Liane GaboraKirsty Kitto Department of Psychology, University of British
Columbia
Fipke Centre for Innovative Research, 3247 University Way, Kelowna, BC
Canada, V1V 1V7
<EMAIL_ADDRESS>
https://people.ok.ubc.ca/lgabora/Science and Engineering Faculty, Mathematical
Sciences
Queensland University of Technology, Brisbane, Australia
<EMAIL_ADDRESS>
http://staff.qut.edu.au/staff/kittok/

Reference:
Gabora, L. & Kitto, K. (2016). Towards a quantum theory of humour. Frontiers
in Physics (section: Interdisciplinary Physics), 4(53).
doi: 10.3389/fphy.2016.00053

# Towards a Quantum Theory of Humour

###### Abstract

This paper proposes that cognitive humour can be modelled using the
mathematical framework of quantum theory, suggesting that a Quantum Theory of
Humour (QTH) is a viable approach. We begin with brief overviews of both
research on humour, and the generalized quantum framework. We show how the
bisociation of incongruous frames or word meanings in jokes can be modelled as
a linear superposition of a set of basis states, or possible interpretations,
in a complex Hilbert space. The choice of possible interpretations depends on
the context provided by the set-up versus the punchline of a joke. We apply
QTH first to a verbal pun, and then consider how this might be extended to
frame blending in cartoons. An initial study of 85 participant responses to 35
jokes (and a number of variants) suggests that there is reason to believe that
a quantum approach to the modelling of cognitive humour is a viable new avenue
of research for the field of quantum cognition.

##  1 Introduction

Humour 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 hundred years
scholars have attempted to make sense of the seemingly nonsensical cognitive
processes that underlie humour. Despite considerable progress with respect to
categorizing different forms of humour (e.g., such as 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 at the instant it is understood?

This paper attempts to answer this question with a new model of humour that
uses a generalization of the quantum formalism. The last two decades have
witnessed an explosion of applications of these formalisms to psychological
phenomena that feature ambiguity and/or contextuality [2, 3, 4]. Many
different psychological phenomena have been studied, including the combination
of words and concepts [5, 6, 7, 8, 9, 10], similarity and memory [11, 12],
information retrieval [13, 14], decision making and probability judgement
errors [15, 16, 17, 18, 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; they draw solely on abstract formal structures
that, as it happens, found their first application in quantum mechanics. The
common approach is to 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
behaviour 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 humour. Humour 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:

> “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 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 humour.

##  2 Brief Background in Humour Research

Even within psychology, humour is approached from multiple directions. Social
psychologists investigate the role of humour in establishing, maintaining, and
disrupting social cohesion and social status, developmental psychologists
investigate how the ability to understand and generate humour changes over a
lifetime, and health psychologists investigate possible therapeutic aspects of
humour. This paper deals solely with the cognitive aspect of humour. Much
cognitive theorizing about humour 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 travelling through the
air. Incongruity is generally accompanied by the violation of expectations and
feelings of surprise. While earlier approaches posited that humour
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., Martin [34]; McGraw
and Warren [35]).

There are computational models of humour detection and understanding (e.g.,
Reyes et al. [36]), in which the interpretation of an ambiguous word or phrase
generally 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 humour that generate jokes through lexical
replacement; for example, by replacing a ‘taboo’ word with a similar-sounding
innocent word (e.g.,[37];Valitutti et al. [38]). These computational
approaches to humour are interesting, and occasionally generate jokes that are
laugh-worthy. However, while they tell us something about humour, 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, humour
psychologists believe that humour 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 modelling the cognitive state of holding two schemas in mind
simultaneously.

##  3 Brief Background in Generalized Quantum Modeling

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 modeller. 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 modelled in quantum theory using the
notion of projection. The _state_ $|\Psi\rangle$ representing some aspect of
interest in our system is written as a linear superposition of a set of _basis
states_ $\\{|\phi_{i}\rangle\\}$ in a _Hilbert space_ $\mathcal{H}$ 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 $|\phi_{i}\rangle$ to the state $|\Psi\rangle$. Hence
$|\Psi\rangle=\sum_{i}a_{i}|\phi_{i}\rangle$. 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_ , $\hat{O}$, 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 $\mathcal{H_{A}}$ and
$\mathcal{H_{B}}$. We may define a basis ${|i\rangle_{A}}$ for
$\mathcal{H_{A}}$ and a basis ${|j\rangle_{B}}$ for $\mathcal{H_{B}}$, and
denote the amplitudes associated with the first as $a_{i}^{A}$ and the
amplitudes associated with the second as $a_{j}^{B}$. The Hilbert space in
which a composite of these entities exists is given by the tensor product
$\mathcal{H_{A}}\otimes\mathcal{H_{B}}$. The most general state in
$\mathcal{H_{A}}\otimes\mathcal{H_{B}}$ has the form

$|\Psi\rangle_{AB}={\sum}_{i,j}a_{ij}|i\rangle_{A}\otimes|j\rangle_{B}\ $ (1)

This state is separable if $a_{ij}=a_{i}^{A}a_{j}^{B}$. It is inseparable, and
therefore an entangled state, if $a_{ij}\neq a_{i}^{A}a_{j}^{B}$.

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 modelling 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 modelling
humour 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
_preadaptation_.111The terms _exaptation_ , _preadaptation_ and _co-option_
are often used interchangeably. 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 artefact (or language, or art
form, etc.) constrain possible re-uses of it. Here, we suggest that
incongruity humour 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.

