The term phi phenomenon is used in a narrow sense for an apparent motion that is observed if two nearby optical stimuli are presented in alternation with a relatively high frequency. In contrast to beta movement, seen at lower frequencies, the stimuli themselves do not appear to move. Instead, a diffuse, amorphous shadowlike something seems to jump in front of the stimuli and occlude them temporarily. This shadow seems to have nearly the color of the background. Max Wertheimer first described this form of apparent movement in his habilitation thesis, published 1912, marking the birth of Gestalt psychology. In a broader sense, particularly if the plural form phi phenomena is used, it applies also to all apparent movements that can be seen if two nearby optical stimuli are presented in alternation. This includes especially beta movement, which has been regarded as the illusion of motion in cinema and animation, although it can be argued that beta movement indicates long-range apparent motion rather than the short-range apparent motion seen in film. Actually, Wertheimer applied the term "φ-phenomenon" to all apparent movements described in his thesis when he introduced the term in 1912, while he used the term "pure φ" for the objectless movement that was observed at high alternation frequencies. Nevertheless, some commentators assert that he reserved the Greek letter φ for pure, objectless movement.
Experimental demonstration Wertheimer's classic experiments used two light lines or curves repeatedly presented one after the other using a tachistoscope. If certain, relatively short, intervals between stimuli were used, and the distance between the stimuli was suitable, then his subjects (who happened to be his colleagues Wolfgang Köhler and Kurt Koffka) reported seeing pure "objectless" motion. However, it turns out to be difficult to demonstrate phi stably and convincingly. To facilitate demonstrating the phenomenon, 21st-century psychologists designed a more vivid experimental arrangement using more than two stimuli. In this demonstration, called "Magni-phi," identical disks are arranged in a circle and, in a rapid sequence, one of the disks is hidden in clockwise or counter-clockwise order. This makes it easier to observe the kind of shadow-like movement Wertheimer discovered. The Magni-phi demonstration is robust to changes of parameters such as timing, size, intensity, number of disks, and viewing distance. Furthermore, the phenomenon may be observed more reliably even with only two elements if a negative interstimulus interval (ISI) is used (that is, if the periods during which the two elements are visible overlap slightly). In that case, the viewer may see the two objects as stationary and suppose unconsciously that the reappearance of the stimulus on one side means that the object previously displayed in that position has reappeared and not, as observed with beta movement, that the object from the opposite side has just moved to a new position. The crucial factor for this perception is the shortness of discontinuity of the stimulus on each side. This is supported by the observation that two parameters have to be chosen properly to produce the pure phi phenomenon: first the absolute duration of the gap on each side must not exceed about 150 ms., and second, the duration of the gap must not exceed 40% of the stimulus period.
History of research In his 1912 thesis, Wertheimer introduced the symbol φ (phi) in the following way:
Besides the "optimal movement" (later called beta movement) and partial movements of both objects, Wertheimer described a phenomenon he called "pure movement." Concerning this, he summarized the descriptions of his test subjects as follows:
Wertheimer attributed much importance to these observations because, in his opinion, they proved that movement could be perceived directly and was not necessarily deduced from the separate sensation of two optical stimuli in slightly different places at slightly different times. This aspect of his thesis was an important trigger in launching Gestalt psychology. Starting in the mid-20th century, confusion arose in the scientific literature as to exactly what the phi phenomenon was. One reason could be that the anglophone scientists had difficulties understanding Wertheimer's thesis, which was published in German. Wertheimer's writing style is also idiosyncratic. Furthermore, Wertheimer's thesis does not specify precisely under which parameters "pure movement" was observed. Moreover, it is difficult to reproduce the phenomenon. Edwin Boring's influential history of the psychology of sensation and perception, first published in 1942, contributed to this confusion. Boring listed the phenomena Wertheimer had observed and sorted them by the length of the interstimulus interval. However, Boring placed the phi phenomenon in the wrong position, namely as having a relatively long inter stimulus interval. In fact, with such long intervals, subjects do not perceive movement at all; they only observe two objects appearing successively. This confusion has probably contributed to the "rediscovery" of the phi phenomenon under other names, for example, as "omega motion," "afterimage motion," and "shadow motion."
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