The Maya: Whence the Fancy Math?
Mysteries, enigmas, riddles and puzzles are no doubt good for us. They keep us mentally alert. Perhaps we may even learn something as we wrestle with possible solutions. Sometimes however we may be happy just to find some clues, some subtle hints as to what the answer might be. Among mysteries with a scientific flavor, few are as intriguing as the ancient Mayas of Central America. Modern mathematicians and astronomers all want to know how the ancient Maya got so smart.
The Mayan civilization flourished when the situation was bleakest in Europe. While European society stagnated in a dark age, the Maya congregated in cities, built monuments and developed a rich culture. Several centuries before the birth of Christ, the Maya had already established settlements in Guatemala, Belize and Honduras. Their civilization reached its peak — extending also throughout Mexico's Yucatan Peninsula — by the eighth century AD.
Before the Mayans
The Maya were not the first people in Central America. A little to the west of the Mayan settlements, the mysterious Olmec had lived and died. Their major claim to fame was massive human heads carved from basalt rocks, which had been apparently transported considerable distances to these towns. Some of these monuments were as much as 3.5 m tall. The pinnacle of Olmec culture had been from 1200 BC to 400 BC. These people may have occupied some centers as early as 2250 BC. The interesting thing about the Olmec is that they wrote in hieroglyphics, built pyramids and kept track of time in a manner much like the more famous Mayas. Thus the superlatives applied to the Mayas, may be applicable to the Olmec as well. Were the Mayas descendants of the Olmec? Some experts think that they were.
As far as culture is concerned, much of Central American artwork is disturbing to our modern sensibilities. An article in National Geographic (November 1993 p.104) declared that a strange melancholy pervaded much of Olmec art. Similarly the Mayan center of astronomy, Copan in Honduras, was characterized as a "disturbing place." Of this center, one observer declared:
Stone demons posture everywhere; an evil jaguar leers from a wall; simian heads surmount sculpted bodies. Copan is sinister. Even the gods depicted here resemble devils.National Geographic December 1975 p.735
It is not however for their cruel customs or religion that the Maya are famous. If it were cruelty that made them famous then the Aztecs, who flourished several centuries later, far outdid the Mayas. The Aztecs however did not exhibit the mathematical expertise of the Mayas.
Date of Creation
Modern computers have enabled us to see just how good the mathematics of the Mayas really was. They employed their skills in the tracking of time. Not only are the calculations interesting, but so is their base line. The Mayas counted days elapsed from a creation date thousands of years in the past. This is remarkable for two reasons. Firstly it meant that they had to manipulate numbers as big as millions and billions, and secondly it seemed as if the Maya must have believed that they were dealing with an actual creation day. Otherwise they could have made their calculations much simpler by placing the base date closer to their own time.
It was a California newspaper editor, Joseph Goodman, who in 1905, worked out the correlations between our own and the Mayan calendars. Accordingly, the Mayan base date "4 Ahau 8 Cumhu" corresponds to August 11, 3114 BC. An article in National Geographic (December 1975 p. 773) called this choice of base date a "tantalizing mystery," but a book on ancient history shed further light on the issue. According to L. Sprague de Camp and Catherine de Camp, in Citadels of Mystery, the Mayan base date is quite similar to that of the Orthodox Jewish calendar which starts from the Creation in 3761 BC. The interesting thing is that these peoples lived on separate continents. Yet the numbers are surprisingly close. Other estimates of the date of creation include that of the much maligned Anglican Archbishop James Ussher (1581-1656) who calculated, on the basis of Old Testament genealogies, that the creation occurred about 4004 BC. Other estimates include those of Josephus at 5555 BC, the Septuagint at 5270 BC and Johannes Kepler at 3993 BC. The European estimates all came from a common cultural base, but the Mayas lived in an entirely separated milieu.
The large numbers which the Mayas were able to manipulate, enabled them to keep track of revolutions of various bodies in the sky. Since these revolutions did not happen instantly, the Maya had perforce, to deal with the phenomenon of passing time. It is said, in fact, that the Maya were obsessed with time. Actually what they were obsessed with, was the planet Venus: its appearances as the evening star and the morning star as well as its conjunctions with various other planets. Also the Maya were interested in lunar and solar eclipses. Of course solstice events were interesting too.
Two Types of Years
The basic unit of time for the Maya, as well as for everyone else, was the 24-hour day. Beyond this, their system quickly became complicated. Rather than one type of year the Maya simultaneously tracked two years of different lengths. The 260-day year was called the Sacred Round. Each day in the year had a different designation, established from the revolutions of a small wheel with 13 cogs (each representing one number from 1-13) inside a larger wheel with 20 names. Suppose for example, that the names were represented by letters A-T. As the small wheel revolved inside the large wheel we would obtain: 1A 2B 3C 4D 5E 6F 7G 8H 9I 10J 11K 12L 13M 1N 2O 3P 4Q 5R 6S 7T 8A 9B 10C etc. No designation was repeated for an entire 260 days. To further complicate things, a larger circle representing a "vague year" meshed with the Sacred Round. The vague year was 365 days long (18 months of 20 days) plus 5 extra days. The period of time required for the sacred year and the vague year to return to the starting place was 18,980 days. In the interim, 52 complete vague years had passed and 73 sacred years. This was just the beginning of Mayan record-keeping however. They also employed a Long Count to better locate the sequence of events in the sky and in their own history.
