Turing’s Golden

7/16/2004

Turing’s Golden: How Well Turing’s Work Stands Today.

It is fifty years since the creator of our age laid down in his Spartan bed, crunched down on an apple laced with potassium cyanide, and died. It behooves us to ask how his achievements stand today. He has, after all, bequeathed us a conceptulary including “Turing, or Turing-Church, thesis,” “Turing machine,” “universal Turing machine,” “Turing test,” and “Turing structures,” plus other unnamed achievements, including a proof that any formal language adequate to express arithmetic contains undecidable formulae, achievements in computer science, artificial intelligence, mathematics, biology, and cognitive science (indeed, Turing’s work became so ubiquitous and impersonal that for decades the Library of Congress lower-cased Turing; its entries read “turing machine” and “universal turing machine,” as if they were farm tools or exotic recreational devices). I have said conceptulary, rather than vocabulary, to note that Turing, after all, did not paste his own last name on things, and, more importantly, because I want to emphasize what these achievements legitimately amount to for us today, rather than adopting a purely historical stance which might allow silly, malicious, wildly-political, or irrelevantly personal supposed counter-examples or psychological deconstructions. Indeed, both scientifically and philosophically, Time has winnowed, honored, and made familial Turing’s now golden offsprings, while cultural mavens and dramatists, and even some scholars and scientists, have perhaps been less than fair, and certainly less than accurate, respecting the man who crunched the apple.

In Turing’s justly famous 1936 paper, “On Computable Numbers,” Turing negatively answered David Hilbert’s question as to whether a “definite, mechanical method” existed that would decide in a finite number of steps whether any given mathematical assertion, or equally any real number, was determinable or computable, as what Turing called a “satisfactory number” or, equivalently in Hilbert’s explicit formulation, a determinably true or false mathematical assertion. Turing continued his paper’s title “with an Application to the Entscheidensdungsproblem” because in order to solve this problem he had to invent what he called “Theoretical [or Logical] Computing Engines” and a particular species of them he called “Universal Theoretical [or Logical] Computing Engines” (these are what we now of course call “Turing machines” and “universal Turing machines”). Turing also put the application as the subtitle because he thought the characterization of TCEs and UTCEs was of considerable independent interest as characterization of real numbers, which prove to include not only computable numbers but also, using a diagonal procedure of the sort Cantor used to establish among the real numbers both the countable rational numbers and uncountable irrational numbers, Turing distinguished computable numbers from uncomputable numbers, including amongst these uncomputable numbers, universal computable-checking machines that cannot determine, or compute, their own description number on pain of contradiction. As Turing’s mathematical biographer remarks,

Turing’s proof can be recast in many ways, but the core idea depends on the self-reference involved in a machine operating on symbols, which is itself described by symbols and so can operate on its own description. Indeed, the self referential aspect of the theory can be high lighted by a different form of the proof…However, the “diagonal” method has the advantage of bringing out the following: that a real number may be defined unequivocally, yet be uncomputable. It is a non-trivial discovery that whereas some infinite decimals (e.g. p ) may be encapsulated in a finite table, other infinite decimals (in fact, almost all), cannot. (Hodges 2002. p. 4).

Even more importantly perhaps, TMs might be a useful précising or formalization of the equivalent informal terms “definite method,” “effective method,” or (as Alonzo Church independently termed it) “effectively calculable method” (Church 1936; Church in the same paper provided “lambda definable function” as his own formalization of the informal notion).

Church, in fact, identified or defined the informal notion with his formalized notion of lambda definable, or recursive, function, latterly recognizing that his formulation also generated the same functions as Turing’s formulation. Emil Post at the time justifiably offered the following caveat to Church’s formulation,

To mask this identification under a definition … blinds us to the need of its continual verification, [for it is just a] “working hypothesis” (Post 1936: p. 105).

Turing indeed did not then identify his formalization of TCE with the informal notion of “definite method,” etc., or claim an equivalence. In Wittgenstein’s Lectures on the Philosophy of Mathematics, Cambridge 1939, Alan Turing does indeed remark that “a [real] number is like a simple kind of device that transforms inputs into outputs in a characteristic way” (Wittgenstein 1976, p. 37).

Twelve years later, however, Turing was to justifiably assert that

LCMs [ Turing machines] can do anything that could be described as “rule of thumb” or “purely mechanical” (Turing 1948: p. 7).

Or as he also then, and more carefully, added the supporting formulation,

This is sufficiently well-established that it is now agreed that “calculable by means of an LCM [Turing machine]” is the correct rendering of such phrases. (Turing 1948: p. 7)

In other words, Turing’s, and Church’s, original working hypotheses amounted to the identification of the informal notion of computable with their own 1936 formalizations. But latterly with the accumulation of ever so many alternative formalizations of computability, with the equivalent effect, converging on their own formulizations, we could now increasingly take the working identification for granted as the now well-established Church-Turing Thesis. This thesis has had nothing but increasing support since 1948. While we today can say that, strictly speaking, the claim that anything that is TM-computable is just plain computable is still unproven (how indeed could it be proved, strictly-speaking, given its informality?), we nonetheless now are quite confident that the formulation will endure. Indeed, since Turing’s formulation seems more clearly mechanized, and more fundamental, fruitful, and physically realized, we might well speak, as some do, of the Turing thesis.

Indeed, both Church and Godel handsomely recognized something like this and both McCulloch-Pitts 1943 and von Neumann 1945 acknowledge Turing’s 1936 paper as stimulus for their own work (for McCulloch-Pitts’ acknowledgement see von Neumann 1951/1963, V: p. 319). In a review of Turing’s paper, Church acknowledges that

As a matter of fact, there is involved here the equivalence of three different notions: computability by a Turing machine, general recursiveness in the sense of Herbrand-Godel-Kleene, and l-definability in the sense of Kleene and the present reviewer. Of these, the first has the advantage of making the identification with effectiveness in the ordinary (not explicitly defined) sense evident immediately (Church 1937a: p. 43).

And Godel writes that

Due to A. M. Turing’s work, a precise and unquestionably adequate definition of the concept of a formal system can now be given … Turing’s work gives us an analysis of the concept of “mechanical procedure” (alias “algorithm,” or “computational procedure,” or “combinatorial procedure”) (Godel 1934/added in 1946).

