All spatial directions are not treated equally. This character of “having different physical properties in different directions” is referred to as “anisotropy” (Collins, 1986). This unequal responding to different spatial directions is indicative of perceptual/memory organisation.

IVA.51 Directional Prototypes in Language.

Cognitive prototypes are evidenced by the specialised terms which have developed in the English language for spatial directions, while deflections (non–prototypes) are referred to according to their relationship to the prototypes. Spatial anisotropy is evident in that dimensions are given the greatest specificity, diagonals are given less, and intermediary deflections are given the least.

Each dimension has been given a specialised name (eg. vertical, lateral, sagittal; see Appendix VIII), each of the two directions within each dimension has also received a special name (eg. up/down, right/left, fore/back), and the group of three dimensions taken together has been designated as the Cartesian cross which are used as the basis of geometric coordinate systems. Dimensions are also sometimes referred to as the “cardinal axes” (eg. Weintraub and Visru, 1971; 1972) containing the “cardinal points” (north, south, east, west) which indicate the “fundamentally important” or “principal” directions (Collins, 1986).

All other directional orientations besides the dimensions are referred to collectively with terms such as “diagonal”, “oblique”, “slanted”, or “tilted” which do not specify any particular orientation other than “not-dimensional”. The particular orientation can only be specified according to the dimensional content of planar diagonals (eg. diagonal right-forward; diagonal up-leftward) or cubic diagonals (eg. diagonal up-right-forwards; diagonal up-left-backwards, etc.). This reveals how the dimensions serve as prototypes with other directions conceived according to their dimensional components.

Specialised terminology has also developed to refer to the most prototypical planes and prototypical angles. The three planes which contain the dimensions are referred to collectively as “Cartesian planes” or “cardinal planes” (Rasch and Burke, 1978, p. 97) and have also been distinguished by the specialised terms “frontal”, “medial”, and “horizontal” (various other terms are also used; see Appendix VIII). The terms “right angle” (90°), and “straight angle” (180°) refer to specific sized prototypical angles. Other less prototypical angles are referred to collectively as “acute” (any angle between 0°-90°) or “obtuse” (any angle between 90°-180°). Thus, the less prototypical angles are conceived according to their relationship to the prototypes.

IVA.52 Directional Prototypes in the “Oblique Effect”.

A perceptual effect has been identified in which vertically or laterally oriented lines are visually perceived better than lines oriented diagonally (45°). This spatial anisotropy, known as the “oblique effect”, has been identified in humans and other animals as higher detection thresholds, slower response, less accurate duplication, and longer training periods required to learn a selective response for oblique compared to vertical or lateral stimuli (Appelle, 1972; Attneave and Olson, 1967; Attneave and Reid, 1968; Matin and Drivas, 1979). Neural electrical recordings have demonstrated that this “neural anisotropy” occurs at some post-retinal processing stage (Maffei and Cambell, 1970). The oblique effect may occur relative to either the exocentric (gravitational) vertical, or egocentric (retinal) vertical, thus it is a cognitive phenomenon dependent on the voluntarily adopted system of reference, rather than being attributable to characteristics of the visual receptors (Attneave and Olson, 1967; Attneave and Reid, 1968).

The oblique effect is similar to effects indicative of prototypes in which prototypical items are learned first and categorised quicker than less prototypical items (see IVA.32) Thus, the oblique effect reveals a neural basis for the conception of greater prototypicality of dimensional oriented directions.

Two prominent theories for the origin of the oblique effect are based in the Nature-versus-Nurture debate (Camisa et al., 1977). The “nurture” view posits that the oblique effect arises from early visual experience of predominately vertical and lateral architectural stimuli which effect neural development. Thus, vertical and lateral lines are experienced as more prototypical of the real-world environment than oblique lines. This is evidenced in findings of “neural plasticity”, that is, neural responses are not predetermined by genetics but are molded by the stimuli experiences which an organism is exposed to during development (Hirsch and Spinelli, 1970; Pettigrew and Freeman, 1973). This is supported by Annis and Frost’s (1973) findings of an absence of the oblique effect in Native-American Cree Indians who had been raised within the oblique structures of tee-pee shelters.

