The mathematical values of Linear A fraction signs

Date:
September 8, 2020
Source:
Elsevier
Summary:
A recent study has shed new light on the Minoan system of fractions,
one of the outstanding enigmas tied to the ancient writing of
numbers.



FULL STORY ==========================================================================
A recent study by a team based at the University of Bologna, published in
the Journal of Archaeological Science, has shed new light on the Minoan
system of fractions, one of the outstanding enigmas tied to the ancient
writing of numbers.


========================================================================== About 3,500 years ago, the Minoan civilization on the island of Crete
developed a writing system composed of syllabic signs, called Linear
A, which they sometimes used to inscribe offerings at sanctuaries and
adorn their jewelry, but mainly assisted the administration of their
palatial centers.

Today, this script remains largely undeciphered and includes a complex
system of numerical notation with signs that indicated not only whole
numbers, but also fractions (such as 1/2, 1/4, 1/8, etc.). While the
whole numbers were deciphered decades ago, scholars have been debating
on the exact mathematical values of the fractional signs.

Principal Investigator Silvia Ferrara, Professor of the Department of
Classical Philology and Italian Studies of the University of Bologna,
said: "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. 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 Scripts and
their Beginnings), Michele Corazza, Barbara Montecchi, Miguel Vale'rio,
and Fabio Tamburini, led by Dr. Ferrara, 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.

The team first studied the rules that the signs followed on the
clay tablets and other accounting documents. Two problems had so far complicated the decipherment of Linear A fractions. First, all documents containing sums of fractional values with a registered total were damaged
or difficult to interpret, and second, they contradicted uses of certain
signs, which suggest the system changed over time. Thus, the starting
premise had to rely on documents concentrated to a specific period
(ca. 1600-1450 BCE), when the numerical system was in coherent use
across Crete.

To investigate the possible values of each fractional sign, the team
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, the team 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.

The system of values suggested by the Bologna team has yielded further important implications.

The results explain how the Linear B script, adopted by the later
Mycenaean Greek culture (ca. 1450-1200 BCE) from Linear A, reused some
of these fractions to express units of measurement. The new 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.

This research aims to show that traditional methods and computational
models, when used in synergy, can help us make remarkable progress
into explaining some unresolved issues tied to ancient scripts that are
still undeciphered.


========================================================================== Story Source: Materials provided by Elsevier. Note: Content may be edited
for style and length.


========================================================================== Journal Reference:
1. Michele Corazza, Silvia Ferrara, Barbara Montecchi, Fabio Tamburini,
Miguel Vale'rio. 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 ==========================================================================

Link to news story: https://www.sciencedaily.com/releases/2020/09/200908113231.htm

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