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Toward a Quantum Theory of Humor Gabora, Liane; Kitto, Kirsty Jan 26, 2017

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ORIGINAL RESEARCHpublished: 26 January 2017doi: 10.3389/fphy.2016.00053Frontiers in Physics | www.frontiersin.org 1 January 2017 | Volume 4 | Article 53Edited by:Andrei Khrennikov,Linnaeus University, SwedenReviewed by:Haroldo Valentin Ribeiro,Universidade Estadual de Maringá,BrazilRaimundo Nogueira Costa Filho,Federal University of Ceará, BrazilIrina Basieva,Graduate School for the Creation ofNew Photonics Industries, Russia*Correspondence:Liane Gaboraliane.gabora@ubc.caSpecialty section:This article was submitted toInterdisciplinary Physics,a section of the journalFrontiers in PhysicsReceived: 01 September 2016Accepted: 21 December 2016Published: 26 January 2017Citation:Gabora L and Kitto K (2017) Toward aQuantum Theory of Humor.Front. Phys. 4:53.doi: 10.3389/fphy.2016.00053Toward a Quantum Theory of HumorLiane Gabora 1* and Kirsty Kitto 21Department of Psychology, University of British Columbia, Kelowna, BC, Canada, 2Department of Mathematical Sciences,Queensland University of Technology, Brisbane, QLD, AustraliaThis paper proposes that cognitive humor can be modeled using the mathematicalframework of quantum theory. We begin with brief overviews of both research on humor,and the generalized quantum framework. We show how the bisociation of incongruousframes or word meanings in jokes can be modeled as a linear superposition of a setof basis states, or possible interpretations, in a complex Hilbert space. The choice ofpossible interpretations depends on the context provided by the set-up vs. the punchlineof a joke. We apply the approach to a verbal pun, and consider how it might be extendedto frame blending. An initial study of that made use of the Law of Total Probability, involving85 participant responses to 35 jokes (as well as variants), suggests that the QuantumTheory of Humor (QTH) proposed here provides a viable new approach to modelinghumor.Keywords: bisociation, context, humor, incongruity, law of total probability, pun, quantum cognition, quantuminteraction1. INTRODUCTIONHumor has been called the “killer app” of language [1]; it showcases the speed, playfulness, andflexibility of human cognition, and can instantaneously put people in a positive mood. For over a100 years scholars have attempted to make sense of the seemingly nonsensical cognitive processesthat underlie humor. Despite considerable progress with respect to categorizing different forms ofhumor (e.g., irony, jokes, cartoons, and slapstick) and understanding what people find funny, therehas been little investigation of the question: What kind of formal theory do we need to model thecognitive representation of a joke as it is being understood?This paper attempts to answer this question with a new model of humor that uses ageneralization of the quantum formalism. The last two decades have witnessed an explosionof applications of quantum models to psychological phenomena that feature ambiguity and/orcontextuality [2–4]. Many psychological phenomena have been studied using quantum models,including the combination of words and concepts [5–10], similarity and memory [11, 12],information retrieval [13, 14], decision making and probability judgment errors [15–19], vision[20, 21], sensation–perception [22], social science [23, 24], cultural evolution [25, 26], and creativity[27, 28]. These quantum inspired approaches make no assumption that phenomena at the quantumlevel affect the brain, but rather, draw solely on abstract formal structures that, as it happens,found their first application in quantum mechanics. They utilize the structurally different natureof quantum probability. While in classical probability theory events are drawn from a commonsample space, quantum models define states and variables with reference to a context, representedusing a basis in a Hilbert space. This results in phenomena such as interference, superposition andentanglement, and ambiguity with respect to the outcome is resolved with a quantummeasurementand a collapse to a definite state.Gabora and Kitto Quantum Theory of HumorThis makes the quantum inspired approach an interestingnew candidate for a theory of humor. Humor often involvesambiguity due to the presence of incongruous schemas: internallycoherent but mutually incompatible ways of interpreting orunderstanding a statement or situation. As a simple example,consider the following pun:“Time flies like an arrow. Fruit flies like a banana.”This joke hangs on the ambiguity of the phrase FRUIT FLIES,where the word FLIES can be either a verb or a noun. As a verb,FLIES means “to travel through the air.” However, as a noun,FRUIT FLIES are “insects that eat fruit.” Quantum formalismsare highly useful for describing cognitive states that entail thisform of ambiguity. This paper will propose that the quantumapproach enables us to naturally represent the process of “gettinga joke.”We start by providing a brief overview of the relevant researchon humor.2. BRIEF BACKGROUND IN HUMORRESEARCHEven within psychology, humor is approached from multipledirections. Social psychologists investigate the role of humor inestablishing, maintaining, and disrupting social cohesion andsocial status, developmental psychologists investigate how theability to understand and generate humor changes over a lifetime,and health psychologists investigate possible therapeutic aspectsof humor. This paper deals solely with the cognitive aspect ofhumor. Much cognitive theorizing about humor assumes that itis driven by the simultaneous perception [29, 30] or “bisociation”[31] of incongruent schemas. Schemas can be either static frames,as in a cartoon, or dynamically unfolding scripts, as in a pun.For example, in the “time flies” joke above, interpreting thephrase FRUIT FLIES as referring to the insect is incompatiblewith interpreting it as food traveling