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Mechanical computing has a surprisingly long history. Archaeologists have found evidence that a calculating device—a forerunner of the abacus—was invented about 4,000 years before the Christian era (4000 b.c.e.). Probably invented in its early forms by the Babylonians, a later, hand-held version of the abacus developed by the Romans was widely used by engineers to calculate viaducts, roads, and land surveys; by tradespeople as cash registers, calcula-tors, and computers; and, probably by tax collectors to figure the amounts due. Eventually, the abacus was used throughout the Near East as well as China.

The abacus is a digital computer in that it works with discrete quantities (one bead is equal to one, 10, 100, and so on, depending on its position.) The other kind of computer is an analog computer—a computing device that operates on measurable quantities (for exam-ple, weight or length) rather than having direct numerical input (and sometimes output). An analog clock is one example

The oldest known analog “computer” is a mysterious machine found in 1901 among the strewn cargo of an ancient shipwreck at the bottom of the Aegean Sea. Dubbed the Antikythera device, it apparently dates from the first century b.c.e., and as far as anyone knows, this calculating machine stands alone in its time—with not even a mention of anything like it in any ancient document. Nothing similar from the same era has ever been found. Was it a one-of-a-kind production?

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Both types of computers were further developed in the Middle Ages and Renaissance periods. In analog computing, Near Eastern astronomers developed the astrolabe and other instruments for mea-suring star positions.

✹ Babbage, lovelace, and Th eir “diff erence engine”

The most remarkable forerunner of the modern computer came in the middle of the 19th century, though its signifi cance would not be realized until well into Turing’s time.

Charles Babbage (1791–1871) was an ingenious British inventor and mathematician. Born in Devonshire, he attended the University of Cambridge, and in 1816, he became a Fellow of the Royal Society—a great honor, especially at the age of 24. Along with a group of friends including astronomer John Herschel, Bab-bage helped establish the Analytical Society in 1812. He was also a founding member of the Royal Astronomical Society (1820), and helped form the Statistical Society (1834).

Babbage became frustrated by the inaccuracy of the hand-compiled tables of logarithms and other quantities that were available of the time. He decided that only a machine that could follow precise, unvarying steps could guarantee the accuracy of calculations. In this era of locomotives and steam-driven looms, it was perhaps not surprising that Babbage thought it quite possible to build a “Difference Engine” to perform complicated calculations quickly and automatically.

Meanwhile, Ada Byron (1815–52), countess of Lovelace and daughter of the British poet Lord Byron, had grown up having an innate interest in mathematics. Self-taught in geometry, she also learned by whatever other means were available to her, including friends, tutors, and classes in astronomy and math. She and Bab-bage met in 1833 (when she was about 18) and these two individu-als with a passion for numbers began collaborating.

Like Jacquard’s loom with its punched-card weaving patterns, the Difference Engine relied on programming concepts and had a complex design capable of handling extensive and involved calcula-tions. Lovelace showed a ready understanding of the concept of a programmed machine when she translated and annotated a paper

In the 1650s, the English mathematician William Oughtred (1575–1660) invented the slide rule, using a stick marked with logarithmic measurements that slid up and down to deliver the results. After various improvements through the years, the slide rule

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written in French about Babbage’s Difference Engine. Money for the project ran out, though, and Babbage and Lovelace never saw it work. However, in 1991 a team of computer experts carefully followed Babbage’s design notes and drawings and found that the design was sound and the Babbage Difference Engine they pro-duced ran perfectly.

Lovelace and Babbage also collaborated on designing a more advanced machine—the Analytical Engine, which is considered the fi rst attempt at a modern digital computer. The machine was designed to read data from a stack of punched cards—much as early digital computers did—and it could store the data and perform calculations. Byron worked on writing the instructions, or programming, recorded by punching the cards—and she therefore receives recognition as the fi rst computer programmer. In 1979, in honor of the contributions to computer science made by Lady Ada Lovelace, the U.S. Department of Defense named a key program-ming language Ada.

The Analytical Engine probably would not have been a very prac-tical machine, however, even if the thousands of precisely machined parts had been manufactured and assembled. These early computer designers had not come up with the idea of using the same format and media for all functions—programming, data storage, results.

Electricity and electronics were not yet in the picture, and the calcu-lating circuits made possible by Boolean logic were as yet unknown.

By the 1930s, however, electrical switches and relays as well as the much faster electronic vacuum tubes were readily available.

A number of people in the United States, Great Britain, and Germany had begun to build electrical or electronic calculators. What was needed were the ideas to put it all together—the universal, program-mable computer. Alan Turing’s work would play a key—perhaps the most decisive—role in this development.

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became a staple instrument for every engineer and scientist well into the 20th century, tucked away in a desk drawer or handy pocket for quick calculations. Finally, in the 1970s handheld calculators replaced them, especially as the microchip-driven pocket calculator became more and more sophisticated.