Emerging infectious diseases (EIDs) occur when pathogens unpredictably spread into new contexts. EID surveillance systems seek to rapidly identify EID outbreaks to contain spread and improve public health outcomes. Sequencing data has historically not been integrated into real‐time responses, but portable DNA sequencing technology has prompted optimism among epidemiologists. Specifically, attention has focused on the goal of a “sequencing singularity”: the integration of portable sequencers in a worldwide event‐based surveillance network with other digital data (Gardy & Loman, Nature Reviews Genetics, 19, 2018, p. 9). The sequencing singularity vision is a powerful socio‐technical imaginary, shaping the discourse around the future of portable sequencing. Ethical and practical issues are bound by the vision in two ways: they are framed only as obstacles, and they are formulated only at the scales made visible by its implicit geography. This geography privileges two extremes of scale – the genomic and the global – and leaves intermediate scales comparatively unmapped. We explore how widespread portable sequencing could challenge this geography. Portable sequencers put the ability to produce genomic data in the hands of the individual. The explicit assertion of rights over data may therefore become a matter disputed more at an interpersonal scale than an international one. Portable sequencers also promise ubiquitous, indiscriminate sequencing of the total metagenomic content of samples, raising the question of what (or who) is under surveillance and inviting consideration of the human microbiome and more‐than‐human geographies. We call into question a conception of a globally integrated stream of sequencing data as composed mostly of “noise,” within which signals of pathogen “emergence” are “hidden,” considering it instead from the perspective of recent work into more‐than‐human geographies. Our work highlights a practical need for researchers to consider both the alternative possibilities they foreclose as well as the exciting opportunities they move towards when they deploy their visions of the future.