calculator

The use of physical objects to assist in performing calcula-tions begins in prehistory with such practices as count-ing with pebbles or making what appears to be counting marks on pieces of bone. Nor should such simple manipula-tions be despised: In somewhat more sophisticated form it yielded the abacus, whose operators regularly outperformed mechanical calculators until the advent of electronics.

Generally, however, the term calculator is used to refer to a device that is able to store a number, add it to another number, and mechanically produce the result, taking care of any carried digits. In 1623, astronomer Johannes Kepler commissioned such a machine from Wilhelm Schickard. The machine combined a set of “Napier’s bones” (slides marked with logarithmic intervals, the ancestor of the slide rule) and a register consisting of a set of toothed wheels that could be rotated to displays the digits 0 to 9, automatically carrying one place to the left. This ingenious machine was destroyed in a fire before it could be delivered to Kepler.

In 1642, French philosopher and mathematician Blaise Pascal invented an improved mechanical calculator. Its mechanism used a carry mechanism with a weight that would drop when a carry was reached, pulling the next wheel into position. This avoided having to use excessive force to carry a digit through several places. Pascal pro-duced a number of his machines and tried to market them to accountants, but they never really caught on.

Schikard’s and Pascal’s calculators could only add, but in 1674 German mathematician Gottfried Wilhelm Leibniz invented a calculator that could work with all the digits of a number at once, rather than carrying from digit to digit. It worked by allowing a variable number of gear teeth to be engaged in each digit wheel. The operator could, for example, set the wheels to a number such as 215, and then turn a crank three times to multiply it by three, giving a result of 645. This mechanism, gradually improved, would remain fundamental to mechanical calculators for the next three centuries.

The first calculator efficient enough for general business use was invented by an American, Dorr E. Felt, in 1886. His machine, called a Comptometer, used the energy trans-mitted through the number-setting mechanism to perform the addition, considerably speeding up the calculating pro-cess. Improved machines by William Burroughs and oth-ers would replace the arm of the operator with an electric motor and provide a printing tape for automatically record-ing input numbers and results.

Electronic Calculators

The final stage in the development of the calculator would be characterized by the use of electronics to replace mechanical (or electromechanical) action. The use of logic circuits to perform calculations electronically was first seen in the giant computers of the late 1940s, but this was obvi-ously impractical for desktop office use. By the late 1960s, however, transistorized calculators comparable in size to mechanical desktop calculators came into use. By the 1970s, the use of integrated circuits made it possible to shrink the calculator down to palm-size and smaller. These calculators use a microprocessor with a set of “microinstructions” that enable them to perform a repertoire of operations ranging from basic arithmetic to trigonometric, statistical, or busi-ness-related functions.

The most advanced calculators are programmable by their user, who can enter a series of steps (including per-haps decisions and branching) as a stored program, and then apply it to data as needed. At this point the calculator can be best thought of as a small, somewhat limited com-puter. However, even these limits are constantly stretched: During the 1990s it became common for students to use graphing calculators to plot equations. Calculator use is now generally accepted in schools and even in the taking of the Scholastic Aptitude Test (SAT). However, some educa-tors are concerned that overdependence on calculators may be depriving students of basic numeracy, including the abil-ity to estimate the magnitude of results.