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The story begins with Dr. Max Greitzer waking to the sound of his telephone. The voice on the other line tells him that a woman he'd dated previously, Liza Nestling, had died and that the funeral was to be held at eleven.
It had been twelve years since the two had broken up. They had a thirteen-year love affair full of many misunderstandings and complications. After the breakup, the two never spoke to one another again.
Dr. Greitzer heads to the funeral parlor and is told by the receptionist that he is too early. He asks if he may see the body, and he is escorted to the room. As he studied the body, a woman who resembled Liza entered the room. Thinking she must be Liza's sister, Dr. Greitzer makes nothing of it. Eventually the two strike up a conversation. The woman tells Max that she'd seen his obituary in the newspapers. It is then revealed that both Liza and Max are dead. They then banter between Max and Liza about the nature of death, the thought of their afterlife and of immortality.
Upon death, Max and Liza show no concern for the fact that they're dead. Nothing seems to have any sort of relevance. What they speak of upon learning they're dead is of what they'll find. They ponder whether or not there is a Hell or Paradise. Liza at one point states "I imagined that the end would be much more dramatic."
The fact that the two characters meet in death seems to mean that they were destined to be together. This "transition between two modes of existence" as Dr. Greitzer calls it, is one mostly of reflection; the characters use it to remember the past and also question the future.
At the end of the story, as they hover aimlessly about, looking down at all that surrounds them, Max Greitzer utters the most profound and meaningful quote in the story when he says "Of all my disenchantments, immortality is the greatest." This makes one question the religious beliefs of the two characters. In death, they still seem to question and interpret what's happened to them as it comes rather than with any sort of conviction.