In visual perception, the world is built up through a succession of physical-sensual encounters (‘R’ ) that are cognitively stabilized by imagined structures of “what’s there.” This estimate includes the weight and solidity of objects, their location, the attractiveness, repulsion, or danger that objects potentially represent, and schemes of potential locomotion. The “hypothetical map” forms a framework for the collation (Ø) of actual experiential “snapshots” that, considered objectively, are discontinuous, fragmented, inconclusive. The map is invisible. As a frame, it guides experience without being a material part of it. Yet, the map extends the body in space “virtually,” as a conditional, future potentiality. This extension uses a logic of touch, conditioned by the left-right structure of the body itself.
Parenthetically, it should be noted that the vast majority of those who use the term, "phi phenomenon," are in fact referring to the beta phenomenon. Both terms were coined by Max Wertheimer, in his 1912 work, "Experimental Studies on the Seeing of Motion." The phi phenomenon should properly refer to the apparent movement of "background space" with the off-on successive flashes of (typically) fixed points or dots of light. The experience of movement generated "between" two still images is, properly, the beta phenomenon, but so few people recognize this distinction that I will repeat the idiotic error of improperly confused terms, trying to add whenever appropriate, this "disclaimer." The discerning reader is referred to the discussion of this confusion in Wikipedia:
"The classic beta phenomenon experiment involves a viewer or audience watching a screen, upon which the experimenter projects two images in succession. The first image depicts a ball on the left side of the frame. The second image depicts a ball on the right side of the frame. The images may be shown quickly, in rapid succession, or each frame may be given several seconds of viewing time. Once both images have been projected, the experimenter asks the viewer or audience to describe what they saw."
Ahem!
Stereognosis, a "logic of touch," plays an important role in this immediate conception of the world by extending the body's structure to the scenes were the body experiences through the senses. As the subject “faces” the scene that yields to perception, the scene itself faces the subject. The subject’s left-to-right is mirrored by the scene’s right-to-left. The subject’s own face is “invisible” as a condition of the visibility of the “face” of the scene. The aspect of the face is, in the first moments of perception, taken almost literally, as an expressive and metaphoric quality. As the subject gazes towards the scene, that gaze is perceived to be returned by a generic gaze that, without an organic optics, conditions the subject’s gaze in reciprocity. All cultures are, at some point in their development, keenly aware of this counter-gaze and incorporate it into their customs and beliefs, whether as an “evil eye” capable of redressing imbalances of luck or wealth, or as an expressive face of objects animated from within (Greek daimon).
The logic of the subject’s secret extension of body-logic into external space is a logic of “contiguity,” one of the two main senses identified by Gelb and Goldstein in their classic study of brain damage of veterans injured in World War I. In perception, it seems as if contiguity “lays the ground” for its complement, semblance, by setting the preconditions for identity. What an object “is” or “looks like” is established through the virtual extension of the body’s interaction with it. The object “faces” the subject and has its own reversed left/right structure. The two “meet” at a point midway — a “screen” for our purposes — where the subject acknowledges the ephemerality of his/her encounter with the scene. Objects may look dark or light, wet or dry, happy or sad, useful or dangerous, but changes to their superficial appearance will not alter the judgment laid down by the continguous logic of the invisible, stabilizing map, which assigns objects their Aristotelian sensus communis capable of transcending the accidents of appearance and perception.
The screen is imaginarily present as both a part of this stabilizing map and as a neutral surface of re-presentation, the necessary condition for defining objects as permanent through their capability of “appearing again.” The defining condition of the screen is that of the potential repetition of the image, appearance, to signal the permanent, signature qualities of the object. Evidence of the screen’s role in stabilizing the subject’s sense of presence in a scene is given by the filmic practice of using reverse-angle shots that alternate between two sides of the scene. The camera is customarily forbidden to cross an imaginary line separating it from the two focal points. Although it may reverse its view, crossing the line would destroy the left-right orientation of the audience and create confusion about the layout of the scene.
The screen and the Ø that invisibly stabilizes the scene by “mapping” components and their potential are related to another aspect of cinema, the well known Ø phenomenon. The Ø connects the static photographs that, collectively, make up the strip of film that dynamically simulates movement. Two stationary lights that glow alternately appear to be one light moving between the two positions. The audience, seeing two “samples” of dynamic motion, “infer” the in between evidence of that motion although motion is not literally present. The audience “experiences” motion by adding the Ø, the missing mental hypothesis of motion.
An analogy to the film strip helps understand how visual and other experience makes us of the ratio between Ø and the literal data of perception. Motion seems smoother if the film has more frames per second. The range between twenty-four to thirty frames per second has been used as a standard for commercial films, but the eye can “tolerate” as few as 16 frames per second before the motion seems too jagged.