Latterly adding,

Tarski has stressed in his lecture (and I think justly) the great importance of the concept of general recursiveness (or Turing’s computability). It seems to me that this importance is largely due to the fact that with this concept one has for the first time succeeded in giving an absolute definition of an interesting epistemological notion, i.e., one not depending on the formalism chosen. In all other cases treated previously, such as demonstrability or definability, one has been able to define them only relative to a given language it is clear that the one thus obtained is not the one looked for. … By a kind of miracle it is not necessary to distinguish orders, and the diagonal procedure does not lead outside the defined notion. This, I think, should encourage one to expect the same thing to be possible also in other cases. (Godel 1946, p. 84).

Indeed, some have gone so far as to suggest that a Turing machine is the Normal Form for reports of psychological states or capacities, whether the attribution is to a human, a computer, or a hypothetical alien intelligence.

Turing machines are minimalist, evocative, and physical – at least sort of physical, although Turing called them Theoretical Machines and he certainly had no intention of building one. They were machines to think with.

Turing machines are certainly minimalist in kinds of symbols – two distinguishable symbols plus blank. The active part of the machine is fed by an indefinitely long tape divided into frames like those on a roll of film. The active part has a “read head” which can tell whether the frame under it has “/,” “\,” or is blank. The read head is also a “write head” that can erase, write in a “/” or do nothing. The machine can move one frame forward or backward or stay in place, and the write head take action, according to what is read and what state the machine is in, among a small number of “internal states.” Then the move is repeated. At the beginning of each move, the machine is in one of a small number of “internal states” and may switch to another after the move. The machine is built to instantiate instructions in its machine table of the form “if / is read and the internal state is 1, then erase, move one frame forward and go into state 2.” A Turing machine for adding would get, say, the input sequence “// //” and then automatically change it into “////” through a long series of steps, shuttle-cocking backwards and forwards, and then stop. For us this would be the computation “2+2=4.” Since Turing was thinking about a theoretical device, he did not mind that a million would be represented by a like number of “/”s.

The tape could also store data and programs (“memory,” “skills,” and “plans”), represent incoming data (“sensory input”), and issue output of a like character (“motor outputs”). So Turing has also given the framework in which to describe any sort of individual thinker, you and me included. As many scientists have said since the 1960s, we are, more or less, universal Turing machines and so are our digital electronic computers. For the same reason, we now think of thinking as computing or data-processing. When Alan Turing showed up at Bletchly for deciphering German Enigma Machine military messages in September, 1939, we might say that he already knew what he had to do theoretically. There was in fact an incredible amount of practical engineering in front of him. In any case, Turing’s theoretical machines have cast much light in formal and cognitive science, light that emphasizes the automation of cognition as a mechanical and purely physical task. Turing’s machines shape our conception of thought and of psychology. Just as time, fertility, multiple convergence, and lack of refutation has shifted us to a thorough acceptance of the equation of the informal notion of computable to TM computable, so we have come a long way toward understanding Turing’s Turing test as a productive criterion for practical cognitive science.

Aside from the initial mid-century reaction that it would be “a simple [but irrelevant] task” to simulate human intelligence or that it would take but a decade to reach the goal, there has developed over the past few decades a consensus in cognitive science about what intelligence a Turing test passer would have to exhibit, under extensive and lengthy interrogation by experts, and a considered agreement that nothing on the near horizon looks likely to succeed. Professor Robinson, to whose objections Turing replies in his famous 1950 paper, may be pardoned for thinking it “would be a simple thing” to program a computer to pass the test but no one now may so be pardoned. It is an impressive testament to the enormous (and heretofore largely unrecognized) complexity of ordinary human intelligence that passage now seems so difficult, even with computers that almost unthinkably exceed in memory size, speed, and programmability those beginning to become available in Turing’s day.

Around 1950, Turing proposed what we now call the Turing test for machine intelligence (Turing 1950, 1948), a goal to which his many contributions to the development of serial-processing programmable digital electronic computers were dedicated. Although many U.S. scientists refer to such as Von Neumann machines, they are as much or more Turing’s achievement. On this last point he has received less than credit due (Carpenter and Dorant while crediting Von Neumann (1945) as well, insist that Turing (1945) “is quite possibly the first complete design of a stored program computer architecture” specifically including “subroutines, the stack and micromachine architecture” as Turing’s contributions (Carpenter and Dorant 1977), see also Hodges 1983)). More expansively, D. C. Ince credits the 1945 paper for hierarchy of programs and Turing’s 1948 paper for computer-based theorem proving and self-organizing machines (Ince 1992; Turing 1945, 1948).

What has largely gone unnoticed is Turing’s 1948 proposal about training and construction methods for “Unorganized Machines,” or what we today call connectionist nets, among which he discriminated a variety of parallel distributed processors with computational capacity comparable to that theoretically available in a Universal Turing Machine or practically in a serial processing programmable digital electronic computer (Turing 1948). Also unnoticed has been his description of the “Child Machine” and importance it might hold, along with the Unorganized Machines, in the attempt to make Turing Test passers (Turing 1948,1950).

Turing envisioned virtually no restrictions on how the Turing Test passer is to be fashioned. It will be quite enough of an achievement to come up with anything whatsoever that does the job (a point rather more vividly evident to us by now than it was in 1950). Turing excludes only one method: to conceive, bear, grow, and properly educate a human being (amusingly, a requirement that John Searle’s Chinese Box counterexample would flunk in that Searle is human). Turing recommends that both programming serial computers and training connectionist nets should be employed. And Turing insists that since a fully disorganized machine could not be efficiently trained (just as a non-specific, all-purpose chordate brain could not effectively reach cognitive maturity), much thought and experiment might need to be devoted to the structure of the Child Machine. Its structure might need to mirror native human cognition to achieve, after training and programming, Turing Test passage.

Hence, for Turing, there is no linkage between the propriety of the Turing Test and the fate of the various theses of what has recently been labeled Good Old A. I. In particular, the passer need not exemplify the “physical symbol hypothesis” or wear on its sleeve the claims about the well-defined autonomy and causality of cognition that Fodor and Pylyshyn (1988) have championed against connectionism. This lack of linkage is important in that Turing’s Turing Test draws, as he remarked, “a fairly sharp line between the physical and intellectual capacities of a human being.”

