Puzzle Theory

By Sarah Perry

Sarah Perry is a contributing editor of Ribbonfarm.

Let me set the mood by revealing that the starting point for this investigation was the movie Room 237, a “fan theory” documentary about people contemplating Stanley Kubrick’s movie The Shining. A fan theory is an interpretation of an item of art, usually fiction of some kind, that is surprising, bizarre, novel, or disturbing, and puts the item of art in a new perspective. TVTropes calls the phenomenon “fridge brilliance” (that is, theories that you fumble toward after the show is over, when you’re camped in front of the fridge swigging from the milk jug). Movies, television, and books are the usual stuff discussed in the mode of fan theory; the phenomenon also manifests in discussions of the meanings of song lyrics.

In Room 237, theories about The Shining range from the plausible to the bizarre. We are presented with evidence for a subtext of the holocaust, and for a related subtext of the genocide of the American Indians. Individual frames are scrutinized for references to minotaurs and labyrinths. The case is made that Kubrick cunningly alludes to faking the documentary footage of the Apollo moon landings (while the fan theorist explicitly says his theory has no bearing on whether the famed moon landings are factual and happened, he proposes that the iconic Apollo video footage is fake).

One has the sensation of creeping into a labyrinth of enormous size and complexity. The movie is pleasantly chilling, but also profoundly satisfying, hinting at promised gifts, unexplored creation, a frontier.

Not everyone likes Room 237. Negative treatment of the movie largely takes the form of appeal to authority, which I can’t help but find interesting. Stephen King has said he hates it, importantly finding the theories it presents implausible, and a Kubrick aide dislikes it for the same reason, terming the theories “balderdash” and offering evidence for why they are unacceptable. (Both use terms for Room 237 fan theorists that emphasize their low status.) Again, I think this is interesting: appeal to authority here reveals an implicit, furtive claim that the author’s intent determines the value of an interpretation, treating the film as first, foremost, and finally a creation of the author, the sole encoder. But I think there is something off about this perspective – it misses the point of why the movie is so great. It doesn’t matter if the fan theories are true, nor is it clear what that would even mean. What is important is that the interviewees treat The Shining, an emotionally involving, ambiguous work, as a puzzle box – and present “solutions” to the puzzle with particular properties that people find acceptable, intriguing, fun, touching, and satisfying – if not epistemologically, in a formal, rigorous sense, then at least aesthetically. Fan theorists see their function as decoding messages, and the encryption and the messages they reveal have more room to be interesting if they are not fettered by author intention.

Shortly after the second time I saw Room 237, I said (on twitter) that I would love to see a version of the movie made not about an important feature film, but rather about a random microwave oven manual from 1985. The folks who write microwave manuals are probably not affirmatively adding anything meaningful or fascinating into their work, but perhaps something can be found nonetheless. Since nobody appeared to be filming my dream creation, I decided to see what I could figure out myself. I could not easily find a fine vintage microwave oven manual from 1985, so I used as my subject matter for this task the first PDF of a microwave oven manual that I found to be easily accessible on the internet.

The first words on this manual are the model name, the Panasonic Inverter. It follows that this anagrams to “Scanner, invite a pro!” – effectively commanding that the puzzle be shared, passed off to experts. (Is its tone affable or ominous? I suppose it depends on the inscrutable sender’s nature.) The first words (after the table of contents and introduction), furiously set off from all others in a box with a grey background, offer certain “IMPORTANT SAFETY INSTRUCTIONS.” This fortuitously anagrams to “Transform tiny spots in Tau Ceti.” Here we have our first hint of who the coy sender of the communication might be.

A few pages into the manual is a table to assist with food preparation, listing the appropriate kinds of cookware for use in this microwave:


The types of cookware are listed next to a “yes” or “no” depending on whether they can safely function in a microwave. This fairly obviously indicates a binary code. There is only one entry that does not take the form of “yes” or “no” – a single question mark in the yes/no column, in the fifth row. This likely delineates a meaningful separation of some kind within the communication.

Transformed into binary, the first number before the question mark, 1101, is a number 13. This may indicate that the binary number that follows it should be converted carefully into base 13. The number (treating qualified affirmative answers as “yes” or 1, and “no” as 0) is 1100101001110110111101, or 1222029 in decimal notation, which is 339415 in base 13. Perhaps it’s not a very interesting number, but it does have a surprising property in light of the information previously brought to light: it corresponds to the file name of a very particular html file: a news story about a habitable planet in Tau Ceti (Archived version.) It has been well known for a few months, at the time of this writing, that aliens who think they are very funny are attempting to send us messages through the obscure but fairly effective medium of microwave ovens; why not also through PDFs of microwave oven manuals?


A Theory of Humor

The above stunt lies somewhere between joke and fan theory, a collection of coincidences designed to support a surprising interpretation of facts, treating an ordinary, non-ambiguous communication as though it were a puzzle containing a hidden message. It’s not exactly a joke, but it’s not exactly sincere. A more representative example of “coincidence joke” is the one about Santa Claus and Satan being the same person: they both wear red, they have the same letters in their name, and have you ever seen them together?

