D-503 thinks he’s recovering—he slept excellently last night. As he travels to work on the subterranean rail, he thinks about how excited he is about his Sex Day with O-90, as it will restore order to his life. D-503 thinks about R-13’s new poems and sees S-4711 and his “twice-bent” body behind him, though he pretends he hasn’t noticed. As D-503 reads a poem called “Happiness,” about the beauty and simplicity of math, he regards S-4711 as his guardian angel, his surveillant eye preventing D-503 from disobeying the One State.
It’s naively optimistic for D-503 to believe he’s recovering, but he’s so upset and in denial about being “sick” that he resorts to this wishful thinking. His hope that having a state-sanctioned Sex Day with O-90 will further restore his health is another instance of misplaced optimism. It’s ironic that D-503 regards S-4711 as his guardian angel, as S-4711, like his body, is “twice-bent”: as readers will soon find out, he pretends to serve the State while simultaneously plotting against them with the rebel group MEPHI.
D-503 thinks about how math is more perfect than the Ancients’ God, as God created humans capable of making mistakes, but the multiplication table is incapable of being wrong. Math is “happy” because it doesn’t have the freedom to be wrong.
D-503 meditates on the happiness of math and certainty to encourage himself to recover from his irrationality-inducing sickness.
D-503’s thoughts are interrupted when he feels S-4711’s breath on the back of his neck. At first, D-503 is worried that S-4711 will see him daydreaming and demand to know about what he was thinking. However, he feels confident that his thoughts—on R-13’s poetry, on the beauty and predictability of math, on the collective superiority of the One State—were completely in line. D-503 reflects some more on the superiority of the One State’s poetry in comparison to the old, Brazen nightingale call[s]” of ancient verse, asserting that, now, “poetry is purpose,” as it inspires ciphers to bow down to the Benefactor.
D-503’s thinks about math because he wants to behave appropriately in front of S-4711. Thus, D-503 is not praising logic because he innately wants to—he’s praising logic to repress other, less rational thoughts. S-4711’s presence intimidates D-503 and makes him keep his desires repressed.