Recent research in numerical cognition has begun to systematically detail the ability of humans and nonhuman animals to perceive the magnitudes of nonsymbolic ratios. These relationally defined analogs to rational numbers offer new potential insights into the nature of human numerical processing. However, research into their similarities with and connections to symbolic numbers remains in its infancy. The current research aims to further explore these similarities by investigating whether the magnitudes of nonsymbolic ratios are associated with space just as symbolic (...) numbers are. In two experiments, we found that responses were faster on the left for smaller nonsymbolic ratio magnitudes and faster on the right for larger nonsymbolic ratio magnitudes. These results further elucidate the nature of nonsymbolic ratio processing, extending the literature of spatial–numerical associations to nonsymbolic relative magnitudes. We discuss potential implications of these findings for theories of human magnitude processing in general and how this general processing relates to numerical processing. (shrink)

Clarke and Beck suggest that the ratio processing system may be a component of the approximate number system, which they suggest represents rational numbers. We argue that available evidence is inconsistent with their account and advocate for a two-systems view. This implies that there may be many access points for numerical cognition – and that privileging the ANS may be a mistake.

Accumulating evidence suggests that different magnitudes (e.g., number, size, and duration) are spatialized in the mind according to a common left–right metric, consistent with a generalized system for representing magnitude. A previous study conducted by two of us (Holmes & Lourenco, ) provided evidence that this metric extends to the processing of emotional magnitude, or the intensity of emotion expressed in faces. Recently, however, Pitt and Casasanto () showed that the earlier effects may have been driven by a left–right mapping (...) of mouth size rather than emotional magnitude, and they found no evidence for an emotional magnitude mapping when using words as stimuli. Here, we report two new experiments that further examine these conclusions. In Experiment 1, using face stimuli with mouths occluded, we replicate the original finding: Less emotional faces were associated with the left and more emotional faces with the right. However, we also find that people can reliably infer the sizes of the occluded mouths, and that these inferred mouth sizes can explain the observed left–right mapping. In Experiment 2, we show that comparative judgments of emotional words yield a left–right mapping of emotional magnitude not attributable to stimulus confounds. Based on these findings, we concur with Pitt and Casasanto that faces pose challenges for isolating the forces driving spatialization, but we suggest that emotional magnitude, when assessed using unconfounded stimuli in a sufficiently sensitive task, may indeed be spatialized as originally proposed. Suggestions for further research on the spatialization of emotional magnitude are discussed. (shrink)

Clarke and Beck use behavioural evidence to argue that approximate ratio computations are sufficient for claiming that the approximate number system represents the rationals, and the ANS does not represent the reals. We argue that pure behaviour is a poor litmus test for this problem, and that we should trust the psychophysical models that place ANS representations within the reals.

The approximate number system (ANS) enables organisms to represent the approximate number of items in an observed collection, quickly and independently of natural language. Recently, it has been proposed that the ANS goes beyond representing natural numbers by extracting and representing rational numbers (Clarke & Beck, 2021a). Prior work demonstrates that adults and children discriminate ratios in an approximate and ratio-dependent manner, consistent with the hallmarks of the ANS. Here, we use a well-known “connectedness illusion” to provide evidence that these (...) ratio-dependent ratio discriminations are (a) based on the perceived number of items in seen displays (and not just non-numerical confounds), (b) are not dependent on verbal working memory, or explicit counting routines, and (c) involve representations with a part-whole (or subset-superset) format, like a fraction, rather than a part-part format, like a ratio. These results vindicate key predictions of the hypothesis that the ANS represents rational numbers. (shrink)