Washington ? Walk through the National Gallery of Art’s “Edward Hopper” exhibit and look at the women.

Beneath the enigma of Hopper’s art, his queasily voyeuristic paintings of human solitude and alienation, lies another conundrum: Those fetishized women, the objects of his obscure desire, so to speak, are not women but WOMAN, and that woman was his wife, Josephine Nivison.

From the time they married in 1924 – she 41, he turning 42 – she was his only model. The marriage was no idyll; they fought, often violently. Her own painting career, which had been by far the more successful, was sublimated to his. She could not help but resent his fame, even as she collaborated in it. Friends of the couple called her “mad, but gloriously mad,” brilliant but humorless. In recent years, she has been alternately defended (mostly by women) as his essential partner and brushed off as, in one online biographer’s phrase, a “busty harridan.”

Still, it is clear that after they joined forces, Hopper found a new painterly vocabulary, even a more striking color palette – reddish, like her hair. It was she who brought him to the attention of the Brooklyn Museum in 1923, which bought a watercolor (a medium she had urged on him) for $100. They were inseparable for the next 43 years, until his death in 1967; she died 10 months later.

Perhaps it helped to be a little mad and brilliant, because playing model/muse to Hopper required a fierce ego. Even nude, his women are not romanticized or even entirely alluring; they seem forlorn, hardened, cold or distracted. In the early 1940s, he painted Nivison as a stripper in full stride (“Girlie Show,” not in the exhibit but reproduced in the catalog), as a secretary dressed more overtly seductively (“Office at Night”) and as a woman taking the air in a shockingly sheer frock in “Summertime.” These were full collaborations; together they invented nicknames and biographies for her characters, and she even took acting lessons.

So although Hopper always publicly insisted that his paintings were not “about” anything, it’s hard not to wonder. A composition such as “Room in New York” (1932), in which the man has just taken off his jacket and sat down with the evening paper while the woman, dressed to go out, picks pettishly at the piano, may have been only colored by a mundane marital tiff, but it’s still suggestive.

These are not exact portraits: Hopper frequently changed Nivison’s hair color a little (or she did); exaggerated, and occasionally celebrated, her muscularity; and even, in the case of the dreamy usherette in “New York Movie” (1939), made her more lithe.

Sometimes she seems ageless, even idealized: The woman in “Morning in a City” (1944) is not much changed from the coffee drinker in “Automat” (1927). But Hopper could also be cruel: The face in “Morning Sun” (1952) is ravaged, and the woman in “Western Motel” (1957), though she seems young again, may be not escaping but at a dead end. Or both: “Going into the West” is an old metaphor for dying OR attaining immortality.

Hers was truly a life given over to art.