Mathematics and Humor: A Study of the Logic of Humor

John Allen Paulos
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Show sample text content. Thus Picasso's Bull, in which the seat and handlebars of a bicycle suggest the head of a bull, is a visual pun linking two different sets of images.

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Magritte's paintings Not to Be Reproduced, and Evening Fails, with their strange mirrors and windows, are reminiscent of the notions of self-reference and levels. Slapstick and physical humor have a logic of their own repetition, exaggeration, inappropriate dress, etc. The dignified movements of Charlie Chaplin clash humorously with his appearance.

John Allen Paulos

John Allen Paulos cleverly scrutinizes the mathematical structures of jokes, puns, paradoxes, spoonerisms, riddles, and other forms of humor, drawing examples. Be the first to ask a question about Mathematics and Humor .. to model the logic of humor in another book, the title of which escapes me at the moment. of humor to provide a compelling baseline for future mathematical/comedic study.

The possible dependence of z on factors other than w will, for the time being, be ignored. I will return to both these matters shortly. There is, of course, no unique way to assign values to z and w, but any reasonable convention will yield the same qualitative shape for these curves and surfaces. Now, as discussed in chapter 3, any self-referential metacue induces an oscillation in the. Bringing together negative assessments of laughter from the Bible with criticisms from Greek philosophy, early Christian leaders such as Ambrose, Jerome, Basil, Ephraim, and John Chrysostom warned against either excessive laughter or laughter generally.

Sometimes what they criticized was laughter in which the person loses self-control. Other times they linked laughter with idleness, irresponsibility, lust, or anger. John Chrysostom, for example, warned that. Laughter often gives birth to foul discourse, and foul discourse to actions still more foul. Often from words and laughter proceed railing and insult; and from railing and insult, blows and wounds; and from blows and wounds, slaughter and murder. If, then, you would take good counsel for yourself, avoid not merely foul words and foul deeds, or blows and wounds and murders, but unseasonable laughter itself in Schaff , Not surprisingly, the Christian institution that most emphasized self-control—the monastery—was harsh in condemning laughter.

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One of the earliest monastic orders, of Pachom of Egypt, forbade joking Adkin , — The Rule of St. The monastery of St.

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The Christian European rejection of laughter and humor continued through the Middle Ages, and whatever the Reformers reformed, it did not include the traditional assessment of humor. Among the strongest condemnations came from the Puritans, who wrote tracts against laughter and comedy. One by William Prynne encouraged Christians to live sober, serious lives. That makes us alert to signs that we are winning or losing. The former make us feel good and the latter bad. If our perception of some sign that we are superior comes over us quickly, our good feelings are likely to issue in laughter.

In Part I, ch. Sudden glory, is the passion which makes those grimaces called laughter; and is caused either by some sudden act of their own, that pleases them; or by the apprehension of some deformed thing in another, by comparison whereof they suddenly applaud themselves. And it is incident most to them, that are conscious of the fewest abilities in themselves; who are forced to keep themselves in their own favor by observing the imperfections of other men.

And therefore much laughter at the defects of others, is a sign of pusillanimity. For of great minds, one of the proper works is, to help and free others from scorn; and to compare themselves only with the most able. He says that laughter accompanies three of the six basic emotions—wonder, love, mild hatred, desire, joy, and sadness. Derision or scorn is a sort of joy mingled with hatred, which proceeds from our perceiving some small evil in a person whom we consider to be deserving of it; we have hatred for this evil, we have joy in seeing it in him who is deserving of it; and when that comes upon us unexpectedly, the surprise of wonder is the cause of our bursting into laughter… And we notice that people with very obvious defects such as those who are lame, blind of an eye, hunched-backed, or who have received some public insult, are specially given to mockery; for, desiring to see all others held in as low estimation as themselves, they are truly rejoiced at the evils that befall them, and they hold them deserving of these art.

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With these comments of Hobbes and Descartes, we have a sketchy psychological theory articulating the view of laughter that started in Plato and the Bible and dominated Western thinking about laughter for two millennia. In the 20 th century, this idea was called the Superiority Theory. Simply put, our laughter expresses feelings of superiority over other people or over a former state of ourselves. Feelings of superiority, Hutcheson argued, are neither necessary nor sufficient for laughter. In laughing, we may not be comparing ourselves with anyone, as when we laugh at odd figures of speech like those in this poem about a sunrise:.

If self-comparison and sudden glory are not necessary for laughter, neither are they sufficient for laughter.

A gentleman riding in a coach who sees ragged beggars in the street, for example, will feel that he is better off than they, but such feelings are unlikely to amuse him. To these counterexamples to the Superiority Theory we could add more. Sometimes we laugh when a comic character shows surprising skills that we lack. In the silent movies of Charlie Chaplin, Harold Lloyd, and Buster Keaton, the hero is often trapped in a situation where he looks doomed.

But then he escapes with a clever acrobatic stunt that we would not have thought of, much less been able to perform. Laughing at such scenes does not seem to require that we compare ourselves with the hero; and if we do make such a comparison, we do not find ourselves superior. At least some people, too, laugh at themselves—not a former state of themselves, but what is happening now. If I search high and low for my eyeglasses only to find them on my head, the Superiority Theory seems unable to explain my laughter at myself. While these examples involve persons with whom we might compare ourselves, there are other cases of laughter where no personal comparisons seem involved.

