Differences and ratios in a nonsymbolic 'Artificial algebra': Effects of extended training

Grace et al. (2018) showed that humans could estimate ratios and differences of stimulus magnitudes by feedback and without explicit instruction in a nonsymbolic 'artificial algebra' task, but that responding depended on both operations even though only one was trained. Here we asked whether control by the trained operation would increase over several sessions, that is, if perceptual learning would occur. Observers (n = 16) completed four sessions in which feedback was based on either ratios or differences for stimulus pairs that varied in brightness (Experiment 1) or line length (Experiment 2). Results showed that control by the trained and untrained operations increased and decreased, respectively, over the sessions, indicating perceptual learning. For about two thirds of individual sessions, regressions indicated significant control by both differences and ratios, suggesting that the perceptual system automatically computes two operations. The similarity of results across experiments with both intensive (brightness) and extensive (line length) stimulus dimensions suggests that differences and ratios are computed centrally, perhaps as part of a general system for processing magnitudes (cf. Walsh, 2003).