Squaring a Triangle : A HOME AT THE END OF THE WORLD <i> By Michael Cunningham (Farrar, Straus & Giroux: $16.95; 333 pp.) </i>

How do we tell a destination from a dead end? The three waifs in Michael Cunningham’s splendidly inflected novel struggle to find their way in a contemporary world whose neglect of its own moral maintenance has left it as overgrown and trackless as a jungle.

The world’s end of the title is ostensibly an old farmhouse in upstate New York where Bobby, his one-time lover, Jonathan, and his present lover, Clare, have moved in order to put their confused lives into shape. It has a darker meaning. We finish the book with a sense of Doomsday. Not the catastrophe itself, but the instinctive unease that precedes it, as when cats agitate seconds before an earthquake, or like the feeling of despair before heart attacks.

The trio that moves through “A Home at the End of the World” has the instability of a musical-chairs variation, where there are two chairs for three players and, by turns, one of them is always left standing. Back in Cleveland, Jonathan, who is gay, and Bobby, who is uncertain, were a high school couple. Jonathan grows up, moves to New York and meets Clare. They live together, loving but necessarily platonic.

Bobby, drifting, joins them. The loving now goes three ways, but no longer platonically. Bobby and Clare become lovers and she lets herself become pregnant. Jonathan flees briefly but returns. He needs them and they need him.

Clinging together, all three move to the country. Bobby and Jonathan open a restaurant, and Clare has her baby. Motherhood pulls her bit by bit to the edge of the circle; partnership pulls Jonathan and Bobby closer.

At the end, she leaves with Rebecca, her baby. Bobby and Jonathan are together once again, but in a minor key. They share the care of Erich, a one-time lover of Jonathan’s, now dying from AIDS. Jonathan waits stoically for his own symptoms to appear.

Jonathan’s homosexuality, Bobby’s passive bisexuality, Clare’s basic heterosexuality are a conspicuous part of this community at world’s end, but they are not the essential part. Each of the three has arrived war-damaged from the half-acknowledged harms of contemporary society; each has lost the underpinnings of structure, direction and commitment; each struggles to invent a replacement.

The trio is what they come up with. Sexuality apart, no permutation of Jonathan, Bobby and Clare can make a genuine couple. The poet Rainer Maria Rilke once hinted at the requirements in his poignant and terrifying definition of marriage. He called it that state in which two people become “guardians of each other’s solitude.”

To be a coupled solitude in a society that offers some kind of place for each one of them, and some kind of link among them all, is hard. In a falling-away world it is immeasurably hard. Cunningham’s three waifs join together to escape individual aloneness; the magnified aloneness of the couple is starker and more demanding than any two of them can bear.

Cunningham writes with power and delicacy of his three characters, of the raft they swim to from their three early shipwrecks, of the raft’s breakup and the courage each begins to learn alone: Clare with her child, Jonathan and Bobby together but in a scaled-down companionship.

The two men are the most vividly drawn; we begin with them as children, and although “End of the World” is beautifully written throughout, Cunningham is at his best with childhood. Both boys are injured early, Bobby by far the more grievously.

With two self-absorbed ex-hippie parents who never have grown up, Bobby becomes the enthralled follower of his troubled older brother, Carlton. At 8, he joins Carlton in drinking and taking drugs; he watches him have sex with a girlfriend, and assumes, from her cries, that it must be a painful thing to do. Later, when Clare seduces him, he will wail at orgasm. Pleasure--the drugs--followed by unbearable pain is his first lesson; he sees Carlton die in a grisly accident at home, and not long afterwards his mother kills herself.

As an adolescent, half-orphaned, wild and passive at the same time, he meets Jonathan. More gently brought up, Jonathan has a home, and Bobby takes refuge there. But Jonathan has been through his own, quieter desert. His father is kind but evasive; at 4, Jonathan longs passionately for him--Cunningham gracefully shows a little boy’s early fascination with male bodies--but can’t find him. His mother, on the other hand, is enveloping.

The author makes us see the wildness of Bobby’s childhood as something both familiar and natural; he makes us feel the sorrowful wilderness in Jonathan’s far more gentle deprivation. He does not stress the connections in any forced fashion. If Jonathan retains a sense of himself and grows up an injured but determined passionate seeker, and if Bobby, more fundamentally injured, grows up passive, it seems absolutely right.

Cunningham gives us the most complete and nuanced of psychological portraits without abridging the freedom of his characters. All three are utterly revealed and utterly unpredictable. A thread leads from the child to the adult, but it is not a binding one; it can break, disappear and be taken up again. We come to feel that we know Jonathan, Bobby and Clare as if we lived with them; yet each one retains the mystery that in people is called soul, and in fiction is called art.

Clare is no less real for standing a little way out of the foreground. Her childhood is not so fully sketched; she is more mysterious than Bobby and Jonathan, and thus more able to provide the abrupt energy that moves the story. She is in her late 30s, 10 years older than her companions. If she seems as appealingly flaky as the others, she is driven, half-consciously, by a fundamental motherhood that comes to determine what will happen to the trio.

It is, of course, a trio of needs as well as of persons. Bobby’s passivity needs to attach itself to a source of strength and energy. Jonathan’s energy needs to create a world around him; most fundamentally, he needs to be a father, and his homosexuality stands in the way.

Clare’s need is akin to Jonathan’s but she is able to fulfill it. She chooses Bobby to make her a mother. And once she is a mother, she can no longer avail herself of the refuge, the escape from fundamental choices provided by this comically warm and funky menage a trois in upstate New York. Lovable and user-friendly to the ultimate degree, it is producer-hostile and as stifling as any unduly prolonged childhood must be.

Clare leaves to grow up; Bobby stays to grow as much as his shattered childhood will allow. Dependent on an older brother-figure--Jonathan--he will develop an independent serenity inside this dependence. Jonathan’s growth is the hardest. The trio was to be his family. He was touchingly serious about being a second father to Rebecca, Clare’s and Bobby’s child. It is a moving illusion; but Cunningham makes the relinquishing of the illusion far more moving.

Accepting his role as mainstay to Bobby and as nurse to the dying Erich, accepting the probability that he will not live long, accepting the bar that his sexual nature places upon his need to make a family, and accepting, finally, his solitude, Jonathan comes authentically and originally upon life.