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Demonstration of phi phenomenon using two black bars (SOA=102 ms, ISI=-51 ms)

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.[1] Max Wertheimer first described this form of apparent movement in his habilitation thesis, published 1912,[2] marking the birth of Gestalt psychology.[3]

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 is important for the illusion of motion in cinema and animation.[4][5] Actually, Wertheimer applied the term "φ-phenomenon" to all apparent movements described in his thesis when he introduced the term in 1912, the objectless movement he called "pure φ".[2] Nevertheless some commentators assert that he reserved the greek letter φ for pure, objectless movement.[6][7]

Experimental demonstrationEdit

"Magni-phi" variant of the classical experimental arrangement with more than two elements.

Wertheimer's classic experiments used two light lines or curves repeatedly presented one after the other using a tachistoscope.[8] 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[9]) reported seeing pure "objectless" motion.[8]

However, it turns out to be difficult to demonstrate phi stably and convincingly. To facilitate demonstrating the phenomonon, 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.[8]

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.[1]

History of researchEdit

In his 1912 thesis, Wertheimer introduced the symbol φ (phi) in the following way:[2]

Gegeben sind sukzessiv zwei Objekte als Reize; diese werden empfunden; zuerst wird a gesehen, zuletzt b; zwischen ihnen war die ‚Bewegung von a nach b gesehen‘; ohne daß die entsprechende Bewegung resp. die raum-zeit-kontinuierlichen Zwischenlagen zwischen a und b wirklich als Reize exponiert gewesen wären. Der psychische Sachverhalt sei – ohne irgendeine Präjudiz – mit a φ b bezeichnet.

Two successive objects are given as stimuli; these are perceived; first a is seen, last b; between them the 'movement from a to b is seen'; without actually having exposed the corresponding movement respectively the time-space-continuous intermediate positions between a and b as stimuli. The physical issue will be denoted – without any prejudice – by a φ b.

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:

Diese Fälle zeigten sich so, daß auch nicht etwa der Gedanke vorhanden war: ein Objekt habe sich hinüberbewegt; was von Objekten vorhanden war, war in den zwei Lagen gegeben; nicht eines oder eines von ihnen oder ein ähnliches betraf die Bewegung; sondern zwischen ihnen war Bewegung gegeben; nicht eine Objektbewegung. Auch nicht: das Objekt bewegt sich hinüber, ich sehe es nur nicht. Sondern es war einfach Bewegung da; nicht auf ein Objekt bezüglich.

These cases appeared in a way, that not even the thought was present: an object has moved across; what was existing of objects was given in two positions; neither one nor the other of them nor a similar one accounted for the movement; but between them there was movement; not a movement of an object. Not even: the object moves across, I just don't see it. Instead, it was just movement there; not regarding an object.

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.[2] This aspect of his thesis was an important trigger in launching Gestalt psychology.[8]

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.[10] 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.[11] 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.[8]

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."[1]

See alsoEdit

External linksEdit


  1. ^ a b c Vebjørn Ekroll, Franz Faul, Jürgen Golz: Classification of apparent motion percepts based on temporal factors. In: Journal of Vision. Volume 8, 2008, Issue 31, p. 1–22 (online).
  2. ^ a b c d Max Wertheimer: Experimentelle Studien über das Sehen von Bewegung. Zeitschrift für Psychologie, Volume 61, 1912, p. 161–265 (online;PDF-Datei; 8,61 MB).
  3. ^ Wagemans, Johan; Elder, James H.; Kubovy, Michael; Palmer, Stephen E.; Peterson, Mary A.; Singh, Manish; von der Heydt, Rüdiger (2012). "A century of Gestalt psychology in visual perception: I. Perceptual grouping and figure-ground organization". Psychological Bulletin. 138 (6): 1172–1217. doi:10.1037/a0029333. ISSN 1939-1455. PMC 3482144. PMID 22845751. Retrieved 2019-10-14.
  4. ^ Friedrich Kenkel: Untersuchungen über den Zusammenhang zwischen Erscheinungsgröße und Erscheinungsbewegung bei einigen sogenannten optischen Täuschungen. In: F. Schumann (ed.): Zeitschrift für Psychologie. Volume 67, Leipzig 1913, p. 363
  5. ^ Martha Blassnigg: Time, Memory, Consciousness and the Cinema Experience: Revisiting Ideas on Matter and Spirit. Edision Rodopi, Amsterdam/New York 2009, ISBN 90-420-2640-5, p. 126 (online).
  6. ^ Boring, Edwin G. (1949). Sensation And Perception In The History Of Experimental Psychology. New York: Appleton-Century-Crofts. p. 595. Retrieved 2019-10-24.
  7. ^ Sekuler, Robert (1996). "Motion Perception: A Modern View of Wertheimer's 1912 Monograph". Perception. 25 (10): 1243–1258. doi:10.1068/p251243. ISSN 0301-0066.
  8. ^ a b c d e Robert M. Steinman, Zygmunt Pizlob, Filip J. Pizlob: Phi is not beta, and why Wertheimer's discovery launched the Gestalt revolution. In: Vision Research. Volume 40, 2000, p. 2257–2264 (online).
  9. ^ Smith, Barry (1988). "Gestalt Theory: An Essay in Philosophy". In Smith, Barry (ed.). Foundations of Gestalt Theory. Vienna: Philosophia Verlag. pp. 11–81. Retrieved 2019-10-12.
  10. ^ Shipley, Thorne, ed. (1961). Classics in Psychology. New York: Philosophical Library. pp. 1032, footnote 1. Retrieved 2019-10-22.
  11. ^ Edwin Boring: Sensation And Perception In The History Of Experimental Psychology. Appleton-Century-Crofts, New York 1942 (online).