63I Am a Strange Loop

Douglas R. Hofstadter, I Am a Strange Loop, Basic Books, 2007

Linked to 25 chapters: supports 17 · contradicts 11 · mechanism 3 · same claim 6 · pairing 5

Hofstadter wrote this book because he thought the first one had failed. Gödel, Escher, Bach appeared in 1979 and was admired, he says, for everything except the thing it had been written to say; in a preface for its twentieth anniversary he complained that he had shouted a cherished message into an empty chasm. In 2003 two philosophers, Ken Williford and Uriah Kriegel, quoted that complaint back at him and invited him to contribute to a volume on self-representational theories of consciousness. The chapter he wrote for them ran four times over the length limit and grew into this. The thesis fits in a sentence. What a person calls "I" is not an object lodged somewhere in the head but a pattern that the head has built, by perceiving, of itself; it feels solid for the same reason that a shape on a television screen stays put when the camera is pointed at the screen; and the formal precedent is Kurt Gödel's construction of 1931, in which a system built to forbid self-reference was shown to talk about itself anyway. The book is also, and not by the way, about his wife Carol, who died of a brain tumour in December 1993, not yet forty-three, leaving two children of five and two; and about what he thinks does and does not survive of her inside him. He warns at the outset that he thinks nothing in philosophy can be proved, only urged, and that his method will be metaphor.

Souls and their sizes

The book opens in a kitchen in early 1991, a few months after his father's death. His mother, looking at a photograph of her husband, says with despair that it means nothing, that it is a flat piece of paper with dark spots on it. Hofstadter answers with the analogy that sets the book going. The Chopin études in the living room are also marks on flat paper, and those marks have sent millions of hours of finger movement through other people's hands, carrying something of what it was like to be Chopin into brains that never met him. He calls the marks soul-shards, and says the photograph is one too: a thing that reactivates, in other people's heads, the patterns that were his father.

From there he asks which beings have souls at all, and answers by way of his own vegetarianism, told as a history of inconsistency rather than a principle. He eats tomatoes without a qualm. At fifteen, asked to fetch two guinea pigs from the cages of a Stanford physiology lab, he fainted and struck his head on the floor. At twenty-one he gave up meat; social pressure brought him back; by his late thirties he had settled on mammals as the line. A postscript reports that writing the chapter undid the settlement, and that he and his two children gave up fish and fowl within weeks of each other. He offers this as a first specimen of what the title names: a choice bounced back at its maker and absorbed into his picture of himself.

The generalisation is that souledness is not a switch. He takes the phrase from the critic James Huneker, who wrote of one of the Chopin études that small-souled men should not attempt it, and proposes, half in earnest, a unit called the huneker, with ordinary adults at around a hundred and a spread around that as wide as the spread in height or in measured intelligence. A zygote scores essentially zero and grows; the growth is the accumulation of a certain kind of pattern. He knows where this leads and says so: it is close to the claim that some lives are worth more than others, which troubles him, and he notes that societies already act on such a scale whenever they go to war.

The second chapter argues that the pattern in question is a legitimate object of brain research, not an ornament on top of one. Concepts, analogies, memories and the "I" itself are as real as neurons, he says, in the way that genes were real before anyone had located them. He is rough with John Searle, who ridiculed computational theories of mind by imagining brains made of beer cans, with a single can popping up to signify thirst: no modeller ever proposed putting a sensation in one component, and the beer can revives the discredited grandmother cell. The chapter takes its title from Russell Edson's phrase about the teetering bulb of dread and dream, and its question from the neurologist Roger Sperry: who shoves whom around in the population of causal forces that occupy the cranium. His own coinage sets up the answer. Thermodynamics is explained by statistical mechanics and can also be done entirely without it; so too, he proposes, thinkodynamics is explained by statistical mentalics and can be done without them.

The causal potency of patterns

Three metaphors carry the argument that a high-level pattern can be a cause. The first is a chain of dominoes, spring-loaded so that each stands back up after it falls, wired into loops that test a number for divisors. Feed it 641 by laying out that many dominoes in a reserved stretch, tip the first, and watch. A bystander points at a domino in the stretch reserved for divisors and asks why it never falls. One answer is that its predecessor never falls, which is true and passes the question along. The other is that 641 is prime, also true, and mentioning nothing physical whatever. The primality of a number, Hofstadter says, is the prime mover here.