No engineer or chemist claims to be able to produce a material that is indistinguishable from the human skin. It is possible that at some time this might be done, but even supposing this invention available we should feel there was little point in trying to make a “thinking machine” more human by dressing it up in such artificial flesh. The form in which we have set the problem reflects this fact in the condition which prevents the interrogator from seeing or touching the other competitors, or hearing their voices …The question and answer method seems to be suitable for introducing almost any one of the fields of human endeavor that we wish to include. (Turing 1950, p. 12)

The rough fact remains evident in everyday life, in law, in science, and in myth that the Turing test is a natural.

But while Turing placed no restrictions on the construction and training of Turing Test passers, for the real interest lies in what the construction and training will have to be, Turing was adamant for just that reason that what counts could only be that a real mechanism should REALLY PASS the test. Moreover, as evinced by Turing’s viva voce example in which the machine is supposed to demonstrate a lively grasp of everyday stereotypes, literary criticism, and the sonnet, Turing expected the passer to prove indistinguishable from as broadly talented and articulate a human as could be produced, under as long an examination as wanted, conducted by knowledgeable and probing experts. Purported theoretical counterexamples to the Turing Test, such as those of John Searle and Ned Block, tend to violate the first point; while purported partial practical counterexamples, such as ELIZA and PARRY, radically loosen up the passing standards.

Block (1978) considers a counter example with a cast of millions who are imagined to instantiate the Turing Machine that represents some normal human’s intellectual capacities. Block considers the claim that this assemblage would be the appropriate, “functionally-equivalent” Turing Machine but that we would hesitate to call it a thinker. John Searle (1980) offers a related argument in which he is to be imagined simulating an intelligent Chinese speaker by reading and sorting for him meaningless Chinese symbols; by any construal of his supposed counterexample, it would take Searle hours to respond to simple questions. Block and Searle’s counterexamples do not bite on Turing’s views. Block’s assemblage would have neither the reliability or speed to have even the feeblest chance of Turing Test passage; Searle would be unmasked at first pass (see Leiber (1992)). What you need to refute Turing’s Turing Test is a reasonably detailed description of a physically possible machine which can indeed be supposed to pass the test in real time but which is somehow not really thinking. That is what the counter- examples do not offer. Turing clearly presumed that the natural laws of our universe obtain for any putative Turing test passer. Philosophers’ counter-examples blatantly demand worlds where these laws do not hold, where things happen at speeds and with reliability not even faintly obtainable in the materials and conditions of our universe -- worlds in which miracles are continually happening. The counter-examples are miracles, while Turing test passage has to be a practical achievement.

Turing, indeed, clearly held that no machine with the literal Turing machine architecture could ever be a viable candidate for Turing test passage (Turing 1948). Further, Turing certainly speculated that even the much speedier and more reliable electronic computer architecture might not allow us to do the job. Perhaps we will also need dense networks of nodes with adjustable weights, “the best eyes and ears money can buy,” and a suitable training program.

Indeed, Turing even considers adding what we might call the “Frankenstein” option.

[One way] of building a “thinking machine” would be to take a man as a whole and try to replace all parts of him by machinery. He would include television cameras, microphones, loudspeakers, wheels, and “handling servo-mechanisms” as well as some sort of “electronic brain.” … In order that the machine should have a chance of finding things out for itself it should be allowed to roam the countryside, and the danger to the ordinary citizen would be serious. …[A]lthough this method is probably the “sure” way of producing a thinking machine it seems altogether too slow and impractical (Turing 1948: p. 13).

Perhaps Turing calls this “the ‘sure’ way” because it is the evolutionary algorithm. The environment will sanction various versions of the machine, until the experimenter, who has been shuttling back and forth from the drawing board to the environmental testing, converges upon a successful version. No wonder Turing calls it too slow. He does allow that the foresighted experimenter may proceed more expeditiously than mother nature.

Given the enormous number of steps a Universal Logical Computing Machine must through in performing relatively simple arithmetical calculations, Turing argues on physical grounds that such machines cannot be constructed unless we severely limit the computations we expect them to realize. Given Brownian movement, there will be no reliability in computations with “very large numbers of steps,” nor, “assuming that a light wave must travel at least 1 cm between steps,” would we be willing to “wait more than 100 years for an answer” (Turing 1948). In reality, Turing argues, we will have to be content with Practical Computing Machines, such as our computers, that exponentially reduce computational steps, thus giving us marked increases in speed and reliability. Today we approach specific forms of the same practical physical limitations on Turing Machine architectures on our computing machines themselves. Minimizing signal distance to maximize speed, Cray computers require liquid nitrogen cooling, suggesting that the architectural change to parallel distributed processing might possibly be forced on purely mechanical grounds (and parallel processors have heat problems coming up too; they in fact are normally run on programmable computers). It has been objected that the Turing Test is behaviorist: to ascribe intelligence we will want not only the right input/output relationships but also a sense that there’s the right architecture inside. Turing’s answer is that the most promising avenue for discovering what’s right about our own architecture is through Turing Test passage research (our armchair architectural intuitions can have at best heuristic value). Engineering/simulation first, theoretical understanding perhaps later. as Professor Chomsky has pointed out,

Engineers knew how to do all sorts of complicated and amazing things for hundreds of years. It wasn’t until the mid-nineteenth century physics began to catch up and to provide some understanding that was actually useful to engineers. (Chomsky 1988: p. 182).

This is only a reasoned rejection, not a refutation of a priori armchair architectural demands.

Turing began “Computing Machinery and Intelligence” by insisting that if the meaning of the words “machine” and “think” are to be found by examining common usage, then the answer to the question, “Can machines think?” is a Gallup poll.

But this is absurd. Instead of attempting such a definition I shall replace the question by another, which is closely related to it and is expressed in relatively unambiguous words. (Turing 1950).

Turing does not say that we logically must accept Turing test passing machines as thinkers, but that, if

the engineering succeeds, we will and should take them to be such. Respecting Gallup, Turing does

speculate that by the end of the century we can expect willy nilly that usage that ascribes intelligence to computers will be common place, whether or not Turing test passage is obtained.

