The highly productive habits of Alan Turing

June 23 marks the 100th birthday of Alan Turing. If I had to name five people whose personal efforts led to the defeat of Nazi Germany, the English mathematician would surely be on my list. Turing's genius played a key role in helping the Allies win the Battle of the Atlantic—a naval blockade against the Third Reich that depended for success on the cracking and re-cracking of Germany's Enigma cipher. That single espionage victory gave the United States control of the Atlantic shipping lanes, eventually setting the stage for the 1944 invasion of Normandy.

But even before this history-changing achievement, Turing laid the groundwork for the world we live in today by positing a "universal computing machine" in 1936. "It is possible to invent a single machine which can be used to compute any computable sequence," he contended. His proposed device could read, write, remember, and erase symbols. It would produce the same results "independent of whether the instructions are executed by tennis balls or electrons," the historian George Dyson notes, "and whether the memory is stored in semiconductors or on paper tape."

Turing's essential idea, aptly summarized by his centenary biographer Andrew Hodges, was "one machine, for all possible tasks." The concept guided the generation of computer theorists and builders who flourished after the Second World War, among them Turing himself for a time.

Sadly, if the saying "no good deed goes unpunished" ever applied to anyone, it applied to Turing. In 1952, as the Cold War accelerated, the British government arrested him for violating the same indecency law that put the playwright Oscar Wilde in prison. The code-breaker made no apology for his homosexuality, but he accepted an alternative punishment of "chemical castration"—injections of estrogen "intended to neutralise his libido," as Hodges puts it. The attention of the case and the "cure" proved too much for him. In 1954, Turing was found dead of cyanide poisoning; a coroner concluded that he had committed suicide.

Alan Turing's achievements speak for themselves—but the way he lived his remarkable and tragically shortened life is less known. What follows are seven Turing Qualities that we could all emulate to our benefit.

1. Try to see things as they are

Alan Turing was born in 1912, the son of a civil servant in Madras, a state within British-controlled India. As Hodges observes in his book, Alan Turing: The Enigma, Alan's father John Mathison Turing was an assiduous student of Indian life. John Turing spent a decade learning everything he could about agriculture and public health across three rural districts, and even mastered the Telugu language. The boy's mother came from a line of railway and hydraulic engineers.

Young Alan appears to have picked up his parent's passions for learning, but he was farmed out to wards as his parents commuted back and forth from India. The result was a "naughty and willful" lad who often rebelled against his betters and showed a yearning for the literal and frank truth.

When Mrs. Turing had to leave for India in 1915, she had a little talk with her three-year old son. "You'll be a good boy, won't you?" she pleaded. "Yes," Alan replied, "but sometimes I shall forget!"

This sort of literal truth drove Alan's superiors to distraction. When his father returned to England, he gave his child a lecture about keeping his shoe-tongues in proper order. "They should be flat as a pancake," Mr. Turing proclaimed. Alan was unimpressed by this dictum. "Pancakes are generally rolled up!" he shot back.

From the beginning, Alan Turing was a dedicated fan of the actual properties of things. His nanny discovered this the hard way. "You couldn't camouflage anything from him," Hodges quotes her recalling. "I remember one day Alan and I playing together. I played so that he should win, but he spotted it. There was a commotion for a few minutes."

When Turing was about ten years old, someone gave him a copy of Edwin Tenney Brewster's popular book, Natural Wonders Every Child Should Know. It made a big impression on the boy.

"For, of course, the body is a machine," the tome explained, and went on:

It is a vastly complex machine, many, many times more complicated than any machine ever made with hands; but still after all a machine. It has been likened to a steam engine. But that was before we knew as much about the way it works as we know now. It really is a gas engine; like the engine of an automobile, a motor boat, or a flying machine.

In a sense, the rest of Alan Turing's life was about collecting small component facts and ideas about human and non-human machines, then putting them together in new and hugely original ways.

2. Don't get sidetracked by ideologies

Turing went to King's College, Cambridge in 1931. Two years later the Oxford Union debating society issued its famous declaration: "That this House will in no circumstances fight for its King and Country." While not an explicitly pacifist statement, the Oxford Pledge reflected enormous disillusionment with the course and consequences of the First World War.

