TEMPUS Magazine redefines time, giving you a glimpse into all things sophisticated, compelling, vibrant, with its pages reflecting the style, luxury and beauty of the world in which we live. A quarterly publication for private aviation enthusiasts.
Issue link: http://tempus-magazine.epubxp.com/i/447005
Computing Machine. Even an irrational number such as π could be calculated indefnitely using a fnite table of instructions. So could the logarithm of 7, or the square root of 2, or the sequence of Bernoulli numbers that Ada Lovelace had helped produce an algorithm for, or any other number or series, no matter how challenging to compute, as long as its calculation was defned by a f- nite set of rules. All of these were, in Turing's parlance, "computable numbers." Turing went on to show that noncomputable num- bers also existed. Tis was related to what he called "the halting problem." Tere can be no method, he showed, to determine in advance whether any given instruction table combined with any given set of inputs will lead the machine to arrive at an answer or go into some loop and continue chugging away indefnitely, getting nowhere. Te insolvability of the halting problem, he showed, meant that Hilbert's decision problem, the Entscheid- ungs problem, was unsolvable. Despite what Hilbert seemed to hope, no mechanical procedure can deter- mine the provability of every mathematical statement. Gödel's incompleteness theory, the indeterminacy of quantum mechanics, and Turing's answer to Hilbert's third challenge all dealt blows to a mechanical, deter- ministic, predictable universe. Turing's paper was published in 1937 with the not so snappy title "On Computable Numbers, with an Appli- cation to the Entscheidungs problem." His answer to Hilbert's third question was useful for the development of mathematical theory. But far more important was the by-product of Turing's proof: his concept of a Logical Computing Machine, which soon came to be known as a Turing machine. "It is possible to invent a single ma- chine which can be used to compute any computable se- quence," he declared. Such a machine would be able to read the instructions of any other machine and carry out whatever task that machine could do. In essence, it em- bodied the dream of Charles Babbage and Ada Lovelace for a completely general-purpose universal machine. A different and less beautiful solution to the Entscheid- ungs problem, with the clunkier name "untyped lamb- da calculus," had been published earlier that year by Alonzo Church, a mathematician at Princeton. Turing's professor Max Newman decided that it would be use- ful for Turing to go there to study under Church. In his letter of recommendation, Newman described Turing's enormous potential. He also added a more personal ap- peal based on Turing's personality. "He has been work- ing without any supervision or criticism from anyone," Newman wrote. "Tis makes it all the more important that he should come into contact as soon as possible with the leading workers on this line, so that he should not develop into a confrmed solitary." Turing did have a tendency toward being a loner. His homosexuality made him feel like an outsider at times; he lived alone and avoided deep personal commitments. At one point he proposed marriage to a female colleague, but then felt compelled to tell her that he was gay; she was unfazed and still willing to get married, but he be- lieved it would be a sham and decided not to proceed. Yet he did not become "a confrmed solitary." He learned to work as part of a team, with collaborators, which was key to allowing his abstract theories to be refected in real and tangible inventions. In September 1936, while waiting for his paper to be published, the twenty-four-year-old doctoral candidate sailed to America in steerage class aboard the aging ocean liner RMS Berengaria, lugging with him a prized brass sextant. His ofce at Princeton was in the Mathematics Department building, which also then housed the Institute for Advanced Study, where Einstein, Gödel, and von Neumann held court. Te cultivated and highly sociable von Neumann became particularly interested in Turing's work, despite their very different personalities. Te seismic shifts and simultaneous advances of 1937 were not directly caused by the publication of Turing's paper. In fact, it got little notice at frst. Turing asked his mother to send out reprints of it to the mathematical philosopher Bertrand Russell and a half dozen other famous scholars, but the only major review was by Alonzo Church, who could afford to be fattering because he had been ahead of Turing in solving Hilbert's decision problem. Church was not only generous; he introduced the term Turing machine for what Turing had called a Logical Computing Machine. Tus at twenty-four, Turing's name became indelibly stamped on one of the most important concepts of the digital age. B L E T C H L E Y PA R K Although few outsiders knew it at the time—and would not know for more than three decades—another elec- tronic computer using vacuum tubes had been secretly built at the end of 1943 on the grounds of a redbrick Vic- torian manor in the town of Bletchley, ffty-four miles northwest of London, where the British had sequestered a team of geniuses and engineers to break the German wartime codes. Te computer, known as Colossus, was the frst all-electronic, partially programmable comput- er. Because it was geared for a special task, it was not a general-purpose or "Turing-complete" computer, but it did have Alan Turing's personal fngerprints on it. Turing had begun to focus on codes and cryptology in the fall of 1936, when he arrived at Princeton just after writing "On Computable Numbers." He explained his P H O T O B Y S S P L / G E T T Y I M A G E S Holiday 2014 / 2015 Tempus-Magazine.com 72 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