Salamis Tablet
Encyclopedia
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 a Babylonian means of performing mathematical calculations common in the ancient world. Pebbles (calculus) 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.
the National Museum of Epigraphy, in Athens
.
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.
zero and four) and a system of lines serves to group them by powers of ten
. A pebble between the lines represents a five.
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, which were displaced later by the Indo–Arabic system.
The two number systems differ 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 letters of the alphabet numbers was for scientific mathematics better suited. For example Archimedes and Diophantos used the Milesian system.
The Greek writer Herodotus
(485–425 BC) reports in his travels through Egypt that the Egyptians moved their pebbles on the boards from right to left, contrary to the Greek custom of left to right.
with powers of ten,
the schema fostered by the Salamis Tablet might have enabled a skilled mathematician
at the time, Archimedes
, to work out how many grains of sand the Universe
might contain.
The counting table gave way to the Roman abacus
for the performance
of routine accounting tasks. Yet the methods of pebbles and lines were
the basis of what was to become the place based Arabic numerals
in later years.
Salamis Island
Salamis , is the largest Greek island in the Saronic Gulf, about 1 nautical mile off-coast from Piraeus and about 16 km west of Athens. The chief city, Salamina , lies in the west-facing core of the crescent on Salamis Bay, which opens into the Saronic Gulf...
in 1846. A precursor to the abacus
Abacus
The abacus, also called a counting frame, is a calculating tool used primarily in parts of Asia for performing arithmetic processes. Today, abaci are often constructed as a bamboo frame with beads sliding on wires, but originally they were beans or stones moved in grooves in sand or on tablets of...
, it is thought that it represents a Babylonian means of performing mathematical calculations common in the ancient world. Pebbles (calculus) 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.
Discovery
Originally thought to be a gaming board, the slab of white marble is currently atthe National Museum of Epigraphy, in Athens
Athens
Athens , is the capital and largest city of Greece. Athens dominates the Attica region and is one of the world's oldest cities, as its recorded history spans around 3,400 years. Classical Athens was a powerful city-state...
.
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 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.
Numerical representations
As with an abacus, pebbles represent small numbers (generally betweenzero and four) and a system of lines serves to group them by powers of ten
Powers of Ten
Powers of Ten is a 1968 American documentary short film written and directed by Charles and Ray Eames. The film depicts the relative scale of the Universe in factors of ten . The film is an adaptation of the book Cosmic View by Dutch educator Kees Boeke, and more recently is the basis of a new...
. A pebble between the lines represents a five.
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, which were displaced later by the Indo–Arabic system.
The two number systems differ 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 letters of the alphabet numbers was for scientific mathematics better suited. For example Archimedes and Diophantos used the Milesian system.
The Greek writer Herodotus
Herodotus
Herodotus was an ancient Greek historian who was born in Halicarnassus, Caria and lived in the 5th century BC . He has been called the "Father of History", and was the first historian known to collect his materials systematically, test their accuracy to a certain extent and arrange them in a...
(485–425 BC) reports in his travels through Egypt that the Egyptians moved their pebbles on the boards from right to left, contrary to the Greek custom of left to right.
Legacy
A powerful means of representing decimal numbers in scientific notationwith powers of ten,
the schema fostered by the Salamis Tablet might have enabled a skilled mathematician
at the time, Archimedes
Archimedes
Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and an...
, to work out how many grains of sand the Universe
might contain.
The counting table gave way to the Roman abacus
Roman abacus
The Romans developed the Roman hand abacus, a portable, but less capable, base-10 version of the previous Babylonian abacus. It was the first portable calculating device for engineers, merchants and presumably tax collectors...
for the performance
of routine accounting tasks. Yet the methods of pebbles and lines were
the basis of what was to become the place based Arabic numerals
Arabic numerals
Arabic numerals or Hindu numerals or Hindu-Arabic numerals or Indo-Arabic numerals are the ten digits . They are descended from the Hindu-Arabic numeral system developed by Indian mathematicians, in which a sequence of digits such as "975" is read as a numeral...
in later years.
- See also Roman abacusRoman abacusThe Romans developed the Roman hand abacus, a portable, but less capable, base-10 version of the previous Babylonian abacus. It was the first portable calculating device for engineers, merchants and presumably tax collectors...
.