Humor has been called the “killer app” of language [1]; it showcases the speed, playfulness, and flexibility of human cognition, and can instantaneously put people in a positive mood. For over a 100 years scholars have attempted to make sense of the seemingly nonsensical cognitive processes that underlie humor. Despite considerable progress with respect to categorizing different forms of humor (e.g., irony, jokes, cartoons, and slapstick) and understanding what people find funny, there has been little investigation of the question: What kind of formal theory do we need to model the cognitive representation of a joke as it is being understood?

This paper attempts to answer this question with a new model of humor that uses a generalization of the quantum formalism. The last two decades have witnessed an explosion of applications of quantum models to psychological phenomena that feature ambiguity and/or contextuality [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 quantum level 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 nature of quantum probability. While in classical probability theory events are drawn from a common sample space, quantum models define states and variables with reference to a context, represented using a basis in a Hilbert space. This results in phenomena such as interference, superposition and entanglement, and ambiguity with respect to the outcome is resolved with a quantum measurement and a collapse to a definite state.

This makes the quantum inspired approach an interesting new candidate for a theory of humor. Humor often involves ambiguity due to the presence of incongruous schemas: internally coherent but mutually incompatible ways of interpreting or understanding a statement or situation. As a simple example, consider the following pun:

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 formalisms are highly useful for describing cognitive states that entail this form of ambiguity. This paper will propose that the quantum approach enables us to naturally represent the process of “getting a joke.”

We start by providing a brief overview of the relevant research on humor.

Even within psychology, humor is approached from multiple directions. Social psychologists investigate the role of humor in establishing, maintaining, and disrupting social cohesion and social status, developmental psychologists investigate how the ability to understand and generate humor changes over a lifetime, and health psychologists investigate possible therapeutic aspects of humor. This paper deals solely with the cognitive aspect of humor. Much cognitive theorizing about humor assumes that it is 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 the phrase FRUIT FLIES as referring to the insect is incompatible with interpreting it as food traveling through the air. Incongruity is generally accompanied by the violation of expectations and feelings of surprise. While earlier approaches posited that humor comprehension involves the resolution of incongruous frames or scripts [32, 33], the notion of resolution often plays a minor role in contemporary theories, which tend to view the punchline as activating multiple schemas simultaneously and thereby underscoring ambiguity (e.g., 34, 35).

There are computational models of humor detection and understanding (e.g., 36), in which the interpretation of an ambiguous word or phrase changes as new surrounding contextual information is parsed. For example, in the “time flies” joke, this kind of model would shift from interpreting FLIES as a verb to interpreting it as a noun. There are also computational models of humor that generate jokes through lexical replacement; for example, by replacing a “taboo” word with a similar-sounding innocent word (e.g., [37, 38]). These computational approaches to humor are interesting, and occasionally generate jokes that are laugh-worthy. However, while they tell us something about humor, we claim that they do not provide an accurate model of the cognitive state of a human mind at the instant of perceiving a joke. As mentioned above, humor psychologists believe that humor often involves not just shifting from one interpretation of an ambiguous stimulus to another, but simultaneously holding in mind the interpretation that was perceived to be relevant during the set-up and the interpretation that is perceived to be relevant during the punchline. For this reason, we turned to the generalized quantum formalism as a possible approach for modeling the cognitive state of holding two schemas in mind simultaneously.

Classical probability describes events by considering subsets of a common sample space [39]. That is, considering a set of elementary events, we find that some event e occurred with probability p_e. Classical probability arises due to a lack of knowledge on the part of the modeler. The act of measurement merely reveals an existing state of affairs; it does not interfere with the results.

In contrast, quantum models use variables and spaces that are defined with respect to a particular context (although this is often done implicitly). Thus, in specifying that an electron has spin “up” or “down,” we are referring to experimental scenarios (e.g., Stern-Gerlach arrangements and polarizers) that denote the context in which a measurement occurred. This is an important subtlety, as many experiments have shown that it is impossible to attribute a pre-existing reality to the state that is measured; measurement necessarily involves an interaction between a state and the context in which it is measured, and this is traditionally modeled in quantum theory using the notion of projection. The state |Ψ〉 representing some aspect of interest in our system is written as a linear superposition of a set of basis states {|ϕ_i〉} in a Hilbert space, denoted H, which allows us to define notions such as distance and inner product. In creating this superposition we weight each basis state with an amplitude term, denoted a_i, which is a complex number representing the contribution of a component basis state |ϕ_i〉 to the state |Ψ〉. Hence |Ψ〉=∑iai|ϕi〉. The square of the absolute value of the amplitude equals the probability that the state changes to that particular basis state upon measurement. This non-unitary change of state is called collapse. The choice of basis states is determined by the observable, Ô, to be measured, and its possible outcomes o_i. The basis states corresponding to an observable are referred to as eigenstates. Observables are represented by self-adjoint operators on the Hilbert space. Upon measurement, the state of the entity is projected onto one of the eigenstates.

