The beginning of the calculus

The first calculations were carried out with the fingers, in Latin “digitus” from which comes the word "digital".

Were later used stones, marking the results on pieces of bone or wood. At this moment the history of calculation begins.

The oldest know calculation tool is the Ishango's bone, found in Africa and dated to 20,000 BC. There are marked groups of numbers that make up a sum, as they do even today the shepherds, and this way of representing the figures remained until recent times. The official use was abolished in England only in 1826!

The Ishango's bone

The marks on the Ishango's bone

The Ishango's bone

The next step was the abacus, a simple tool to organize piles of stones (in Latin "calculi" and hence the term "calculate"), while the numbers were now represented by symbols and recorded on clay tablets. This is a digital calculator. Below you can see the attempt to solve the Pythagorean Theorem on a Babylonian tablet and in Excel, really very similar. The systems created by the use of the fingers are often in base 12 (10 fingers + 2 hands) or its multiples. The Babylonians counted in sexagesimal and trace remains in the division of time and angles.

Plimpton 322   Babylonian tablet in Excel

Babylonian tablet (1800 BC) and the same calculation made in Excel

The abacus, invented around 2500 BC in Mesopotamia, spread everywhere in various forms. The older models had the bottom filled with sand ('Abaq in Sumerian) to keep track of the operations: it was the first silicon memory!

Roman abacus    Modern abacus

Roman abacus and its modern equivalent.

The abacus was adopted by all the people and the Incas had a particular model, composed of cords with knots, which allows to keep track of the transactions still used by the U.S. Special Forces in operational theaters climatically extremes because ... it works in every condition!

Quipu Inca    Ranger Beads

Quipu Inca and modern "Ranger Beads", used by US Army

Suanpan cinese

Chinese's Suanpan

The abacus is not a real calculator because it merely assist the operator in performing the operations, but allows to add and subtract very quickly. It was abandoned by Europeans in the Middle Ages and only in Russia continued to be used in stores until the collapse of the Soviet Union.

Abacus     Schoty

European abacus and Russian Schoty

There was also the abacus “exchequer” consisting of a board divided into squares on which were moved some small stones, called "jetons". Hence the term "Chancellor of the Exchequer" which designates the English Minister of Finance. His predecessors kept the accounts of the crown thanks to an abacus of this type located in the London's tower.

Exchequer abacus

Exchequer abacus

With the development of trade, the Europeans needed more sophisticated tools. Luca Pacioli in 1494 published his "Summa de Arithmetica". He presented the modern concept of double-entry bookkeeping (give and take, budget, inventory) and proposing the use of Arabic numerals instead of Roman ones. To perform the bookkeeping of the new companies was necessary a calculator.

Beginning of calculus on Wikipedia

Abacus patent

The abacus is hard to die: this model was patented in 1998!

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