Number estimation relies on a set of segmented objects
Section snippets
Experiment 1
Experiment 1 tested whether connecting pairs of squares with a set of lines reduces estimates of the number of individual squares in a display. Grouping multiple regions of a display so that they become physically continuous is a particularly strong grouping manipulation that may even precede other types of grouping, such as color or shape similarity (Palmer & Rock, 1994). This connectivity grouping also appears to be mandatory for small groups of objects that are in the current focus of
Experiment 2
In Experiment 1, participants estimated the number of squares in each display within 450 ms, suggesting that they did not count them serially (Gallistel and Gelman, 1992, Trick and Pylyshyn, 1993). While these results suggest that participants generated their estimates from a broad snapshot of each display, it is also possible that participants relied on a sampling process in which only a few items from a small portion of each display were counted and compared for each trial. A similar ambiguity
Experiment 3
The first two experiments show that participants rapidly segment pairs of squares that are connected together, in a spatially broad way, leading to an underestimation of the number of distinct squares appearing in a connected display. While the linear correlation between accuracy differences and percent connectedness suggests that the magnitude of the effect depends on the percentage of connected pairs, it should be possible to quantitatively determine the amount of underestimation. The present
Experiment 4
The previous experiments demonstrate that connecting squares with a set of irrelevant lines causes observers to underestimate the number of squares in the display. However using four lines may have led observers to perceive the squares and lines as parts of as a three-dimensional extended cube. Also, using four parallel lines might have led to a stronger low-spatial frequency representation of a single large bar, which might alter unexpected aspects of the displays, such as object size or
General discussion
In Experiment 1, we found that connecting a display of squares into pairs with lines led participants to greatly underestimate the number of squares present in the display, relative to when the connecting lines were broken. Participants underestimated connected displays despite explicit instructions that the lines were irrelevant and should be ignored throughout the task. Even practiced participants, including the authors, could not avoid greatly underestimating displays of connected elements.
Broad segmentation
The finding that number estimation operates over a segmented collection is also important to our understanding of visual processing more generally because it suggests that the larger visual world is segmented broadly. A fundamental question about any visual process is whether it can occur broadly over the visual field, or whether the scope of the process is restricted to a narrow subset of incoming visual information (Neisser, 1967). In general, simpler processes are thought to occur broadly,
Acknowledgements
G.A.A. was supported by NEI/NIH fellowship F32 EY016982. We thank Patrick Cavanagh, Stanislas Dehaene, Laura Ortega, Julia Mossbridge, Lance Rips, Liz Spelke, and Jeremy Wolfe for helpful discussion.
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