through the air. Incongruityis generally accompanied by the violation of expectations andfeelings of surprise. While earlier approaches posited that humorcomprehension involves the resolution of incongruous framesor scripts [32, 33], the notion of resolution often plays aminor role in contemporary theories, which tend to view thepunchline as activating multiple schemas simultaneously andthereby underscoring ambiguity (e.g., 34, 35).There are computational models of humor detection andunderstanding (e.g., 36), in which the interpretation of anambiguous word or phrase changes as new surroundingcontextual information is parsed. For example, in the “time flies”joke, this kind of model would shift from interpreting FLIES asa verb to interpreting it as a noun. There are also computationalmodels of humor that generate jokes through lexical replacement;for example, by replacing a “taboo” word with a similar-soundinginnocent word (e.g., [37, 38]). These computational approachesto humor are interesting, and occasionally generate jokes thatare laugh-worthy. However, while they tell us something abouthumor, we claim that they do not provide an accurate model ofthe cognitive state of a human mind at the instant of perceivinga joke. As mentioned above, humor psychologists believe thathumor often involves not just shifting from one interpretation ofan ambiguous stimulus to another, but simultaneously holdingin mind the interpretation that was perceived to be relevantduring the set-up and the interpretation that is perceived to berelevant during the punchline. For this reason, we turned tothe generalized quantum formalism as a possible approach formodeling the cognitive state of holding two schemas in mindsimultaneously.3. BRIEF BACKGROUND IN GENERALIZEDQUANTUM MODELINGClassical probability describes events by considering subsets ofa common sample space [39]. That is, considering a set ofelementary events, we find that some event e occurred withprobability pe. Classical probability arises due to a lack ofknowledge on the part of the modeler. The act of measurementmerely reveals an existing state of affairs; it does not interfere withthe results.In contrast, quantum models use variables and spaces thatare defined with respect to a particular context (although this isoften done implicitly). Thus, in specifying that an electron hasspin “up” or “down,” we are referring to experimental scenarios(e.g., Stern-Gerlach arrangements and polarizers) that denote thecontext in which a measurement occurred. This is an importantsubtlety, as many experiments have shown that it is impossibleto attribute a pre-existing reality to the state that is measured;measurement necessarily involves an interaction between a stateand the context in which it is measured, and this is traditionallymodeled in quantum theory using the notion of projection. Thestate |9〉 representing some aspect of interest in our system iswritten as a linear superposition of a set of basis states {|φi〉} ina Hilbert space, denoted H, which allows us to define notionssuch as distance and inner product. In creating this superpositionwe weight each basis state with an amplitude term, denoted ai,which is a complex number representing the contribution ofa component basis state |φi〉 to the state |9〉. Hence |9〉 =∑i ai|φi〉. The square of the absolute value of the amplitudeequals the probability that the state changes to that particularbasis state upon measurement. This non-unitary change of stateis called collapse. The choice of basis states is determined by theobservable, Oˆ, to be measured, and its possible outcomes oi. Thebasis states corresponding to an observable are referred to aseigenstates. Observables are represented by self-adjoint operatorson the Hilbert space. Uponmeasurement, the state of the entity isprojected onto one of the eigenstates.It is also possible to describe combinations of two entitieswithin this framework, and to learn about how they mightinfluence one another, or not. Consider two entities A and B withHilbert spaces HA and HB . We may define a basis |i〉A for HAand a basis |j〉B for HB , and denote the amplitudes associatedwith the first as aAi and the amplitudes associated with the secondas aBj . The Hilbert space in which a composite of these entitiesexists is given by the tensor productHA⊗HB . The most generalstate inHA ⊗HB has the formFrontiers in Physics | www.frontiersin.org 2 January 2017 | Volume 4 | Article 53Gabora and Kitto Quantum Theory of Humor|9〉AB =∑i,jaij|i〉A ⊗ |j〉B (1)This state is separable if aij = aAi aBj . It is inseparable, andtherefore an entangled state, if aij 6= aAi aBj .In some applications, the procedure for describingentanglement is more complicated than what is describedhere. For example, it has been argued that the quantum fieldtheory procedure, which uses Fock space to describe multipleentities, gives a kind of internal structure that is superior to thetensor product for modeling concept combination [5]. Fockspace is the direct sum of tensor products of Hilbert spaces, soit is also a Hilbert space. For simplicity, this initial applicationof the quantum formalsm to modeling humor will omit suchrefinements, but such a move may become necessary in furtherdevelopments of the model.Quantum models can be useful for describing situationsinvolving potentiality, in which change of state isnondeterministic and contextual. The concept of potentialityhas broad implications across the sciences; for example, everybiological trait not only has direct implications for existingphenotypic properties such as fitness, but both enables andconstrains potential future evolutionary changes for a givenspecies. The quantum approach been used to model thebiological phenomenon of exaptation—wherein a trait thatoriginally evolved for one purpose is co-opted for another(possibly after some modification) [40]. The term exaptationwas coined by Gould and Vrba [41] to denote what Darwinreferred to as preadaptation1. Exaptation occurs