Notes from Underground

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Two Times Two Equals Four Symbol Analysis

Two Times Two Equals Four Symbol Icon
This simple equation epitomizes rationality and scientific and mathematical fact for the underground man. In its simplicity and truth, it is undeniable and leaves no room for disagreement or protest. The underground man says that some people think the whole world and all of human life can be understood according to reason and logic of the kind exemplified by two-times-two-equals-four. But, he strongly disagrees with this notion. He asserts that if life were nothing but a series of equations and logical laws to be figured out, mankind would have no free will; life would simply be dictated by reason and logic, and man would be nothing but an “organ stop,” acted upon by natural forces. In the face of this, the underground man stresses the importance of man’s irrationality and his ability to behave illogically. The equation two-times-two-equals-four symbolizes the oppressive reason and logic against which the underground man struggles. Arguing for the importance of free will, he insists that two-times-two-equals-four is “no longer life,” and claims that mankind’s freedom lies in its ability to believe illogically that “two times two makes five.”

Two Times Two Equals Four Quotes in Notes from Underground

The Notes from Underground quotes below all refer to the symbol of Two Times Two Equals Four. For each quote, you can also see the other characters and themes related to it (each theme is indicated by its own dot and icon, like this one:
Thought vs. Action Theme Icon
). Note: all page and citation info for the quotes below refers to the W. W. Norton & Company edition of Notes from Underground published in 2000.
Part 1, Chapter 9 Quotes

Two times two makes four—why, in my opinion, it’s mere insolence. Two times two makes four stands there brazenly with its hands on its hips, blocking your path and spitting at you. I agree that two times two makes four is a splendid thing; but if we’re going to lavish praise, then two times two makes five is sometimes also a very charming little thing.

Related Symbols: Two Times Two Equals Four
Page Number: 24
Explanation and Analysis:

The Underground Man has claimed that the reader whom he is addressing wishes to make people more rational using the laws of science, a notion he finds outrageous. In this passage, he declares that "two times two makes four" is "mere insolence." He personifies this mathematical formula, describing it as standing brazenly with its hands on its hips." Through this personification, the Underground Man makes explicit the connection between logical thinking and rigid authoritarianism. Of course, mathematics by itself is merely an abstract mode of thought, and thus it is strange to describe it as "insolent." On the other hand, by making the connection between mathematical reason and authority, the Underground Man emphasizes that logic is used in a cruel and oppressive way.

Such thinking stands in direct opposition to the contention of Enlightenment thinkers (who were influential at the time when the novel was written) that scientific reason will automatically lead to a more humane, compassionate world. However, the Underground Man also contradicts himself in this passage; having called two times two makes four "insolence," he then describes it as "a splendid thing." Rather than undermining the Underground Man's argument, however, this contradiction actually supports it, as contradiction itself (like two times two equals five) is an example of illogical thinking. The Underground Man thereby emphasizes the connection between irrationality and freedom, even if that means the freedom to contradict oneself and not make any sense. 

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Two Times Two Equals Four Symbol Timeline in Notes from Underground

The timeline below shows where the symbol Two Times Two Equals Four appears in Notes from Underground. The colored dots and icons indicate which themes are associated with that appearance.
Part 1, Chapter 3
Reason and Rationality Theme Icon
Spite, Pain, and Suffering Theme Icon
...nature and mathematics as inviolable, thinking it is impossible to protest, for example, that “ two times two makes four .” He says that he is disgusted by the “impossibilities of stone walls,” represented by... (full context)
Part 1, Chapter 9
Reason and Rationality Theme Icon
...process of achieving his goal and not the goal itself,” which is “none other than two times two makes four , that is, a formula.” He says that “two times two makes four is no... (full context)