The 'Faust' in the song's title is probably the Faust in German legend who made a pact with the devil. In the closing song of the album, 'Videotape,' Mephistopheles is name checked. Mephistopheles is the name given to the devil in the Faust legend.
The Faust legend originated from Johann Faust (c1480-1540) of Germany, a wandering astrologist, scholar and magician who slighted Jesus' miracles and bragged that he could do the same. He was hated and feared by Martin Luther and when he disappeared in a strange manner and was later found dead in a pile of dung, many felt his strange demise was the work of the devil. Subsequently his name became the center of a great body of legend and poetry in European literature.
'Arp' may refer to Jean Arp, the founder of the Dadaist movement, or to the ARP synthesizer manufacturer. A third alternative is that, like the fourth track on the album 'Weird Fishes / Arpeggi' it is a reference to the musical term 'arpeggio'.
In an interview with the Observer Music Magazine December 2007, Thom Yorke was asked about the theory that In Rainbows is conceptually linked with German writer Johann Goethe's adaptation of the legend of Faust. The Radiohead lyricist responded: 'I vaguely know the story of Faust. But that would involve me having remembered it in some detail or picked it off the shelf. Which I didn't. But yes, hmm, Goethe's Faust. I'm going to have to look that one up, actually, 'cause that sounds suitably pretentious. We live in Oxford, after all'.
In an interview with Mojo magazine February 2008, Thom Yorke discussed his creative methodology: 'The more you absorb yourself in the present tense, the more likely that what you write will be good. Especially in this f--king town, where everybody's sitting in front of their desks for far too long, endlessly sweating over words that don't ever get heard. People are obsessive in this city and work becomes an end in itself. The polar opposite of that is Michael Stipe, who absorbs himself in other people and the life around him, and that's where he gets his ideas. I'm not like that, but I absolutely understand why he does it. Neil Young claims he writes lyrics and doesn't go back to them. If he does, he says, the worse they become. But that's scary. I mean, 'Faust Arp' is the exact opposite of that, pages and pages and pages and pages and pages and pages until eventually, the good ones stick'.