In this article I take the US television series Mad Men (2007-present) as an exemplary 'approximation', a term I adopt to signal the way in which certain texts construct a changeable, fluid 'truth' resulting from collisions, exchange and dialectical argument. Approximations are layered, their formal layerings mirroring a layered, multifaceted argument. Mad Men integrates and represents real historical events within a fictional setting, and act that suggests that an event or action can never be finished, fixed and not open to reassessment. Specifically, this article examines 'The Grown Ups', Episode 12 of Season 3, which charts the events of 22 November 1963, the day Kennedy was assassinated. Although we might be able to bring to mind the images and conspiracy theories that have been made available since (such Abraham Zapruder's 8 mm home movie footage of the assassination), these images were not available at the time. Mad Men as a series always strives to represent its historical milieu as authentically as possible, so the characters re-enact 22 November 1963 as authentically as possible by watching only what was on television that day (the news bulletin, Walter Kronkite's announcement that Kennedy is dead). The contemporary backdrop to these events, including the resonances of '9/11' through Mad Men, inform and collide with the authenticity on the screen.