As Turing’s engaging insistence on “playing fair with the machine” suggests, Turing happily deployed moral justifications for the Turing Test. He disarmingly introduces the now familiar interrogative format as a game in which a man (A) (“My hair is shingled...” is trying to simulate the replies of a woman (B) (“I am the woman, don’t listen to him...”). Then he suggests substituting a computer for A (so that, perversely and curiously, the computer’s assignment briefly appears to be that of simulating a man simulating a woman (Moody 1993)). Responding to the claim that computers can’t “pass” because they aren’t “beautiful, friendly, etc.” and don’t “fall in love [or] enjoy strawberries,” Turing’s devastating reply is

The ability to enjoy strawberries and cream may have struck the reader as frivolous. Possibly a machine might be made to enjoy this delicious dish, but any attempt to make one do so would be idiotic. What is important about this disability is that it contributes to some of the other disabilities, e.g., to the difficulty of the same kind of friendliness occurring between man and machine as between white man and white man, or between black man and black man. (Turing 1950: p. 24)

Over half a century ago, Turing suggested that we might need to construct neural nets, trying out various “initial states” for the Child Machine, and then train these nets with a view to Turing Test passage (Turing 1948, 1950).

Crucially but briskly, Turing also dismissed what he called the “solipsist objection.” Echoing a number of philosophers and some philosophy undergraduates, Turing’s solipsist maintains that the only way to really know that you think is through introspection, through consciously experiencing your own thinking. Turing’s solipsist therefore reasons that since he can’t introspect or experience other people’s thinking, he cannot really know whether anyone else thinks. Turing asks us to imagine that we have built a successful imitation of human intelligence, a Turing test passer. Someone may raise the objection, “Yes, it is an amazing trick, a sort of cognitive wax museum construction, but there is no real thinking going on inside, no consciousness, no inner life like I have.” Turing, momentarily accepting the solipsistic criterion, suggests we should conclude that then the only one who could ever know that the machine thinks is the machine itself, and we of course would not take its word for it. By the same token, however, Turing suggests that his solipsist must also conclude that only I can really know that I think and I can’t know whether anyone else does. Everyone else, then, is in the same position. Turing jokes that we have a “polite convention” of assuming that other humans think. However, if we can’t establish that a computer thinks through its observable behavior, then surely we can’t establish that other humans think either, because all we see is their observable behavior (we can see inside their brains but we don’t of course see thoughts there, just brain tissue; whatever neurology brings us, it won’t be our old familiar little man in the head).

What endures is the native plausibility of the Test, which recalls Rene Descartes’s “respond in a suitable fashion to whatever may be said in its presence.” It provides a most suitable pre-theoretical target without which we are unable to draw a line between modeling human intelligence and simulating the human brain, neurological and sensory systems, and the rest of the body, and all their biological, psychological, and social features. Refreshingly, Turing’s Turing test sets us an experimental and constructive engineering task. Literal Turing machine architecture maximizes simplicity by making tape length infinite and computative steps of the simplest possible sort, so it is literally wholly impractical for all but the simplest computations. Now our empirical problem becomes one of engineering, one of finding the materials and shortcuts, the many clever hacks, training regimes, and complications that allow each of us to instantiate a Turing Machine with a light years long tape in three pints of neurological nets.

A philosophical critic may say, We are also interested in what intelligence or mind IS. Might not engineers even actually build and train a passer WITHOUT knowing what intelligence really IS? Should we not, therefore, preserve a conceptual and philosophical concern with the nature of intelligence (or mind)?

The question what is intelligence? resembles the question what is life? Answers to this latter question - the soul, Aristotle’s vegetative and animating principles, elan vital, etc. - now seem as much irrelevant as mistaken. We know very roughly how the DNA coding-structures arose and how these organism-building instructions for protein structures have been winnowed by evolutionary accident into the vast profusion of particular and peculiar organisms that have teemed our planet, how ingenious and baroque mechanisms have actually done the job here. While artificial life is a recent coinage, the engineering orientation reminds one of Turing. But while biologists occasionally speculate about whether silicon could play the same biochemical role as carbon in a vastly different planetary environment, or wonder how much structural variation on the double helix or the amino acid alphabet might arise on other earth-like planets, or did arise early in Earth’s history, etc., the cosmic and portentous question what is life?, along with its Gallup Poll answers, now seems lost, and well lost, in the shuffle.

Turing prepared us to regard the equally cosmic and portentous question what is intelligence?, or what is mind?, in a similar way. As his work on morphogenesis and his equating, “structure of the Child Machine” with “hereditary material” and “natural selection” with “judgement of the experimenter” suggest, Turing’s biological and cognitive investigations are closely interrelated. Just as biologists speculate as to whether silicon life forms might evolve, so biological and cognitive scientists may wonder as to whether such organisms could, when winnowed by a suitable environment, evolve to exhibit something comparable to our cognitive processes and powers. Biologists hold that the reproductive peculiarities of the social insects make it nearly inevitable that they evolve into species with elaborate architectural proclivities (hence bee hives, ant hills, termite mounds). Perhaps biologists and cognitive scientists may speculate, similarly, that “naturally evolved” intelligence, whether carbon or silicon based, will inevitably build electronic computers. But though these are biological and cognitive questions, they are not questions to which we should expect answers too soon and still less questions that arm chair intuitions can hope to decide. Beyond answers to these sorts of biological and cognitive questions, what else could we reasonably expect to know?

Someone may well reply, But what about consciousness? THAT I understand. It’s not like elan vital, for consciousness is exposed directly to my observation. I know intimately what it is to think and no engineering simulation is going to convince me that a machine thinks. But the cases are parallel. You not only think, you live. Your living is just as exposed directly to your observation as your thinking. Still, your intimate experience of living doesn’t make you an oracular biologist: you are a specimen. The same goes for cognition.

Cognitive science can burgeon as an investigation of engineering possibilities with a merely heuristic interest in simulating cognitive aspects of successful biological models, or additionally aided by an historical account of what has happened to be thrown up biologically and cognitively on this peculiar planet. Turing saw that it might have to be both; that realization is exemplified by his test. Tens of thousands of scientists and philosophers today continue to pursue Turing’s quest through vigorous, far-ranging construction and experiment. Like Turing’s thesis, time has indeed been kind to Turing’s test as currently construed, and it is clearly central to cognitive science. It is not only a test to profitably pursue in all of its special branches and central requirements, but a test to think with as well. It stands well today.

