Alan Turing: The Enigma

Part One: The Logical

1. Esprit de Corps (to 13 February 1930)

Alan was slow to learn that indistinct line that separated initiative from disobedience and resisted the duties of childhood.
He had identified the crucial point, that Einstein doubted the axioms. Not for Alan the 'obvious duties', for nothing was obvious to him.

2. The Spirit of Truth (to 14 April 1936)

For a person with a mathematical mind, an ability to deal with very abstract relations and symbols as thought with tangible everyday objects...
He had thought deeply about Einstein and had broken the rules to do so.
For science, to Alan Turing, was thinking for himself, and seeing for himself, and not a collection of facts. Science was doubting the axioms. He had the pure mathematical approach to the subject, allowing a free rein to thought, and seeing afterwards whether or not it had application to the physical world.
The distinction between science and mathematics had only been clarified in the late 19th C. Until then it might be supposed that mathematics necessarily represented the relations of numbers and quantities appearing in the physical world, although this point of view had really been doomed as soon as such concepts as the 'negative numbers" were developed. The 19th C however, had seen developments in many branches of mathematics towards an abstract point of view. Mathematical symbols became less and less obliged to correspond directly with physical entities.
One remarkable thing about Gödel's special assertion was that since it was not provable, it was, in a sense, true. But to say it was true required an observer who could, as it were, look at the system from outside. It could not be shown by working within the axiomatic system.

3. New Men (to 3 September 1939)

Curiously, the failure of the Hilbert programme had also meant the end of the point of view advanced by Wittgenstein in his first phase, in the Tractatus Logico-Philosophicus, that every well-posed problem could be solved.
... overcoming the line drawn between mathematics and engineering, the logical and the physical.
It was not science, not 'applied mathematics', but a sort of applied logic, something that had no name.

4. The Relay Race (to 10 November 1942)

Indeed, discerning a pattern in the apparently patternless was essentially the work of the cryptanalyst, as of the scientist.
The English mathematician Thomas Bayes had seen how to formalise the concept of "inverse probability" - this being the technical term for the likely cause of an effect, rather than the probable effect of a cause.
English "eccentricity" served as a safety valve for those who doubted the general rules of society.
He was fascinated that people could be taking part in something clever, in a quite mindless way.

Bridge Passage (to 1 April 1943)

Part Two: The Physical

5. Running Up (to 2 September 1945)

He wanted "to build a brain".
In his view, the physics and chemistry were relevant only in as much as they sustained the medium for the embodiment of discrete "states", "reading", and "writing". Only the logical pattern of these "states" could really matter. The claim was that whatever a brain did, it did by virtue of its structure as a logical system, and not because it was inside a person's head, or because it was a spongy tissue made up of a particular kind of biological cell formation.
The Turing model did not seek to explain one kind of phenomenon, that of mind, in terms of another. It did not expect to "reduce" psychology to anything. The thesis was that "mind" or psychology could propertly be described in terms of Turing machines because they both lay on the same level of description of the world, that of descrete logical systems. It was not a reduction, but an attempt at transference, when he imagined embodying such systems in an artificial "brain".
He had rejected the idea of a "we" behind the brain that somehow "did" this signaling and organizing of the memory. The signalling and the organization had to be all that there was.
The logical transformation of symbols was what mattered, not physical power .
His "weight of evidence" theory had shown how to transfer certain kinds of human recognition, judgment and decision into an "instruction note" form. His chess-playing methods did the same thing - as did the games on the Colossi - and posed the question as to where a line could be drawn between the "intelligent" and the "mechanical". His view, expressed in terms of the imitation principle, was that there was no such line, and neither did he ever draw a sharp distinction between the "states of mind" approach and the "instruction note" approach to the problem of reconciling the appearances of freedom and of determinism.
"We do not need to have an infinity of different machines doing different jobs. A single one will suffice. The engineering problem of producing various machines for various jobs is replaced by the office work of "programming" the universal machine to do these jobs."
He had learned how to build a brain - not an electric brain, as he might possibly have imagined before the war - but an electronic brain.
An English homosexual atheist mathematician had conceived of the computer (ie, an automatic electronic digital computer with internal program storage).
Analogue machines measured physical quantities, while digital machines were for organizing symbols. For every increase in accuracy a new analogue machine is needed, while digital machines just need to be reprogrammed.
After working on a Difference Engine, to mechanize the particular numerical method used in the construction of mathematical tables, Babbage had conceived (by 1937) of an Analytical Engine, whose essential property was that of mechanising any mathematical operation.
It was the mechanisation of the organizing or logical control of the arithmetic that mattered.
Without conditional branching, the ability to mechanize the word IF, the grandest calculator would be no more than a glorified adding machine.
The ENIAC - the Electronic Numerical Integrator and Calculator (started April 1943).
Every tradition of common sense and clear thinking would tend to suggest that "numbers" were entirely different in kind from instructions. The obvious thing was to keep them apart: the data in one place and the stock of instructions to operate on the date, in another place. It was obvious - but wrong.

