Hofstadterismus

These two books are completely different in form and content, but one common thread is the concern of both writers to combine a logical discourse with a social critique. Dorothy Stein brings psychological and historical understanding to an important topic in the modern development of logical ideas, while Douglas Hofstadter tries to bring logic and mathematics to bear upon the human condition. Both writers also share a panoramic, polymathic, total vision of their tasks.

The second is the more familiar to us. Hofstadter attained great fame with his Gödel, Escher, Bach, which appeared in 1979. Gödel was the logician who in 1931 showed the extraordinary implications that follow from the ability of a logical system to refer to itself. Hofstadter found new ways to explain these ideas and to ask what, if anything, they could tell us about mind and its ability to think about itself. He went on to co-edit with the philosopher Daniel Dennett an annotated anthology of essays, The Mind’s I. Meanwhile, between 1981 and 1983, he wrote a sequence of some twenty-five columns for Scientific American, adopting the heading of Metamagical Themas – an anagram of the formula ‘Mathematical Games’ used by his predecessor Martin Gardner, but also referring to the ‘metamathematics’ rooted in Gödel’s discovery.

These columns are now collected together in this new book. But there is more to it than this, not only because of its new postscripts, but also because it embraces some seven further essays, including some of the most striking pieces in the book. Some of this will appear as familiar territory to readers of Hofstadter’s earlier books. In particular, there is much material revolving around the ideas of self-reference and its relationship to consciousness. Here, to give an example of hardcore Hofstadterismus, is a telling passage buried for the assiduous or serendipitous reader to spot in the bibliography:

Gebstedter, Egbert B. Thetamagical Memas: Seeking the Whence of Letter and Spirit. Perth: Acidic Books, 1985. A curious pot-pourri, bloated and muddled – yet remarkably similar to the present work. This is a collection of Gebstedter’s monthly rows in Literary Australian together with a few other articles, all with prescripts. Gebstedter is well-known for his love of twisty analogies, such as this one (unfortunately not found in his book): ‘Egbert Gebstedter is the Egbert Gebstedter of indirect self-reference.’

It must be explained that even the jokes, the groan-worthy crossword-clue puns, have a serious content, for they relate to the questions Hofstadter raises in the text about what it means to ask for ‘the opposite of’ or ‘the analogy of’ – and to how such questions bear on the nature of mental faculties. And it is typical of, and important to, Hofstadter’s style of communication that such questions should infiltrate themselves into the reader’s mind from oblique, quizzical angles, as well as from direct confrontation. Such obliqueness is itself a reflection of his picture of mind – a picture which constantly defies the restrictions on communication imposed by standard academic styles and textual forms.

It is not a picture which lends itself to economy or conciseness. Hofstadter is, of course, perfectly aware of this. Anyone attempting a criticism of his writing should note the appearance in this extract of Professor Gebstedter (of Pakistania University, Wiltington, Pakistania – work it out), Gebstedter being the alter ego through whom Hofstadter acknowledges these criticisms. ‘Bloated and muddled’, Hofstadter calls Gebstedter, and many readers may agree. The book is long. It is a pot-pourri. It is repetitive. The structure is haphazard. These are fair criticisms, but they are criticisms which miss one essential point of what is new and interesting in the Hofstadter phenomenon. This is a quality perhaps better described as moral than as intellectual.

Douglas Hofstadter wants to give a true picture of thought. The book must not be merely about thought: it must in itself be a true representation of thought. If thought is complex, paradoxical, humorous, sprawling, the book must be complex, paradoxical, humorous, sprawling. Every pun and allusion is relevant because it reflects a truth about how his mind works in writing and rewriting. Even in bibliography and index, the process of brain-dumping must go on. Such an approach is very different from the style of scientific papers – a style intended to present conclusions in a manner bearing no relation to the personal thought-processes by which they were actually arrived at.

