Abstract
The systematic investigation of sexagesimal numbers, by means of reciprocals and ratios, led to a ‘dualism’ in the numerical theory developed in ancient Mesopotamia. The historical development of mathematical thinking — the mathopoeic mind — resulted in a proto-science, including arithmetic, geometry, astronomy and possibly harmonics, which attempted to formulate a structural theory for the pantheon and cosmos. An exponential matrix, based on sexagesimal considerations, is proposed as a means of exlploring the mathopoeic component in ancient mythology, which often incorporates significant proto-scientific data. Since the mathopoeic mind in Mesopotomian civilization is fully developed by 1750 BC, it is likely that the vast body of data gathered by Near Eastern proto-science served as the historical reference reservoir for the Greek mathopoeic mind — especially for the Pythagoreans. Both of these mathopoeic traditions were, however, de-emphasized in Graeco—Roman Judaism because it appeared that they could divert the believer to pagan ‘natural philosophy’.
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