In 1428, in the church of Santa Maria Novella in Florence, an artist called Masaccio used the new rules of perspective to make the world's first fully illusionistic painting. From that moment on, Western art would focus on all the ways the visible world could come to life in art.

But surely there's more to life, and art, than what meets the eyes?

How about gravity, time, direction, growth, decay and all the other crucial intangibles -- don't they deserve an artist's time and thought?

More than five centuries after Masaccio did his thing for sight, a flock of his descendants turned their attention to such neglected aspects of reality. For a fertile decade from about 1962, the 15 or so artists of the loose-knit Arte Povera movement, based in Rome, Turin and Genoa, threw out all the rules and goals of their great Italian predecessors. They struggled to rewrite everything that artmaking could be about, and be.

Starting from scratch, and moving into the unknown: That's the extraordinary project documented in "Zero to Infinity: Arte Povera 1962-1972," a breathtaking, mind-bending touring show now at the Smithsonian's Hirshhorn Museum.

Take one of the first pieces you encounter in the Hirshhorn show, titled "A Cubic Meter of Infinity." It was completed in 1966 by Michelangelo Pistoletto, the only arte poverist who made much of a splash in the United States. The work consists of a tidy cube, one meter across, made of six mirrors carefully lashed together so that their silvered sides face inward, with only slivers of reflecting surface showing at the edges. We see a sober and imposing piece of gray minimalist sculpture -- American minimalism was Arte Povera's biggest competition at the time -- but we know that its insides are crowded with infinitude.

I first came across this piece when I was young, before I'd been taught what great art was supposed to be, and it wasn't hard to see what the work was all about. My only complaint was that Pistoletto hadn't scratched a hole in the back of one of the mirrors, to let us glimpse all that infinity he'd trapped -- which, even if there were any light inside to see by, would only have ruined the conceptual perfection of his infinitely reflected nothingness.

But this isn't really conceptual art, where the work is just an illustration for an idea that might as well be jotted down on paper. It is truly a materialization of infinity; like much of Arte Povera, it wants to bring us close as we can come to grasping the ungraspable. Or at any rate, it comes as close to giving presence to infinity as any Renaissance painting could to giving us real access to the saints.

This review may have just broken some kind of rule. It seems that every essay or talk on Arte Povera is supposed to launch with a discussion of the term itself, coined by curator Germano Celant in 1967, after the art form was already well underway. First you declare the phrase untranslatable -- even though "poor art" has almost exactly the same range of cryptic connotations as the Italian words -- and then you declare it indefinable, too.

Maybe the problem is that Arte Povera isn't really a descriptive term at all. It is a proper noun, in the full sense of the word, used only to pick out one place and moment and a varied group of people, rather than to describe the kind of art that they produced. Just as Italians don't translate Johnny Cash as "Giovanni Soldi," and we don't take Federico Fellini and rename him "Freddy Cats," so the term Arte Povera has to stand unchanged and unexplained. It picks out a movement with a very special personality within the history of art, but without any one mission or unifying look.

At most Arte Povera names a certain kind of radical creative character -- a kind of total creative rebel that Italy, with its almost oppressive history of classic art, was unusually likely to turn out. It's the kind of rebellious character that says, "Let's throw out everything our parents said art had to be about and see if we can still make objects that mean something."

In this country, Arte Povera has never had much recognition. The Hirshhorn's new show, which fills the museum's entire second floor, should fix that. It reveals huge depth and range in this short-lived Italian movement. By comparison, some of the same era's most touted American experiments in art come off looking tame and unambitious. And if you didn't know when they were made, many of the vintage pieces now in Washington could pass as fine examples of today's most forward-looking creativity.

It's hard to think of any single-movement show this big that has so little repetition and that sticks so well in memory. Each of the nearly 150 works on view, by 14 different artists, has its own peculiar charms and quirks that set it off quite clearly from its neighbors.

One of the purest, most pared-down thinkers and makers of Arte Povera was Giovanni Anselmo. A 1971 piece called "Invisible" is just a slide in a projector, turned on and pointed out into the exhibition space. There's nothing to see -- the art is quite invisible -- until you happen to stroll by at just the right distance, so that your clothing can act as the work's temporary screen. At which point, if you're attentive, you notice the Italian word visibile in little white letters floating on your clothes. This is truly visibility reduced to its purest components: a collection of light rays momentarily brought into focus to spell out their simple presence, then allowed to scatter off, ungraspable and invisible again, into the cosmic mix.

