In Quincunx (New York, 1983), what Haertel did at seventeen was to assume that the geometry of ultimate particles was Pythagorean, not Euclidean (p. 61). That does not sound very much like his achievement at age seventeen in Welcome to Mars, which I will probably reread also.
In Blish's Black Easter, a handful of characters invokes demons and causes Armageddon. In Quincunx, a handful of characters invokes the future and initiates utopia. Baines and Hess of Black Easter are an unreservedly bad company director and scientific consultant; Weinbaum and Wald in Quincunx are their benign counterparts.
Service agents in "Beep"/Quincunx have the same reason for optimism as the protagonist of Robert Heinlein's "By His Bootstraps." They have not yet experienced certain events but know with full confidence that those events will turn out for the best. Whether we contemplate a four dimensional continuum or eternal divine omniscience, we imagine a perspective from which events that are future to some observers can be present or past to another observer. Both Heinlein and Blish imagine situations in which knowledge of an assured future can be put to good use in the present.
Quincunx begins optimistically with a Service agent on a "...boy-meets-girl assignment..." (p. 15), confident that the couple who meet in a park will have children with a role in the course of the future history that is guarded by the Service - just as Poul Anderson's Patrol guards our history.
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