However, as with any such central and portentous scientific development, particularly one that touches our sense of ourselves, Turing’s test and indeed its author, have been subjected to wild misunderstandings and demonic flights of malicious fancy that far exceed Professor Robinson’s “It would be a simple task.” Al though the examples of this are legion, I shall content myself with rebuking some of the characteristic mistakes that Jean Lassegue makes in his recent paper, “What Kind of Test Did Turing have in Mind?”

Lassegue writes,

[I]s the so-called “Turing test” as objective and scientific as it is claimed to be in the AI and cognitive science community? Do we have to consider it as a threshold one has to cross to be able to enter the realm of a scientific approach to the mind? My answer is “no” because the so-called Turing test [as Turing actually formulated it] says in fact more about Turing’s psychological life than about the science of mind itself. (Lassegue 2002: p. 4)

Informal logic teachers will doubtless groan at this elementary example of the genetic fallacy. If it is true that the Cretan, Epimenides, who is credited with originating the liar paradox by saying “All Cretans are liars,” did not actually recognize there was anything paradoxical in his pronouncement and he gave in any case a loose version of it, this is hardly grounds for denying that the liar paradox has an objective meaning in logic and mathematics (St. Paul, in his letter to Titus quotes Epimenides (“even one of their own”) as evidence that the Cretans are habitual liars; Paul even adds that Cretans always lie, thus tightening the paradox without in fact suspecting that there is anything paradoxical about what he is writing). If the “Turing test” has a clear, useful, and established sense in the cognitive science, it is simply irrelevant to cognitive science whether Turing mis-formulated it originally or expressed it bizarrely through some unconscious, self-revealing, pathological cause. But he didn’t do that either.

After dismissing the question “Can a computing machine think?” as unsuitably vague, Turing proposed to operationalize the issue by substituting what he called the imitation game, the genesis of the Turing test. But he first introduced a preliminary version (game 1) in which a man and a woman compete and then substituted the machine for the man (game 2). I will quote the same lines that Lassegue quotes but I will also insert and italicize the material that Lassegue crucially leaves out, replacing them with three dots, thus sanctioning his perverse misreading. Additionally, I have bold-faced the most crucial excision.

It is played between three people, a man (A), a woman (B), and an interrogator (C) who may be of either sex. The interrogator stays in a room apart from the other two. The object of the game for the interrogator is to determine which of the two is the man and which is the woman. He knows them by labels X and Y, and at the end of the game he says either “X is A and Y is B” or “X is B and Y is A.” The interrogator is allowed to put questions to A and B [so Turing’s original continues:]

C: Will X please tell me the length of his or her hair?

Now suppose X is actually A [the male], then A must answer. It is A’s object in the game to try and cause C to make the wrong identification. His answer might therefore be:

My hair is shingled, and the longest strands are about nine inches long.

In order that tones of voice may not help the interrogator ... a teleprinter will

communicate between the two rooms. The object of the game for the third player (B) [the woman] is to help the interrogator. The best strategy for her is probably to give truthful answers ...

Thusly Lassegue resumes quoting Turing:

We now ask the question, “What will happen when a machine takes the part of A [the male] in the 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 woman?” These questions replace our original “Can machines think?”

Having finished his doctored Turing quote, Lassegue now triumphantly pounces on Turing as

follows:

Let us go back to Turing’s description of his first game and to the strategies displayed

by the players. In fact, the only example given by Turing would not lead to a successful

imitation but on the contrary to an unsuccessful one, that is to say to an unreciprocal

imitation.

Here is how Turing describes the woman’strategy:

The best strategy for her is probably to give truthful answers. She can add such

things as “I am the woman, don’t listen to him!” to her answers, but it will avail nothing as the man can make similar remarks.

What can we infer from this description? That the woman will at once be recognized by the interrogator and that the match will end immediately. If the strategy followed by the woman is to tell the truth about herself without imitating the man’s behavior, this truth will become very quickly apparent to the interrogator.

Why should the woman speak the truth? It is obviously a very bad strategy, since it should be characterized, more than anything else, as an absence of strategy ... In Turing’s article the odds are weighed too heavily against the woman and this fact must somehow be explained. (Lassegue 2001, p. 9).

But of course, as Turing very clearly stated in the sentence Lassegue left out, the woman’s task is to help the interrogator! This is exactly parallel to her task of helping the interrogator in the second game, where a computer is substituted for the man. So, pace Lassegue, the strategy Turing recommends for her is not at all a very bad strategy, one so bizarre that Turing’s recommendation cries out for psychological explanation. To the contrary, the strategy that Turing suggests is clearly the best possible strategy and, again in parallel, exactly the right strategy for her (or any human) to follow in the second game. The natural way for the interrogator to start the full blown test is familiar to real professional interrogators: What is your name?, Where were you born and when? ... You’ve told us that you grew up living at 526 Chartres St., New Orleans. Tell us about the buildings near your home then. ... Can you hum “When the saints come marching in”? ... Didn’t you previously say that your boy friend’s name was Xavier? ... What did you say your address was in New Orleans?

It is elementary that when you want the authorities to believe that you really are you, you don’t start making things up! This maxim also applies when the interrogator, in the second game, not only asks you personal questions but more general ones. The best strategy for the woman will be to give the most competent answer she can manage rather than giving lots of ad hoc, deliberately stupid answers, for it will be much easier for a computer to simulate dumbness than human competence. It is, for example, child’s play to program a computer to simulate human like mistakes and slowness in mathematical questions but extraordinarily hard to display the talents humans characteristically deploy in ordinary conversation over a range of topics (it certainly hasn’t been done). To repeat Turing, who makes its roots in interrogation techniques clear, “The question and answer method seems to be suitable for introducing almost any one of the fields of human endeavor that we wish to include.”