Underlying Hofstadter’s work is a suggestion that this ‘proper’ way of conducting scientific discussion is in fact quite improper, because it disguises the truth about how thinking is actually done. Such a suggestion is particularly relevant to one focal point of Hofstadter’s concerns – the discussion of the prospects for Artificial Intelligence. The breadth and the freedom of his mental world makes much writing by the proponents of AI appear shallow, shabby and constricted by comparison. We are made to realise the highly restricted scope of the successes claimed for computer-based systems. On the other hand, the unity of Hofstadter’s thought, through its constant reference back to his own mental processes, allows him to avoid the equally shallow device of the opponents of AI, that of brandishing a Shakespeare sonnet or some other unique work and asking: ‘Could a machine have written that?’

There may be readers who find tiresome the self-referential egocentricity of Hofstadter’s writing. Perhaps there is a sort of arrogance in assuming that we can be gripped by every facet of the Hofstadter mind: but then Hofstadter is prepared to work extremely hard to win us over. I myself take a much more positive view of an exercise in intellectual integrity which demands a kind of courage not always found in academic writers. Self-exposure is brave. Actually, even the business of serious communication to a general audience is a job which requires courage for anyone in the academic world. It is by no means approved of, especially in this country. Not long ago I listened to a British university lecturer in mathematical logic who complained of the influence that Hofstadter had won with Gödel, Escher, Bach. Why, several students had applied to follow a combined course in computer science and philosophy, simply because of it!

That said, what do we actually find in this pot-pourri? Yes, a reworking of the logic of self-reference, as I have already indicated; yes, much discussion of Artificial Intelligence, in which Hofstadter takes a line which tackles both the objections of John Searle to the very proposition of machine-based intelligence and the claims of Herbert Simon that such an intelligence is already emerging. But there are many other topics, which take him well beyond the terrain of the earlier books. Some of these seem to me of less permanent value, or to fit in less well, than others. I am not sure that the properties of the Rubik cube, of the two-against-three rhythmic patterns in Chopin’s music, or of his own whirly doodles, can play the rather substantial role he expects of them. Another topic, the interpretation of quantum physics, is certainly both weighty and relevant, but it does not seem to elicit any really fresh ideas, and his essay (which rather uncritically purveys the Everett interpretation) sits oddly apart from the rest of his material.

What interested me most about the new book is the growing importance to Hofstadter of the relationship between individual minds and the social environment. The most mordant essay in the book concerns the hold that society exercises over the individual through its language. Hofstadter chooses to address the question of sexism in language, and to do so in terms of satire. He imagines that the English language evolved in such a way that pronouns and grammatical forms must respect the colour of the people referred to rather than their gender – not ‘he’ and ‘she’, but ‘whe’ and ‘ble’. He (or rather ‘whe’) then produces a resourceful defence of such language, written in such language with great verve and logical consistency – and with an insight into racist thought that has been enough to shock some liberal readers. This is a most powerful polemical exposure of ‘man-made language’. It is not clear, however, that Hofstadter has thought through the intellectual implications of saying that such supposedly commonsensical particles of speech as ‘he’ and ‘she’ are social constructs, as oppressive in their application as would be the racist usages he has imagined. If he is saying that ‘ordinary’ language in everyday use is the language of social hierarchy, what does he believe this tells us about the use by computers of ‘natural language’ – indeed of the very concept of ‘natural’ language? There is something important missing here, something that ought to be bridging the disjointed mental worlds inhabited by social criticism and by Artificial Intelligencers.

The relation between the individual and the collective also appears in Hofstadter’s introduction to a fascinating area of post-war mathematics – the study of crises, catastrophes and chaos in physical systems. It turns out that even when the elements of a system interact in the most rigid and simple way, the system as a whole can evolve infinite complexity. This is an insight which, developed mathematically, has quite transformed the classical picture of iron laws and inexorable unfoldings.

