The beginning of the calculus
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. 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.
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 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 and modern "Ranger Beads", used by US Army
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.
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.
With the development of trade, the Europeans needed more sophisticated tools. Luca Pacioli in 1494 published his "Summa de Arithmetica," presenting in the "Tractatus de computis et scripturis" 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.
The abacus is hard to die: this model was patented in 1998!
Nicola Marras 2008
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