Yesterday I went to a big exhibition at the Musée du Quai Branly (the anthropological museum of Paris). The exhibition was entitled “Mayas: Revelation d’un temps sans fin”, and with that enticing reference to infinity, I hoped that they would tell me something about the Mayans’ numeration system.
It was a very interesting exhibition. Among other things, it included everyday objects produced by the Mayans: beautiful polychrome pots and beakers, lovely figurines of real people, jade death masks. But virtually nothing about either the writing system or the numeration system they used; it is because of the deciphering of these that we know as much as we do about their remarkable civilisation.
There was a film showing which gave a little more information, mainly about the writing.
If you have an unknown language to decipher, the first thing is to make a complete list of all the glyphs used. The size of the list gives valuable information. If it has between 15 and 30 elements, it is very likely to be an alphabet similar to our own. If it has around 100, it is probably a syllabary (a set of symbols each representing a syllable, typically consonant+vowel, as in Linear B. If it contains many thousands, each symbol probably represents a word, as in Chinese.
The Mayan inscriptions contained about 3000 identifiable glyphs, so it was first assumed that they represented words, in which case only a small part of the language could be shown. This led researchers astray for some time. Two special features helped. Firstly, there were obvious pictures interspersed with the glyphs, which could identify some words (for example, “turkey”). Second, the people of Yucatan and Guatemala speak a language which is descended from the language the Mayans spoke, so we have some cribs, e.g. we can look up “turkey” in a dictionary.
The final conclusion is that it is a syllabary (with some symbols for words, and some pictorial elements). The reason it is so large is that the Mayans had many (maybe as many as 15) different ways to represent the same syllable, and mixed them freely. It seems that they had a love of variety and a horror of repetition: the last fact may be connected with the enormous length of their astronomical cycle.
A further complication is that several syllables can be combined into a single glyph.
Wikipedia gives at least one illustration of Mayan orthography:
You can see that many of the glyphs are “cephalomorphic”, shaped like heads or faces. One of the glyphs resembles an astronaut in a spacesuit, which of course gave rise to a lot of bizarre speculation by a few people. The exposition contained a good example of this.
The interpretation of numbers is more straightforward, but was also complicated by the fact that the first researchers did not expect that the Mayans would have a positional system, with a symbol for zero. Their system used base 20, the digits being made up of combinations of a dot (for 1) and a bar (for 5).
Of course, it is their calendrical and astronomical cycles which have attracted the most attention, and about which I would have liked to learn more. Their many stelae recorded historical events, and began with precise dates: one example in the exhibition (lintel 48 from Yaxchelán) begins 184.108.40.206.16 2Ki6, that is, 11 February 526 in our system. It is really remarkable that events a millennium and a half ago can be dated so precisely and so certainly.
According to the exhibition catalogue, the Mayans took both the Long Count and the Calendar Round from the Olmecs, as well as their vigesimal numeration system. The Olmecs developed the system in about 100 BCE, and may have been the first civilisation to do so.
Towards the end of the exhibition, there was a striking figure, with a science-fiction feel to it, consisting of a terracotta incense-burner in the figure of the god of night, which had been kept in a limestone cave so that one half was encased in limestone. I was reminded of Herbert Read’s novel The Green Child.