THIS IS A NOVEL written in the purest style imaginable. Americans are people easily embarrassed - by unearned emotion and unconversational rhetoric. Nothing in Sleepless Nights will embarrass its readers. Even its experimentalism is quiet, unobtrusive, growth rings secreted around a core that remains invisible.

The author implies that a great life of passion - full of ambition and ambition rewarded, of power and love and tragedy - has lived by the protagonist, the woman who narrates the tale, but this story is told only by indirection, as though a more head-on account would plunge her into the terror of self-disclosure and the tedium of comprehensiveness. For narrative is fatiguing, the eternal and then, and then, the slow accumulation of names, dates, pedigrees, of intrigue, deception, elation and despair.

What she has given us instead are loosely linked portraits of the minor characters in a life, those people met at a resort or a party, those acquaintances one never knows well. Or she shows us the Don Juan of Amsterdam, simultaneously uxorious and faithless. Or she tells us of the gay man who lived in the same New York boarding house so many years ago and with whom she established a bickering but tender mariage blanc. Here we have the bit players and the second leads; the stars hide behind clouds of discretion.

These portraits have been etched on glass by a diamond, and then the glass has been held up to the full light of a splendid intelligence. The picture of Billie Holiday, for instance, is just ten pages long, but it is only account of the singer I've read that gives a sense of what she was like - what she looked like, how she moved, talked, entered a room. "And of course the lascivious gardenias, worn like a large, white, beautiful ear, the heavy laugh, marvelous teeth, and the splendid head, archaic, as if washed up from the Aegean. Sometimes she dyed her hair red and the curls lay flat against her skull, like dried blood." In these two sentences can be glimpsed the natural impulsed of the Hardwick style: the slowly building breaker of accurate, striking detail, the language at once relaxed and terse; the deceptively gentle, throw-away little sentence; the final phrase (Like dried blood") that slaps the beach with unexpected force.

Or take this paragraph that fixes, as a naturalist might fix a butterfly, a New York intellectual: "She has a Ph.D., a credential very agreeable and surprising, since her life was all about love and disillusionment, as if she had been a courtesan rather than a scholar. She was wearing silk pants and a blouse of flowered chiffon. She sighed behind her smile, with the resignation of experience, the harem resignation. All of her news was bad and so her talk was punctuated with 'of course' and 'naturall.' "The writing is tight, though it swells for a moment, expands, stretches, before darting in with the killing detail ("the harem resignation," "'of course'").

The decision to chronicle the minor characters surrounding a life has proved astonishingly successful. For what Elizabeth Hardwick has understood is that character and destiny become muddy the more we know of them. The ultimate in opaqueness is oneself. What is your character? You will not be able to answer, since you know too much and too little. No wonder we consult psychics and astrologers and psychiatrists so avidly; perhaps they will finally be able to lend some shape to this incoherence.

But other people's lives do not lack definition. They are plots waiting to unfold, and so they do with satisfying verve - the recognition scene, the flight from necessity, the reversion type. In this novel these stories - seen from a distance or out of the corner of the eye - are no longer peripheral. They are brought to the center of vision and scrutinized wtih a greedy, clear eye.

This novel, then, is a wisdom book, for we can be wise only about other people. Through it flows a melancholy, humorous worldliness, as unsentimental affection for the poor and a cool appraisal of the rich. I trust and admire this writer. Unlike Lillian Hellman, she is not posing as the most honest woman in the world; unlike Colette, she does not want to come off as the most desirable. In fact, she scarcely seems aware of the image of herself she is presenting, so absorbed is she in getting down the story of all these other lives. But the wisdom - drawn from a particular juncture of actor and incident, never laid down as an enduring imperative strikes me as sound, a coin whose value is equal to the worth of the precious metal it contains. This is a magnificent achievement; I recommend it to you without hesitation. CAPTION: Illustration, no caption, by Vint Lawrence for The Washington Post