Winston Niles Rumfoord runs his private spaceship into an uncharted chrono-synclastic infundibulum. The result is that he and his dog Kazak exist as wave phenomena, materializing and dematerializing on Earth and on Mars, where Rumfoord plans an invasion of Earth. On Mars, he transforms disaffected Americans into an army, literally washing out their brains through surgical procedures and directing their wills through antennas implanted in their heads. On Earth, Rumfoord lures Malachi Constant, the richest American, into his plot, inviting him to witness his materialization.
Constant is ripe for Rumfoord’s exploitation because he has lost all sense of purpose. He inherited his money from his father and takes no interest in the financial maneuvers of his father’s company, Magnum Opus, which becomes bankrupt. Rumfoord makes Constant his tool, then flies Constant to Mars, along with Rumfoord’s wife, Beatrice. She become Constant’s wife and bears his child.
Constant’s own story is hidden from him (and from the reader) because on Mars, much of his memory is erased. There he is Unk, a soldier with an antenna in his head that sends pain signals any time Unk tries to act on his own. Unk runs away from the army and tries to find his wife, Bee (Beatrice Rumfoord) and his son, Chrono. Unk is fortified by a letter from his best friend, Stony Stevenson, who has warned him to try to remember as much as possible because the surgical brainwashing does not destroy all memory, only the middle part. Unk does not realize that while still brainwashed, he obeyed an order to strangle Stevenson.
Unk, Bee, and Chrono eventually are reunited and survive the disastrous Martian invasion of Earth, in which Rumfoord’s forces are easily defeated. This apparently is part of his plan, allowing him to present himself as a kind of latter-day savior of humankind and to change human values. In this role, he establishes the Church of God the Utterly Indifferent, under the leadership of the Reverend C. Horner Redwine. Rumfoord, who suffers severe reactions to his constant materializing and dematerializing, is hardly triumphant. He feels manipulated by the Tralfamadores, machinelike creatures from another galaxy, one of whom, Salo, has helped Rumfoord accomplish his scheme. Rumfoord’s dream of dominating humanity is merely that—an illusion, like the beautiful sirens of Titan, inhabitants of one of Saturn’s moons.