Notice that the Santa/Satan coincidence joke does not work if you rearrange the order of the coincidences so that the final coincidence is not last. This “punch line” works because there are, in fact, very good reasons why Santa and Satan don’t appear together: they occupy different mythologies, and they have dramatically opposed emotional valences (fun for kids versus personified evil).

This joke, and in fact every joke, gag, pun, humorous incident, and funny cat picture, can be understood under the theory of humor presented by Hurley, Dennett and Adams in their book Inside Jokes: Using Humor to Reverse-Engineer the Mind.

In Hurley et al.’s model, the emotion of mirth is a built-in reward, incentivizing the discovery of an error in committed belief. People are constantly activating concepts in mental space, concepts learned from previous experience and communication. Jokes and comedy are designed to take advantage of this reward system. The comedian leads the listener down a “garden path,” covertly introducing a committed belief that will later turn out to be faulty. Then the listener “tumbles” to the realization that the belief was faulty. The purpose of humor, Hurley et al. say, is to protect us from epistemic catastrophe – to prevent the storage of a faulty belief in long-term memory – and serving this very important debugging function is how the phenomenon of humor “pays for its extensive reward system.” From p. 121:

The picture that emerges [of humor] is a time-pressured, involuntary heuristic search for valid expectations, which generates mental spaces in which elements are constantly being tested. According to this model, then, basic humor occurs when

1. an active element in a mental space that has
2. covertly entered that space (for one reason or another), and is
3. taken to be true (i.e., epistemically committed) within that space, 4. is diagnosed to be false in that space – simply in the sense that it is the loser in an epistemic reconciliation process [ed.: “tumbling” to the correct interpretation]

5. and (trivially) the discovery is not accompanied by any (strong) negative emotional valence.

More simply put: Humor happens when an assumption is epistemically committed to in a mental space and then discovered to have been a mistake. These five conditions are the necessary and sufficient setup for the pleasurable experience of humor. Notice that these conditions are not the kinds of conditions that can be applied directly to a stimulus such as a joke. They are conditions regarding mental behaviors – behaviors that can sometimes, but not always, be well predicted by a joke or other stimulus. This model of humor, then, avoids the projection error categorically.

[Inside Jokes, p. 121; emphasis in original.]

To analyze a joke or anything funny, then, locate the covertly introduced, but mistaken, epistemic commitment – the “garden path” that someone has been led down.

In physical humor, someone demonstrates a strong belief that turns out to be faulty – that a chair is present (when it has been removed), or that a dance floor is free from toddlers (the latter video being one of Hurley et al.’s examples). “Epistemic caution is the foretaste of behavioral caution, and epistemic commitment engenders behavioral audacity,” say Hurley et al. (p. 110). We must commit in order to act effectively; but commitment is risky. Physical humor allows us to take pleasurable emotion from being reminded of the risks we face.

What makes cat pictures funny? Or animal pictures in general? One very common “covertly introduced mistaken commitment” in humor is anthropomorphism of some non-human entity, the perception of a mind with human-like goals and emotions where no such mind can be. Pictures of animals judged to be funny usually capture the animals engaged in some activity or making some expression that is impossible not to perceive as that of a human mind. The realization that is “tumbled to” (sometimes instantaneously) is that the inference or projection of a mind is mistaken.

This explains why merely drawing eyes on an inanimate is funny. This is a portrait I drew of St. Rev and a featureless black obelisk eyeing each other suspiciously:


It is very minimal, and what humor there is lies in the illusion created by the eyes, of mutual suspicion, when no such suspicion can of course exist in a featureless black obelisk. In my research I also applied this procedure to graphical depictions of the un-knot and the Hairy Ball Theorem:


Any joke about nonhuman subjects, Hurley et al. say, must necessarily anthropomorphize; the subjects must be “imaginatively endowed with human characteristics such as vanity or laziness and some capacity to perceive their circumstances.” (p. 156).

Humor is an important epistemic phenomenon, core to our mode of cognition, conserving cognitive resources while preventing epistemic catastrophe. The next section will examine another epistemic phenomenon: the spectrum from coincidence to evidence.

Mere Coincidence, Suspicious Coincidence, and Evidence

Coincidences are fun, engendering the emotion of wonder or the uncanny. They are “remarkable,” in the sense that they often feature in stories that humans deem important or interesting enough to relate. But “Coincidence” is often used as a pejorative, as an illustration of the human capacity for irrationality and error when it comes to probabilities.

