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Calculation is an integral part of how societies function and has been used since ancient times to regulate trade and fix dimensions of land and buildings. Theoretical developments in mathematics, along with the growing complexity of calculations, inspired the design of calculating machines during the Early Modern period. These analogue devices, along with technologies developed for factory automation and advances in electronics engineering, gave rise to the first digital computers.

"[I]t is unworthy of excellent men to lose hours like slaves in the labor of calculation, which could safely be relegated to anyone else if machines were used." Gottfried Wilhelm von Leibniz, 1671.(1)

Employed by the ancient Egyptians, Greeks, and Mesopotamians, the earliest calculating devices were systems of writing that used shorthand to denote specific and often large quantities. These written forms differed between cultures but usually involved groups of lines representing single units, with modified characters for intervals of five or ten.

Counting sticks, knots, and tally sticks - with values denoted by specific notches - were common forms of counting and numerical record-keeping throughout the world. These systems, along with the use of Roman numerals, persisted through the Renaissance G , as many were hesitant to adopt the Hindu-Arabic numerals used today out of concern for accuracy and the potential for forgery.

The abacus is perhaps the most well known pre-modern calculating device, and is often associated with the wire-and-bead devices that originated in the Middle East. While its true origins remain debatable, the word abacus would have referred to an ancient practice of moving pebbles ('calculi') along lines written in sand.

A common abacus today is the Japanese 'soroban', which has one 'heavenly' bead per wire representing 5, and four 'earthly' beads representing 1 each. This is a simplification of the Chinese 'Suanpan', in which more beads per wire can accommodate other decimal systems such as duodecimal (i.e. base 12, rather than base 10) **(Image 1)**.

Pure mathematics has its own history alongside that of counting. The origins of geometry, for example, stretch back to Ancient Greece, and Euclid's XR Elements, first compiled around 300 BCE, would become, in various forms, the standard mathematical textbook for nearly two millennia **(Image 2)**.

» A brief history of calculating devices is continued here

» You can read more about how models were used to aid the teaching of Euclid's *Elements* here.

- Quoted in: D. E. Smith,
*A source book in mathematics*(New York, 1929), pp. 180-181. (Find in text ^)

Mikey McGovern

Mikey McGovern, 'A brief history of calculating devices', *Explore Whipple Collections*, Whipple Museum of the History of Science, University of Cambridge, [http://www.hps.cam.ac.uk/whipple/explore/calculatingdevices/abriefhistory/, accessed 19 July 2019]

http://www.hps.cam.ac.uk/whipple/explore/calculatingdevices/abriefhistory/