Additive progression in prehistoric mathematics: A conjecture (Q1059060)

The reviewer remarks that ancient systems of numeration show alternating bundles: in Sumer 6,10, in Greece and Rome, 2,5, in Egypt mostly 10- bundles. There is no question of a positional system. In addition to that we have in Egypt two cubit values, the ''normal'' of 7 palms, the ''royal'' of 8 palms, and the Roman ''as'' was subdivided in 12 unciae, which had in sets containing a smaller number each their own name. The present author treats weights found in a shipwreck near Cape Gelidonya: thirteen weights of which once a multiple of 3,12,31,50,54, twice a multiple 5 and five times a multiple 7 was approximately present. Multiplying the unit as experimentally, and thus with the greatest experimental error determined at 9.3 he suggests a relation with distorted Fibonacci numbers: 1,2,3,5,8,13,21,34,55,89... assuming a diminishing of 8 to 7, leading to 1,2,3,5,7,12,19,31,50,54. No bothering about the tremendous difference of 54 and 81 he considers this system as warranted. The reviewer computed the ''most probable line'' \(y=mx.\). on which these shifts from 30-31 etc. had hardly any influence and found the inclination m to be 9,307.. leading to a set of most probable values in the series 1- 3,5,7,12,30,50,55 slightly better represented than the values obtained by the author with 9.3-multiple and shifting to 31 and 54 at two places.. the gap 54-81 not being explained by the author.