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by analogy. Analog computers do not rely on discrete in- tegers to make their calculations; instead, they use con- tinuous functions. In analog computers, a variable quan- tity such as electrical voltage, the position of a rope on a pulley, hydraulic pressure, or a measurement of distance is employed as an analog for the corresponding quanti- ties of the problem to be solved. A slide rule is analog; an abacus is digital. Clocks with sweeping hands are analog, and those with displayed numerals are digital. Around the time that Hollerith was building his digital tabulator, Lord Kelvin and his brother James Tomson, two of England's most distinguished scientists, were creating an analog machine. It was designed to handle the tedious task of solving differential equations, which would help in the creation of tide charts and of tables showing the fring angles that would generate different trajectories of artillery shells. Beginning in the 1870s, the brothers devised a system that was based on a planim- eter, an instrument that can measure the area of a two- dimensional shape, such as the space under a curved line on a piece of paper. Te user would trace the out- line of the curve with the device, which would calculate the area by using a small sphere that was slowly pushed across the surface of a large rotating disk. By calculating the area under the curve, it could thus solve equations by integration—in other words, it could perform a ba- sic task of calculus. Kelvin and his brother were able to use this method to create a "harmonic synthesizer" that could churn out an annual tide chart in four hours. But they were never able to conquer the mechanical difcul- ties of linking together many of these devices in order to solve equations with a lot of variables. Tat challenge of linking together multiple integrators was not mastered until 1931, when an MIT engineering professor, Vannevar (rhymes with beaver) Bush—re- member his name, for he is a key character in this book— was able to build the world's frst analogelectrical-me- chanical computer. He dubbed his machine a Differential Analyzer. It consisted of six wheel-and-disk integrators, not all that different from Lord Kelvin's, that were con- nected by an array of gears, pulleys, and shafts rotated by electric motors. It helped that Bush was at MIT; there were a lot of people around who could assemble and cal- ibrate complex contraptions. Te fnal machine, which was the size of a small bedroom, could solve equations with as many as eighteen independent variables. Over the next decade, versions of Bush's Differential Analyzer were replicated at the U.S. Army's Aberdeen Proving Ground in Maryland, the Moore School of Electrical En- gineering at the University of Pennsylvania, and Man- chester and Cambridge universities in England. Tey proved particularly useful in churning out artillery fring C O M P U T E R C O D E Computer code-breaking equipment at Bletchley Park. C O D E B R E A K E R A Bombe unit room at Eastcote in Middlesex. The Bombe machine was used extensively during WWII to crack top secret German military code. P H O T O B Y S S P L / G E T T Y I M A G E S O N E O F T H E S E M A T H E M A T I C A L L E A P S L E D T O T H E F O R M A L C O N C E P T O F A A G E N E R A L - P U R P O S E M A C H I N E T H A T C O U L D B E P R O G R A M M E D T O P E R F O R M A N Y L O G I C A L T A S K A N D S I M U L A T E T H E B E H A V I O R O F A N Y O T H E R L O G I C A L M A C H I N E . " U N I V E R S A L C O M P U T E R , "