In “From mere coincidences to meaningful discoveries,” Thomas Griffiths and Joshua Tenenbaum argue that while the perception of coincidence is often epistemic error, the same phenomenon underlies our ability to understand the world at all. Coincidences, they say, “are not just unlikely events, but rather events that are less likely under our currently favored theory of how the world works than under an alternative theory.” They are an invitation to possibly change beliefs – the perception of a pattern in causal space whose existence had not been suspected before. A “mere coincidence” provides very weak evidence or supports a theory that is very unlikely according to evidence other than the coincidence. A new theory will not be adopted based on a “mere coincidence.” A “suspicious coincidence,” however, provides somewhat stronger evidence, or supports a more plausible hypothesis. The old, pre-existing theory and the new theory are rendered about equally likely by a “suspicious coincidence.” And when a new theory is very plausible, or when the event supplies very strong evidence for it, it is not called a coincidence at all, but rather “evidence.” The continuum is illustrated in a beautiful graphical and mathematical compression:


Griffiths and Tenenbaum go on to provide evidence that people are actually pretty good Bayesians when working on problems close to their experience. The brain naturally performs unconscious math, not with symbols but with a complicated array of emotions, neurotransmitters, and who knows what else. Hurley et al. say:

There are intrinsic statistics to our knowledge. When something is unlikely, we don’t calculate the statistics – we simply know (or, rather, feel) that it is unlikely. The statistics have been precalculated for us, in our experience with the world such that our knowledge reflects the likelihood of events, and when these likelihoods are contradicted we are surprised.

[Inside Jokes, p. 242.]

Surprise is an essential feature of coincidence. Surprising phenomena are the most fertile grounds for adapting our models of the universe; surprise is even “believed to be a trigger for associative learning.” An entity that cannot be surprised cannot learn, because its model of the universe is already so perfect that it cannot be improved.

Surprise also often triggers the suspicion that someone is playing a joke on us (Hurley et al., p. 243). Positing a mind, with intention, behind suspicious happenings is sometimes an unavoidable inference, even if it is seen to be ridiculous immediately after being perceived. Hurley et al. note that for children, the world really is run by an inscrutable conspiracy of powerful beings: adults. The error of attributing intention where none exists is often incorrect, but it’s so often and importantly correct that our cognitive architecture has deemed it worth the risk to get false positives. And some of the potential false positives, in the form of gods and spirits, may have value orthogonal to their actual existence, providing a locus of coordination, among other benefits.

A good coincidence is eerie, arousing wonder and a sense of the uncanny, because it points to a missing causation where none was suspected to be. Often the missing causation can be filled in by an entity with agency, as described in the previous paragraph – a ghost, fairy, or god meddling in worldly affairs. But just as often the missing causation is left empty, not explicitly accounted for. “Dark Side of the Rainbow” is made of many surprising coincidences, but you can appreciate them with wonder without proposing any particular reason for their existence. Similarly, older versions of the Book of Mark in the New Testament end abruptly at the discovery of Jesus’ empty tomb; the ambiguity is not explicitly resolved, and the uncanny, unlikely coincidence is left unexplained. The book ends merely by noting that the witnesses were afraid. The later-added ending of Mark can be regarded as a fan theory resolving the ambiguity of the original, resulting in a text that is less ambiguous and, I think, less wondrous.

Ambiguity and Incongruity

Now we have some idea of the roles of humor and coincidence in cognition, so we can turn to fan theories. Fan theories are produced by approaching items of culture as if they were puzzles, secret communications to be decoded and solved. Fan theories, silly as they may seem, provide the basis for a model of cognition present in all “serious” human epistemology, from law to science. Solving puzzles from ambiguous subject matter represents an evolutionarily important mode of interacting with reality – especially social reality. This puzzle orientation is consistent with my social model of human consciousness presented in “The Essence of Peopling” – the main puzzle we are always solving is, what do other people have in their minds?

Fan theories are successful to the extent that they can find work – just like cognitive concepts. By work, I mean the ways in which a theory interacts with reality, operating on the world and reproducing itself. The germ theory of disease finds work in hand washing and the manufacture of antibiotics. Fan theories about movies find work on internet discussion groups and at the kind of parties where people talk to each other (and, of course, in Room 237). Theories that correspond tightly to reality are often very useful, and find a great deal of work; however, theories that do not have much physical-world relevance are often very competitive if they manage to do social work. Some theories may compete by offering hedonic rewards, which can add to their social transmissibility – that is, they are fun, satisfying, exciting, touching, awe-inspiring, or pleasantly horrifying. Theories that optimize for social transmissibility and reward packages may have to sacrifice other qualities, such as strict correlation to reality, but despite this limitation, they can become very powerful and do a great deal of work in the world.

One of the most important features of the source material upon which “fan theories” may be created – what makes them plausibly puzzles – is that they are ambiguous. Visual information, in rich supply in movies such as The Shining, is inherently ambiguous. Language is ambiguous too; words may have multiple denotative meanings, or may be anagrams or numbers (as with my microwave aliens). The sound of words is another source of ambiguity, the ambiguity underlying the humor of puns. The sound of words may be experienced backwards for even more ambiguity, a feature explored in the “backwards Satanic messages” craze of the 1970s and 1980s. (The existence of these backwards messages as well as their purported content constitute an important 20th century fan theory.)