We might say that the higher frame rate corresponds to the perfection of the illusion and lessened (conscious) dependence on Ø, while lower frame rates require more Ø and suffer in their ability to deliver illusion. Imagine how this ratio might characterize perception in general. If Ø is “robust” — an example would be the well memorized spaces of the blind or even the familiar environments of sighted people — minimal cues are required to confirm the imagined map and screen that establish the subject’s stable presence in a stable scene. Ø, in turn, can be weakened whenever contrary evidence suggests that the map is inaccurate, that the screen (‘R’) capable of the repetition of expected images. Tension between Ø and R can be purposefully developed in the phenomenon known as “anamorphosis” — the co-presence within a single image of two distinct and often contrasting “interpretations.” Anamorphosis requires that Ø materialize itself as a “competing” R, rather than remaining in the background or invisible.
Note: Terminology is confusing because 'R', representation, is the "artifact" that physically constitutes the "illusion" of motion, Ø. Ø in the largest sense is the "world" conceived as naturally perceived, just as in cinema, "illusory" motion is the "reality" of the scene. The instants, R, that accumulate in sequence to establish this conception constitute the data for this world. This relationship is clearer when conscious construction wanes, as in sleep, and the influence of proprioception relaxes. In Proust's description of the gradual lapse into sleep, the bedroom dissolves into other places, and all places get merged with Proust's drowsing body.
Ø’s invisibility has been used in fantasy writing as a means of concealment. Fairies in Eoin Colfer’s popular Artemis Fowl books disappear by vibrating back and forth — an ingenious reversal of the Ø phenomenon’s usual production of visibility.
This “vibratory” disappearance of fairies in Artemis Fowl borrows from the tradition of the “fourth dimension” as a mysterious dimension of space connected with gnosis, “impossible” movements, and magic action, but it returns this spatial idea to a temporal basis. Time may be the “fourth dimension,” but it is not in the simple way that simply stacks experiences in their sequential order, but a sequence like a film’s strip of static images connected by “empty space” filled in by the subject. Artemis Fowl simply uses the same idea from the opposite “side,” occupying invisibility as if it were a positive resource.
Parminides wrote that “about Nothing we cannot speak,” perhaps the most notoriously double-edged statement in the history of philosophy. Curiously the most famous modern exponent of Nothingness, Jean-Paul Sartre, includes an anecdote about the returned generic Gaze of the world as he builds up a composite picture of the role of Nothingness. A voyeur kneeling before a keyhole, spying on the occupants of a closed room, hears a footstep on the stair. The condition that immediately arises is amplified by the parallel between the voyeur, who sees without being seen; and the voyeur’s own “Voyeur,” who is not seen but only heard. Significantly, the “fourth dimension” idea of Ø carries with it a distinctively ethical quality. We should not forget that this ethics, perhaps all ethics, is dependent on its reciprocal term, invisibility. The voyeur is not looking “face to face” but “awry,” sideways, through a Ø dimension, along an “anamorphic” line. The positive payoff of this is that the spy learns the truth by being invisible and not appearing face to face, one part of a reciprocal process. This is, in fact, the goal of scientific “objectivity”! The “subject supposed to know” in Lacan’s psychology, is the one with access to this anamorphic line, one with “insight.”
Put into the animated sequence of R/Ø, the voyeur and the face-to-face subject contend over the surface of re--presentation that, entirely temporal, is the place of the sequential encounters, spaced out by the subject’s interpolative contextual contribution, Ø. Every subject, S, is bound by the “points of view” the scene seems to require. Every subject imagines an ideal self, a representative subject “supposed to know,” whose ideal vantage point escapes the limitations of the imminent view. The occupant/prisoner of a labyrinth imagines that someone has a map, or can see the building from above. At the every appearance, which takes place at the site of a screen, at least two subjects are present.
For a review of the dimensionality of Ø follow this link.
For a more detailed discussion of the use of Ø as a model, follow this link.
Henri Bergson, Matter and Memory, trans. Nancy Margartet Paul (London: George Allen & Unwin, 1911).
Henri Bergson, Creative Evolution, trans. Arthur Mitchell (New York: H. Holt and Company, 1931).
Gilles Deleuze, Cinema 1: The Movement Image, trans. Hugh Tomlinson and Barbara Habberjam (Minneapolis, MI: University of Minnesota Press, 1986).
Eoin Colfer, Artemis Fowl (New York: Hyperion Books for Children, 2001).
The materialization of Ø is central in the construction and reception of works of art. Ø, as the “artifact” of perception’s representational aspect, acts as a storage space (poché) for elements that, intentionally cached for later use, return at crucial points in the work of art to effect surprise, new levels of meaning, and logical twists. The structure that manages this concealment and return is “chiasmus,” an X-style technique used by poets and artists since ancient times. “A wit among dunces and a dunce among wits” is a short chiasmus coined by Alexander Pope; John F. Kennedy’s advice “Ask not what your country can do for you …” is a more modern example. Chiasmus has its own extensive history and logic, but in its role in perception, chiasmus is an economic way of understanding the role of stereognosis and proprioception. A diagram can summarize the case for using sterognostic and propriocept in the context of perception:
