Spatial number estimation has a higher linear range than temporal number estimation; differential affordances for subdivision might help to explain why

Abstract

Estimation of visuospatial number typically has a limited linear range that goes well beyond the subitizing range but typically not beyond 20 items without calibration procedures. Three experiments involving a total of 104 undergraduate students, each tested once, sought to determine if the limit on the linear range represented a capacity limitation of a linear accumulator or might be the result of a strategy based on subdividing spatial displays into potentially subitizable subsets. For visual and auditory temporal numbers for a large range of numbers (2–58; Experiment 1), the (unbiased) linear range was found to be quite restricted (three or four items). Using matched linear spatial number stimuli (Experiment 2), the linear range observed extended to about nine or 10 items. Experiment 3 compared estimates when simultaneous two-dimensional spatial number displays were presented briefly, with estimates for identical displays that accumulated over time. The linear range of estimates for accumulating spatial displays reached only 11 items, whereas that for briefly presented displays extended to about 20 items. These results suggest that the limit on the linear range is not simply a capacity limitation in a linear accumulator. Rather, they support the idea that linear spatial number estimation for the range from five to 20 may be based on subdividing the display into a subitizable number of (potentially) subitizable groups, even if those groups are not outwardly marked.

Relative numerosity is constructed from size and density information: Evidence from adaptation

“…as a signature of “density,” bears a striking resemblance to the central limit theorem. If number comparisons are accomplished by sampling (as has been shown by Solomon and Morgan, 2018 ; see also Durgin, Aubry, Balisanyuka-Smith, & Yavuz, 2022 ), then random samples that contain more data (i.e., larger numbers of dots) should reduce uncertainty concerning mean as a function of the square root of N. This has nothing to do with average distance and everything to do with sampling over a limited area (i.e., density in the sense of local dots/deg 2 ). Simulations confirm that the “density” function (1/√ N ) for Weber fractions reported by Anobile et al., (2014) can be produced by randomly sampling half the display (e.g., by simply limiting consideration to one hemifield of each of two dot patches) in displays statistically similar to those they used (theoretically, any sample area would do).…”

Is the approximate number system capacity limited? Extended display duration does not increase the limits of linear number estimation.

“…Additional support for the idea that the capacity for the perceived number depends on the type of perceptual information available comes from a recent study that compared the limits of linearity for temporal number and linear spatial number with that for the kinds of two-dimensional visual displays most usually studied (Durgin et al, 2022). With stochastically timed temporal signals, modeled after those of Whalen et al (1999), Durgin et al found that linear number estimation extended to only about five items, consistent with the typical unidimensional capacity suggested by Miller (1956).…”