Alan Turing was born on June 23, 1912 into a British upper-middle class family. He was a very intelligent boy fascinated with the science’s chemistry in particular. Performing experiments and making things seemed his fascination. He was a very poor speller and his penmanship was bad. He did not seem well at expressing himself. This was especially detrimental, in that, in the British schooling in which he found himself penmanship, spelling, and able expression were what distinguished good students from poor students. He was good at science and math. But although he had insight into the problems he did not seem to have the attention to see the hard work through. As a student he would do the experiment or problem, but it seemed a nuisance to him to have to explain his results or methods or show what he had learned. Today he would probably be classified as ADD (attention deficit disorder).

He graduated from Kings College, Cambridge University with a distinction in mathematics in 1933, and was later elected to a Fellowship of Kings Collage. In 1935, he attended a course taught by M.H.A. Newman and became interested in the third of Hilberts questions.

Von Newman had stated is there "a mechanical process which could be applied to a mathematical statement, and which would come up with the answer as to whether it was provable. (1)" Alan had always loved to build things, machines in particular. So this was right up his ally. Alan sets out to design a machine that will solve any mathematical expression. " It was not the determinism of physics or chemistry, or of biological cells, that was involved in Hilbert's question about decidability. It was something more abstract. It was the quality of being fixed in advance, in such a way that nothing new could arise and the operations were to be operations on symbols, rather than on things of any particular mass or chemical composition. Alan had to abstract this quality of being determined and apply it to the manipulation of symbols. People had spoken, as Hardy did of 'mechanical rules' for mathematics, of 'turning the handle' of a miraculous machine, but no one had actually sat down to design one. This was what he set out to


The machine itself consisted of an infinitely long tape marked off into squares on which the machine could read or write symbols, move one space at a time either way along the tape, a head or scanner to read and write on the tape, and a 'table of behavior'

Containing 'states' or configurations of the machine. This 'table of behavior' would determine for any given square whether to change the symbol (write a new one, erase old one, leave it unchanged) and/or change the state, and/or move to a new square.

An example of machine states:

Imagine a gumball machine that dispenses gumballs that cost a penny (yes I said imagine) it only takes pennies (other coins will not fit in the slot). The machine would start in beginning state in which no action is taken (waiting). When it receives a penny it changes to state two where the action is to dispense a gumball and change to state one. These two states completely determine the actions taken by the machine.

In the Turing machine the 'table of behavior' must cover all allowable actions for the machine. In a strong sense the table is the machine. In computer science terms this is the algorithm or code to solve a problem.

Because of uncomputable numbers (the diagonal argument); Alan answered no to Hilberts question. But he had made this new machine that could solve any problem given a 'definite method' a table of behavior. But given that the table is the machine you really didn't have one machine that could solve any problem given a definite method but a variety of machines where each one was designed to solve a particular problem. But Turing took this a step farther in that their existed a definite method for installing any table of behavior into the Turing machine, thus, the Turing machine could solve any 'solvable' problem. This was the universal Turing machine.

In 1950, Alan Turing wrote a paper called "computing Machinery and Intelligence" in this paper he considered the question "can machines think". To answer this question he introduced a game called "The imitation game" in this game an interrogator is allowed to ask questions of another person (called A) to try and determine their sex. The interrogator is in a room alone and questions are asked via teletype. The goal of A is to fool the interrogator into guessing the wrong sex. There is a third player (B) who also is asked questions by the interrogator but does not try to fool him. The interrogator knows one player is a man and one is a women but not which. Turing goes on to state " "What will happen when a machine takes the part of A in this game?" Will the interrogator decide wrongly as often when the game is played like this as he does when the game is played between a man and a women? These questions replace our original, " can machines think? (2)". In the paper Turing acknowledges the question "is this new question a worthy one to investigate? (2)". But I do not believe he ever answers it. Later in the paper he states that the question "can machines think (2)", "is too meaningless to deserve discussion (2)". But I am not sure he makes clear what the question "can a machine play the imitation game as well as a man or women (2)" leads to, more on this later. The machines involved in this game are expressly stated to be digital computers. I thought it was interesting that Turing excludes cloned humans as they are not "constructed". It is important to note that in this section of the paper, he makes it clear that the question is not is there a computer that could do well in the game but can we imagine a computer that would do well in the game. The next two sections of the paper describe digital computers and the universality of digital computers.

He then has a section where he tells us his own thoughts and contrary views on the subject. Turing believed that by the year 2000 there would be digital computers that could play the game well enough to fool an interrogator thirty percent of the time given a game time of five minutes.

Turing then proceeds to consider opposing views. The first is the theological objection. He states the opposing view as "Thinking is a function of mans immortal soul." Turing of course could not accept this, and I will not waste space on it. I must digress a bit here. He uses the word thinking here to describe the opposing view, but no where in the paper can I find where he states that if a machine could play the imitation game that it would be thinking. More on this later.