##  4 A Quantum Inspired Model of Humour

A quantum theory of humour (QTH) could potentially inherit several core of
from previous cognitive theories of humour while providing a unified
underlying model. Considering the past work discussed in section 2, it seems
reasonable to focus on the notion that cognitive humour involves an ambiguity
brought on by the bisociation of internally consistent but mutually
incongruous schemas. Thus, cognitive humour appears to arise from the double
think that is brought about by being forced to reconsider some currently held
interpretation of a joke within the light of new information: a frame shift.
Such an insight opens up humour to quantum-like models, as a frame shift of an
ambiguous concept is well modelled 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 shall introduce some features that would be required in a
formal QTH as we start to sketch out a preliminary quantum inspired model of
humour. This initial model provided enough insight to formulate an
experimental procedure aimed at discovering whether humour was likely to
behave in a quantum-like manner. A preliminary study is introduced in section
5.3, which has provided insights and opened up a rich set of avenues for
future investigation. Thus, this paper is a first step towards the development
of a formal theory for a field that to date has not been well modelled.

###  4.1 The Mathematical Structure of QTH

We start our journey toward a QTH by building upon an existing model of
conceptual combination first proposed by Gabora and Aerts [8]: the
State–COntext–Property (SCOP) model. As per the standard approach used in most
quantum-like models of cognition, $|\Psi\rangle$ represents the state of an
ambiguous element, be it a word, phrase, object, or something else, and its
different possible interpretations are represented by basis states. Core to
the SCOP model is a treatment of the context in which every measurement of a
state occurred, and the resultant property that was measured. These three
variables are stored as a triple in a lattice.

####  4.1.1 The State Space.

Following Aerts and Gabora [6], the set of all possible interpretation states
for the ambiguous element of a joke is given by a state space $\Sigma$.
Specific interpretations of a joke are denoted by
$|p\rangle,|q\rangle,|r\rangle,\dots\in\Sigma$ which form a basis in a complex
Hilbert space $\mathcal{H}$. Before the ambiguous element of the joke is
resolved, it is in a state of potentiality, represented by a superposition
state of all possible interpretations. Each of these represents a possible
understanding arising due to activation of a schema associated with a
particular interpretation of an ambiguous word or situation. The
interpretations that are most likely are most heavily weighted. The amplitude
term associated with each basis state represented by a complex number
coefficient $a_{i}$ gives a measure of how likely an interpretation is given
the current contextual information available to the listener. We assume that
all basis states have unit length, are mutually orthogonal, and are complete,
thus $\sum_{i}|a_{i}|^{2}=1$.

####  4.1.2 The Context.

In the context of a traditional verbal joke the context consists primarily of
the setup, and the setup is the only contextual element considered in the
study in Section 4. However, it should be kept in mind that several other
contextual factors not considered in our analysis can affect perceived
funniness. Prominent amongst these is the delivery; the way in which a joke is
delivered can be everything when it comes to whether or not it is deemed
funny. Other factors include the surroundings, the person delivering the joke,
the power relationships among different members of the audience, and so forth.

As a first step, we might represent the set of possible contexts for a given
joke as $c_{i}\in\mathcal{C}$. Each possible interpretation of a joke comes
with a set $f_{i}\in\mathcal{F}$ of features (or properties), which may be
weighted according to their relevance with respect to this contextual
information. The _weight_ (or renormalized applicability) of a certain
property given a specific interpretation $|p\rangle$ in a specific context
$c_{i}\in\mathcal{C}$ is given by $\nu$. For example, $\nu(p,f_{1})$ is the
weight of feature ${f_{i}}$ for state $|p\rangle$, which is determined by a
function from the set $\Sigma\times{\mathcal{F}}$ to the interval $[0,1]$. We
write:

$\displaystyle\ \nu:\Sigma\times{\mathcal{F}}$ $\displaystyle\rightarrow[0,1]$
(2) $\displaystyle(p,f_{i})$ $\displaystyle\mapsto\nu(p,f_{i}).$

####  4.1.3 Transition probabilities.

A second function $\mu$ describes the transition probability from one state to
another under the influence of a particular context. For example, $\mu$(q, e,
p) is the probability that state $|p\rangle$ under the influence of context
$c_{i}$ changes to state $|q\rangle$. Mathematically, $\mu$ is a function from
the set $\Sigma\times\mathcal{C}\times\Sigma$ to the interval $[0,1]$, where
$\mu(q,e,p)$ is the probability that state $|p\rangle$ under the influence of
context $|e\rangle$ changes to state $|q\rangle$. We write:

$\displaystyle\mu:\Sigma\times\mathcal{C}\times\Sigma$
$\displaystyle\rightarrow[0,1]$ (3) $\displaystyle(q,e,p)$
$\displaystyle\mapsto\mu(q,e,p).$

Thus, a first step towards a full quantum model of humour consists of the
3-tuple $(\Sigma,\mathcal{C},\mathcal{F})$, and the functions $\nu$ and $\mu$.
However, we have yet to address the core questions that should be asked of any
cognitive theory of humour: what is the underlying cognitive model of the
funniness of a joke?

###  4.2 The Humour of a Joke

As the listener hears a joke, more context is provided, and in our model their
understanding (i.e., the cognitive state of the listener) evolves according to
the transition probabilities associated with the cognitive state and the
emerging context. When the listener interprets the joke the listener is
perceiving a bisociation of meaning. That is, the first interpretation that
the listener ascribes to the joke changes because two meanings are possible
for the core concept in the joke. A projective measurement onto a funniness
frame is the mechanism that we use to model the likelihood that a given joke
is considered funny.

Thus, in our model, funniness plays the role of a measurement operator, and it
is affected by the shift that occurs in the understanding of a joke with
respect to two possible framings: one created by the setup, and one by the
punchline. The probability of a joke being regarded as funny or not is
proportional to the projection of the individual’s understanding of the joke
($|\Psi\rangle$) onto a basis representing funniness. This means that the
probability of a joke being considered as funny, $p_{F}$ is given by a
projection onto the $|1\rangle$ axis in $\mathcal{H}_{F}^{2}$, a 2 dimensional
Hilbert sub-space where $|0\rangle$ represents ‘not funny’ and $|1\rangle$
represents ‘funny’.