It is also possible to describe combinations of two entities within this framework, and to learn about how they might influence one another, or not. Consider two entities A and B with Hilbert spaces HA and HB. We may define a basis |i〉_A for HA and a basis |j〉_B for HB, and denote the amplitudes associated with the first as aiA and the amplitudes associated with the second as ajB. The Hilbert space in which a composite of these entities exists is given by the tensor product HA⊗HB. The most general state in HA⊗HB has the form

This state is separable if aij=aiAajB. It is inseparable, and therefore an entangled state, if aij≠aiAajB.

In some applications, the procedure for describing entanglement is more complicated than what is described here. For example, it has been argued that the quantum field theory procedure, which uses Fock space to describe multiple entities, gives a kind of internal structure that is superior to the tensor product for modeling concept combination [5]. Fock space is the direct sum of tensor products of Hilbert spaces, so it is also a Hilbert space. For simplicity, this initial application of the quantum formalsm to modeling humor will omit such refinements, but such a move may become necessary in further developments of the model.

Quantum models can be useful for describing situations involving potentiality, in which change of state is nondeterministic and contextual. The concept of potentiality has broad implications across the sciences; for example, every biological trait not only has direct implications for existing phenotypic properties such as fitness, but both enables and constrains potential future evolutionary changes for a given species. The quantum approach been used to model the biological phenomenon of exaptation—wherein a trait that originally evolved for one purpose is co-opted for another (possibly after some modification) [40]. The term exaptation was coined by Gould and Vrba [41] to denote what Darwin referred to as preadaptation¹. Exaptation occurs when selective pressure causes this potentiality to be exploited. Like other kinds of evolutionary change, exaptation is observed across all levels of biological organization, i.e., at the level of genes, tissue, organs, limbs, and behavior. Quantum models have also been used to model the cultural analog of exaptation, wherein an idea that was originally developed to solve one problem is applied to a different problem [40]. For example, consider the invention of the tire swing. It came into existence when someone re-conceived of a tire as an object that could form the part of a swing that one sits on. This re-purposing of an object designed for one use for use in another context is referred to as cultural exaptation. Much as the current structural and material properties of an organ or appendage constrain possible re-uses of it, the current structural and material properties of a cultural artifact (or language, or art form, etc.) constrain possible re-uses of it. We suggest that incongruity humor constitutes another form of exaptation; an ambiguous word, phrase, or situation, that was initially interpreted one way is revealed to have a second, incongruous interpretation. Thus, it is perhaps unsurprising that, as with other forms of exaptation, a quantum model is explored.

A quantum theory of humor (QTH) could potentially inherit several core concepts from previous cognitive theories of humor while providing a unified underlying model. Considering the past work discussed in Section 2, it seems reasonable to focus on the notion that cognitive humor involves an ambiguity brought on by the bisociation of internally consistent but mutually incongruous schemas. Thus, cognitive humor appears to arise from the double think that is brought about by being forced to reconsider some currently held interpretation of a joke in light of new information: a frame shift. Such an insight opens humor upto quantum-like models, as a frame shift of an ambiguous concept is well modeled by the notion of a quantum superposition described using two sets of incompatible basis states within some underlying Hilbert space structure.

In what follows we sketch out a preliminary quantum inspired model of humor and discuss what would be required for a full-fledged formal QTH. Next, we outline a study aimed at discovering whether humor behaves in a quantum-like manner. The last section discusses how the QTH opens up avenues for future investigation in a field that to date has not been well modeled.

Returning to the question raised by Equation (7), a QTH should be justified by considering whether humor does indeed violate the Law of Total Probability (LTP) [3]. However, the complexity of language makes it difficult to test how humor might violate the LTP using a method similar to those followed for decision making [11]. Past work on humor is unlikely to yield the data required to perform tests such as this. For example, we currently have no experimental understanding of how the semantics of a joke interplays with its perceived funniness. It seems reasonable to suppose that the two are related, but how? We are not aware of any data that provide a way to evaluate this relationship. This is problematic, as there are a number of interdependencies in the framing of a joke that make it difficult to construct a model (even before considering factors such as the context in which the joke is made, and the socio-cultural background of the teller and the listener). In this section we present results from an exploratory study designed to start unpacking whether humor should indeed be considered within the framework of quantum cognition. As an illustrative example, consider the following joke:

As with the joke discussed in Section 4.3, the humor arises from the 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 a preposition, but the second frame (F2, the punchline), leads one to interpret FRUIT FLIES as a noun and LIKE as a verb. A QTH must be able to explain how the funniness of the joke depends upon a shift in the semantic understanding of the two frames, F1 and F2.

