Mapping visual features onto numbers

Abstract

Modern society frequently requires that we express our subjective senses in objective, shared formal systems; this entails mapping multiple internal variables onto a common scale. Here we ask whether we accomplish this feat in the case of estimating number by learning a single mapping between explicit numbers and one integrated subjective estimate of numerosity, or if we separately map different perceptual features onto numbers. We present people with arrays of dots and ask them to report how many dots there are; we rely on the systematic under/overestimation of number at higher quantities to estimate error in the mapping function. By comparing how this error changes over time, as the mapping fluctuates for different visual cues to numerosity, we can evaluate whether these cues share a single mapping, or are mapped onto number individually. We find that area, size, and density all share a common mapping, indicating that people obtain a unified subjective estimate of numerosity before mapping it onto the formal number line.

Children dynamically update and extend the interface between number words and perceptual magnitudes

“…The other set of models that are challenged by our finding are those that propose that estimation occurs through relative comparison (Brockbank et al., 2019; Garner, 1954a, 1954b; Laming, 1984). For example, Laming (1984) proposes that observers make estimates not through structure mapping, but instead by keeping track of their estimates across successive trials (see also Brockbank et al., 2019; Vul et al., 2013).…”

“…The other set of models that are challenged by our finding are those that propose that estimation occurs through relative comparison (Brockbank et al, 2019;Garner, 1954aGarner, , 1954bLaming, 1984).…”

“…To better characterize the relationship between children's PS and VE performance, we examine correlations across the two tasks. Existing models of Number estimation (Brockbank et al., 2019; Vul et al., 2013; Laming, 1984) predict an especially robust relationship between β s/CVs and w because variability in verbal estimates is theorized to be a mixture of the imprecision in the perceptual representations, themselves, and the imprecision in holding a constant mapping. However, as shown in Table 3, when controlling for any age‐related improvements, we find no significant correlations between estimation CVs and w values for Number, Length, nor Area.…”

“…Recently, Brockbank et al. (2019) proposed a significantly more powerful and dynamic version of a “relative comparison” model for Number perception, showing that it can account for a variety of patterns in adult Number estimation performance. However, both accounts make the prediction that the perceptual acuity within a dimension dictates estimation slopes ( β ) and CVs: the more reliably you can differentiate between target values, the better and less variably you should be at attaching further apart number words to these targets.…”

“…This was primarily done to reduce working memory demands on children's performance. One possibility is that this could have also allowed children with worse perceptual acuity to have access to more precise representations for relative comparison compared to having to retrieve the unit from (memory demands are also a key part of the Brockbank et al., 2019 model). Our interpretation of the existing relative comparison models is that observers will always rely on comparing perceptual representations, whether in memory or those immediately available.…”