Next he takes on "The heads in the sand objection" "The consequences of machines thinking would be too dreadful. Let us hope and believe they cannot do so." I particularly liked Turings response to this. He did not believe this argument was valid enough for argument and offers "Consolation would be more appropriate".

The mathematical objection states that because Godel's theorem (1931) shows

" That in any sufficiently powerful logical system statements can neither be proved nor disproved within the system, unless possibly the system itself is inconsistent. (2)" This idea as it applies to set theory is the fact that sets may contain themselves. But what about the set that includes all sets that does not contain themselves. If the set does not contain itself then it must be a member, but if it is a member then it can not contain itself. This and similar results shown by others "establish that there are limitations to the powers of any particular machine (2)". Turing believes that the same is true of the human intellect, although he seems to admit the validity of this argument.

The argument from consciousness is the idea that a machine has no self-awareness. (I think this is true of a lot of humans as well, just kidding) taken to the extreme "the only way by which one could be sure that a machine thinks is to be the machine and feel oneself thinking. (2)". Turing did not believe the mysteries of consciousness need be solved in his paper.

The next section 'Arguments from various disabilities' really contains more of the above, as Turing put it "The criticisms that we are considering here are often disguised forms of the argument from consciousness (2)".

After this objection, the paper addresses the one I feel is the probably the best. A small history note here. The Analytical Engine was a machine designed by Charles Babbage (1822) it was a machine similar in concept to digital computers. Ada Augusta, Countess of Lovlace was a mathematician who wrote algorithms for it. Lady Lovlace's objection is best stated by her. "The Analytical Engine has no pretensions to originate anything. It can do whatever we know how to order it to perform" (memoir by Lady Lovlace (1842)). Turing never seems to address this directly instead varying it first into " a machine can "never do anything really new" (2)". And then into "a machine can "never take us by surprise" (2)". He argues this second variant by stating that machines take him by surprise all the time, for example by requiring a different voltage then he had anticipated. This seems very weak to me. I can only suppose he had no better direct arguments to this objection. To me his answer is like saying that because I am surprised when my car breaks down that it has originated something new, I do not believe this. This idea of originating something new seems to me to be the "game" of intelligence. Invariably when I ask someone to give me a definition of intelligence this idea of originating something new comes up. Having this ability is the difference between having "intelligence" and having computation-storage capabilities. This is not to say I disagree with Turings paper but more so to say I wish he had a better argument on this point.

The argument from continuity in the nervous system is the fact that a human is a continuous machine and computers are state machines. Turing argues the fact that a differential analyzer is a continuous machine and a computer (a state machine) can imitate its output.

The argument from informality of behavior is that humans do not have " rules of conduct" that governs our behavior. That is there is no algorithm for each situation in which we find ourselves that tells us what to do. Turing agrees with this but points out that this is because "rules of conduct" are being confused with "laws of behavior". "Laws of behavior" are the laws that make us behave in certain ways. Such as the fact that if a human touches a flame they will pull away. As Turing puts it "If you pinch him he will squeak (2)" and so it is these "laws of behavior" that govern human actions.

The fact that we have not discovered such laws does not preclude their existence.

The argument from Extrasensory Perception does not seem to belong here at all.

Turing states that the "statistical evidence, at least for telepathy, is overwhelming (2)". I am not aware that the evidence might be so overwhelming. Perhaps at this time (1950) there did seem do be evidence of telepathy. As I am not familiar with this topic I must keep my opinions out of this paper. Turings opinion was that should telepathy be admitted into the game one would only have to play it in a "telepathy-proof room" to solve the problem.

That was the last argument in Turings paper. He proceeds to discuss learning machines. He offers the idea that to build a machine to imitate an adult human, maybe one should start with a machine that can imitate a child and teach it. He offers different ideas about how this might be accomplished. In simple terms you might do something like program into the machine --if you know one way of doing something and are taught another chose the quicker of the two from now on-- or rather -- if you have two algorithms for doing some task chose the quicker and give it a priority of 1 for these

Tasks --. He talks about giving the machine a "complete system of logical inference built in" it would have the idea of "imperatives" that after being classified as "well established" (perhaps after proving correct a certain number of times) would begin to be executed automatically without prompting from the (programmer) teacher.

He offers the analogy of an atomic pile of a certain mass (subcritical) such that when a neutron strikes it causes a reaction but this reaction dies away. If however the mass is made to be sufficiently large (supercritical) the reaction continues until the pile is consumed. As this applies to thought, if the system is not sufficiently complex enough the idea or stimulus introduced causes some output but no further result. But, however if the system is sufficiently complex then the idea takes on a life of its own. Turing asks

" can a machine be supercritical (2)".