Even a spy doesn’t make things up if this can be avoided. There is nothing like being a practiced plastic surgeon (named Mallory) as the most successful way to pretend to be a practicing plastic surgeon who goes by the name Sorge and is really secretly reporting political gossip among his patients to the CIA. Fake as little as possible because the truth is much easier to keep track of and make convincing. So the man in Turing’s first interrogation game would do best to leave all the details of his own life unchanged except those that must be changed to maintain the impression that he is a she. In the second case, the computer has to put together whole cloth the complex identity structure of a person with characteristically human competencies and beliefs, along with characteristically human performance mistakes, prejudices, and emotions.

Turing takes personal narrative as basic. It is certainly quintessential in his first sketch in the 1950s paper. Personal narrative aptly fits his general formulations of the test. Turing always takes it that the machine must pass as a particular human identity, not as some reified human in general, although the machine must also exhibit multiple talents that are characteristically human, talents grounded especially in natural language and folk psychology (his second exemplary interrogation in the 1950s paper, Turing seems to call for a refined sense of metaphor in English and a passing acquaintance with Charles Dickens’ novels). Turing’s formulation also seems apt because personal narrative is found not only in interrogations but in a large, and often vital, portion of our daily interchanges with other people (and with ourselves) and in our oral story-telling, our novels, plays, movies, operas, and TV narratives of all sorts. No one seeks to pass as a human in general. We have no training in that enterprise, while we have scads of experience in individual self-narrations, whether respecting ourselves or others.

Lassegue also tries to suggest another way in which the first test and the second are suspiciously dis-analogous. He points out that if, in the first test, the man pulls off his imitation of a woman, this doesn’t in any way establish that he is a woman, while in the second test, passage by the computer is supposed to establish that the computer is, genuinely, a thinker or intelligent. But this is silly. Turing’s whole point is to distinguish physical traits from mental ones. As Turing emphasizes, “playing fair with the machine” is like blind refereeing or putting an opaque screen between musical performers and their judges. If the man in the first test passes, then it establishes that he can think like (or can cognitively/affectively pass as) a woman. Similarly, just as the man’s passage in the first test does not of course establish that he is a woman, the computer’s passage in the second test does not of course establish that the computer is a woman (or a human being). And again, in precise analogy, what the computer’s passage of the second test would establish is that it can think like (or can cognitively/affectively pass as) a woman (or more generally, a human being).

Turing, who was no human chauvinist, also makes it amply clear that passage would be a sufficient condition for being intelligent, not at all a necessary one. It might well be, he suggests, that a computer might be produced that really ought to be considered intelligent but would not be able to pass the test. It is perhaps also important to add that while Turing speaks of “playing fair with the machine,” it would be absurd to think, as Lassegue seems to argue, that Turing identified himself with the machine or with “pure intelligence.” In fact, as his biographer makes clear, Turing felt contempt for the airs put on by upper middle class Englishmen who prided themselves in their capacity for “abstract thought”; thinking machines would take them down a peg (Hodges 1983).

His perverse misreading now allows Lassegue to go on, preposterously, to write,

Little by little, a kind of hierarchy in the players’ responses emerges from the text: the woman imitates herself (that is why she is a poor player), the man imitates the woman (he is therefore a better player than the woman). What about the machine which replaces the man in the second game? (Lassague 2001: p. 10)

Lassegue’s response to his wholly contrived and mis-premissed question is that the computer, when passing, really shows itself, and intelligence itself, to be male. To the contrary, and to insist on the literal reading of Turing that Lassegue officially demands (but hardly follows), what the computer has to do to pass, to prove it is a thinker, is to be cognitively indistinguishable from a human female. (I am reminded of one of my daughter Casey’s first sentences, in her twenty sixth month, “I am a person,” which elicited a matronly “Of course you are, my dear” from the next table in a Cotswold restaurant. Baffled, and seeking to understand what this Cartesian announcement could possibly mean, I asked “Is Mommy a person?” and after some repetition eventually got a lisped “yesh.” My further inquiry, “Is Daddy a person?” eventually elicited a “No.”)

For an amusing account of a related attack on Turing that also fizzled, consult Leiber (1992: p. 127-28). In Ian McEwan’s TV drama, The Imitation Game, protagonist Cathy Raine, hoping to do her bit despite the granite assurance of her male chauvinist society that she is a decorative, know-nothing non-entity, becomes one of the hundreds of Bletchley women who, in complete ignorance of what they are really doing, endlessly record and transcribe the radio signals that feed the fledgling electronic brains that “Turner” and other males in Hut Eight direct. By seducing Turner, Raines manages to learn what is really going on and as “the woman who knows” she is locked up for the War’s duration (McEwan also cannot resist having Turner prove impotent in the climax of his tete-a-tete with Raine). Indeed, McEwan even has Turner speak several lines from Turing 1950’s paper as if they were Turner’s own thoughts and these lines are apparently intended to unmask Turner as a sexist, misanthropic machine-lover. In fact, however, the real Hut Eight contained a female mathematician who was perfectly aware of what was going on and, like Turing, a graduate of Cambridge University; Turing eventually proposed marriage to her, and the two retained a friendly relationship long after she withdrew from the engagement (Hodges 1983).

Over the past fifty years computers have grown almost immeasurably in speed and memory capacity, and all the methods Turing suggested have been zealously pursued (except the Frankenstein option), with much inevitably learned about human intelligence. But the goal of Turing test passage now seems ever more formidable in just the area C human language and the folk psychology it embodies in personal narrative C that the Turing test makes central. The magnitude of the difficulty is now perhaps most dramatically obvious in the much simpler but related task of machine translation between human languages. After a half century of concerted effort by linguists, psycholinguists, programmers and indeed cognitive scientists of all ilk, the best that can be said of current machine translations is that by scanning the often absurd muddle for key words, and the occasional viable phrase or even intelligible sentence, you may be able to guess whether it will be worth while to call in a human translator. And something like the largely tacit and profoundly human knowledge that the translator employs must be available to a Turing test passing machine. That and ever so much more, for the machine must not only be able to manage coherent narrative but also must be able to flesh it out in every conceivable way in response to skilled, real-time interrogation. Of course, the translation machine’s success can be better with highly restricted technical writing. Failure is most complete with the words and constructions of what Ludwig Wittgenstein called the “old city,” the core words and narrative structures, and personal knowledge, common to speakers of a natural language.