$p_{F}=||1\rangle\langle 1|\Psi\rangle|^{2}$ (4)

Similarly, the probability of a joke being regarded as not funny is
represented by

$p_{\bar{F}}=||0\rangle\langle 0|\Psi\rangle|^{2}.$ (5)

Note that $|\Psi\rangle$ evolves as the initial conceptualisation of the joke
is reinterpreted with respect to the frame of the punchline. This is a
difficult process to model, and we consider the work in this paper to be an
early first step towards an eventually more comprehensive theory of humour
that includes predictive models.

To start in this journey towards a QTH, we will now present two examples in
which two specific instances of humour are considered within the perspective
of this basic quantum 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 the significant complexity
of humour, and the difficulties associated with creating a mathematical model
of this important human phenomenon.

###  4.3 Example 1: A Pun

Consider the pun: “Why was 6 afraid of 7? Because 789.” The humour of this pun
hinges on the fact that the pronunciation of the number EIGHT, a noun, is
identical to that of the verb ATE. We refer to this ambiguous word, with its
two possible meanings, as EYT. An individual’s interpretation of the word EYT
is represented by $|\Psi\rangle$, a vector of length equal to 1. This is a
linear superposition of basis states in the semantic sub-space
$\mathcal{H}^{2}_{M}$ which represents possible states (meanings) of the word
EYT: EIGHT or ATE.222We acknowledge that other interpretations are possible,
and so this is a simplified model. It is straightforward to extend the model
into higher dimensions by adding further interpretations as basis states. The
interpretation of EYT as a noun, and specifically the number EIGHT, will be
denoted by the unit vector $|n\rangle$. The verb interpretation, ATE, is
denoted by the unit vector $|v\rangle$. The set $\\{|n\rangle,|v\rangle\\}$
forms a basis in $\mathcal{H}^{2}_{M}$. Thus, we have now expanded our
original 2-dimensional funniness space with an additional 2-dimensional
semantic space, where the full space
$\mathcal{H}^{4}=\mathcal{H}^{2}_{F}\otimes\mathcal{H}^{2}_{M}$. We note that
these two spaces should not be considered as mutually orthogonal, but that
they will overlap. If they were orthogonal then the funniness of a joke would
be independent of the interpretation that a person attributes to it.

With this added mathematical structure, we can represent the interpretation of
the joke as a superposition state in $\mathcal{H}^{2}_{M}$

$|\Psi\rangle=a_{n}|n\rangle+a_{v}|v\rangle,$ (6)

where $a_{n}$ and $a_{v}$ are amplitudes which, when squared, represent the
probability of a listener interpreting the joke in a noun or a verb form
($|n\rangle$ and $|v\rangle$) respectively. This state is depicted in Fig.
1(a), which shows a superposition state in the semantic space. When given no
context in the form of the actual presentation of the joke, these amplitudes
represent the prior likelihood of a listener interpreting the uncontextualized
word (i.e. EYT) in either of the noun or verb senses (e.g. a free association
probability, see [12] for a review). However, we would expect to see these
probabilities evolving throughout the course of the pun as more and more
context is provided (in the form of additional sentence structure). Throughout
the course of the joke, the state vector $|\Psi\rangle$ therefore evolves to a
new position in $\mathcal{H}^{4}$.

$|\Psi\rangle$$|n\rangle$$|v\rangle$

$|\Psi\rangle$$|0\rangle$$|1\rangle$

$|\Psi\rangle$$|0\rangle$$|1\rangle$$|n\rangle$$|v\rangle$

(a) (b) (c)

Figure 1: The humour of a joke can be explained as arising from a measurement
process that occurs with respect to two incompatible frames. Using the example
of the pun, (a) the meaning of the set-up is reinterpreted with EYT updating
towards the interpretations ATE. (b) Funniness is then treated as a
measurement, with the probability of funniness being judged with respect to a
projection on the $\\{|0\rangle,|1\rangle\\}$ basis. In this case there is a
large probability of the joke being considered funny due to the dominant
component of the projection of $|\Psi\rangle$ lying on the $|1\rangle$ axis.
(c) The cognitive state of the subject then collapses to the observed state
(i.e. funny or not).

Since the set-up of the joke,“Why was 6 afraid of 7?”, contains two numbers,
it is likely that the numbers interpretation of EYT is activated (a situation
represented in Figure 1(a)). The listener is biased towards an interpretation
of EYT in this sense, and so we would expect that $a_{n}>>a_{v}$. However, a
careful listener will feel confused upon considering this set-up because we do
not think of numbers as beings that experience fear. This keeps the
interpretation of EYT shifted away from an equivalence with the eigenvector
$|n\rangle$. As the joke unfolds, the predator interpretation that was hinted
at in the set-up by the word “afraid”, and reinforced by “789”, activates a
more definite alternative meaning, ATE represented by $|v\rangle$. This
generates an alternative interpretation of the punchline: that the number 7
ate the number 9. The cognitive state $|\Psi\rangle$ has evolved to a new
position in $\mathcal{H}^{4}$, a scenario that is represented in Figure 1(b).
At this point a measurement occurs: the individual either considers the joke
as funny or not within the context represented by the funniness sub space
$\mathcal{H}^{2}_{F}$, and a collapse to the relevant funniness basis state
occurs (see Figure 1(c)). Note that this final state still contains a
superposition within the meaning subspace $H_{M}^{2}$ — the funniness
judgement merely shifts the interpretation of the joke, it does not eliminate
the bisociation. Rather, it depends upon it.

If we consider the set of properties associated with EYT then we would expect
to see two very different prototypical characteristics associated with each
interpretation. For example, the EIGHT interpretation is difficult to map into
properties such as ‘food’ denoted $f_{1}$, and ‘not living’ denoted $f_{2}$
(since when something is eaten it is usually no longer alive). Because ‘food’
and ‘not living’ are not properties of EIGHT, $\nu(p,f_{0})<<\nu(n,f_{0})$,
and similarly $\nu(p,f_{1})<<\nu(n,f_{1})$. However, ‘food’ and ‘not living’
are properties of EYT, $\nu(p,f_{0})<<\nu(v,f_{0})$, and similarly
$\nu(p,f_{1})<<\nu(v,f_{1})$.

