shed new light on the meanings, associations, and arrangement of the Mesoamerican day names.  That evidence seems to point to the 20 Mesoamerican day names as being, in some respects, a synthesis of both the 10 Chinese Heavenly Stems and the 12 Earthly Branches.  On the other hand, it may prove to be the case that the numerical connotations of the 10 Chinese Heavenly Stems (i.e., their use to enumerate any set of ten objects) may presage the Mesoamerican use of the 13 number prefixes, seen in the complete Tzolk’in cycle of 260 days.  After all, a 260-day cycle has its uses in both parts of the world, to mark the passages of both Mars and Venus.  

David H. Kelley (e.g., 1974, 1983) has also published several important articles on the so-called “correlation problem.”  And so, another of my intentions in writing this paper was to offer a different perspective on that problem.  I do not, here, offer a specific correlation constant.  Rather, what this paper suggests is that there may be a relevant framework in which a wide range of constants may be a bit more reasonable than others.  For example, the same results shown in this paper by using the JD 584279 correlation constant can be achieved by the use of JD 584299.  In fact, any JD number ending in “9,” and which differs from either JD 584279 or JD 584299 by a number evenly divisible by “20,” will yield the same results (because JD 584279 and JD 584299 differ by exactly twenty days).  If, indeed, it can be demonstrated that there is any reasonable degree of relevance for the idea that the Mesoamerican calendar system may be related, even in some minor way, to the Chinese calendar system, then an opportunity to test the Mesoamerican calendrical calculations against a known system (i.e., the Chinese) becomes available, and may help (even in some small way to) determine which correlation constant is true and accurate.

In this paper, I have focused on the 20 Mesoamerican day names and the 10 Chinese Heavenly Stems and 12 Earthly Branches.  Whether or not my analyses and conclusions are correct or have any relevancy, the fact remains that my focus in this paper is very restricted.  My unpublished research has carried me far beyond what has been presented here.  There are calendrical associations that do not involve either the Heavenly Stems or the Earthly Branches which indicate, in just as objective a manner as in this paper, the depth and breadth of the connections between the Mesoamerican and Chinese (and other Asian) calendar systems.  The very system of dots and bars used in Mesoamerica to represent numbers, first by the Olmec and Zapotec peoples, and later by the Maya, have their counterparts in China.  And as far as the use of the Mesoamerican vigesimal and Chinese decimal system is concerned, by investigating the origin of the Mesoamerican dot-and-bar system just mentioned, it can be demonstrated that the two systems do not differ as much as one might suppose.  But perhaps one of the most tantalizing aspects of a comparison of the Mesoamerican systems of numerals lies in linguistics, where it can demonstrated that the words reflecting vigesimal orders of magnitude, in certain Mayan dialects, and the words reflecting decimal orders of magnitude, in certain Chinese dialects, are almost interchangeable.  Thus, much remains to be shown. 

NOTE

¹A 27-by-27 inch version of the poster is currently available from Ten Speed Press, but with a 12-page-only guide.

REFERENCES CITED

The following include general references utilized but not explicitly cited in the text.

Dershowitz, Nachum, and Edward M. Reingold

2001 Calendrical Calculations: The Millennium Edition.  Cambridge University 

Press.

Elliott, Denis A.

1998 Calendar System Facts.  [Part of the documentation that accompanies Denis Elliott’s InterCal software (Version 2.1)] 

Feuchtwang, Stephan D. R.

1978 An Anthropological Analysis of Chinese Geomancy.  Taipei:  Southern Materials Center.

Filsinger, Tomas J.

1984 The Aztec Cosmos.  Berkeley:  Celestial Arts. 

Hinata, Kazuo

1973 Kodai Moji [Ancient Writings]. Tokyo:  Gurafikku Sha.

Kelley, David B.

1995a The Twenty-Eight Lunar Mansions of China (Part Three: A Possible Relationship with the Ancient Central-American Calendar).  Reports of Liberal Arts, Hamamatsu University School of Medicine 9:23-60.

1995b Possible Evidence of Contact Between China and Mexico in Ancient Times.NEARA Journal 30(1&2):16-31.

Kelley, David H.

1974 Eurasian Evidence and the Mayan Calendar Correlation Problem. In MesoamericanArchaeology: New Approaches. Proceedings of a Symposium on Mesoamerican Archaeology Held by the University of Cambridge Centre of Latin American Studies, ed. Norman Hammond, pp. 135-43.  Austin:  University of Texas Press.

1980 Astronomical Identities of Mesoamerican Gods. In Archaeoastronomy, supplement to Journal for the History of Astronomy 2:S1-S5.

1983 The Maya Calendar Correlation Problem.  In Civilization in the Ancient Americas, ed. Alan L. Kolata and Richard M. Leventhal, pp. 157-208.  Albuquerque: University of New Mexico.

n.d. “The Invention of the Mesoamerican Calendar.”  Unpublished manuscript in the possession of the author.

Mathews, R. H.

1943 Mathew’s Chinese-English Dictionary.  Cambridge:  Harvard University Press.

Mayers, William Frederick

The Chinese Reader’s Manual.  Detroit:  Gale Research Company.

Miller, Mary and Karl Taube

1993 The Gods and Symbols of Ancient Mexico and the Maya.  Detroit:  Gale Research Company.  London:  Thames and Hudson.

Moran, Hugh A., and David H. Kelley

1969 The Alphabet and the Ancient Calendar Signs.  Palo Alto:  Daily Press.

Palmer, Martin 

1986 T’ung Shu: The Ancient Chinese Almanac.  London:  Rider & Company.

Thompson, J. Eric S.

1960 Maya Hieroglyphic Writing.  Norman:  University of Oklahoma Press. 

Tompkins, Peter

1976 Mysteries of the Mexican Pyramids.  New York:  Harper and Row, Publishers.