A recent study by a team from the University of Bologna published in the Journal of Archaeological Science , has shed new light on the Minoan system of fractions, one of the most prominent enigmas of ancient number writing.
About 3,500 years ago, the Minoan civilization on the island of Crete developed a writing system made up of syllabic signs, called Linear A , which they sometimes used to inscribe offerings in the shrines and adorn their jewelry, but mainly helped with the administration of their palatial centers.
Today, this script remains largely undeciphered and includes a complex system of numerical notation with signs indicating not only whole numbers, but also fractions (such as 1/2, 1/4, 1/8, etc.). While whole numbers were figured out decades ago, scholars have been debating the exact mathematical values of fractional signs.
According to lead researcher Silvia Ferrara, professor at the Department of Classical Philology and Italian Studies at the University of Bologna, we set out to solve the problem through a method that combined different lines of research, rarely linked together, and a detailed paleographical analysis of the signs and calculation methods. In this way we realized that we could access information from a new perspective .
The members of the European Research Council project INSCRIBE (Invention of signs and their beginnings), Michele Corazza, Barbara Montecchi, Miguel Valério and Fabio Tamburini, led by Dr. Ferrara, applied a method that combines the analysis of forms of signs and their use in inscriptions together with statistical, computational and typological strategies to assign mathematical values to the signs of Linear A for fractions.
The team first studied the rules that the signs followed on clay tablets and other accounting documents. Two problems had so far complicated the deciphering of Linear A fractions. . First, all the documents that contained sums of fractional values with a recorded total were corrupted or difficult to interpret, and second, they contradicted the uses of certain signs, which suggest that the system changed over time. Thus, the initial premise had to be based on documents concentrated in a specific period (ca. 1600-1450 BC), when the numerical system was used consistently throughout Crete.
To investigate the possible values of each fractional sign, the team excluded impossible results with the help of computational methods. Then all possible solutions – nearly four million – were also narrowed down by comparing fractions that are common in world history (eg typological data) and using statistical tests. Finally, the team applied other strategies that considered the integrity and coherence of the fractions as a system and in this way the best values were identified, with the fewest redundancies. The result, in this case, was a system whose lowest fraction is 1/60 and which shows the ability to represent most values of type n/60.
This value system suggested by the Bologna team has had other important implications.
The results explain how writing Linear B , adopted by the later Mycenaean Greek culture (ca. 1450-1200 BC) from Linear A , reused some of these fractions to express units of measurement. The new results suggest that, for example, the sign Linear A for 1/10 it was adapted to represent a unit of capacity for measuring dry goods which was itself 1/10 of a larger unit. This explains a historical continuity of use of fractions to units of measurement in two different cultures.
This research aims to show that traditional methods and computational models, when used in synergy, can help us make remarkable progress in explaining some unresolved questions linked to ancient scripts that have not yet been deciphered.