when selectivepressure causes this potentiality to be exploited. Like other kindsof evolutionary change, exaptation is observed across all levels ofbiological organization, i.e., at the level of genes, tissue, organs,limbs, and behavior. Quantum models have also been used tomodel the cultural analog of exaptation, wherein an idea that wasoriginally developed to solve one problem is applied to a differentproblem [40]. For example, consider the invention of the tireswing. It came into existence when someone re-conceived of atire as an object that could form the part of a swing that one sitson. This re-purposing of an object designed for one use for usein another context is referred to as cultural exaptation. Muchas the current structural and material properties of an organ orappendage constrain possible re-uses of it, the current structuraland material properties of a cultural artifact (or language, orart form, etc.) constrain possible re-uses of it. We suggest thatincongruity humor constitutes another form of exaptation;an ambiguous word, phrase, or situation, that was initiallyinterpreted one way is revealed to have a second, incongruousinterpretation. Thus, it is perhaps unsurprising that, as withother forms of exaptation, a quantum model is explored.4. A QUANTUM INSPIRED MODEL OFHUMORA quantum theory of humor (QTH) could potentially inheritseveral core concepts from previous cognitive theories of humor1The terms exaptation, preadaptation and co-option are often used interchangeably.while providing a unified underlyingmodel. Considering the pastwork discussed in Section 2, it seems reasonable to focus on thenotion that cognitive humor involves an ambiguity brought on bythe bisociation of internally consistent but mutually incongruousschemas. Thus, cognitive humor appears to arise from thedouble think that is brought about by being forced to reconsidersome currently held interpretation of a joke in light of newinformation: a frame shift. Such an insight opens humor uptoquantum-like models, as a frame shift of an ambiguous conceptis well modeled by the notion of a quantum superpositiondescribed using two sets of incompatible basis states within someunderlying Hilbert space structure.In what follows we sketch out a preliminary quantum inspiredmodel of humor and discuss what would be required for afull-fledged formal QTH. Next, we outline a study aimed atdiscovering whether humor behaves in a quantum-like manner.The last section discusses how the QTH opens up avenues forfuture investigation in a field that to date has not been wellmodeled.4.1. The Mathematical Structure of QTHWe start our journey toward a QTH by building upon an existingmodel of conceptual combination [8]: the State–COntext–Property (SCOP) model. As per the standard approach usedin most quantum-like models of cognition, |9〉 represents thestate of an ambiguous element, be it a word, phrase, object,or something else, and its different possible interpretations arerepresented by basis states. Core to the SCOP model is atreatment of the context in which every measurement of a stateoccurred, and the resultant property that was measured. Thesethree variables are stored as a triple in a lattice.4.1.1. The State SpaceFollowing Aerts and Gabora [6], the set of all possibleinterpretation states for the ambiguous element of a joke is givenby a state space 6. Specific interpretations of a joke are denotedby |p〉, |q〉, |r〉, · · · ∈ 6 which form a basis in a complex Hilbertspace H. Before the ambiguous element of the joke is resolved,it is in a state of potentiality, represented by a superpositionstate of all possible interpretations. Each of these represents apossible understanding arising due to activation of a schemaassociated with a particular interpretation of an ambiguous wordor situation. The interpretations that are most likely are mostheavily weighted. The amplitude term associated with each basisstate represented by a complex number coefficient ai gives ameasure of how likely an interpretation is given the currentcontextual information available to the listener. We assume thatall basis states have unit length, are mutually orthogonal, and arecomplete, thus∑i |ai|2 = The ContextIn the context of a traditional verbal joke, the context consistsprimarily of the setup, and the setup is the only contextualelement considered in the study in Section 5. However,it should be kept in mind that several other contextualfactors not considered in our analysis can affect perceivedfunniness. Prominent amongst these is the delivery; the wayFrontiers in Physics | www.frontiersin.org 3 January 2017 | Volume 4 | Article 53Gabora and Kitto Quantum Theory of Humorin which a joke is delivered can be everything when itcomes to whether or not it is deemed funny. Other factorsinclude the surroundings, the person delivering the joke, thepower relationships among different members of the audience,and so forth.As a first step, we might represent the set of possible contextsfor a given joke as ci ∈ C. Each possible interpretation of ajoke comes with a set fi ∈ F of properties (i.e., features orattributes), which may be weighted according to their relevancewith respect to this contextual information. The weight (orrenormalized applicability) of a certain property given a specificinterpretation |p〉 in a specific context ci ∈ C is given by ν. Forexample, ν(p, f1) is the weight of feature fi for state |p〉, which isdetermined by a function from the set6×F to the interval [0, 1].We write:ν :6 × F → [0, 1] (2)(p, fi) 7→ ν(p, fi).4.1.3. Transition ProbabilitiesA second function µ describes the transition probability fromone state to another under the influence of a particular context.For example, µ(q, e, p) is the probability that state |p〉 under theinfluence of context ci changes to state |q〉. Mathematically, µ isa function from the set 6 × C × 6 to the interval [0, 1], whereµ(q, e, p) is the probability that state |p〉 under the influence ofcontext |e〉 changes to