In his 1948 paper, Turing lists five areas he thinks will prove most fruitful for intelligence research:

(i) Various games, e.g., chess, noughts and crosses, bridge, poker

(ii) The learning of languages

(iii) Translation of language

(iv) Cryptography

(v) Mathematics

Turing had already introduced rudimentary chess-playing programs and automated theorem-proving programs. The other three areas center on natural language and the folk psychology it animates. Turing comments that among these language learning is “the most human of these activities” but adds that this field “will depend rather too much on sense organs and locomotion.” Some have questioned the inclusion of cryptography. Turing, however, remarks “The field of cryptography will perhaps be the most rewarding.” All that Turing offers to explain this startling claim is

There is a remarkably close parallel between problems of physicist and those of the cryptographer. The system on which a message is enciphered corresponds to the laws of the universe, the intercepted messages to the evidence available, the keys for a day or a message to important constants which have to be determined. [The “keys for the day” refers to the enigma setting the Kriegsmarine specified for all encrypters to use on a particular day for the first part of their messages, while the “keys for [the rest of] a message” would be supplied in that first part. I will ignore this further complication.]

Cryptography, of course, had been Turing’s most important and time-consuming activity during WWII and the needs of cryptography forced the creation of high speed, automated computation through special-purpose magnetic relay and vacuum tube computers. “The system on which a message is enciphered” is the German enigma machine, which looked like a typewriter attached to a series of rotors that operated like the one, ten, hundred, and thousand mile rotors on a car’s odometer. When each letter is typed in, the impulse travels through the rotors, which turn periodically as the message proceeds, eventually producing the now enciphered letter sequence, a result which effectively runs the input letter around an alphabetic circle, changing the letter to another that is a particular number of spaces from it (since one of the rotors will now move, striking the same letter twice will produce two different letters). The evidence for the structure and settings of the machine, akin to the physicist’s data, is the enciphered sequences produced by that machine, which are a tiny portion of the countless messages that might have been sent, given the machine’s structure and settings. Receiving these symbol-string messages, Turing and his Bletchley colleagues had to distinguish the features of the messages due to the enigma machine’s structure and settings from those due to the syntax, semantics, and pragmatics of the German language in the plain input message (in the context of what Bletchley knew about U-boat war dispositions and communications). Given the enciphered message and an adequate characterization of these two distinct factors, you can then retrodict the original German message.

Fortunately for Turing, and Britain, the effect of the machine on the message is quite different from the prior effect of the German language, etc. The enigma machine is a rudimentary finite state machine that simply changes one letter to another by counting through the circular alphabet a certain number of spaces as dictated by the structure of the machine and its settings. Unlike the German language, the enigma machine supplies no phrase or transformational structure, no anaphora, indeed essentially no syntax, semantics, or pragmatics. Familiarly, the transformational-generative German language provides all of these. Enigma does not supply the familiar cipher-breaking, natural language redundancy features such as frequency of letter and letter combination frequency (in English, for example, e is the most frequent vowel and t the most frequent consonant, q is always followed by u, yxu is impossible while all is common, SUBJECT, VERB, OBJECT is the standard sentence structure, in “The barber used his razor to shave Tom’s father,” Tom and father can’t be the barber, while his must be the barber, and so on; no laws of this sort govern the enigma machine contribution).

Since Turing’s analogy likens enigma, as “the system on which a message is enciphered,” to “the laws of the universe,” Turing is sharply distinguishing everything that determines the regularities and meaning of the input German message from the enigma system for which the enciphered message strings are “evidence.” This is natural enough, for the military cryptographer, militarily speaking, only seeks to determine the original plain text German sentences by determining the system that enciphered them and all the other texts enciphered by the same system. It is not the cryptographer’s job to determine what significance the plain texts have for the war, although of course the cryptographer will most importantly use knowledge of the German language and the war to determine the operation of the system. But for Turing’s post war intelligence work, for building Turing test passers, the information about natural language and folk psychology would surely be central, not just a vital way toward the goal of deciphering. One is tempted to assume that the analogy indeed is “the system of enciphering” to the “physical laws of the universe,” with the features of natural language and folk psychology equaling the mental. Cryptographic work, of the sort Turing envisioned, would presumably seek to distinguish natural language and folk psychology in general from the effects of any mechanical enciphering system (or at least any simple mechanical system of enigma’s sort). It is the commonplace distinction that psychologists and linguists use in taking speaking and hearing to be “encoding” and “decoding” -- i.e., converting thoughts, or mental items, into the physical speech stream, and converting the physical speech stream into thoughts, or mental items. Turing said that his test draws a clear line between the physical and the mental; the goal is to duplicate us mentally.

Because common, native, and, like visual perception, its operations largely opaque to conscious introspection, this human competence initially had seemed apt to computer simulation. We know better now. While computers can simulate or exceed the performance of human experts in narrowly defined areas, they are laughably far from simulating the core human competencies most called for in the Turing test. These core cognitive competencies were hewn and shaped by natural selection over the several hundred thousand years of human existence C historically speaking, complex adaptations to a hunter/gatherer existence, or so the currently fashionable evolutionary psychologists assure us.

In a passage sometimes eliminated when the familiar 1950 paper is anthologized, Turing specifically suggests attempting to simulate Athe initial state of the mind, say at birth” and then giving “the Child Machine an education” (Turing 1950, p. 31). He points out that the experimenter would not be likely to happen on an appropriate Child Machine simulation immediately but would have to try out various possibilities and he compares this process with biological evolution through the following equations (anticipating rather similar formulations in Noam Chomsky@s radical reformation of linguistic theory (Chomsky 1957) and in subsequent work in modular, mentalist psychology):

Structure of the Child Machine = hereditary material

Changes of the Child Machine = mutations

Judgement of the experimenter = natural selection. (Turing 1950/1963, p. 32)

Turing pointed out that the experimenter can proceed rather more quickly than natural selection, making carefully planned and rapid changes. Similarly, Turing suggests that a “blank tablet at birth” animal will be wholly improbable, so he supposes that the successful “Child Machine” will have plenty of native structure (Turing 1948). I hasten to add, as his use of the locution “the initial state of the mind, say at birth” suggests, that Turing, anticipating Chomsky, does not mean just the genes (i.e. DNA) by “hereditary material” but rather the child’s full cognitive apparatus insofar as this is attributable to natural growth and development as opposed to peculiarities of the local environment. Although evolutionary biologists sometimes appear to suggest that DNA does all the work (even providing a “blue print” of the mature organism), DNA just provides templates that cell protein structures use to make more proteins and to join them in more complex configurations, soon to spin out multicellular structures that are the beginnings of organs that now as structured wholes direct differentiation into a couple hundred cell types placed into complex larger structures (the first and master developer is the nervous system, which directs the development of the fetus, starting a few days after the zygote is attached to the womb). “Say at birth” leaves Turing wiggle room, for he of course recognizes that the child at birth is not through with what Turing called the “morphogens” of development (Turing 1952). If anything, subsequent work has made it even more clear that lots of biologically directed growth, rather than general purpose learning, is needed.