The second metaphor returns throughout the book. Imagine a frictionless table covered in tiny magnetic marbles, which he names simms, careening about and sometimes sticking together into large, slow clusters, which he names simmballs. The walls flex when something touches them from outside, and the flexing works through the simms into the arrangement of the simmballs, so that the clusters come to record what has happened in the world. Watched in real time and close up, the story is complete: simms bounce, simmballs sit there like furniture. Now change two things about the watching — speed up the film until slow motions become visible, and pull back until the simms vanish — and the table shows something else entirely. The simmballs move, trigger each other, and follow a logic that has to do with what they stand for. Which description is true has no answer; both are complete and neither can be dispensed with.

He is careful about why the lower description cannot simply be preferred. Strict reductionism erases every natural boundary: particles respect no line drawn around a volcano or a brain, and the system under study grows until it is the whole universe over all of time. In November 1993, he points out, a comet still eight months from Jupiter was already causing missed aeroplanes and chipped cups on this planet, because people were reading about it.

The third metaphor is the one he carries to lectures. Years ago, gripping a hundred envelopes to lift them from a box, he felt a marble floating in the middle of the stack. He looked; nothing. He shook the envelopes out; each was empty. Squeezed together again, the marble was back, as hard and round as ever. What he was feeling was the triple thickness of paper and the smear of glue at the vertex of each flap, aligned across a hundred envelopes into a zone that would not compress. He named the box Epi and hands it round audiences so that they can feel a thing that is not there. An epiphenomenon, on his definition, is a large-scale illusion produced by the collusion of many small events that are not illusions at all, and the word "marble" describes what the hand feels better than any accurate account of paper and glue would.

Of selves and symbols

Between the metaphors and the mathematics he puts a chapter on video feedback, the book's working model of a loop. He spent an afternoon in the Stanford television studios in the mid-1970s making the photographs that went into Gödel, Escher, Bach, and three decades later a dozen hours doing it again with his editor Bill Frucht. A strip of chrome on the borrowed set made the nested screens countable, and there was a critical angle at which the corridor of screens stopped being truncated and appeared to run away forever. Blocking the lens with his hand and taking it away produced a pattern that throbbed about once a second and went on throbbing, because a live image of something changing must itself keep changing. He calls what happens locking-in: from the barest hint, after twenty or thirty trips round the loop, a stable structure appears whose only cause is that the loop keeps refreshing it. The vocabulary he had to invent for any of this — corridors, galaxies, starfish, cheese, foam — is his evidence that a loop can manufacture a level of description that was not there before.

Self-perception, he then argues, is almost an accident. Any creature that perceives its surroundings is part of its surroundings, so its apparatus points at itself sooner or later. What decides how much comes of this is not the loop but the stock of categories the loop can trigger. He distinguishes reception, the arrival of raw signal, from perception, the funnelling of signal down to a few discrete structures in the brain that stand for things; those structures are what he calls symbols. A mosquito, he guesses, has none, and can be described well enough as having a goodie, a port and a baddie, or perhaps not even those; its flight from a swatting hand may be no more perceptual than a knee jerking under a hammer. He puts its soul at one ten-billionth of a huneker, admits the number is flippant, and invites anyone who disagrees to slide up the scale until they reach the creature they mean — adding that people who say a mosquito might be as conscious as they are should be judged by whether they swat. A dog has dozens of categories and among them one for its own tail, which is the germ of the thing. A human has no ceiling, because concepts nest inside concepts without limit and because episodic memory holds particular dated events that can be reactivated and compared.

Only now does he define the title. A strange loop, on his formulation, is an abstract cycle in which each step feels like a move upward in a hierarchy and yet the steps close into a ring: "a strange loop is a paradoxical level-crossing feedback loop". Escher's Drawing Hands illustrates it and fails to be one, because the two hands are a drawing, and the paradox dissolves the moment one remembers this. Video feedback fails too, because there was no genuine hierarchy to violate. The one place a real one has been found is inside mathematics. He approaches it through the librarian G. G. Berry, who in 1904 defined the smallest integer whose English descriptions all run to at least thirty syllables, and described it in twenty-four. Russell publicised the paradox in 1906 and answered it by forbidding self-reference outright; Hofstadter thinks the diagnosis wrong, since what fails in Berry's number is the vagueness of English.

Gödel's quintessential strange loop

Principia Mathematica, which Whitehead and Russell published between 1910 and 1913, was built to make every valid mathematical argument a matter of shuffling symbols by rule, and was fortified by a theory of types under which nothing could refer to itself. Hofstadter lays out the hope it embodied, which he calls the Mathematician's Credo: a statement is true because there is a proof of it, and true statements therefore have proofs. Consistency would mean the system never produced a falsehood; completeness would mean it eventually produced every truth.