In contrast, the “nature” view posits that the oblique effect is a genetically determined character of visual perception. This is supported by Leventhal and Hirsch’s (1975) findings of limits on neural plasticity; even with solely oblique visual stimuli during development, 71% of cats’ visual cortex cells respond selectively to horizontal and vertical stimuli, but only 29% respond to obliques. Leehey and Colleagues (1975) also found that children as young as six-weeks old fixate on vertical or horizontal grids rather than oblique grids 75% of the time. This would be too young for neural plasticity to have already caused an effect.

IVA.53 Perceptual Bias Toward Vertical and Horizontal Orientations.

It is commonly found that Subjects perceive and remember orientations to be more dimensional than they actually are. This is indicative of dimensions serving as cognitive prototypes (see IVA.32f). In one type of task Subjects were presented with two converging line segments on a sheet of paper and asked to place a dot at the point where the lines would intersect if they were extended. Results were interpreted according to misperceptions of the slope of the line segments. The general trend indicated that “tilted lines tend to appear as either more horizontal or more vertical . . . than they actually are”, that is “perceptual tilts [of the line] toward the nearer cardinal axis of the visual field” (Weintraub and Virsu, 1971, p. 7). These results led to the development of “the principal of assimilation toward a cardinal viewing axis”, that is “A line segment appears perceptually tilted toward the more closely aligned axis either the horizontal or vertical” (Weintraub and Virsu, 1972, pp. 277, 282). Similar results were found by Bouma and Andriessen (1968) where the prototypical vertical and horizontal are considered to be “anchor orientations”.

The perceptual tilt of lines toward the vertical or lateral dimensions may be an example of perceptual/memory “heuristics” (ie. a general “rule of thumb”; Collins, 1986). Tversky (1981) suggested that heuristics “may be adopted to facilitate encoding and retrieval of the spatial orientations and locations of figures” (p. 410). Two possible heuristics are outlined. In a rotation heuristic “the natural axes induced by a figure and the axes of its frame of reference converge”, thus “figures that are slightly tilted will be remembered as more vertical or horizontal than they [actually] were”. In an alignment heuristic “arrays of figures will be remembered as more lined up, more orderly, than they [actually] were” (p. 410).

Tversky (1981) found that Subjects recalled directions between locations in small neighborhoods, cities, countries, continents, and make-believe maps as being aligned closer to the vertical or lateral dimensions (north/south or east/west) than they actually are. Moar (1978, p. 92) found a similar effect in that Subjects recall the long axis of Great Britain as running north/south (vertical dimension) rather than its actual alignment of (roughly) a 20° incline towards the southeast/northwest.

Rosch (1975a) presented Subjects with pairs of line segments ranging from 0° (horizontal) to 152° in an attempt to discern whether vertical, horizontal and diagonal orientations serve as reference points for other orientations. Subjects inserted the lines within blanks of a “linguistic ‘hedge’” (eg. “____ is essentially ____”) or within a semi-circular grid at a distance which represented the perceived similarity between the two orientations. These tests were hypothesized to reveal whether the vertical, horizontal, and 45° diagonal orientations serve as reference-points for other orientations (for details see IVA.111). Results in the sentence-completion task indicated that vertical, horizontal and diagonal orientations all served as reference points for other orientations. In the grid task only the vertical and horizontal orientations were indicated as reference points.

These results of bias toward a dimensional or diagonal orientation are entirely consistent with the choreutic prototype/deflection hypothesis. This grid task (Rosch, 1975a) was used in this thesis to probe whether reference point effects would also be found for kinesthetic spatial orientations (see IVA.110).

IVA.54 Prototypical Angles.

Angles are also perceived and remembered to be more similar to prototypical angles than they actually are. Perception and memory of angles is inseparable from the perception and memory of line orientations since an orientation is defined by its angle relative to a reference line. Thus, the perception of an angle between two lines can also be interpreted as the perception of the orientation of the lines and vice versa (Weintraub and Virsu, 1971; 1972).

