Wertheimer and Phi Phenomenon
Boring’s description of Wertheimer’s work
in Sensation and Perception in the History of Experimental Psychology (1942):
Wertheimer simplified the observational situation. ... he arranged ... for a single discrete displacement of a simple geometric figure, a line or a curve. The first member he designated a the second member b. When the time interval between a and b was relatively long (above 200 ms) the subject perceived succession, first a, then b. When the interval was very short (less than 30 ms), the perception was one of simultaneity, a and b together. In between successivity and simultaneity, he got movement, the optimal interval for which was about 60 ms.
For times within the movement — optimum and successivity [i.e. when switching was slowed down from where a single object appeared to move from one place to another until the subject saw a followed by b, rather than a single moving object] the subject perceived various kinds of partial movement. For instance, as the time-interval is increased above the optimum [i.e. the switching of a and b is slowed down, moving the percept towards successivity], the seen movement tends to break up into a dual movement in which each part moves with a lack of continuity, or into a singular movement in which one part moves and the other is stationary. In these cases, instead of seeing a single object move, the subject sees two successive objects with one or both of them moving. Within this interval there is also the case of pure movement named ϕ, movement which connects the objects and has direction between them but seems not in itself to be an object. The series for increasing time-intervals [i.e. from faster to slower alternations] is therefore something like this: simultaneity — optimal movement — partial movement — pure movement (ϕ) — succession. …ϕ-movement ( Wertheimer, 1912) is pure movement that is seen without a moving object and the basis for the claim that movement is as primary as any other sensory phenomenon. (p. 595).
Robert M. Steinmana, Zygmunt Pizlob, Filip J. Pizlob
Phi is not beta, and why Wertheimer’s discovery launched the Gestalt revolution
Boring’s definitions of ϕ and optimal movement (β) are fine. His description of Wertheimer’s observations are also. He got only one thing wrong. Namely, the ϕ-phenomenon is observed near simultaneity not near successivity, i.e. near where alternation is fast and both a and b are visible simultaneously. The ϕ-phenomenon is not observed when the switching speed is increased from successivity towards optimal-movement (β). This, rather mysterious, error in Boring’s influential book probably led to the confusion about Wertheimer’s revolutionary phenomenon that is evident in most contemporary textbooks. One will not see ϕ if one looks for it where Boring suggested.
All of these studies, as well as our own observations, show that in the range between simultaneity and successivity, there are only two distinctive percepts, each corresponding to clearly different frequency ranges. ... ϕ is always observed for frequencies higher than those for β (by a factor of about two), and it is described as a shadow moving between and around the targets. (Robert M. Steinmana, et al)