jon parise // thursday, december 8, 2016

Alan Turing: The Enigma

Jon Parise <jon@csh.rit.edu>

Alan Mathison Turing was born in England on June 23, 1912, two years before the outbreak of World War I. At the time of his birth, Europe was undergoing a great deal of strain. England, in partition, had a number of domestic troubles. Throughout the country, suffragettes were organizing demonstrations and hunger strikes. Ireland was becoming fiercely anti-British, on the verge of civil war, and the conflict between labor and capital in Great Britain was coming to a head.

Julius Turing, Alan's father, lived and worked in the British possession of India as an assistant tax collector and magistrate. Life back home in Britain was calm in comparison. The native Indians organized and launched a series of upheavals against both their British oppressors and other Indian groups. Still, Julius remained at his post with his new wife, Ethel, whom he had met aboard a cruise ship in the Orient. Their first child, named John, was born in India in 1908. They were expecting their second child in 1912 when they decided that India was becoming an increasingly dangerous place to raise a child. Alan Turing was thus born in Paddington, London, shortly after their return to England.

Julius didn't remain home in England for long, however. When Alan was but nine months old, he returned to his position on India. Six months later, his wife rejoined him. The two boys, John, nearly five, and Alan, still a toddler, were left in the care of Colonel and Mrs. Ward, strict disciplinarians who were accustomed to boarding young boys.

The Wards were staunch patriots. They emphasized the importance of militaristic play amongst the boys in hopes of encouraging them to grow up as "real men." John, and Alan by his older brother's example, rebelled against this sort of establishment. They refused to fight back when bullied. This behavior often caused the Wards to write to the Turings concerning their sons' attitudes. Their letters indicate that they found Alan's behavior the most disturbing, describing him as willful, sloppy, and impudent.

Ethel returned home in 1917, to remain until the war's end. John was away at boarding school by this time, so Alan alone was put under his mother's singular care. He often protested against her insistence that he attend Anglican high mass with her; the incense tormented his sensitive nose. Alan was a marvel of little contradictions that often irritated the adults around him, but there was no denying his gifted mind. His nanny, a Ms. Thompson, noted "his integrity and his intelligence for a child so young."*

Young Alan displayed a keen ability to learn. He is said to have taught himself to read in just three weeks, but his greatest abilities were always mathematical. Ironically, however, there were some aspects of mathematics that he had to struggle to master, such as long division, and it took years for him to learn the difference between his right and left hand. He solved the latter problem by painting a red spot on his left hand. He called this "the knowing spot."*

A few months before his tenth birthday, Alan was enrolled in a small boys school. His lack of athletic prowess made him the least popular among the other students. There are indications that he was bored at school. His marks were merely average, and his teachers often noted his "attitude problem." He excelled at self-education, however, and became quite interested in the sciences, particularly chemistry and biology.

A few years later, Alan started at Sherborne, an English public school. It was there that he began displaying a talent for mathematics, an ability that would later make him famous. His mathematics teacher, a Mr. Randolph, declared the young Alan Turing a genius when the boy presented some complex computations he had performed on his own.* Alan also took up a keen interest in chess, later considered "a metaphor for explaining his theories regarding the nature and limitations of computers."*

One area that Turing would never master was writing and literature. He was terrible with spelling and grammar, English literature, and biblical studies, subjects of great importance in the English public school curriculum. One of his literary instructors wrote of him, "I can forgive his writing, though it is the worst I have ever seen, and ... his ... slipshod, dirty work ... but I can not forgive the stupidity of his attitude towards sane discussion on the New Testament."*

Alan's interest in mathematics and science continued to grow. While the instructors taught art, music, and literature, Alan would toil with complex equations in notebooks hidden under his desk.* He was caught and punished several times, but he continued to pursue these interests. At the end of his first year at Sherborne, Alan was not permitted to pass to the next grade. He was, however, allowed to take an advanced course in mathematics. On his own time, he discovered Albert Einstein's writings. He read them with great thoroughness and would then write his own commentaries. These reflections would later indicate that Turing had an uncommonly firm grasp on Einstein's theories.

Turing made few friends while at school, with the exception of one Christopher Morcom. Morcom was a year Turing's senior and, like Turing, was gifted with both an acute intellect and an interest in careful experimentation. They became extremely close friends during these years and mutually benefited from each other's company. Turing introduced Morcom to Einstein while Morcom attempt to refine Turing's social graces. By this time, too, Alan Turing had started to find himself attracted to members of the same sex, but Christopher Morcom made it quite clear that their relationship would never take that turn. For all other purposes, however, they developed a strong love for one another.

