Just about a century ago came one of those seemingly small innovations in art that unleashes epochal forces of transformation. In 1912, Georges Braque began using paper and fabric on the surface of his paintings, inaugurating not just a technique, but a form, the “pasted paper” work. The surface of the image was suddenly a thing to be played with, and a host of ancient assumptions, and categories, began to fall apart. A new exhibition at the Hirshhorn Museum explores the viral spread of this one very small idea into new media, from collage and assemblage to montage and installation pieces.

“Over, Under, Next,” billed as the first in a series of exhibitions showcasing the Hirshhorn’s permanent collection in advance of its 40th anniversary next year, takes on an enormous topic. The incorporation and manipulation of found materials are so fundamental to art over the past century that attempting to cover it all in one exhibition is like trying to survey 19th-century art in a show called “Painting and Sculpture.” Yet a respectable effort has been made to create threads of connection and striking juxtapositions, to give some order to the overabundance of ideas and methods on display.

First, there is a roughly chronological overlay, with a 1913 Braque opening the exhibition, and a 2009 sound suit by Nick Cave at the end. Braque’s “Aria de Bach,” borrowed from the National Gallery of Art, uses black and wood-grain paper swatches to disassemble the elements of a two-dimensional image. A basic charcoal sketch of a guitar floats in what may be a three-dimensional space, with rough shadows giving a sense of depth.

The guitar strings exist in different spaces simultaneously, connected to the sketch on white paper and crossing over the added piece of black paper. To one side, the wood-grain cutout suggests color and texture, now disconnected from the guitar’s surface, but not entirely fugitive from the picture. What may be a piece of music — the “Aria de Bach” — is lying on the base of the guitar body, suggesting the work that needs to be done: This is now an image that must be performed, rather than taken in at a glance, with the viewer in the disconcerting position of reconnecting its polyphonic elements into something harmonious.

Braque couldn’t possibly know that his small game with materials and form would, through generations of exploration, lead to things like Nick Cave’s 2009 “Soundsuit,” a hybrid of costume and sculpture that revels in gaudy, kitschy exuberance. But one senses that he was aware of the potential unleashed. Examine “Aria de Bach” closely and you see a delicate outline around the pasted paper pieces, almost as if they need to be contained or cordoned off from the rest of the picture.

Man Ray, "Nut Girls [Les Filles des Noix]," 1941 (PHOTOGRAPHY BY LEE STALSWORTH; Copyright 2013 Artists Rights Society (ARS), New York/ADAGP, Paris/PHOTOGRAPHY BY LEE STALSWORTH)

The same sense of needing to contain an unruly new invention can be felt in Hannah Hoch’s exquisitely made 1920 collage “Tailor’s Flower,” in which a floral motif sits on top of a dense grid of mechanically drawn lines, a basic juxtaposition that cascades with ideas about men and women, sterility and generation, rationality and beauty.

Juxtaposition is, of course, the basic operating principle of assemblage, and so too the exhibition proceeds mainly by compelling juxtapositions of humor and darkness, and a recurring confrontation between organic and inorganic materials. In one room, Hans Richter’s 1943-44 “Stalingrad,” a horizontal scroll covered with newsprint and other materials that gives a poetic and visual account of a turning point in World War II, is seen near Alexander Calder’s 1944 whimsical “Fish,” assembled from metal rods, plastic, wood, glass and ceramic fragments.

Jean Dubuffet’s 1953 “Butterfly-Wing Figure” returns to the subtle play with surface inaugurated by Braque. Using micro-thin butterfly wings to compose a primitive human figure, Dubuffet seems to recall the 16th-century Giuseppe Arcimboldo’s two-dimensional painted composite portraits made of found objects (fruits, shells, vegetables, flowers). Butterfly wings — almost a cliche for defining beauty in nature — are put in the service of grotesquerie and one is left with the troubling sense that this isn’t just a human figure, but Man in the larger sense, voracious and destructive in his tyranny over other beings.

A decade later, experimental filmmaker Stan Brakhage would sandwich insect wings and other natural materials between strips of film, then reproduce the image onto a single length of film. It recalls one of the most basic, and earliest of photographic techniques, the contact print made by exposing light sensitive paper with a thin object, such as a leaf, on top. But the 1963 short film was as radical when it was made as anything in the exhibition. Superficially it seems connected to Dubuffet’s “Butterfly-Wing Figure,” but is much harder, and sadder, as thin slices of organic material flit rapidly across the screen. The viewer can decide: A moth to flame is a figure of death, or a metaphor for how we relate to intoxicating media such as film, or both.

Visitors emerge from Brakhage’s powerful film into a room of inorganic materials and sculpture, including an abstract form by John Chamberlain made in 1961 from enameled metal that looks to be part of a car. David Smith’s 1951-52 “Agricola,” a loosely anthropomorphic form, is made from painted steel, and its title — Latin for farmer — seems a deliberate provocation, underscoring the sharp contrast between a resistant industrial material and the age-old need of human beings to muck around in the dirt and humus.

As one artist in the exhibition said, “I work with materials that are already charged with significance.” That could be said of almost every artist in the exhibition. By using found materials to assemble new forms, you inevitably import more meaning than you can control. Scraps of paper, newsprint, candy wrappers, pills, pins and other thoroughly quotidian objects carry with them both public and private associations.

An 1989 installation piece called “Palimpsest,” by Ann Hamilton and Kathryn Clark, uses thousands of tiny, handwritten pieces of paper pinned to the wall of a rectangular room to suggest both its title — a text overwritten with successive layers of new writing — and a powerful sense how delicate and fleeting our private experience of the world truly is. An oscillating fan gently blows the papers, creating rustling pattern on the walls.

Robert Rauschenberg, "Dam," 1959. (Copyright Estate of Robert Rauschenberg/Licensed by VAGA, New York, NY)

A rustling of meaning isn’t a bad way to describe many of the best works on display, which often feel like microcosms of emotional energy, small, contained systems set in motion by the powerful resistance or attraction of the objects they contain. Michelangelo Pistoletto’s 1967 “Venus of the Rags” takes this to extremes, with a plaster cast of the Roman goddess confronting a huge heap of cheap fabric, suggesting past and present, hierarchies of value, and the basic contrast between an art that imitates the world and an art that is inseparable from the world it critiques.

Inevitably, “Over, Under, Next” feels diffuse, coming into focus when the associative logic of its layout is strongest, weakening when the connections are more superficial or perhaps too idiosyncratic to be detected. A room with a large Damien Hirst installation feels like futile space, and one can’t help wishing that the work of Sarah Sze, who will represent the United States at this year’s Venice Biennale, was represented.

But the idea is to showcase the Hirshhorn collection in a new way, and there is enough powerful work in the loose layout to make it very much worth a visit.

Over, Under, Next

“Over, Under, Next: Experiments in Mixed Media 1913-Present” is on view at the Hirshhorn Museum through Sept. 8. For more information call 202-633-1000 or visit www.hirshhorn.si.edu.