Turings last paragraph contains "We may hope that machines will eventually compete with men in all purely intellectual fields.(2)" As to the ones to start with he offers the playing of chess and the speaking and understanding of English as two good approaches.

Turing never actually states in his paper that if a machine could play the imitation game and fool a human that it would be thinking. He even states that the two questions are different "these questions replace are original "can machines think? (2)" and " is this

new question a worthy one to investigate?(2)". I believe Turing published this paper to play "devils advocate", that is to get a person thinking about the possibilities of machines thinking. And, to generate ideas on how this could be accomplished, what sorts of pitfalls there might be, and if it is a good idea or not. I do not think Turing cared if people said about this paper "that is absurd how can a machine think, it will never happen" as long as that response generated a discussion about why not?

Turings ideas (all his ideas not just the paper discussed above) generated work by numerous people into intelligence, computation and the study of thought. The book Machines and Thought: the Legacy of Alan Turing is a collection of papers that discus ideas that have arisen from Turings work. One such paper is about the Church-Turing thesis (The Church-Turing Thesis: Its Nature and Status by Antony Galton) and the equivalence of Turing machine computability, lambda-definability, and Markov algorithm computability. Another (Human versus Mechanical Intelligence by Robin Gandy) is about the differences between human and mechanical intelligence, that human thought is non-mechanical, non-algorithmic, that it contains the "spark' of intuition. Given this, the author still believed that machines would become colleagues and not just remain tools. Along this same idea of the differences between human intelligence and machine intelligence is another (The Turing Test: AI's biggest Blind Ally? by Blay Whitby) where the author among many other things, argues that machine flight does not occur in the same way that flight does in animals, so why should we expect machine intelligence to imitate human intelligence. It will probably be some new form of intelligence. I thought this was an interesting point but what other starting point to we have. I do agree that in the end machine intelligence will be different then human intelligence. If you grab this book be prepared to do some math.

I have been trying to make a distinction between thinking, learning, and possessing intelligence. I have not been very successful. Thinking to me is very much like computation (crunching numbers) if I ask a child to add 2 +2 +2 they "think" about it for a moment and then reply 6. They are merely applying the algorithm they have been taught and giving me the output. This is thinking at its most basic level, and machines can do this. The problem is that with the child learning is also a part of that thinking process. Each time the child is asked, even a simple question, they are altering the "adding algorithm" perhaps making it faster, more efficient, or shortening the time required to access it. Learning machines may do this. But, I am not familiar enough with this subject to simply state "a machine can do this also". People seem to assume humans think they give them the benefit of the doubt. As Turing says "it is usual to have the polite convention that everyone thinks. (2)". Why hold a machine to a higher standard. If I said to someone "prove I do not think" what sort of criteria would they find convincing.

Could they prove a machine does not think, that a machine could never think?

Alan Turing did so much more then just these things I have concentrated on in this paper, he worked to deduce the workings of the Enigma, a machine that produced code in world war two. I believe that out of this work came ideas on deducing a mechanical process from its logical output. Also, there is controversy surrounding his suicide that I was not able to research to my liking.

I have learned a great respect for Alan Turing and his accomplishments. He was truly a pioneer in computer science. It is sad to think of what he might have accomplished had his life not been cut short. I did not realize that AI was generating all this research into learning and intelligence. I am amazed at how ignorant the average populace is about the science of computing, the "I thought Bill Gates invented the computer?" sort of understanding. Learning about Alan Turing has made definite something of which I was already aware namely that computer science and mathematics are incredibly closely intertwined. There is so much that was touched on in the books about Turing that I want to explore. Formal systems, self reference in formal systems, isomorphic equivalence, learning machines, and more. I started reading " Godel Escher Bach: " by Douglas R. Hofstadter and it is going to be a long time before I understand it.

I have come to the conclusion that computers, and the philosophical intellectual discourse and discoveries on computing, learning, and intelligence is going to have (or is having) a profound effect on the path of human evolution.

Final note:

One can not study computer science and mathematics without ending up at philosophy.


(1) Alan Turing: The Enigma

by Andrew Hodges Burnett Books Limited 1983

(2) Computing Machinery and Intelligence

by A.M. Turing (1950)



Alan Turing: the enigma

by Andrew Hodges Burnett Books Limited 1983

Computing Machinery and Intelligence

by A.M. Turing 1950

The Universal Turing Machine "A half century survey"

edited by Rolf Herkin Oxford University Press 1988

Machines and Thought: The legacy of Alan Turing

edited by Millican and Clark Clarendon Press Oxford 1996

Thanks to Lisa Maynes Desjarlais for sitting down and discussing this subject with me.

Thanks to all who answered my e-mail on this topic, see attached.