What is the Meaning of Shape? - Gestalt Theory

Baingio Pinna 

What is the Meaning of Shape? 

1. On the Shape 

The shape of an object is a primary condition fundamental for our lives. Shape 

is the primary visual attribute among others (color, shade, lighting) that elicits 

unambiguous identification due mainly to its constancy. Another relevant 

perceptual property is its uniqueness. Indeed, it is unique and much more 

informative than any other object properties, i.e. color, shading (depth) and 

lighting (illumination). 

Shapes are not usually regarded as a creation of our brain but appear veridically, 

as part of the physical world. As a matter of fact, the core meaning of shape 

is one of the main interests and targets of mathematics (from topology and 

mathematical analysis to trigonometry and geometry) aimed to describe and 

study the main properties of shapes and the relationship among them. No other 

property has been studied from so many different perspectives and so deeply as 

shape (see Palmer, 1999; Pizlo, 2008). It is useful to distinguish between shape 

in the mathematical sense (i.e. as an ideal object) and shape as encoded in the 

physical world. In the former sense, objects are ontologically neutral and not 

always perceptually possible and relevant. 

1.1. The Invention of the Square 

Among all the known shapes, the square is a unique and special one. The 

emergence of the square and its geometrical/phenomenal components (sides and 

angles) is the consequence of the way four segments go together according to 

the Gestalt grouping and organization principles. Phenomenally, its singularity, 

homogeneity, regularity and symmetry are among the strongest of all the known 

shapes. The circle also shows unique properties, but unlike the square it is 

present in nature (e.g. the full moon and the sun). The square is instead a human 

invention. It is a pure creation of the human mind. 

The invention of the wheel (i.e. the circle) is likely one of the most important 

inventions of all time. It was at the root of the Industrial Revolution. The oldest 

known wheel was attributed to the ancient Mesopotamian culture of Sumer 

around 3500 B.C., but it is supposed to have been invented much earlier. If 

the potter’s wheels were the very first wheels, the invention of the square was 

GESTALT THEORY 

© 2011(ISSN 0170-057 X) 

Vol. 33, No.3/4, 383-422

GESTALT THEORY, Vol. 33, No.3/4 

likely as important as the wheel. The square is, in fact, a basic shape used to 

measure any kind of object, shape or space. Every shape either regular or irregular 

is measured in squares (m2 ) or in the 3-D version of the square, cubes (m3 ). 

The square is the unit and, more generally, the ‘brick’ of all the other shapes. By 

moving around the gaze and focusing the attention on the shapes, one notices 

that almost everything has a square shape. Most of the human artifacts are made 

up of squares or its variations. For instance, houses are composed of windows, 

floors, tables, televisions and doors that are squares or square-like shapes. 

As concerns these special phenomenal properties, we will study the meaning of 

shape starting from the square. 

1.2. The Shape before the “Shape”: Grouping and Figure-Ground Segregation 

Gestalt psychologists were the first to study and develop a theory of shape, 

considered as an emergent quality. They studied the shape mostly in terms of 

grouping and figure-ground segregation. (Other Gestalt approaches to shape 

perception will be discussed in section 3.3.) 

Rubin (1915, 1921) studied the problem of shape formation in terms of figureground 

segregation, by asking what appears as a figure and what as a background. 

He discovered the following general figure-ground principles: surroundedness, 

size, orientation, contrast, symmetry, convexity, and parallelism. Rubin also 

suggested the following main phenomenal attributes, belonging to the figure but 

not to the background. (i) The figure takes on the shape traced by the contour, 

implying that the contour belongs unilaterally to the figure (see Nakayama & 

Shimojo, 1990; Spillmann, 2012; Spillmann & Ehrenstein, 2004), not to the 

background. (ii) Its color/brightness is perceived full like a surface and denser 

than the same physical color/brightness on the background that appear instead 

transparent and empty. (iii) The figure appears closer to the observer than the 

background. 