state |q〉. We write:µ :6 × C ×6 → [0, 1] (3)(q, e, p) 7→ µ(q, e, p).Thus, a first step toward a full quantum model of humor consistsof the 3-tuple (6, C,F), and the functions ν and µ. Next weaddress a key question that should be asked of any cognitivetheory of humor: what is the underlying cognitive model of thefunniness of a joke?4.2. The Humor of a JokeAs the listener hears a joke, more context is provided, andin our model the listener’s understanding evolves according tothe transition probabilities associated with the cognitive stateand the emerging context. When the listener hear the jokea bisociation of meaning is percieved; that is, the listenerrealizes that a second way of interpreting it is possible.A projective measurement onto a funniness frame is themechanism that we use tomodel the likelihood that a given joke isconsidered funny.Thus, in our model, funniness plays the role of a measurementoperator, and it is affected by the shift that occurs in theunderstanding of a joke with respect to two possible framings:one created by the setup, and one by the punchline. Theprobability of a joke being regarded as funny or not isproportional to the projection of the individual’s understandingof the joke (|9〉) onto a basis representing funniness. This meansthat the probability of a joke being considered as funny, pF isgiven by a projection onto the |1〉 axis in H2F , a two-dimensionalHilbert sub-space where |0〉 represents “not funny” and |1〉represents “funny.”pF = ||1〉〈1|9〉|2 (4)Similarly, the probability of a joke being regarded as not funny isrepresented bypF¯ = ||0〉〈0|9〉|2. (5)Note that |9〉 evolves as the initial conceptualization of the joke isreinterpreted with respect to the frame of the punchline. This is adifficult process to model, and we consider the work in this paperto be an early first step toward an eventually more comprehensivetheory of humor that includes predictive models.We now present two examples in which specific instancesof humor are considered within the perspective of this basicquantum inspired model. First the approach is applied to a pun.Second, the approach is applied to a cartoon that is a frame blend.Both scenarios will help to deepen our understanding of thesignificant complexity of humor, and the difficulties associatedwith creating a mathematical model of this important humanphenomenon.4.3. Applying QTH to a PunConsider the pun: “Why was 6 afraid of 7? Because 789.” Thehumor of this pun hinges on the fact that the pronunciationof the number EIGHT, a noun, is identical to that of the verbATE. We refer to this ambiguous word, with its two possiblemeanings, as EYT. An individual’s interpretation of the wordEYT is represented by |9〉, a vector of length equal to 1. Thisis a linear superposition of basis states in the semantic sub-space H2M which represents possible states (meanings) of theword EYT: EIGHT or ATE2. The interpretation of EYT as anoun, and specifically the number EIGHT, is denoted by theunit vector |n〉. The verb interpretation, ATE, is denoted by theunit vector |v〉. The set {|n〉, |v〉} forms a basis in H2M . Thus,we have now expanded our original two-dimensional funninessspace with an additional two-dimensional semantic space, wherethe full space H4 = H2F ⊗ H2M . We note that these two spacesshould not be considered as mutually orthogonal, but that theywill overlap. If they were orthogonal then the funniness of ajoke would be independent of the interpretation that a personattributes to it.With this added mathematical structure, we can represent theinterpretation of the joke as a superposition state inH2M|9〉 = an|n〉 + av|v〉, (6)where an and av are amplitudes which, when squared, representthe probability of a listener interpreting the joke in a noun ora verb form (|n〉 and |v〉) respectively. This state is depicted inFigure 1A, which shows a superposition state in the semanticspace. When given no context in the form of the actualpresentation of the joke, these amplitudes represent the prior2We acknowledge that other interpretations are possible, and so this is a simplifiedmodel. It is straightforward to extend the model into higher dimensions by addingfurther interpretations as basis states.Frontiers in Physics | www.frontiersin.org 4 January 2017 | Volume 4 | Article 53Gabora and Kitto Quantum Theory of HumorFIGURE 1 | The humor of a joke can be explained as arising from a measurement process that occurs with respect to two incompatible frames. Usingthe example of the pun, (A) the meaning of the set-up is reinterpreted with EYT updating toward the interpretations ATE. (B) Funniness is then treated as ameasurement, with the probability of funniness being judged with respect to a projection on the {|0〉, |1〉} basis. In this case there is a large probability of the joke beingconsidered funny due to the dominant component of the projection of |9〉 lying on the |1〉 axis. (C) The cognitive state of the subject then collapses to the observedstate (i.e., funny or not).likelihood of a listener interpreting the uncontextualized word(i.e., EYT) in either of the noun or verb senses (e.g., a freeassociation probability; see [12] for a review). However, we wouldexpect to see these probabilities evolving throughout the courseof the pun as more and more context is provided (in the formof additional sentence structure). Throughout the course of thejoke, the state vector |9〉 therefore evolves to a new positioninH4.Since the set-up of the joke,“Why was 6 afraid of 7?,” containstwo numbers, it is likely that the numbers interpretation ofEYT is activated (a situation represented in Figure 1A). Thelistener is biased toward an interpretation of EYT in this sense,and so we would expect that an >> av. However, a carefullistener will feel confused upon considering this set-up becausewe do not think of numbers as beings that experience fear.This keeps the interpretation of EYT shifted away from anequivalence with the eigenvector |n〉. As the joke unfolds, thepredator interpretation