Misidentification
Today summer classes started up. The professor for my class walks in and I can't believe my eyes. My professor looks like he can be the older brother of a particular person I don't like very much, and at first I thought it was that very person. I had a few seconds of shock and disbelief accompanied with my heart beating a little hard and then, after realizing he wasn't that person, a bit of feeling stupid over the misidentification.
Alan Turing
Alan Turing was born 23 June 1912 in England. He did not see much of his parents though because they lived in India; his father was in the Indian Civil Service. There was not much time for personal attention from adults, so Turing was an independent character. He was a bright boy, he taught himself to read at the age of three, but he never liked the rigor of school as he only did well in what he was interested in. His learning abilities did not help him for he scored poorly in his school work. He was very withdrawn, anti-social, clumsy, and disorderly. As Andrew Hodges, Turing's biographer, put it
... he had a a jolly way of coming out with scientific facts, and of telling jokes against his own clumsiness, naive and free from showing off, ... He was certainly foolish in not making life easier for himself; lazy and perhaps arrogant in supposing he knew what was good for him; but he was not so obstreperous as bewildered by demands which had nothing to do with his interests.
Turing was very independent when it came to math and science. He sought his own answers; he did not simply follow along with what his textbooks taught. He widely ignored what his teachers where teaching and was prone to study material outside the school's curriculum. While still in school he read Einstein's own work on relativity and Arthur Eddington's book
The Nature of the Physical World. Later on, he independently came up with a proof for the Central Limit Theorem, not knowing of its existence. This independence was not taken very well in school, which valued above all discipline and conformity. The school's main responsibility was to create loyal subjects of the British Empire, not to broaden the mind. Turing's school master said:
If he is to stay at 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.
This independence was critical to Turing's work though. It was fortunate that the Public School, which we would call a private school in America, did not beat it out of him.
Alan Turing's contributions to mathematics are rooted in philosophical questions about truth, the mind, and machines. Can machines think? Or maybe we should put it this way today: Can computers think? One of Turing's earliest scientifical influences was a book about biology by Edwin Tenney Brewster called
Natural Wonders Every Child Should Know. In this book the author likened the human body to a machine, although a very complex one. Later, the death of a close friend, one that shared Turing's same passion for science but was a better scholar, Christopher Morcom led him to thoughts about the relationship between spirit, body, and free will. Also mathematics, once thought of as absolute truth, was now reduced to little more than a game with axioms the starting point and logic the rules. In this state of things, what was truth? These are the ideas that drove Alan Turing's work.
Starting with the creation of non-euclidean geometry in the 19th century, it became evident that mathematics was not absolute truths about the physical world. This drove many mathematicians to study the foundations of their field and gave rise to formalism. Although this liberated mathematics, it created other problems. Many, such as Bertrand Russell, tried to obtain mathematics purely from logic. In the process of doing this problems and paradoxes came up, even in things as simple as sets. It also disturbed some because it seemed to throw the idea of truth out the window. Many felt that mathematics was in crisis. David Hilbert, in order to sure up the ship, proposed a question. If a group of axioms was given, would the theorems obtained from them be consistent, complete, and decidable? To be consistent meant that the system would have no contradictions. The system being complete meant that for any statement a proof or disproof could be found for it. If for any statement a method could be found to determine if the statement was true or not, then the system would be decidable. Hilbert thought all these things to be true, but he was to be proved wrong. A few years after Hilbert posed this question, Kurt Gödel proved that arithmetic was incomplete.
While taking a course in the Foundations of Mathematics given by M.H.A. Newman, Turing was introduced to Gödel's proof. Newman, speaking of the still open decidable question, wondered if there was a mechanical process that could be applied to a statement to determine it's truth value. If the answer was to come out to yes on decidability then maybe Gödel's proof could be show as some rare occurrence and could largely be overlooked. Turing was very interested in this area of mathematics and the idea of a mechanical process sparked his interest, so he created some imaginary machines that would solve the problem.
Turing defined computable numbers as
the real numbers whose expressions as decimals are calculable by finite means.
He was able to show that the computable numbers where countable. This meant that there were uncomputable numbers, so already he new that Hilbert was wrong. Then he imagined machines, which could only be in a finite number of states, that could manipulate symbols. The symbols it manipulated where on a strip of paper tape divided up into cells. These cells could contain a symbol or be blank. The machine could only
see
one cell at a time. It could write a symbol in the cell or erase it. It could move to the left or to the right along this tape and it could change its state. All of these actions depended only on the state the machine was in and what the the current symbol was. The actions of the machine could be written out as a finite table, much like a computer program. Turing realized that the table for each machine could be assigned a description number.
Now some of these machines would fall into an infinite loop and some would not. Let us call these machines
bad
and
good
respectively. Turing assumed that there was a machine that would tell you if a machine was bad or not. He also showed that there was a machine he called the universal machine that could imitate any machine. Like any other machine, the universal machine had a description number. Then Turing created a third machine by chaining these the two previous ones up. This machine had a description number. What would happen if you feed this number to the machine? First it would test to see if the machine was good or bad, which it should come out good. But when it got to the universal machine part it would start imitating itself. Turing showed that this would create an infinite loop, which mean that is
bad
. So there is a contradiction. Turing had found an example of an undecidable statement.
Turing was also one of the first persons to take machine intelligence, or artificial intelligence as it would be called today, seriously. During World War II, Turing had worked for the British government in decoding German naval communications, messages encoded with the enigma machine. The amount of calculations involved in attempting to crack the encoding created the need for massive calculating machines. These factors, and many others that arose because of war, gave rise to the first electronic stored program computers soon after the end of the war. Turing was right in the midst of these first steps that would shape the modern world. As the machines were being created Turing wondered if they could be programmed to mimic the brain. In the journal
Mind Turing wrote:
I believe that at the end of century the use of words and general educated opinion will have altered so much that one will be able to speak of machines thinking without expecting to be contradicted.
It was in this this article that he gave his famous test for intelligence. Say that you where having a conversation with someone in another room through some type of communication device. If this person could be replaced by a machine and still carry on a conversation with you without you knowing the difference, then the machine could be considered intelligent. This mindset is still behind much of the artificial intelligence research being done today.
Turing's later life saw him doing work in computer design and programming and in biology. Turing died in 1954 after eating an apple with cyanide on it. Although his death is mysterious, some think that he committed suicide because of his earlier conviction for homosexuality. He was forced to take hormone treatments in stead of going to prison.
References
Cops
Last night I saw a police officer pull over a guy on a bike.
