In his recent book Dividuum, the philosopher Gerald Raunig hypothesizes that current technology offers the possibility of a new “type of interactive and activating writing.” Raunig imagines a future in which data about reading is harvested from e-book readers to “recursively affect the production of books, of texts altogether.” Writers would be required to revise, abridge, or otherwise recast their now perpetually unfinished books in accordance with data about the “democratically” determined preferences of readers. All books would be crowdsourced, and writers would become the slaves of “an endless feedback loop and chain of ever new versions.” The modernist idea of “the open art work,” Raunig warns, could become a “Sisyphean nightmare.”

What Raunig envisions is a far cry from the “definitively unfinished” works that we’re familiar with from history. On the one hand, there are those that have come down to us in an unpolished or fragmentary state—because of, say, the artist’s untimely death, their inability to envision a way to proceed past a certain point, or simply the intervention of chance. On the other hand, there are works that are deliberately unfinished or unfinishable, including all instances of what Umberto Eco characterized as “the open work” in his in his 1962 classic of the same name—works whose very structure depends on indeterminacy, most obviously the aleatoric music of Karlheinz Stockhausen or Luciano Berio. (Strangely, Eco doesn’t mention John Cage.)

Other art forms have their own variants, such as Nanni Balestrini’s novel Tristano, in which the order of the text varies in every printed copy—its publishers claim there are 109,027,350,432,000 possible variations—or Stan Douglas’s video Journey Into Fear (2001), in which a 15-minute film loop is synched to bits of dialogue that are scrambled and recombined by a computer in combinations that play out for more than six consecutive days. Such works may not be literally infinite in scope, but no one reader could ever experience all their various instantiations. They evoke what might be called a kind of mathematical sublime, to borrow Kant’s phrase.

The question of finish was crucial to the emergence of modernism. The gauntlet was first thrown down by Manet, whose works in the 1860s were declared by critics to be unfinished—in fact, not even paintings but mere sketches. Similarly, a few years later, Whistler was accused by the Victorian sage himself, John Ruskin, of doing nothing more than “flinging a pot of paint in the public’s face.” But Baudelaire had already anticipated the howls of Manet’s and Whistler’s denigrators when he observed, in 1845, “that in general what is ‘completed’ is not ‘finished’ and that a thing ‘finished’ in detail may well lack the unity of the ‘completed’ thing.” From Manet and Whistler (or, indeed, from their predecessor Corot, who was the object of Baudelaire’s defense) until today, artistic modernism has been inseparable from the critique of finish. And this change in painting and sculpture occurred in tandem with similar developments in the other arts. Consider the difference, for example, between the omniscient narrator of the high Victorian novel and Flaubert’s style indirect libre, which depends on the reader making implicit connections and intuiting unmarked shifts in viewpoint; or, in the 20th century, the rejection by modernist architects of ornament—which had long been considered indispensable to a building’s finish—as something that, as August Perret remarked, “generally conceals a defect in construction.”

For all that, the force of the unfinished was far from a discovery of the 19th century, as Kelly Baum and Andrea Bayer point out in the catalog for “Unfinished: Thoughts Left Visible,” the exhibition they’ve curated with Sheena Wagstaff at the Metropolitan Museum of Art. (The exhibition, with which the museum has inaugurated its tenancy of the former Whitney Museum of American Art—henceforth to be known as the Met Breuer after its architect, Marcel Breuer—is on view through September 4.) They cite the Roman naturalist Pliny the Elder, who observed in the first century “that the last works of artists and their unfinished pictures…are more admired than those which they finished, because in them are seen the preliminary drawings left visible and the artists’ actual thoughts.”

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The evident congruence across the centuries between Pliny and Baudelaire suggests that, at least in its origins, modernism was the outbreak of a sensibility that had already flourished in various times and places. In the 19th century, it was called “art for art’s sake,” and it involved not only a commitment to art as such rather than the various instrumental purposes to which it is normally put, but also a recognition that what counts is the artist’s conception of a work, which generates criteria that are incommensurable with putatively objective standards. (It’s no accident that the two artists who have always been taken to exemplify the Renaissance notion of genius, Leonardo and Michelangelo, are precisely the ones who left the greatest number of unfinished projects.) For this reason, one can understand why the Met’s curators have divided their exhibition into two parts—before and after the onset of modernism—though it’s odd that they draw the line at the beginning of the 20th century rather than the middle of the 19th, when a recurring engagement with the unfinished became a conviction.

The irony, though, is that it’s the pre- and early-modernist portions of the exhibition that are its real draw. Along with gems from its own collection—among them Albrecht Dürer’s Salvator Mundi (ca. 1505) and El Greco’s The Vision of St. John (ca. 1608–14)—the Met has been able to call in some extraordinary loans: Jan van Eyck’s Saint Barbara (1437), from the Royal Museum of Fine Arts Antwerp; Titian’s Portrait of Pietro Aretino (1545), from the Palazzo Pitti in Florence; Jacques Louis David’s The Death of Bara (1794), from the Musée Calvet, Avignon; a whole raft of late Turners from the Tate, London; Edgar Degas’s The Fallen Jockey (1866–80/1881–97) from the National Gallery in Washington, DC; and Willem de Kooning’s Woman, I (1950–52) from MoMA. These are among the works that have provided the most fuel for the ever-unfinished debate about the meaning of distinctions like “finished” and “unfinished,” or “finished” and “completed.”