that was hinted at in the set-up by theword “afraid,” and reinforced by “789,” activates a more definitealternative meaning, ATE, represented by |v〉. This generates analternative interpretation of the punchline: that the number 7ate the number 9. The cognitive state |9〉 has evolved to a newposition in H4, a scenario that is represented in Figure 1B. Atthis point a measurement occurs: the individual either considersthe joke as funny or not within the context represented by thefunniness sub space H2F , and a collapse to the relevant funninessbasis state occurs (see Figure 1C). Note that this final state stillcontains a superposition within the meaning subspace H2M—thefunniness judgment merely shifts the interpretation of the joke, itdoes not eliminate the bisociation. Rather, it depends upon it.If we consider the set of properties associated with EYTthen we would expect to see two very different prototypicalcharacteristics associated with each interpretation. For example,the EIGHT interpretation is difficult to map into properties suchas “food” denoted f1, and “not living” denoted f2 (since whensomething is eaten it is usually no longer alive). Because “food”and “not living” are not properties of EIGHT, ν(p, f0) << ν(n, f0),and similarly ν(p, f1) << ν(n, f1). However, “food” and “notliving” are properties of EYT, ν(p, f0) << ν(v, f0), and similarlyν(p, f1) << ν(v, f1).We can now start to construct a model of humor that couldbe correlated with data. If jokes satisfy the law of total probability(LTP) then their funniness should satisfy the distributive axiom,which states that the total probability of some observable shouldbe equal to the sum of the probabilities of it under sets of morespecific conditions. Thus, considering a funniness observable OˆF(with eigenstates {|1〉, |0〉} and the semantic observable OˆM (witha simplified two eigenstate structure {|M〉, |M¯〉} representing twopossible meanings that could be attributed to the joke). We cantake the spectral decomposition of OˆM = m|M〉〈M| + m¯|M¯〉〈M¯|,where m, m¯ are eigenvalues of the two eigenstates {|M〉, |M¯〉}.Doing this, we should find that if this system satisfies the LTPthen the probability of the joke being judged as funny is equal tothe sum of the probability of it being judged funny given eithersemantic interpretationp(F) = p(|1〉) = p(M) · p(F|M)+ p(M¯) · p(F|M¯). (7)We can manipulate the interpretation that a participant is likelyto attribute to a joke by changing the semantics of the joke itself.Thus, changing the joke should change the semantics, and soaffect the humor that is attributed to the joke. We shall returnto this idea in Section 5.This section has demonstrated that a formal approachto concept interactions that has been previously shown tobe consistent with human data [5] can be adapted toFrontiers in Physics | www.frontiersin.org 5 January 2017 | Volume 4 | Article 53Gabora and Kitto Quantum Theory of Humorthe simultaneous perception of incongruous meanings of anambiguous word or phrase in the understanding of a pun.4.4. Applying QTH to a Frame BlendAlthough our first example used a pun for simplicity, we believethat quantum inspired models may also be useful for moreelaborate forms of humor, such as jokes and cartoons referredto as frame blends. A frame blend involves the merging ofincongruous frames of reference [42]. A common example of aframe blend is a cartoon in which animals are engaged in somekind of human behavior (such as a cartoon of a cow with allher teats pierced saying “Just gotta be me”). In a frame blendrather than being led “down the garden path” by the setupand subsequent re-interpretation in light of the punchline, thehumor results from the simultaneous presentation of seeminglyincompatible frames. Using QTH, the two interpretations of theincongruous situation would be designated by the unit vectors{|d〉, |o〉}. The cognitive state of perceiving the blended framesis represented as a superposition of the two frames. As withphenomena such as conceptual combination, there are likely tobe constraints on how frames can be successfully blended, and itwill be necessary to consider this when constructing models offrame blends. We reserve further exploration of this interestingclass of humor for future work.5. PROBING THE STATE SPACE OFHUMORReturning to the question raised by Equation (7), a QTH shouldbe justified by considering whether humor does indeed violatethe Law of Total Probability (LTP) [3]. However, the complexityof language makes it difficult to test how humor might violatethe LTP using a method similar to those followed for decisionmaking [11]. Past work on humor is unlikely to yield the datarequired to perform tests such as this. For example, we currentlyhave no experimental understanding of how the semantics of ajoke interplays with its perceived funniness. It seems reasonableto suppose that the two are related, but how? We are not awareof any data that provide a way to evaluate this relationship. Thisis problematic, as there are a number of interdependencies in theframing of a joke that make it difficult to construct a model (evenbefore considering factors such as the context in which the jokeis made, and the socio-cultural background of the teller and thelistener). In this section we present results from an exploratorystudy designed to start unpacking whether humor should indeedbe considered within the framework of quantum cognition. As anillustrative example, consider the following joke:VO: “Time flies like an arrow. Fruit flies like abanana.”As with the joke discussed in Section 4.3, the humor arises fromthe ambiguity of the words FRUIT and FLIES. The first frame (F1,the set-up), leads one to interpret FLIES as a verb and LIKE as apreposition, but the second frame (F2, the punchline), leads oneto interpret FRUIT FLIES as a noun and LIKE as a verb. A QTHmust be able to explain how the funniness of the joke dependsupon a shift in the semantic understanding of the two frames, F1and F2.We now