Note: "A Greater Infinity" was previously published in three parts in Analog magazine: July 1979; November 1980; and July 1981. Publishing note from 1982 Del Rey ed. copyright page.

Synopsis: A man from Earth joins a multiple-parallel-earths-spanning civilization. It is locked in an apparently centuries old war with another such civilization that developed on a parallel Earth where the Neanderthals did not die out. What maintains the balance is the fact that there are only certain portals between parallel earths. The action heats up when they discover that the portals are locked to gravity wells, which leads to unforeseen ramifications.