We can now start to construct a model of humour that could be 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 should be equal to the sum of the probabilities of it under
a set of more specific conditions. Thus, considering a funniness observable
$\hat{O}_{F}$ (with eigenstates $\\{|1\rangle,|0\rangle\\}$ and the semantic
observable $\hat{O}_{M}$ (with a simplified two eigenstate structure
$\\{|M\rangle,|\bar{M}\rangle\\}$ representing two possible meanings that
could be attributed to the joke). We can take the spectral decomposition of
$\hat{O}_{M}=m|M\rangle\langle M|+\bar{m}|\bar{M}\rangle\langle\bar{M}|$,
where $m,\bar{m}$ are eigenvalues of the two eigenstates
$\\{|M\rangle,|\bar{M}\rangle\\}$. Doing this, we should find that if this
system satisfies the LTP then the probability of the joke being judged as
funny is equal to the sum of the probability of it being judged funny _g_ iven
either semantic interpretation

$p(F)=p(|1\rangle)=p(M)\cdot p(F|M)+p(\bar{M})\cdot p(F|\bar{M}).$ (7)

We can manipulate the interpretation that a participant is likely to attribute
to a joke by changing the semantics of the joke itself. Thus, changing the
joke should change the semantics and so affect the humour that is attributed
to the joke. We shall return to this idea in Section 5.

This section has demonstrated that a formal approach to concept interactions
which has been previously shown to be consistent with human data [5] can be
adapted to the simultaneous perception of incongruous meanings of an ambiguous
word or phrase in the understanding of a pun. What other aspects of cognitive
humour might this new mathematical apparatus be applied to?

###  4.4 Example 2: A Frame Blend

Although our first example used a pun for simplicity, we believe that quantum
inspired models can be fruitfully applied to more elaborate forms of humour,
such as jokes involving incompatible frames or scripts. Our second example is
a cartoon that was initially analysed in terms of the concept of a frame
blend, which involves the merging of incongruous frames [42]. The cartoon is
shown in Figure 2(a) and the frame blend analysis is shown in Figure 2(b).

(a) (b)

Figure 2:  An example of a Frame blend in the QTH. (a) An Off the Leash
cartoon by W. B. Park that blends two frames: a human courtship frame and an
octopus frame. (b) An illustration of how the human courtship frame and the
octopus frame map onto one another in the frame blend. (Both examples first
appeared in [42]).

In a QTH, the two interpretations of the incongruous situation represented by
the scene in Figure 2, as a dating scene and as an octopus scene, would be
designated by the unit vectors $\\{|d\rangle,|o\rangle$}. The cognitive state
of perceiving the blended frames is represented as a superposition of the two
frames, however the underlying dynamics behind this joke are likely to be
different. That is, rather than being led “down the garden path” by the setup
and subsequent re-interpretation in light of the punchline, in this scenario
the humour appears to result from the immediate simultaneous presentation of
seemingly incompatible frames, which creates a similar tension or bisociation
as eventually arose in the previous example. As with phenomena such as
conceptual combination, in this scenario there are likely to be constraints on
how the frames can be successfully blended, and it will be necessary to
consider this when constructing a model of humour for this scenario. We
reserve further exploration of this interesting class of humour for future
work.

##  5 Probing the State Space of Humour

Returning to the question raised by equation (7), a QTH should be justified by
considering whether humour does indeed violate the Law of Total Probability
(LTP) [3]. However, the complexity of language makes it difficult to test how
humour might violate the LTP using a method similar to those followed for
decision making [11]. The model discussed above brings us to a position where
past work on humour is unlikely to yield the data that is 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 sets that provide a way in which 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 humour should indeed be considered within the framework of quantum
cognition. As an illustrative example, consider the following joke:

> $V_{O}$: “Time flies like an arrow. Fruit flies like a banana.”

As with the joke discussed in section 4.3, the humour 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 humour.

###  5.1 Stimuli

We collected a set of 35 jokes and for each joke we developed a set of joke
variants. A $V_{S}$ variant consisted of the set-up only for the original
($V_{O}$ joke). Thus the $V_{S}$ variant of the $V_{O}$ joke is

> $V_{S}$: “Time flies like an arrow.”

A $V_{P}$ variant consists of the original punchline only. Thus the $V_{P}$
variant of the $V_{O}$ joke is

> $V_{P}$: “Fruit flies like a banana.”

We then considered the notion of a congruent punchline as one that does not
introduce a new interpretation or context for an ambiguous element of the set-
up (or punchline). Congruence was achieved by modifying the set-up to make it
congruent with the punchline, or by modifying the punchline to make it
congruent with the set-up. Thus, if the set-up makes use of a noun then a
congruent modification would still do this (and similarly for the punchline).

A $V_{CP}$ variant consists of the original set-up followed a congruent
version of the punchline. Thus a $V_{CP}$ variant of the $V_{O}$ joke is:

> $V_{CP}$: “Time flies like an arrow; time flies like a bird.”

A $V_{CS}$ variant consists of the original punchline preceded by a congruent
version of the set-up. Thus a $V_{CS}$ variant of the $V_{O}$’ joke is

> $V_{CS}$: “Horses like carrots; fruit flies like a banana.”

For some jokes we had a fifth kind of variant. A $V_{IS}$ variant consists of
the original set-up followed an incongruent version of the punchline that we
believed was comparable in funniness to the original. Thus considering the
joke discussed in section 4.3:

> $V_{O}$: “Why was 6 afraid of 7? Because 789.”

A $V_{IS}$ variant of this joke is:

> $V_{IS}$: “Why was 6 afraid of 7? Because 7 was a six offender.”

Thus the stimuli consisted of a questionnaire containing original jokes, and
the above variants presented in randomized order. The complete collection of
jokes and their variants is presented in the Appendix.

