Mathematics in India 4248

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But, while a major part of the Mayan script is still not deciphered, there are parts of it that have been deciphered, and already long ago. One of those were the calendrical notations, one of the first parts of the script that have been decyphered. In calendrical notations, the Mayans counted days from some fixed date (long into history). They used for this 20 day, 360 day, 7200 day and longer periods where each subsequent period was 20 times as long as the previous period. So the system is base-20, except for the 360 day period (where base 18 crept in). All those periods had specific names, and dates were recorded by those names preceded by the count of it, from 0 to 19 (except in the last but one case where it was 0 to 17). Not a true base 20 system, but with an attested 0. Later on dates were also recorded without the specific names for those periods, creating a semi base 20 system for counting (with positional 0).

See for instance: From one to zero, a universal history of numbers by Georges Ifrah. The English version dates from 1985. Also all other literature about mayan I have read state the same. The calendar has been in use until (for certain) the 19th century.

I have no idea whether the Indian 0 came before or after the South American 0 (the dating of the emerging of the concept in both cultures is conflicting). The only thing you can say is that the concept is invented independently in both places. And I think about the same time (7th century A.D.). The problem with the Mayan (and Aztec) culture is of course that most of it has been destroyed by the Spanish. Which is a shame.

It may be noted that also the Babylonians have introduced some form of 0 in their (cuneiform) writing. While in most texts trailing 0's were omitted and a succession of 0's was represented by a single 0, there are also astronomical texts that record all 0's. But when? Nobody knows. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131