Salamis Tablet

The Salamis Tablet was an early counting device (also known as a "counting board") dating from around 300 B.C. that was discovered on the island of Salamis in 1846. A precursor to the abacus, it is thought that it represents an Ancient Greek means of performing mathematical calculations common in the ancient world. Pebbles (calculi) were placed at various locations and could be moved as calculations were performed. The marble tablet itself has dimensions of approximately 150 × 75 × 4.5 cm.

Originally thought to be a gaming board, the slab of white marble is currently at the National Museum of Epigraphy, in Athens.

Five groups of markings appear on the tablet. The three sets of Greek symbols arranged along the left, right and bottom edges of the tablet are numbers from the acrophonic system. In the center of the tablet – a set of 5 parallel lines equally divided by a vertical line, capped with a semicircle at the intersection of the bottom-most horizontal line and the single vertical line. Below a wide horizontal crack is another group of eleven parallel lines. These are divided into two sections by a line perpendicular to them but with the semicircle at the top of the intersection; the third, sixth and ninth of these lines are marked with a cross where they intersect with the vertical line.

As with an abacus, pebbles represent small numbers (generally between zero and four) and a system of lines serves to group them by powers of ten. A pebble between the lines represents half the value of a pebble on the line above it. So a pebble on the first line represents a 1; above the first line is a 5; second line is 10; above the second line is 50; etc.

The vertical line divides positive and negative portions of the Salamis Tablet. Pebbles on the right side of the vertical line represent positive digits and those on the left side of the line represent negative digits.

A complete number is composed of various pebbles on lines and spaces, both on the positive and negative sides. For example, the number 4 might be represented as a pebble above the right side of the first line plus a pebble on the left side of the first line; the pebble on the right side lies between the first and second lines so it counts as a +5, whereas the pebble on the left side of the first line represents a −1, so the two pebbles together represent +4. Likewise, the number 90 might be represented as a pebble on the right side of the third line plus a pebble on the left side of the second line. Note that this way of representing integers corresponds to the set-theoretic (or foundational) construction of the integers as ordered pairs of natural numbers. (Cf. balanced ternary.)

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