Gödel, struck by the way Fibonacci's numbers grow from two seeds by a rule, saw that the system's theorems grow the same way, from axioms by rules of inference. His first move was to give every string of the system a number. Assign each of the dozen basic symbols a small code; take the codes of a formula's symbols in order; raise the ascending primes to those codes and multiply. If "0" codes as 2 and "=" as 6, then the formula 0=0 becomes two squared times three to the sixth times five squared, which is 72900, and the unique prime factorisation of 72900 gives the formula back. Since there are infinitely many primes, any formula, and any proof, has a number.

His second move was to notice that the typographical rules could be matched, one for one, by arithmetical rules on those numbers. That gives two new classes of integer. The wff numbers are the codes of well-formed formulas; 576 and 2916 are not among them, because they decode to fragments that say nothing. The prim numbers are the codes of provable formulas, and 72900 is one, because 0=0 has a proof. A machine that told prime from composite would surprise nobody; one that told prim from not prim would, if the Credo held, settle every question in mathematics: write the conjecture in the system's notation, encode it, ask. The prim numbers would hold all mathematical knowledge in cipher.

The third move builds a formula whose plain arithmetical content is that a certain enormous integer is not prim, and which has been arranged so that the enormous integer is its own code number. Read as arithmetic, it is a claim about a number. Read through the code, it says that the formula with that number has no proof, which is to say: I am unprovable. Hofstadter pauses over how the number gets inside the formula, since the numeral is far longer than the formula that must contain it: an elephant and a matchbox. The answer is that a short recipe for a huge number goes in where the numeral cannot, which he explains through Quine's sentence that talks about itself by quoting a copy of its own subjectless half. The contrast is between the cartoon in which Sluggo dreams of himself dreaming, needing infinite depth, and the Morton Salt girl, whose arm covers the place where the regress would have to continue.

What follows is short. Suppose the system never proves a falsehood. If the formula were provable, then what it says would be false, and the system would have proved a falsehood. So it is not provable; and since that is exactly what it says, it is true. It is unprovable because it is true. Negation has nothing to do with the strangeness, he insists — Drawing Hands contains none, and both hands are drawing — and neither do words like "this". The strangeness comes from a system rich enough to mirror any pattern at all, and therefore its own workings. He calls the resulting relation downward causality: a formula's high-level meaning settles what happens at the level of proofs, and no bottom-up search will explain it. This, rather than any claim about the limits of machines, is the analogy he wants. A system of meaningless parts, read at the level of what those parts have come to stand for, can contain something that points at itself.

The elusive apple of my "I"

The brain, he now argues, is the second instance. We know ourselves the way we know other people, through categories like hope and belief and stubbornness, because those are the only categories evolution equipped us to perceive, and the summarising category we build for our own mental life is "I". It reaches backward through episodic memory and forward through what he names the episodic projectory, the anticipated future, and sideways through the episodic subjunctory, the replayed versions of what might have happened. It builds by a loop: an action is taken, the world bounces it back, the result is filed under a coarse label, and the label steers the next action. His own specimen is a boy announcing at show-and-tell that he can smile just like Hopalong Cassidy; his larger one is Karen Horney's idealised image, a partly invented self-portrait that nonetheless governs what a person does. The loop locks in, as an audio loop locks on to the resonance of a room.

A television pointed at itself is a feedback loop and not a strange one, because nothing in it perceives and so there is no level shift. The self-loop is strange because perception sits inside it. And the reason it feels absolute rather than approximate is a second fact, which is an incapacity: we have no access whatever to the neurons doing the work. Both are required. A system with symbols but no blindness could see through itself; a system with blindness but no symbols, like a mosquito, would have nothing to see.

The same test disposes of a contemporary enthusiasm. Stanley, the Stanford vehicle that drove itself across the desert in the 2005 Grand Challenge, was said by an executive at Intel to be thinking. Hofstadter calls the remark shameless and naïve hype: Stanley has categories of a sort, for road and mud and rock, but no memory of its own episodes, no anticipated future and no might-have-beens, so its loop is not strange enough. He is equally hard on the opposite dogma, and says that crossing that desert gives the lie to Searle's insistence that a computer can only ever simulate.