We now outline a preliminary study that has helped us to explore the state space of humor.

It would appear that there is some support for the hypothesis that the humor arising from bisociation can be modeled by a quantum inspired approach. Furthermore, the experimental results presented in section 5 suggest that this model might more appropriate than one grounded in classical probability. However, much work remains to be completed before we can consider these findings anything but preliminary.

Firstly, the model presented in Section 4 is simple, and will need to be extended. While an extension to more senses for an ambiguous element of a joke is straightforward with a move to higher dimensions, the model is currently not well suited to the set of variants discussed in Section 5.3. A model that can show how they interrelate, and how their underlying semantics affects the perceived humor in a joke is desirable. Furthermore, the funniness of the joke was simplistically represented by a projection onto the “funny”/“not funny” axis. A more theoretically grounded treatment of the Likert data is desirable. For example, the current threshold value of 2.5 was chosen somewhat arbitrarily [although could be justified by a consideration of the mean values for funniness scores reported in the Appendix (Supplementary Material)—see Table 2]. A more systematic way of considering the Likert scale measures to allow for a normalization of funniness ratings at the level of an individual is also desirable. As a highly subjective phenomenon, funniness is liable to be judged by different individuals inconsistently and so it will be important that we control for this effect in comparing Likert responses among individuals.

Considering experimental results, the sample size of the data set is somewhat small (85 participants), although our funniness ratings appear to be reasonably stable for this cohort. A more concerning problem revolves around the construction of a LTP relationship for our simple model. There are many alternative ways in which a LTP could be constructed for puns, and more sophisticated models need to be investigated before we can be confident that our results conclusively demonstrate that humor must be modeled using a quantum inspired approach. In particular, we require a more sophisticated method that facilitates the extraction of data about the semantics attributed by a participant to a joke. A two stage protocol may be the answer for obtaining the necessary semantic information for a more rigorously founded test of the violation of LTP. It would be useful to construct a systematic study of the manner in which adjusting the congruence of the set-ups and punchlines influences perception of the joke. The quantum inspired semantic space approaches of Van Rijsbergen [13] and Widdows [43] may prove fruitful in this regard, as they would facilitate the creation of similarity models such as those explored by Aerts et al. [44] and Pothos and Trueblood [45].

In summary, humor is complex, and it will take an ongoing program of research to understand the interplay between the semantics of a joke and its perceived funniness. However, at this point we might pause to consider the broader question of why humor might be better modeled by a quantum inspired approach than by one grounded in classical probability? To this end we return to the discussion of Section 3. As we saw, the humor of a pun involves the bisociation of incongruent frames, i.e., re-viewing a setup frame in light of new contextual information provided by a punchline frame. Moreover, the broader contextuality of humor means that even the funniest of jokes can become markedly unfunny if delivered in the wrong 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 emerges from an interaction between the underlying nature of the joke, the cognitive state of the listener, and other social and environmental factors. This makes the quantum formalism an excellent candidate for modeling humor, as this interaction is well described by the concept of a vector state embedded in a space which is represented using basis states that can be reoriented according to the framing of the joke. However, this paper only provides a preliminary indication that a QTH may indeed provide a good theoretical underpinning for this complex process. Much more work remains to be done.

This paper has provided a first step toward a quantum theory humor (QTH). We constructed a model where frame blends are represented in a Hilbert space spanned by two sets of basis states, one representing the ambiguous framing of a joke, and the other representing funniness. The process of “getting a joke” then consists of a dual stage scenario, where the cognitive state of a person evolves toward a re-interpretation of the meaning attributed to the joke, followed by a measurement of funniness. We conducted a study in which participants rated the funniness of jokes as well as the funniness of variants of those jokes consisting of setting or punchline by alone. The results demonstrate that the funniness of the jokes is significantly greater than that of their components, which is not particularly surprising, but does show that there is something cognitive taking place above and beyond the information content delivered in the joke. A preliminary test to see whether the humor in a joke violates the law of total probability appears to suggest that there is reason to suppose that a quantum inspired model is indeed appropriate.

Our QTH is not proposed as an all-encompassing theory of humor; for example, it cannot explain why laughter is contagious, or why children tease each other, or why people might find it funny when someone is hit in the face with a pie (and laugh even if they know it will happen in advance). It aims to model the cognitive aspect of humor only. Moreover, despite the intuitive appeal of the approach, it is still rudimentary, and more research is needed to determine to what extent it is consistent with empirical data. Nevertheless, we believe that the approach promises an exciting step toward a formal theory of humor. It is hoped that future research will build upon this modest beginning.

This research was approved by the Behavioral Research Ethics Board at the University of British Columbia (Okanagan Campus).

LG had the idea for the paper and designed and conducted the study. Both authors contributed equally to all other aspects of the research and the writing of the paper.