The Underground Man asks his audience: even if it were possible to reform men to act "in accordance with science and good sense," is it desirable to do so? Do "man's inclinations need reforming?" and would it be a benefit to man? Recognizing that man is essentially a creative person, he asserts that the act of creating is more important than the final product. It may be that man's "passionate love for destruction and chaos" is because he is afraid of attaining his object. Man, unlike a race of ants which dies in an ant-heap, is frivolous and unpredictable, and thus loves the game of living even though the act of living is filled with uncertainties. If life were a mathematical certainty, then all the mystery of living is done away with and the act of living becomes "the beginning of death." Man likes the "process of attaining," but not the final product. Consequently, mathematical certainty is intolerable. And, even though two times two makes four is good logic, two times two is five "is sometimes a very charming thing too."
Man, perhaps, does not want a mathematical calculation for his well-being — because, perhaps, suffering is just as great a benefit for him. Some men do passionately love suffering and this fact stands in opposition to the idea that man should logically work only for his well-being. Man will never renounce real suffering because, through suffering, man's consciousness is heightened and consciousness is "infinitely superior to two times two makes four."
To disprove the rationalist's attempt to force man into a scientific pattern, to make man no more than an organ stop, the Underground Man continues presenting examples which prove the duality of man's nature. As noted earlier, man's duality is central to all of Dostoevsky's writings. For example, in Crime and Punishment, the work following Notes from Underground, the plot is built on the duality of its main character, Raskolnikov.
Still attempting to prove that the utopia proposed for man would relegate man to a mechanized existence, the Underground Man uses in this section the image of the ant-heap. Ants are industrious insects admired by the utilitarians for their predictable nature. Unlike man, they are not frivolous and incongruous. The Underground Man continues the image by pointing out that if man imitates the ant in joining a socialistic community, then man will end up in an ant-heap. But, he emphasizes, the nature of man should transcend that of an ant and mankind deserves something better than ending up on an ant-heap.
Speaking of man's duality, the Underground Man further illustrates man's conflicting desires to create and to destroy.
"Man likes to make roads and to create, that is a fact beyond dispute. But why has he such a passionate love for destruction and chaos also?" Because of man's duality, the narrator says, man enjoys the process of attaining rather than the actual object or goal. It is the process of living with all of its uncertainties which man finds attractive. In contrast, "mathematical certainty is . . . something insufferable." Thus, the Underground Man despises and rejects any organized society of robots and prefers a life filled with uncertainties and freedom. When he says "twice two makes four," he means that this is a mathematical certainty. But he adds, "Twice two makes five is sometimes a very charming thing too," meaning that it is often pleasant to contemplate the absurd, the unpredictable, or the irrational.
The Underground Man's insistence that suffering is valuable is central to all of Dostoevsky's writing. The Underground Man attacks the utopian society as a place where suffering would cease to exist. The paradox is that man is "sometimes extraordinarily, passionately, in love with suffering," and if suffering ceases to exist, then man loses something he deeply desires. The value of suffering is that it increases one's consciousness and, in doing so, makes the idea of a socialistic society loathsome.