One Mayan day was called a kin. Twenty kins represented one uinal. Eighteen uinals represented one tun or 360 days. Twenty tuns was 1 katun or 7200 days. Twenty katuns was 1 baktun or 144,000 days. Twenty baktuns was 1 pictum or 2,880,000 days. The count progressed through three more levels to 1 alutun or twenty three billion 40 million days. A sample Long Count date of 184.108.40.206.0 would be calculated thus:
9 [(20 x 20) x 360] + 9 (20 x 360) + 9 (360) + 16 (20) + 0 (1) = 1,364,360 days
This means that 1,364,360 days had passed since their creation date (or roughly 3750 years). In our calendar, the calculated sample date would have been made by Mayans living at about 650 AD. At that time, on a worldwide basis, only the Maya were able to carry out such calculations. They possessed a concept that nobody else understood. That concept was zero.
Zero is a Good Thing
Apparently only three cultures in history have understood the concept of zero. The Babylonians did, but their knowledge disappeared with the fall of their civilization several centuries before Christ's birth. In the new world, the Maya possessed this mathematical know how. Presumably also the earlier Olmec had the same skill with numbers. A four-ton monument found in Olmec territory, included two dates in the Long Count system. The dates were 143 AD and 156, well after most Olmec communities had gone into decline. However the monument is in Olmec territory and includes glyphs in a language somewhat different from Mayan. In Europe, until the Middle Ages, nobody could carry out calculations involving such large numbers. Awkward Roman numerals simply were not suitable. The Hindus of India apparently discovered zero in the ninth century AD. Eventually this useful idea made its way to Europe and the rest, as they say, is history.
As far as the Maya were concerned, the revolutions of Venus relative to Earth, were integral to the structure of their calendar. Somehow the Maya were able to keep track of Venus with an astonishing accuracy. As a matter of fact, their figure of 584 days for one revolution of Venus around the Sun is almost identical to our modern estimate of 583.92166 days. Nevertheless the small difference would, over the course of 52 years, translate into an error of five days. Apparently however, the Mayas knew how to correct for this discrepancy. Scholars suspect that the Maya understood the revolutions of Venus to an accuracy of one half hour per century or one day's error in 5000 years. Indeed, commentators in New Scientist (18 October 1979 p. 206) remark concerning this situation:
If true, this is incredible; such accuracies were not achieved in Western planetary astronomy until modern times. It is twice as accurate as the Gregorian solar calendar which we use today and 40 times more accurate than the Julian calendar in use in the west at the time the Maya flourished.
In mathematical terms, the Maya understood that 5 Venus years equalled 2920 days which equalled eight vague years. Moreover 13 multiples of 2920 days equalled 2 calendar round revolutions for a total of 104 vague years. It is clear that the Maya had fun with figures!
The real mystique of the Maya remains the question of the source of their mathematics. Did this ancient society develop sophisticated mathematics in order to track celestial bodies, or did they simply employ skills which they already possessed? The only other ancient culture with similar know how was that of the Babylonians in the Middle East. Could the Maya have learned about zero from the Babylonians?
There are some tantalizing hints that this was indeed the case. Besides zero, the similarities between the two cultures included a fascination with Venus, hieroglyphic systems of writing and pyramid monuments.
Other than calendar glyphs, the inscriptions of the Maya seemed highly inscrutable but a breakthrough in their decoding came in 1952. The story goes that Yuri Knosorov, a young Russian soldier present at the fall of Berlin in 1945, found himself near the burning German National Library. Apparently he was able to rescue a single book, which turned out to be a copy of three extremely rare Mayan manuscripts. Seven years later, Mr. Knosorov declared that the Mayan characters were partly pictorial and partly phonetic. In fact, the Mayan script (and also the Olmec) was just like every other hieroglyphic system. Thus in their writing style the Olmec and the Maya closely resembled their old world counterparts.
Egypt, Babylon and Maya?
As far as monuments are concerned, the Mayan pyramids certainly resembled, at least superficially, the pyramids of Egypt and the ziggurats of Babylon. Nevertheless it was a common view among experts that the Mayan examples had "nothing to do" with the old world constructions. When some Mayan pyramids were discovered to function as tombs (like the Egyptian models), some experts began to emphasize similarities rather than differences. For example, concerning the Mayan temple in Palenque, the 1975 National Geographic article declared:
The similarities between the tomb of Pacal (Mayan) and those who ruled earlier beside the Nile are striking. In each instance pyramids rise above the burial sites and the builders took elaborate precautions to conceal entries; inside the tombs grave goods accompanied the corpse into the afterlife; the sarcophagus top bore the likeness of the dead king.National Geographic p. 762
The similarities between Central American Maya and Middle Eastern cultures (Babylon and Egypt) thus include hieroglyphic type script, sophisticated mathematics, and pyramid shaped monuments. Also the planet Venus was of particular interest both to the Babylonians and the Maya. Various cuneiform tablets describing conjunctions of Venus with the Sun, for example, were discovered in 1850 in the remains of the library of Ashurbanipal at ancient Nineveh.
If the Maya and ancient middle eastern cultures had a common origin, as does appear to be the case, the question remains where and when they were in contact. The Babylonian ziggurat, of course, has always been associated with the Tower of Babel. If the Flood occurred about 2350 BC, and the events of Babel occurred some years later, then the common origin of these cultures is accounted for, and the mystery of the Maya is answered. Of course not everyone will agree with such conclusions, but then the puzzle remains.