A partially shared magnitude system: Common and specialized neural substrates underlying spatial, numerical, and temporal arithmetic.

Magnitude, such as time, space and number, constitutes a foundational construction of perceptual and cognitive experience. A Theory of Magnitude proposes that these dimensions are processed by a shared magnitude system. However, it remains unclear how this system supports the manipulation of multiple continuous magnitude information, such as arithmetic operation across domains and whether it operates as a fully shared or partially specialized subsystem. Using functional magnetic resonance imaging, we investigated magnitude arithmetic in numerical, spatial and temporal domains. Conjunction analyses were conducted at each arithmetic stage (first operand, second operand, and probe) to identify overlapping activations across magnitude dimensions. To explore domain-specific differences, voxel-wise factorial ANOVA and task-dependent functional connectivity analyses were applied. Conjunction analyses revealed several overlapping neural substrates at each stage, including key components of the magnitude system. Voxel-wise factorial ANOVA demonstrated that numerical and spatial arithmetic showed greater activation in the bilateral superior occipital gyrus and left middle occipital gyrus, whereas temporal arithmetic elicited stronger activation in left precentral gyrus. Functional connectivity analyses revealed that temporal arithmetic showed greater coupling with bilateral precentral gyrus and cerebellum, whereas numerical and spatial arithmetic elicited stronger coupling with left inferior occipital gyrus, by using bilateral IPS as seed regions. In summary, arithmetic across different magnitude domains relies on a shared magnitude network, with numerical and spatial operations depending on visuospatial mechanisms while temporal operations depend on sensorimotor mechanisms. This dissociation indicates that static and dynamic magnitudes are supported by distinct subsystems, providing evidence for a partially shared magnitude system.