Again, this isn't just a clever idea illustrated. It is a genuine, lyrical realization, in art, of the very nearly intangible. And it gives great pleasure to those who get to know it: One security guard at the Hirshhorn takes pride in sharing the work's secret with any patron about to wander past; even when he's all alone, he can be seen making the invisible visible on his regulation crisp white shirt.

In another piece, first realized in 1968, Anselmo takes a large, squared-off block of polished granite, about the size of a stand-up drinking fountain, and uses a loop of wire to lash another piece of granite, about dictionary-size, against one of its flanks. Before the wire is completely tightened, a large, fresh head of lettuce is placed between the mommy block and its little chip, so the three objects form a kind of rock-and-lettuce sandwich. And then time, decay and gravity -- the real subjects of the piece -- all begin to do their stuff, until there's too little lettuce left to keep the wire tensioned, and the baby block slides to the floor.

For all the grand, timeless forces of nature that this piece brings to life, however, it is very down to earth. It is above all a charming, witty, splendidly peculiar object, whose look is almost as off-kilter as the thinking it sets off. It is "poor art" in the sense that some folk crafts might be described as such -- foursquare, playful and immediate.

But there is more here than first meets eye or mind, just as the Old Master pictures we first grasp as "portraits" or "still lifes" can turn out to be much more than records of dead people and long-gone fruits.

One series by Giuseppe Penone began as a suite of massive wooden beams, milled from the hearts of ancient trees. Meticulously following the grain in the lumber, the artist whittled down through layer after layer of the outer, older wood, revealing the twiggy sapling that each beam started out as many years before. Some part of the young wood is always left embedded in the uncarved plank below, to show both what the sapling grew up to become and the artwork's starting point. This is a lovely, cryptic statement about human labor, both artistic and industrial, and the way that nature gets wrapped up in it -- or unwrapped, in this case.

Covering similar territory -- but years before the environmental movement had built a head of steam -- Piero Gilardi cast and dyed foam rubber into a perfect duplicate of a patch of forest floor, complete with weathered stones and mossy branches. You could once install his "Nature Carpets" by the yard, for urbanites who didn't favor the trouble of a real country jaunt.

Other members of the movement made art that riffed on what art once had been, before they and their colleagues got their hands on it.

Pistoletto's "Lunch Painting," from 1965, is an upright square framed out of planks of rough-cut lumber 18 inches wide and 7 feet long, like a giant cigar box with its bottom knocked out and then set up on end against the wall. Built into the box, out of the same coarse wood, are two right-angled chairs with a T-shaped table set between them. In profile, the whole thing looks almost like a drawing of a breakfast nook, done by a toddler out of cracked spaghetti. When in use by an intended owner, Pistoletto's wood construction would have become both a frame for eating lunch within, and a framed picture of the act in progress -- as well as a witty crossover between that era's latest modernist design (those were the woody days of Danish modern, don't forget) and the rigid forms of 1960s abstract sculpture.

Pistoletto's quirky colleague Alighiero Boetti, who died in 1994 after years of working far from home with Afghan and Pakistani weavers, also made an almost-abstract sculpture that plays with pictureness. His 1969 "Nothing to See, Nothing to Hide" is a massive window frame in metal and glass, three panes by four and each a meter square, leaned flat against the wall. It takes Masaccio's famous idea that pictures are a window on the world, and sees what happens if you make that window real, but get rid of the world beyond.

Like much of Arte Povera, it takes the old idea of seeing the world through a work of art, and asks us to gaze steadily at what's in front of us instead.

Giovanni Anselmo's "Invisible" is just a slide projected into air -- until a visitor becomes its screen.Anselmo's granite and lettuce commen-

tary on decay and gravity, part of the Arte Povera exhibition at the Hirshhorn Museum.Pistoletto's "Three Girls on a Balcony" reflects other art, and visitors, nearby.Piero Gilardi's "Nature Carpet," a dyed foam rubber patch of a forest floor.Pistoletto's "Lunch Painting," a witty crossover between '60s design and the rigid forms of abstract sculpture.A plank carved down to its younger self by Giuseppe Penone: A cryptic statement about human labor and the way that nature gets wrapped up in it -- or vice versa.