Of course Turing loved his machines, both theoretical and practical, but it was the same love he much earlier formed for the tubular hydra, for the explosion of dappling in leopards, and for the unfolding of the growing leaf pattern (phyllotaxis) on many plants whose expanding distribution came out in the Fibonacci numbers (1, 1, 2, 3, 5, 8, 13, 21, etc.) – a love of nature’s machines to which he would specifically return in the embryological work of the last few years of his life, finally returning to the puzzle about daffodils that led him to science at age ten (Hodges 1989). What continues to be refreshing about Turing’s Turing test is that it endorses an experimental and constructive engineering task, a proper change indeed from twenty-five hundred years of introspective chatter and anecdotal observation. As La Mettrie, the first modern mechanist, remarked, insisting that the task is indeed empirical,

Man is a machine so complicated that it is impossible at first to form a clear idea of it, and consequently to describe it This is why all the investigations the greatest philosophers have made a priori, that is by wanting to take flight with the wings of the mind, have been in vain. Only a posteriori, by unraveling the soul as one pulls out the guts of the body, can one, I do not say discover with clarity what the nature of man is, but rather attain the highest degree of probability possible on the subject ( L’Homme Machine 1748/1994: p. 30).

Alan Turing has done more than anyone to give a clear mathematical, theoretical, and constructive foundation to a further rapsody of La Mettrie, whose erotic attitude toward natural and artificial machines knew no bounds,

Man is to apes and the most intelligent animals what Huygens’ planetary pendulum is to a watch of Julien le Roy. If more instruments, wheelwork, and springs are required to show the movements of the planets than to mark and repeat the hours, if Vaucanson needed more art to make his flute player than his duck, he would need even more to make a talker, which can no longer be regarded as impossible, particularly in the hands of a new Prometheus. To be a machine, to feel, think, know how to distinguish good from evil like blue from yellow, in a word, to be born with intelligence and a sure instinct for morality, and yet be only an animal, are things no more contradictory than to be an ape or a parrot and know how to find sexual pleasure.... Thought is so far from being incompatible with organized matter that it seems to me to be just another of its properties, such as electricity, the faculty of motion, impenetrability, extension, etc. (1748/19: p. 69-71)

There is evidence that Turing went as far in his enthusiasm for natural and artificial machines as La Mettrie, only the less effusive Turing was not inclined to publicly display his affection.

In La Mettrie’s Man a Machine, a cardinal example for La Mettrie’s mechanistic views is “Trembley’s polyp” (Chlorohydra viridissima), a tubular, tenticled, fresh water coelenterate (Trembley 1744). Diderot makes the same example central in his D’Alembert’s Dream for the same reasons. The polyp, which can be cut into scores of pieces, each growing into the mature form, demonstrates asexual reproduction and suggests that life is a natural property of matter, not passive stuff conjured into life by an active, Aristotelian form (or soul). Since Turing seems not to have been familiar with La Mettrie, it is remarkable that one of the five biological phenomena that Turing modeled is the development of the fresh water polyp, specifically the Hydra.

In “On Computable Numbers,” Turing tackles a fundamental and well known mathematical problem that is also a problem about doing mathematics, about computing as a kind of thinking. While what he came up with is highly original and widely fertile, it was immediately recognized as good mathematics. In his Turing test papers, Turing briskly sets a goal for cognitive science, elucidates a variety of ways to approach this goal, and helps design, build, and program the first generation of digital electronic computers. Prometheus like, he sees himself in a line from Charles Babbage and Mary Shelley back to the earliest materialists. But neither “On Computable Numbers” nor “Computing Machinery and Intelligence” explicitly acknowledge a precursor figure or movement. In “On the Chemical Basis of Morphogenesis” and in his related papers and notes, Turing explicitly presents his work as flowing out of D’Arcy Wentworth Thompson’s materialist and anti-adaptationist views and Thompson’s magisterial exposition of purely physical and chemical explanation in his On Growth and Form (Thompson 1917).

Broadly speaking, the Thompson/Turing biological tradition goes back to the early Greek naturalists such as Empedocles and Democritus, and their followers such as Lucretius, who rebuked intentional, functional, and teleological biological explanations (Thompson 1917). Growth and biological form, insofar as they can be scientifically characterized, arise through physical and structural necessity and chance, leaving talk of proper function, purpose, goal, and design aside. Thompson/Turing regard teleology, evolutionary phylogeny, natural selection, and history to be irrelevant distractions from fundamental biological explanation. As Turing puts his general project, his new ideas were sought to “defeat the argument from design” (Hodges 1983, p. 431). Turing is not referring to William Paley=s watchmaker argument for the existence of God, an argument long before displaced by Lamarck and Darwin. Darwin endorsed Aristotle=s biological work, writing that his “idols,” Covier and Linnaeus, seemed “mere school boys” compared to “old Aristotle.” Darwin cut his biological teeth in rapt fascination with Paley=s detailed teleology, whose designed-ness Darwin in no way wished to dispel from biological descriptions but sought to derive it, following a line of thought established by Aristotle, through mother nature=s rather than God=s selections (in Aristotle, the god of nature intends the design it constructs to reach the various goals it designs them for – and the intends and constructs for are efficient causality in Aristotle’s original sense). Indeed, as Darwin insists in his Autobiography, he intended Origin of Species to express the Deism he endorsed when he wrote it, not the atheism he eventually adopted. Life’s initial conditions were created by God, whose design unfolded from thence into mother nature’s tree of life, all in keeping with God’s intention (Darwin 1958).