From designs for renaissance forts to a replica of the sexy robot from Fritz Lang's Metropolis, 1926. From baroque engravings of New World cannibals in grass huts to pictures of yuppies enjoying a stroll through Celebration, Disney's "ideal town" in Florida. From Nazi racial propaganda to unalluring photos of early kibbutzim in Israel. From Stalinist kitsch in the '30s to Haight-Ashbury peace-and-love kitsch in the '60s. This intriguing range of objects and images is contained in "Utopia: The Search for the Ideal Society in the Western World," the sprawling show that runs until next January at the New York Public Library. It was jointly organized by the library and the mighty Bibliothèque Nationale in Paris-a rare enough collaboration in itself- and its catalog features essays by some 22 scholars, French and American.

Even so, there are some surprising omissions. The grid city of 19th century Barcelona, designed from the ground up as an ideal townscape by the socialist engineer Ildefons Cerdà, is the biggest example of would-be Utopian town design that ever got built-but neither it nor its inventor rates a mention in the catalog.

This is a show about failure. Necessarily so: its subject is the fallacies and delusions of human hope. Utopia has never existed. It is one of the enduring phantoms of the human mind, because it cannot be tested; every time someone tries it, it fails, and whenever it fails, there is always someone around to tell you the wrong reasons for the failure and propose another model, which in turn proves equally unworkable. This is as true of nutty little proposals by discontented geniuses-like the idea of communalist, rural "pantisocracy" put forward by Shelley, Coleridge and others in their youth -as it is of paranoid, pseudo-collectivist systems that take over whole societies and make huge contributions to the sum of human misery, like Stalinism. We flawed animals can be somewhat improved, spottily and with difficulty; but we cannot be perfected, which is what the Utopian project, in its various forms, is all about.

Utopia means conformity, a surrender of the individual will to the collective or the divine. "In la sua voluntate e nostra pace" (In His will is our peace), wrote Dante of the joys of heaven, where all choice is excluded by contemplation of the Divine: perfect obedience, perfect happiness, no worries. For God, substitute adepts, the People, the Charismatic Leader, or any one of a number of beguiling gurus, from Maharishi Mahesh Yogi to Jim Jones with his refreshing drafts of Kool-Aid in distant, steamy Guyana. The Utopian state of mind indicates a yearning to be released from history, to shed the burdens of free will, failure, improvisation.

Basically, Utopia is for authoritarians and weaklings. But it was also loved by philosophers, when they were in a what-if frame of mind, dreaming up systems. Two of Plato's works, The Republic and The Laws, have recognizably Utopian elements. One of the most charming items in this show is a Renaissance miniature from Florence by Zanobi di Strozzi, circa 1470, showing St. Augustine of Hippo dreaming up the City of God, taking dictation (so to speak) from an image of Florence itself, complete with Brunelleschi's great dome, which floats in the blue air before him.

On one side, all notions of Utopia touch heaven, or at least the primal Garden of Eden-that state of nature before mankind's fall, when all creatures coexisted in harmony and there was no sin in the world. The trouble with this is that Utopias are, or ought to be, whole societies, in which many conflicts of desire are solved and aligned-and Eden had only two people in it, plus a snake. Can you call heaven a Utopia? Probably not, but this is a question the show tends to fudge.

Is the idea of Utopia old? Depends on how you define it. The poet Hesiod, in the 8th century B.C., wrote about a Golden Age of perfect ease and social cooperation. The biblical vision of the New Jerusalem-as in the Apocalypse-is full of Utopian elements. One thing is sure: there is no standard model of Utopia, and it is always somewhere else. That came from its inventor, Thomas More, who in 1516 published the didactic tract that gave Utopia ("no-place" or "good place," depending on which similar-sounding Greek root you prefer) its name. He put it on an island, as others would; later versions placed it on an unexplored continent or, when those were used up, put it in outer space, or even below the crust of the earth.

If Utopia stayed on the earth, it had to be shifted in time, not space, to a Radiant Future: the future of Marx's dictatorship of the proletariat, filled with eupeptic workers and peasants striding into the future like electrified pouter pigeons. Or the future of Hitler's Jewless Europe. Or the milder anarchist fantasies of peace and ease that were common in late 19th century France and commemorated in a work like Paul Signac's In the Age of Harmony, 1895-96.

The fallout from the French Revolution, reverberating into the 19th century, made human hope seem infinitely large. Etienne-Louis Boullée's preposterous and magnificent ideal architecture-like his vast planetarium of a cenotaph to Newton-testifies to that, and such schemes set up echoes in the equally unbuilt Radiant Cities of Le Corbusier and others. They have a parallel in the insane size and detail of the social fantasies of French control freaks like that egregious crackpot Charles Fourier (1772-1837), who envisaged a society composed of "phalansteries" (so named because they would hold phalanxes of true believers), each with 1,700 souls living communally and practicing free love in barracks. By perfect mutual help, Fourier figured, paradise would return, the world would have 37 million musical geniuses the equal of Mozart and 37 million mathematical ones to rival Newton, and its oceans would turn to lemonade.

You can't fit that kind of transformation into the New York Public Library, but a poignant souvenir of its mindset is the sleeveless vest worn by Barthélemy Prosper Enfantin, a leader who with 40 disciples set up a barracks of a commune at Ménilmontant on the outskirts of Paris, in 1832. There they sang socially idealist hymns to soften the monotony of their labor, and wore clothes that symbolized their standing and ideals. On Enfantin's vest was emblazoned Le Pere (The Father). But it, like all the others, was designed to button up the back, so that you couldn't put it on without the help of your fellow Utopians. (If it had had no buttons, like a T shirt, it would have implied that you could look after yourself, heresy to the Utopians.)

Père Enfantin's vest is close to that great therapeutic invention of the time, the straitjacket. You can't look without dread at the photos and engravings of panopticons, meeting houses, commune buildings, phalansteries and other social-idealist architecture in the 19th century stretch of this show. They resemble prisons and nunneries because they were prisons and nunneries, the difference being that the prisons meant to keep sinners in, whereas the Utopian buildings aimed to keep them out. But the same grim coerciveness suffused both, as we know from their ultimate state forms in the 20th century: Nazism and communism.