What One Owes : An elegant novel poses complex issues of personal debt : THE DISTINGUISHED GUEST, <i> By Sue Miller (HarperCollins: $24; 288 pp.)</i>

There is a certain kind of knowledge that we reach only through a certain kind of fiction: fiction so rich, so thoughtful, so absorbing that reading it is like experiencing the passage in our own lives. When we reach the end of these books we think: Yes. That is how it must have been.

Sue Miller writes this sort of fiction. Her brilliant, heart-rending first novel, “The Good Mother,” opposed the forces of motherhood, sexuality and society in a story as complex and inexorable as a Greek tragedy.

“The Distinguished Guest,” her fourth novel, deals again with contemporary issues that disturb and concern us: the relationship between aging parents and grown children, and the relationship between white liberals and American blacks. Both are complex and highly charged, both provoke public debate and private anguish. Both raise the question of personal debt: what one owes, and is owed. These problems require complicated calculations: adult need measured against childhood need, past debts against present ones, love against resentment. This elegant geometry of emotion forms a framework and pattern for the narrative; this is enacted by marvelously interesting and refreshingly grown-up characters.

Alan Maynard is an architect and teacher in his late 40s. He lives in a small coastal town in Massachusetts with his French wife, Gaby, who runs a catering business. They have one son at college, one at graduate school. Alan has built a house; he is financially secure; his children give him great pleasure. He loves his wife, and the vivid and hideous storms--infidelity, rage--of his marriage arc behind him. He is intelligent, thoughtful and generous. He seems, in his life, content.

Gaby’s French past is vivid: the big house outside Paris, the lace curtains and long sacramental meals, the self-important opinionated father. Gaby herself is entirely Gallic: deeply pragmatic, kind, utterly lacking in self-pity or self-doubt. She is hard-working, compassionate and self-contained. Her passion is for her family.

Lily Maynard, Alan’s mother, is a celebrated octogenarian writer. Ten years ago, Lily published her deeply personal memoirs, recounting her experience with her minister husband, Paul, and their efforts at integration in a white Chicago church in the 1960s. The marriage foundered on disagreement about the increasingly radical and violent direction of liberal activism. Lily has Parkinson’s disease, and is palsied and frail but still fiercely opinionated, idealistic and powerful.

Linnett, a free-lance journalist writing a profile of Lily, is the least admirable of these characters. She’s smart (though not as smart as the others), a bit predatory and not wholly trustworthy. She’s a snoop, drinks too much and is sexually indiscriminate. Her writing is pedestrian. Still, she is sympathetic--diligent, struggling with her life. (Linnett also has the funniest line in the book, from an old fight with her ex-husband.)

The distinguished guest is Lily herself, staying with Alan and Gaby while waiting for a place in a nursing home. Alan had welcomed Lily, but “almost from the moment she moved into his life here . . . he has been angry at her, and then at himself for his anger. He’s . . . come to think that at the center of these feelings is his response to what she seems to be using this visit for: the destruction of his past.”

Lily’s view is different. Alan’s past, of course, is hers as well. She feels, with calm parental certainty, that she is in charge of it. Her memories, now published, have a public authority. They show both her passion and her conviction: “We met on Tuesday night for fourteen years. We met to read the Bible, and we did read the Bible, but we also made a world, and with my dying breath I will bear witness, I will testify, that that world worked. We were all women, we were all colors, and when we gathered, all that mattered to us was the love that coursed among us.”

For Alan, that time was different. At school and on the street, the blacks he met were not there to read the Bible. They were tough and hostile, but “being scared of black kids . . . was not a thing I was allowed to feel.”

Lily still refuses to credit Alan’s view, and here, in Alan’s pain and resentment, Lily’s implacable resistance, is the crux of the book. This is a struggle for control of the past, of one’s own experience: the right to name it, define it, own it. The parent’s instinctive urge is to dictate her version; the child’s deep need is to declare his experience his own.

Finally, a third point of view is offered by a young black woman who comes to interview Lily. Marcea, devastatingly cool and articulate, lays her own claim to that past.

There are no simple resolutions to these conflicts between idealism and realism, parent and child, black and white. But Miller’s compassionate narrative explores the problems and reveals the possibilities for change.

The pace of the book is smooth but rapid. We move from past to present, from character to character, following them through their days, their thoughts, their pasts. There are many pleasures here, besides these thoughtful, interesting and deeply sympathetic sensibilities. There is the informed use of music as a source of imaginative sustenance. There is the skillful contrasting of writing styles--Miller’s own, brisk and unpretentious; Lily’s, rather elegant and lyrical; and Linnett’s, prosaic and “magaziney.” There are brief, marvelous images: a wild animal’s midnight death scream, an entrancing performance of Handel’s “Messiah.”

All this is wonderful stuff--rich, intelligent and moving. This is the fiction we need.