Byrne (1979) asked Subjects to draw the intersections between pairs of roads in a well-known city. In 80% of the cases, angles between roads from 60° to 120° were recalled with no significant difference from 90°. In the other 20% of cases the angles were recalled significantly closer to 90° than to their actual angle. It is concluded that spatial angles are encoded according to a “heuristic that junctions and turns are based on a right angle” (p. 152). That is, the 90° angle is the prototype.

Similar effects were found by Tversky (1981) whose Subjects recalled the intersections of streets in a neighborhood as being closer to 90° than they actually are. Lynch (1960) also found a similar effect in that residents of Boston conceived of its park to be square-shaped, with each of the five corners to be 90° (even though this is an impossibility). And angles between visual line segments are judged to be closer to the 45° or 90° prototypical angles than they actually are (Beery, 1968; Maclean and Stacey, 1971).

Moar and Bower (1983) had Subjects imagine that they were standing at a location in a well-known town and facing a particular direction. They would then draw a line on a piece of paper in the perceived direction towards another location in the town. Actual angles ranging from 50° to 100° were judged to be not significantly different than 90°. They interpret this according to the 90° angle perceptual/memory heuristic. Moar (1978, pp. 203, 299) found a similar bias of angles toward 90° in judgments of directions within a well-known town centre, or directions between locations within a familiar building.

Ross and Colleagues (1970) guided blindfolded Subjects along two edges (18 feet and 20 feet long) of a large triangle (walking on land or swimming under water) and asked them to return to the starting location. The correct 57° turn was overestimated (closer to 90°) by almost all Subjects. Likewise, the Gestalt psychologist Wertheimer (1923) reports that when Subjects see very brief presentations of an angle between two lines that “the observer frequently sees a right angle even when objectively a more acute or more obtuse angle is being presented” (p. 79 [italics his]).

All of the tasks described above implicitly include the use of the kinesthetic perceptual-motor system (see IIC.33). In a task which explicitly involves memory for limb position, Subjects recalled the position of their arm in several orientations ranging from 50° below and 50° above the pure sagittal dimension. After a 24 hour retention interval Subjects recalled their arm orientations closer to the sagittal dimensional direction than they were originally (Clark and Burgess, 1984). Thus, memory for arm position was bias toward a dimensional prototype. Wyke (1965) also found that recalling the dimensionally forward arm position is more accurate than recalling arm positions to the right or left of forward.

Tversky (1981) relates these heuristics to the Gestalt principles of common fate and proximity according to which similar and nearby oriented lines will be perceived as lined up with each other. The basis of these perceptual/memory heuristics is that they “distort visual scenes by imposing more order or regularity than actually exists in the scene” (p. 409).

This process is described by the fundamental Gestalt principal of pragnanz, literally translated from German as “concise” or “terse” (Collins, 1969), which are defined as “neatly brief” and “expressing much in few words” (Collins, 1986). Koffka (1935, pp. 108-145) and Wertheimer (1923, pp. 79-83) describe pragnanz as groupings of stimuli which are the most “good”, “regular”, “simple”, “stable”, “logically demanded”, with “inner coherence”, “inner necessity”, and “wholeness”. Orientations tend to be perceived or remembered as dimensional, and angles tend to be perceived or remembered as 90° because (in most cases) these are the most ordered, most regular, symmetrical, “good” arrangements of stimuli (see IVB.27).

IVA.55 Balance System of a Figure.

In a landmark analysis of forms in Art, Rudolf Arnheim (1974) draws on an abundance of sources to describe characteristics of visual perception similar to those described by the Gestalt principles. Arnheim discusses how observers never see a visual stimulus in isolation but always perceive it in relationship to the whole surrounding array of stimulation (pp. 10-16). For example, certain directions and locations can be identified within an “empty” square which are the most prototypical, or most regular and “good” (in the Gestalt sense). This can be referred to as the “hidden structure of a square” (p. 10). In the simplest experiment a black disk is placed just slightly away from the centre of the square. This creates a certain perception in the observer:

