Le frazioni, gli errori di calcolo e le unità di misura nella documentazione in lineare A

This paper offers a complete and updated analysis of the textual evidence for fractions, miscalculations, and units of measurement in Linear A documents.The following relative values are suggested for the most frequently attested Linear A fraction signs: J = ½, D = 1/3, E = ¼, B = 1/5, F = 1/8. The formal resemblance between three Linear B measuring signs and three Linear A fraction signs could suggest K = 1/10, DD = 1/30, X = 1/120, but the possible geometric progression on HT Zd 156 would suggest that K = 1/16. Nine tablets from Ayia Triada show miscalculations (HT 9a, 123a.b, 94a, 118) or other problems in calculations (HT 13, 102, 116, 119, 127). Two tablets seem to contain partial sums (HT 110a e 11a) and, like HT 10, they could be part of missing sets of tablets. The highest units of measurement are implicit in the commodities’ ideograms and smaller quantities are pointed out by fraction signs. Only the unit for weight has a distinguishing symbol, the ideogram AB 118, and it probably has the same value in Linear A and in Linear B (31.2 g.). Because the inscription incised on the pithos ZA Zb 3 mentions 32 units of wine and the volume of the pithos is about 556 l, the absolute value of the Minoan unit for liquids could be about 17.4 l, but the analysis of the other two inscribed pithoi with ideograms and numerals (KN Zb <27> and KN Zb 35) shows that the inscriptions on pithoi had administrative purposes and dealt with certain products not exclusively contained in the pithos bearing the inscription. The pithoi were used for long periods, on the contrary the function of the inscriptions was limited to the first stuffing of the vase and this fact explains why the inscriptions on pithoi are occasional and have a low degree of visibility.