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The New York Times

As if in direct response to its overscaled, canon-cementing Abstract Expressionism display, the Museum of Modern Art is also giving us something quirky, speculative, physically light, a show called “On Line: Drawing Through the Twentieth Century.”

The first exhibition is a pat march through old history; the second, a tangly exploration of undertraveled paths that intersect in surprising ways.

The museum does drawing surveys at regular intervals. The last one was “Drawing Now: Eight Propositions” in 2002, which focused on young artists and defined drawing quite conventionally, as work in pencil, ink or paint on a flat surface, usually paper. That show came at a time when figurative painting was being pushed very hard, and stylistic references to 19th-century academic art and contemporary cartooning were in favor.

The new survey reflects developments since then, among them a renewed interest in performance and abstraction, and a simultaneous embrace and rejection of digital media. Rather than narrowing a definition of drawing, as the older show did, this one loosens everything up.

Yes, you can draw a line on a flat surface using traditional tools. But you can also sculpture a line, or cut, dig, drip, sew, walk, dance or weave one. You can make a line bold or all but invisible, tiny or 16 miles long. You can draw it with a well-schooled skill or with no skill at all, hands off.

Given such options, any attempt to put a seal on a specific history of drawing is, to say the least, premature. “On Line” organized by Connie Butler, chief curator of drawings at MoMA, and a guest curator, Catherine de Zegher, the former director of the Drawing Center in SoHo is very much about history, specifically that of Western modernism, but lays out variant beginnings for it.

We get the standard MoMA beginning in the up-front presence of Picasso. But at least it’s Picasso at his most daring, when, in tandem with Georges Braque, he shattered the flatness of the picture plane and angled some of the pieces so they jutted out into space.

It’s hard to recapture how disorienting this must have felt at the time, though the inclusion of one of Picasso’s 1912 cut-cardboard guitars near the entrance to the show reminds us what the revolution once looked like. Suddenly we were seeing draftsmanship in the round, in depth, lines shooting straight out at us, like bullet trajectories. (MoMA has a show devoted entirely to these early guitar pieces coming in February; it could be, should be, great.)

Grouped around the Picasso object are other artists who did their bit to send 19th-century aesthetics into a tailspin. We see Malevich using drawn lines to stake out the fourth dimension, Umberto Boccioni turning lines into emblems of technological speed, Kurt Schwitters treating lines like beams and risers in architectural collages, and Kandinsky the show’s title is from his writing transforming lines into jazzy visual dances.

And high above all of them in the gallery, some real dancing is in progress, and a different beginning to a history of drawing as line is proposed. Projected on a floating screen is a late-19th-century film of a woman flapping and swirling the long silk sleeves of her dress as she performs a piece by the choreographer Loie Fuller (1862-1928).

Born in America, Fuller was a Folies-Bergère star and avant-garde darling who inspired artists to think of drawing not as static and finite but as action in space and lines as points in motion.

The fluttering dancer in the film, like some exuberant angel, offers a welcome break from the usual-suspects story of modernism, as does another work near the show’s entrance, an installation by the young Indian artist Ranjani Shettar.

Composed of hundreds of floating, hand-modeled beeswax pellets linked by an openwork mesh of string, it alludes both to the natural world (buds, stars) and to the Internet, and points to the networking concept of art in the exhibition ahead. Her piece also anticipates the increasing presence of women as the show progresses through the 20th century and into the 21st. If you wanted to choose a single route to trace, theirs is an exciting one.

Early modernism was a largely male preserve, and it is so here, though already in Malevich’s Russia we’re seeing the abstract textile designs of the great Lyubov Popova. And in the 1950s Georges Vantongerloo’s mystical twists of transparent tubing, suspended in a vitrine like marine specimens, are beautifully matched by Sophie Taeuber-Arp’s color pencil drawings, like scatterings of tossed-down thread.

In the 1960s and ’70s an “open sesame” time for art, sculpture sends organic lines out into space. We see this in Eva Hesse’s “Hang Up” with its escapee loop of metal cord; in Edward Krasinski’s blue cables leaking across the floor; and in the free-hanging, lopsided steel-wire grids of the Venezuelan artist Gego, born Gertrud Goldschmidt in Germany.

The grid was, of course, the signature form of those years. Ostensibly an emblem of order and stability, it often has a very different effect here. Gego makes a small grid from jigsaw blades; Mona Hatoum a big one from barbed wire; Cornelia Parker another from bullet lead turned into thin wiring.

And like Ms. Parker’s, a lot of drawing in the show implies or entails motion. For her well-known performance “Up To and Including Her Limits” (1973-76) Carolee Schneemann made wall-size crayon drawings while swinging above the floor in a harness, as we see her doing in a video. In a 1997 film the choreographer William Forsythe virtually ties his body into knots. In her filmed “Trio A,” Yvonne Rainer unfurls a series of everyday moves the head toss, the walking slouch, the pick-up-the-dropped-key bend then repeats them in the same order backward. (Ms. Butler contributes a lucid catalog essay, full of ideas, about the movement-line collection.)

Two Canadian artists Françoise Sullivan in 1948, and Mimi Gellman in 2009 drew abstract patterns with their movements through snow, while, in a hypnotic 1968 film, the Japanese artist Atsuko Tanaka, famed for her dress made of wires and electric bulbs, used a stick to inscribe huge designs of circles a circulatory system in seaside sand as a tide creeps in.

Viewers hungry for more conventional formats will find them, early and late, in work by Paul Klee, by Tomás Maldonado in the 1950s, and by the sublime Nasreen Mohamedi (1937-1990), one of several remarkable Indian artists here, others being Ms. Shettar, A. Balasubramaniam and Sheila Makhijani, who is currently making her New York solo debut at Talwar Gallery in Manhattan.

Their presence along with that of figures like Zilvinas Kempinas, Vera Molnar, Karel Malich, Lotte Rosenfeld and Emily Kam Kngwarray lifts the show out of museum business as usual. Unlike the roster selected for “Drawing Now” in 2002, which was almost entirely market preapproved, many of these artists are still trying to secure a place in the international scheme of things.

True, much of their art is ultralow key, though discretion can have advantages. When I visited “On Line” during museum hours, I found a good-size and attentive crowd and a notable absence of drive-by shutterbugs. It’s hard to photograph what you can barely see, whether apparent smudges on a wall (stretched wires wound with horse hair by the French artist Pierrette Bloch) or a big gray blur (waves of concentric ink lines rippling out from a single fingerprint in a wall drawing by Giuseppe Penone).

Although the show barely tiptoes into the digital realm with a few tame samplings, it at least points to it as a direction for further treks. And in general Ms. Butler and Ms. de Zegher have done what curators should do. They’ve dug deep into near-at-hand sources and pulled out little-seen material. (Most of the show is from MoMA’s collection.) They’ve introduced artists from outside, some of whom we can look forward to seeing more of.

In the process they’ve knocked given histories off of pedestals and left old hierarchies off balance. Maybe most important, apart from giving us stimulating art to look at, they’ve continued the job of writing women into art history, not as also-rans but as primary makers and shapers, and quietly but forcefully re-inscribing a political line now ineradicably drawn in the sand.

-Holland Cotter