One of the byproducts of an ambiguous communicate system is that speakers can exploit this ambiguity. Sometimes this is done to deceive or manipulate, as with bribes (Pinker et al, 2008) or so-called “dog-whistle politics” (Safire, 2008; López, 2015). But this exploitation is often more innocuous and commonplace, as in the case of humor.
Examples of ambiguity-based humor range from puns, e.g. “During branding, cowboys have sore calves” (Coulson & Severens, 2007), to phrases with multiple syntactic interpretations, e.g. “Tuna biting off Washington coast” (Wasow et al, 2005).
Clearly, understanding these examples requires a listener to activate both interpretations of the ambiguous expression. But what kinds of cognitive processes does this actually engage? How could these processes be described computationally? And ultimately, why do some jokes make us laugh, and why do others––like many puns––make us groan?
Getting the joke: an information-processing approach
One particularly well-known model of joke comprehension (Suls, 1972) posits that understanding proceeds in two, qualitatively discrete stages. First, the comprehender is surprised in some way, usually by an apparently incongruous punchline. Second, the comprehender resolves this incongruity using some kind of general “problem solver”, of the kind presented by Newell and Simon (1956), to establish coherence. This latter step is assumed to draw on a comprehender’s world knowledge, and likely involves searching for some re-interpretation of the incongruity (or preceding context) such that it makes sense.
Suls (1972) gives the following example:
“Try our cigars. You can’t get better!”
“I know, I tried one last week, and I’m still not better!”
This joke rests on the ambiguity of the phrase You can’t get better. Most readers probably interpret the utterance first to mean: Our cigars are the best, and you won’t find any that surpass them. Indeed, this is likely the speaker’s intended interpretation. And the first half of the other speaker’s reply is still consistent with this interpretation––they’ve already tried one of the cigars, and agrees that they are the best. But the final clause, I’m still not better, subverts this interpretation, and seems incongruous. Why is the second speaker now referring to their own state, as opposed to the quality of the cigars?
As a reader, you’re forced to engage some mysterious cognitive processes to reconfigure your interpretation. That is, you realize that the second speaker has––perhaps deliberately––misinterpreted You can’t get better as referring to the decline of their own bodily state, as opposed to the more conventional, idiomatic interpretation. The reply now makes sense, particularly in light of our knowledge that cigars are unhealthy: the second speaker still hasn’t recovered.
This two-stage framework is a computational-level description: that is, it doesn’t make reference to specific cognitive or neural mechanisms, but rather describes the process of comprehension as one would describe pseudo-code for a computer program.
Formalizing pun comprehension
A more recent computational model (Kao et al, 2016) formalizes the process of pun comprehension using an information-theoretic approach. As in Suls (1972), the model in Kao et al (2016) seems to imply a two-step process, in which incongruity (introduced by ambiguity) is first recognized, then resolved. However, a major departure is that this newer model is formalized and implemented in considerably more detail, and relies on statistics and information theory in lieu of the “script”-based approach taken by Suls (1972). Critically, this allows for a more precise operationalization of previously fuzzy terms like incongruity.
Kao et al (2016) argue that two information-theoretic measures are critical to distinguishing puns from non-puns. The first measure is ambiguity. Consider the sentence:
(1) The magician got so mad he pulled his hare/hair out.
This sentence contains at least one phonetically ambiguous word, leading to two different interpretations: either the magician a) performed a trick of pulling a rabbit out of a hat, or b) pulled the hair from his head. But ambiguity isn’t the only necessary index of a pun. Consider:
(2) Look at that hare/hair.
This licenses at least two interpretations as well: a) look at that rabbit; b) look at that person’s hair. But in the absence of some other context, doesn’t have the “flavor” of a joke. Thus, Kao et al (2016) introduce their second measure: distinctiveness. That is, how much overlap is there across the words that are relevant for each interpretation of the utterance? They argue that the relevant words for each interpretation of (1) are quite distinct: a) [magician, hare] vs. b) [mad, pulled, hair], whereas the competing interpretations of (2) have more overlap.
Ambiguity is operationalized as the entropy over sentence meanings. “Entropy” sounds fancy, but it really just means: how likely are each of the interpretations of the sentence? A distribution like [.5, .5] has high entropy, since each interpretation is quite likely, while a distribution like [.1, .9] has low entropy, since one interpretation is much more likely than the other.
Distinctiveness is operationalized as the Kullback-Liebler divergence (KL-D) between the distributions of relevant words for each interpretation. Again, KL-D sounds complicated, but is really just a measure of how much overlap two probability distributions (e.g. P vs. Q) have. The formal definition translates to something like: if we thought we were sampling from P, but were actually sampling from Q, how much more surprised would we be than if we were truly sampling from P? If P and Q are very similar, then accidentally sampling from Q won’t be very surprising, because it’ll look basically like sampling from P; but if P and Q are very different, then accidentally from Q will be surprising, because each observation will be unexpected.
Kao et al (2016) compute a score for both the ambiguity and distinctiveness for a bunch of different sentences––some puns, some non-puns. The first question is whether these scores distinguish puns from non-puns. As depicted in Figure 1, they do a very good job: puns are well-differentiated from non-puns on the basis of being more ambiguous, and also having more distinctive words associated with each of their interpretations. (This is true for puns based on homophones, e.g. hare/hair, and near-puns, like tooth/truth.)
Their second question is whether these scores correspond to how funny each pun or non-pun is. Separately, the authors obtained a set of “funniness” ratings from participants on Amazon Mechanical Turk; participants read a series of sentences, and rated how funny they thought each one was, on a scale from 1 (not at all funny) to 7 (extremely funny).
