Catherine Black, a celebrated neurologist and the main character of ABC’s risible “Black Box” is known as “the Marco Polo of the brain.” That shouldn’t come as much of a surprise: It is a truth universally acknowledged that a television procedural’s protagonist must always be the very best at what she does. Dr. Gregory House, despite being an asshole and a Vicodin addict, is a genius at diagnosing obscure illnesses; Adrian Monk’s OCD helps him solve cases no one else can; Dr. Temperance “Bones” Brennan’s Asperger's-like detachment make her the FBI’s go-to for unsolved deaths. That’s another thing Catherine Black (Kelly Reilly) has in common with all these other TV doctors/detectives/investigators. She’s so good at understanding the intricacies of the brain because—irony!—there’s something wrong with her own brain. She has a secret: she’s bipolar. In an age of high-school teachers cooking meth and suburban parents doubling as Soviet spies, this secret may seem somewhat ho-hum. But “Black Box,” debuting Thursday night, offers a glaring example of one of pop culture’s most noxious tropes: mental illness as superpower.

Catherine, the medical director of a fancy neurological center known as the Cube, is apparently amazing at her job, and “Black Box” doesn’t hesitate to draw a connection between her genius and her illness: “Catherine has an insight into her patients that no one else has, allowing her to communicate with them on a different level,” according to ABC’s press notes. She’s fabulously empathetic and intuitive, somehow able to see what all the other doctors miss (though her cases should be familiar to anyone who reads Oliver Sacks's essays). That’s because, the show keeps reminding us, mental illness goes along with greatness. “Hemingway. Sylvia Plath. Billie Holiday. Dickens. Melville. These are just a few of the great minds that suffered from a fine madness. Should they be medicated into mediocrity?” Catherine asks after skipping her meds. She’s particularly taken with Van Gogh; in the middle of a manic episode, we see the sky transform into “Starry Night,” as it does in her hallucinations.

If all this sounds ludicrous, that’s because it is. Catherine explains to her psychiatrist (played by the always luminous Vanessa Redgrave) that her manic episodes are “a freaking rocket ride”— but they mostly just involve dancing in the moonlight to smooth jazz. She does bad things, which basically means sex with strangers and spinning in circles on a balcony in her silk nightgown. Still, the show exults in the character’s self-destructive tendencies; she goes off her medication at least once an episode, providing lots of opportunities for surprise twists and wild sex. “Do you want to be exceptional and dead?” her psychiatrist asks her, as though that’s the only alternative to a life of mediocrity.

The show’s particular absurdities are all its own, but “Black Box” is part of a long line of fictions that treat psychological disorders as a professional asset. On TNT’s “Perception,” which will soon air a third season, Eric McCormack plays a schizophrenic neuroscience professor who moonlights as an FBI consultant, solving murders with the help of witnesses he hallucinates. “Mind Games,” which lasted five episodes this spring before getting the axe, starred Steve Zahn as a bipolar genius who used to teach psychology and now runs a “problem-solving” business. Benedict Cumberbatch’s Sherlock Holmes coolly calls himself a “high-functioning sociopath,” but Sherlock fans have been offering competing psychological profiles for Arthur Conan Doyle’s character for decades. “Homeland,” at its best, complicated this dynamic, but Claire Danes’s Carrie Mathison was still gifted with a perception that her saner C.I.A. colleagues lacked. She was a superhero, until she was a lovesick lackey. Because it’s so painfully clumsy and thoughtlessly constructed, “Black Box” distills what’s unsettling in the rest of these shows into something wholly unpleasant.

Many of these series do display greater realism than prior portrayals and have been duly praised for that. Better to fill our screens with magical madwomen, perhaps, than to push mentally ill characters to the narrative margins or portray them as only criminal or dangerous. Determined to play-act a kind of verisimilitude, “Black Box” is filled with lists of medications and symptoms, as though its cribbing its clunky dialogue from the Wikipedia page for bipolar disorder. But some of the best portrayals of mental illness on TV ignore questions of accuracy and take a more roundabout route to emotional truth. Take Showtime’s “United States of Tara,” which made no effort to be a diagnostically accurate portrait of dissociative identity disorder, but managed to offer a devastating portrayal of what it’s like to love someone who is very sick. In “Wilfred,” an absurdist comedy on FX, a young man moves on from a suicide attempt by hanging out with a talking dog.