Wertheimer (1923, see also Spillmann, 2012) approached this problem in terms 

of grouping. The questions he answered is: how do the elements in the visual field 

‘go together’ to form an integrated percept? How do individual elements create 

larger wholes? He studied some basic grouping principles useful to answer the 

previous questions. They are: proximity, similarity, good continuation, closure, 

symmetry, convexity, prägnanz, past experience, common fate, and parallelism. 

It is reasonable to consider that figure–ground segregation must operate before 

grouping (Hoffman & Richards, 1984; Palmer, 1999). For example, dot 

elements on which grouping acts must be already segregated as a figure from 

the background, otherwise the visual system would not know which elements 

to group. Nevertheless, the same elements do not possess the figural properties 

of holistic organized and segregated figures; rather, they appear as elementary 

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components necessary to create boundaries. They are not surfaces, but something 

similar to perceptual ‘bricks’ necessary to create something more holistic. In spite 

of the apparent differences between figure-ground segregation and grouping, 

what is phenomenally clear is that both dynamics are so intimately intertwined 

that a sharp distinction is likely impossible and maybe useless from a scientific 

point of view. 

Within Rubin’s and Wertheimer’s works, the problem of shape formation is 

approached in terms of the main conditions operating in two of the processes 

(grouping and figure-ground segregation) underlying but preceding the formation 

of the shape. For example, the unilateral belongingness of the boundaries can be 

considered as a shape issue before the “shape” meaning. It talked about shape 

but it did not explain its meaning. Similarly, even if the closure principle can 

describe the perception of a square, it cannot say anything about its properties 

and about the way its properties assign the special meanings we have previously 

described. Furthermore, it cannot explain the square variations described in the 

next sections. 

Even if Gestalt grouping and figure-ground principles are part of the problem of 

shape perception, they do not face directly this problem and, more importantly, 

they do not answer basic questions like: what is shape? What is its meaning? 

2. General Methods 

2.1. Subjects 

Different groups of 12 undergraduate students of architecture, design, linguistics 

participated in the experiments. Subjects had some basic knowledge of Gestalt 

psychology and visual illusions, but they were naive both to the stimuli and to 

the purpose of the experiments. They were male and female with normal or 

corrected-to-normal vision. 

2.2. Stimuli 

The stimuli were the figures shown in the next sections. The overall sizes of the 

visual stimuli were ~3.5 deg visual angle. The figures were shown on a computer 

screen with ambient illumination from a Osram Daylight fluorescent light (250 

lux, 5600° K). Stimuli were displayed on a 33 cm color CRT monitor (Sony 

GDM-F520 1600x1200 pixels, refresh rate 100 Hz), driven by a MacBook Pro 

computer with an NVIDIA GeForce 8600M GT. Viewing was binocular in the 

frontoparallel plane at a distance of 50 cm from the monitor. 

2.3. Procedure 

Two methods, similar to those used by Gestalt psychologists, were used.


Phenomenological task: The task of the subjects was to report spontaneously what 

they perceived by providing a complete description of the main visual property. 

The descriptions were provided by at least 10 out of 12 subjects and were reported 

concisely within the main text to aid the reader in the stream of argumentations. 

The descriptions were judged by three graduate students of linguistics, naive as 

to the hypotheses, to get a fair representation of the ones given by the observers. 

Subjects were allowed to make free comparisons, confrontations, afterthoughts, 

to see in different ways, distance, etc.; to match the stimulus with every other 

one. Variations and possible comparisons occurring during the free exploration 

were noted down by the experimenter. The selection of the stimuli with opposite 

conditions and controls and the possible comparisons among the stimuli prevent 

the problem of generating biased experiences. This is clearly shown by the 

differences in the results (see next sections). 

Scaling task: The subjects were instructed to rate (in percent) the descriptions 

of the specific attribute obtained in the phenomenological experiments. New 

groups of 12 subjects were instructed to scale the relative strength or salience (in 

percent) of the descriptions of the phenomenological task: “please rate whether 

this statement is an accurate reflection of your perception of the stimulus, on a 

scale from 100 (perfect agreement) to 0 (complete disagreement)”. Throughout 

the text we reported descriptions whose mean ratings were greater than 80. As 

concerns these tasks and procedure see Pinna, (2010a, b; Pinna & Albertazzi, 

2011; Pinna & Sirigu, in press; Pinna & Reeves, 2009). 

