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Stratum Plus. 1997

Leo Klejn (St.-Petersburg, Russia)

The origin of zero: the evolution of dice game between Indus and Danube

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Pages: 47-66

A detailed study of one category of Bronze Age finds in Northern and north-eastern Black Sea area, namely dice, is the basis of this paper. These finds began occurring since early this century, and at present 49 dice from at least 19 sets are known to the author. The finds belong to two kinds: one (two sets) appeared in royal interment of Novosvobodnaya culture, the other in the graves of Catacomb cultural community. Both are similar to each other and are distinguished by their form from the rest of dice known in the world. Everywhere dice are usually cubes, i. e. they have six sides, while these dice are bipyramidal with a smoothed middle rib, i. e. they have four bent sides. In this, they are similar only to Indian dice. Since the author considers the Catacomb cultural community of the Bronze Age as the original area of Aryan migration to India, he supposes the similarity of the dice is not a chance one. Having isolated the most ancient from the Indian descriptions of the game, he reconstructed the Bronze Age game which had existed in the Pontic steppes. However as the sites are not simultaneous, he could reconstruct different stages of the game evolution since the time of Novosvobodnaya (the first half of the 3d mill. B. C.) until the medieval times. The most ancient dice, the Oriental ones, were cubical, i. e. they had six sides each and correspondingly designations of the six first numerals of the natural sequence (“one” to “six”). This had influenced the whole culture: in the Ancient Orient, in Sumer, the hexadic-sexagesimal scale of notation was established. Yet in the Ancient Orient, still before the Novosvobodnaya stage, the evolution went through the stage of Semitic influence, and the Semites used the astragali for the game. At an astragalus the both butt ends have no possibilities of being cast by the throw, thus only four designations are usual on them, most often not digits. Dice began imitating astragali, so four-sided dice appeared, but the tradition of digit designations was retained on them. In order to save the traditional gain meaning of the “six” some middle digits had to be dropped and the natural sequence of numerals was destroyed. In the Caucasian milieu “three” was saved, in the Indo- European milieu “four”, depending on the general cultural traditions with different sacred numerals. In the run of this evolution the notion of zero emerged among Aryans. Brought from the North-Pontic area by the Aryans, zero went from the Indian mathematics into Arabian and from the last one into European. Originally zero resulted from the necessity to grant the number one in the sum of three dice cast: the digit “one” on one die while the rest two should have the possibility to show zero designation — the sign “nothing”, “empty”. In addition to this sign other digits of the Bronze Age are revealed: made by incisions (in Novosvobodnaya), by dots and figures (the Catacomb-grave cultural community).

Information about author:

Leo Klejn (St.-Petersburg, Russia). Professor. European University at Saint-Petersburg.
Е-mail: [email protected]

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