The opening stanza of Lewis Carroll's poem “Jabberwocky” goes like this:

'Twas brillig, and the slithy toves

Did gyre and gimble in the wabe:

All mimsy were the borogoves;

And the mome raths outgrabe.

Perhaps such nonsense verse and satirically inverted logic, also found in Carroll's books such as Alice's Adventures in Wonderland and its sequel, Through the Looking Glass, and What Alice Found There, stemmed from his vocation as a mathematician. It's not difficult to speculate on the tension between math's pristine rationality as an explanation of natural phenomena and the senseless and pointless misery of so much human behavior. One can imagine “Jabberwocky” as a mockery of his more orderly mathematical studies.

Carroll, aka Charles Dodgson, was one of the more temperamentally curious inhabitants of Victorian England, being also a photographer and inventor. He's been showing up recently on local stages as a character — first at South Pasadena's Fremont Centre Theatre, in which he meets Charles Dickens, in Daniel Rover Singer's A Perfect Likeness (running through Dec. 22).

And here he is again, in an authentically stammering, reflective and self-effacing performance by Hap Lawrence at the Odyssey Theatre, courtesy of the Porters of Hellsgate.

The Porters usually tackle Shakespeare, with an occasional foray into a play from ancient Greece. Writer-director Gus Krieger's Sherlock Through the Looking Glass is an exception, being a newish play. (It premiered in August as part of the Hollywood Fringe Festival.)

The central characters are fictional — Sherlock Holmes (Kevin Stidham) and Dr. Watson (Timothy Portnoy) — as opposed to being other authors, such as Sherlock's Arthur Conan Doyle. Holmes and Watson are, at least in Doyle's pen, flip sides of the same mastermind. Where Doyle portrays Holmes as extravagant and boastful, Watson is droll. Holmes routinely downs a 7 percent solution of cocaine, which Watson can't abide. But their joint gifts of understanding the world through empirical evidence have logic doing somersaults over Scotland Yard, leading to the team's capacity to identify beyond reasonable doubt every villain and criminal in their net. Though shrouded in eccentricity and wit, their Jekyll-and-Hyde antics are a monument to the capacities of reason.

The play puts these characters together with Lewis Carroll and his capacity to send reason down the rabbit hole. Can Sherlock and Watson compete? That is the play's central question.

Before getting to that, Krieger's play is also a play about words; aphorisms and quotes from the Alice books and from the Sherlock mysteries resound throughout. Though Krieger loves to strain Doyle's erudition to the breaking point, the play sparkles for stretches — thanks also to the accomplished cast.

Krieger directs his fantasia on a stage containing a large lighting grid and a couple of platforms. The spectacle resides in Jessica Pasternak's lush costumes, Charles Pasternak's fight choreography, and draperies that adorn the set, made wonderfully lurid by Sterling Hall's lighting design.

Krieger's ensemble of 14 doubles and triples roles as mid–19th century thugs, coppers, Scotland Yard detectives, damsels in distress and, in one large section, the cabal of nightmare visions populating Wonderland. (The masks are designed and constructed by Amelia Gotham.) Certain points get punctuated by the ensemble reciting in unison, and entire scenes are beautifully choreographed by Louise Gassman.

The plot starts with news of a series of diabolical crimes wherein the victims have imbibed some chemical that has driven them insane. Lillian Childress (Jennifer Bronstein) reports that very plight has struck her beloved sister, Josephine (Dana DeRuyck). (Lillian was a real person, a child whom Carroll used to see frequently when he visited her family.) There's white fur, perhaps from the rabbit in Carroll's story, at every crime scene — which makes Carroll the prime suspect. He is no angel, and says so, but he's also being framed. There's a real-life parallel in that, given questionable accusations through the decades of his being a pedophile. But that's the topic of another play.

Holmes and Watson defy Scotland Yard in trying to defend Carroll. Let's leave the plot there, except to say that it has more twists, turns, reversals and double reversals than a big-rig on a mountain highway. Trying to follow it all boggles the mind, which isn't necessarily a good thing in a clash between what's real and what's surreal. It is, however, artfully conceived and a source of endless curiosity.

I wish Holmes and Watson were two dimensions of the same brain, as they are in Doyle's books. Here, they're good friends who annoy one another and save each other from their lives' abounding peril. Their connection is more from circumstance than from personality, which diminishes the force of the logic they represent, in opposition to that of Carroll. This diffusion is what makes it difficult to isolate the play's clash of ideas, despite the very clever, goofy acrobatics with words, and with the literature they come from.

SHERLOCK THROUGH THE LOOKING GLASS | Written and directed by Gus Krieger | Presented by Porters of Hellsgate and the Odyssey Theatre, 2055 S. Sepulveda Blvd., W.L.A. | Fri., 8 p.m.; Sun., 2 p.m.; through Dec. 22 | (310) 477-2055 |

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