From Psychophysics to Artificial Algebra: Is Mathematics Embedded in Our Perception of the World?
Randolph C Grace
Department of Psychology, University of Canterbury
Time & Place
Fri, 26 May 2017 11:00:00 NZST in Rutherford 531
All are welcome
Physical theories use mathematics to describe the world with astonishing precision, while how we perceive the world has been studied by psychology from its inception as an experimental discipline in 1860 by the German physicist, Gustav Fechner. I will briefly describe the history of research which has tried to specify the relationship between subjective sensation and stimulus magnitude as a “psychophysical law”, leading to an influential conjecture by Torgerson (1961): Observers perceive one relation when comparing stimuli, either a difference or ratio, but which one cannot be empirically determined. Research in the 1970s and 1980s attempted to test Torgerson’s conjecture using procedures in which observers were asked directly to estimate differences and ratios, but was inconclusive. Because our perceptual systems evolved long before the invention of mathematics, we propose that Torgerson’s conjecture should be tested under conditions in which observers cannot use their mathematical knowledge. We have conducted several experiments in which observers have learned to produce differences or ratios by trial-and-error feedback, without the use of numbers or explicit instruction. Our experimental procedure, which teaches mathematical relations without numbers or symbols, may be regarded as an artificial algebra. Results show that observers quickly learn to respond accurately and suggest that both differences and ratios are computed by the perceptual system, so Torgerson’s conjecture is false. Based on these results, we speculate that the perceptual system may represent elements of an algebraic field, so that mathematical knowledge is embedded in how we perceive the world.