We revisit the origins of the modern, so-called 'stored program" computer during the 1940s from a media-centric viewpoint, from tape-driven relay computers to the introduction of delay line and cathode ray tube memories. Some early machines embodied fixed programs, but all general-purpose computers use a medium of some kind to store control information. The idea of a "memory space" composed of sequentially numbered 'storage locations' is crucial to modern computing, but we show that this idea developed incrementally and was not fully articulated in John von Neumann's First Draft of a Report on the EDVAC. Instead, the designers of computers based around delay line memories conceptualized their structure using different temporal and spatial schemes. Referencing the correct data was not just a question of "where" but also one of "when."