Parallel to Odysseus (dramatic irony)
"The Swimmer" has often been compared to The Odyssey, in which a great hero traverses long distances and overcomes challenging obstacles to make his way home to his wife. These same plot points exist in "The Swimmer," thereby positioning Neddy Merrill in parallel to Odysseus. The irony here, which is almost immediately apparent, is that Neddy is a poor stand-in for Odysseus. Neddy's idea of courage is jumping in a shallow pool rather than walking down the steps to enter; his idea of adventure is swimming the length of the same, tame pools for an hour or two until he reaches his house; and his idea of social responsibility is simply the need to garner flattery from women and praise from his neighbors.
The Lucinda River (dramatic irony)
Neddy imagines the route home as the "Lucinda River," a great voyage that will earn him his place among famous explorers. Yet the novel route home is nothing but a series of private pools. The "unknown" that Neddy imagines is actually well-known, even banal: the homes of friends, neighbors, and former lovers. Thus, in reality, there is nothing innovative nor pilgrim-like about this journey. Neddy's image of it as such is ironic, casting him as a slightly delusional, self-important suburbanite looking for a purpose in the wrong place.