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COMPUTING with QUANTUM CATS
FROM COLOSSUS TO QUBITS
By JOHN GRIBBIN Prometheus Books
Copyright © 2014 John Gribbin
All rights reserved.
ISBN: 978-1-61614-922-2
CHAPTER 1
Turing and the Machine
If necessity is the mother of invention, the computer had two mothers—cryptography and the hydrogen bomb. But there was only one father: Alan Mathison Turing.
A CHILD OF EMPIRE
Turing was conceived in India, where his father, Julius, was a member of the Indian Civil Service helping to administer this jewel in the crown of the British Empire; but he was born, on June 23, 1912, in Maida Vale, London, when his parents were on home leave. He already had a brother, John, born in India on September 1, 1908. When Julius returned to India their mother, Sara, stayed in England with the two boys, but only until September 1913, when she rejoined her husband and left the children in the care of a retired army colonel and his wife, who lived at St. Leonards-on-Sea in Sussex. There was a nanny who looked after the two boys and the colonel's four daughters, together with another boy whose parents were overseas, and later three cousins of Alan and John. Their mother returned for the summer of 1915, staying with the boys in rented rooms in St. Leonards, and both parents came to England in the spring of 1916—the first time that Alan really had an opportunity to get to know his father. At the end of this leave, in August, Julius Turing returned to India for his next three years' tour of duty. John had already been sent away to school at Hazelhurst, in Kent; Alan, having been just one of a motley group of children, now became in effect the only child of a single parent, who took him almost everywhere with her, including to the High Anglican church she attended (which he hated) and to art classes (she was an accomplished watercolorist), where he was the darling of the female students.
Alan was remembered as a bright, untidy child with a predilection for inventing his own words, such as "quockling" to describe the sound of seagulls and "greasicle" for a guttering candle. It was impossible to pull the wool over his eyes—when his nanny tried to let him win a game they were playing by making poor moves, he saw through the subterfuge and was infuriated; when his mother was reading him a story and left a dull passage out, he yelled: "You spoil the whole thing." Nor was he ever in any doubt about the accuracy of his own worldview: he knew, for example, that the fruit which tempted Eve in the Garden of Eden was a plum. But he never could tell left from right, and marked his left thumb with a red spot so that he would know which was which.
Having taught himself to read (from a book appropriately called Reading without Tears), Alan first encountered formal education at the age of six, when his mother sent him to a local day school to learn Latin. This failed to stir his interest, but highlighted his great difficulty with the physical process of writing, especially with the ink pens in use at the time. His work was always a mess of scratchy scribbles, crossings-out and blots, reminiscent of nothing so much as the spoof handiwork of Nigel Molesworth in the stories by Geoffrey Willans and Ronald Searle.
Alan's next meeting with his father came in 1919, when Julius's leave included a holiday in Scotland: here the seven-year-old boy impressed his family on a picnic by tracking the flights of wild bees to their intersection to find honey. But in December both parents sailed for India, and Alan returned to the colonel's house in St. Leonards while John went back to school in Hazelhurst. The next two years saw a change in Alan. When his mother next returned, in 1921, she found that the vivacious and friendly boy she had left in England had become "unsociable and dreamy," while his education had been so neglected that at nearly nine he had not learned how to do long division. She took him away for a holiday in Brittany, and then to London, where she taught him long division herself. She later recalled that when he had been shown how to find the square root of a number, he worked out for himself how to find the cube root.
At the beginning of 1922, it was time for Alan to follow his brother John to Hazelhurst, a small school for thirty-six boys aged from nine to thirteen, with just three teachers and a matron who looked after the boys. The brothers were together at Hazelhurst for only one term before John left at Easter for Marlborough College and the public-school education for which "prep" schools such as Hazelhurst were preparing their boys. The same year, Alan was given a book called Natural Wonders Every Child Should Know, by Edwin Brewster. This first encounter with science made a deep impression on him, especially the way the author likened the workings of the body, even the brain, to a machine. He was less impressed by the sporting activities that young English gentlemen of the time were expected to enjoy (or at least endure), and later claimed that he had learned to run fast (he became a very good long-distance runner as an adult) in order to keep away from the ball during hockey. He was also disturbed by the imprecision of some of his teachers, and wrote to John that one of them "gave a quite false impression of what is meant by x." His concern was not for himself, but that the other boys might be misled.
