How do you make a movie, in 2004, about a man who wants to conquer the world? That question hangs uneasily over Oliver Stone's three-hour epic about Alexander the Great, the Macedonian king who, by the age of 25, dominated the greater part of the known world, lording it over an empire that stretched from Greece to India. To contemporary eyes that kind of ambition might seem a tad, shall we say, insane. And on screen, world domination has tended to be the purview of James Bond villains and aliens from outer space.

That's not the way Stone sees it. He's always been, for all his anti-establishment rages, a hero worshiper. Powerful men fascinate him ("Wall Street," "JFK," "Nixon"); "Alexander" is clearly meant as a celebration of the most powerful of them all. But with this sometimes stunning, ultimately stupefying epic Stone has met his Waterloo. Though filled with spectacular battles, opulent sets and grand Hellenic passions, this madly ambitious film doesn't compute. Stone's movies, love them or loathe them, have always aroused powerful emotions. But by the end of this histrionic historical slog, you are more likely to feel numb, and not at all sure what compelled him to tell this story. It's a long march with no destination in sight.

Stone's Alexander (Colin Farrell) is an idealistic visionary who dreams of uniting the world, bringing freedom and Hellenic values to the barbarous East. He slaughters in order to liberate. Sound familiar? But the images that unavoidably arise of Bush, Cheney and Wolfowitz in Iraq seem unintentional: Stone has no political agenda this time; he'd never equate those chicken hawks with the mighty warrior king who led his soldiers across Asia for eight years, never losing a battle. The movie claims Alexander as a multiculturalist before his time; unlike most of his comrades, he respects the mores of the cultures he vanquishes. But there's the rub--before he respects them, he's killed them. We're supposed to root for this guy? I found myself identifying with his rebellious foot soldiers, angry, beat up and eager to return home after seven years of bloody swordplay.

Still, though "Alexander" is emotionally and intellectually incoherent, it's the work of a first-rate filmmaker who creates unforgettable images. The Battle of Gaugamela, in which Alexander's vastly outnumbered troops rout the Persian Army, is swift, savage and stunning, and it's equaled by an almost surreal engagement in the forests of India, where the spear-bearing enemy streaks through the trees atop running elephants.

But the movie is not all battles and global strategy: Stone tries to get inside his hero's psyche with a little Freudian assist. The boy Alexander (Connor Paolo) is the product of a more-than-dysfunctional family: a debauched, one-eyed father, King Philip (Val Kilmer), who won't give him the love, or the throne, that he covets, and an estranged, ambitious, conniving mother, Olympias (Angelina Jolie), who raises him to be a colossus like the mythic Achilles. Jolie, eyes blazing, arms and shoulders accessorized with serpents, delivers a grand-opera turn that falls just short of high camp. In fact, Stone encourages all his actors to go full throttle: those ancient Greeks didn't know from half measures. Neither does the score, by Vangelis, which ranges from the exalted to the overbearing.

To his credit, Stone doesn't duck the issue of Alexander's pansexuality. It's clear that the love of his life is his childhood friend and loyal comrade Hephaistion (Jared Leto). Their affection, however, is expressed in manly hugs; the real eroticism is reserved for a hot scene with his Asiatic wife, Roxanne (Rosario Dawson). (With lovers like Dawson and Leto, it's a wonder he gets any world-conquering done.) Farrell works mightily to hold Stone's sprawling history lesson together, convincingly morphing from eager boy to battle-weary conqueror. But could any young contemporary actor fill Alexander's globe-bestriding shoes? He remains beyond Farrell's grasp. And, as Stone conceives him, beyond ours.