Then the book turns personal. One head, he argues, does not hold one loop. We represent other people, and what we hold of them is their loops at lower resolution. He builds the case out of ordinary experience: fear on a stationary cinema seat during a rollercoaster film; the mouth watering when his sister describes a falafel eaten a thousand miles away. He invents a world where nearly every birth is an identical pair treated, by others and by themselves, as one person with one pronoun, then points out that our own two hemispheres are already such a pair and that nobody counts them as two.

Carol's death occupies a chapter that is mostly the edited record of his own side of an email correspondence with Dan Dennett from the spring and summer of 1994. It records his exclamation, months afterwards, on looking at a photograph of her — that's me — and his attempt to say what he meant. Dennett, borrowing from Marvin Minsky, had told him that Carol would be thinking with his brain for some time to come, and Hofstadter takes the remark literally and carefully. His claim is that the pattern that was Carol is instantiated, at lower fidelity, in the brains of those who knew her; that his own copy was built over thousands of hours of talk and is the second-finest that exists; and that when his experience runs through it, it acquires her meaning. He refuses to claim more. No copy is perfect, he writes, his own are defective and incomplete, and death's sting cannot be denied. The image he settles on is the corona round an eclipse: a glow in other people, dimming across a generation or two. A postscript answers the charge that grief invented the doctrine, by reporting that he found notes on the same ideas in files written before she died.

A courteous crossing of words

Four chapters near the end put the position under attack, and two are dialogues, a form he had told himself he would not use again. The longer is a fencing match between Strange Loop #641, who holds the book's view, and Strange Loop #642, who does not. The doubter's objections are the ones a reader will have. If the self is an abstractly swirling pattern, what makes it different from a whirlpool. If it is an illusion, who is being fooled. Why am I in this brain and not another. The answers: a Gödel formula is not an ordinary formula though both are strings; the marble cannot be dispelled by turning the box over, because we cannot get at our own envelopes; and asking why one started out in a particular brain assumes the thing in dispute, since an "I" is not issued to a body but grown by one. The exchange produces the book's most quoted phrase, repeated a chapter later: the "I" is "a hallucination hallucinated by a hallucination".

The philosophy that follows is done at close quarters with people he knows. Derek Parfit's teletransporter is reproduced nearly whole: in the first version the traveller is scanned, destroyed and rebuilt on Mars, and the reader accepts without effort that the man on Mars is him; in the second the scanner leaves the original alive but dying, and the reader instantly decides that the man on Earth is the real one and the Martian a copy. Nothing in the two procedures differs except whether the original survives, so our confidence tracks spatial continuity rather than anything about persons. Hofstadter adds a third version, in which the traveller is sent to Venus and Mars at once, and sides cautiously with saying there are then two of him, since both will insist with equal sincerity and equal groundlessness that they are the one. He follows Parfit into a thought experiment taken from Bernard Williams, a surgery with numbered switches that convert Parfit's traits one at a time into Napoleon's, then runs the same switches on himself. And he quotes Parfit admitting that he cannot believe his own reductionist conclusions all the way down, and Thomas Nagel's claim, which Parfit cites, that nobody can.

The zombie chapter is a quarrel with David Chalmers, a friend and his own former doctoral student, who argues that a machine could think without there being anything it is like to be it. Hofstadter reconstructs the two identical machines in two identical universes, one of which contains an extra ingredient and one of which does not, names the ingredient élan mental, and answers with a parody. He invents a school of philosophy whose adherents hold that leaf piles, and only leaf piles, possess a nonphysical quality of Leafpilishness, and works through the questions this generates — how many leaves make a pile, what if an ant crawls in, can a pile be a zombie — to show what the same questions look like asked about dollops of consciousness. Consciousness, he says, is not an optional extra that could have been left off the order form, but the upper end of a continuous range that self-perceiving systems have automatically, as any sufficiently rich arithmetical system automatically has its Gödel sentence. The next chapter dispatches two more positions: the inverted spectrum, which he pushes until it must be applied to whole nations and to political sentiments before it will look as strange as he thinks it is, and free will, of which he keeps the part that says our wants cause our actions and discards the part that says the wants are free.

The last chapter returns to the scale the first proposed and says what its high end looks like. Magnanimity, he notices, is Latin for having a great soul, and Mahatma means the same thing. His example is Albert Schweitzer, born in Alsace in 1875, who founded the hospital at Lambaréné in 1913 and worked there for over fifty years, who told a child about to step on an ant that it was his personal ant, and whose principle of reverence for life he quotes from the Nobel address of 1953. The argument is that a generous person is not a diminished self but an enlarged one, housing more other people and therefore more conscious rather than less; the threshold at which he will use the word is the capacity to have a friend. He tells, without drawing a moral, the evening he spent listening to Schweitzer's Bach recordings, during which he carried a grasshopper outside on a record sleeve, then a carpenter ant, and then killed a mosquito without hesitation.

