I Am a Strange Loop

by Douglas R. Hofstadter

one of my firmest conclusions is that we always think by seeking and drawing parallels to things we know from our past, and that we therefore communicate best when we exploit examples, analogies, and metaphors galore, when we avoid abstract generalities, when we use very down-to-earth, concrete, and simple language, and when we talk directly about our own experiences.

don’t think one can truly prove anything in philosophy; I think one can merely try to convince, and probably one will wind up convincing only those people who started out fairly close to the position one is advocating.

Saying that studying the brain is limited to the study of physical entities such as these would be like saying that literary criticism must focus on paper and bookbinding, ink and its chemistry, page sizes and margin widths, typefaces and paragraph lengths, and so forth. But what about the high abstractions that are the heart of literature — plot and character, style and point of view, irony and humor, allusion and metaphor, empathy and distance, and so on? Where did these crucial essences disappear in the list of topics for literary critics?

Man over the chimpanzee has ideas and ideals. In the brain model proposed here, the causal potency of an idea, or an ideal, becomes just as real as that of a molecule, a cell, or a nerve impulse. Ideas cause ideas and help evolve new ideas. They interact with each other and with other mental forces in the same brain, in neighboring brains, and, thanks to global communication, in far distant, foreign brains. And they also interact with the external surroundings to produce in toto a burst-wise advance in evolution that is far beyond anything to hit the evolutionary scene yet, including the emergence of the living cell.

Statistical mechanics can be bypassed by talking at the level of thermodynamics. Our existence as animals whose perception is limited to the world of everyday macroscopic objects forces us, quite obviously, to function without any reference to entities and processes at microscopic levels. No one really knew the slightest thing about atoms until only about a hundred years ago, and yet people got along perfectly well.

Statistical mentalics can be bypassed by talking at the level of thinkodynamics. What do I mean by these two terms, “thinkodynamics” and “statistical mentalics”? It is pretty straightforward. Thinkodynamics is analogous to thermodynamics; it involves large-scale structures and patterns in the brain, and makes no reference to microscopic events such as neural firings. Thinkodynamics is what psychologists study: how people make choices, commit errors, perceive patterns, experience novel remindings, and so on. By contrast, by “mentalics” I mean the small-scale phenomena that neurologists traditionally study: how neurotransmitters cross synapses, how cells are wired together, how cell assemblies reverberate in synchrony, and so forth. And by “statistical mentalics”, I mean the averaged-out, collective behavior of these very small entities — in other words, the behavior of a huge swarm as a whole, as opposed to a tiny buzz inside it.

We mortals are condemned not to speak at that level of no information loss. We necessarily simplify, and indeed, vastly so. But that sacrifice is also our glory. Drastic simplification is what allows us to reduce situations to their bare bones, to discover abstract essences, to put our fingers on what matters, to understand phenomena at amazingly high levels, to survive reliably in this world, and to formulate literature, art, music, and science.

Deep understanding of causality sometimes requires the understanding of very large patterns and their abstract relationships and interactions, not just the understanding of microscopic objects interacting in microscopic time intervals.

This idea — that the bottom level, though 100 percent responsible for what is happening, is nonetheless irrelevant to what happens — sounds almost paradoxical, and yet it is an everyday truism.

To put it another way, feedback gives rise to a new kind of abstract phenomenon that can be called “locking-in”. From just the barest hint (the very first image sent to the TV screen in the first tiny fraction of a second) comes, almost instantly (after perhaps twenty or thirty iterations), the full realization of all the implications of this hint — and this new higher-level structure, this emergent pattern on the screen, this epiphenomenon, is then “locked in”, thanks to the loop.

there are surprising new structures that looping gives rise to that constitute a new level of reality that could in principle be deduced from the basic loop and its detailed properties, but that in practice have a different kind of “life of their own”

there is a great deal of two-way flow. Signals don’t propagate solely from the outside inwards, towards symbols; expectations from past experiences simultaneously give rise to signals propagating outwards from certain symbols. There takes place a kind of negotiation between inward-bound and outward-bound signals, and the result is the locking-in of a pathway connecting raw input to symbolic interpretation. This mixture of directions of flow in the brain makes perception a truly complex process.

Concepts in the brains of humans acquired the property that they could get rolled together with other concepts into larger packets, and any such larger packet could then become a new concept in its own right. In other words, concepts could nest inside each other hierarchically, and such nesting could go on to arbitrary degrees.

