Alan Turing and the Thinking Machine — Part I
Alan Mathison Turing was one of the most brilliant and least appreciated minds of the 20th Century. He was born June 23rd, 1912, and if you were going to be a math prodigy you could hardly pick a better time to be born. Seven years earlier Einstein had published his Special Theory of Relativity, and in 1916 would publish the General Theory. In 1923 Edwin Hubble would prove that some of those faint lights in the night sky are actually other galaxies, expanding our perception of the universe a million fold. Quantum physics was in its swaddling clothes, and the Age of Electronics was, well, getting charged up.
Before he learned to read Alan had a fascination with numbers, stopping to examine them on lampposts and street signs. When he was 10, he wrote an unflattering critique of his algebra teacher, Mr. Blenkins: “He gave a quite false impression of what is meant by x.” He was also given a book that helped to chart his direction, Natural Wonders Every Child Should Know. It opened him to the world of science, and the idea that the body and brain could be compared to machines. He didn’t care much for sports like soccer, and preferred to be linesman, judging precisely the point the ball crossed a line. Someone made up the verse: “Turing’s fond of the football field, for geometric patterns the touch lines yield.”
He was shy, mostly keeping to himself, not making friends easily. He had trouble lining up the buttons on his jacket, or remembering which was his right or left hand, until he painted a red mark on one thumb. His clothes and fingers always seemed to be ink-stained. Maybe numbers were his friends, and he was more comfortable with them. At the age of 15 he was reading Einstein’s relativity theories, and had calculated “the infinite series for the inverse tangent function, starting from the trigonometric formula for tan½x.” I don’t know what that means, but his teacher was quite impressed. Still, many of his teachers said his work was sloppy, and that he preferred his own independent arithmetic methods rather than those taught in the book. He had a particularly annoying habit of ignoring teaching during the term, then coming first in the exams.
Alan knew from an early age that he was attracted to boys, but when he was 16 he met Christopher Morcom, a boy a year older. Whether Alan had a crush on him, who can say? They seemed to have formed a mind meld; two bright young men who shared a passion for all things science or math. Sadly, Morcom died two years later of tuberculosis, but Alan stayed in touch with his family for years. He wondered from time to time if Christopher’s mind (or anyone’s) could exist apart from his body.
In 1931 he was accepted at King’s College, Cambridge, for studies in mathematics. But he was also thinking about thinking, and whether that was possible for a machine. He may have been shy and disheveled looking, easy enough to ignore, except for his intellect. He graduated with honors, and in 1935 was elected Fellow of the college, at the age of 22 (at the urging of prominent economist John Maynard Keynes). Some classmates made up another verse for him: “Turing/must have been alluring/to be made a don/so early on.”
He was wondering, if the brain is a machine, could a machine be like the brain? Mechanical calculating machines had been around a long time. In 1835 Charles Babbage designed a computational machine he called an “Analytical Engine,” but it was never built. Turing got an early idea from a more primitive machine, the typewriter. It had two “configurations,” upper and lower case. By means of the Shift key one could alter the configuration. He observed how humans compute numbers, one digit at a time. Say you multiply 135 by 14. 4 times 5 is 20, record the zero, carry the 2. One step at a time.
He took a course on the Foundations of Mathematics, taught by a giant in the field, Max Newman. Newman thought there could be a mechanical process that could be applied to any mathematical statement. The following year, 1936, Turing wrote his classic paper, “On Computable Numbers, With an Application to the Entscheidungsproblem,” Also known as the decidability or decision problem, it was proposed by German mathematician David Hilbert. He basically asked if there was some formula to determine if any mathematical assertion could be provable. Turing’s paper said no, but before he could publish it, he was beaten to the punch by Alonzo Church at Princeton, using something called lambda-calculus. During the same time, he independently re-discovered a version of the Central Limit Theorem (having to do with probability theory), not knowing he was duplicating work done 12 years before. But he would later use those statistical methods to break German codes during WWII. Doing it his way, working from first principles as he did back in school math, was characteristic of his creative approach, what we call thinking outside the box.