The role of ambiguity is preventing any one hypothesis from being so plausible that it crowds out other possible hypotheses, consigning all possible “evidence” to “mere coincidence” territory in the coincidence model above. Fan theories are distinct from humor in that the emotion triggered is not mirth, but something like wonder, insight, or a sense of the uncanny. And with fan theories, there is no obviously correct interpretation to “tumble to.” In humor, hidden ambiguity or conflict is exploited for laughs by revealing a faulty assumption; in fan theory, ambiguity is exploited to produce insight or wonder by building a case for a surprising hypothesis, rather than suddenly “tumbling to” an error. Humor is destructive; fan theory is constructive. Fan theories grow best on subject matter that does not have a single, obvious interpretation or explanation. Displacing an apparently obvious, well-accepted explanation is a coup for a fan theory, but it is rare, and to do so it will need to make a case for the existence of ambiguity in the subject matter.

Another important feature is incongruity or contradiction. In Room 237, much is made of the fact that much of the architecture presented is impossible – an impossible window that shines bright outdoor light but is clearly in the middle of a building with hallways behind it, for instance. Here is how ambiguity is used, from the perspective of the maker of meaning:


Ambiguity is what allows for multiple interpretations; contradiction is what calls out for an explanation or even introduces ambiguity where none appeared to be before.

Ambiguity and contradiction are important principles in the practice of law. There is no such thing as “the law” as a static object; rather, law is a social process of encoding and decoding, statement and interpretation. No legislation or case law is purely unambiguous (it’s made of language, after all), and ambiguity is even intentionally included in legislation. Any specific version of legislation may not be able to find the necessary coalition to pass it; but an ambiguous version may be acceptable to enough participants to pass. Ambiguity is central to contract law; the interpretation of words is the essence of the practice. Most contracts have an “integration clause” that states that the written contract expresses the entire agreement of the parties, and that no party may later introduce evidence of oral agreements or understandings outside the “four corners” of the document. But what if the document is ambiguous? If ambiguity is demonstrated (for instance, the meaning of a word), then outside evidence is suddenly admissible to resolve the ambiguity. Writing contracts is therefore a puzzle of removing ambiguity; interpreting contracts can be a puzzle of locating hidden ambiguity.

Ambiguity means more work for lawyers as puzzle solvers (and lawyers are generally the ones writing the rules). A “bright line” rule (one with clear application) may not get the fairest result in each case, but it provides the benefit of making it clear to parties and potential parties just what the result of litigation would be. In contrast, “factor tests” (lists of factors for judges to consider in deciding the outcome of a case) may give fairer results on a case-by-case basis, but they also invite litigation by not providing a clear indication of the result. The inclusion of ambiguity distributes the expected value of future litigation more evenly between potential parties by making its eventual result hard to predict. (Note the similarities between this observation and a conspiracy theory.)

Contradiction is extremely important in the practice of law. For example, a jury’s verdict is somewhat sacred, in that a judge cannot usually overturn a jury verdict. An important exception is when a jury’s verdict is found to contain a contradiction – for instance, finding that a party was not negligent (responsible) but still awarding damages against that party. In contract law, an apparent contradiction can demonstrate that ambiguity exists.

More people are probably familiar with criminal law than contract law, as it is “sexier” and earns more popular portrayals. Both prosecutions and defenses take the form of fan theories, in the sense that they seek to unite inherently ambiguous facts, evidence, and law according to some central theory. In jury trials, these presentations must be geared to the cognitive limitations of jurors, and so cannot be more cognitively demanding than a television show. But even in appellate cases, where only judges are evaluating the theories, the cognitive demands the theories make are limited to the capacity of humans to understand them. Appellate rulings are frequently split; not even all the judges on an appellate panel (importantly composed of an odd number of judges, perhaps three or nine) frequently agree as to which side’s fan theory is “the law.” Reality is interpreted as a puzzle; lawyers on each side form theories of solutions to the puzzle; then juries and judges decide which theory is more convincing, according to specific rules of the game (including the rules of evidence as well as “canons of construction” – rules for interpreting language).

Language is inherently ambiguous. And we know how ambiguity gets resolved: through ritual. The most extreme rituals of law are the trial and the appellate decision; these are guaranteed to give some result, like the toss of a coin. (This is why it’s important that appellate panels generally have an odd number of judges. Many sporting contests, like fencing bouts, have procedures to avoid a tie; these rituals are also guaranteed to give some definite result, and that is the point of them.) And so the domain of law continues, despite the failure of what Seligman and Weller call “notational” understanding; there is ritual at the bottom, to resolve things. The less extreme ritual, accounting for the resolution of the vast majority of cases, civil and criminal, is the settlement or plea agreement. The costs and uncertainty of the extreme ritual incentivize its avoidance as much as possible.

Both scientific theories and theological interpretations may be regarded as fan theories of reality itself. Both identify and interpret information according to a few underlying principles. They function as compression of existing data, organizing previously unconnected information into a cognitively thrifty, and perhaps valuable, form. They resolve apparent ambiguity or contradiction in reality, they connect many observations together, and they often include multiple layers of support for themselves – for instance, answer to “why” questions (causal interpretations) or “how” questions (explanations of mechanism). They must defend themselves against counterarguments to remain plausible. Their defenses must be hermeneutic, responding to small-scale and large-scale concerns, in example and in theory. And rituals are often a crucial part of their plausibility structure.