In one of his many postscripts, he refers warmly to one particular applied mathematician, S.M. Ulam, who developed these ideas. Hofstadter is too honest to pass over the fact that Ulam was deeply involved with the development of the American hydrogen bomb. ‘Stan Ulam was an ant in a vast ant colony, and though his role was more significant than that of most ants, he still had no control over the nature of the colony itself ... A good and generous person like Stan Ulam can still be part of a bad and frightful thing like the arms race.’ Hofstadter readers will know that ants and their colonies can be used to teach us about the relation of individual braincells to the collective action of the brain. Here, however, they appear as a metaphor for individual actions within the world of social and political forces over which individuals have ‘no control’. Or is it true that they have no control? The question arouses a key anxiety in the latter part of the book.

Ulam’s afterthoughts are expressed in his autobiography. ‘Once such possibilities exist, is it not better to examine whether or not they are real? An even greater conceit is to assume that if you yourself won’t work on it, it can’t be done at all.’ The argument that ‘if I didn’t do it, someone else would anyway’ is a case of ‘thinking it through rationally’, as Hofstadter says: but it is the kind of thing that many people might feel shows the limitations of rationality. It is perhaps a pity that Hofstadter’s rather over-protective tribute passes up the opportunity to expose and analyse these limitations. However, this is exactly what he does do for us in a later chapter.

This explores the mathematical theory of games and strategies, in order to analyse situations where the pursuit of immediate individual advantage dictates actions which are, or are not, in the end, to the collective disadvantage. One very concrete application of this analysis is to the problem of ‘altruism’ in evolutionary biology – the analysis also has a deep resonance in the domain of moral and political affairs. Always bursting out of the confines of the printed page, Douglas Hofstadter conducted a wonderful public experiment through the pages of Scientific American. He offered a cash prize of a million dollars divided by N, where N was to be the number of applications for the prize. Readers could put in as many applications as they liked. This sets up a model situation where, given the assumption that everyone else is going to be greedy, there seems no point in individual restraint. Yet it is obvious that general greed will result in a worthless prize. How should the individual behave? The story of the response to this and other such experiments reads like a thriller. Excitement comes, not only from Hofstadter’s acute psychological analysis, but from his unveiling of a strategy which achieves a balance between assertion and restraint, optimising the collective gain. Hofstadter calls it a ‘super-rational’ strategy, one requiring both rationality and a consciousness of everyone else’s rationality. Unfortunately, even though the theory had been explained to them, the readers of Scientific American failed dismally to apply it. The prize turned out to be incalculably worthless.

Hofstadter is no natural pessimist, but he admits that the prospects hardly look any brighter when it comes to the adoption of super-rational strategies by nuclear-armed powers – the subject which engages him most urgently. It is a topic on which Hofstadter writes as a common citizen, not from de haut – a standpoint which contrasts strongly with, for instance, that of Freeman Dyson’s Weapons and Hope. The approach leaves me moved, and yet unsatisfied. For Hofstadter is not a common citizen, but one with access to fortresses and showpieces of American technology such as MIT and Stanford – shrines of the can-do, must-win ideology. There is so much to be said on the psychology, internal politics and strategies of weapon-building – which powerfully affects Artificial Intelligence research, one may add. And there are very few who are as well qualified to say it as Hofstadter.

In his concluding essay he makes explicit his analogy between ‘collective phenomena’ in the brain and in society, and, using a thermodynamic metaphor, hopes for a ‘phase transition’ in American military policy – a shift analogous to that mysterious process of the individual brain called ‘taking a decision’. The word ‘revolution’ is gently smuggled into and then out of the argument. It is hard to tell whether he sees the oddity of addressing fundamental questions of sociology and politics as if no one had ever discussed them before. Even in this all-inclusive work there is no reference to any political or social theorist, unless we count Nixonides the Cretin, who said ‘this statement is inoperative.’ The references to Marx point only to a George Marx, for Rubik cubology, and a Groucho Marx, for comic analogy.

