Pierced by the number line: Integers are associated with back-to-front sagittal space

Mathematical cognition, paragon of abstraction, is marked by systematic associations between number and space, often described as “mental number lines.” In three experiments, we demonstrate a novel effect: a sagittal (back-to-front) number line for negative and positive integers. In a paradigm requiring full-body movements, participants judged numerical magnitude (Exp. 1-2) and parity (Exp. 3). Across all three experiments, participants associated numerical magnitude with locations in front of and behind the body. Responses to negative integers were faster when moving backward than forward; responses to positive integers, faster forward than backward. This sagittal number line appears to require the involvement of negative numbers (Exp. 1-2) and is most pronounced when judging magnitude (Exp. 3). In sum, reasoning about integers induces systematic dispositions to act along the sagittal axis. Such dispositions may reflect our mathematical habitus, habits of action and thought that reflect and enact our conceptual systems.