A Four-Part Compression of Ambiguous Information

I have suggested four characteristics which are common to satisfying epistemic explanations, regardless of the status of the claim: ambiguity and contradiction in the subject matter; many instances of contact with the subject matter, multi-level explanations and defenses; and compression of observed facts into one (or at most a few) unifying lens. Here is a graphic representation to make it, perhaps, cognitively cheaper to hold in mind:


We have already seen some of the ways in which ambiguity and contradiction create the possibility for a meaningful “solution.” I think this is why the songs of the Beatles and Bob Dylan (for example) are frequently interrogated and discussed for their “meanings.” They are appealingly ambiguous, rich with incongruous information. The relatively unambiguous songs of, say, Kitty Wells (country songs with only one possible meaning, usually romantic suffering and loss) are not the subject of community interpretation precisely because the interpretation is so clearly communicated by the words. Lateral thinking puzzles often present an apparent contradiction or impossibility in the puzzle prompt, which is resolved by the solution.

There is likely a sweet spot of ambiguity: music in a nonsense language would be maximally ambiguous, but outright gibberish does not seem to attract interpretive attention. The suggestion of hidden meaning to be found must be present. Even gibberish, because it is presented as potentially language by the very fact that it is spoken or written in speech or writing forms, contains a hint that it might be meaningful (as with the Voynich manuscript). However, most discussion of the “meaning” of songs and other items is not performed on apparent nonsense, but on words with clear denotative meanings, even if the overall denotative meaning is not clear.

The resolution of ambiguity and contradiction underlies the religious fan theory (sometimes described as heresy) known as Preterism. Preterism is the belief that biblical events usually interpreted to be in the future, such as the return of Christ, have already happened. An important source of the ambiguity underlying Preterism is Matthew 24:34, in which Jesus says “Verily I say unto you, This generation shall not pass, till all these things be fulfilled” (King James Version). This is a problem, as it appears that Jesus has made a false prediction: the events Jesus describes (such as his return) are seen as being in the future, but he says they will happen within one generation. Preterism resolves the contradiction by positing that Jesus was correct, but that the events actually did occur – in the past. Most Christians resolve the apparent contradiction by locating ambiguity in the meaning of Jesus’ prediction, suggesting that it does not describe all the events mentioned, or questioning whether a proper translation of the words has been achieved. Internet atheists like to point out the contradiction in service of the theory that the prediction was wrong. And Philip K. Dick interpreted the contradiction by positing that the two time periods – 70 A.D. and the 1970s – are in fact overlapping and both present at the same time. Here we have at least four fan theories for a single apparent contradiction.

This last paragraph has been an example – a point of contact with reality for my theory. These are the second feature of a good theory, fan or otherwise, and of a good solution to a puzzle. Points of contact with reality may take many forms. They may be literary examples from extinct languages and neurological observations, as in Julian Jaynes’ excellent book-length fan theory The Origin of Consciousness in the Breakdown of the Bicameral Mind. They may be the behaviors of subjects observed in a laboratory under particular conditions, as in the social sciences. They may be planet positions, historical events, economic data, or snippets of conversation. The most useful theories unite the most diverse and numerous contacts with reality. But non-useful theories share this property as well. Schegloff’s theory of confirming allusions is persuasive in part because of all of his examples. The same goes for Hurley, Dennett and Adams’ theory of humor- and, more dubiously, for Sigmund Freud’s theory of dream interpretation. (Your average published scientific study with a small sample size and tortured statistics just barely reaching a p-value of 0.05 is on similar epistemic ground with my microwave aliens theory.) But regardless of their epistemic value, fan theories, appreciated for their aesthetic and emotional value rather than their usefulness, are generally appreciated more when they explain many data points.

The third feature is that the theory anticipates many levels of interrogation. In Room 237, an example of this is interviewees emphasizing the personal care Kubrick took in arranging objects on the set, indicating that he intentionally added barely perceptible information to his films, inviting “solution.” This claim is popped out a level from of the particular theories themselves: it is a claim for the plausibility of any such theory.

If I were to take my microwave oven aliens very seriously, I might begin by asking why, if aliens are communicating with us, they choose to do so ambiguously and through such strange mechanisms. I might suggest in reply that we know very little about our supposed interlocutors; they may have any number of reasons and limitations that we cannot be aware of – an argument from ignorance. (Kilgore Trout, a fictional Vonnegut character who writes science fiction stories, posits benevolent aliens that can only communicate by tap dancing and farting.) This would be an attempt to connect the fortuitous evidence in a wider causal structure, with more layers of explanation. It is also anticipating an objection and positing a defense, as in law, science, or theology.

Finally, good theories are compressions of information, representations that use limited cognitive resources efficiently, elegantly summarizing what is important about disparate pieces of evidence that were hard to harmonize or organize before. A good compression generates a moment of “aha!” whether discovered at second hand or figured out for oneself. (This pleasurable sensation is related to (though distinct from) the sensation of mirth when one “gets” a joke.) A good theory explains a large number of observations or phenomena with only one explanatory concept or axis (“Maverick and Iceman are gay”), or at the very most a few concepts that link together (evolution by natural and sexual selection).