Perhaps I enjoy Hofstadter’s discussion of super-rational strategy for the wrong reasons. It flatters my mathematical senses with the sensation that mathematical analysis can yield non-obvious solutions to problems. But such a feeling comes as the exception rather than the rule in Metamagical Themas. This is no work of scientific triumphalism, claiming to possess rational or super-rational solutions to our problems. One of its most important features is that, without in any way demoting the role of rational thought, he conveys the vast and serious unknowns in modern scientific enquiry, of which the relationship of mind to brain is just one. But I have to say that the part of me which was brought up on the mathematical sciences is left unsatisfied by this feature, by such an ocean of open-ended analogies, suggestions, hints, ideas: perhaps wrongly, it craves something more definite.

In addressing the subject of Ada Augusta Lovelace, Dorothy Stein poses more directly a problem of intellectual disappointment. First, who was Ada? She put her name, or at least her initials, to the definitive Notes on the Analytical Engine designed by Charles Babbage, a plan which embodied essential ideas of the computer a hundred years before its time. She has been credited with more – in effect, with the writing of the first computer programme. And she was Byron’s daughter. These are romantic ingredients, the more so when combined with ruinous gambling and an early death from dreadful illness. Ada’s life, as it slices through aristocratic England from 1815 to 1852, cannot be said to disappoint in this respect.

But although Stein is a writer fascinated by the succession of extraordinary events, vigorously documented by means of letters written, as were Queen Victoria’s, with wonderful underlinings, her serious book can also be seen as the first scholarly examination of the claims that Ada originated a far-sighted view of the future potential of Babbage’s machine, and worked out a first programme for herself. I have myself blindly copied the assertion of others that she did just those things, and it is likely that many people have done this from a desire to turn the tables for once and ensure that a woman receives due credit for her intellectual achievements. It therefore comes as a disappointment to learn that the evidence does not justify these claims.

Dorothy Stein’s interest in her subject began with her training as a psychologist, but this biography is not a work of ‘psycho-history’. It begins, not with infant predilections, but with an analysis of the marriage mechanism for the transfer of money and power in the landed England of the late 18th century. Stein’s description of her participants’ motives, and her analysis of the family life of the Byrons and Lovelaces, has about as much sentimentality as Richard Dawkins’s description of the strategy of the cuckoo. She is also a clear writer on the abject role demanded of women, and particularly insistent on the realities of physical suffering, and of 19th-century medical practice. This combination of freedom from sentimentality with a seemingly encyclopedic knowledge of Early Victorian England lends strength to her analysis of Ada Lovelace’s intellectual development. Stein has read the letters that show that simple algebraic manipulations were beyond her competence. Babbage himself oversaw in great detail the ‘Notes’ that went out over the initials A.A.L.

Yet now the question of Ada seems to turn back on itself. If she was, in fact, so incompetent, how was it that she, of all people, took upon herself this Babbage-expanding role – something that a million would not have cared or dared to do? It seems from Stein’s evidence that Ada had a kind of reckless talent, an ability to grasp at possibilities of generalisation and abstraction which transcended the elementary ideas with which she struggled. It becomes evident that this could be a hit-and-miss effect: but when she hit, she scored some bull’s-eyes. One of the most striking passages in the Notes suggests the possibility that the Analytic Engine might undertake general algebraic manipulations – on the face of it, an extraordinarily advanced and prophetic insight. Stein indicates that Ada’s ideas on this subject were vague and muddled, and compares them with other nebulous and hyperbolic effusions in her writing – though it is striking that even leading mathematicians of the period were still quite vague about how algebraic expressions were to be understood. We could not claim, as some have done, that Ada actually foresaw the modern development of the computer programs which perform algebraic calculations. Still less that, because she used the words ‘a thinking machine’, she articulated the modern claim that, by embracing all possible symbolic manipulations, the computer can embody an artificial intelligence. But we might take a more Hofstadterish view of the scientific ant-colony, and allow for the role of half-formed analogies and images, celebrating the fact that some of the ants have the power to envision and articulate a novel image of great significance. If only the heap could organise itself so as to nurture such insights, and to sustain and amplify those that prove to be of worth! Dorothy Stein’s bleak book shows how wretchedly unfit were Victorian values – even at the prime time of British industrial expansion – to do anything of the kind.