Ed Wesly, 1/18/07 TIE 532


Alan Mathison Turing was born on June 23rd, 1912, in Paddington, UK. In 1931 he matriculated at King’s College, Cambridge, to study mathematics. By 1935 he became a fellow of the school thanks to his dissertation, “On the Gaussian Error Function”. He received a stipend of £300 per year to continue his research in pure mathematics, and tackled a thorny problem, the Entscheidungsproblem, or in English, the decision problem.


The rather abstruse question posed by this problem relates to being able to prove the truth or falsehood of a mathematical statement that is theoretically impossible to solve. This seems to be contradictory for us mere mortals who have studied classical Euclidean high school geometry with its axioms, theorems and proofs (since that is the methodology that is taught) that there are uncertainties in mathematics, but there are some paradoxes that worry the ivory tower mathematicians.


Turing’s approach to solving this problem (and for the curious, the details are to be found in the man… since describing the problem would take more than the 300 words allotted to us) was to invent an imaginary calculating device, which he dubbed the Universal Machine.


This hypothetical device would be able to cope with every sort of legitimate, that is solvable, problem, whether mathematical or logical. Data would be fed into the machine on a paper tape divided into squares, each square marked with a symbol or left blank. The machine would not only act upon these data squares but modify them as well, erasing and replacing the symbols in accordance with instructions stored in its internal memory. It would be programmed with an algorithm, and some of the examples he used in the paper were to generate the counting numbers, the odd numbers, etc.


Although the paper proved what it set out to do, its importance was not noticed immediately, because Turing used an analogy instead of rigorous logical proofs.

But this universal machine (sometimes called a Turing machine) concept turns up in our contemporary computers, who are a clean slate, capable of doing anything that a program loaded into it tells it to do. But Turing’s biggest practical contribution to computing would come in the form of a specialized machine, one designed to battle another, the German military Enigma machine.


The Enigma was at first designed to encrypt business messages in the calm between the World Wars, and then it was taken over by the military. The sender would type in a letter in his message and the Enigma would light up a bulb with an encrypted letter. The receiver would type in a letter from the encrypted message, and the machine would light up with the deciphered letters.


This was accomplished by a set of discs or rotors that had the letters of the alphabet visible on its tread, and inside there would be a group of wires that would scramble-connect each of the letters’ positions; i.e. a wire would enter under the “a” and exit under the “w” for instance. Three (and later more) of these rotors would be stacked next to each other, so that the input letters could be further scrambled. There was a “reflector” of the series of trotors so the signals would pass through them twice, so there could be at least 266 permutations at the end. There would be a code word of the day, so the rotors would be rotated so that the code letters were on top of the rim, so the scrambling would change on a daily basis, plus some cords like an old-fashioned telephone switchboard which also vary the output letter. Receivers and transmitters had a pad of code word keys to keep themselves in sync.


Polish cryptographers were fortunate to have a business Enigma machine and other insights which they transferred to the British, so there was a foundation to start with, but more so due to Turing’s mathematical insights and his fondness for putting them into machinery, which got built this time, many lives were saved by cracking the code. “I won’t say what Turing did made us win the war,”said a mathematician who served under him, “but I daresay we might have lost it without him.”


Since all this work was done under the veil of war-time secrecy, Turing’s role was under appreciated. But still his connection to the Bletchley Park (the site where the machines were built) Project gained him recognition as a computing genius.


Although he did take a few wrong turns. He proposed several machines that were never built, to compete with the American ENIAC computer. (He had a little bit of a problem in the social skills department, plus was easily distracted into flights of purely abstract thought.) And one of the devices he did build which he christened “Baby”, deviated from the binary input and used a cumbersome 32 character input which it seemed only he could understand, further isolating him from the other computing gurus of the era in the immediate post-war era.


But he was outspoken when it came to predicting the rise of artificial intelligence. One monument to his insight is the “Turing Test” of artificial reasoning. The test as first proposed would pit a human against an unseen opponent in a chess game, and the human would have to figure out whether he was playing against another human or a machine. It evolved into a question and answer game wherein the human had to decide whether its unseen nemesis were really a human or a machine answering questions as to whether it was in fact a human or machine. I would guess the former has come true, the latter might be possible through skillful programming of possible responses to probable questions, but whether or not a Mac is possible of spoofing a human under its own artificial intelligence is open to conjecture.


One of his personality quirks was his open homosexuality, which eventually led to his arrest in 1952 under the “gross indecency with an adult male” law, the same rap that brought down Oscar Wilde. He was sentenced to psychoanalysis and estrogen treatments to curb his “perversion”. His runner’s body became fat and flabby and he started to develop breasts. This punishment seems unbelievable to the denizens of the more liberated (or at least, tolerant) 21st Century where Englishmen can not only flaunt their homosexuality (Freddie Mercury of Queen) but even be knighted in spite of it (Elton John).


Because of these pressures, he invented his “desert island” game in which he manufactured chemicals out of common household substance. Turing made potassium cyanide from apple seeds (remember your parents telling you not to eat the apple cores?) coated an apple with it, like the poison apple from Snow White and the Seven Dwarfs, his favorite movie (Freudians can read a lot into this one!) and ate it. He was 41 years young.


His name lives on in an award in his name given annually by the Association for Computing Machinery, and is sometimes recognized as the Nobel Prize of Computing. It is currently sponsored by Intel and is accompanied by a prize of a 100 kilobucks.




THE MAN WHO KNEW TOO MUCH: Alan Turing and the Invention of the Computer, David Leavitt, Atlas Books, NY, NY, 2006


COMPUTER BASICS, Editors of Time-Life Books, Alexandria, Virginia, surprisingly no date