The band's self-titled first album provided the soundtrack for the documentary Zizek!, which features Slovenian cultural theorist Slavoj Zizek (the film's director, Astra Taylor, is married to Barnes' former Neutral Milk Hotel bandmate Jeff Mangum).
thumb|right|295px|A Hawk and a Hacksaw performing in 2009 In an interview with Splendid magazine, Barnes said of the group's name "The reason that I use it is the book Don Quixote, by Cervantes." He added: "It's basically that someone who has gone mad can't tell the difference between a Hawk and a Hacksaw, that's what they say in Don Quixote."[http://www.splendidezine.com/features/ahawk/]
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