Nicholson is a young teacher (possibly still in graduate school) who, having heard of Teddy by reputation, seeks the boy out on board the ship. He is a contrast to Teddy in that his character is driven by ego and physicality. His jacket "looked as though it had been properly aged in some of the more popular postgraduate seminars at Yale, or Harvard, or Princeton," "his speaking voice was, in the usual connotation, well bred, it carried considerably more than adequately, as though he had some sort of understanding with himself that anything he had to say would sound pretty much all right – intelligent, literate, even amusing or stimulating," and he has "a kind of poise about him […] that looked as though it might hold up indefinitely, with the very small proviso that he keep at least one hand in one pocket" (4.29, 4.23). He's got an air of self-satisfaction that borders on narcissism.
Not that there's anything wrong with that – Nicholson isn't a bad guy and certainly not the story's antagonist. It just means that, from Teddy's point of view, Nicholson is not so spiritually advanced. Fittingly, then, Nicholson's body gets a lot of attention. We learn that his legs are "unusually heavy at the thighs, almost like human bodies in themselves" (4.29). Later he "crosse[s] his heavy legs, at the ankles" and again several minutes later crosses his "heavy, outstretched legs" (4.29, 4.70). If Teddy is free of material and physical concerns and dwells in the realm of the spirit, then Nicholson is firmly weighed down to earth by his body (a body that is physically, and also metaphorically, heavy).
These qualities of Nicholson's determine the way he approaches and engages Teddy. Nicholson's initial perspective is clear and can best be described by the word "amused." He doesn't take Teddy seriously, at last not completely, and he can't seem to get past the fact that he's talking to a little boy. He seems to be humoring Teddy.
When Teddy asks if he knows what "affinity" means, Nicholson responds "dryly" with "I have a rough idea" (4.65). When Teddy mentions that he could get out of the finite dimensions when he was a boy, Nicholson asks him how but does so with "a short laugh" (4.80). When Teddy tells him he's being logical, Nicholson responds "with a little excess of politeness," "I'm just being what?" (4.90). And when Teddy asks, "You know Adam, […] In the Bible," Nicholson responds with sarcasm: "Not personally" (4.93-6). (Of course, it is a testament to Teddy's wisdom-beyond-his-years that he picks up on Nicholson's attitude and even calls him on it: "Don't be angry with me," he responds to Nicholson's sarcasm; "You asked me a question" (4.97).)
As their dialogue continues, we see, of course, that Nicholson is definitely one of the apple-eaters to whom Teddy refers. (See "Symbols, Imagery, Allegory" for a discussion of the apple-eating concept.) He keeps trying to argue logically with Teddy, which is quite a barrier to understanding what the boy has to say.
When Teddy tries to explain the real nature of death, Nicholson points out that Teddy's parents would feel hurt if he died (even though Teddy has already explained the uselessness of emotions). When Teddy is explaining about the apple of logic, or poetry, Nicholson keeps trying to change the subject; Nicholson wants to know if Teddy really did predict the deaths of some professors in Boston. Nicholson seems to be more interested in the juicy gossip he heard about Teddy than the real heart of the lessons Teddy has to offer.
Yet as the conversation progresses, Nicholson makes fewer and fewer smart-aleck responses. Instead, he seems to be either listening or thinking. When the deck steward comes around to ask if they want some soup, "Nicholson [doesn't] respond to the question at all" (5.1). He's lost in thought. When Teddy pauses in his explanation of death, Nicholson, rather than interrupt or retort as he's been doing all along, does not: "Nicholson [doesn't] say anything" (5.6) Salinger tells us (in a lone paragraph, no less, as if to highlight its significance).
The interesting question to consider, then, is how Nicholson is ultimately affected by his conversation with Teddy. Does he learn something? Does he change his mind? Or is he the same guy at the end of the conversation that he was at the beginning? For all his apple-eating habits, after all, Nicholson is still the one who sought Teddy out, and he stops the boy from leaving several times by practically begging that they continue their conversation. He may be full of sarcasm on the surface, but he's definitely interested in what Teddy has to say. So how does it all impact him?
Salinger doesn't give us much on Nicholson after Teddy leaves, so we need to take a close look at the little bit of text we do have:
Nicholson sat motionless for some few minutes after he left, his hands on the armrests of the chair, his unlighted cigarette still between the fingers of his left hand. Finally, he raised his right hand and used it as if to check whether his collar was still open. Then he lit his cigarette, and sat quite still again.
He smoked the cigarette down to its end, then abruptly let one foot over the side of the chair, stepped on the cigarette, got to his feet, and made his way, rather quickly, out of the aisle. (2.29-30)
We can fairly safely assume from this first paragraph that Nicholson is thinking; he's mulling over everything Teddy said to him in the course of their conversation. But what do we make of his exit? He realizes something quite suddenly, and it would seem to be rather urgent. We see this urgency clearly if we consider Salinger's word choices in these last few paragraphs. Nicholson gets up "abruptly" and walks "rather quickly" off the sun deck before taking the stairs "fairly briskly" and continuing "quite rapidly" downwards (5.30, 31). Then "he continue[s] on down, still quite rapidly, to Main Deck. Then to A Deck. Then to B Deck. Then to C Deck. Then to D Deck" (5.31). Something has got Nicholson's attention, and that something is important.
If it were not for this elaborate suspense we might think little of Nicholson's exit; maybe he just thought of another question to ask Teddy. But the urgency of his departure suggests otherwise. It seems more likely that Nicholson has put two and two together and realized that Teddy wasn't just supposing a "what if" about death; he really was predicting that he would die today. Maybe he rushes to the pool to see if Teddy's prediction has come true, or maybe to prevent the thing from happening. Either way, what we do see is that Nicholson suspends his skepticism because he's finally taking Teddy seriously – seriously enough to rush down to the pool and witness the story's conclusion, whatever that happens to be.