outline a preliminary study that has helped us toexplore the state space of humor.5.1. StimuliWe collected a set of 35 jokes and for each joke we developed aset of joke variants. A VS variant consisted of the set-up only forthe original, VO. Thus, the VS variant of the VO joke isVS: “Time flies like an arrow.”AVP variant consists of the original punchline only. Thus, theVPvariant of the VO joke isVP: “Fruit flies like a banana.”We then considered the notion of a congruent punchline as onethat does not introduce a new interpretation or context for anambiguous element of the set-up (or punchline). Congruence wasachieved by modifying the set-up to make it congruent with thepunchline, or by modifying the punchline to make it congruentwith the set-up. Thus, if the original set-up makes use of a noun,then so does a congruent modification (and similarly for thepunchline).A CP variant consists of the original set-up followed acongruent version of the punchline. Thus, a CP variant of the Ojoke is:CP: “Time flies like an arrow; time flies like a bird.”A CS variant consists of the original punchline preceded by acongruent version of the set-up. Thus, a CS variant of the O’joke isCS: “Horses like carrots; fruit flies like a banana.”For some jokes we had a fifth kind of variant. A IS variant consistsof the original set-up followed an incongruent version of thepunchline that we believed was comparable in funniness to theoriginal. Thus, considering the joke discussed in Section 4.3:O: “Why was 6 afraid of 7? Because 789.”A IS variant of this joke is:IS: “Why was 6 afraid of 7? Because 7 was a sixoffender.”Thus the stimuli consisted of a questionnaire containing originaljokes, and the above variants presented in randomized order. Thecomplete collection of jokes and their variants is presented in theAppendix (Supplementary Material).5.2. ParticipantsThe participants in this study were 85 first year undergraduatestudents enrolled in an introductory psychology course atthe University of British Columbia (Okanagan campus). Theyreceived partial course credit for their participation.Frontiers in Physics | www.frontiersin.org 6 January 2017 | Volume 4 | Article 53Gabora and Kitto Quantum Theory of Humor5.3. ProcedureParticipants signed up for the study using the SONA recruitmentsystem, and subsequently responded at their convenience toan online questionnaire hosted by FluidSurveys. They wereinformed that the study was completely voluntary, and that theywere free to withdraw at any point in time. They were alsoinformed that the researcher would not have any knowledge ofwho participated in the study, and that their participation wouldnot affect their standing in the psychology class or relationshipwith the university. Participants were told that the purpose ofthe study was to investigate humor, and to help contribute to abetter understanding the cognitive process of “getting” a joke.Participants were asked to fill out consent forms. If they agreedto participate, they were provided a questionnaire consisting of aseries of jokes and joke variants (as described above) and askedto rate the funniness of each using a Likert scale, from 1 (notfunny) to 5 (hilarious). The questionnaire took approximately25 min to complete. They received partial course credit for theirparticipation.5.4. ResultsThe mean funniness ratings across all participants for the entirecollection of jokes and their variants (as well as the jokes andvariants themselves) is provided in the Appendix (SupplementaryMaterial). Table 1 provides a summary of this information (themean funniness rating of each kind of joke variant acrossall participants) aggregated across all joke sets. As expected,the original joke (O) was funniest (mean funniness = 2.70),followed by those jokes that had been intentionally modified tobe funny: Incongruent Setup (IS) (mean funniness = 2.37) andIncongruent Punchline (IP) (mean funniness = 2.12). Next infunniness were the jokes that had been modified to eradicatethe incongruency and thus the source of the humor: CongruentSetup (CS) (mean funniness = 1.41) and Congruent Punchline(CP) (mean funniness = 1.47). The joke fragments without acounterpart–i.e., either Setup (S) or Punchline (P) alone–wereconsidered least funny of all (the mean funniness of both was1.22). The dataset is entirely consistent with the view that thehumor derives from incongruence due to bisociation.5.5. Toward a Test of the QTHRecall that the Law of Total Probability (LTP) as representedby Equation (7) suggests that the mean funniness of a jokeshould be equal to the sum of its funniness as judged underall possible semantic interpretations. This is not an equalitythat we can directly test given our current understanding oflanguage and how it might interplay with humor. However, theTABLE 1 | The mean funniness ratings across all participants and all jokesets for each kind of joke variant.Joke variant O S P CS CP IS IPMean funniness 2.70 1.22 1.22 1.41 1.47 2.37 2.12O, Original; S, Set-up only; P, Punchline only; CS, Congruent Set-up; CP, CongruentPunchline; IS, Incongruent Set-up; IP, Incongruent Punchline.dataset reported here gives us some initial ways to address this.With a methodology for converting the Likert scale ratings intoprojective measurements of a joke being funny or not, we canstart to consider the relative frequency that an original joke isjudged as funny and compare this result with the individualcomponents.We start by translating the Likert scale responses into asimplified measurement of funniness, by mapping the funninessratings into a designation of funny or not. In order to run a quickcomparison between the relative frequencies that participantsdecided the full joke (VO) was funny when compared to thecomponents of the joke (VS and VP), we took the mean valueof the components for each subject. Given that puns are notgenerally considered particularly funny (a result backed up byour participant ratings) we used a fairly low threshold value