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“How did they do that?”

That was the first thing my friend said to me during the intermission of the London production of “The Book of Mormon,” which was then in its last week of previews. My friend is a writer of considerable erudition, and there was much she was eager to discuss about this American-born musical, which appealed in equal measures to the moralist and the hedonist in her.

But what she wanted to know right away was this: How was it possible that a phalanx of soberly dressed Mormon missionaries were transformed – during a blackout that couldn’t have lasted more than a few seconds — into sequined-vest-wearing chorus boys out of a Busby Berkeley fantasy?

Simple sleight of hand. It gets ‘em every time.

Such basic moments of metamorphosis still wow us at the theater in a way movies never can, no matter how much digital trickery is deployed. After all, actors on screen have been changing shape before our eyes – whether from Dr. Jekyll into Mr. Hyde, or from Lon Chaney Jr. into the Werewolf — for almost as long as there have been moving pictures.

The Red Sea is parted, the Titanic goes down again in a wall of water and human beings turn into their blue-skinned avatars, in three dimensions to boot. Yet as scenic and spectacular as these moments may be, we always appreciate on some level that they are the product of long hours of technological manipulation, achieved on sound stages and in editing rooms.

In theater, on the other hand, something as rudimentary as an instant change of costume makes grown-ups gasp. Go to the current Broadway production of “Rodgers and Hammerstein’s Cinderella,” and listen for the ascending chorus of “ooohs” that arises on the two occasions the title heroine (played by Laura Osnes) spins out of her sad rags and into glittering ball gowns without ever leaving our sight. (William Ivey Long did the costumes.)

Or, if you’re in London and can score a ticket, check out the wondering murmurs that course through the John Gielgud Theater every time Helen Mirren gains or sheds decades in Peter Morgan’s “Audience,” in which she portrays Queen Elizabeth II at different points in her reign. True, most often Ms. Mirren accomplishes these wonders off stage (though in less time than it takes most of us to put on a coat and scarf).

But there’s also that moment when the Queen, surrounded by a throng of courtiers, steps out from the protective huddle in a different gown, with a different hairstyle and is both of a different age and from a different age than she was seconds before. Ah, if only we could juggle styles – and time — so effortlessly when we get dressed in the morning.

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These are all, to some extent, magician’s tricks. And I suppose you could argue that in their use of show-biz expertise they’re not all that different from the gizmo-driven gimmickry of movie makers. It’s that these reinventions of living people take place in real time and space that makes us feel like little kids at their first county fair. Such metamorphoses also embody the larger process and very essence of theater.

The leapfrogging through time in “The Audience” — especially as embodied by its leading lady – is a virtuoso version of what happens every time a performer convinces us that she’s someone else, existing in a breathing moment that only those of us who are gathered in this place at this time have access to.

The quick-change artistry of the young missionaries in “The Book of Mormon” is a happy, gaudy metaphor for the way musicals give extravagant color and rhythm to gray, chaotic reality. That’s what this show is about, finally — the alchemical power of the religion that is theater, and specifically, the American musical. (For the record, some of the more eminent London critics thought the show was at best middle-brow and at worst gratuitously offensive. But for me, it felt as joyous as it had in New York.)

In another London show, Alan Bennett’s “People” at the National Theater, there’s a sequence in which a shabby, long-neglected English country castle is recast into sparkling, immaculate luxury as we watch. This is not necessarily a cause for celebration in a play that is highly ambivalent, if now downright censorious, about the way Britain polishes and re-styles its own past for profit.

But the feeling that emanated from the audience in that makeover scene was of the pure giddiness that comes when the theater shows off its sorcerer’s technique. Anyway, we all knew that the big house would be a dump again in time for the next performance of “People.” And that it would turn back into a palace for another audience’s delectation and then turn back into a dump again to begin another evening at the theater, where some performers, some designers, some stage hands and a willing group of watchers would collude in marvelous illusion-making.

What are some of your memories of stage magic, of moments – whether elaborate or simple – when impossible metamorphoses take place in plain view?