My friend waved his hand dismissively when I mentioned that I’d recently seen an outstanding exhibition about Edgar Degas: “How can you go wrong with Degas?” he said. True enough. But what I’d seen was more than just another guided tour of the artist’s greatest hits. Instead, “Degas’ Method,” on view through September 1 at the Ny Carlsberg Glyptotek in Copenhagen, is an intellectually and aesthetically challenging exhibition that promises not just familiar pleasures but a deeper understanding. Instead of organizing Degas’s oeuvre around its subject matter (ballet dancers, racehorses, landscapes) or the diverse media he employed (oils, pastels, bronze) or even chronology, it focuses on his aesthetic premises and representational strategies as they cut across medium, motif and the artist’s career. Line Clausen Pedersen, the exhibition’s curator, has articulated this approach by singling out Degas’s relation to Impressionism—as ambivalent as it was  essential—and his ideas of process, draftsmanship and artifice. Pedersen’s sort of daring ought to be more widespread among museum curators but isn’t, perhaps because it requires thinking more like an artist and less like a collector or product manager.

But there’s an irony in the title “Degas’ Method.” As Pedersen points out, when a fellow painter proudly boasted of having found his own method, Degas replied, “Fortunately for me, I have not found my method; that would only bore me.” In his once-famous and appropriately titled essay “Against Method,” Paul Feyerabend wrote, speaking of revolution and implicitly of science, that “participation in a process of this kind is possible only for a ruthless opportunist who is not tied to any particular philosophy and who adopts whatever procedure seems to fit the occasion.” Degas, who was born in 1834 in Paris and died there in 1917, would have said the same of art. As Pedersen writes, he is “faithful to no one and nothing, at most to himself and the idea that his art makes a difference—to art.” Such self-absorption is as modest as it is arrogant: “you must have an elevated idea,” Degas believed, “not of what you do, but of what you can one day do; without this it is not worth the trouble working.”

And yet, allergic as he was to the idea of method, of devising a formula and then unfailingly applying it, Degas was nothing if not methodical, working with great diligence and intense application. He disavowed impulse and extemporization as much as he did method. “I assure you,” he liked to say, “no art was ever less spontaneous than mine. What I do is the result of reflection and study of the great masters; of inspiration, spontaneity, temperament…I know nothing.” The key is repetition: “It is necessary to execute a motif ten times, a hundred times. Nothing in art must look accidental.”

Knowingly or not, Degas kept violating his own strictures: his works often appear casual and immediate, deceptive as that impression may be. That he would contradict himself is hardly surprising. The English painter Walter Sickert, in his memoir of Degas, reports various opinions of the master’s—that one should use oil paint as if it were pastel, or that “the art of painting was so to surround a patch of, say, Venetian red, that it appeared to be a patch of vermilion.” (Josef Albers would have agreed!) But Sickert is mindful that, with Degas, occasion is all: “It must be remembered that I am only recording what he said at a given date, and to a given person. It in no wise follows that, by advising a certain course, he was stating that he had himself refrained from ever taking another.”

In painting as in conversation, Degas knew how to take hold of a transitory observation and generalize it—to lend a percept the solidity of a precept. Yet he never lost sight of life being perpetually in transition. In his depictions of dancers at the barre, jockeys on their mounts or women bathing, he catches his subjects in an “off” moment. He is less likely to show the performance or the race than he is the moment before or after when nothing much is happening, and he excels in capturing these interludes without imposing any ulterior formality on them, either by training a too obviously intent gaze on his subjects or by depicting them in a way that advertises how much study he’s invested in them. Degas’s sense of organization and accident is eccentric. His studio, as the gallerist Ambroise Vollard recalled, was “always in complete disorder,” yet when Vollard accidentally dropped a scrap of paper, the painter scooped it up and threw it in the stove, saying, “I do not care for untidiness.” His works are like that, too: Unfussy and teeming with the random stuff of life, they cohere around a hidden sense of order that lies just beyond one’s grasp, yet no less palpable for that.

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Degas’s propensity for saying one thing and doing another is undoubtedly linked to his inveterate experimentalism (or opportunism, as Feyerabend would put it), his propensity to try anything that might lead to new ways of reinterpreting and revising his customary subjects and compositions. Consequently, for all their pungency and quotability, his quips—which I don’t intend to stop quoting—cannot be taken as entirely descriptive of his practice. Pedersen and her colleagues are not as careful about this as they should be. They take at face value the artist’s repeated assertions that, contrary to his fellow Impressionists, he had upheld the classical tradition of draftsmanship as transmitted through Ingres: “I've always tried to urge my colleagues to seek for new combinations along the path of draftsmanship, which I consider a more fruitful field than that of color. But they wouldn’t listen to me and have gone the other way.”