3. Squares, Rotated Square and Diamonds 

3.1. Non-Square Shapes that Appear Like Squares 

Shape illusions are only apparently in contrast with the properties previously 

described: unambiguous identification, constancy, uniqueness and veridicality. 

These illusions are, in fact, considered to be exceptions visible under specific and 

rare conditions and, thus, ineffective for real life. 

The strong shape illusion, illustrated in Fig. 1a, was described like a large square 

with concave and convex sides. This description reveals a “distortion” that does 

not change the basic meaning of the square shape. In fact, the main shape even 

if distorted is still perceived like a square. Moreover, paradoxically the distortion 

reinforces and strengthens the perception of the square. In fact, the square is 

amodally seen as the whole shape supporting the perceived distortion. Conversely, 

the distortion is what elicits the amodal wholeness of the square (see Pinna, 

2010b). This kind of phenomenal dynamics also occurs when the perceived 

distortion is not illusory but “real”, as shown in Fig. 1b. 

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Fig. 1 Non-square shapes that appear like squares 

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In more intense conditions in terms of distortion (see Figs. 1c-i), where the square 

and its sides or angles appear beveled, broken, crashed, gnawed, deliquescing, 

deformed, protruding, the main shape is again perceived as a square, while 

those specific descriptions reveal what happens to each square. They appear 

like “happenings” of a square (Pinna, 2010b; Pinna & Albertazzi, 2011). These 

changes and happenings can be seen as depending on or related to specific and 

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“invisible” but perceptible causes affecting the shape and the material properties 

of the square. They add visual meanings but do not really change the shape of the 

square, which is perceived like the amodal invariant shape supporting all those 

happenings (see also section 5.6). From a geometrical point of view, these are 

non-square shapes that appear like squares. 

These results suggest the following questions: Why do we perceive a square plus a 

happening in each of these cases, instead of a set of irregular shapes, one different 

from the other? What is the role of the happening and of other possible shape 

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attributes in shape formation? Which properties influence and determine the 

meaning of shape? 

An answer to the first question was previously reported by Pinna (2010b). In the 

next sections, possible responses to the other questions will be proposed. We will 

first start by showing opposite conditions, where squares are perceived like nonsquare 

shapes, to understand the ways and under which conditions a square shape 

can be influenced and changed. 

3.2. Squares that Appear Like Non-Square Shapes 

3.2.1. Square 

Fig. 2a shows a square. The figure, here illustrated, appears like a “true” square, 

i.e. a shape that appears like a square tout court, a square without anything else. 

This one-word description, “square”, does not reveal any happening or any other 

relevant emerging attribute. Shape properties, like orientation, size and position, 

are left off, because, under these conditions, they are “invisible” or unnoticeable 

like the background. These omitted properties are superfluous. The word “square” 

seems to contain, in fact, everything to recreate exactly the same figure and, thus, 

does not need any further information. This square appears like the best example 

and the model of every “square”. 

It is worthwhile noticing that the omissions are important information useful 

to understand the phenomenology of shape perception. Related to our square, 

we can state that the more numerous are the omissions (invisible attributes), the 

better is the appearance as a model of this shape, or, conversely the less is the 

information described, the better is the squareness of the shape. We define as 

“phenomenal singularity” the instance of a shape that does not need to be defined 

by attributes and that correspond to a one-word description. In other words, the 

phenomenal singularity is the best instance of a specific shape. 

By asking naive subjects “draw a square” and, afterwards, “choose the square that 

is the most ‘square’ among those illustrated” (see Figs. 2a-c), we found that most 

of them (99%) represented the square exactly like the one of Fig. 2a and chose 

this figure as the best example of square among the three. 

These results suggest the following questions: What is the relationship between 

the descriptive and the phenomenal notion of shape? More particularly, what is 

the meaning of the term “square” when it denotes a singularity like the shape of 

the object perceived in Fig. 2a? By complementation, what is the meaning of the 

same term when it does not refer to a phenomenal singularity but emerges with 

visible attributes? What is the visual meaning of the square? What does this shape 

convey, express or reveal in the way it appears? 

