If stereotypes are unhealthy, then Paul Haggis’ “Crash” could well be the unhealthiest movie ever made. At least on the surface.

Certainly, Haggis — the Oscar-nominated screenwriter of “Million Dollar Baby” and Emmy-winning producer of “thirtysomething” — indulges many of society's ugliest racial presumptions in this roving, provocative snapshot of modern-day Los Angeles. There's the hot-headed Iranian shopkeeper (Shaun Toub); the shrill, spoiled Brentwood wife (Sandra Bullock); and the racist, authority-abusing LAPD patrolman (Matt Dillon).

And, not to be forgotten, the strutting South Central street punk (rap star Ludacris) who decries racial prejudice on one hand and waves a handgun in the other.

To a degree, these characters are designed to titillate our collective sense of paranoia, distrust and contempt. And admittedly, there is something deliciously provocative about the way Haggis offers them to us without apology. The ugliness proves particularly therapeutic for Bullock (“Miss Congeniality”), who — as the frustrated, carjacking-traumatized wife of the city's young district attorney (Brendan Fraser) — is obliged to do the gutsiest acting of her career.

It's all a magic act, of course. Haggis doesn't want to perpetuate stereotypes; he wants to defuse them. So he shows us the characters in their most humane, vulnerable moments — these aren't horrible people, merely angry and frustrated, stalled at a uniquely American crossroads. Don Cheadle (“Hotel Rwanda”) is commanding as a cynical vice detective who finds himself privy to the ingrained racial hypocrisy at City Hall, and Terrence Howard (“The Best Man”) gives a dynamite performance as a successful black TV director whose mild assimilationist attitudes are crumpled by the Man.

In setting us up as he does, Haggis — a Canadian — is like the shrink who digs for reactions before making his diagnosis. Likewise, “Crash” bears all the stress points you might expect from a movie that presumes to put the whole of society on the analyst's couch. It tends to be manipulative and sensationalistic, and Haggis doesn't seem to know when to stop tuning his characters. This is particularly true in the case of a well-meaning rookie cop (Ryan Phillippe from “Cruel Intentions”) who is proved mortal after performing a good deed.

If one had to classify “Crash” — not to be confused with David Cronenberg's 1996 autoerotic snoozer of the same name — it would pair nicely with Paul Thomas Anderson's “Magnolia,” Lawrence Kasdan's “Grand Canyon” or any other ensemble drama in which Los Angeles served as theater for the human divide. Though not as formally daring as the former or endearing as the latter, “Crash” has a more focused moral: We're better than people think we are.