Probably the most dazzling of the loans, though, is the first thing you see when the third-floor elevators open onto the show: Titian’s The Flaying of Marsyas (ca. 1570s). I am surprised there hasn’t been more buzz, because the painting is, after all, one of the strangest and most extraordinary in history. The first time it was shown in this country, in 1986, the National Gallery became a site of pilgrimage for painters who had never expected to be able to see it in person. (The painting belongs to the Olomouc Museum of Art in Kromeriz, Czech Republic, from which it has traveled only once in its more than 300 years there.) In Greek mythology, Marsyas was a satyr who, having challenged Apollo to a musical competition—what jazz musicians used to call a “cutting contest”—and lost, is flayed alive as punishment for his hubris. Titian’s treatment of the subject somehow manages to present the cruelty and horror of the satyr’s torture not just unflinchingly, but with a kind of eerie serenity. That this is in some fashion an allegory of art is suggested by the way the god of light handles his knife so delicately, like a pencil or brush. The painting’s surface, with its subtle transitions from rough and seemingly hasty passages to ones of great refinement, appears to echo the unresolvable dualities of its subject. You’d almost think blood was part of the alchemy of its pigments.

David Bomford, in his contribution to the Met’s exhibition catalog, might as well be crediting Titian with the inauguration of modernism when he writes that the great Venetian, “in his late works, effectively authorized a whole new aesthetic in European art, in which a sketchlike technique and painterly brushwork fundamentally redefined what constituted a finished painting.” If Bomford is right, then so was the 19th-century critic Jules Castagnary in maintaining that the Impressionists did not invent the aesthetic of the unfinished. Instead, “They extoll it, they exalt it, they elevate it to a system, they turn it into the keystone of art, they place it on a pedestal and worship it; that’s all.”

As the catalog points out, it remains unclear whether Titian considered The Flaying of Marsyas unfinished. The situation of a work like his Aretino portrait is something else again: The sitter himself may have complained of its sketchiness, but it was a deliberate choice on Titian’s part—the non finito was a recognized stylistic trope, a way of evoking a sense of boldness, energy, and brilliance. What sets the 20th- and 21st-century portions of “Unfinished” apart from the earlier ones is that cases of doubt, like those occasioned by Marsyas, become rarer, especially as the exhibition inches closer to the present. Baum identifies four forms in which the unfinished manifests itself in post–World War II art: the provisional (e.g., de Kooning’s Woman, I, in which the work, in principle, could have been continued but was cut off); the infinite (among them works in series that could have been extended indefinitely, such as Yayoi Kusama’s Infinity Net paintings of the late 1950s and early ’60s); the entropic (works that somehow incorporate their own decay or ruin, such as Robert Smithson’s 1969–70 Mirrors and Shelly Sand, which loses some of its matter every time it’s shown and then packed up); and the participatory (works that have to be activated and therefore to some degree remade, such as Hélio Oiticica’s Bólides, 1965–66). All of these, except perhaps the first, are developments of the non finito as a stylistic option rather than the more troubling phenomenon of the work that was not and perhaps could not have been finished.

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Such truly unfinished works are rare in the second act of “Unfinished,” as are those whose status is ambiguous, where it’s unclear whether they were finished or not—as in the case of the van Eyck Saint Barbara or some of the Turners—or are obviously incomplete yet somehow unaccountably powerful, leaving viewers in doubt as to how they could have possibly been brought to any greater degree of completion. These are the cases in which art presents the problem of finish as an irresolvable epistemological question. True, something similar could be argued for many of the modern works. Diana Widmaier Picasso, the art historian who is also the painter’s granddaughter, asks in her catalog essay about his works: “Since interpretation is central to our perception of non finito, how are we to discern whether or not the artist deliberately suspended a work in a state of incompletion in order to produce an effect?” It’s true that the impulsive nature of Picasso’s approach to art meant that he could always change his mind about a work that had not yet left his possession—but precisely because his style assumes the legitimacy of the unfinished, it’s usually pretty evident that his use of it is deliberate. With Picasso, as with the artists who succeeded him, the question is rarely whether he deliberately stopped his work at a given point, but rather why: What did he see that satisfied him enough to stop? Likewise with de Kooning, whose wife Elaine recalled: “On any given canvas, I saw hundreds of images go by. I mean, paintings that were masterpieces. I would come in at night and find they had all been painted away.” What was de Kooning looking for through this relentless making and unmaking? One can no more put it into words than he did, but to understand his art, one has to form an intuition about what it was he was trying to glimpse.

