Linear A, a writing system that was used by the ancient Minoans from 1800 to 1450 BC, has never been fully decrypted. Used in governmental and religious writings of the Minoan Civilization, the script has intrigued and frustrated experts for centuries.
Now, for the first time, scientists and archaeologists believe that they have decrypted symbols denoting numerical fractions in the Linear A writing system.
The alphabet called Linear A was first discovered and named by British archaeologist Sir Arthur Evans, who lived from 1851-1941. It was succeeded by Linear B, which was used by the Mycenaeans to write an early form of Greek. No complete texts in Linear A have ever been deciphered.
The term ‘linear’ derives from script that was written by using a stylus to cut lines into a clay tablet, as opposed to “cuneiform,” which was written by using a stylus to press wedge shaped letters into the clay.
Linear A belongs to a group of scripts which are similar to hieroglyphics, but they evolved independently from the Egyptian and Mesopotamian writing systems. During the second millennium BC, there were four major branches of this alphabet: Linear A, Linear B, Cypro-Minoan, and Cretan hieroglyphic.
In the 1950s, archaeologists deciphered Linear B as Mycenaean Greek. They found that Linear B shares many symbols with Linear A, and they may notate similar syllabic values. But neither those nor any other proposed readings led to a language that can be read by experts.
The only part of the script that can be deciphered and read are the signs for numbers — which, however, are still only known as numerical values. The actual words for those numbers remain unknown.
One symbol for each fraction
But now, researchers in Bologna, Italy have deciphered the mathematical quantities for these symbols by combining methods of linguistics, mathematics and archeology and comparing the material with the corresponding hieroglyphic symbols from Egypt and Mesopotamia, which are known.
The researchers started with the hypothesis that the simple division by two, the fraction ½, was the most common and that any fraction greater than ½ can be expressed as ½ + x. On this basis, the researchers calculated the various combinations and the frequency of the fractions they saw.
The Bologna researchers created a table in which all the possible symbols of the fractions of Linear A were classified into specific numerical quantities. Published in the Journal of Archaeological Science, the table shows semicircular symbols with a serial number of lines for the fractions 1/4, 1/5 or 1/20, 1/30 and so on up to 1/60.
The symbol for 1/10 is reminiscent of the letter T. However, the fraction most often found on clay tablets is ½, which is like the letter J. The researchers from Bologna are optimistic that the combined method they used will one day lead to the decipherment of the entire enigmatic Linear A writing system.
The researchers found that tens were marked with horizontal lines or dots, hundreds with circles and thousands with circles framed by lines. What is striking is that the Minoans used even decimal fractions for their calculations and for recording quantities.
According to the researchers, Linear A contains 17 symbols which obviously meant fractions. These decimal fractions were represented by triangular or semicircular symbols supplemented by one or more dots.
Scientists had already discovered this, but to date they had not been able to find the correspondence of the symbols with specific fractions. The clay tablets that have survived are often fragmentary, and the correspondences have changed over time.
Linear A texts have been found throughout the island of Crete and also on Kythera, Kea, Thera, and Melos in the Aegean and on the Greek mainland.
The Bologna researchers believe that by continuing the study, they will one day decipher all the Linear A symbols and gain better insight into the language.