1933 was a year for radical credos. The global Great Depression was in full swing. "Am thinking of going to Russia some time in vac[ation] but have not yet quite made up my mind," Alan wrote to his mother. He also joined an organization called the Anti-War Council. "Politically rather communist. Its programme is principally to organize strikes amongst munitions and chemical workers when government intends to go to war."

But none of this ever came to anything. Turing didn't go to the Soviet Union, and he found the Marxist institutions on campus just as suffocating as the public school that he attended. Turing "was not interested in organising anyone," Hodges observes, "and did not wish to be organised by anyone else. He had escaped from one totalitarian system, and had no yearning for another."

Not only did Alan Turing reject a Marxist framework, but he would soon fix his skeptical sights on an overarching question haunting theoretical mathematicians at the time:

"Could there exist, at least in principle, a definite method or process by which it could be decided whether any given mathematical assertion was provable?"

3. Be practical

This question was called the Entscheidungsproblem, or the "decision problem" in English. The influential mathematician David Hilbert posed this and two other questions at a major conference in 1928. All three are summarized by Hodges:

First, was mathematics complete in the technical sense that every statement (such as 'every integer is the sum of four squares') could either be proved, or disproved. Second, was mathematics consistent, in the sense that the statement '2 + 2 = 5' could never be arrived at by a sequence of valid steps of proof. And thirdly, was mathematics decidable? By this he meant, did there exist a definite method which could, in principle, be applied to any assertion, and which was guaranteed to produce a correct decision as to whether that assertion was true.

Hilbert thought that the answer to all three of these conundrums was yes. But a young mathematician named Kurt Gödel countered with several "incompleteness theorems" that pretty much knocked questions one and two out of the room. As his biographers Ernest Nagel and James B. Newman put it, Gödel showed that it was:

impossible to establish the internal logical consistency of a very large class of deductive systems - elementary arithmetic, for example - unless one adopts principles of reasoning so complex that their internal consistency is as open to doubt as that of the systems themselves . . . Second main conclusion is . . . Gödel showed that Principia, or any other system within which arithmetic can be developed, is essentially incomplete. In other words, given any consistent set of arithmetical axioms, there are true mathematical statements that cannot be derived from the set . . . Even if the axioms of arithmetic are augmented by an indefinite number of other true ones, there will always be further mathematical truths that are not formally derivable from the augmented set.

You could even come up with your own statement that proved its own unprovability, Gödel noted, such as "Formula G, for which the Gödel number is g, states that there is a formula with Gödel number g that is not provable within [Whitehead and Russell's Principia Mathematica] or any related system."

But then there was that thorny third question, the Entscheidungsproblem. One fine day in 1935, Turing lay in a meadow after a long distance run when the answer came to him—how to determine the existence or non-existence of such a "definite method." He envisioned a machine that functioned as a kind of super-typewriter with an unlimited supply of paper. It could produce symbols, of course, but it could also scan them and move to the left and right at will. Such a machine could resolve the dilemma.

In his famous essay "On Computable Numbers, with an Application to the Entscheidungsproblem," Turing took the reader through a mechanically constructed algorithmic process that demonstrated there existed no "definite method" for solving each and every mathematical question—the machine would produce "uncomputable" numbers that, by their nature, were unsolvable. As Turing biographer Jack Copeland observes, Turing's machine showed that the decimal representations of some real numbers were "so completely lacking in pattern" that no finite table of instructions it could read would be able to follow them.

Turing had done more than resolve a thorny philosophical/mathematical question, however. By tackling the Entscheidungsproblem in practical terms, he had outlined the framework for a universal or "Turing" machine, as it would be called.

"Alan had proved that there was no 'miraculous machine' that could solve all mathematical problems," Hodges explains, "but in the process he had discovered something almost equally miraculous, the idea of a universal machine that could take over the work of any machine."