The disk . . . is not simply displaced with regard to the center of the square. There is something restless about it. It looks as though it had been at the center and wished to return, or as though it wants to move away even farther. And the disk’s relations to the edges of the square are a similar play of attraction and repulsion. (Arnheim, 1974, p. 11)

Arnheim (1974, pp. 12-14) refers to the perceived locations and lines within the “empty” square as the “‘induced structure’” or “perceptual inductions” which are derived spontaneously during perception and so are different from conscious interpretations or “logical inferences”. An induced structure is perceived which is likened to “lines of force in a magnetic field” with each induced (prototypical) location being analogous to a magnet. Because of this a visual figure (eg. a square) can be described as “empty and not empty at the same time”.

A procedure is suggested for probing the prototypical locations and orientations within the induced structure. Arnheim (1974) observes that when an object is placed within a space that there will be a perceived “pull” in which it “tends to strive” according to the balance system (p. 14) such that if an object is only briefly, or not clearly seen, that it will be perceived to be closer to one of the locations of the balance system than it actually was.

If a disk is placed at various locations within the square, it looks solidly at rest at some points; at others it exhibits a pull in a definite direction; and in others its situation seems unclear and wavering. (Arnheim, 1974, p. 12)

Arnheim (1974) calls this a “reduction of tension” (p. 15) which is identical to the perceptual/memory effect of bias toward a prototype (see IVA.32f). From “informal explorations” Arnheim reports that a black disk appears most “stably settled” when it is at the centre of the square, and if the disk is placed near to one of the square’s edges it appears to be “drawn toward” that edge. The centre appears to be the “principal locus of attraction and repulsion”. Other structural elements of the square also create induced perceptions, namely; the four corners; the vertical and horizontal lines passing through the centre and bisecting opposite cubic edges; and the two diagonal lines passing through the centre and intersecting opposite cubic corners; that is, the symmetrical axes of the square. Arnheim (1974) refers to these perceived elements within a square as its “structural skeleton” (pp. 12-13) or a “balance system” (p. 15) which is essentially a map of the prototypical locations and orientations spontaneously perceived within a particular spatial form.

Likewise, Arnheim (1974, pp. 14-16) reports on unpublished experiments by Goude and Hjortzberg (1967) in which Subjects were asked to report on their introspective perceptions of whether a black disk (4cm diameter) appeared to strive in particular directions when it was placed in various locations within a square (46cm x 46cm). The disk appeared to move least when it was placed at the centre of the square. When the disk was placed near a symmetrical axis of the square (ie. an imagined vertical, lateral, or diagonal line passing through the centre of the square) then it appeared to move in a direction parallel to the nearby axis.

Similarly, Nelson and Chaiklin (1980) found that dots are recalled closer to the exterior visual border than they actually are (ie. the dots perceptually strive toward the border). Also, Huttenlocher and Colleagues (1991) briefly presented a dot within a circle and asked Subjects to report its location. The dots were recalled as being closer to a position along a diagonal line through the circle than they actually were. They conclude that “Subjects spontaneously impose horizontal and vertical boundaries that divide the circle into quadrants. They misplace dots toward a central (prototypic) location in each quadrant” (p. 352).

Arnheim (1974) uses the phrase “directed tension” to refer to the perceived stress, pull, attraction, or tension between a prototypical location or orientation and a less-typical location or orientation. When a form does not exhibit the prototype then a “tension” is created between the actual form and the prototypical form. Arnheim refers to the prototype as the “norm position” (p. 426) or the “norm image” (p. 429) and the actual form as the “deformation” or the “deviation” (p. 428). As an example Arnheim considers the orientation of the arms of windmills in Dutch landscapes. When they are painted in a vertical/lateral orientation they do not appear to turn and when painted in diagonals (45°) they appear to turn slightly. However when painted in an “asymmetrical, unbalanced” orientation, at an odd angle somewhere between the dimensions and the diagonals (cf. inclinations IVA.25) then they induce the greatest amount of perceived motion (p. 425). This unbalanced position is farthest from the symmetric prototypes (dimensions or diagonals) and thus create the greatest amount of perceived motion as a striving toward the prototypes.