"To the one who invented a nothing," begins Guillaume Apollinaire's personal inscription to painter Robert Delaunay in an exhibition catalogue of 1913. Abstraction usually describes a process of lessening, but for Apollinaire, a poet and critic who was one of abstraction's key supporters, the term implied plenitude: a nothing that was nonetheless something. But what was it? In the autumn of 1911, when pictures without recognizable subject matter emerged simultaneously from the studios of Delaunay, Vasily Kandinsky, František Kupka, Arthur Dove and Francis Picabia, it was hardly clear that these efforts added up to a cohesive program, much less a movement. The appeal of abstraction was its promise of universality, but in practice it yielded the opposite: nothing meant something different to everyone.

Making sense of abstraction has long been at the core of the Museum of Modern Art's historicizing mission, beginning with Alfred Barr's 1936 show "Cubism and Abstract Art," famous for its phylogenetic schema of modernism's origins and influences. Now, just after the centenary of its birth, abstract painting is again in MoMA's spotlight thanks to curator Leah Dickerman's magisterial survey, an exhibition spanning the movement's first decade and a half and comprising over 350 artworks by dozens of artists from across Europe, Eurasia and the United States. The show is a jewel box for the eye, with color as its main idea. But dazzle is not everything: Dickerman's curatorial argument is dead serious, challenging Barr's flow-chart version of history by emphasizing the movement of ideas from individual maker to maker. The term "social network" looms large in the exhibition wall text, ascribing to abstraction the status of open-source code—a point illustrated by a sprawling hub-and-spoke chart at the entrance to the show, which marks social ties between artists as so many vectors (too many to unravel, in fact).

A leveler in the church of Barr, Dickerman urges against defining abstraction in terms of forward progress; indeed, the show is less interested in the invention of abstraction than in abstraction as invention. The main impact of this horizontalist approach is geographic, bringing peripheral sites into focus without denying the importance of major hubs. America and Britain fare particularly well in the wake of this reorientation: for example, London-based Vorticist painter David Bomberg's combustive canvas, In the Hold (ca. 1913-14), is one of the exhibition's many unexpected pleasures—a carefully managed bomb blast of crosscutting grids and jagged edges. That said, few visitors will fail to recognize Paris's importance as the focal point of prewar abstraction, or its waning status thereafter, succeeded by Russia, Germany and the Netherlands.

Dickerman also seeks to overcome the traditional separation of art forms, representing abstraction as an exchange between painting, poetry, dance, music, photography and film. We learn, for example, that Kandinsky's first efforts at nonobjective painting were catalyzed by a performance of Arnold Schoenberg's atonal music, inspiring the exuberant gyrations of the painter's massive Composition V (1911). We are reminded, too, that women artists played a key role as inter-media pioneers: Sonia Delaunay-Terk's collaboration with poet Blaise Cendrars, a radiant fold-out poem titled Prose of the Trans-Siberian and of Little Joan of France (1913), ranks among the greatest art-literature assemblages of the century. In a wholly different scene and moment—the antiestablishment circle of Zurich Dada—Sophie Taeuber-Arp's needlework canvases, such as Untitled (Composition with Squares, Circle, Rectangles, Triangles), 1918, subversively remade abstraction as anonymous handicraft, accomplishable by anyone, anywhere.

Exploring these farther shores of abstraction is an achievement worth celebrating in itself, and Dickerman pulls it off without ceding an iota of visual intensity. Still, visitors may find themselves asking whether the term "invention" does not paper over a vein of doubt, the unhappy knowledge that nothing might truly be nothing. Encountering the wooden model of Vladimir Tatlin's Monument to the Third International (1920/1979) beneath MoMA's skylight is one of the show's many sublime moments, but ebullience is not its mood. Designed during the Russian civil war as a proletarian cultural center and broadcast tower, Tatlin's monument is modernism at its most desperate—art hanging by the thread of Marx's mantra, "I am nothing and I should be everything." Abstraction meant invention, but also free fall. No one could say what the ground would look like when it got close.

FrantisÌ?ek Kupka:
Localization of Graphic Motifs II, 1912-13, oil on canvas, approx. 61⁄2 by 61⁄4 feet; in "Inventing Abstraction" at MoMA. ©ARS.