###  5.2 Participants

The participants in this study were 85 first year undergraduate students
enrolled in an introductory psychology course at the University of British
Columbia (Okanagan campus). They received partial course credit for their
participation.

###  5.3 Procedure

Participants signed up for the study using the SONA recruitment system, and
subsequently responded at their convenience to an online questionnaire hosted
by FluidSurveys. They were informed that the study was completely voluntary,
and that they were free to withdraw from the study at any point in time. They
were also informed that the researcher would not have any knowledge of who
participated in the study, and that their participation would not affect their
standing in the psychology class or relationship with the university.
Participants were told that the purpose of the study was to investigate
humour, and to help contribute to a better understanding the cognitive process
of ‘getting’ a joke. Participants were asked to fill out consent forms. If
they agreed to participate, they were provided a questionnaire consisting of a
series of jokes and joke variants (as described above) and asked to rate the
funniness of each using a Likert scale, from 1 (not funny) to 5 (hilarious).
The questionnaire took approximately 25 minutes to complete. They received
partial course credit for their participation.

###  5.4 Results

The mean funniness ratings across all participants for the entire collection
of jokes and their variants (as well as the jokes and variants themselves) is
provided in the Appendix. Table 5.4 provides a summary of this information
(the mean funniness rating of each kind of joke variant across all
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 to be funny: Incongruent Setup ($IS$) (mean
funniness = 2.37) and Incongruent Punchline ($IP$) (mean funniness = 2.12).
Next in funniness were the jokes that had been modified to eradicate the
incongruency and thus the source of the humour: Congruent Setup ($CS$) (mean
funniness = 1.41) and Congruent Punchline ($CP$) (mean funniness = 1.47). The
joke fragments without a counterpart–i.e., either Setup ($S$) or Punchline
($P$) alone–were considered least funny of all (the mean funniness of both was
1.22). The dataset is entirely consistent with the view that the humour
derives from incongruence due to bisociation.

Joke Variant | O | S | P | CS | CP | IS | IP
---|---|---|---|---|---|---|---
Mean Funniness | 2.70 | 1.22 | 1.22 | 1.41 | 1.47 | 2.37 | 2.12

Table 1.  The mean funniness ratings across all participants and all joke sets
for each kind of joke variant. O refers to Original; S refers to Set-up only;
P refers to Punchline only; CS refers to Congruent Set-up; CP refers to
Congruent Punchline; IS refers to Incongruent Set-up; IP refers to Incongruent
Punchline.

###  5.5 Towards a test of the QTH

Recall that the Law of Total Probability (LTP) as represented by equation (7)
suggests that the mean funniness of a joke should be equal to the sum of its
funniness as judged under all possible semantic interpretations. This is not
an equality that we can directly test given our current understanding of
language and how it might interplay with humour. However, the dataset reported
here gives us some initial ways in which to consider this question. With a
methodology for converting the Likert scale ratings into projective
measurements of a a joke being funny or not, we can start to consider the
relative frequency that an original joke is judged as funny and comparing this
result with the individual components.

We start by translating the Likert scale responses into a simplified
measurement of funniness, by mapping the funniness ratings into a designation
of funny or not. In order to run a quick comparison between the relative
frequencies that participants decided the full joke ($V_{O}$) was funny when
compared to the simple components of the joke ($V_{S}$ and $V_{P}$), we took
the mean value of the components for each subject. Given that puns are not
generally considered particularly funny (a result backed up by our participant
ratings) we used a fairly low threshold value of 2.5 (i.e. if the mean was
less than 2.5 then the components were judged as unfunny, and vice versa).
Exploring the results of this mapping gives us the data reported in Figure 3
for the $V_{O}$, $V_{S}$ and $V_{P}$ variants of the jokes, listing the
frequency at which participants judged the joke and subcomponents funny. A
mean value for the joke fragments is also presented. All data uses confidence
intervals at the 95% level.

Figure 3: A comparison of the frequency with which a specific joke and its
fragments are considered funny for participants in the pilot trial (using a
threshold value of 2.5, n=85). A mean of the set-up and the punchline variants
($V_{S}$ and $V_{P}$) is also given. Confidence intervals are set at 95%.

We see a significant discrepancy between the funniness of the original and the
combined funniness of its components. This is not a terribly surprising
result, jokes are not funny when the set-up is not followed by the punchline,
and participants usually rated $V_{S}$ and $V_{P}$ variants as unfunny (i.e.
scoring them at 1). Table LABEL:tab:long in the Appendix shows that in the
participant pool of 85, the set-up and punchline variants of the joke rarely
had a mean funniness rating above 1.5. However, to extract a violation of the
LTP for this scenario, we would need to construct expressions such as the
following

$p(F)=p(EIGHT).p(F|EIGHT)+p(ATE).p(F|ATE).$ (8)

How precisely could such a relationship be tested? Two forms of data are
required to test whether the simple puns used in our experiment actually
violate the LTP:

  1. 1.

Funniness ratings: These are the probabilities regarding the probability that
different components of the joke are considered funny (the whole joke
($p(F)$); just the setup ($p(F|EIGHT)$); and just the punchline ($p(F|ATE)$);
and

  2. 2.

Semantic probabilities: These list the probability of EYT being 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 funniness ratings above. How
might we obtain data for the semantic probabilities? First we must consider
the precise interpretation of what these probabilities might actually be.
Firstly, we note that it seems likely participants will interpret just a set-
up or a punchline in the sense that the fragment represents. The bisociation
that humour relies upon is not present for a fragment, and so a person hearing
a fragment will be primed by its surrounding context towards interpreting an
ambiguous word in precisely the sense intended for that fragment. Indeed, the
incongruity that results from having to readjust the interpretation of the
joke, and the resulting bisociation, lies at the very base of the humour that
arises. Free association probabilities will not give these values. To test the
LTP, it would be necessary to extract information about how a participant is
interpreting core terms in the joke as it progresses; some form of
nondestructive measurement is required, and a new experimental protocol will
have to be defined. We reserve this for future work.

