Abstract
It has recently been demonstrated that there are two discontinuities in the estimation of visual number: For very low, numbers up to about 4 or 5, estimation is exact, thereafter, it is inexact. There is evidence for a second discontinuity at about 20 items (Durgin, 2016), which is stable against changes in the range of numbers estimated (Portley & Durgin, submitted). Below 20 items, number estimates have a slope of about 1; above 20, estimates are best fit with a power function with an exponent less than 1. Here we tested the stability of the second visual number estimation discontinuity across a six-fold change in exposure duration. Forty undergraduates participated. Half were tested with brief (500 ms) presentations; half were tested with long (3000 ms) exposures. The dots were white-center, black surround luminance-balanced dots presented in one of two display sizes at 24 numerosities ranging (logarithmically) from 3 to 224, with 8 trials per numerosity. Subjects typed estimates on screen with neither time pressure nor the requirement of a delay. Analyses were conducted of the mean estimates, the variance of the estimates and the response times. Three major observations emerged: (1) mean estimates were essentially identical across exposure durations (2) within-subject variance was higher for brief durations between about 6 dots and 20 dots (i.e., in this range added time was particularly useful), (3) response times increased with number similarly in both conditions until they plateaued, for brief exposures, at about 3200 ms for 8 dots or more. For long exposures the plateau occurred at about 4200 ms for 20 dots or more. Overall, extended time increased the precision of estimates between 6 and 20 dots, but did not substantively effect estimates beyond 20 dots either in precision or accuracy. The cause of the discontinuity at 20 is unclear.