The summer of 1922 brought the return of Alan's father on leave once more, and another happy family holiday in Scotland. But in September his parents left him back at Hazelhurst, departing down the drive of the school with Sara biting her lip as she watched her son running futilely after the taxi, trying to catch up with them. Bored by school, Alan achieved nothing spectacular in the way of marks, but loved inventing things and developed a passion for chemistry—which was purely a hobby: God forbid that a prep school like Hazelhurst should have anything to do with science. Science was almost as conspicuous by its absence at most public schools, so when in the autumn of 1925 Alan surprised everyone by doing well in the Common Entrance examination that was a prerequisite to the transition, his future presented his parents with something of a conundrum. John made an impassioned plea to their parents not to send his unusual younger brother to Marlborough, which "will crush the life out of him," and Sara Turing worried that her son might "become a mere intellectual crank" if he failed to adapt to public school life. The puzzle of what to do with him was solved by a friend of hers who was married to a science master at Sherborne, a school in Dorset established back in 1550 and brought into the modern public school system in 1869. The friend assured Sara that this would be a safe haven for her boy, and Alan started there in 1926.
SHERBORNE
He was due to arrive for the start of the summer term, on May 3, from Brittany, where his parents were living to avoid paying British income tax. On the ferry to Southampton, Alan learned that there would be no trains, because of the general strike; totally unfazed, and still a month short of his fourteenth birthday, he cycled the 60 miles to Sherborne, staying overnight at Blandford Forum. This initiative was sufficiently unusual to merit a comment in the Western Gazette on May 14. The same initiative and independence were shown a little later when Alan worked out for himself the formula known as "Gregory's series" for the inverse tangent, unaware that it had been discovered in 1668 by the Scottish mathematician James Gregory (inventor of a kind of telescope that also bears his name), and even earlier by the Indian mathematician Madhava.
Alan soon settled into his old habit of largely ignoring lessons that he found boring, then doing well in examinations, while continuing his private chemistry experiments and amusing himself with advanced mathematics. At Sherborne, grades depended on a combination of continuous assessment and examinations, each marked separately but with a final combined mark. On one occasion, Alan came twenty-second out of twenty-three for his term's work, first in the examinations, and third overall. His headmaster did not approve of such behavior, and wrote to Alan's father: "I hope he will not fall between two stools. If he is to stay at a Public School, he must aim at becoming educated. If he is to be solely a Scientific Specialist, he is wasting his time at a Public School." But Alan escaped expulsion, and was rather grudgingly allowed to take the School Certificate examination, which had to be passed before he could move on to the sixth form at the beginning of 1929. His immediate future after school, however, was decided as much by love as by logic.
As in all public schools, filled with teenage boys with no other outlet for their burgeoning sexuality, there were inevitably liaisons between older and younger pupils, no matter how much such relationships might be officially frowned upon. It was in this environment that Alan realized that he was homosexual, although there is no record of his having any physical relationships with other boys at school. He did, though, develop something more than a crush on a boy a year ahead of him at school, Christopher Morcom.
The attraction was as much mental as physical (indeed, from Morcom's side it was all mental). Morcom was another mathematician, with whom Alan could discuss science, including Einstein's general theory of relativity, astronomy, and quantum mechanics. He was a star pupil who worked hard at school and achieved high grades in examinations, giving Alan, used to taking it easy and relying on brilliance to get him through, something to strive to emulate. The examination they were both working for, the Higher School Certificate (or just "Higher"), was a prerequisite to moving on to university. In the mathematics paper they sat, Alan scored a respectable 1,033 marks; but Morcom, the elder by a year, scored 1,436.
In 1929, Morcom was to take the examination for a scholarship at Trinity College, Cambridge. He was eighteen, and expected to pass. Alan was desperate not to see his friend go on to Cambridge without him. He decided to take the scholarship examination at the same time, even though he was still only seventeen and Trinity was the top college in Britain (arguably, in the world) for the study of math and science, with a correspondingly high admission standard. The examinations were held over a week in Cambridge, giving the two Shirburnians a chance to live the life of undergraduates, and to meet new people, including Maurice Pryce, another candidate, whom Alan would meet again when their paths crossed in Princeton a few years later.
