# Part–whole effects in visual number estimation

## TL;DR

People tend to underestimate the number of objects in a display when the objects can be combined into whole items, even if they are physically separate.

## Contribution

This study reveals that visual number estimation is influenced by part–whole relationships, challenging assumptions about how we perceive numerosity.

## Key findings

- Displays with combinable puzzle pieces were judged as less numerous than those with noncombinable pieces.
- The underestimation effect persisted even after participants were trained to count individual pieces.
- The effect was not explained by low-level visual factors.

## Abstract

In a single glance at a collection of objects, we can appreciate their numerosity. But what are the “objects” over which this number sense operates? Most work in this domain has implicitly assumed that we estimate the number of discrete, bounded individuals actually present in the visual field. However, in many instances we can construe such individuals as potential parts of composite objects that they can create—as when we assemble furniture or complete a jigsaw puzzle. Here, we demonstrate that visual numerosity estimation is sensitive to such part–whole relations, such that the number of items in a display is underestimated when it contains spatially separated but easily combinable objects. Participants saw brief displays containing noncontiguous “puzzle-piece” stimuli, and reported which display had more pieces. Crucially, most of the pieces appeared in pairs that either could or could not efficiently combine into new objects. In four experiments, displays with combinable pieces were judged as less numerous than displays with noncombinable pieces—as if the mind treated two geometrically compatible pieces as being the single whole object they could create. These effects went beyond various low-level factors, and they persisted even when participants were explicitly trained to treat individual pieces as the units that should be counted. Thus, despite the many ways that sets of objects may be construed for the purposes of counting, visual perception automatically takes into account the ways that object parts may combine into wholes when extracting numerosity from visual displays.