Degas’s drawings are marvelous, and the early ones, cool and linear, show Ingres’s unmistakable influence. But in the practice of drawing, Degas radically departed from the method of Ingres and the academic tradition of which his work is the apotheosis. Ingres’s neoclassical drawing was never a matter of simply inscribing a beautiful line. Its purpose was always teleological; no matter how much observation it involved, no matter how much trial and error, it was always oriented toward composition and the idea of a completed picture. This composition, in turn, was to be based on an analysis of the narrative to be conveyed; it had to coherently present what would later, in a completely different context, be called the decisive moment, the moment in which the truth of an action reveals itself. This kind of drawing is essentially a sort of coding.

Degas seizes upon moments that Ingres would have found utterly insignificant. In his images of dancers, for instance, he rarely shows the dance itself; what interests him is the rehearsal, or even the warm-up for the rehearsal. Likewise, he will sometimes paint a horse race, but more often he shows the period before the race has started or after it’s over. As Pedersen says, “Degas chooses unstable moments and situations that are not long-lasting, but not instantaneous either,” ones in which “the figure is preparing for something else—something that lies further out in the future or is perhaps over.”

The allure of ambiguous moments led Degas to reconceive the purpose of drawing: instead of crystallizing a moment, it liquefies a momentary order. A fascination with instability is especially evident in the many small wax or clay figure studies that Degas kept in his studio. The only sculpture of his own that he ever exhibited was the famous Little Dancer Aged Fourteen, but after his death, seventy-four others that he’d made were cast in bronze. (The Ny Carlsberg Glyptotek is one of the few institutions to own a complete set of them, and Pedersen has put them to excellent use in the exhibition.) Not only do they often represent unbalanced poses, but the sculptures themselves are also unbalanced: their original wax or clay forms required external as well as internal armatures to keep them upright. These sculptures were not meant to bear their own weight.

Degas’s conception of drawing led him in the direction of a second master who has always been considered Ingres’s dialectical opposite: Eugène Delacroix, who is often made to play the colorist to Ingres’s draftsman. But Degas understood that, while both artists were great draftsmen and great colorists, they had two different ideas of drawing that entailed two different ideas of color: Ingres uses drawing and color to establish clear distinctions, Delacroix to make those distinctions less so. Likewise with Degas, the mark is smudged, blurred—an area that looks like a pure transition of color appears on closer examination to be composed of innumerable little crisscrossing lines of different hues that have been blotted and interfused. A Degas line is always a quantity of substances, not a bounded singularity. The matter of which the image is composed is fundamentally mixed; indistinctions are the image’s basis. For Degas, any dichotomy between drawing and color is meaningless, and drawing loses any specific identity; it is no more the essence of a painting than an armature is the essence of a sculpture.

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Pedersen may overemphasize Degas the draftsman, but no viewer can walk away from the exhibition without having been amazed by his radical use of color. If his approach to drawing tends to scramble its ability to function as a code, his use of color does the opposite: because he restricts his palette to a few colors—and ones that are hardly the “natural” hues of the things he’s painting—color ends up having an independent impact of its own. It was undoubtedly his palette that gave rise to the mutual admiration between Degas and his younger colleague, Paul Gauguin, whose strange and disquieting clouds of color might well have floated out of a Degas painting like The Milliners (1882–1905). Likewise, I am almost reconciled to the mawkishness of Picasso’s Blue Period now that I can see its cooler, drier precedents in a Degas pastel like Portrait of a Woman in a Green Blouse (ca. 1884). Degas is normally cast as a realist, but his incessant transformations of the real lead his art in the direction of Symbolism. When he supposedly told the Irish writer George Moore that “la danseuse n’est qu’un prétexte pour le dessin” (the dancer is only a pretext for the drawing), he wasn’t emphasizing the centrality of drawing once more; rather, he was intimating that the dancer is transformed into something else. As his friend Stéphane Mallarmé put it, “the dancer is not a woman who dances, for these juxtaposed reasons that she is not a woman, but a metaphor resuming one of the elementary aspects of our form, sword, cup, flower, etc….and that she does not dance, suggesting, by miraculous short-cuts or élans, with a bodily writing what it would take paragraphs of prose with dialogues as well as descriptions to express: a poem freed from any scribe's instrument.”

And yet Degas’s art is too complex and multifarious to be tagged as Symbolism. “Degas’ Method” reminds us that, after Ingres and Delacroix, Degas took on a third great influence, an artist only a little older than himself, namely Honoré Daumier—another great draftsman, but one who worked for the popular press and showed that great art could be bent to the service of journalism without losing its integrity or aesthetic force. In his own way, Degas was no less intent than Daumier on being an observer of his time. He once told Sickert that he hated taking cabs because “you don’t see anyone.” He preferred taking the bus: “On est fait pour se regarder les uns les autres, quoi?” (We’re made for looking at each other, you know?) His search for what Mallarmé called the elementary aspects of form was intense, but it was inextricable from the endless pleasure he took in looking at people. And Degas saw things that no artist had committed to canvas before, little gestures that are insignificant but touching in a strangely anonymous way because they are simply human: a woman’s arm stretched out as she towels her hair dry, a dancer’s leg lifted up to the barre as she practices.