Note the tension between the second and fourth aspects – number of contacts with reality and tight compression. The explanatory power of a very tight compression is best demonstrated with a giant pile of disparate examples; William James calls this the “apperceiving mass.” But the union of the theory and all the examples it explains is not a small piece of information. Inside Jokes, “From mere coincidences to meaningful discoveries,” and the paper described in the next section are all elegant compressions with many examples – attached to reality at many points. Much is lost in my summaries, and this is likely true for any theory. The elegant solution may be preserved in a summary, but the magnitude of its elegance can only be perceived after comparing it to a large number of examples.

Language as Puzzle

Why do humans do puzzles? Why do we insist that puzzles exist in unlikely documents, like movies and religious texts and microwave oven manuals?

An answer is hinted at in a 1996 paper by the sociologist Emmanuel Schegloff, entitled “Confirming Allusions: Toward an Empirical Account of Action.” Schegloff presents a phenomenon (which he emphasizes is just a tiny phenomenon) within the field of conversation analysis – recording actual conversations between people and paying careful attention to their actual words, rather than imagining what conversations are supposed to be like or might plausibly be like. The phenomenon Schegloff analyzes is the repetition of the exact words of one speaker, immediately, by another speaker. He demonstrates that this phenomenon is usually employed to confirm an allusion – to say “yes, you are correct, that is what I was implying in my earlier statement.” In other words, people are constantly presented with puzzles in language – implications and hidden meanings that are not stated explicitly. And we are always trying to “solve” these hidden meanings. When we do so correctly, an interlocutor will often respond not by simply agreeing, but by repeating our exact words.

I am hesitant to assign 60-page papers to my readers, but Schlegoff’s examples hold a great deal of value and make the phenomenon crystal clear. For instance, here is a typical exchange demonstrating the phenomenon, one of a couple dozen presented in the text (I quote them in image form because of the difficulty of transcribing the exchange):


In the above example, “making money” is the repeated phrase, the solution to the allusive “puzzle” presented by the euphemistic “practical reasons.” In another case, in a newsroom, an editor (the city editor, “CE”) presents a potential story to the staff:


Here Schegloff is explicit about the puzzle nature of language as presented. He notes:

The story is recounted in a manner that requires its hearers to “solve it” for its interest as (presumably) a “human interest story.” In particular, the final components of the telling are left for “working up” by its recipients, and the telling is directly followed by such interpretive upshots. First the final component of the story has its implied contrast made explicit; “hated the cat until this morning” (line 30) being contrasted with “loves the cat now” (line 32), while leaving the basis for this turnaround still unexplicated. Then the penultimate component of the telling, which had been delivered as a stripped-down direct quotation of the mother’s utterance upon opening the door and seeing the child outside (“What the heck are you doing out here?” lines 28-29), has its import formulated by a recipient for confirmation by the teller (“She didn’t realize her son was missing”). The teller both confirms the understanding that it makes explicit and confirms that the telling had been designed to convey it without saying it in so many words – perhaps achieving thereby a demonstration of its potential solvability by readers as well and, accordingly, its worthy candidacy as a publishable human interest story.

[Schegloff at p. 206; bolded emphasis mine.]

I would be interested to know if this phenomenon of confirming allusions (affirming that a correct summary of previously implied information has been made) by repeating the exact words of the speaker is invariant across languages. If there are languages that do not have the feature, I would be interested to know whether they have other linguistic features that regularly accomplish the same function. (Notice that these ways of exploring the phenomenon of confirming allusions (in this case, positing a falsification, and noting a case in which a falsification would not really be a falsification) are also ways of defending the theory against falsification, thereby protecting it. Defenses anticipate the path of ordinary cognitive investigation, blocking objections at each potentially disconfirming junction. The existence of defenses need not be evidence that the defended theory is suspicious or false; it is just evidence that the ordinary paths of epistemic investigation have been followed. I ask the reader to disregard this parenthetical if it feels dizzyingly meta-.)

Schegloff quotes Harvey Sacks, who defines culture as “an apparatus for generating recognizable actions.” The main problem that humans have to solve is communication: creating and decoding puzzles in the form of language.

Recall my revised Maslow’s hierarchy: social belonging is key to all material needs in our environments of evolutionary adaptedness, the crucial key to access to culture, the stuff of which gives us our devastating advantage over nature.


Humans are not that rational and not that smart, but they are brilliant at creating and interpreting social information. Social information is as much our food as food; we need it, desire it, seek it out if we don’t find enough of it. I have long suspected that interest in things like strong AI and the search for intelligent extraterrestrial life stem from our inherent loneliness and desire for connection. Philip K. Dick, in an “afterthought” to a volume of short stories in 1977, says

The basic premise dominating my stories is that if I ever met an extraterrestrial intelligence (more commonly called a “creature from outer space”) I would find I had more to say to it than to my next-door neighbor…. The way out of living in the middle of an under-imaginative figment is to make contact, in your own mind, with other civilizations as yet unborn. You’re doing the same thing when your read sf that I’m doing when I write it; your neighbor probably is as alien a life form to you as mine is to me.