By the 1960s, though, the method of doubt cultivated by Abstract Expressionists like de Kooning, their cult of improvisation and revision, had started to seem a stale cliché to many of their younger counterparts—those who would become Pop artists, Minimalists, and Conceptualists. As Sol LeWitt wrote in his “Sentences on Conceptual Art” (1969): “Irrational thoughts should be followed absolutely and logically…. If the artist changes his mind midway through the execution of the piece he compromises the result and repeats past results.” Furthermore, “Once the idea of the piece is established in the artist’s mind and the final form is decided, the process is carried out blindly…. The process is mechanical and should not be tampered with. It should run its course.” But what LeWitt proposed was far from a return to classical notions of finish, since the works generated by his systematic pursuit of intuition amount to what Rosalind Krauss once called an “immense spectacle of the irrational”—an outrage to meaning, at once blank and excessive. Compared with this, the curators’ suggestion that the point of LeWitt’s Variations of Incomplete Open Cubes (1974/82) is mainly how the viewer “mentally reconstructs the missing edges and ‘infers the unknown by clues from the known’” seems tame.

Just as the modernist sense of provisionality eventually became a game familiar enough to play well without conviction, so too did postmodern infinity, entropy, and participation. That’s certainly the feeling I get from works like Tatsuo Miyajima’s light installation Arrow of Time (Unfinished Life). But perhaps a complacency about the unfinished has been hardwired into contemporary work ever since artists succeeded in overthrowing the authority of the salons and academies and installing the idea that every artist is his or her own authority. I can’t help thinking of Robert Rauschenberg’s 1961 Portrait of Iris Clert, which really should have been included here. The work is the telegrammed statement “this is a portrait of iris clert if I say so.” Although Rauschenberg left himself a curious out—he doesn’t say if he does say so—the artist’s fiat is presented as the magic formula that forecloses all skepticism. I prefer de Kooning’s self-questioning, which preserves an enigma: The matter of whether the artist has fulfilled his intention remains ambiguous, and so does the intention itself.

Miyajima—along with Kusama—is one of just two Asian artists included in the exhibition. And there are no artists from Africa (with the exception of the South African–born Marlene Dumas, whose professional life has been in the Netherlands). If the Met really wanted to show what it could do with a new space for temporary exhibitions beyond the boundaries of its established departments, then limiting “Unfinished” to art from Europe and the Americas represents a huge lost opportunity. Classical Asian art—for example, Chinese literati painting, or those scholar’s rocks that only become artworks in the eyes of the prepared observer (although in some instances they may be subtly “enhanced” by an understated human intervention)—gives tremendous emphasis to what is left unpainted, unworked. A comparative, cross-cultural examination of the differing ideas of “finish” and the “unfinished” over the centuries would have been a tremendous contribution to knowledge.

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By chance, a small exhibition on the same theme was mounted last summer at the Courtauld Gallery in London. Among the works included—all from the gallery’s collection—was a Monet Vase of Flowers, dated 1881–82. But perhaps the dating should be more open-ended. According to Karen Serres, the curator of the Courtauld show, Monet expressed his dissatisfaction with the painting in the painting itself: “He just cannot express the light falling on the flowers and the leaves to his satisfaction. In some places he has scraped paint off while, in others, he has painted over dried paint. Every so often he must have returned to this painting and added a few brushstrokes in an attempt to improve it.” In this way, the painting remained in Monet’s studio as an open question nearly until the end of his life. “It was only in the 1920s that he finally decided to add his signature,” Serres explains. (A similar case would be French Window at Collioure, which Henri Matisse painted in 1914 but never allowed out of his studio.)

At what point does the conscientiousness that forbade Monet from signing his painting for 40 years become self-defeating? It’s hard to say. Is Walter Benjamin’s unfinished, perhaps unfinishable Arcades Project a quagmire or a posthumous triumph? I can’t help but think of a line that has haunted me for years, though I’ve forgotten the name of the book where I found it. Somewhere, the Mexican mystery writer Paco Ignacio Taibo II speaks of the absurd marriage between a book that will never be written and the man who will never write it. One’s involuted relation to the work is that of a debt in the worst sense: “the relation of a debtor who will never finish paying to a creditor who will never finish up using the interest on the debt” (the words are Gilles Deleuze’s).

The Met Breuer’s treatment of the unfinished is itself unfinished, because the true saints or heroes or victims of the unfinished cannot be seen there or anywhere. They are its unknown masters. In his 1988 novel The Botanical Garden, Jean Frémon—a remarkable writer who also happens to be a gallerist—introduces a minor character, one Pinto, a painter “who managed to pass unseen.” I assume that, like many of the book’s other characters, Pinto is based on a real person. “The devotion he bore for painting was equaled in intensity only by the hatred he expressed for his own production,” Frémon writes.

As a general rule, his passion for self-denigration led him to destroy any painting which might be able to pass as finished and to retain only those in which failure was manifest, the only ones toward which he showed a little interest and affection. “It’s because,” he said, “they still need me, they call to me, they keep me alive, they are still waiting for the inner light, a simple stroke, perhaps a single brush-stroke.”

There were thus hundreds of them, arranged standing, in staggered rows, leaning against one another, and he wandered among them all day murmuring, “A stroke, just a stroke.”

Later, toward the end of the novel, Pinto is given a posthumous retrospective by the Museum of Modern Art. That, I suspect, is the wholly invented part of his story.