The Evolution of Calculating Devices and Machines

The abacus was an early aid for mathematical computations. Its only value is that it aids the memory of the human performing the calculation. A skilled abacus operator can work on addition and subtraction problems at the speed of a person equipped with a hand calculator. The abacus is often wrongly attributed to China. In fact, the oldest surviving abacus was used in 300 B. C. by the Babylonians. The abacus is still in use today, principally in the far east.

A modern abacus consists of rings that slide over rods, but the older one pictured below dates from the time when pebbles were used for counting (the word "calculus" comes from the Latin word for pebble).

In 1617 an eccentric Scotsman named John Napier invented logarithms, which are a technology that allows multiplication to be performed via addition. The magic ingredient is the logarithm of each operand, which was originally obtained from a printed table. But Napier also invented an alternative to tables, where the logarithm values were carved on ivory sticks which are now called Napier's Bones.

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In 1642 Blaise Pascal, at age 19, invented the Pascaline as an aid for his father who was a tax collector. Pascal built 50 of this gear-driven one-function calculator but couldn't sell many because of their exorbitant cost and because they really weren't that accurate. Up until the present age when car dashboards went digital, the odometer portion of a car's speedometer used the very same mechanism as the Pascaline to increment the next wheel after each full revolution of the prior wheel.

Pascal was a child prodigy. At the age of 12, he was discovered doing his version of Euclid's thirty-second proposition on the kitchen floor.

Pascal went on to invent probability theory, the hydraulic press, and the syringe. Shown below is an 8 digit version of the Pascaline. Just a few years after Pascal, the German Gottfried Wilhelm Leibniz managed to build a four calculator that he called the stepped reckoner because, instead of gears, it employed fluted drums having ten flutes arranged around their circumference in a stair-step fashion. Although the stepped reckoner employed the decimal number system, Leibniz was the first to advocate use of the binary number system which is fundamental to the operation of modern computers.

Leibniz is considered one of the greatest of the philosophers but he died poor and alone. In 1801 the Frenchman Joseph Marie Jacquard invented a power loom that could base its weave (and hence the design on the fabric) upon a pattern automatically read from punched wooden cards, held together in a long row by rope. Descendents of these punched cards have been in use ever since. By 1822 the English mathematician Charles Babbage was proposing a steam driven calculating machine the size of a room, which he called the Difference Engine.

This machine would be able to compute tables of numbers, such as logarithm tables. Hollerith's invention, known as the Hollerith desk, consisted of a card reader which sensed the holes in the cards, a gear driven mechanism which could count, and a large wall of dial indicators to display the results of the count. Hollerith built a company, the Tabulating Machine Company which, after a few buyouts, eventually became International Business Machines, known today as IBM. IBM grew rapidly and punched cards became ubiquitous. Your gas bill would arrive each month with a punch card you had to return with your payment.