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3.2.2. Rotated Square 

Fig. 2b represents an intermediate but crucial step in answering the previous 

questions. This figure is mostly described as a rotated square. Under these 

conditions, subjects introduced spontaneously information about orientation, 

thus, creating a two-word description. The rotation becomes now visible, noticeable 

like a figure. The exact orientation is, instead, not specified spontaneously in 

words. Only after asking them to describe the apparent direction and degree of 

rotation, our subjects reported ~10° anticlockwise. 

These results suggest a twofold perception: a “true” square plus something that 

happens to it, namely, the rotation. In other words, unlike Fig. 2a the square is, 

now, not only a square, but also a square with a “happening” (Pinna, 2010b) 

defined in terms of rotation. The anti-clockwise rotation suggests some kind of 

minimum rotation pathway starting from the “true” square of Fig. 2a. 

Structurally, this happening is similar to those described for Figs. 1c-i. 

Linguistically, the rotation is an adjective that describes the noun, which is the 

square. Phenomenally, it is what happens to the shape. The primary role of the 

shape (square) in relation to the adjective (rotation) can be clearly perceived 

by comparing the two following possible descriptions: “a rotated square” and 

“a rotation with a square shape”. The second description appears meaningless 

and odd. A rotation cannot have a shape, while the shape can have a rotation. 

This suggests a clear asymmetrical hierarchy between the two terms. The shape 

is primary, earlier in time and order than the rotation. Therefore, the shape is a 

noun and as such it is a word generally used to identify a class of elements. As a 

noun, the shape is like “a thing”, which can appear in many different ways, and 

the rotation is one of this ways of being of the shape, i.e. the attribute of that 

specific thing. 

These phenomenal observations suggest the following methodological note: 

the asymmetrical descriptions represent a useful method of understanding the 

primary role of one visual component over another, e.g. of the shape over the 

rotation and, more generally, of something that becomes the primary thing over 

another perceived like its attribute. Another example useful to understand the 

effectiveness of this method is represented by the relation between shape and 

color: we say “a red square” and not “a square-shaped red”. The distinction 

between things and attributes can also be demonstrated through the position 

of the words one relative to the other and through the phenomenal invisibility, 

i.e. an attribute (way of being of a thing) can be invisible or unnoticed like a 

background much more than a thing. 

Despite this asymmetry, rotation and square define themselves reciprocally. The 

rotation is defined by the shape, i.e. the rotation can be perceived if and only 

if the square as a singularity is also perceived. Conversely, the rotation defines


the shape, i.e. without the rotation the square as a singularity could not be 

perceived. As soon as they are defined, square and rotation organize themselves 

asymmetrically as suggested by the two previous descriptions. 

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Fig. 2 A square (a), a rotated square (b) and a diamond (c) 

3.2.3. Diamond 

By increasing the rotation of Fig. 2b up to 45° as shown in Fig. 2c, both the 

happening (rotation) and the square are replaced by another one-word description: 

a diamond. This outcome is unexpected, if compared with the square of Fig. 2a. 

It represents a hard problem for an invariant features hypothesis. In fact, if shapes 

are defined by virtue of attributes invariant over rotations, then the two shapes 

of Figs. 2a and 2c should be perceived as having the same shape. Therefore, the 

square and the diamond demonstrate that different shape rotations cannot be 

perceived as having the same shape. 

Figs. 2a and 2c show the so-called Mach’s square/diamond illusion (Mach, 

1914/1959; Schumann, 1900), according to which the same geometrical figure is 

perceived as a square when its sides are vertical and horizontal, but as a diamond 

when they are diagonal. From a phenomenal point of view, it is more correct to 

state that the square is perceived when the sides are vertical and horizontal, while 

a diamond is seen when its angles or vertices are vertical and horizontal. This 

description is more appropriate if we consider what emerges more strongly in the 

two conditions: the sides in the case of the square, and the angles/vertices in the 

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of the diamond. We will see in section 5 some important consequences of these 

phenomenal observations for a better understanding of the meaning of shape. 

