Like obsessed viewers of “Sherlock,” Dr. John Watson is a fan of Sherlock Holmes. Illustration by Marc Aspinall

The third season of “Sherlock” opens with an homage to its online fans, but tensions between the classic detective story and its audience go way back. In 1893, Arthur Conan Doyle famously killed Sherlock Holmes, chucking him off Reichenbach Falls. Protesters wore black armbands in the streets. Even the author’s mother was opposed, writing to him, “You won’t! You can’t! You mustn’t!” A few years later, Conan Doyle gave in and rolled back the rock, but Sherlockians call the period in between the Great Hiatus. According to Anne Jamison’s terrific “Fic: Why Fanfiction Is Taking Over the World,” when the author retreated his fans stepped in, writing their own Sherlock mysteries: the origin of modern fan fiction.

The men behind “Sherlock,” which airs in the U.S. on PBS, are major fans themselves: the showrunners Mark Gatiss and Steven Moffat (who also oversees “Doctor Who”) have done a nifty job of transplanting the detective to contemporary London, finding digital analogues for Holmes’s feats of cognition. (When Sherlock “reads” a crime scene, enormous words appear on the screen, like an online “word cloud.”) Many of their plots are twists on Conan Doyle’s, and Season 2 ended with a reference to Reichenbach Falls: Holmes (Benedict Cumberbatch) plummeted from a rooftop, seemingly to his death. Yet somehow he survived. In this season’s first episode, “The Empty Hearse,” Holmes returns to his old stomping grounds, and, at first, the show feels tentative, and slightly cartoonish, as if its hard drive were being defragged, the anxieties of its writers reorganized and purged. By the end of the episode, the story coheres, and the series is rebooted with a ping.

In real life, since the Season 2 finale, “Sherlock” buffs have collaborated to solve the mystery of the detective’s survival—even creating a Google Street Map that allowed amateur sleuths to test hypotheses. In “The Empty Hearse,” these followers become characters: they meet in a support group and use hashtags like #sherlocklives. The first scene is classic bait and switch: we see Holmes escape, with some Bond-like derring-do and a romantic kiss, and then the story is abruptly revealed as one of the club members’ theories. Later, a goth teen-age girl presents another version, in which Sherlock and his nemesis Moriarty lock lips. The episode isn’t perfect: there’s a mystery, involving an Underground train, that is downright goofy—as the British writer Laurie Penny notes in a lovely manifesto defending Sherlock “fan-ficcers,” it’s as silly as any “amateur” plot. But “The Empty Hearse” is, finally, an affectionate episode, at once a hat-tip and an exorcism, and a coded confession of its own status as fan fiction. When the mystery is explained, at last, it’s with a shrug of humility. “Not the way I’d have done it,” a club member says. “Everyone’s a critic,” Holmes replies.

The new season reunites Holmes with his primal fan: that love addict Dr. John Watson, played by Martin Freeman. Watson has been grieving Sherlock’s suicide for two years, but he’s now dating a nurse, Mary (played by Freeman’s partner, Amanda Abbington, for added intertextuality), and he’s bought an engagement ring. When Sherlock shows up, the men’s intimacy reignites, and the game is on.

Like many genre stories, “Sherlock” has inspired reams of “slash fiction” among its viewers, especially its female ones: the term goes back to the homoerotic Kirk/Spock stories of the nineteen-seventies, written pornography in which the shouty captain and the Sherlock-like half-Vulcan went for it. The genre exploded once the Internet came along: you can find slash fic about almost any characters you can imagine, from Harry Potter/Draco Malfoy onward. Rather than play innocent about these dynamics, “Sherlock” mines them heavily, for humor and frisson. Yet for all the “Wait, are they actually gay?” gags, the show is admirably committed to something more serious: the notion of Sherlock/Watson as both True Detective and True Romance. This is a real love affair, not a joke one.

It’s also a central shift from the original: Sherlock is still a detective, there are episodic mysteries, there is still Baker Street (now equipped with Web access), but the subject of the show is not so much Sherlock’s deductions as this relationship, which is itself a kind of mystery. Sherlock and Watson are best friends, certainly. They’re also chaste boyfriends, as well as a captain and his first mate. Mostly, though, they’re a god and a mortal, mutually besotted—the most impossible love affair of all. When viewers “read” this relationship (and Sherlock’s relationship with his other intra-show fans, who include the morgue employee, Molly, and Lestrade, the admiring police inspector), it’s similar to the way Sherlock “reads” a crime scene: intuiting clues that “normals” might dismiss. And, of course, Watson is implicitly a writer of Sherlock Holmes fan fiction. In Conan Doyle’s books, he keeps notes of their adventures, which he publishes in magazines. On the television show, naturally, it’s a blog.

The second episode dives into the question of what Watson is to Holmes, and it’s one of the best so far—a daring display of nested mysteries that also inverts the central love dynamic. Set mostly at Watson’s wedding, it’s framed by Holmes’s best-man toast, a dilatory, frequently belligerent, then suddenly tearjerking monologue, studded with anti-marriage zingers and hilarious accounts of their drunken bachelor party, in which the word clouds go blurry. (The signature of a good, serious TV drama is, ironically, a sense of humor: if it’s glum and gluey, run for it.)

The speech is punctuated by flashbacks to cases that the two men have investigated. Some are very short: “And of course I have to mention the Elephant in the Room!” Sherlock says, and there’s a quick shot of the two men standing in a doorway, and from offscreen we hear a loud jungle roar. With each tale, Holmes builds the case for the doctor’s insight, his warmth and humanity—and why these are useful to Sherlock. Yet he’s also humbling himself. A reflexively arrogant individual who refers to himself as a “high-functioning sociopath,” Holmes now takes Watson’s role. He burnishes Watson’s legend, rather than Watson burnishing his. In other words, it’s an episode about Sherlock Holmes as a fan—the god stooping to praise the human. In one flashback, the two sit on a London park bench, framed by dark trees, as Watson struggles to reassure Holmes that their relationship won’t change. The shot emphasizes the impossibility of their kinship: Watson is half the size of Holmes; as he slumps, the cadaverous Holmes sits up rigidly, so that their conversation feels as if it were taking place not merely between two men but between two different species, or possibly between a mountain and a shrub. Then Watson turns, and finds that Holmes has disappeared.

The show has always been fascinated by Holmes’s callousness toward those who love him, his tendency to abandon and exploit them: like Bones, House, and other dark TV geniuses who are his unacknowledged offspring, Holmes sees connections but can’t connect. He’s like a Google algorithm, if it were sexy and wore dashing wool coats. Halfway through his best-man speech, he describes a case in which a number of lovelorn women have had one-night stands with a “ghost” who disappears the next day. Sherlock gathers these lonely hearts in an elegant auditorium, where he interrogates them, searching for a pattern. It’s only gradually, as the camera toggles from closeups to dramatic shots from above, and then abruptly to images of Sherlock in his office, that we recognize what we’re actually seeing: a poetic representation of a virtual experience—Holmes is online, meeting the women through a discussion board. When his conversations end, the women vanish, and he closes his laptop.

The show is at its best in such moments, these sequences that capture the semi-virtual, semi-real ways that we think, and feel, and meet, and connect today. It’s a rare attempt to make visible something that we take for granted: a new kind of cognition, inflected by passion, that allows strangers to think out loud, solving mysteries together. ♦