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Fermi and Frost is a science fiction short story by Frederik Pohl. You can read it online here. It begins,
On Timothy Clary's ninth birthday he got no cake. He spent all of it in a bay of the TWA terminal at John F. Kennedy airport in New York, sleeping fitfully, crying now and then from exhaustion or fear. All he had to eat was stale Danish pastries from the buffet wagon and not many of them, and he was fearfully embarrassed because he had wet his pants. Three times. Getting to the toilets over the packed refugee bodies was just about impossible. There were twenty-eight hundred people in a space designed for a fraction that many, and all of them with the same idea. Get away! Climb the highest mountain! Drop yourself splat, spang, right in the middle of the widest desert! Run! Hide! —
And pray. Pray as hard as you can, because even the occasional planeload of refugees that managed to fight their way aboard and even take off had no sure hope of refuge when they got wherever the plane was going. Families parted. Mothers pushed their screaming children aboard a jet and melted back into the crowd before screaming, more quietly, themselves.
Because there had been no launch order yet, or none that the public had heard about anyway, there might still be time for escape. A little time. Time enough for the TWA terminal, and every other airport terminal everywhere, to jam up with terrified lemmings. There was no doubt that the missiles were poised to fly. The attempted Cuban coup had escalated wildly, and one nuclear sub had attacked another with a nuclear charge. That, everyone agreed, was the signal. The next event would be the final one.
Timothy knew little of this, but there would have been nothing he could have done about it—except perhaps cry, or have nightmares, or wet himself, and young Timothy was doing all of those anyway. He did not know where his father was. He didn't know where his mother was, either, except that she had gone somewhere to try to call his father; but then there had been a surge that could not be resisted when three 747s at once had announced boarding, and Timothy had been carried far from where he had been left. Worse than that. Wet as he was, with a cold already, he was beginning to be very sick. The young woman who had brought him the Danish pastries put a worried hand to his forehead and drew it away helplessly. The boy needed a doctor. But so did a hundred others, elderly heart patients and hungry babies and at least two women close to childbirth.
If the terror had passed and the frantic negotiations had succeeded, Timothy might have found his parents again in time to grow up and marry and give them grandchildren. If one side or the other had been able to preempt, and destroy the other, and save itself, Timothy forty years later might have been a graying, cynical colonel in the American military government of Leningrad. (Or body servant to a Russian one in Detroit.) Or if his mother had pushed just a little harder earlier on, he might have wound up in the plane of refugees that reached Pittsburgh just in time to become plasma. Or if the girl who was watching him had become just a little more scared, and a little more brave, and somehow managed to get him through the throng to the improvised clinics in the main terminal, he might have been given medicine, and found somebody to protect him, and take him to a refuge, and live. . . .
But that is in fact what did happen!