6. Mercury Delayed (to 2 October 1948)

"When we have decided what machine we wish to imitate, we punch a description of it on the tape of the universal machine. This description explains what the machine would do in every configuration in which it might find itself. The universal machine has only to keep looking at this description in order to find out what it should do at each stage. Thus, the complexity of the machine to be imitated is concentrated in the tape and does not appear in the universal machine proper in any way."
His idea was that anything in the way of refinement or convenience for the user could be performed by thought and not be machinery, by instructions and not by hardware.
To Alan Turing, the multiplier was a rather tiresome technicality; the heart lay in the logical control, which took the instructions from the memory, and put them in operation.
He had invented the art of computer programming.
His mind still straddled mathematics, engineering and philosophy in a way that the academic structure could not accommodate.
"We believe then that there are large parts of the brain, chiefly in the cortex, whose function is largely indeterminate. In the infant these parts do not have much effect: the effect they have is uncoordinated. In the adult they have great and purposive effect: the form of this effect depends on the training in childhood. A large remnant of the random behavior of infancy remains in the adult. All this suggests that the cortex of the infant is an unorganized machines, which can be organized by suitable interfering training. The organizing might result in the modification of the machine into a universal machine or something like it."
They had (in Manchester), on 21 June 1948, successfully run the first program on the first working stored program electronic digital computer in the world.
"To a large extent I agree with you about 'thinking in analogies', but I do not think of the brain as 'searching for analogies' so much as having analogies forced upon it by its own limitations..."