Communication is a form of social belonging; the fewer people that read the message, the more intimate the communication, and the more meaningful it is experienced as being. Being the first to solve a difficult puzzle is meaningful; but solving a secret, hidden puzzle that no one else even suspected was there may be even more meaningful. It is as intimate as a communication whispered into a particular person’s ear.

Our relationship with evidence is very personal and social. When using the relatively new mode of scientific thinking, we personify evidence: it “suggests” and “implies” various theories, and we are invited to “listen to” what the data “say.” It is as if we must posit a communicator in order to think about information. Another aspect of personification manifests in the Myth of the Great Man in science. When information is judged particularly important in our society, the creator or discoverer of the information is often accorded special personal status. He is presumed to have consistent, almost infallible epistemic superpowers.


Many puzzles go unsolved. Even when the author of a puzzle puts the equivalent of a big sign that says

There totally is

few notice the hint enough to bother to solve the puzzle. Vladimir Nabokov’s short story “The Vane Sisters” contains a hidden puzzle, and the mechanism is even explained in the text (the final paragraph contains an acrostic, the first letter of each word spelling out the creepy and very satisfying key to the story). But it was rejected by the New Yorker, and Nabokov had to explain the puzzle to the fiction editor in order to get it published. I have to admit that I would not have noticed the puzzle if I had not been pointed to its existence.

The reason for this is that, as demonstrated above in the microwave oven manual example, there are potential puzzles everywhere, more than could be solved in a million human lifetimes, mostly of dubious significance, and it’s difficult to know where to apply cognitive resources toward solving them. And most proposed “solutions” will be nonsense. One phenomenon that both alerts people to the existence of a puzzle and suggests that a particular solution is correct is what are called confirmers. In a 1987 essay on hidden meanings in The Shining, published in the San Francisco Chronicle, Bill Blakemore defines “confirmers” as clues puzzle makers often use “to tell you you’re on the right track.”

Of course, humans are subject to what is called “confirmation bias” – we tend to choose a theory and then find confirmers for it everywhere, ignoring discrepant evidence and evidence for alternate theories. I would like to present one beautiful example of this. In the early 2000s, the magician David Blaine published a book that contained a puzzle encoding the location of a treasure, exchangeable for a hefty cash prize. The puzzle was extremely complex, involving multiple layers of encoding. (He also gave a separate clue in an interview on a television show.) One would-be solver attempted a solution on some of the decoded clues. Here is the first part of his solution:

First Part: IF MY TATTOO.

Rearrange the spacing to form IFMY TAT TOO. ‘Tat’ is a verb that means to ‘interweave’. It’s a wordplay command that means to combine letters.

‘Also’ is a definition of ‘too’.


It creates an internal riddle. Who is the ‘Os family’?

Answer: The Osbournes

The first answer to our first puzzle is ‘The Osbournes’. How do we know it’s correct? Because the Osbournes have ‘tattoos’.

The solver continues, finding interpretations – with confirmers – for more parts of the clues, converging in a location in Kansas. I find the intricacy and plausibility of this solution profoundly disturbing, because it is so plausible, yet it is completely wrong. The actual location of the treasure was in Los Angeles, California, down Laurel Canyon Road. The official solution is very intricate and complex, with many stages of solutions – clues are hidden in alphabetic codes for things like the curls of toes on dragons and combinations of card suits printed on page after page of the book. Once those clues are decoded, complex rules must be applied to whittle them down to the actual clues.

The winner of the prize apparently drove to the site where the prize was hidden and looked around but couldn’t find it. As she was driving away, she happened to see the word “TATTOO” on big letters on the back of a truck, which reminded her of the separate clue Blaine had given on a television show. That clue finally triggered the specific location of the prize, and she successfully located it.

Even when the existence of a puzzle is clearly indicated, most solutions will be failures. And when a puzzle is not clearly indicated, however broadly its existence may be hinted at, it will most often go unsolved, with no cognitive resources devoted to it. This is interesting from the point of view of cryptography (and its arcane forms like steganography): when the existence of a communication (and its method of encoding) is ambiguous, it may be more likely that a particular encoded transmission goes unsolved by its intended recipient than that an enemy solves it. This is good news: it indicates that unsolved puzzles are everywhere. The real puzzles (those intentionally encoded by an intelligent life form) may be difficult to differentiate from spurious “puzzles” – but they are there, hidden somewhere in the haystack of human communication. Philip K. Dick says:

One time a whole class of kids wrote me about my story The Father Thing and every kid wanted to know where I got my idea. That was easy, because it was based on childhood memories of my father; but later on, in rereading my answers, I noticed that I never said the same thing twice. With all intent at honesty, I gave each kid a different answer. I guess this is what makes a fiction writer. Give him six facts and he’ll link them together first one way and then another, on and on until you forcibly stop him.

[Afterthought by the Author, The Best of Philip K. Dick, 1977.]