German operators altered Enigma machine settings on a daily basis. They switched the device's rotors. They repositioned the rotor rings. They rearranged the patch panel linking letter keys to cables. Nazi encryption experts assumed that even if some group of experts possessed the skills necessary to crack Enigma transmissions, the amount of time it would take would make the process irrelevant.

But at Bletchley Park, otherwise known as "Station X," Turing and his crew laid the Enigma code system bare. Ever since his childhood, Turing saw that the lines between mechanical and human thinking were hazy and blurred. He had crossed them himself with his "computable numbers" essay, and he now put this insight to use on the Enigma wheels.

First, Turing and company noted that Enigma machines could not encrypt any letter as that letter itself—this eliminated thousands of possible combinations. Then his team seized on patterns revealed when sloppy German operators neglected to change their settings. The British navy captured Enigma gear—codebooks, instruction books, and even Enigma rotors on occasion. These came in handy for the challenging work ahead.

But the first big breakthrough came when Station X staff noticed that the Germans were preceding their messages to U-boat operators with regular weather reports. These relatively predictable missives opened a new window into Enigma transmissions. The code breakers constantly tested Enigma "cribs," likely German phrases repetitively matched against Enigma missives.

To speed up the cracking of Enigma using these insights, Bletchley Park deployed an expanded version of an Enigma simulation machine first pioneered by Marian Rejewski. The Polish cryptographer called it "the Bombe" either "because of the ticking sound it made," explains Turing biographer David Leavitt, "or (a less likely explanation) because he was eating an ice cream bombe at a cafe when the idea for it hit him."

Here was the "computable numbers" concept set to work. One step at a time; one breakthrough after another. The first Bletchley Bombe weighed a ton and implemented all these code-cracking procedures by replicating the activities of around thirty Enigma gadgets working at the same time.

The "fundamental mathematical insight behind the British bombe was wholly Turing's," explains historian Stephen Budiansky. It was a performance in which Turing "was the undisputed organizer," writes Leavitt, and through his insights and leadership, the mathematician "managed to render the Enigma, if not a powerless antagonist, at least a manageable one."

5. Just keep going

Alan Turing spent much of his life dealing with personal and professional setbacks. For instance, at the same time he wrote his "computable numbers" paper, a Princeton theoretician named Alonzo Church published an essay with similar conclusions. It too argued that the Entscheidungsproblem could not be solved, albeit via purely theoretical logic.

What did Turing do? After the shock of the publication wore off, his mentor Max Newman wrote to Church. Your publication "had a rather painful interest for a young man, A.M. Turing, here," Newman disclosed, "who was just about to send in for publication a paper in which he used a definition of 'Computable Numbers' for the same purpose... I think it of great importance that he should come and work with you next year if that is at all possible."

And so it happened. Turing acknowledged Church in his paper and went to study with him at Princeton, where he also worked with the great computer theorist and innovator John von Neumann. Church in turn acknowledged Turing, even coining the phrase "Turing machine." Church's thesis "would be the Church-Turing thesis from then on," Dyson notes.

Von Neumann offered Turing a temporary position at Princeton in 1938, which Turing turned down to return to England. After the war, he became an advocate for artificial intelligence but found himself once again outpaced by activities in the United States.

In 1945, working as a consultant for World War II computer pioneers John Mauchly and J. Presper Eckert, von Neumann produced his influential "First Draft Report on the EDVAC," Mauchly and Eckert's newest machine. Von Neumann called it a "very high speed automatic digital computing system."

"Once again, British originality had been pipped at the post by an American publication," Hodges notes in his Turing biography, "and at a time when everyone was looking at the west. The Americans had won, and Alan was a sporting second." Yet ENIAC and EDVAC fired up the British to launch a competing machine with a superior acronym: the Automatic Computing Engine (ACE). The National Physics Laboratory then appointed Turing the Temporary Senior Scientific Officer of the project at £800 a year.

6. Be playful

Alan Turing loved movies, verse, and games. He wrote an algorithm that played chess. He was a huge fan of the 1938 Disney movie Snow White and the Seven Dwarfs, and he took to chanting out loud the wicked Queen's verses:

When she breaks the tender peel,
To taste the apple from my hand,
Her breath will still, her blood congeal,
Then I'll be the fairest in the land!

