In an age of Google Earth and Twitter, when Facebook knows more about you than your mother does, and advertisers track your every move online, would anyone have need of Sherlock Holmes for his deductive powers?

Absolutely yes, according to Sherlock, a brilliant new television version of Sir Arthur Conan Doyle’s immortal stories. Airing on PBS’s Masterpiece Mystery! on October 24 and 31 and November 7 (check local listings) after a UK debut last summer, this riveting update plunks down the great detective in twenty-first-century London, surrounded by smart phones, antismoking laws, and the trappings of the “war on terror.” As the show’s taut plotting unfolds, this young, antisocial, technologically proficient Sherlock becomes recognizable as a private eye who could go toe-to-toe with Stieg Larsson’s Lisbeth Salander, an alienated character he resembles more than a little.

We first meet the 221B Baker Street resident (an aptly dweeby-looking Benedict Cumberbatch) as he examines a corpse in a morgue. The camera is positioned inside a body bag that he unzips, so the introductory shot captures his face above us, upside down. Like the show’s credit sequence, featuring sped-up footage of cars careening across modern London, this topsy-turvy portrait is a visual signal that program creators Steven Moffat and Mark Gatiss (veterans of the BBC sci-fi series Doctor Who) intend to upend our preconceptions about the sleuth. And yet the body-bag moment refers to Conan Doyle’s book A Study in Scarlet, in which the detective studies a corpse to see how readily bruises may be produced after death.

Many of these references are ingeniously and cheekily skewed. For example: The title of the first episode is “A Study in Pink.” The new Watson (Martin Freeman) blogs about his adventures instead of recounting them in print. And the revamped Holmes slaps on three nicotine patches during a particularly tough case—like his pipe-smoking forebear, who called the “The Red-Headed League” mystery “quite a three-pipe problem.”

But Sherlock also makes deeper acknowledgment of the way social attitudes and entertainment standards have shifted since iconic Holmes interpreters like Basil Rathbone and Jeremy Brett donned their deerstalkers. Like the messy but not heretical 2009 Robert Downey Jr. movie Sherlock Holmes, the TV reinvention ratchets up the story’s pace. Plot twists fly as fast as text messages—indeed they frequently take the form of text messages. Art directors have lingered lovingly on the show’s décor (check out Baker Street’s fleur-de-lis wallpaper, or the Rubik’s Cube marked with Chinese characters on Sherlock’s desk)—and yet, at times the show’s pace and look seem to borrow from video games. When this Holmes exclaims excitedly, “The game’s on!” instead of “The game is afoot,” you half-expect him to switch on an Xbox.

Moffat and Gatiss express a distinctly modern attitude toward the sleuth’s eccentricities. Holmes’s extreme rationality, his apparent asexuality, and his indifference to social convention might have led Conan Doyle’s Watson to term him “the best and the wisest man whom I have ever known” (The Final Problem). But Freud, existentialists, the self-esteem movement, and other modern phenomena have left us with a different sense of human nature; today, the cerebral, unemotional, violin-playing detective can seem psychologically disturbed (see Fox TV’s House).

Sherlock acknowledges that and uses it to leverage suspense—even a little of the atmospheric paranoia that TV shows like Lost and Dexter have conditioned us to expect. In “A Study in Pink,” two police colleagues of Inspector Lestrade (Rupert Graves) call Holmes “a psychopath.” Holmes snaps back: “I’m a high-functioning sociopath!”—as if he’s just been reading Oliver Sacks. But the viewer can’t help feeling that the police may have a point: with his brusque, obsessive manner and pinched, pale face, this Holmes looks as if he might someday cross over to the wrong side of sanity and the law. For that matter, Watson—a military veteran who suffers from post-traumatic stress disorder after a tour in Afghanistan—doesn’t seem too stable either.

Will they snap? Won’t they? You’ll get no spoilers here. To paraphrase a note that Conan Doyle’s Holmes once sent to Watson: Tune in to Sherlock if convenient! If inconvenient, tune in all the same.