This paper explores how ‘ice’ is woven into the spaces and practices of the state in Norway and Canada and, specifically, how representations of the sea ice edge become political agents in that process. We focus in particular on how these states have used science to ‘map’ sea ice – both graphically and legally – over the past decades. This culminated with two maps produced in 2015, a Norwegian map that moved the Arctic sea‐ice edge 70 km northward and a Canadian map that moved it 200 km southward. Using the maps and their genealogies to explore how designations of sea ice are entangled with political objectives (oil drilling in Norway, sovereignty claims in Canada), we place the maps within the more general tendency of states to assign fixed categories to portions of the earth's surface and define distinct lines between them. We propose that the production of static ontologies through cartographic representations becomes particularly problematic in an icy environment of extraordinary temporal and spatial dynamism, where complex ocean–atmospheric processes and their biogeographic impacts are reduced to lines on a map.