Human nonverbal discrimination of relative and absolute number

Abstract

The nonverbal discrimination of relative and absolute number of sequential visual stimuli was investigated with humans in bisection, reproduction, and report tasks. Participants viewed a sequence of 40 red and black objects on each trial, randomly intermixed, and had to identify the number of red objects, which varied from 1 to 20. To prevent the use of a verbal-counting strategy, participants were required to name the objects as they appeared. The characteristics of human performance resembled those of pigeons in analogous procedures (Tan & Grace Learning and Behavior 38:408-417, 2010; Tan, Grace, Holland, & McLean Journal of Experimental Psychology 33:409-427, 2007): Average response number increased systematically with sample number, and bisection points were located at the arithmetic, not the geometric, mean. Additionally, in both the reproduction and report tasks, coefficients of variation decreased for values less than 6 but increased or remained constant for larger values, suggesting that different representations were used for small and large numbers.Keywords Numerical processing . Nonverbal . Number representation . Numerosity Numerical ability has been widely investigated in humans, often using adaptations of nonhuman numerical discrimination procedures. Yet relatively few studies have directly compared human and nonhuman performance, and those have been limited mostly to nonhuman primates and relative numerosity discriminations (Beran, Johnson-Pynn, & Ready, 2008; Jordan & Brannon, 2006a, b). The aim of the present experiment was to investigate further the processes underlying the nonverbal discrimination of number; it replicates and extends previous research with pigeons by Tan, Grace, Holland, and McLean (2007) and Tan and Grace (2010) with human participants in both relative and absolute numerical tasks. Relative numerosity discriminationsOne procedure commonly used to investigate relative numerosity discrimination in various species is the bisection task. In Meck and Church's (1983) original experiment, rats were trained to discriminate between two sequences of white noise bursts in which duration and number were confounded; responses to the left or right lever were reinforced depending on whether the preceding sequence was small/short or large/long. Numerical and temporal discriminations were tested, respectively, by holding duration or number constant at an intermediate value while varying the other on test trials. For both discriminations, bisection points were located near the geometric mean of the extreme values used in training.The location of the bisection point has implications for the representation of number. Assuming similar representational structures for time and number, arithmetic mean bisection would characterize a linear numerical scale, with constant spacing and generalization between values. Conversely, bisection at the geometric mean is predicted by either a logarithmic scale with decreasing spacing and constant generalization between values or a linear scale

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

“…Questions about whether magnitudes should be scaled linearly or logarithmically may reflect the same fundamental indeterminacy (e.g., Dehaene, 2003;Dehaene, Izard, Spelke, & Pica, 2008;Gibbon & Church, 1981;Tan & Grace, 2012). Models for nonhuman choice behavior have also disagreed about whether differences or ratios of reinforcement-related variables control responding (Mazur, 2002;Savastano & Fantino, 1996).…”