Why are small and large numbers enumerated differently? A limited-capacity preattentive stage in vision. Trick, L. & Pylyshyn, Z. W. Psychol Rev, 101(1):80-102, 1994.
abstract   bibtex   
"Subitizing," the process of enumeration when there are fewer than 4 items, is rapid (40-100 ms/item), effortless, and accurate. "Counting," the process of enumeration when there are more than 4 items, is slow (250-350 ms/item), effortful, and error-prone. Why is there a difference in the way the small and large numbers of items are enumerated? A theory of enumeration is proposed that emerges from a general theory of vision, yet explains the numeric abilities of preverbal infants, children, and adults. We argue that subitizing exploits a limited-capacity parallel mechanism for item individuation, the FINST mechanism, associated with the multiple target tracking task (Pylyshyn, 1989; Pylyshyn & Storm, 1988). Two kinds of evidence support the claim that subitizing relies on preattentive information, whereas counting requires spatial attention. First, whenever spatial attention is needed to compute a spatial relation (cf. Ullman, 1984) or to perform feature integration (cf. Treisman & Gelade, 1980), subitizing does not occur (Trick & Pylyshyn, 1993a). Second, the position of the attentional focus, as manipulated by cue validity, has a greater effect on counting than subitizing latencies (Trick & Pylyshyn, 1993b).
@Article{Trick1994,
  author   = {LM Trick and Zenon W. Pylyshyn},
  journal  = {Psychol Rev},
  title    = {Why are small and large numbers enumerated differently? {A} limited-capacity preattentive stage in vision.},
  year     = {1994},
  number   = {1},
  pages    = {80-102},
  volume   = {101},
  abstract = {"Subitizing," the process of enumeration when there are fewer than
	4 items, is rapid (40-100 ms/item), effortless, and accurate. "Counting,"
	the process of enumeration when there are more than 4 items, is slow
	(250-350 ms/item), effortful, and error-prone. Why is there a difference
	in the way the small and large numbers of items are enumerated? A
	theory of enumeration is proposed that emerges from a general theory
	of vision, yet explains the numeric abilities of preverbal infants,
	children, and adults. We argue that subitizing exploits a limited-capacity
	parallel mechanism for item individuation, the FINST mechanism, associated
	with the multiple target tracking task (Pylyshyn, 1989; Pylyshyn
	& Storm, 1988). Two kinds of evidence support the claim that subitizing
	relies on preattentive information, whereas counting requires spatial
	attention. First, whenever spatial attention is needed to compute
	a spatial relation (cf. Ullman, 1984) or to perform feature integration
	(cf. Treisman & Gelade, 1980), subitizing does not occur (Trick &
	Pylyshyn, 1993a). Second, the position of the attentional focus,
	as manipulated by cue validity, has a greater effect on counting
	than subitizing latencies (Trick & Pylyshyn, 1993b).},
  keywords = {Adolescent, Adult, Attention, Child, Preschool, Discrimination Learning, Human, Infant, Orientation, Pattern Recognition, Visual, Problem Solving, Reaction Time, 8121961},
}

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