Muse
Character Role Analysis
Faxe
In ancient Greece, a muse was a goddess who brought inspiration to struggling artists—though we imagine they might have preferred that some nice patron pay their rent. In literature, the muse serves the same purpose. (Inspiration, not rent.)
Faxe acts as Ai's muse because he prophesies that Gethen will join the Ekumen. With this knowledge, Ai sets out to do just that. Very inspirational when you know your mission will succeed. (Less inspirational when you find out what you have to actually go through.)