There was something about Turing that made his friends and family want to compose rhymes. His proud father openly admitted that he hadn't the vaguest idea what his son's mathematical inquiries were about, but it was all good anyway. "I don't know what the 'ell 'e meant / But that is what 'e said 'e meant," John wrote to Alan, who took delight in reading the couplet to friends.

His fellow students sang songs about him at the dinner table: "The maths brain lies often awake in his bed / Doing logs to ten places and trig in his head."

His gym class colleagues even sang his praises as a linesman: "Turing's fond of the football field / For geometric problems the touch-lines yield."

Turing's favorite physical activity, however, was running, especially the long-distance variety. "He would amaze his colleagues by running to scientific meetings," Hodges writes, "beating the travelers by public transport." He even came close to a shot at the 1948 Olympic Games, a bid cut short by an injury.

7. Remember that it is people who matter

While Alan Turing enjoyed the pleasures of this world, he loved people the most. It wasn't always easy to see this part of him. For much of his life he wasn't particularly outgoing, but after the Second World War he came close to having something like a "normal" schedule, full of friends and acquaintances, among them his housekeeper, Mrs. Clayton. Turing's mother noted the friendship:

...he delighted to regale her with tales against himself. There was, for instance, the occasion when, his watch being under repair, he carried a little clock in his pocket. Suddenly in the crowded train to Manchester the alarm went off and everyone in the compartment jumped. On his runs he often forgot to take his door-key, so one was kept hidden near the spout of the garage gutter. One day he knocked it over the spout and it just slipped away into the ground, a fact which he reported to Mrs. Clayton with much relish.

Even as a youngster, however, friendships were crucial to him. When his best friend in public school, Christopher Morcom, unexpectedly died, young Alan was devastated. He wrote to Christopher's mother about the tragedy, and then wrote to his own:

Dear Mother:

I feel sure that I shall meet Morcom again somewhere and that there will be some work for us to do together, and as I believed there was for us to do here. Now that I am left to do it alone I must not let him down but put as much energy into it, if not as much interest, as if he were still here. If I succeed I shall be more fit to enjoy his company than I am now.

Later, Turing sent Mrs. Morcom a letter more fully suggesting why he thought he would eventually be reunited with his dear friend:

...as regards the actual connection between spirit and body I consider the body by reason of being a living body can 'attract' and hold on to a 'spirit,' whilst the body is alive and awake the two are firmly connected. When the body is asleep I cannot guess what happens but when the body dies the 'mechanism' of the body holding the spirit is gone and the spirit finds a new body sooner or later, perhaps immediately.

As regards the question of why we have bodies at all; why we do not or cannot live free as spirits and communicate as such, we probably could do so but there would be nothing whatever to do. The body provides something for the spirit to look after and use.

Apologies to the past

In 2009, the British government apologized to the long-dead Alan Turing for its own actions. "It is no exaggeration to say that, without [Alan Turing's] outstanding contribution, the history of World War Two could well have been very different," Prime Minister Gordon Brown declared:

Alan deserves recognition for his contribution to humankind. For those of us born after 1945, into a Europe which is united, democratic, and at peace, it is hard to imagine that our continent was once the theatre of mankind's darkest hour. It is difficult to believe that in living memory, people could become so consumed by hate—by anti-Semitism, by homophobia, by xenophobia and other murderous prejudices—that the gas chambers and crematoria became a piece of the European landscape as surely as the galleries and universities and concert halls which had marked out the European civilisation for hundreds of years. It is thanks to men and women who were totally committed to fighting fascism, people like Alan Turing, that the horrors of the Holocaust and of total war are part of Europe's history and not Europe's present.

"We're sorry, you deserved so much better," the Prime Minister's statement concluded.

We should remember Alan Turing for his achievements, of course. We also would do well to remember him for the unique person that he was.

Further reading

• George Dyson, Turing's Cathedral: The Origins of the Digital Universe
• Andrew Hodges, Alan Turing: The Enigma
• David Leavitt, The Man Who Knew Too Much: Alan Turing and the Invention of the Computer