In experiments by Lambert Deckers , subjects were asked to lift a series of apparently identical weights. The first several weights turned out to be identical, and that strengthened the expectation that the remaining weights would be the same. But then subjects picked up a weight that was much heavier or lighter than the others. Further weakening the dominance of the Superiority Theory in the 18 th century were two new accounts of laughter which are now called the Relief Theory and the Incongruity Theory.

Neither even mentions feelings of superiority. The Relief Theory is an hydraulic explanation in which laughter does in the nervous system what a pressure-relief valve does in a steam boiler. John Locke , Book 3, ch. The natural free spirits of ingenious men, if imprisoned or controlled, will find out other ways of motion to relieve themselves in their constraint; and whether it be in burlesque, mimicry, or buffoonery, they will be glad at any rate to vent themselves, and be revenged upon their constrainers. Over the next two centuries, as the nervous system came to be better understood, thinkers such as Herbert Spencer and Sigmund Freud revised the biology behind the Relief Theory but kept the idea that laughter relieves pent-up nervous energy.

When we are angry, for example, nervous energy produces small aggressive movements such as clenching our fists; and if the energy reaches a certain level, we attack the offending person. In fear, the energy produces small-scale movements in preparation for fleeing; and if the fear gets strong enough, we flee. The movements associated with emotions, then, discharge or release the built-up nervous energy.

Laughter releases nervous energy, too, Spencer says, but with this important difference: the muscular movements in laughter are not the early stages of larger practical actions such as attacking or fleeing.

Mathematics and Humor : A Study of the Logic of Humor by John Allen Paulos (1982, Paperback)

Unlike emotions, laughter does not involve the motivation to do anything. The nervous energy relieved through laughter, according to Spencer, is the energy of emotions that have been found to be inappropriate. Reading the first three lines, we might feel pity for the bereaved nephew writing the poem. But the last line makes us reinterpret those lines. Far from being a loving nephew in mourning, he turns out to be an insensitive cheapskate.

So the nervous energy of our pity, now superfluous, is released in laughter. If still more energy needs to be relieved, it spills over to the muscles connected with breathing, and if the movements of those muscles do not release all the energy, the remainder moves the arms, legs, and other muscle groups In the 20 th century, John Dewey — had a similar version of the Relief Theory. In der Witz , that superfluous energy is energy used to repress feelings; in the comic it is energy used to think, and in humor it is the energy of feeling emotions.

Der Witz includes telling prepared fictional jokes, making spontaneous witty comments, and repartee. In der Witz , Freud says, the psychic energy released is the energy that would have repressed the emotions that are being expressed as the person laughs.

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According to Freud, the emotions which are most repressed are sexual desire and hostility, and so most jokes and witty remarks are about sex, hostility, or both. In telling a sexual joke or listening to one, we bypass our internal censor and give vent to our libido. In telling or listening to a joke that puts down an individual or group we dislike, similarly, we let out the hostility we usually repress. In both cases, the psychic energy normally used to do the repressing becomes superfluous, and is released in laughter.

Here it is the energy normally devoted to thinking. An example is laughter at the clumsy actions of a clown. Our laughter at the clown is our venting of that surplus energy. These two possibilities in my imagination amount to a comparison between the observed movement and my own. His example is a story told by Mark Twain in which his brother was building a road when a charge of dynamite went off prematurely, blowing him high into the sky.

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Having sketched several versions of the Relief Theory, we can note that today almost no scholar in philosophy or psychology explains laughter or humor as a process of releasing pent-up nervous energy. There is, of course, a connection between laughter and the expenditure of energy. Hearty laughter involves many muscle groups and several areas of the nervous system. Laughing hard gives our lungs a workout, too, as we take in far more oxygen than usual. But few contemporary scholars defend the claims of Spencer and Freud that the energy expended in laughter is the energy of feeling emotions, the energy of repressing emotions, or the energy of thinking, which have built up and require venting.

Funny things and situations may evoke emotions, but many seem not to. Consider P. These do not seem to vent emotions that had built up before we read them, and they do not seem to evoke emotions and then render them superfluous. So whatever energy is expended in laughing at them does not seem to be superfluous energy being vented. In fact, the whole hydraulic model of the nervous system on which the Relief Theory is based seems outdated.

Mathematics and Humor

The former make us feel good and the latter bad. Ruch W. Oh well, Photoshop can fix all that. Both authors contributed to the writing of the manuscript, read it critically, and gave consent to its publication. Paulos finishes with a short wrap-up of the subject, and I think that this book is going to face its own Catastrophe Theory, in that how it is perceived by the reader is going to be based on the circumstances surrounding the event of reading it. Specifically, the pigeon is reasoning like this:. Question: how many times can you subtract 7 from 83, and what is left afterwards?

To that hydraulic model, Freud adds several questionable claims derived from his general psychoanalytic theory of the mind. He says that the creation of der Witz —jokes and witty comments—is an unconscious process of letting repressed thoughts and feelings into the conscious mind. This claim seems falsified by professional humorists who approach the creation of jokes and cartoons with conscious strategies. If Freud is right that the energy released in laughing at a joke is the energy normally used to repress hostile and sexual feelings, then it seems that those who laugh hardest at aggressive and sexual jokes should be people who usually repress such feelings.

But studies about joke preferences by Hans Jurgen Eysenck , xvi have shown that the people who enjoy aggressive and sexual humor the most are not those who usually repress hostile and sexual feelings, but those who express them.