The epilogue refuses to tidy any of it. Either consciousness lies outside physical law, which he regards as belief in magic, or it does not, in which case the question of what could make a mere physical pattern be oneself — the Hard Problem, in Chalmers's phrase — is no nearer an answer than it was centuries ago. He concedes that the imagery of the first option still works on him, and offers as evidence against himself the end of Carol's memorial, where he played the last two and a half minutes of the first movement of Prokofiev's first violin concerto, a passage that might have been written to depict a soul rising, though neither of them had been religious and though what her soul was rising into was him. His answer is not a solution but a change of subject: self-reflecting patterns are the only magic a law-governed universe permits. He ends on the scale of what we cannot feel — six billion trillion haemoglobin molecules in a body, four hundred trillion destroyed and as many built every second — and on the claim that losing the solid self is worth what replaces it.

Since 2007

The book was widely and warmly reviewed and has not had the afterlife of its predecessor. The most careful early notice was friendly and unpersuaded: Martin Gardner, reviewing it in the Notices of the American Mathematical Society in August 2007 under the title "Do Loops Explain Consciousness?", used it to declare himself a mysterian, holding the question beyond us rather than answered by loops. The recurring technical objection is to the analogy itself. Gödel's construction closes because a formula's highest-level reading refers to the lowest-level machinery that generates it, whereas in Hofstadter's brain the high level refers to the high level, and critics have argued that the two twists are not the same twist. Torkel Franzén's survey of misuses of the theorem had appeared in 2005 and named most of the traps; Hofstadter avoids the famous one, since he is not arguing, as Lucas and Penrose did, that Gödel shows minds are not machines, but the reverse, that Gödel shows how machinery can come to point at itself. What remains contested is whether the parallel is an argument or an illustration, and a writer who says in his preface that nothing in philosophy can be proved is not well placed to insist on the first.

The book's interlocutors have gone on without changing their minds. Chalmers has continued to defend the hard problem and the conceivability of zombies, and the position parodied here as liphosophy is still the live opposition rather than a period curiosity. Parfit published On What Matters in 2011 and died in 2017; his reductionism about personal identity remains one of two standard positions, against an animalism which holds that a person is an organism and that the copy on Mars is therefore someone else. Nagel moved the opposite way, arguing in Mind and Cosmos in 2012 that materialism is probably false. Hofstadter wrote no sequel on the self; his next large book, Surfaces and Essences, with Emmanuel Sander, in 2013, turned the preface's aside into a thesis, that analogy is not a device of thought but its substance.

The empirical sciences of consciousness have grown up around the book without settling it, and the family of views it belongs to has become respectable: self-representational theories of the kind Kriegel and Williford were assembling in 2006 are now a named position. Predictive processing then supplied an account of the mechanism Hofstadter left as a metaphor — the brain as a builder of models it cannot recognise as models, the self among them — which is close to a locked-in loop and much more specific about how the locking happens. Integrated information theory shares his insistence that consciousness comes in degrees and a scale is worth having, though it measures integration rather than self-reference; its direct comparison with global workspace theory, reported from 2023 by the adversarial collaboration set up to decide between them, embarrassed both. No candidate theory has adopted the strange loop as its mechanism.

The claim about Carol is the part nothing has touched, because no evidence bears on it. Grief research has moved away from the idea that mourning ends in detachment, and toward the view that a continuing relationship with the dead is ordinary rather than pathological; but that is a finding about what mourners do, not about where a self is. Hofstadter had already conceded the point at issue, saying that his copies were defective and that death's sting could not be denied.

The passage that has aged least comfortably is the one on Stanley. The hype Hofstadter called shameless in 2005 has been surpassed many times over by claims made for systems that do have very large repertoires of triggerable structures, though not the episodic memory or the self-model his test demands. He has said where that leaves him. In 2023, after the arrival of large language models, he described himself as terrified, not that such systems would prove dangerous, but that intelligence and creativity might turn out to be cheap — that what he had spent his life treating as the deepest thing about human beings might come apart into a bag of tricks. It is the position the book left him in. If an "I" is a pattern with no special substance, what makes it rare is only that it is hard to build, and that is a claim the world can refute.