of2.5 (i.e., if the mean was less than 2.5 then the componentswere judged as unfunny, and vice versa). Exploring the resultsof this mapping gives us the data reported in Figure 2 for theVO, VS and VP variants of the jokes, listing the frequency atwhich participants judged the joke and subcomponents funny. Amean value for the joke fragments is also presented. All data usesconfidence intervals at the 95% level.We see a significant discrepancy between the funniness of theoriginal and the combined funniness of its components. This isnot a terribly surprising result; jokes are not funny when theset-up is not followed by the punchline, and participants usuallyrated VS and VP variants as unfunny (i.e., scoring them at 1).Table 2 in the Appendix (Supplementary Material) shows that inthe participant pool of 85, the set-up and punchline variants ofthe joke rarely had a mean funniness rating above 1.5. However,to extract a violation of the LTP for this scenario, we would needto construct expressions such as the followingp(F) = p(EIGHT).p(F|EIGHT)+ p(ATE).p(F|ATE). (8)How precisely could such a relationship be tested? Two formsof data are required to test whether the simple puns used in ourexperiment actually violate the LTP:1. Funniness ratings: These are the probabilities regardingthe probability that different components of the joke areconsidered funny (the whole joke (p(F)); just the setup(p(F|EIGHT)); and just the punchline (p(F|ATE)); and2. Semantic probabilities: These list the probability of EYTbeing interpreted as EIGHT: p(EIGHT), or ATE: p(ATE),within the context of the specific joke fragment.We have demonstrated a method for extracting the funninessratings above. How might we obtain data for the semanticprobabilities? We must consider the precise interpretation ofwhat these probabilities might actually be. Firstly, we note that itseems likely participants will interpret just a set-up or a punchlinein the sense that the fragment represents. The bisociation thathumor relies upon is not present for a fragment, and so a personhearing a fragment will be primed by its surrounding contexttoward interpreting an ambiguous word in precisely the senseintended for that fragment. Indeed, the incongruity that resultsfrom having to readjust the interpretation of the joke, and theFrontiers in Physics | www.frontiersin.org 7 January 2017 | Volume 4 | Article 53Gabora and Kitto Quantum Theory of HumorFIGURE 2 | A comparison of the frequency with which a specific joke and its fragments are considered funny for participants in the pilot trial (using athreshold value of 2.5, n = 85). A mean of the set-up and the punchline variants (VS and VP ) is also given. Confidence intervals are set at 95%.resulting bisociation, lies at the very base of the humor that arises.Free association probabilities will not give these values. To testthe LTP, it would be necessary to extract information about howa participant is interpreting core terms in the joke as it progresses;some form of nondestructivemeasurement is required, and a newexperimental protocol will have to be defined. We reserve this forfuture work.However, the significant difference between the ratedfunniness of the fragments and that of the original joke allowsus to formulate an alternative mechanism for testing equationsof the form (7) and (8). We can do this by asking whether thereis any way in which the semantic probabilities could have valuesthat would satisfice the LTP? An examination of Figure 2 for thesetup and punchline variants of the jokes suggests that there isno way in which to chose semantic probabilities that will satisfythe LTP. Thus, we have preliminary evidence that humor shouldperhaps be treated using a quantum inspired model.6. DISCUSSIONIt would appear that there is some support for the hypothesisthat the humor arising from bisociation can be modeled bya quantum inspired approach. Furthermore, the experimentalresults presented in section 5 suggest that this model might moreappropriate than one grounded in classical probability. However,much work remains to be completed before we can consider thesefindings anything but preliminary.Firstly, the model presented in Section 4 is simple, andwill need to be extended. While an extension to more sensesfor an ambiguous element of a joke is straightforward with amove to higher dimensions, the model is currently not wellsuited to the set of variants discussed in Section 5.3. A modelthat can show how they interrelate, and how their underlyingsemantics affects the perceived humor in a joke is desirable.Furthermore, the funniness of the joke was simplisticallyrepresented by a projection onto the “funny”/“not funny”axis. A more theoretically grounded treatment of the Likertdata is desirable. For example, the current threshold valueof 2.5 was chosen somewhat arbitrarily [although could bejustified by a consideration of the mean values for funninessscores reported in the Appendix (Supplementary Material)—seeTable 2]. A more systematic way of considering the Likert scalemeasures to allow for a normalization of funniness ratings atthe level of an individual is also desirable. As a highly subjectivephenomenon, funniness is liable to be judged by differentindividuals inconsistently and so it will be important that wecontrol for this effect in comparing Likert responses amongindividuals.Considering experimental results, the sample size of the dataset is somewhat small (85 participants), although our funninessratings appear to be reasonably stable for this cohort. A moreconcerning problem revolves around the construction of a LTPrelationship for our simple model. There are many alternativeways in which a LTP could be constructed for puns, andmore sophisticated models need to be investigated before wecan be confident that our results conclusively demonstrate thathumor must be modeled using a quantum inspired approach.In particular, we require a more sophisticated method thatfacilitates the extraction of data about