Two Cognitive Functions

Returning to the theory of humor, Hurley et al. use a model of cognitive processing that they call JITSA, for just-in-time spreading activation. In this model, people construct mental spaces on the fly, with sensation, perception, and inference activating associated concepts from long-term memory. Often, concepts and beliefs are activated without even rising to explicit conscious awareness. The mind instantly activates some concepts and not others, and combines them to make predictions about what will come next. (When a prediction is violated, the result is surprise, as described above.)

Just-in-time spreading activation is a thrifty mechanism, bringing into limited active mental space only those memories and concepts that it deems relevant. It is impossible to bring to mind simultaneously all the information stored in long-term memory; awareness is a limited resource, especially under time pressure, as is the case in conversation. Hurley et al. describe two “forces” that limit and modulate the spread of activation: friction and closure. Friction refers to the natural “petering out” of energy assigned to the cognitive task. “Whatever the energy limitations on spreading activation are, the energy budget for this activation avenue is exhausted and it ceases operation wherever it is,” they say (at p. 107). Closure is the active function of blocking closing off further exploration along a certain path. “This kind of heuristic search terminator is necessarily risky and crude, not involving further analysis of the path,” say Hurley et al. “All of the cognitive power of an individual person’s JITSA system lies in the use of closure, since friction is as good as content-blind, stopping the search for no reason at all other than running out of time or energy. Closure, in contrast, is teachable, adjustable by experience.”

Closure is critically important as a procedure, but one of its risks is that it is extremely difficult to reverse, or even to be aware of. When we have closed off a potential avenue of investigation, we are rarely conscious of it. If you imagine lions basking in the shade under acacia trees on the Serengeti, you do not expect the lions to be wearing socks. But you are certainly not aware of having “closed” that particular line of thinking, or billions of others, every moment.

Closure is productive (but risky) thought-stopping, pruning the branches of a cognitive search tree so that healthier branches can have more energy. Those individuals whose closure function does not operate well often think poorly, in a “loose” fashion. This “closure deficit” is sometimes called allusive thinking, a cognitive style characterized by poor inhibition of irrelevant memories and forming loose associations.

However, in a person who thinks well, occasional allusive thinking may be a valuable function. The stuff of genius – new compressions, connections, models – is often the result of a novel, loose association pursued by a mind capable of closure, but not as constrained by closure as is normal. The subtype of puzzles called lateral thinking puzzles are exercises in un-blocking, reversing a closure that was covertly accomplished by the statement of the problem.

The “two cognitive functions” I allude to in my subheading of this section are thus closure and allusive thinking – blocking and un-blocking. Cognition is a resource management game, and, broadly speaking, the two functions adjust and direct resource flows (cognitive resources, time). Consider the career of Kary Mullis for a sobering illustration of genius and epistemic catastrophe existing together in one mind. Some degree of allusive thinking seems to underlie both phenomena, though perhaps it is just a coincidence. Can we hope to do better?

Solving a puzzle, as a subset of cognition, is therefore a resource management game exercising these two functions. Is there a puzzle or secret information here? Is it likely worth the cognitive effort to try to solve it? What avenues should be pursued in decoding the communication or finding the solution? Where might ambiguity lie? What concepts might connect? What operations might be performed? Are you on the right track?

Confirmers are themselves hidden communications that indicate that you are on the right track, that cognitive resources should (continue to) be allocated to this branch of the search space. As we have seen, this kind of confirming communication may be inferred erroneously. Nonetheless we continue look for confirmers, because they are useful for directing cognitive resources. In the Schegloff paper on confirming allusions, verbatim repetition of the exact words of the speaker operates as a confirmer for a very common and important kind of “puzzle” – the puzzle of guessing the contents of the minds of other people, given their ambiguous words and actions.

What I have called “the essence of peopling” can be seen as a kind of puzzle – figuring out what other people have on their minds, relevant to you. One of the most important, recurring puzzles in human existence is this: “How hard should I cooperate with this person or group?” It’s a complicated judgment to make, and mistakes can have serious consequences (fitness costs as well as hedonic costs). Then there is figuring out how to cooperate with a chosen cooperation partner. Both involve interpreting ambiguous information, the possibility of mistake or deception, and the necessity of pursuing some cognitive paths and blocking others.

Undecidability and the Consolation of Conspiracy

Consider Oedipa Maas, the heroine of Pynchon’s The Crying of Lot 49. Faced with a pile of suspicious coincidences, haunted by confirmers, she is never able to settle on one theory that resolves all the ambiguity. She sees hints and suggestions of a secret conspiracy; she sees its apparent work in the world. The conspiracy explanation is appealing; it posits order, and, perhaps, belonging. Here is a portrait of her situation, reflecting the epistemic situations all of us find ourselves in at some point:


Converge on 49, 42 – something that we only really know from whispered hints – incipient, tentative enlightenment – coincidence. Beyond lies agony. Certain kinds of knowledge are necessary for our comfort and flourishing; each epistemic emotion (surprise, mirth, wonder, insight) reflects an epistemic need. And underneath all the needs, belonging, and perhaps the outline of a mysterious purpose, just barely suggested by strange coincidences.