For instance, the phenomenon of having offspring gave rise to concepts such as “mother”, “father”, and “child”. These concepts gave rise to the nested concept of “parent” — nested because forming it depends upon having three prior concepts: “mother”, “father”, and the abstract idea of “either/or”. (Do dogs have the concept “either/or”? Do mosquitoes?)

An epiphenomenon, as you probably recall from earlier chapters, is a collective and unitary-seeming outcome of many small, often invisible or unperceived, quite possibly utterly unsuspected, events. In other words, an epiphenomenon could be said to be a large-scale illusion created by the collusion of many small and indisputably non-illusory events.

The thesis of this book is that in a non-embryonic, non-infantile human brain, there is a special type of abstract structure or pattern that plays the same role as does that precise alignment of layers of paper and glue — an abstract pattern that gives rise to what feels like a self.

What I mean by “strange loop” is — here goes a first stab, anyway — not a physical circuit but an abstract loop in which, in the series of stages that constitute the cycling-around, there is a shift from one level of abstraction (or structure) to another, which feels like an upwards movement in a hierarchy, and yet somehow the successive “upward” shifts turn out to give rise to a closed cycle. That is, despite one’s sense of departing ever further from one’s origin, one winds up, to one’s shock, exactly where one had started out. In short, a strange loop is a paradoxical level-crossing feedback loop.

“algorithmic information theory”.

X is true because there is a proof of X; X is true and so there is a proof of X. Notice that this is a two-way street. The first half of the Credo asserts that proofs are guarantors of truth, and the second half asserts that where there is a regularity, there is a reason.

X is false because there is no proof of X; X is false and so there is no proof of X. In a word, just as provability and truth are the same thing for a mathematician, so are nonprovability and falsity. They are synonymous.

X is true because there is a proof of X; X is true and so there is a proof of X. The first line expresses the first hope expressed above — consistency. The second line expresses the second hope expressed above — completeness.

Gödel showed how any visual symbol-pattern whatsoever in the idiosyncratic notation of Principia Mathematica could be assigned a unique number, which could easily be decoded to give back the visual pattern (i.e., sequence of symbols) to which it corresponded. Conceiving of and polishing this precise two-way mapping, now universally called “Gödel numbering”, constituted the first key step of Gödel’s work.

once strings of symbols had been “arithmetized” (given numerical counterparts), then any kind of rule-based typographical shunting-around of strings on paper could be perfectly paralleled by some kind of purely arithmetical calculation involving their numerical proxies —

An elephant will not fit inside a matchbox! On the other hand, an elephant’s DNA will easily fit inside a matchbox… And indeed, just as DNA is a description of an elephant rather than the elephant itself, so there is a way of getting around the obstacle by using a description of the huge number rather than the huge number itself.

“preceded by itself in quote marks yields a full sentence” preceded by itself in quote marks yields a full sentence. I hope you are not lost at this point, for we really have hit the crux of the matter. Quine’s Quip turns out to be talking about a phrase that is identical to the Quip itself! It is claiming that something is a full sentence, and when you go about constructing that thing, it turns out to be Quine’s Quip itself.

Russell’s dependence on a systematic mapping to read meanings into his fortress of symbols is quite telling, because what the young Turk Gödel had discovered was simply a different systematic mapping (a much more complicated one, admittedly) by which one could read different meanings into the selfsame fortress. Ironically, then, Gödel’s discovery was very much in the Russellian spirit. By virtue of Gödel’s subtle new code, which systematically mapped strings of symbols onto numbers and vice versa (recall also that it mapped typographical shunting laws onto numerical calculations, and vice versa), many formulas could be read on a second level. The first level of meaning, obtained via the old standard mapping, was always about numbers, just as Russell claimed, but the second level of meaning, using Gödel’s newly revealed mapping (piggybacked on top of Russell’s first mapping), was about formulas, and since both levels of meaning depended on mappings, Gödel’s new level of meaning was no less real and no less valid than Russell’s original one — just somewhat harder to see.

We have repeatedly seen how analogies and mappings give rise to secondary meanings that ride on the backs of primary meanings. We have seen that even primary meanings depend on unspoken mappings, and so in the end, we have seen that all meaning is mapping-mediated, which is to say, all meaning comes from analogies. This is Gödel’s profound insight, exploited to the hilt in his 1931 paper, bringing the aspirations embodied in Principia Mathematica tumbling to the ground.

