Imagine you’re at an all-you-can-eat buffet. Just with one glance, you quickly count the plates of food on the table – that’s subitizing! But as the table gets bigger, you need to estimate the number of plates because it’s too much to count exactly. Now, what if there’s a sweet spot where you can use both techniques together? This study explores the idea that our brains strategically combine subitizing (quick counting) and estimation to be more accurate and precise in perceiving numbers. By deploying attention strategically, we can maximize the precision of estimation, even with time or attentional constraints. The researchers developed a computational model to demonstrate this process and tested it in two experimental simulations. While some recent theories suggest that there’s only one way our brains represent numbers, this study argues for a more comprehensive view: two systems working together with a unified attentional mechanism. If you’re interested in how our brains perceive numerosity and juggle attention, dive into the full article below!

Abstract
The common view of the transition between subitizing and numerosity estimation regimes is that there is a hard bound on the subitizing range, and beyond this range, people estimate. However, this view does not adequately address the behavioral signatures of enumeration under conditions of attentional load or in the immediate post-subitizing range. The possibility that there might exist a numerosity range where both processes of subitizing and estimation operate in conjunction has so far been ignored. Here, we investigate this new proposal, that people strategically combine the processes of subitizing and estimation to maximize accuracy and precision, given time or attentional constraints. We present a process-level account of how subitizing and estimation can be combined through strategic deployment of attention to maximize the precision of perceived numerosity given time constraints. We then describe a computational model of this account and apply it in two experimental simulations to demonstrate how it can explain key findings in prior enumeration research. While recent modeling work has argued that the behavioral signatures of enumeration can best be explained through a single numerosity system with a single form of representation, we argue that our model demonstrates how the traditional two-systems view of numerical representation accounts for behavioral data through coordination with a unified attentional mechanism, rather than a unified representation.

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