The Salamis Tablet is a marble

counting board The counting board is the precursor of the abacus, and the earliest known form of a counting device (excluding fingers and other very simple methods). Counting boards were made of stone or wood, and the counting was done on the board with beads, ...

(an early counting device) dating from around 300 BC, that was discovered on the island of Salamis in 1846. A precursor to the

abacus An abacus ( abaci or abacuses), also called a counting frame, is a hand-operated calculating tool which was used from ancient times in the ancient Near East, Europe, China, and Russia, until the adoption of the Hindu–Arabic numeral system. A ...

, it is thought that it represents an

ancient Greek Ancient Greek (, ; ) includes the forms of the Greek language used in ancient Greece and the classical antiquity, ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Greek ...

means of performing mathematical calculations common in the ancient world. Pebbles () were placed at various locations and could be moved as calculations were performed. The marble tablet measures approximately 150 × 75 × 4.5 cm.

Discovery

Originally thought to be a gaming board, the slab of

white marble Marble is a metamorphic rock consisting of carbonate minerals (most commonly calcite (CaCO3) or dolomite (CaMg(CO3)2) that have recrystallized under the influence of heat and pressure. It has a crystalline texture, and is typically not foliat ...

is currently at the Epigraphical Museum in

Athens Athens ( ) is the Capital city, capital and List of cities and towns in Greece, largest city of Greece. A significant coastal urban area in the Mediterranean, Athens is also the capital of the Attica (region), Attica region and is the southe ...

Description

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 five 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.

Numerical representations

As with other counting boards and abaci, each counter represents one unit of a magnitude determined by position. The precise interpretation of counters and methods used with the tablet is unknown, but it is possible that use was similar to medieval European counting boards in which counters on the lines represented powers of ten and counters between the lines represented 5 times the previous line. Retired engineer and high school teacher Stephen Stephenson (1942–2022) speculated that counters placed on either side of the dividing line might represent positive and negative quantities, and that the smaller area at the "top" (as shown in the picture above) of the tablet might represent the exponent of a

floating-point number In computing, floating-point arithmetic (FP) is arithmetic on subsets of real numbers formed by a ''significand'' (a signed sequence of a fixed number of digits in some base) multiplied by an integer power of that base. Numbers of this form ...

, with the larger area at the "bottom" representing the mantissa.

Calculations

On this board, physical markers (indicators) were placed on the various rows or columns that represented different values. The indicators were not physically attached to the board. On the tablet Greek numbers are represented. Already in the Ionian time period number systems were responsible for the written use, which became necessary because of the expanding commercial activity. Two different number systems were developed, the older Attic or Herodian number system and the younger, Milesian system. The two number systems differed in their use: the Attic predominantly served the commercial life for the adjustment of funds and goods data as well as for the designation of the columns on the abacus. For written calculations the Attic numeral system was unsuitable. The Milesian number system, with which one likewise assigned numbers to letters of the alphabet, was better suited for scientific mathematics. For example, Archimedes and

Diophantus Diophantus of Alexandria () (; ) was a Greek mathematician who was the author of the '' Arithmetica'' in thirteen books, ten of which are still extant, made up of arithmetical problems that are solved through algebraic equations. Although Jose ...

used the Milesian system. The Greek writer

Herodotus Herodotus (; BC) was a Greek historian and geographer from the Greek city of Halicarnassus (now Bodrum, Turkey), under Persian control in the 5th century BC, and a later citizen of Thurii in modern Calabria, Italy. He wrote the '' Histori ...

(485–425 BC) reports in his travels through Egypt that the Egyptians calculated from right to left, contrary to the Greek custom of left to right. This may refer to moving pebbles on the counting board.

Notes

References

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External links

* * , a speculative reconstruction of how the Salamis tablet might be used as a counting board {{Calculator navbox Greek mathematics Abacus Archaeological discoveries in the Aegean Islands 1846 archaeological discoveries