In this book, a loop’s strangeness comes purely from the way in which a system can seem to “engulf itself ” through an unexpected twisting-around, rudely violating what we had taken to be an inviolable hierarchical order.

Kurt Gödel was the first person to realize and exploit the fact that the positive integers, though they might superficially seem to be very austere and isolated, in fact constitute a profoundly rich representational medium. They can mimic or mirror any kind of pattern. Like any human language, where nouns and verbs (etc.) can engage in unlimitedly complex dancing, the natural numbers too, can engage in unlimitedly complex additive and multiplicative (etc.) dancing, and can thereby “talk”, via code or analogy, about events of any sort, numerical or non-numerical. This is what I meant when I wrote, in Chapter 9, that the seeds of PM’s destruction were already hinted at by the seemingly innocent fact that PM had enough power to talk about arbitrarily subtle properties of whole numbers.

one of the domains that mathematics can model is the doing of mathematics itself.

here is a statement of arithmetic (or number theory, to be slightly more precise) that we are sure is true, and yet we are equally sure it is unprovable — and to cap it off, these two contradictory-sounding facts are consequences of each other! In other words, KG is unprovable not only although it is true, but worse yet, because it is true.

…It [the idealized image] represents a kind of artistic creation in which opposites appear reconciled… The idealized image might be called a fictitious or illusory self, but that would be only a half truth and hence misleading. The wishful thinking operating in its creation is certainly striking, particularly since it occurs in persons who otherwise stand on a ground of firm reality. But this does not make it wholly fictitious. It is an imaginative creation interwoven with and determined by very realistic factors. It usually contains traces of the person’s genuine ideals. While the grandiose achievements are illusory, the potentialities underlying them are often real. More relevant, it is born of very real inner necessities, it fulfills very real functions, and it has a very real influence on its creator. The processes operating in its creation are determined by such definite laws that a knowledge of its specific features permits us to make accurate inferences as to the true character structure of the particular person.

And thus the current “I” — the most up-to-date set of recollections and aspirations and passions and confusions — by tampering with the vast, unpredictable world of objects and other people, has sparked some rapid feedback, which, once absorbed in the form of symbol activations, gives rise to an infinitesimally modified “I”; thus round and round it goes, moment after moment, day after day, year after year. In this fashion, via the loop of symbols sparking actions and repercussions triggering symbols, the abstract structure serving us as our innermost essence evolves slowly but surely, and in so doing it locks itself ever more rigidly into our mind.

In any strange loop that gives rise to human selfhood, by contrast, the level-shifting acts of perception, abstraction, and categorization are central, indispensable elements. It is the upward leap from raw stimuli to symbols that imbues the loop with “strangeness”.

If abbreviations could thus be piled on abbreviations in an unlimited fashion, then it is likely that instead of producing a book-length Sanskrit explanation of “soap digest rack”, you would need only a few pages, perhaps even less. Of course, in all this, you would have radically changed the Sanskrit language, carrying it forwards in time a few thousand years, but that is how languages always progress. And that is also the way the human mind works — by the compounding of old ideas into new structures that become new ideas that can themselves be used in compounds,

What makes a strange loop appear in a brain and not in a video feedback system, then, is an ability — the ability to think — which is, in effect, a one-syllable word standing for the possession of a sufficiently large repertoire of triggerable symbols. Just as the richness of whole numbers gave PM the power to represent phenomena of unlimited complexity and thus to twist back and engulf itself via Gödel’s construction, so our extensible repertoires of symbols give our brains the power to represent phenomena of unlimited complexity and thus to twist back and to engulf themselves via a strange loop.

Intellectually knowing that our brains are dense networks of neurons doesn’t make us familiar with our brains at that level, no more than knowing that French poems are made of letters of the roman alphabet makes us experts on French poetry. We are creatures that congenitally cannot focus on the micromachinery that makes our minds tick

Klagsbrun writes, “I believe that a therapist should be neutral and impartial toward the partners, the two patients in the marriage, but that there is no breach of ethics in being biased toward the third patient, the marriage.”

