This doesn’t mean, however, that “Wit’s End” could ever be mistaken for an earnest, academic tract. Far from it. In a chapter titled “Wisdom of the Sages,” Geary relates a story about Hershele Ostropoler, an 18th-century Eastern European butcher who became a kind of jester to a melancholy Rabbi Barukh. Once when the rabbi was too depressed to eat, “Hershele sat down across from him and slipped a silver tea spoon into his pocket. Before Barukh could rebuke him for the theft, Hershele said, ‘Doctor’s orders: Take a teaspoon with every meal.’ ” The rabbi, smiling, recovered his appetite.

Like Frederick Crews’s “The Pooh Perplex,” which brilliantly parodies a dozen schools of literary criticism, and Robert K. Merton’s “On the Shoulders of Giants,” which tracks, through myriad personal and learned digressions, the history of Newton’s phrase “If I have seen further it is only by standing on the shoulders of giants,” “Wit’s End” juggles scholarship, humorous anecdote and critical insight with a diabolical, almost sinister dexterity. No shrinking violet, Geary fully intends to strut his stuff, to glitter and beguile, and he does so with remarkable ingenuity and chutzpah.

As Geary explains in a prefatory poem, composed in 18th-century heroic couplets, his book’s various chapters exemplify what they describe: “Each theme matched to the style in which it’s writ,/ Thus to show, not tell, the story of Wit.”As a result, the advancing text kaleidoscopes from philosophical dialogue to sermon to scholarly paper to ode to an over-the-top emulation of 1920s African American jive. The book’s designer even complements this narrative jazziness by varying the typefaces and page layouts.

Geary’s intellectual reach is just as dizzying. He parses both enigmatic Buddhist koans and the put-downs used in playing the Dozens, the African American game of competitive insults: “You’re so dumb you think the Supreme Court is where Diana Ross plays tennis.” He probes the grammatical shifts in that classic truism, “Time flies like an arrow; fruit flies like a banana,”as well as the levels of meaning in Stanislaw Lec’s haunting aphorism: “No snowflake in an avalanche ever feels responsible.” There are jokes about Irishmen in bars, and anecdotes about Buster Keaton and Harpo Marx, and even some deliberately groan-inducing phrases such as “puns about German sausage are generally considered the worst.”

Still, Geary’s aim isn’t to make you laugh (or grimace), it’s to make you think. To begin with, he grants the pun a kind of foundational primacy, viewing it as the template for every sort of wit, here loosely defined as “the ability to hold in the mind two different ideas about the same thing at the same time.” As Geary points out, even Jesus — no ordinary jokester — employed wordplay when he declared that he would build his church upon Peter “whose name in Aramaic and in Greek means ‘rock.’ ” Perhaps the world’s most difficult “novel,” James Joyce’s “Finnegans Wake,” is almost entirely constructed of multilayered puns, often macaronic puns, which draw on two or more languages. A simple example would be calling an elegant frankfurter a “haute dog.”

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From this meditation on punmanship, Geary next proceeds to a philosophical dialogue between Denis Diderot and Germaine de Staël. The duo starts by looking at wit’s relationship to fencing (well-aimed thrusts, bold sallies), then considers the importance of sprezzatura — the studied nonchalance that conceals mastery — and finally affirms that “to ‘get’ a witticism you must take the same mental path as the person who said it.”

Geary subsequently shows that wit thrives best when the brain’s policeman-like rationality lets down its guard and allows free association to run wild, releasing our inner Robin Williams. Improvisational comedy, in particular, requires mental nimbleness, a trait that Aristotle extolled as eutrapelia and that John Donne and other metaphysical poets regularly demonstrate in their intricate analogies and sometimes salacious double-meanings. “O my America! my new-found-land!” may sound innocuously geographical but isn’t.

Like metaphor, the subject of Geary’s previous book “I Is an Other,” wit often yokes together dissimilar entities to achieve a sudden illumination. Geary devotes several pages to the Russian formalist theory of art as “defamiliarization”: By making the habitual and familiar seem strange, great works open our eyes, blinded by routine, and allow us to see the world afresh. He adds that there’s a simple way for non-artists to achieve such perceptiveness: Go live in a foreign country. Unaccustomed to its ways, you will be compelled to notice, really notice, everything around you. In a related chapter on visual wit, Geary naturally begins with psychology’s favorite critter, the duck-rabbit — a drawing that alternately resembles one animal or the other, depending on how you focus your eyes. From here, he deconstructs some contemporary artworks cleverly based on trompe l’oeil effects. To see clearly, Geary concludes, look askance.

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Geary’s scholarship, supported by 30 pages of endnotes identifying his sources, could easily be heart-sinking, if his own prose wasn’t so frisky. As the playwright Sacha Guitry so shrewdly observed, “you can pretend to be serious, but you can’t pretend to be witty.” Happily, Geary manages to be both, as one might expect from an avid juggler whose day job is working as deputy curator of Harvard’s Nieman Foundation.

Okay, there’s time for one more story. In early 16th-century India, Tenali Rama, the court jester of Prince Krishnadevaraya, grew so impertinent that he was sentenced to death but was graciously allowed to select the method of his execution. Tenali Rama’s choice: old age. Bada-boom.

Michael Dirda reviews books each Thursday in Style.

WIT'S END

What Wit Is, How itWorks, and Why We Need It