Subitizing

For the Buddhist concept of instantaneous enlightenment, see Subitism.
An observer may be able to instantly judge how many red circles are present without counting them, but would find it harder to do so for the greater number of blue circles.

Subitizing is the rapid, accurate, and confident judgments of numbers performed for small numbers of items. The term was coined in 1949 by E. L. Kaufman et al.,[1] and is derived from the Latin adjective subitus (meaning "sudden") and captures a feeling of immediately knowing how many items lie within the visual scene, when the number of items present falls within the subitizing range.[1] Sets larger than about four to five items cannot be subitized unless the items appear in a pattern with which the person is familiar (such as the six dots on one face of a die). Large, familiar sets might be counted one-by-one (or the person might calculate the number through a rapid calculation if they can mentally group the elements into a few small sets). A person could also estimate the number of a large set—a skill similar to, but different from, subitizing.

The accuracy, speed, and confidence with which observers make judgments of the number of items are critically dependent on the number of elements to be enumerated. Judgments made for displays composed of around one to four items are rapid,[2] accurate,[3] and confident.[4] However, once there are more than four items to count, judgments are made with decreasing accuracy and confidence.[1] In addition, response times rise in a dramatic fashion, with an extra 250–350 ms added for each additional item within the display beyond about four.[5]

While the increase in response time for each additional element within a display is 250–350 ms per item outside the subitizing range, there is still a significant, albeit smaller, increase of 40–100 ms per item within the subitizing range.[2] A similar pattern of reaction times is found in young children, although with steeper slopes for both the subitizing range and the enumeration range.[6] This suggests there is no span of apprehension as such, if this is defined as the number of items which can be immediately apprehended by cognitive processes, since there is an extra cost associated with each additional item enumerated. However, the relative differences in costs associated with enumerating items within the subitizing range are small, whether measured in terms of accuracy, confidence, or speed of response. Furthermore, the values of all measures appear to differ markedly inside and outside the subitizing range.[1] So, while there may be no span of apprehension, there appear to be real differences in the ways in which a small number of elements is processed by the visual system (i.e. approximately four or fewer items), compared with larger numbers of elements (i.e. approximately more than four items).

A 2006 study demonstrated that subitizing and counting are not restricted to visual perception, but also extend to tactile perception, when observers had to name the number of stimulated fingertips.[7] A 2008 study also demonstrated subitizing and counting in auditory perception.[8] Even though the existence of subitizing in tactile perception has been questioned,[9] this effect has been replicated many times and can be therefore considered as robust.[10][11][12] The subitizing effect has also been obtained in tactile perception with congenitally blind adults.[13] Together, these findings support the idea that subitizing is a general perceptual mechanism extending to auditory and tactile processing.

  1. ^ a b c d Kaufman, E.L.; Lord, M.W.; Reese, T.W. & Volkmann, J. (1949). "The discrimination of visual number". American Journal of Psychology. 62 (4). The American Journal of Psychology: 498–525. doi:10.2307/1418556. JSTOR 1418556. PMID 15392567.
  2. ^ a b Saltzman, I.J. & Garner, W.R. (1948). "Reaction time as a measure of span of attention". The Journal of Psychology. 25 (2): 227–241. doi:10.1080/00223980.1948.9917373. PMID 18907281.
  3. ^ Jevons, W.S. (1871). "The power of numerical discrimination". Nature. 3 (67): 281–282. Bibcode:1871Natur...3..281J. doi:10.1038/003281a0.
  4. ^ Taves, E.H. (1941). "Two mechanisms for the perception of visual numerousness". Archives of Psychology. 37: 1–47.
  5. ^ Trick, L.M. & Pylyshyn, Z.W. (1994). "Why are small and large numbers enumerated differently? A limited-capacity preattentive stage in vision". Psychological Review. 101 (1): 80–102. doi:10.1037/0033-295X.101.1.80. PMID 8121961.
  6. ^ Chi, M.T.H. & Klahr, D. (1975). "Span and rate of apprehension in children and adults". Journal of Experimental Child Psychology. 19 (3): 434–439. doi:10.1016/0022-0965(75)90072-7. PMID 1236928.
  7. ^ Riggs, K.J.; Ferrand, L.; Lancelin, D.; Fryziel, L.; Dumur, G. & Simpson, A. (2006). "Subitizing in tactile perception". Psychological Science. 17 (4): 271–272. doi:10.1111/j.1467-9280.2006.01696.x. PMID 16623680. S2CID 37333935.
  8. ^ Camos, V. & Tillmann, B. (2008). "Discontinuity in the enumeration of sequentially presented auditory and visual stimuli". Cognition. 107 (3): 1135–1143. doi:10.1016/j.cognition.2007.11.002. PMID 18068696. S2CID 14999504.
  9. ^ Gallace A.; Tan H.Z.; Spence C. (2008). "Can tactile stimuli be subitised? An unresolved controversy within the literature on numerosity judgments". Perception. 37 (5): 782–800. doi:10.1068/p5767. PMID 18605150. S2CID 2820818.
  10. ^ Plaisier, M.A.; Bergmann Tiest, W.M. & Kappers, A.M.L. (2009). "One, two, three, many - Subitizing in active touch". Acta Psychologica. 131 (2): 163–170. doi:10.1016/j.actpsy.2009.04.003. hdl:1874/35195. PMID 19460685.
  11. ^ Plaisier, M.A.; Bergmann Tiest, W.M. & Kappers, A.M.L. (2010). "Range dependent processing of visual numerosity: similarities across vision and haptics". Experimental Brain Research. 204 (4): 525–537. doi:10.1007/s00221-010-2319-y. PMC 2903696. PMID 20549196.
  12. ^ Plaisier, M.A. & Smeets, J.B.J. (2011). "Haptic subitizing across the fingers". Attention, Perception, & Psychophysics. 73 (5): 1579–1585. doi:10.3758/s13414-011-0124-8. PMC 3118010. PMID 21479724.
  13. ^ Ferrand, L.; Riggs, K.J. & Castronovo, J. (2010). "Subitizing in congenitally blind adults". Psychonomic Bulletin & Review. 17 (6): 840–845. doi:10.3758/PBR.17.6.840. PMID 21169578.