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tables—and in training and inspiring the next generation of computer pioneers. Bush's machine, however, was not destined to be a major advance in computing history because it was an analog device. In fact, it turned out to be the last gasp for analog computing, at least for many decades. New approaches, technologies, and theories began to emerge in 1937, exactly a hundred years after Babbage frst published his paper on the Analytical Engine. It would be- come an annus mirabilis of the computer age, and the re- sult would be the triumph of four properties, somewhat interrelated, that would defne modern computing: D I G I TA L . A fundamental trait of the computer revolution was that it was based on digital, not analog, computers. Tis occurred for many reasons, as we shall soon see, in- cluding simultaneous advances in logic theory, circuits, and electronic on-off switches that made a digital rath- er than an analog approach more fruitful. It would not be until the 2010s that computer scientists, seeking to mimic the human brain, would seriously begin working on ways to revive analog computing. B I N A RY. Not only would modern computers be digital, but the digital system they would adopt would be bi- nary, or base-2, meaning that it employs just 0s and 1s rather than all ten digits of our everyday decimal system. Like many mathematical concepts, binary theory was pioneered by Leibniz in the late seventeenth century. During the 1940s, it became increasingly clear that the binary system worked better than other digital forms, including the decimal system, for performing logical op- erations using circuits composed of on-off switches. E L E C T R O N I C . In the mid-1930s, the British engineer Tommy Flowers pioneered the use of vacuum tubes as on-off switches in electronic circuits. Until then, cir- cuits had relied on mechanical and electromechanical switches, such as the clacking electromagnetic relays that were used by phone companies. Vacuum tubes had mainly been employed to amplify signals rather than as on-off switches. By using electronic components such as vacuum tubes, and later transistors and microchips, computers could operate thousands of times faster than machines that had moving electromechanical switches. G E N E R A L P U R P O S E . Finally, the machines would even- tually have the ability to be programmed and repro- grammed—and even reprogram themselves—for a vari- ety of purposes. Tey would be able to solve not just one form of mathematical calculation, such as differential equations, but could handle a multiplicity of tasks and symbol manipulations, involving words and music and pictures as well as numbers, thus fulflling the potential that Lady Lovelace had celebrated when describing Bab- bage's Analytical Engine. Innovation occurs when ripe seeds fall on fertile ground. Instead of having a single cause, the great ad- vances of 1937 came from a combination of capabilities, ideas, and needs that coincided in multiple places. As of- ten happens in the annals of invention, especially infor- mation technology invention, the time was right and the atmosphere was charged. Te development of vacuum tubes for the radio industry paved the way for the cre- ation of electronic digital circuits. Tat was accompanied by theoretical advances in logic that made circuits more useful. And the march was quickened by the drums of war. As nations began arming for the looming confict, it became clear that computational power was as important as frepower. Advances fed on one another, occurring al- most simultaneously and spontaneously, at Harvard and MIT and Princeton and Bell Labs and an apartment in Berlin and even, most improbably but interestingly, in a basement in Ames, Iowa. Underpinning all of these advances were some beauti- ful—Ada might call them poetic—leaps of mathematics. One of these leaps led to the formal concept of a "univer- sal computer," a general-purpose machine that could be programmed to perform any logical task and simulate the behavior of any other logical machine. It was conjured up as a thought experiment by a brilliant English mathemati- cian with a life story that was both inspiring and tragic. A L A N T U R I N G Alan Turing had the cold upbringing of a child born on the fraying fringe of the British gentry. His family had been graced since 1638 with a baronetcy, which had me- andered down the lineage to one of his nephews. But for the younger sons on the family tree, which Turing and his father and grandfather were, there was no land and little wealth. Most went into felds such as the clergy, like Alan's grandfather, and the colonial civil service, like his father, who served as a minor administrator in remote regions of India. Alan was conceived in Chhatra- pur, India, and born on June 23, 1912, in London, while his parents were on home leave. When he was only one, his parents went back to India for a few years, and handed him and his older brother off to a retired army colonel and his wife to be raised in a seaside town on the south coast of England. "I am no child psychologist," his brother, John, later noted, "but I am assured that it is a bad thing for an infant in arms to be uprooted and put into a strange environment." When his mother returned, Alan lived with her for a few years and then, at age thirteen, was sent to boarding school. He rode there on his bicycle, taking two days to cover more than sixty miles, alone. Tere was a lonely intensity to him, refected in his love of long-distance 69 Tempus-Magazine.com Holiday 2014 / 2015 CH . 2 T H E I N N O V A T O R S : HOW A GROUP OF HACKERS, GENIUSES AND GEEKS CREATED THE DIGITAL REVOLUTION