One main effect related to Mach’s square/diamond illusion is the fact that the 

diamond appears larger than the square. Schumann (1900) suggested that this is 

related to the fact that visual attention is placed on the vertical-horizontal axes, 

which are clearly longer in the diamond condition. This explanation is supported 

by the results of a simple control experiment according to which, by focusing 

the attention on one side of the diamond rather than on one angle, during the 

comparison of the size of Fig. 2a and 2c, the apparent size difference between the 

square and the diamond is strongly reduced or even annulled. 

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3.3. The Role of the Frame of Reference in Shape Perception 

More recent and complex explanations of the square/diamond illusion are based 

on object-centered reference frames. Rock (1973, 1983; see also Clément & 

Bukley, 2008), starting from previous Gestalt studies (Asch & Witkin, 1948a, 

1948b; Koffka, 1935; Metzger, 1941, 1975), suggested that the perceived 

shape is a description relative to a perceptual frame of reference, i.e. the visual 

system prefers gravitational axes over retinal or head axes. In other words, Rock 

considered Mach’s square/diamond illusion as a clear evidence that a shape 

is perceived in relation to an environmental frame of reference where gravity 

defines the reference orientation, at least in the absence of intrinsic axes in the 

object itself. If the environmental orientation of the figure changes with respect 

to the two figures, the description of one shape does not match the description 

stored in memory for the other shape, therefore the observer fails to perceive the 

equivalence of the two figures. 

The stimulus factors important in determining the intrinsic reference frame 

are: gravitational orientation; directional symmetry (Pinna, 2010b; Pinna & 

Reeves, 2009); axes of reflectional symmetry, configural orientation (Attneave, 

1968; Palmer, 1980) and axes of elongation (Marr & Nishihara, 1978; Palmer, 

1975a, 1983, 1985; Rock, 1973). These factors rule the relation between shape 

and orientation as it happens in other phenomena (e.g., the rod-and-frame and 

Kopfermann’s effects; Davi & Profitt, 1993; Kopfermann, 1930; see also Marr & 

Nishihara, 1978; Palmer, 1975b, 1989, 1999; Witkins & Asch, 1948). 

These explanations contain some serious limits especially within the context of 

phenomenology. More particularly, they cannot account for the reason why we 

perceive a square, a diamond or a rotated square without invoking names and 

descriptions stored in memory. More specifically, they do not say anything about 

what changes phenomenally inside the shape properties when axes of reflection, 

gravitation and other factors change and about which shape properties switch 

when a square switches to a diamond. 

These limits are accompanied by the following questions: why are two names/ 

descriptions (square and diamond) stored so differently? Are they stored as different 

names because they are perceived differently or are they perceived differently 

because they are stored in memory with different names/descriptions? These last 

questions are not trivial because they are related to the important problem of 

the primary role of visual perception over the higher cognitive processes (see 

Kanizsa, 1980, 1985, 1991). This implies that the difference between square and 

diamond can be accounted for within the domain of vision alone and in terms of 

perceptual organization of shape attributes. 

In addition to these issues, the previous hypotheses cannot explain what shapes, 

such as squares, diamonds or rotated squares, are, and, even more generally, they


do not say anything about what a shape is. They only state that in the case of the 

square/diamond illusion some factors influence the switch from one shape to 

another. Even if these factors are likely really effective, they cannot explain the 

meaning of shape. As a consequence, on the basis of these factors what determines 

the perception of a square and a diamond is not accounted for. 

4. Doubts about the Role of Frame of Reference 

4.1. On the Second Order Square/Diamond Illusion 

The limits of these hypotheses can be highlighted even more effectively through 

some new phenomenal conditions useful to understand the meaning of shape. 

Their rationale is the following: if the perceived shape is a description relative 

to a perceptual frame of reference, then results analogous to those achieved with 

the square/diamond illusion are expected to be attained through second order 

variations of squares and diamonds. 

In Fig. 3a, the square and the diamond of Figs. 2a and 2c and the rotated square 

of Fig. 2b are changed by making the sides concave. Under these conditions the 

two main effects previously described, i.e. the square/diamond switch and the size 

difference between the horizontal and vertical conditions, are strongly reduced or 

even absent. They appear more easily like the same figure with different amount 

of rotation. 

