A Theory of Perceptual Number Encoding

There has long been interest in how the mind represents numerical magnitude, particularly in the absence of symbols. For humans and nonhuman animals, number represents a core dimension of perceptual experience by which objects in the physical world are delineated. The physical world is also well characterized by other dimensions, many of which covary with number. Yet the general consensus is that number is perceived independently of other magnitudes that co-occur with it. Here we present evidence against the independence of number perception. In particular, we use evidence from neuroimaging, computational modeling, visual illusions, and psychophysics to introduce a novel theory of visual number encoding, wherein non-numerical magnitude information such as cumulative surface area is encoded along with number and sustained throughout visual perception. Moreover, we propose that the experience of number per se reflects the read-out of a multidimensional (i.e., integral) representation vis-à-vis selective attention, not the independent encoding of number.