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Even though Mia only sees Billy a couple of times in the book, he's important to her figuring out who she is. Why? He lets her in on a secret: She's not the only one who sees colors in letters or sounds; Billy is a synesthete, too. When she first meets him at the grocery store, Mia tells us:
I hear Billy's mother scolding him for making up stories. The laughter of my classmates pops into my head. (2.93)
Ah, so not only is Mia not the only synesthete around, she's also not the only person who nobody believes when she talks about her synesthesia. Billy's mom sure doesn't think anything of her son's rambling. Billy's outburst in the store helps Mia realize that her condition isn't just in her head, and she helps him out later by giving him all the juicy details about synesthesia. We might not get to know Billy, but as the book comes to a close, he seems on his way to figuring out his colors, too.