A neural model of how the brain represents and compares multi-digit numbers: spatial and categorical processes.

Both animals and humans represent and compare numerical quantities, but only humans have evolved multi-digit place-value number systems. This article develops a Spatial Number Network, or SpaN, model to explain how these shared numerical capabilities are computed using a spatial representation of number quantities in the Where cortical processing stream, notably the inferior parietal cortex. Multi-digit numerical representations that obey a place-value principle are proposed to arise through learned interactions between categorical language representations in the What cortical processing stream and the Where spatial representation. Learned semantic categories that symbolize separate digits, as well as place markers like 'ty,' 'hundred,' and 'thousand,' are associated through learning with the corresponding spatial locations of the Where representation. Such What-to-Where auditory-to-visual learning generates place-value numbers as an emergent property, and may be compared with other examples of multi-modal cross-modality learning, including synesthesia. The model quantitatively simulates error rates in quantification and numerical comparison tasks, and reaction times for number priming and numerical assessment and comparison tasks. In the Where cortical process, transient responses to inputs are integrated before they activate an ordered spatial map that selectively responds to the number of events in a sequence and exhibits Weber law properties. Numerical comparison arises from activity pattern changes across the spatial map that define a 'directional comparison wave.' Variants of these model mechanisms have elsewhere been used to explain data about other Where stream phenomena, such as motion perception, spatial attention, and target tracking. The model is compared with other models of numerical representation.