7. The Greenwood Tree (to 7 February 1952)

"Computing Machinery and Intelligence" in Mind in October 1950
- There was no way of telling that other people were 'thinking' or 'conscious' except by a process of comparison with oneself, and he saw no reason to treat computers any differently.
- A learning machine might achieve a 'supercritical' state when, in analogy with the atomic pile, it would produce more ideas than those with which it had been fed.
- From a philosophical point of view, it could be said to fit in with Ryle's The Concept of Mind, which had appeared in 1949, and which put forward the idea of mind not as something added to the brain, but as a kind of description of the world. But Alan's paper proposed a specific kind of description, namely of the discrete state machine.
Edward Carpenter: "The method of Science is the method of all mundane knowledge; it is that of limitation or actual ignorance. Placed in face of the great uncontained unity of Nature we can only deal with it in thought by selecting certain details and isolating those (either wilfully of unconsciously) from the rest."
To model the activity of the brain as a 'discrete controlling machine' was a good example of 'selecting certain details', since the brain could, if desired, be described in many other ways. Alan's theses was, however, that this was the model relevant to what was called 'thinking'.
The structure of the brain must connect the words it stores, with the occasions for using those words, and with the fists and tears, blushes and fright associated with them, or for which they substitute. Could the words be stored for 'intelligent' use, within a discrete-state machine model of the brain, unless that model were also equipped with the brain's sensory and motor and chemical peripheries? Is there intelligence without life? Is there mind without communication? Is there language without living? Is there thought without experience? These were the questions posed by Alan Turing's argument - questions close to those that worried Wittgenstein. Is language a game, or must it have a connection with real life?
Having set down a highly intelligent plan, Alan tended to assume that the political wheels would turn as if by magic to put it into effect. He never allowed for the interaction required to achieve anything in the real world.
Orwell's passion was reserved for intellectual integrity: keeping the mind whole, keeping it in contact with external reality.
Science and sex! - they had been the two things that allowed Alan Turing to jump out of the social system in which he was trained.
People had always use the word 'intelligence' in a broader sense, involving some insight into reality, rather than the ability to achieve goals or solve puzzles or break ciphers.
The formalist school of mathematics, which had given such a start to his career, had explicitly been concerned to treat mathematics as if it were a chess game, without asking for a connection with the world.
It might be said that the kind of machine behavior that he was describing, a behavior unrelated to action, was not so much the ability to think as the ability to dream.
The discrete-state machine was like an ideal for his own life, in which he would be left alone in a room of his own, to deal with the outside world solely by rational argument.
He had an extreme consciousness of the social rules and conventions placed upon him. Puzzled since childhood by the 'obvious duties', he was doubly detached from the imitation game of social life, as pure scientist and homosexual. Manners, committees, examinations, interrogations, German codes and fixed moral codes - they all threatened his freedom. Some he would accept, some actually enjoy obeying, others reject, but in any case he was peculiarly conscious, self-conscious of things that other people accepted 'without thinking'.
The free individual, sometimes working with the social machine, more often against it, learning by 'interference' from outside, yet resenting that interference: the interplay between intelligence and duty; the abrasion and stimulation of interaction with the environment - this was his life.
Gastrulation - the process in which a perfect sphere of cells would suddenly develop a groove, determining the head and tail ends of the emergent animal. The problem was this: if the sphere were symmetrical, without knowledge of left or right, up or down, where did this decision come from? In some way information was being created at this point, and this went against what was normally expected. When the lump of sugar has been dissolved in the tea, no information remains, at the chemical level, as to where it was. But in certain phenomena, those of crystallization for instance, the reverse process could occur.
Random disturbances on a sphere could lead to a particular axis being picked out.
How analogy could work - When two or more sets of ideas have the same pattern of logical connections, the brain may very likely economize parts by using some of them twice over, to remember the logical connections both in the one case and in the other. One must suppose that some part of my brain was used twice over in this way, once for the idea of double negation, and once for crossing the road, there and back; I am really supposed to know about both these things but can't get what it is the man is driving at, so long as he is talking about all these dreary nots and not-nots. Somehow it doesn't get through to the right part of the brain. But as soon as he says his piece about crossing the road it gets through to the right part, but by a different route. If there is some purely mechanical explanation of how this argument by analogy goes on in the brain, one could make a digital computer do the same.

8. On The Beach (to 7 June 1954)

"In considering the functions of the mind or the brain we find certain operations which we can explain in purely mathematical terms. This we say does not correspond to the real mind: it is a sort of skin which we must strip off if we are to find the real mind. But then in what remains we find a further skin to be stripped off, and so on. Proceeding in this way do we ever come to the 'real' mind, or do we eventually come to the skin which had nothing in it?
The arrest obliged him to become more conscious of the conduct of his life and more conscious of the environment.
"Thinking is those mental processes we don't understand."
His emphasis, as with Jung, was on the integration of 'thinking' and 'feeling'. To apply intelligence to himself; to look at his own system from outside like Gödel, and break his own code.
"Description must be non-linear, prediction must be linear."
There was certainly a part of his mind that his friends did not know, and which did not belong to himself, but to those who moved the pieces.
He had never sought to change the world, only to interpret it.
There was no such thing as a 'simple' life for him, no more than there was a 'simple' science. Bletchley had proved GH Hardy wrong about pure mathematics; nothing was pure, and no one could be an island.
Lonely consciousness of self-consciousness was at the center of his ideas.
He had given himself to ideas and things rather than to people, many of those things and ideas were the means by which he tried to approach the understanding of himself and other human beings, and ot do so from first principles.
Science for him remained independent of human purposes, judgments and feelings that were entirely irrelevant to the question of what was so.
Concepts of objective truth that worked so well for the prime numbers could not so straightforwardly be applied by scientists to other people.
This was a super-Gödelian problem, concerning the capacity of scientific language to jump outside the society in which it was embodied, and a problem to which Alan Turing's mind was not attuned.
His life belied his work, for it could not be contained by the discrete-state machine. At every stage his life raised question about the connection (or lack of it) between the mind and the body, thought and action, intelligence and operations, science and society, the individual and history.
Although driven by the desire to do something, he wanted to remain ordinary, to be left alone in peace. These were incompatible goals, and there was no consistency in him.
Orwell's dream of the plain-speaking Englishman was close to Alan Turing's simple model of the mind - the vision of a science independent of human error.