However, the significant difference between the rated funniness of the
fragments and that of the original joke allows us to formulate an alternative
mechanism for testing equations of the form (7) and (8). We can do this by
asking whether there is _any_ way in which the semantic probabilities could
have values that would satisfice the LTP? An examination of Figure 3 for the
setup and punchline variants of the jokes suggests that there is no way in
which to chose semantic probabilities that will satisfy the LTP. Thus, we have
preliminary evidence that humour should perhaps be treated using a quantum
inspired model.

##  6 Discussion

It would appear that there is some support for the hypothesis that the humour
arising from bisociation can be modelled 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 different variants discussed in section 5.3. A
model that can show how they interrelate, and how their underlying semantics
affects the perceived humour 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 — see Table
LABEL:tab:long). A more systematic way of considering the Likert scale
measures to allow for a normalisation 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 feel confident that
our results do indeed demonstrate that humour _must_ be modelled 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 and so providing 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], Widdows [43] may
prove fruitful in this case, as they would facilitate the creation of
similarity models such as those explored by Aerts et al. [44], Pothos and
Trueblood [45].

In summary, humour is complex, and it will take an ongoing program of research
to gradually 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_ humour might be better modelled 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 humour 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 humour 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 modelling
humour, 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.

##  7 Conclusions

This paper has provided a first step towards a quantum theory humour (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 towards 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 humour in
a joke violates the law of total probability appears to suggest that there is
some reason to suppose that a quantum inspired model is indeed appropriate.

Our QTH is not proposed as an all-encompassing theory of humour; 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 humour 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 humour. It is hoped that future research will build upon this modest
beginning.

## Acknowledgements

This work was supported by a grant (62R06523) from the Natural Sciences and
Engineering Research Council of Canada. We are grateful to Samantha Thomson
who assisted with the development of the questionnaire and the collection of
the data for the study reported here.

