Differences and ratios in free and learned non-symbolic perceptual comparisons

How are comparisons of magnitude achieved by the perceptual system? The most common approach to answering this question has typically centred on explicit numeric estimation of differences or ratios of various continuous phenomena, and an assumption that comparative judgements instantiate one or the other of these operations. A research literature dating back to the 1970s has delivered no clear consensus on the subject, meanwhile considerable advances have been made in our understanding of how number and magnitude are represented non-symbolically in the brain. In 2018, Grace, Morton, Ward, Wilson, and Kemp pioneered a behavioural learning task in which observers were trained via feedback to estimate the differences or ratios of pairs of stimulus magnitudes without explicit instruction or use of symbolic notation. Contrary to the majority of previous studies, which concluded a single operation (probably differences) governs comparative judgements, these authors found evidence for control by two operations. The current research adopts and extends Grace et al’s non-symbolic paradigm in two key ways: an empirically important distinction is identified between two types of ratio judgement (‘big ratios’ and ‘small ratios’), bringing the total number of candidate comparative operations to three; and the feedback component, which potentially obscured evidence of the perceptual system’s true underlying structure, is gradually removed from the experimental procedure. Without feedback, observers in two experiments consistently compared brightnesses and line lengths according to both the differences and ratios of their magnitudes, as in Grace et al (2018). The ratio function employed, however, differed from that used by Grace et al (and all previous perceptual comparison studies), and dominated responding overall. This was in contrast to two feedback-based experiments, whose results suggested a predisposition toward difference-based comparisons. A strong capacity to learn each operation was evident, however, indicating a high degree of flexibility on the part of the perceptual system. Overall results were largely consistent between brightness and line length modalities, suggesting a common mechanism for perceptual comparisons of intensive and extensive stimuli, with respect to which both differences and (small) ratios play an integral part