The outcome was as Alan had feared. Morcom passed, gaining a scholarship to Trinity that gave him sufficient income to live on as an undergraduate. Alan did not, and faced a separation of at least a year from his first love. But the separation became permanent when Morcom died, of tuberculosis, on February 13, 1930. Alan wrote to his own mother: "I feel that I shall meet Morcom again somewhere and that there will be some work for us to do together.... Now that I am left to do it alone I must not let him down." And in the spirit of doing the work that they might have done together, or that Morcom might have done alone, and "not letting him down," Alan tried once again for Cambridge in 1930. Once again, he failed to obtain a Trinity scholarship; but this time he was offered a scholarship worth £80 a year at his second choice of college, King's. He started there in 1931, when he was nineteen.
CAMBRIDGE ...
Turing managed the unusual feat of joining in both the sporting life (as a runner and rower) and the academic life in Cambridge, while never quite fitting in anywhere socially. He also enjoyed at least one homosexual relationship, with another math student, James Atkins. But it is his mathematical work that is important here. Turing's parting gift from Sherborne, in the form of a prize for his work, had been the book Mathematical Foundations of Quantum Mechanics, by the Hungarian-born mathematician John von Neumann, who would soon play a personal part in Turing's story. In an echo of his early days at Sherborne, not long after he arrived in Cambridge Turing independently came up with a theorem previously (unbeknown to him) proven by the Polish mathematician Waclaw Sierpinski; when Sierpinski's priority was pointed out to him, he was delighted to find that his proof was simpler than that of the Pole. Polish mathematicians would also soon loom large in Turing's life.
In the early 1930s, the structure of the mathematics course in Cambridge was changing. Everybody who entered in 1931 (eighty-five students in all) took two key examinations, Part I at the end of the first year and Part II at the end of the third year. So-called "Schedule A" students left it at that, which was sufficient to gain them their degrees. But "Schedule B" students, including Turing, took a further, more advanced, examination, also at the end of their third year. For the intake which followed Turing's year, the extra examination was taken after a further (fourth) year of study, as it has been ever since: it became known as Part III, and is now roughly equivalent to a Master's degree from other universities.
This peculiarity of the Cambridge system partly explains why Turing never worked for a PhD in Cambridge. Having passed his examinations with flying colors, he was offered a studentship worth £200 which enabled him to stay on at Cambridge for a year to write a dissertation with which he hoped to impress the authorities sufficiently to be awarded a fellowship at King's. In the spring of 1935, still only twenty-two years old, Turing was indeed elected as a Fellow of King's for three years, with the prospect of renewal for at least a further three years, at a stipend of £300 per year; the success was sufficiently remarkable that the boys at Sherborne were given a half-day holiday in his honor. But something much more significant had happened to Turing during his studentship year. He had been introduced to the puzzle of whether it was possible to establish, from some kind of mathematical first principles, whether or not a mathematical statement (such as Fermat's famous Last Theorem) was provable. Apart from the philosophical interest in the problem, if such a technique existed it would save mathematicians from wasting time trying to prove the unprovable.
A very simple example of an unprovable statement is "this statement is false." If it is true, then it must be false, and if it is false, it must be true. So it cannot be proven to be either true or false. The mathematical examples are more tricky, for those of us without a Part III in math, but the principle is still the same. Embarrassingly for mathematicians, it turns out that there are mathematical statements which are true, but cannot be proven to be true, and the question is whether provable statements (equivalent to "this statement is true") in mathematics can be distinguished from unprovable statements using some set of rules applied in a certain way.
Turing's introduction to these ideas came from a series of lectures given by Max Newman on "The Foundations of Mathematics," drawing heavily on the work of the German mathematician David Hilbert. Newman described the application of this kind of set of rules as a "mechanical process," meaning that it could be carried out by a human being (or a team of such human "computers") following the rules blindly, without having any deep insight. As the Cambridge mathematician G. H. Hardy had commented, "it is only the very unsophisticated outsider who imagines that mathematicians make discoveries by turning the handle of some miraculous machine." But Turing, always idiosyncratic and literal-minded, saw that a "mechanical process" carried out by a team of people could be carried out by a machine, in the everyday sense of the word. And he carried with him the idea, from his childhood reading, of even the human body as a kind of machine. In the early summer of 1935, as he lay in a meadow at Grantchester taking a rest from a long run, something clicked in his mind, and he decided to try to devise a machine that could test the provability of any mathematical statement. By then, he had already met von Neumann, who visited Cambridge in the spring of 1935, and had applied for a visiting fellowship at Princeton, von Neumann's base, for the following year. He would not arrive empty-handed.
(Continues...)
Excerpted from COMPUTING with QUANTUM CATS by JOHN GRIBBIN. Copyright © 2014 John Gribbin. Excerpted by permission of Prometheus Books.
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