To add to the excellent reading provided in the previous post here, we can take a look at how this passage functions as a rather pointed metaphor for the action of the novel, foreshadowing McMurphy's fate. We can also note some motifs at work in the passage that lend meaning to the episode where Bromden looks out the window and watches the dog.
First, the dog's behavior is entirely natural and uninhibited. These are the traits that McMurphy brings to the ward. Frolicking by itself and willing to indulge its innate energies, the dog is a very good analogy for McMurphy, who likewise has taken a risk in opting for the mental ward and has metaphorically "slipped off from home to find out about things went on after dark."
The dog pursues its own ends, regardless of the world around it, investigating gopher holes and drunk with the wild freedom of the night. But its own interests collide with that of another world, one that is mechanized, socialized and ordered by rules. A distinct implication is...
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