Together, Turing and Morcom made an excellent research team. They worked out mathematical proofs together, discussed physics, and studied astronomy. Their scientific interests and abilities complemented one another. For once, Turing had a true friend and companion. That's why, when Morcom died from tuberculosis just three years after they first met, he was devastated. However, upon reflection, Alan determined that he would continue his work to the glory of Christopher Morcom's memory, and, in 1931, Turing achieved his goal of being accepted to Cambridge University's King's College, renowned for its excellence in mathematics and physics.

Back in Sherborne, Turing had never really taken to team sports. He had, however, become quite a runner. He started to run as a way of dealing with feelings and impulses he did not know how to handle.* He excelled at distance running, and for the first time in his life, he was able to compete with other boys his age athletically ... and win. Turing was never much of a competitor, due mainly to his solitary attitude, but now that he was achieving success in competition, he began to thrive off of it, both athletically and academically. When he came to Cambridge, Turing continued his running. In addition, he also joined the prestigious Boat Club as an oarsman. Although he did not distinguish himself as extraordinary on the crew team, he was accepted by the populace, and the childhood taunting stoiped for good.

During the 1930's, the world could smell a war brewing. Italy was under fascist rule, Stalin controlled the Soviet Union, and the Nazi party had come to power in Germany. The academics and scientists in England tended to be pacifists in the face of impending world conflict. Alan Turing fell in with this crowd, joining a Cambridge organization known as the Anti-War Council. Turing described it in a letter to his mother as a program "to organize strikes among munitions and chemical workers when government intends to go to war. It [raises] a … fund to support the workers who strike ..."* Interestingly, the summer before Turing came to Cambridge, he had attended an army officers' training course, a program in which he did quite well, especially in the areas of drill and tactics.*

In June 1934, Alan Turing graduated from King's College "with distinction."* He was awarded a research grant worth 200 pounds a year that allowed him to remain at Cambridge. What Turing really wanted, however, was the security of a full fellowship at King's. Later on that year, Turing submitted his explanation of the common patterns found in all scientific graphs, which he called the Central Limit Theorem. Unfortunately, he had been so engrossed in this work that he neglected to research the full history of the problem, and it was soon discovered that this problem had already been solved, twelve years earlier. However, the judges considered Turing's new work far superior and simpler than the original solution, and at the exceptionally young age of twenty-two, he was given a three-year fellowship worth 300 pounds a year.*

Turing's next major accomplishment was the development of his Turing machine. The Turing machine was Alan Turing's response to the Entscheidungs-problem (decision-making problem), raised by the German mathematician David Hilbert. The Entscheidungs-problem asserted that the truth or falsity of a mathematical problem can always be determined, and that this could be accomplished by an "activity that could be performed by an automatic machine."* Turing recognized this entire idea as something of a paradox and approached it with skepticism. He was intrigued, however, by the mechanical aspect of Hilbert's "automatic machine," and gave the problem a great deal of thought. He knew that logic dictated that some questions simply can't be solved, but this contradicted Hilbert's claim that "there is no such thing as an unsolvable problem." On the other hand, Turing knew that some problems were solvable, simple arithmetic, for example, and from these axioms and a stroke of creative genius, Turing developed the Turing machine.

The Turing machine never actually existed; it is entirely theoretical. A rather good explanation of the mythical machine is given by Ted Gottfried:*

A Turing machine consists of a head and a narrow paper tape that is divided into frames like those on a roll of film. The tape can be infinitely long - a benefit of an imaginary machine. Each frame may either be blank or printed with one symbol from a finite, prespecified set of symbols. The input tape, the tape as it is presented to the machine before it begins its task, may have a finite number of frames marked, or they can all be blank. At any step, the head can read the contents of a frame with its attached scanner. If the frame is blank, the head can either leave the frame blank or print one of the symbols. It can then move one frame to the right or left, or not move at all. If the frame already contains a symbol, the head can erase the symbol, replace it with a different symbol, or leave it alone. It can then move one frame to the right or left, or not move at all.

