One way to compare John Green’s novel Turtles All the Way Down to the Mumford & Sons's song “Hopeless Wanderer” is to think about how the melody relates to the novel. The music itself, separate from the lyrics, suggests an emotive, urgent, and anxious state. This doesn’t seem like the kind of song a person would listen to if they wanted to relax or try to get in a peaceful frame of mind. This is arguably the type of song a person listens to when they’re having strong feelings.
Throughout the novel, Aza, the main character, has strong feelings. She has to grapple with debilitating anxiety issues that cause her to harp on bacteria and engage in harmful activity, like ingesting hand sanitizer. The fierce, conflicting melody of the song might also link to Aza’s relationship with Davis. She likes him a lot, but her anxiety about bacteria disrupts their intimacy on multiple occasions.
As for the lyrics, they could connect to Davis as well. Consider the first line of the song: “You heard my voice, I came out of the woods.” It’s possible to claim that Davis is the voice that Aza hears. His voice eventually causes Aza to come out of her woods, which, figuratively speaking, could be her deep anxiety problems.
The song also grapples with dislocation and hard truths. At one point in the song, the lyrics read
But do not tell me all is fine
When I lose my head, I lose my spine.
Here, there is an explicit connection, as both the song and the novel directly address mental issues. They do so, some might say, without sugarcoating them and without telling the reader/listener that “all is fine.” Although, Aza does get an optimistic ending, and the wanderer in the song ultimately doesn't come across as so hopeless.