If there’s one thing Hollywood is obsessed with, it’s reimagining what has been done before. Why else would we have two “Spider-Man” franchises in six years, multiple fairy-tale retellings and reboots of classics like “Planet of the Apes”? The reason producers can’t just leave established works alone is because they’re still trying to figure out how best to reinterpret classic stories. This brings us to the BBC’s “Sherlock,” the best show you’re not watching.

A modern retelling of Sir Arthur Conan Doyle’s beloved canon, “Sherlock” puts the titular consulting detective (Benedict Cumberbatch, “Tinker Tailor Soldier Spy”) in present-day London. It sounds simple enough, but the execution is pure genius.

Creators Mark Gatiss and Steven Moffat (who helped revive cult favorite “Doctor Who” for the 21st-century) have done what so many couldn’t, capturing the essence of these stories in a modern setting. It’s beyond just having Sherlock and Dr. John Watson (Martin Freeman, “The Hitchhiker’s Guide to the Galaxy”) traipse about wearing jeans. Sherlock frequently texts his friends and enemies, or he quickly looks up a fact on the Internet. His fame rises because of hits on John’s blog. In one episode, a locked camera phone is a major plot device. The Hounds of Baskerville are genetically modified experiments — or are they?

Each of the six episodes — three per season — is approximately 90 minutes, a length worthy of feature films. But they don’t feel like feature films. They go by as quickly as a standard 42-minute drama, each more suspenseful and brilliant than the last. The titles usually play on Doyle’s original stories, such as “A Study in Pink” (originally “A Study in Scarlet”) or “A Scandal in Belgravia” (“A Scandal in Bohemia”). At their first meeting, Sherlock asks John, a soldier, “Afghanistan or Iraq?” The explanation of what inferences led him to this question — everything from tan lines on his wrists to how he stands — is copied almost verbatim from Doyle’s prose.

Though there is no intention of stepping on the toes of Guy Ritchie’s “Sherlock Holmes” films, the comparison is inevitable. And “Sherlock” has one crucial element that gives it the edge: It actually puts the viewer in Sherlock Holmes’s mind. Ritchie’s films usually do this when Robert Downey Jr. is calculating his punches, but Sherlock’s mind is so much more complex than that. He specializes in logic and inference, thinking at speeds that would make most of our heads spin — and indeed, they do. At the top of many scenes, camerawork is done from Sherlock’s point of view, pointing out stains on clothes or other clues the rest of us just aren’t perceptive enough to notice. Other times, he fills us in with an impressively rapid monologue explaining the deductions he made while everyone else was busy doing trivial things like having social skills. On such occasions, Cumberbatch’s delivery is nothing short of mesmerizing.

The few relationships the reclusive Baker Street detective manages to maintain are so subtly and skillfully developed that they feel natural from the outset. Sherlock and John take to each other instantly because of a shared thirst for adventure, and because John is the first person to not be thoroughly repelled by the arrogance that accompanies Sherlock’s unnerving brilliance. The fun part of setting the show in the current era is that people aren’t embarrassed to ask if Sherlock and John are dating — or to just go ahead and assume they’re a couple. After a while, John stops denying it, especially when his string of relationships fail because all girlfriends play second fiddle to Sherlock Holmes.

And of course, no version of “Sherlock Holmes” would be complete without the detective’s arch-nemesis, James Moriarty (Andrew Scott, “John Adams”). Ritchie’s films depict a Moriarty that is Sherlock’s intellectual equal, but what they don’t show is how utterly deranged he is. Scott plays Moriarty without any restraint, creating an unhinged image of chaos, much like Heath Ledger’s Joker.

Scott’s unsettling sadism adds to the chemistry of a fantastically three-dimensional cast of characters. Cumberbatch and Freeman play Sherlock and John so naturally that they feel like friends from the moment they meet. Gatiss doubles as Mycroft Holmes, coldly indifferent but also grappling with how to take care of his little brother. When Lana Pulver (“True Blood”) shows up as Irene Adler in season two, the sexual tension between her and Sherlock is so palpable that it practically jumps out of the screen.

Allow me to take a leaf out of the Reichenbach hero’s book and speak to you in simple facts: Sherlock is the best show on television. It’s perfectly cast, expertly written, stunningly acted and just a pleasure to watch. If only all shows could be on this level. Then again, if it were ordinary, it wouldn’t be “Sherlock,” would it?

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