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Proximity model of perceived numerosity.

Jüri Allik1,2, Aire Raidvee3

  • 1Institute of Psychology, University of Tartu, Näituse 2, 50409, Tartu, Estonia. juri.allik@ut.ee.

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The occupancy model (OM) suggests perceived numerosity depends on dot area. However, the proximity model (PM) indicates element spacing is key, challenging the OM's assumptions.

Keywords:
Nearest neighbor distanceNumerosity illusionsPerceived numberSpatial statisticsThe occupancy modelVisual crowding

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Area of Science:

  • Visual Perception
  • Computational Neuroscience
  • Psychophysics

Background:

  • The occupancy model (OM) posits perceived numerosity relates to the spatial area occupied by elements.
  • This model assumes dots fill a fixed radius, influencing apparent number.
  • The OM's computational nature may not reflect actual perceptual processes.

Purpose of the Study:

  • To investigate the spatial arrangement's effect on perceived numerosity.
  • To compare the occupancy model (OM) with an alternative proximity model (PM).
  • To determine the critical factors influencing numerosity perception.

Main Methods:

  • Proposed the proximity model (PM) based on binomial probability (β).
  • Assumed β magnitude is inversely proportional to nearest neighbor distance.
  • Conducted a simulation experiment to compare OM and PM predictions.

Main Results:

  • The OM's calculated occupancy area was closely replicated by the mean nearest neighbor distance.
  • Simulation results support the importance of proximity in numerosity perception.
  • Demonstrated a strong correlation between element spacing and perceived quantity.

Conclusions:

  • Proximity between elements is a critical factor in perceived numerosity.
  • The exact algorithm for measuring proximity in perception remains to be determined.
  • Suggests spatial relationships, not just area, are fundamental to how we perceive number.