Though there are many passages in the novel to consider in this context, an especially appropriate one might be the Underground Man’s description of his servant Apollon in Chapter XIII of “Apropos of the Wet Snow.” In this passage, the Underground Man describes Apollon as pedantic, vain, and extremely disdainful of the Underground Man. He complains that when Apollon does any work at all, he completes it “as if he were bestowing the highest favor upon me.” Apollon comes off as a truly insufferable person, and initially we sympathize with the Underground Man for having to put up with him.

A closer analysis of the Underground Man’s description, however, reveals that most of his complaints against Apollon regard his servant’s physical description. The Underground Man is annoyed with the way Apollon styles his hair, with the expression on his face, and with his lisp, even though the Underground Man admits Apollon only lisps because “his tongue was a bit longer than it should have been.” If we look through the text for any evidence of Apollon actually exhibiting rude behavior, we find that though he does speak somewhat haughtily to the Underground Man, he does so only after the Underground Man has hurled unprovoked insults and abuse at him. We must also consider that an important component of what we know about the Underground Man comes from his interactions with other people. For instance, in the dinner scene, when we see the Underground Man explode at Zverkov in the same way he explodes at Apollon, the other characters’ reactions help us to understand how irrational the Underground Man’s behavior appears. In the scene with Apollon, however, we have access only to the Underground Man’s account of the conflict. We know that the Underground Man’s pride has been hurt, that he is anxious about Liza’s possible arrival, that he is ashamed of his apartment and his servant, that he is feeling powerless, and that he has a tendency to take his aggression out on other people. Knowing what we do and lacking any real evidence of Apollon’s allegedly rude behavior, we can infer that the Underground Man’s narration is unreliable here. Throughout the novel, then, we must keep in mind that we cannot always trust the Underground Man’s descriptions of other characters whose perspectives we do not get to hear.

The crystal palace and the idea of “two-times-two-makes-four” are both related to the Underground Man’s argument against mankind’s excessive trust in reason. Both are metaphors for the tendency of progressive thinkers and “rational egoists” to set up “laws of reason” as absolutes beyond all possible doubt. The crystal palace symbolizes the ideal utopian society that humanity will be able to achieve once it has discovered all of the laws of nature that govern human behavior. “Two-times-two-makes-four” represents all mathematical laws which have been proved inalienably true. The application of laws such as these is what will make the crystal palace possible. The Underground Man distrusts these laws because, though they might work in logical formulas, he does not think they can be applied to human beings. He believes that to shut up humanity in a crystal palace based on the law of “two-times-two-makes-four” destroys the complexity and variety of human personalities. Such overly rigid thinking discounts the importance of individual free will, which the Underground Man claims will always want to run up against the “stone wall” of logical fact. It is impossible to disprove “two-times-two-equals-four,” and since the crystal palace is built on “two-times-two-equals-four,” it follows that it is impossible to protest the crystal palace. By definition, the crystal palace is good for humankind. But the Underground Man wants to be able to stick his tongue out at the crystal palace, and he says that “two-times-two-equals-five” is sometimes more satisfying than “two-times-two-equals-four.” The human mind delights in the irrational as much as the rational, which implies that the human experience includes, but is not limited to “two-times-two-equals-four,” and therefore cannot be confined to the crystal palace.

Whenever the Underground Man meets another person, he immediately feels the need to size him or her up in comparison to himself. He usually decides that he is much more intelligent, conscious, and sensitive than the other person, but he is nonetheless almost always intimidated by the person’s confidence, wealth, attractiveness, or social standing. The Underground Man feels a strange mixture of smug pride—stemming from his knowledge of his superior intellect—and such deep shame about his clothes, his job, his face, or his apartment that he cannot bear to look the other person in the face. His shame before others makes him resent them even more, until he strongly desires to hurt or humiliate them as punishment for making him feel this shame. However, because the Underground Man feels so inferior to them, he is powerless to do anything about these desires. As a result, he is obsessed with power relationships. He craves the attention of the people whom he believes to have power over him, like the officer and his former schoolmates, while believing he should be able to exert power over them at the same time. Because the Underground Man’s constant feeling of powerlessness is painful to him, he seeks out situations in which he can feel powerful. He wants to dominate those whom he feels he outranks in social or economic standing, such his servant, Apollon, or the prostitute Liza. However, the Underground Man’s obsession with maintaining his power over others is so strong that any normal reversal of power in the relationship—Apollon expecting his wages, Liza seeing the Underground Man in a position of distress or embarrassment—fills him with shame and rage. Having accepted the superiority of people he sees as higher in rank than he, he expects to be able to feel the same kind of superiority over those who are lower than he. Any disturbance of that power structure is damaging to his ego.