Because the Turing machine could be given a rule set upon which to base its actions, it could be programmed to solve an infinite number of problems. In fact, it could solve any problem for which there was a solution. When faced with an unsolvable problem, the machine would either stop or compute forever. The result can't be determined beforehand, which makes the machine itself an example of a problem that can't be solved, even though there does exist some answer (either stopping or computer forever). With his theoretical machine, Alan Turing had not only disproved Hilbert's theory, but he had also unintentionally laid the foundation for modern computer science and theory. The computer historian Stan Augarten sums up the accomplishment thus: "Turing had come up with a litmus test of decidability - a mechanical method that showed that the only way to determine whether a statement was true or false was ... to try to solve it."*

In 1936, Alan Turing set sail for America. He had accepted a research position at Princeton University in order to complete his doctoral work with his mathematical idols Albert Einstein, Kurt Gödel, and Alonso Church. Church had actually published a similar paper on Hilbert's Entscheidungs-problem that was quite popular in the United States, and Turing feared that Church's work would overshadow his own. This was true to an extent, especially because few mathematicians took serious interest in Alan's Turing machine. However, his machine was getting serious attention by the top-secret British Government Code and Cypher School, and they were able to successfully recruit Turing once he completed his Ph.D. at Princeton. He returned to England in July 1938.

The impending outbreak of war influenced Turing's decision to join the code breaking effort. It is clear that he still sympathized with the anti-war crowd, however, and, his mother wrote, "just before the Second World War he made himself responsible for all the expenses ... of an Austrian refugee of fifteen."*

While working at the code breaking school at Bletchley Park, Turing began a relationship with Joan Clarke, a very intelligent young woman who was a member of the code breaking labor force. Turing had remained a closet homosexual to this point, but he found a certain irresistible companionship in Joan. They went on frequent walks and had conversations on everything from botany to mathematics. Their relationship blossomed into a sort of fraternal love, and Turing went so far as to ask her to marry him. Once she accepted, Alan explained his homosexual tendencies to her, but she was undeterred. However, once he explained that he had acted upon them in the past, she struggled to understand, and Alan broke off the engagement.

Alan continued his work at Bletchley Park until the conclusion of the war in Europe in May 1945. While there, he made a number of advances in computing which culminated in the construction and application of a large computer, named "Colossus", for processing encoded messages. After the war, Alan signed on as a "Scientific Officer" with the National Physical Laboratory (NPL) at Teddington. He was assigned to design a working prototype of his universal Turing machine based on his experiences with Colossus. However, in 1947, Turing quit the project due to lack of funding. He was uncomfortable with the idea of scaling down his grand designs in order fit within budgetary constraints. Instead, in 1948, he transferred to Manchester University to work on their Manchester Automatic Digital Machine and to pursue other research interests.

During this period of his life, Alan Turing started taking his running very seriously. He stuck to a regimented practice scheduled and competed as a member of a local track club. He often ran marathon distances, and when he visited his mother, he usually ran the eighteen miles to her home.* He became so successful as a runner that he began having Olympic aspirations. He started training for the Olympic trials, but disaster struck when he tripped while out for a run and smashed his hip. The doctors were unable to fully repair the damage done by the fall, and Alan's Olympic dreams ended. He still ran for exercise, but he was no longer a serious competitor.

Also at this time, Turing began toying with the idea of mechanical intelligence (what today has become commonly known as artificial intelligence). In a landmark paper published in the philosophical journal Mind entitled "Computing Machinery and Intelligence," Turing predicted, "One will be able to speak of machines thinking without expecting to be contradicted."* This paper launched a debate concerning the very nature of intelligence and whether it could be quantified and measured. Turing's solution was to avoid as many difficulties in this problem as possible. Instead, he developed a simple test, known as the Turing test, that, if passed, proved the subject was intelligent.

The Turing test is really nothing more than a clever adaptation of a party game. The test has three participants. One of them, the interrogator, is placed in a separate room from the other two, one a male and the other female. Questions and responses are typed and passed under the door. The goal of the game is for the interrogator to determine through the line of questioning which of the interviewees is the male and which is the female. To further complicate the situation, the male is supposed to attempt to throw off the hunt while the female is supposed to aid the interrogator. Turing reasoned the role of the male could very well be played by a computer, and if the interrogator, a human, could not tell the which of the two interviewees was man or machine, the computer could be considered intelligent. After all, it is undeniable that humans are intelligent, so if a computer can fool a human into making him think it is also a human, the machine must also be considered intelligent. The Turing test is considered Alan Turing's single greatest accomplishment in the realm of artificial intelligence, and, to date, no machine has been able to pass the test.

