This story is a parallel to the concluding story of Nine Stories, Teddy. "Teddy" revolves around mankind's eating of the Biblical apple and gaining knowledge that could never be lost again. The title character, Teddy, undergoes a series of reincarnations, finally reaching a mental state where he can repudiate knowledge and logic and form his own understanding of the universe.

Teddy, theoretically, is a reincarnation of Seymour Glass, subsequent to his death in the first story. This is suggested by the lines describing Teddy's eyes, which also appear in "Seymour, An Introduction", indicating some connection between the two. Seymour and Buddy Glass studied reincarnation implicitly in other "Glass books", although Teddy appears both wiser and more spiritually advanced than Seymour.

The metaphor of the fish eating the bananas in "Perfect Day..." is equivalent to mankind eating the apple of knowledge. The bananafish are unable to leave the cave -- mankind is unable to eliminate the preconcieved notions that it obtained from the apple.

Teddy is killed at the end of "Teddy", in what is generally agreed to be his final death before ascending to a higher plane of consciousness.

WaldemarExkul destroys my point by exposing an obvious flaw in my interpretation, namely the dates on which Seymour died and Teddy was born. Okay. So, rule out literal reincarnation, at least until I do some research. It is instead suggested that Teddy is a projection of Seymour on the part of Buddy -- hence the eyes -- but not literally him. Nonetheless, it seems similar to what Buddy would expect from his brother. Good point!