Quantity representation in children and rhesus monkeys: Linear versus logarithmic scales

Abstract

The performance of 4-and 5-year-old children and rhesus monkeys was compared using a computerized task for quantity assessment. Participants first learned two quantity anchor values and then responded to intermediate values by classifying them as either similar to the large anchor or the small anchor. Of primary interest was an assessment of where the point of subjective equality (PSE) occurred for each species across four different sets of anchors to determine whether the PSE occurred at the arithmetic mean or the geometric mean. Both species produced PSEs that were closer to the geometric mean for three of four anchor sets. This indicates that monkeys and children access either a logarithmic scale for quantity representation or a linear scale that is subject to scalar variability, both of which are consistent with Weber's law and representation of quantity that takes the form of analog magnitudes. KeywordsQuantity Judgments; Representational Scale; Children; Monkeys; Bisection TaskThe quantity discriminations made by many species are restricted in their accuracy on the basis of the ratio between those sets (e.g., Barth, Kanwisher, & Spelke, 2003;Beran, 2007;Beran, Taglialatela, Flemming, James, & Washburn, 2006;Brannon, Cantlon, & Terrace, 2006;Brannon & Terrace, 2000;Call, 2000;Huntley-Fenner, 2001). Comparisons with larger ratios (as determined by dividing the smaller quantity by the larger quantity) lead to lower performance levels, even when the distance between sets is constant (e.g., 8 versus 10 is more difficult than 2 versus 4). This suggests that an analog magnitude system produces discriminable representations of sets, and this system is consistent with Weber's law, which states that discrimination of sets becomes more difficult for a fixed difference as the magnitude of those sets increases.Correspondence to: Michael Beran, Language Research Center, Georgia State University, University Plaza, Atlanta, GA 30303, Telephone -404-244-2469, Fax -404-244-5829, E-mail -mjberan@yahoo.com. Publisher's Disclaimer: This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Evidence for discrimination performance being modulated by Weber's Law comes from differing sources. One task, used primarily with nonhuman primates, involves judgments between two sets of items (e.g., Beran, 2004;Brannon & Terrace, 2000;Call, 2000; Judge, Evans, & Vias, 2005). This task also sometimes is used with human children (e.g., Brannon & Van de Walle, 2001; Feigenson, Carey, & Hauser, 2003). The second task is the bisection task that has been used extensively with rats and pigeons (e.g., Emmerton & Renner, 2006;Fetterm...

Human nonverbal discrimination of relative and absolute number

“…In the bisection task, large responses increased with number, and the average bisection point was located closer to the arithmetic than to the geometric mean, similar to Droit-Volet et al (2003) and Tan and Grace (2010), although inconsistent with other numerical bisection studies (e.g., Beran et al, 2008;Jordan & Brannon, 2006a;Roitman et al, 2007). This suggests that participants used a linear number scale with constant variability, rather than one with scalar characteristics that conforms to Weber's law (Roitman et al, 2007).…”

“…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 with constant spacing and increasing generalization between values (see Gibbon, 1981). Similar to Meck and Church (1983), studies with nonhumans have typically obtained bisection at the geometric mean (Beran et al, 2008;Breukelaar & Dalrymple-Alford, 1998;Emmerton & Renner, 2006;Fetterman, 1993;Jordan & Brannon, 2006a, b;Roberts, 2005;Roberts & Mitchell, 1994).…”

“…Numerical bisection has also been investigated in adults (Roitman, Brannon, Andrews, & Platt, 2007) and children (Beran et al, 2008;Droit-Volet, Clement, & Fayol, 2003;Jordan & Brannon, 2006a). In these experiments, temporal and visual nonnumerical cues were varied to limit confounds, and procedural manipulations, such as response time limits and verbal distractor tasks, prevented verbal counting.…”

“…For both adults and children, results were similar to those obtained with nonhumans: The proportion of large responses increased with number, and bisection points were located at the geometric mean, consistent with Weber's law and supporting a representation of number that produces scalar variability. Additionally, bisection functions of children and primates could be superimposed when plotted along the same scale (Beran et al, 2008;Jordan & Brannon, 2006a).…”

“…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.…”