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## Appendix

Table 2: Mean funniness ratings across all participants for the entire collection of jokes and their variants. O refers to Original; S refers to Set-up only; P refers to Punchline only; CS refers to Congruent Set-up; CP refers to Congruent Punchline; IS refers to Incongruent Set-up; IP refers to Incongruent Punchline. The CS, CP, IS, and IP data was not included in this analysis, but it is clearly consistent with the hypothesis that incongruency is important to humour. Joke Set | Type | Joke | Funniness
---|---|---|---
1 | O |  Why was 6 afraid of 7? Because 7, 8, 9. | 2.62
1 | S |  Why was 6 afraid of 7? | 1.00
1 | P |  Because 7, 8, 9. | 1.43
1 | IS |  Why was the child afraid of getting older? Because 7, 8, 9. | 2.33
1 | IP |  Why was 6 afraid of 7? Because 7 is an odd number. | 2.90
2 | O |  What do you call someone else’s cheese? Nacho cheese! | 3.24
2 | S |  What do you call someone else’s cheese? | 1.00
2 | P |  Nacho cheese! | 2.14
2 | CP |  What do you call someone else’s cheese? Cheese that doesn’t belong to you! | 1.76
2 | IS |  What did the boy say when someone tried to take his cheese? Nacho cheese! | 3.38
3 | O |  Why did the boy bring a ladder to school? Because he wanted to go to high school! | 3.33
3 | S |  Why did the boy bring a ladder to school? | 1.24
3 | P |  Because he wanted to go to high school! | 1.00
3 | IS |  Why did the boy smoke pot before school? Because he wanted to go to high school! | 3.48
3 | IP |  Why did the boy bring the ladder to school? Because the teacher said she had high standards for him. | 2.52
4 | O |  Two jumper cables walk into a bar. The bartender says “I’ll serve you, but don’t start anything!” | 2.95
4 | S |  Two jumper cables walk into a bar. | 2.00
4 | P |  The bartender says “I’ll serve you, but don’t start anything!” | 1.81
4 | CS |  A man known for his violent tendencies walks into a bar. The bartender says “I’ll serve you, but don’t start anything!” | 1.86
4 | CP |  Two jumper cables walk into a bar. Because they are being carried by a person who frequents the bar. | 1.52
5 | O |  Why is air a lot like sex? Because it is no big deal unless you’re not getting any. | 3.86
5 | S |  Why is air a lot like sex? | 1.71
5 | P |  Because it is no big deal unless you’re not getting any. | 1.24
5 | IS |  Why is air a lot like food? Because it is no big deal unless you’re not getting any. | 3.19
5 | IP |  Why is air a lot like sex? Both are vital to the continuation of human life. | 2.76
6 | O |  A guy shows up late for work. The boss yells at him, “You should have been here at 8:30!” He replies, “Why? What happened at 8:30?” | 2.52
6 | S |  A guy shows up late for work. The boss yells at him, “You should have been here at 8:30!” | 1.00
6 | P |  He replies, “Why? What happened at 8:30?” | 1.57
6 | CS |  A guy shows up late for work and his coworker says, “You should have been here earlier, something crazy happened at 8:30!” He replies, “Why? What happened at 8:30?” | 1.33
6 | CS |  A guy shows up late for work. The boss yells at him, “You should have been here at 8:30!” He replies, “I know, I’m sorry!” | 1.24
7 | O |  You don’t need a parachute to go skydiving. You need a parachute to go skydiving twice. | 3.62
7 | S |  You don’t need a parachute to go skydiving. | 1.24
7 | P |  You need a parachute to go skydiving twice. | 1.81
7 | CP |  You don’t need a parachute to go skydiving, but it helps to with the landing. | 2.57
7 | IS |  You need a plane to go skydiving. You need a parachute to go skydiving twice. | 2.80
8 | O |  Want to hear a word I just made up? Plagiarism. | 3.29
8 | S |  Want to hear a word I just made up? | 1.14
8 | P |  Plagiarism. | 1.24
8 | CS |  Do I need to cite the word ?plagiarism’? | 2.48
8 | IP |  Want to hear a word I just made up? Gullible. | 3.57
9 | O |  A police officer called the station and said “I have an interesting case. A woman shot her husband for stepping on the floor she just mopped.” “Have you arrested this woman?” “No, the floor is still wet.” | 3.62
9 | S |  A police officer called the station and said “I have an interesting case. A woman shot her husband for stepping on the floor she just mopped.” “Have you arrested this woman?” | 1.19
9 | P |  “No, the floor is still wet.” | 1.00
9 | CS |  The husband asked his wife if he could come into the kitchen after she mopped it and she said, “No, the floor is still wet.” | 1.19
9 | CP |  A police officer called the station and said “I have an interesting case. A woman shot her husband for stepping on the floor she just mopped.” “Have you arrested this woman?” “No, she fled the scene.” | 2.14
10 | O |  Why did the cookie go to the doctor’s office? Because it was feeling crummy. | 3.57
10 | S |  Why did the cookie go to the doctor’s office? | 1.14
10 | P |  Because it was feeling crummy. | 1.00
10 | IS |  Why did the cookie need a napkin? Because it was feeling crummy. | 2.33
10 | IP |  Why did the cookie go to the doctor’s office? Because it was sick. | 1.29
11 | O |  What happens to a frog’s car when it breaks down? It gets toad. | 2.72
11 | S |  What happens to a frog’s car when it breaks down? | 1.20
11 | P |  It gets toad. | 1.15
11 | CP |  What happens to a frog’s car when it breaks down? It gets it towed. | 1.82
11 | IS |  What happens when the frog parks illegally? It gets toad! | 2.94
11 | IP |  What does a frog say when it’s car breaks down? ”It croaked!” | 2.09
12 | O |  My friend thinks he is so smart. He told me an onion is the only food that makes you cry. To prove him wrong I threw a coconut at his face. | 3.20
12 | S |  My friend thinks he is so smart. He told me an onion is the only food that makes you cry. | 1.35
12 | P |  To prove him wrong I threw a coconut at his face. | 1.47
12 | IP |  My friend thinks he is so smart. He told me an onion is the only food that makes you cry. I told him a coconut would make you cry if I threw it at him. | 2.33
12 | IS |  My friend thinks he is so smart. He told me that all fruits are good for you. I threw a coconut at his face to prove him wrong. | 2.41
13 | O |  What did the duck say when she bought the lipstick? “Put it on my bill.” | 2.68
13 | S |  What did the duck say when she bought the lipstick? | 1.25
13 | P |  “Put it on my bill.” | 1.19
13 | CP |  What did the duck say when she bought the lipstick? “Does this colour look good on me?” | 1.25
13 | CS |  The bar patron asked the bartender for another drink and told him, “Put it on my bill.” | 1.22
13 | IP |  What did the duck say when she bought the lipstick? “Was this tested on animals?” | 2.07
13 | IS |  The duck asked the bartender for another drink and told him, “Put it on my bill.” | 2.69
14 | O |  In a Catholic school cafeteria, a nun places a sign in front of a pile of apples, “Only take one, God is watching”. Further down the line is a pile of cookies. A little boy makes his own sign, “Take all you want, God is watching the apples”. | 3.33
14 | S |  In a Catholic school cafeteria, a nun places a sign in front of a pile of apples, “Only take one, God is watching”. Further down the line is a pile of cookies. | 1.49
14 | P |  A little boy makes his own sign, “Take all you want, God is watching the apples”. | 1.32
14 | CP |  In a Catholic school cafeteria, a nun places a sign in front of a pile of apples, “Only take one, God is watching”. Further down the line is a pile of cookies with the same sign. | 1.36