Turing's work on artificial intelligence rekindled his interest in biology. He focused his attention on morphology, the branch of biology that deals with the form and structure of animals and plants.* This led him to the study of morphogenesis - "evolution as applied to structured forms" - and he published several important papers on the subject, including a 1951 treatise entitled The Chemical Basis of Morphogenesis. This work is continued even today, as the basis for modern cancer studies.

It was also at this time that Alan Turing's life took a turn for the worst. Alan had started a brief relationship with an unemployed young man named Arnold Murray. Alan took a liking to Arnold because of their shared interest in the sciences, but after a few meetings, it was clear that their relationship would never go anywhere. Arnold was stealing money from Alan, and Turing broke off the relationship asking Arnold never to return to his home.

When Turing's home was burglarized a few months later in 1952, Turing went to the police. Arnold Murray insisted he was not the perpetrator, but he said that he knew who had committed the crime. That man, a petty thief named Harry, was arrested. At the trial, Harry exposed the homosexual relationship between Alan and Arnold. As homosexuality was against the law in Britain at the time, the robbery case took on an entirely different form. Alan Turing soon found himself on trial, charged with "gross indecency." He pleaded guilty to all twelve counts against him and was sentenced to his choice of one year in prison or a year on probation while undergoing treatment for his "condition." Alan chose the latter and began undergoing organo-therapy, which centered on large doses of estrogen intended to reduce his sex drive.

The treatment had severe, negative effects on Turing. He became impotent and his breasts grew larger. More damaging, however, were the effects on his nervous system. The treatment also caused waves of depression and despair. Turing continued his biological research but soon became involved in what he called "the desert island game." The game involved the manufacture of as many household substances from scratch using as few of the materials Turing had in his home as possible. This set Alan off on such varied activities as producing a nonpoisonous weedkiller and gold-plating a spoon. The gold-plating process called for the use of potassium cyanide to facilitate the melting of the metal.*

On Tuesday, June 8, 1954, Turing's housekeeper discovered Alan lying still in his bed. There was a congealed white froth around the corners of his mouth. He had been dead for some time at this point. The medical examiner determined the cause of death as cyanide poisoning, concluding that "the poison was self-administered while the balance of his mind was disturbed." A few weeks before his 42nd birthday, Alan Turing had committed suicide.

It is clear the Alan Turing's numerous contributions to the various fields of mathematics, computer science, artificial intelligence, and biology are both monumental and innovative. He was a man of many contradictions, and his numerous accomplishments are the result of a unique personal drive to learn, question, and solve. Turing biographer Andrew Hodges writes, "Science, to Alan Turing, was thinking for himself, and seeing for himself, not a collection of facts. Science was the doubting of axioms."

Endnotes

  1. S. Turing, 12.
  2. Hodges, 7.
  3. S. Turing, 28.
  4. Gottfried, 33.
  5. Gottfried, 31.
  6. Gottfried, 33.
  7. Gottfried, 39.
  8. Hodges, 71.
  9. Gottfried, 51.
  10. Ince, VIII.
  11. Gottfried, 62.
  12. Slater, 15.
  13. Gottfried, 66.
  14. Augarten, 144.
  15. S. Turing, 57.
  16. Gottfried, 85.
  17. Hodges, 417.
  18. Merriam-Webster's Collegiate Dictionary (10th ed.)
  19. Gottfried, 102.

Bibliography

  • Augarten, Stan. Bit By Bit: An Illustrated History of Computers. Boston: Unwin Paperbacks, 1985
  • Gottfried, Ted. Alan Turing: The Architect of the Computer Age. New York: Franklin Watts, 1996.
  • Hodges, Andrew. Alan Turing, the Enigma. New York: Simon and Schuster, 1983.
  • Hodges, Andrew. Alan Turing - Home Page
  • Ince, D.C., ed., Mechanical Intelligence: Collected Works of A. M. Turing. New York: Elsevier, 1992.
  • Saunders, P.T., ed. Morphogenesis: Collected Works of A. M. Turing. New York: Elsevier, 1992.
  • Slater, Robert. Portraits in Silicon. Cambridge, MA: MIT Press, 1987.
  • Turing, A.M. "Can a Machine Think?" in Newman, James R., ed. World of Mathematics, Redmond, WA: Tempus Books, 1988.
  • Turing, Sara. Alan M. Turing. Cambridge, England: W. Heffner & Sons, 1959.