Why do some artists embrace jarring material? I can only speak for myself. My work has been described as nasty, insulting, sexist, violent and in bad taste--among other things. But accusations like that won't change the way I paint.

First, I don't like to be told what to do. We artists are stubborn individualists, in constant quest of a means to express that individuality. You can say that I shock you just to draw attention to myself, but I don't. Sure, drawing attention is sometimes part of it, but only a small part.

In the 1960s, some of my work satirized and attacked domestic violence, gang rape, blind patriotism and the Vietnam War. One painting was called "Helicopter." The central figure was a cop, naked except for his gun belt, sunglasses and helmet; he had angry private parts. He was giving the middle-finger salute to a hanging Vietnamese boy. In a bucolic forest behind him, Asian people were fleeing in horror. Over this mayhem hovered a combat helicopter.

This piece was one of many in a show of my work in 1969 at the Corcoran Gallery of Art. It generated a protest letter from a man, which was published in the Washington Star, saying that, somewhere in all the good reviews, he should have been warned that some of the works on display were obscene. The Star's art critic was upbraided. There were calls to the director of the Corcoran. It was just a tiny flap compared with the uproar over the "Sensation" exhibit at the Brooklyn Museum of Art in New York. But I was surprised, not because people reacted strongly to my political statement, but because their reaction was of shock. I continue to be surprised when people express shock at my work.

What was I doing? I was blasting the establishment. I was attacking the Vietnam War, the government and police brutality. The raw image of the nude cop gave the work its punch. I was proud that I had the nerve to be on the right side--and to make such a political statement. I was not trying to shock.

It's not only sex, violence and politics that extend the borders of art and stir up controversy. Any dramatic change in art can cause a firestorm. If at the turn of the century some people were outraged by impressionism, can you imagine the shock of seeing Pablo Picasso's "Demoiselles D'Avignon" for the first time? (Henri Matisse thought Picasso had gone too far.) Or the shock of seeing Marcel Duchamp put a urinal on the wall and call it "Art," as he did in 1917?

With that decision, Duchamp opened a gate to much of today's conceptual art--art that is not necessarily based on skill or handiwork, but on ideas. Yet when people visit museums, many still expect to see handcrafted images, not neon words suspended in space, or a room full of rags, or stones piled in a line, or a Brazil nut inscribed with a racial epithet. These conceptual works are designed to stir the imagination, even if the response can be repugnance, shock and confusion.

There is a John Baldessari work (he's one of those "idea" artists whom Duchamp influenced) in the exhibition currently on show at the Smithsonian's Hirshhorn Museum. "Regarding Beauty: A View of the Late Twentieth Century," is a grand thematic exhibition, summing up what art has been about these past 50 years. Baldessari's piece is composed of a panel painted off-white, with the words PURE BEAUTY boldly printed in its center. On one of my five or six visits to the show I overheard a man exclaim to his companion, "What the hell is that supposed to mean?" I hear comments like this all the time. For some, Baldessari's bland, laconic presentation makes a bold and transcendent critique of the elitism of high art; the point is lost on others. Understanding much of today's art takes some education.

The Hirshhorn tries to offer that in "Regarding Beauty," one of the museum's best shows ever. (Perhaps I'm biased. Having worked as an exhibits designer at the museum for 12 years, it is a place dear to my heart.) The show's installation is grand and graceful; the arrangement is clear, stately and stimulating. Add into the mix its gorgeous catalogue, with text and illustrations explaining the movements and issues that engendered the works.

None of this will guarantee that every visitor understands every object exhibited there. They won't. I don't. To like it is something else.

As I strolled through the exhibit one day, I noticed a family ahead of me: a mother and father and two children, perhaps ages 11 and 8. As we turned the corner, three huge Lucian Freud nudes confronted us. Two were of Leigh Bowery, the late performance artist who was a favorite model of Freud's; the third was of a grotesquely fat middle-aged woman. The family stood for a moment, transfixed. Suddenly, the father whispered something to the mother, who took the children by the shoulders and pushed them out of the room. She looked for a second at me, turned away and gasped something that sounded like "God!" She looked shocked.

I walked closer to Freud's work. One image had the giant Leigh reclining on the floor, his head and shoulders resting on a pile of rags, his legs spread wide, his right leg propped up on a sheetless cot, his left leg bent at the knee. Every part of the immense man was shown in detail. Did Freud want to shock folks? Maybe. But probably not. He was depicting raw reality, unvarnished by idealism. Representational artists are always stretching and reaching for new motifs to stir the imagination, but not to be shocking, even if some folks find them so.

Did the German Renaissance painter Matthias Grunewald want to shock us by rendering a broken and bruised Christ in agony on the cross? Most certainly. But he was showing Jesus as a human being, violated by torturers, in sharp contrast to the Italian Renaissance tradition of depicting the crucified Christ as a spiritual being gazing languidly to heaven--almost unharmed. Grunewald showed how very cruel humans can be.

If the family that ran from Freud trekked up north to see the "Sensation" exhibit, they would have plenty to be shocked about. Putting aside for the moment Chris Ofili's notorious "The Holy Virgin Mary," the Brooklyn show is full of shockers. There's Jake and Dinos Chapman's sly, pop-arty takeoff of Francisco Goya's "Disasters of War"--mannequin-like sculptures, castrated, beheaded, limbless and impaled on a broken tree. The same artists present a cluster of little girls, some of whom have erect penises for noses. By now, I can imagine our family running for the doors--possibly passing by sectioned parts of large animals in pristine tanks of formaldehyde by Damien Hirst.

There are some great, thought-provoking works in this show. The "Virgin" is not one of them. It is no more than an attention-seeker, a brazen and gratuitously vulgar cartoon. (I'm not talking about the elephant dung, which Ofili uses in all his work to symbolize his African roots.) In this case, the curator should, in my opinion, have edited out the bad painting--but for aesthetic reasons, not moral ones. All artists, alas, make bad work on occasion. Good or bad, they will keep things stirred up. That's a good thing. That's our job.

Joe Shannon's paintings are shown at Gallery K in Washington.