the semantics attributedby a participant to a joke. A two stage protocol may bethe answer for obtaining the necessary semantic informationfor a more rigorously founded test of the violation of LTP.It would be useful to construct a systematic study of themanner in which adjusting the congruence of the set-ups andpunchlines influences perception of the joke. The quantuminspired semantic space approaches of Van Rijsbergen [13]and Widdows [43] may prove fruitful in this regard, asthey would facilitate the creation of similarity models suchas those explored by Aerts et al. [44] and Pothos andTrueblood [45].In summary, humor is complex, and it will take an ongoingprogram of research to understand the interplay between thesemantics of a joke and its perceived funniness. However, atthis point we might pause to consider the broader question ofwhy humor might be better modeled by a quantum inspiredapproach than by one grounded in classical probability? ToFrontiers in Physics | www.frontiersin.org 8 January 2017 | Volume 4 | Article 53Gabora and Kitto Quantum Theory of Humorthis end we return to the discussion of Section 3. As we saw,the humor of a pun involves the bisociation of incongruentframes, i.e., re-viewing a setup frame in light of new contextualinformation provided by a punchline frame. Moreover, thebroader contextuality of humor means that even the funniestof jokes can become markedly unfunny if delivered in thewrong way (e.g., a monotone voice), or in the wrong situation(e.g., after receiving very bad news). Funniness is not a pre-existing “element of reality” that can be measured; it emergesfrom an interaction between the underlying nature of thejoke, the cognitive state of the listener, and other social andenvironmental factors. This makes the quantum formalism anexcellent candidate for modeling humor, as this interaction iswell described by the concept of a vector state embedded ina space which is represented using basis states that can bereoriented according to the framing of the joke. However, thispaper only provides a preliminary indication that a QTH mayindeed provide a good theoretical underpinning for this complexprocess. Much more work remains to be done.7. CONCLUSIONSThis paper has provided a first step toward a quantum theoryhumor (QTH). We constructed a model where frame blendsare represented in a Hilbert space spanned by two sets of basisstates, one representing the ambiguous framing of a joke, andthe other representing funniness. The process of “getting ajoke” then consists of a dual stage scenario, where the cognitivestate of a person evolves toward a re-interpretation of themeaning attributed to the joke, followed by a measurement offunniness. We conducted a study in which participants ratedthe funniness of jokes as well as the funniness of variants ofthose jokes consisting of setting or punchline by alone. Theresults demonstrate that the funniness of the jokes is significantlygreater than that of their components, which is not particularlysurprising, but does show that there is something cognitive takingplace above and beyond the information content delivered inthe joke. A preliminary test to see whether the humor in a jokeviolates the law of total probability appears to suggest that thereis reason to suppose that a quantum inspired model is indeedappropriate.Our QTH is not proposed as an all-encompassing theory ofhumor; for example, it cannot explain why laughter is contagious,or why children tease each other, or why people might findit funny when someone is hit in the face with a pie (andlaugh even if they know it will happen in advance). It aims tomodel the cognitive aspect of humor only. Moreover, despite theintuitive appeal of the approach, it is still rudimentary, and moreresearch is needed to determine to what extent it is consistentwith empirical data. Nevertheless, we believe that the approachpromises an exciting step toward a formal theory of humor. It ishoped that future research will build upon this modest beginning.ETHICS STATEMENTThis research was approved by the Behavioral Research EthicsBoard at theUniversity of British Columbia (OkanaganCampus).AUTHOR CONTRIBUTIONSLG had the idea for the paper and designed and conducted thestudy. Both authors contributed equally to all other aspects of theresearch and the writing of the paper.ACKNOWLEDGMENTSThis work was supported by a grant (62R06523) from theNatural Sciences and Engineering Research Council of Canada.We are grateful to Samantha Thomson who assisted with thedevelopment of the questionnaire and the collection of the datafor the study reported here.SUPPLEMENTARY MATERIALThe Supplementary Material for this article can be foundonline at: http://journal.frontiersin.org/article/10.3389/fphy.2016.00053/full#supplementary-materialREFERENCES1. Veale T, Brone G, Feyaerts K. Humour as the killer-app of language: a viewfromCognitive Linguistics. 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Aberdeen: Springer (2011). p. 13–24.doi: 10.1007/978-3-642-24971-6_345. Pothos EM, Trueblood JS. Structured representations in a quantumprobability model of similarity. J Math Psychol. (2015) 64:35–43.doi: 10.1016/j.jmp.2014.12.001Conflict of Interest Statement: The authors declare that the research wasconducted in the absence of any commercial or financial relationships that couldbe construed as a potential conflict of interest.Copyright © 2017 Gabora and Kitto. This is an open-access article distributedunder the terms of the Creative Commons Attribution License (CC BY). The use,distribution or reproduction in other forums is permitted, provided the originalauthor(s) or licensor are credited and that the original publication in this journalis cited, in accordance with accepted academic practice. No use, distribution orreproduction is permitted which does not comply with these terms.Frontiers in Physics | www.frontiersin.org 10 January 2017 | Volume 4 | Article 53


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