The Mathematical Values of Linear A Fraction Indication
Recent research by a team based at the University of Bologna, released in the Journal of Archaeological Science, has shed light on the Minoan system of fractions, among the exceptional enigmas linked to the age-old writing of numbers.
Around 3,500 years ago, the Minoan civilization on the island of Crete created a system made up of syllabic signs called Linear A. They occasionally utilized to etch offerings at sanctuaries and adorn their jewelry, mainly helping the management of their palatial centers.
Today, this manuscript remains largely undeciphered and includes a complex system of mathematical notation with indications that suggested whole numbers and fractions (such as 1/2, 1/4, 1/8, etc.). While the whole numbers were understood decades ago, scholars have been questioning the specific mathematical values of the fractional signs.
Lead Investigator Silvia Ferrara, Professor of the Department of Timeless Philology and Italian Studies of the University of Bologna, stated: “We intended to fix the problem through a lens integrating various strands of research, very seldom looped: close paleographical analysis of the indications as well as computational methods. This way, we understood that we can access information from a brand-new point of view.”
The members of the European Research Council project INSCRIBE (Invention of Scripts and their Beginnings), Michele Corazza, Barbara Montecchi, Miguel Valério, and Fabio Tamburini, led by Dr. Ferrara, used a method that combines the evaluation of the sign shapes as well as their usage in the engravings combined with statistical, computational and typological approaches to appoint mathematical worths to the Linear A signs for fractions.
The group first studied the signs’ guidelines on the clay tablets and various other accounting files. Two issues have until now made complex the decipherment of Linear A fractions. Initially, all documents with the sums of fractional values with a registered total were damaged or too hard to analyze. Second, they contradicted the uses of specific signs, which indicates that the system changed gradually. Therefore, the starting premise needed to depend on records concentrated to a detailed period (ca. 1600-1450 BCE), when Crete’s numerical system was in use across the region.
To examine the possible values of each fractional sign, the team left out impossible results with the help of computational techniques. After that, all possible solutions-virtually four million-were trimmed by comparing fractions that prevail in the history of the world (e.g., typological data) and utilizing statistical tests. Finally, the group applied various other approaches that considered the completeness and coherence of the fractions as a system. In this way, the very best values were identified with the least redundancies. The result, in this case, was a system whose lowest fraction is 1/60 and revealing the ability to represent the most worths of the type n/60.
The system of values proposed by the Bologna group has produced even more essential implications.
The outcomes clarify precisely how the Linear B script, embraced the later Mycenaean Greek culture (ca. 1450-1200 BCE) from Linear A, reused some of these fractions to express units of measurement. The new outcomes indicate that, for example, the Linear A sign for 1/10 evolved to represent a capacity unit for determining dry products, consequently, 1/10 of a larger unit. This explains a historical continuation of use from fractions to units of measurement across two different cultures.
This study intends to show that traditional approaches and computational versions, when used in harmony, can help us make impressive development into clarifying some unsettled problems linked to old scripts that are still undeciphered.
Originally published on Sciencedaily.com. Read the original article.
Michele Corazza, Silvia Ferrara, Barbara Montecchi, Fabio Tamburini, Miguel Valério. The mathematical values of fraction signs in the Linear A script: A computational, statistical and typological approach. Journal of Archaeological Science, 2020; 105214 DOI: 10.1016/j.jas.2020.105214