14 | IS |  In a Catholic school cafeteria, a little boy places a sign in front of a pile of apples, “Only take one, God is watching”. Further down the line is a pile of cookies. The boy makes another sign, “Take all you want, God is watching the apples”. | 3.05
15 | O |  Can a kangaroo jump higher than the Empire State Building? Of course it can, the Empire State Building can’t jump! | 2.54
15 | S |  Can a kangaroo jump higher than the Empire State Building? | 1.09
15 | P |  Of course it can, the Empire State Building can’t jump! | 1.19
15 | CP |  Can a kangaroo jump higher than the Empire State Building? No, that is impossible. | 1.32
15 | CS |  Which can jump higher, the Empire State Building or a kangaroo? A kangaroo, the Empire State Building can’t jump! | 2.04
16 | O |  What do you call a pig that does karate? A pork chop! | 2.54
16 | S |  What do you call a pig that does karate? | 1.29
16 | P |  A pork chop! | 1.13
16 | CP |  What do you call a pig that does karate? A pig that does karate! | 1.52
16 | CS |  What is a popular cut of meat? A pork chop. | 1.45
16 | IP |  What do you call a pig that does karate? A kung pow piggy. | 1.87
17 | O |  How do trees access the internet? They log in. | 2.84
17 | S |  How do trees access the internet? | 1.14
17 | P |  They log in. | 1.19
17 | CP |  How do trees access the internet? They don’t. | 1.78
17 | CS |  How does one access the internet? They log in. | 1.32
18 | O |  Why can’t you trust an atom? Because they make up everything! | 3.16
18 | S |  Why can’t you trust an atom? | 1.21
18 | P |  Because they make up everything! | 1.12
18 | IP |  Why can’t you trust an atom? Because they’re always moving! | 1.79
18 | CS |  Why can’t you trust a liar? Because they make up everything! | 1.54
19 | O |  What kind of nails do carpenters hate to hit? Fingernails! | 2.58
19 | S |  What kind of nails do carpenters hate to hit? | 1.14
19 | P |  Fingernails! | 1.09
19 | CP |  What kind of nails do carpenters hate to hit? Tough ones. | 1.58
19 | CS |  What kind of nails do people paint? Fingernails! | 1.40
20 | O |  The energizer bunny was arrested on a charge of battery. | 2.79
20 | S |  The energizer bunny was arrested. | 1.33
20 | P |  on a charge of battery. | 1.14
20 | IP |  The energizer bunny was arrested on a charge of false advertisement. | 1.53
20 | CS |  The angry man was arrested on a charge of battery. | 1.28
21 | O |  Why did the skeleton cross the road? To get to the body shop! | 2.20
21 | S |  Why did the skeleton cross the road? | 1.12
21 | P |  To get to the body shop! | 1.17
21 | IP |  Why did the skeleton cross the road? To stretch his legs. | 1.41
21 | IS |  Why did the invisible man cross the road? To get to the body shop! | 2.13
22 | O |  Why did the fish blush? Because it saw the ocean’s bottom! | 2.82
22 | S |  Why did the fish blush? | 1.16
22 | P |  Because it saw the ocean’s bottom! | 1.14
22 | IP |  Why did the fish blush? Because it puffed in front of his friends. | 1.69
22 | IS |  Why did the surfer crash? Because he saw the ocean’s bottom! | 2.12
23 | O |  What do you call a fake noodle? An impasta! | 3.01
23 | S |  What do you call a fake noodle? | 1.24
23 | P |  An impasta! | 1.42
23 | IP |  What do you call a fake noodle? A lack-aroni. | 2.15
23 | IS |  What did the mobster say when he found out his friend was a traitor? An impasta! | 1.81
24 | O |  What do you call an alligator in a vest? An investigator! | 2.73
24 | S |  What do you call an alligator in a vest? | 1.19
24 | P |  An investigator! | 1.13
24 | IP |  What do you call an alligator in a vest? A well-dressed reptile. | 1.86
24 | IS |  What do you call an alligator that is a detective? An investigator! | 2.54
25 | O |  What do you call a pile of kittens? A meowntain! | 2.58
25 | S |  What do you call a pile of kittens? | 1.16
25 | P |  A meowntain! | 1.34
25 | IP |  What do you call a pile of kittens? Mount Kili-meow-jaro. | 2.61
25 | IS |  What do you call a mountain for cats? A meowtain! | 2.51
26 | O |  What do you get from a pampered cow? Spoiled milk! | 2.80
26 | S |  What do you get from a pampered cow? | 1.24
26 | P |  Spoiled milk! | 1.16
26 | IP |  What do you get from a pampered cow? Udder sass! | 2.72
26 | CS |  What do you get when you leave out milk overnight? Spoiled milk! | 1.51
27 | O |  How do you make holy water? Boil the hell out of it! | 2.96
27 | S |  How do you make holy water? | 1.18
27 | P |  Boil the hell out of it! | 1.24
27 | IP |  How do you make holy water? Hole punch it! | 1.85
27 | CS |  How do you make water really hot? Boil the hell out of it! | 1.62
27 | CP |  How do you make holy water? Get a priest to bless it. | 1.41
28 | O |  How do you make an octopus laugh? With ten-tickles! | 2.58
28 | S |  How do you make an octopus laugh? | 1.15
28 | P |  With ten-tickles! | 1.18
28 | CP |  How do you make an octopus laugh? Tell it jokes. | 1.50
28 | IS |  How many tickles does it take to make an octopus laugh? Ten-tickles! | 2.78
29 | O |  What do you call a boy who finally stood up to the bullies? An ambulance. | 2.07
29 | S |  What do you call a boy who finally stood up to the bullies? | 1.08
29 | P |  An ambulance. | 1.06
29 | CP |  What do you call a boy who finally stood up to the bullies? A brave person. | 1.26
29 | CS |  What is the name of an emergency vehicle? An ambulance. | 1.18
29 | IP |  What do you call a boy who finally stood up to the bullies? An idiot! | 1.69
30 | O |  Did you hear the one about the geologist? He took his wife for granite so she left him! | 2.67
30 | S |  Did you hear the one about the geologist? | 1.22
30 | P |  He took his wife for granite so she left him! | 1.38
30 | IP |  Did you hear the one about the geologist? He felt that no one appreciated his work; they took him for granite! | 2.53
30 | IS |  What happened to The Rock’s marriage? He took his wife for granite so she left him! | 2.76
31 | O |  What did the tailor think of her new job? It was sew-sew. | 2.45
31 | S |  What did the tailor think of her new job? | 1.18
31 | P |  It was sew-sew. | 1.15
31 | IP |  What did the tailor think of her new job? She loved her new coworkers, they left her in stitches! | 2.21
31 | IS |  What did the sewing teacher say about her student’s skills? It was sew-sew. | 2.31
32 | O |  I tried to catch some fog earlier. I mist. | 2.85
32 | S |  I tried to catch some fog earlier. | 1.26
32 | P |  I mist. | 1.36
32 | CP |  I tried to catch some fog earlier. It was hard! | 1.48
32 | IS |  I couldn’t see where I was throwing my ball through the fog so I mist. | 2.48
33 | O |  What happened to the plant in math class? It grew square roots! | 2.73
33 | S |  What happened to the plant in math class? | 1.10
33 | P |  It grew square roots! | 1.14
33 | IP |  What happened to the plant in math class? It died of boredom! | 1.93
33 | IS |  What happened when the tree went to college? It grew square roots! | 2.34
34 | O |  What kind of bus can you never enter? A syllabus. | 2.29
34 | S |  What kind of bus can you never enter? | 1.11
34 | P |  A syllabus. | 1.10
34 | IP |  What kind of bus can you never enter? A rhombus! | 2.20
34 | CS |  What do you look at to learn about a class? A syllabus. | 1.34
35 | O |  What kind of dress can’t be worn? An address! | 2.43
35 | S |  What kind of dress can’t be worn? | 1.09
35 | P |  An address! | 1.10
35 | CP |  What kind of dress can’t be worn? One that is too small. | 1.53
35 | IS |  Where can you find a dressmaker? Their address! | 1.91