All the while, Turing was living the life of a closeted gay man in a country where it was a serious crime. He had always accepted his sexuality, and never understood why others couldn’t. Sure, there were taverns or certain districts where people could meet up, but he had trouble connecting with people. He never seemed to comprehend that others didn’t always say what they meant, almost as if everyone got that but him. Reading between the lines was not one of his strengths. He had relationships over the years, but it couldn’t have been easy for him. And none of them would have Christopher Morcom’s mind.
In 1936-1937 he attended Princeton, eventually studying under and working with Alonzo Church. Princeton was a hotbed of the mathematical elite; John von Neumann, whose primary interest was quantum mechanics, was there. Albert Einstein was there. The machine Turing imagined was evolving, too. He thought it should be able to carry out any operation as simply as a human, provided the instructions (programs) were well written. It would also have to be able to “read” the instructions; the word Turing used was “scan.” Sound familiar? As much as possible it would have to be automatic, i.e., working without what he called “screwdriver interference.” And rather than decimal notation, Boolean algebra, with its on/off, true/false structure, suggested using the binary numbers 1 and 0.
In 1938 he earned his Ph.D. and went back to England. Germany was becoming a serious concern, and he wanted to be of help. He’d always been interested in cryptology, and took a course at the Government Code and Cipher School, GS & CS (now the intel/security agency GCHQ). Something else significant happened that year, too, the British premiere of Walt Disney’s “Snow White and the Seven Dwarfs,” which made a huge impact on him. He’d walk around reciting the lines, “Dip the apple in the brew, let the sleeping death seep through.” After completing the course he was recruited to join the GS & CS. On September 1, 1939, the Germans invaded Poland, and war was declared. Three days later he reported for duty at a place called Bletchley Park.
He was assigned to Hut 8 with the team working on breaking the German code, Enigma. The Enigma machine looked like a big typewriter with three rotors, each containing the letters of the alphabet. Each rotor could multiply the complexity of what were basically substitution codes, up to over 17,000 possible routes for each letter. And they changed codes daily. Both sender and receiver would have an Enigma machine and codebook. It was thought to be unbreakable, but Turing thought it would take a machine to defeat a machine. The Poles had previously captured a couple of Enigma machines, and had built machines to decode it. They were called bombes, due to the sound of the switches ticking and clicking.
Turing was a unique character, maybe the original absent-minded professor. During hay fever season he’d wear a WWI gas mask as he bicycled to work. He would chain his favorite tea mug to a radiator. It wasn’t long before he was considered in control of the project, though (they called him the Prof), but they were always short on funding. So he did an end run around the military, writing directly to PM Winston Churchill. Turing never did have much respect for authority. Churchill responded immediately, and funding was no longer a problem. The first British bombe, what might be called a Turing Machine, was over 6 feet high and 7 feet long, weighing a ton. It was a mass of switches and cables, literally a number-cruncher, and when in operation it sounded like a thousand knitting needles. At first they’d be able to decode a message weeks old, but by 1941, they could crack the daily code in less than an hour, by sheer speed and brute force. This despite the Germans having added three more rotors, each one multiplying possibilities.
They also got help from a most unlikely source — the Germans themselves. Their national temperament tends to be grounded on routine and precision thinking (ironically like a machine. That’s why German engineering is a marvel). Combined with a lack of imagination by the military command, the Germans left bread crumbs. The word ‘weather’ would usually appear in morning messages. Most, if not all, concluded with an even better clue, ‘Heil Hitler.’ Here you have a four-letter word followed by a six-letter word, both beginning with the same letter. These clues were called cribs, and they’re what you look for in any substitution code. They could be likened to a “tell” in poker. Still, the British had to be crafty. If they suddenly were able to stop each German attack or locate every U-boat, it would tip off the Germans, who might engineer a more difficult new code. So they had to pick and choose their battles, and always under the utmost secrecy.
In 1942 Turing also spent time in the U.S. at Bell Laboratories, working on a speech encipherment project, another of his interests. In 1946 he was presented the OBE, Order of the British Empire, for his efforts in the war. He took the medal home and put it in a drawer; he had better things to think about. He had said he envisioned a time, in perhaps thirty years, when it would be as easy to ask a machine a question as to ask a human.
I n Part II I’ll attempt to examine Turing’s ideas further, including the Turing test (originally called the Imitation Game), his arrest, trial, and punishment for being gay, and just how much of Alan Turing is in the computer you use every day.