In the 19th and early 20th centuries, cattlemen of Khakassia, who were not literate, used an ancient system of counting. They marked numbers with signs that resembled Roman numerals. Symbols were carved on a special four-sided wooden stick. Those sticks were 40–50 centimeters long, two to three centimeters wide, and about one centimeter thick.
Counting sticks existed all over Khakassia but had different names throughout it. The Kachin people called them rubas, in the Kyzyl language it sounded as rugash, in Sagai it was kirtiges or sirebe, and in Beltyr it was kirsen.
Essentially, in the relationship between a shepherd and the owner of animals, rubas was kind of a control tool. The signs on the front of the stick were called ‘sirt’ and denoted the number of heads in the herd that was trusted to the shepherd for grazing. The symbols on the back indicated how many animals returned to the owner. The number of fallen cattle was marked on the side of the stick.
Such stick was usually split in half. One half was kept by a shepherd and the other half was kept by the herd’s owner. If it was necessary to clarify how many animals were turned over to the shepherd for grazing, the two halves were put together and the numbers were cross-referenced.
Sometimes two of them were made instead of one, of the same size and with the same numbers. One was left with the owner and the other was given to the shepherd. So that neither the master nor the shepherd was confused, each such stick had a dot, colon, or special signs cut out at the end of the last calculations. They meant that the herd was already counted.
A herd’s owner usually carved a sign of ownership — tamga — on the stick. Such symbols are found, for example, on stones with ancient Turkic texts that were found in southern Siberia. Tamgas also marked the belonging to a certain clan.
Due to the simple counting system used on rubas, Khakasses knew basic arithmetic operations: subtraction (khyzyrarga), addition (khozarga), multiplication (khatirga), and division (polerge). However, the Khakass system of numerical signs was imperfect, unmanageable, and suitable only for counting livestock.
Counting sticks existed all over Khakassia but had different names throughout it. The Kachin people called them rubas, in the Kyzyl language it sounded as rugash, in Sagai it was kirtiges or sirebe, and in Beltyr it was kirsen.
Essentially, in the relationship between a shepherd and the owner of animals, rubas was kind of a control tool. The signs on the front of the stick were called ‘sirt’ and denoted the number of heads in the herd that was trusted to the shepherd for grazing. The symbols on the back indicated how many animals returned to the owner. The number of fallen cattle was marked on the side of the stick.
Such stick was usually split in half. One half was kept by a shepherd and the other half was kept by the herd’s owner. If it was necessary to clarify how many animals were turned over to the shepherd for grazing, the two halves were put together and the numbers were cross-referenced.
Sometimes two of them were made instead of one, of the same size and with the same numbers. One was left with the owner and the other was given to the shepherd. So that neither the master nor the shepherd was confused, each such stick had a dot, colon, or special signs cut out at the end of the last calculations. They meant that the herd was already counted.
A herd’s owner usually carved a sign of ownership — tamga — on the stick. Such symbols are found, for example, on stones with ancient Turkic texts that were found in southern Siberia. Tamgas also marked the belonging to a certain clan.
Due to the simple counting system used on rubas, Khakasses knew basic arithmetic operations: subtraction (khyzyrarga), addition (khozarga), multiplication (khatirga), and division (polerge). However, the Khakass system of numerical signs was imperfect, unmanageable, and suitable only for counting livestock.