Minoan Linear A is still an undeciphered script mainly used on the island of Crete from 1700 to 1400 BCE. A new study published in the published in the Journal of Archaeological Science sheds light on one of the most enigmatic features of Linear A — the precise mathematical values of its system of numerical fractions (such as 1/2, 1/4, 1/8).
Linear A is a logo-syllabic script used for administrative purposes on Bronze Age Crete. Together with Cretan Hieroglyphic, it is one of two writing systems created by the Minoan civilization.
Upon its template, the Mycenaeans later created the Linear B script to register their dialect of ancient Greek.
Today, the Linear A corpus comprises more than 7,400 signs on 1,527 inscriptions, 90% of which are clay documents of administrative nature, such as tablets, roundels, and nodules.
As for numerical notations, Linear A employs a decimal system, with signs representing four magnitudes: units are written with vertical strokes, tens with horizontal strokes or dots, hundreds with circles, and thousands with circles surrounded by strokes.
The system is cumulative and additive, and numbers are written from left to right with the powers in descending order: thus, e.g. 6,352 would be written with six ‘1,000’ signs, three ‘100,’ five ‘10’ and two ‘1.’
Linear A also includes a set of 17 signs that stand for fractions. They are transcribed via capital letters: A, B, D, E, F, H, J, K, L, L2, L3, L4, L6, W, X, Y, and Ω.
To shed light on the values of these fractions, University of Bologna’s Professor Silvia Ferrara and colleagues focused on a specific set of Linear A documents dated to the Late Minoan I period (ca. 1600-1450 BCE).
“We aimed to solve the problem through a lens combining different strands of research, very seldom tied together: close paleographical analysis of the signs and computational methods,” Professor Ferrara said.
“In this way we realized that we could access information from a new perspective.”
The researchers applied a method that combines the analysis of the sign shapes and their use in the inscriptions together with statistical, computational and typological strategies to assign mathematical values to the Linear A signs for fractions.
They studied the rules that the signs followed on the clay tablets and other accounting documents.
To investigate the possible values of each fractional sign, they excluded impossible outcomes with the aid of computational methods.
Then all possible solutions — almost four million — were whittled down also comparing fractions that are common in the history of the world (e.g., typological data) and using statistical tests.
Finally, they applied other strategies that considered the completeness and coherence of the fractions as a system and in this way the best values were identified, with the least 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 the type n/60.
“Our results explain how the Linear B script reused some of these fractions to express units of measurement,” the authors said.
“The results suggest that, for example, the Linear A sign for 1/10 was adapted to represent a capacity unit for measuring dry products which was, in turn, 1/10 of a larger unit.”
“This explains a historical continuity of use from fractions to units of measurements across two different cultures.”
Michele Corazza et al. The mathematical values of fraction signs in the Linear A script: A computational, statistical and typological approach. Journal of Archaeological Science, published online September 7, 2020; doi: 10.1016/j.jas.2020.105214