Ratios and differences in perceptual comparison: A reexamination of Torgerson’s conjecture

Tests of the abilities to judge ratios of extensive and intensive sensory magnitudes

“…Supporting this hypothesis, analyses of people's orderings of sensory intensity ratios and sensory intensity differences have indicated that some people respond to both sensory intensity ratios and sensory intensity differences, whereas others respond only to sensory intensity differences (Parker & Hickman, 1990;Popper, Parker, & Galanter, 1986;Schneider, 1980;Schneider, Parker, Farrell, & Kanow, 1976). In line with these findings, Grace, Morton, Ward, Wilson, and Kemp (2018) reported that only half of their participants could be trained with feedback to differentially respond to both brightness ratios and brightness differences. The ability to judge sensory intensity ratios might be confined to individuals who respond to sensory intensity ratios.…”

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

“…Rule, Curtis & Mullin, 1981). Grace, Morton, Ward, Wilson, and Kemp (2018) developed a novel, nonsymbolic procedure for testing Torgerson's conjecture that did not require explicit instruction about ratios or differences. They argued that previous research might have found mixed results because observers were required to give numerical responses and thus to access their mathematical knowledge.…”

“…Based on this result, Grace et al (2018) proposed that the perceptual system automatically computed both differences and ratios when comparing stimulus magnitudes, so that Torgerson's conjecture was false. They suggested that two operations might indicate that the perceptual system represents an algebraic field, which is an abstract mathematical concept that generalizes the symmetries underlying arithmetic.…”

“…Although the 'artificial algebra' task used by Grace et al (2018) is novel, it has some connections to other experimental and theoretical work that are worth exploring. As a procedure, it resembles a function learning task, in which participants learn by feedback to make an analogue response with a specified mathematical relationship to a stimulus magnitude (Lucas, Griffiths, Williams, & Kalish, 2015;McDaniel, Cahill, Robbins, & Wiener, 2014).…”

“…Performance in the artificial algebra task could be regarded as demonstrating perceptual learning to the extent that accuracy of responding improved with continued training. However, participants in Grace et al's (2018) study only completed single sessions (four blocks of 84 trials each) in the difference or ratio condition. They reported that both operations were learned rapidly; performance improved from the first to second block, but not thereafter.…”