Both ambiguity and distinctiveness predicted participant funniness ratings, which isn’t particularly surprising, given that the dataset was split into puns and non-puns (see Figure 1 above). That said, this indicates that their metric is capturing something about what constitutes a joke involving puns. Importantly, puns had more distinctive relevant words for each interpretation, and non-puns––while technically ambiguous––often had little to no distinctive words.
Connecting this model back to Suls (1972), the authors write: “We can construe our measures as corresponding roughly to incongruity and resolution in this sense, where ambiguity represents the presence of incongruous sentence meanings, and distinctiveness represents the degree to which each meaning is strongly supported by different parts of the stimulus” (pg. 1281).
The takeaway; or, complicating the picture
Many jokes rely on ambiguity. How do people understand these jokes? And what differentiates them from other expressions that contain ambiguity? Suls (1972) presents a model of the first question, suggesting that comprehenders employ a two-stage process––first recognizing an incongruity, then resolving it. Kao et al (2016) formalize this two-stage process, suggesting that at least certain incongruities arise from ambiguity (e.g. puns), and that their humor comes from the consideration of radically distinct sets of words supporting each interpretation.
Both of these models are theoretical, even though the latter is computationally implemented. But they do make certain concrete predictions. For example, if pun comprehension (or joke comprehension more generally) is really a two-stage process, these processes should be cognitively differentiable somehow––either in space (e.g. distinct brain regions), or in time (e.g. occurring in serial). Is this true?
As usual, the picture is complicated. There’s some evidence that the processes are dissociable; Bihrle et al (1986) found that individuals with right-hemisphere brain damage (RHD) were able to recognize that joke punchlines generally involve some kind of surprise (Step 1), but were unable to identify the most coherent punchline (Step 2). Individuals with left-hemisphere brain damage (LHD) showed the inverse pattern, suggesting that these processes may be dissociable, and possibly subserved by distinct hemispheres of the brain. But later work on neurotypical individuals, e.g. those without brain damage, suggests that these processes may not occur at distinct times (Kutas & Coulson, 2001), raising questions about how separable they really are.
So what makes a joke funny? Ritchie (2005) suggests that there’s an important role for cleverness; this is hard to operationalize, but has something to do with how many ambiguities are resolved by the punchline. But as Ritchie (2005) also notes, there’s often an important social element to good jokes, puns or otherwise: “A really good joke expresses some deeper and at least partially suppressed social truth” (pg. 280). This isn’t something that Kao et al (2016) address, partly because encoding this kind of social knowledge in a computational model is really, really difficult.
More skeptical readers might be wondering: what’s the point? Does it really matter whether we engage these processes in serial or in parallel? Does it matter whether we know what makes something “funny” or not? I’d argue that understanding humor matters for a couple reasons. First, “funniness” appears to be an important quality; while “funny” is subjective and culturally defined, funny people are usually fun to be around. And second, humor a pervasive kind of creative language use, which isn’t really well-described by traditional models of meaning. What is it, exactly, that we humans are doing when we crack a joke? Why do we do it? These kinds of questions have existed at least since Aristotle (Attardo, 1994), and while we’ll never have a definitive “answer”––that’s not really the nature of science––we can perhaps come closer to understanding which cognitive resources comprehenders deploy online to understand jokes, as well as the kinds of knowledge that’s required for their successful resolution.
Attardo, S. (1994). Linguistic theories of humor. Berlin: Walter de Gruyter.
Bihrle, A. M., Brownell, H. H., Powelson, J. A., & Gardner, H. (1986). Comprehension of humorous and nonhumorous materials by left and right brain-damaged patients. Brain and cognition, 5(4), 399-411.
Coulson, S., & Severens, E. (2007). Hemispheric asymmetry and pun comprehension: When cowboys have sore calves. Brain and Language, 100(2), 172-187.
López, I. H. (2015). Dog whistle politics: How coded racial appeals have reinvented racism and wrecked the middle class. Oxford University Press.
Newell, A., & Simon, H. (1956). The logic theory machine–A complex information processing system. IRE Transactions on information theory, 2(3), 61-79.
Pinker, S., Nowak, M. A., & Lee, J. J. (2008). The logic of indirect speech. Proceedings of the National Academy of sciences, 105(3), 833-838.
Ritchie, D. (2005). Frame-shifting in humor and irony. Metaphor and Symbol, 20(4), 275-294.
Suls, J. M. (1972). A two-stage model for the appreciation of jokes and cartoons: An information-processing analysis. The psychology of humor: Theoretical perspectives and empirical issues, 1, 81-100.
Safire, W. (2008). Safire’s political dictionary. Oxford University Press.
Wasow, T., Perfors, A., & Beaver, D. (2005). The puzzle of ambiguity. Morphology and the web of grammar: Essays in memory of Steven G. Lapointe, 265-282.
 See also this older post on how speakers use ambiguous expressions for the sake of “plausible deniability” (https://seantrott.com/2017/08/22/you-got-heat-indirect-speech-acts-in-the-wire/).
 People obviously vary in the extent to which they find puns genuinely funny, and puns themselves vary greatly in quality, but nonetheless, the entire point of a successful pun is to activate two or more meanings of a given word
 Of course, understanding this joke doesn’t just require world knowledge about cigars and their deleterious health effects, but also about the mechanics social interaction. For example, part of the humor comes from our knowledge that shopkeepers have the goal of selling their products, and often do this by proclaiming that they are the best, and thus You can’t get better is almost certainly intended as a reference to the quality of their cigars; and that in a conversation, people are meant to produce a response that’s somehow contingent on what’s just been said, and thus the second speaker’s (deliberate) misinterpretation subverts our expectations of how conversations normally proceed.