Degas painted dancers more than any other subject because he identified with them—not as performers but as workers, and above all because they are not only artists but also, in themselves, art. Their training endows them with bodies already imbued with artifice. Similarly, if Degas had to repeat the same motif “ten times, a hundred times,” this was not only in order to revise and remake it, but also to revise and remake himself in his developing capacity to reveal the motif. He explained it this way, with an extraordinary metaphor: “Art does not expand, it repeats itself. And, if you want comparisons at all costs, I may tell you that in order to produce good fruit one must line up on an espalier. One remains thus all one’s life, arms extended, mouth open, so as to assimilate what is happening, what is around one and alive.” The horizontal beam on which the espaliered fruit tree is trained resembles, more than anything else, the dancer’s barre.

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Degas’s art was inimitable, and it survived him in its reinterpretation by Gauguin and, at times, Picasso, as well as in the work of Matisse and Bonnard and, later, de Kooning. But it was Degas’s rival Claude Monet who succeeded in imposing his idea of Impressionism on history: an analysis of natural perception, an art at home in the outdoors, rather than Degas’s distillation of memory into symbol through repetition, an art more at home in the studio. More important in the long run is that Monet’s commitment to serial production (which was very different, as Pedersen points out, from Degas’s own practice of making independent variants without sequence) leads to the systemic abstraction of the 1960s, not to mention Andy Warhol’s reiterations of mass-produced imagery and Sol LeWitt’s definition of conceptualism as an art where “the idea is the machine that makes the work.” It’s Monet and not Degas whose work points toward the origins of most of what today is called contemporary art. Is Degas now a relic, or does he still have living artistic progeny?

Degas’s children may be a distinct minority among contemporary artists, but they’re out there if you look hard enough. If you happen to be in London this summer, one of the most engaging of them has a substantial show on view at Parasol unit, a nonprofit exhibition space, through August 10. Merlin James is a painter of Welsh origin, currently living in Glasgow, who has been exhibiting to increasing critical interest since the early 1990s. Like Degas, he emphasizes his attachment to tradition, and not only in his paintings; James is a critic, too. But instead of publishing in a slick contemporary art journal, he’s found a home at the dowdy old Burlington Magazine, where Moore and Sickert published their memoirs of Degas back in the day. And yet for all his supposed traditionalism, James takes no aspect of painting for granted. He has made some of his works by stretching sheer polyester over an elaborate frame and touching the translucent surface with ghostly splotches of color. Others, painted on canvas, have holes gouged in them or objects of various sorts collaged on top. The paint itself sometimes seems to be mixed up with some nameless schmutz—it could be hair or who knows what studio muck. This approach reminds me of Degas’s remark that “with a bowl of soup and three old brushes you can make the finest landscape ever painted!” James is not a showman aiming at sheer novelty; he seems to want to avoid following any formula and, per Feyerabend, to “adopt whatever procedure seems to fit the occasion.” This means, above all, that James uses representation or abstraction as he sees fit, and always methodically.

Also like Degas, he tinkers for years with works in the studio. The nocturnal landscape Dark (Trees), for instance, bears the dates 1989–2012; it is one of the simplest-seeming paintings in the show, so we have to assume that what happened to it over twenty-three years was a gradual editing out or paring down. Another lengthy effort, Black (1984–2008), is a more elaborately composed abstraction whose surface suggests that what is visible was painted on top of another sort of work entirely; it’s not so much that a painting has been revised over time as that one painting has been entirely replaced by another.

When James discusses painting he often speaks of “plasticity,” and when in his work he uses paint to form a determinate image, what seems to interest him most is manipulating it as a malleable material, something to be pushed and pulled, pressed and dragged to create endlessly different sorts of marks. He tries to handle the surface he paints on and the structure that keeps the surface taut and on the wall with the same freedom. He likes to quote old paintings—Sower (2001) derives from Millet, while Large Sea (2005) conjures up Courbet—but less to commemorate the past than to see how much a familiar image can be transformed. James often paints buildings, but as the critic John Yau has pointed out, the construction of a building seems to stand, in his art, for the construction of a painting. I’d extend the thought: you can make a building or a painting out of the remains of existing ones and achieve something habitable.

Like all good painters, James suffuses his work with a very personal intuition of the qualities and capacities of light. It is through the medium of light that the emotional quality of his art materializes. Yet light is also the favored medium of his quest for plasticity: he wants it to be something he can grasp, mold, make an impression on, rather than something ethereal, immaterial, that enters the eyes from some great distance. It is hard to tell whether or not he fulfills this desire, but the results are equally poignant either way.