No one has trouble with the idea that “the same novel” can exist in two different languages, in two different cultures. But what is a novel? A novel is not a specific sequence of words, because if it were, it could only be written in one language, in one culture. No, a novel is a pattern — a particular collection of characters, events, moods, tones, jokes, allusions, and much more. And so a novel is an abstraction, and thus “the very same novel” can exist in different languages, different cultures, even cultures thriving hundreds of years apart. And so no one should have trouble with the idea that “the same hopes and dreams” can inhabit two different people’s brains, especially when those two people live together for years and have, as a couple, engendered new entities on which these hopes and dreams are all centered.

The name “Carol” denotes, for me, far more than just a body, which is now gone, but rather a very vast pattern, a style, a set of things including memories, hopes, dreams, beliefs, loves, reactions to music, sense of humor, self-doubt, generosity, compassion, and so on. Those things are to some extent sharable, objective, and multiply instantiatable, a bit like software on a diskette.

A person is a point of view — not only a physical point of view (looking out of certain eyes in a certain physical place in the universe), but more importantly a psyche’s point of view: a set of hair-trigger associations rooted in a huge bank of memories. The latter can be absorbed, more and more over time, by someone else. Thus it’s like acquiring a foreign language step by step.

There are shallower aspects of a person and there are deeper aspects, and the deeper aspects are what imbue the shallower ones with genuine meaning. I guess that sounds cryptic. What I mean is that if I believe statement X (for example, “Chopin is a great composer”) and someone else also believes X, then, despite this ostensible agreement between us, our internal feelings when we think X may be unutterably different even though, on the superficial verbal level, our belief is “the same”. On the other hand, if our souls have a deep resemblance, then our two beliefs in X will in fact be very similar, and we will intuitively resonate with each other. Communication (at least on that topic) will be nearly effortless.

we are capable of seeing the world through their eyes. Their psychic point of view is transportable and modular — not trapped inside just one perishable piece of hardware. If this is true, then Carol survives because her point of view survives — or rather, she survives to the extent that her point of view survives — in my brain and those of others. This is why it is so good to keep records, to write down memories, to have photos and videotapes, and to do so with maximal clarity

concepts are active symbols in a brain, and if furthermore you seriously believe that people, no less than objects, are represented by symbols in the brain

it is a necessary and unavoidable consequence of this set of beliefs that your brain is inhabited to varying extents by other I’s, other souls, the extent of each one depending on the degree to which you faithfully represent, and resonate with, the individual in question.

The cells inside a brain are not the bearers of its consciousness; the bearers of consciousness are patterns. The pattern of organization is what matters, not the substance.

Though the primary brain has been eclipsed, there is, in those who remain and who are gathered to remember and reactivate the spirit of the departed, a collective corona that still glows. This is what human love means. The word “love” cannot, thus, be separated from the word “I”; the more deeply rooted the symbol for someone inside you, the greater the love, the brighter the light that remains behind.

On the one hand, “I” is an expression denoting a set of very high abstractions: a life story, a set of tastes, a bundle of hopes and fears, some talents and lacunas, a certain degree of wittiness, some other degree of absent-mindedness, and on and on. And yet on the other hand, “I” is an expression denoting a physical object made of trillions of cells, each of which is doing its own thing without the slightest regard for the supposed “whole” of which it is but an infinitesimal part. Put another way, “I” refers at one and the same time to a highly tangible and palpable biological substrate and also to a highly intangible and abstract psychological pattern. When you say “I am hungry”, which one of these levels are you referring to?

In Parfit’s view, the Cartesian Ego of Napoleon is not indivisible, nor is that of Derek Parfit. Rather, it is as if there were a slider on a wire, and the two individuals (who are not really “individuals” in the etymological sense, since the word means “undividable”) can be merged or morphed arbitrarily by sliding that slider to any desired position on the wire. The result is a hybrid person, a tenth or a third or halfway or three-quarters of the way between the two ends — whatever proportions one wishes,

In order to regain some semblance of consistency, I have to return to SL #641’s theme in the dialogue, which is that the “I” notion is, fundamentally and in the end, a hallucination. Let’s let Episode III, my teleportation scenario with fresh copies on Venus and Mars and no copy left on Earth, apply to me instead of to Parfit. In that case, each of the new brains — the one on Mars and the one on Venus — is convinced that it is me. It feels just like it always felt to be me. The same old urge to say, “I am here and not there” zooms up in both brains as automatically as when someone taps my knee and my leg jerks upwards. But knee-jerk reflex or not, the truth of the matter is that there is no thing called “I” — no hard marble, no precious yolk protected by a Cartesian