Editing Subitizing (section)

{{Short description|Assessing the quantity of objects in a visual scene without individually counting each item}}
{{For|the Buddhist concept of instantaneous enlightenment|Subitism}}
{{lead extra info|date=June 2019}}
[[File:Fractions 4 of 12.svg|thumb|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 effortless ability to perceive small quantities of items in a [[Set (mathematics)|set]], typically when there are four or fewer items, without relying on linguistic or arithmetic processes. The term refers to the sensation of instantly knowing how many objects are in the visual scene when their number falls within the subitizing range.<ref name="kaufman">{{Cite journal |author1=Kaufman, E.L. |author2=Lord, M.W. |author3=Reese, T.W. |author4=Volkmann, J. |name-list-style=amp |year=1949 |title=The discrimination of visual number |journal=[[American Journal of Psychology]] |volume=62 |pages=498–525 |doi=10.2307/1418556 |pmid=15392567 |issue=4 |publisher=The American Journal of Psychology |jstor=1418556}}</ref>

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 [[counting|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 [[Estimation|estimate]] the number of a large set—a skill similar to, but different from, subitizing. The term subitizing was coined in 1949 by E. L. Kaufman et al.,<ref name="kaufman" /> and is derived from the Latin adjective ''[[wikt:subitus|subitus]]'' (meaning "sudden").

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,<ref name="saltzman">{{Cite journal |author1=Saltzman, I.J. |author2=Garner, W.R. |name-list-style=amp |year=1948 |title=Reaction time as a measure of span of attention |journal=[[The Journal of Psychology]] |volume=25 |pages=227–241 |pmid=18907281 |doi=10.1080/00223980.1948.9917373 |issue=2}}</ref> accurate,<ref name="jevons">{{Cite journal |author=Jevons, W.S. |year=1871 |title=The power of numerical discrimination |journal=Nature |volume=3 |pages=281–282 |doi=10.1038/003281a0 |issue=67|bibcode=1871Natur...3..281J |doi-access=free }}</ref> and confident.<ref>{{Cite journal |author=Taves, E.H. |year=1941 |title=Two mechanisms for the perception of visual numerousness |journal= Archives of Psychology |volume=37 |pages=1–47}}</ref> However, once there are more than four items to count, judgments are made with decreasing accuracy and confidence.<ref name= "kaufman"/> In addition, response times rise in a dramatic fashion, with an extra 250–350{{nbsp}}ms added for each additional item within the display beyond about four.<ref>{{Cite journal |author1=Trick, L.M. |author2=Pylyshyn, Z.W. |name-list-style=amp |year=1994 |title=Why are small and large numbers enumerated differently? A limited-capacity preattentive stage in vision |journal=Psychological Review |volume=101 |issue=1 |pages=80–102 |pmid= 8121961 |doi=10.1037/0033-295X.101.1.80}}</ref>

While the increase in response time for each additional element within a display is 250–350{{nbsp}}ms per item outside the subitizing range, there is still a significant, albeit smaller, increase of 40–100{{nbsp}}ms per item within the subitizing range.<ref name="saltzman"/> A similar pattern of reaction times is found in young children, although with steeper slopes for both the subitizing range and the enumeration range.<ref>{{Cite journal |author1=Chi, M.T.H.  |author2=Klahr, D.  |name-list-style=amp |year=1975 |title=Span and rate of apprehension in children and adults |journal= Journal of Experimental Child Psychology |volume=19 |pages=434–439 |doi=10.1016/0022-0965(75)90072-7 |pmid=1236928 |issue=3}}</ref> This suggests there is no span of [[apprehension (understanding)|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 [[reaction time|speed of response]]. Furthermore, the values of all measures appear to differ markedly inside and outside the subitizing range.<ref name="kaufman"/> 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.<ref>{{Cite journal |author1=Riggs, K.J. |author2=Ferrand, L. |author3=Lancelin, D. |author4=Fryziel, L. |author5=Dumur, G. |author6=Simpson, A. |name-list-style=amp |year=2006 |title=Subitizing in tactile perception |journal=Psychological Science |volume=17 |issue=4 |pages=271–272 |pmid= 16623680 |doi=10.1111/j.1467-9280.2006.01696.x|s2cid=37333935 }}</ref> A 2008 study also demonstrated subitizing and counting in auditory perception.<ref>{{Cite journal |author1=Camos, V. |author2=Tillmann, B. |name-list-style=amp |year=2008 |title=Discontinuity in the enumeration of sequentially presented auditory and visual stimuli |journal=Cognition |volume=107 |issue=3 |pages=1135–1143 |doi=10.1016/j.cognition.2007.11.002 |pmid=18068696|s2cid=14999504 }}</ref>  Even though the existence of subitizing in tactile perception has been questioned,<ref>{{cite journal |author1=Gallace A. |author2=Tan H.Z.|author2-link=Hong Z. Tan |author3=Spence C. | year = 2008 | title = Can tactile stimuli be subitised? An unresolved controversy within the literature on numerosity judgments | journal = Perception | volume = 37 | issue = 5| pages = 782–800 | doi=10.1068/p5767 |pmid=18605150|s2cid=2820818 }}</ref> this effect has been replicated many times and can be therefore considered as robust.<ref>{{Cite journal |author1=Plaisier, M.A. |author2=Bergmann Tiest, W.M. |author3=Kappers, A.M.L. |name-list-style=amp |year=2009 |title=One, two, three, many - Subitizing in active touch |journal=Acta Psychologica |volume=131 |issue=2 |pages=163–170 |doi=10.1016/j.actpsy.2009.04.003 |pmid=19460685|hdl=1874/35195 |hdl-access=free }}</ref><ref>{{Cite journal |author1=Plaisier, M.A. |author2=Bergmann Tiest, W.M. |author3=Kappers, A.M.L. |name-list-style=amp |year=2010 |title=Range dependent processing of visual numerosity: similarities across vision and haptics |journal=Experimental Brain Research |volume=204 |issue=4 |pages=525–537 |doi=10.1007/s00221-010-2319-y|pmc=2903696|pmid=20549196 }}</ref><ref>{{Cite journal |author1=Plaisier, M.A. |author2=Smeets, J.B.J. |name-list-style=amp |year=2011 |title=Haptic subitizing across the fingers |journal=Attention, Perception, & Psychophysics |volume=73 |issue=5 |pages=1579–1585 |doi=10.3758/s13414-011-0124-8|pmc=3118010 |pmid=21479724}}</ref> The subitizing effect has also been obtained in tactile perception with congenitally blind adults.<ref>{{Cite journal |author1=Ferrand, L. |author2=Riggs, K.J. |author3=Castronovo, J. |name-list-style=amp |year=2010 |title=Subitizing in congenitally blind adults |journal=Psychonomic Bulletin & Review |volume=17 |issue=6 |pages=840–845 |doi=10.3758/PBR.17.6.840|pmid=21169578|doi-access=free }}</ref> Together, these findings support the idea that subitizing is a general perceptual mechanism extending to auditory and tactile processing.