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Fig. 3b, the angles are now rounded. The two main effects of the square/ 

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illusion are clearly absent. They are also absent in the further conditions 

illustrated in Figs. 3c-g, where the changes involve the whole shapes. In Figs. 3hj, 

only one angle of each shape has been changed, but again the square/diamond


and the size difference effects are very weak or absent. These results demonstrate 

that under these conditions the vertical/horizontal and gravitational axis do not 

define the reference orientation and, thus, do not influence shape perception. 

4.2. The Square/Diamond Illusion with Polygons 

A second set of conditions that weaken the previous hypotheses and, at the same 

time, contribute to an understanding that the meaning of shape is related to the 

orientation of polygons. If the rotation of a square by 45 deg induces the square/ 

diamond illusion, similar results are expected by rotating polygons. 

In Fig. 4, several polygons in two orientations with a different number of sides 

are illustrated. The polygons do not show any kind of difference in the two 

orientations. Furthermore, they do not have different names stored in memory 

and, finally, they do not show a clear size change like the one reported in the 

square/diamond illusion. 

Fig. 4 Polygons and the square/diamond illusion 

Why does only the square induce this kind of illusion, while other polygons do 

not? The octagon, shown in two orientations, with the sides or with the angles 

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along the vertical/horizontal axis (see Fig. 5), is useful when answering this 

question. Under these conditions, the two figures appear different: one flattened 

and the other pointed. Sides or angles emerge more strongly in one but not in the 

other condition and vice versa. The vertical/horizontal alignments strengthen the 

salience of the sides and the angles. (It is worthwhile clarifying that, among the 

previous polygons, the one geometrically and phenomenally closer to the octagon 

is the hexagon, where sides and angles are as well placed both on the vertical and 

on the horizontal axis.) Although the two octagons show the difference previously 

described, they do not have different names stored in memory and do not show 

a clear size difference like the square/diamond illusion. 

Fig. 5 Flattened and pointed octagons 

A new effect emerging in these figures is an illusion of numerosity: the number 

of angles and sides is perceived higher in the octagon with the angles along the 

vertical and horizontal axes. This phenomenon is likely related to the phenomenal 

asymmetry between the emergence of the sides and the angles. This asymmetry 

will be dealt in greater depth in the next section. 

5. Inside the Shape: What is a Shape? 

5.1. What are Squares and Diamonds? Sidedness and Pointedness 

To understand why the second order variations illustrated in Fig. 3 are not 

influenced in the two main properties of the square/diamond effect, it is 

necessary to go back to the properties emerging in the two octagons, which help 

the understanding of the meaning of the square and the diamond. 

In geometry, a square is defined as a regular quadrilateral, namely a shape with 

four equal sides and four equal angles. Sides and angles are the components of a 

square that emerge more easily within the gradient of visibility, i.e. the gradient of 

phenomenal vividness of different visual attributes that do not pop out with the 

same strength (Pinna, 2010a). If a square shape is made up of sides and angles, 

then it shows phenomenal properties such as “sidedness” and “pointedness” related 

to these components. These two properties are only apparently equipollent. The 

square/diamond illusion demonstrates the vividness asymmetry between these 

properties. In the square the sidedness appears stronger than the pointedness, 

while the diamond shows more strongly the pointedness. The perceived strength 

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of one or of the other property is influenced by the vertical/horizontal and 

gravitational axis that plays by accentuating the sidedness against the pointedness 

in the square and, vice versa, the pointedness against the sidedness in the diamond. 

On the basis of these properties, it appears clear why the second order variations 

of Fig. 3 are not involved in the square/diamond illusions. In fact, in all the 

conditions illustrated sidedness and pointedness are not in contrast but either the 

sidedness or the pointedness are attenuated or emphasized, thus weakening only 

one of the two effects. This entails that one of the two singularities is weakened, 

therefore appearing as a rotation of the other. 

The two properties can also account for the reason why we perceive a rotated 

square in Fig. 2b. This is due to the strength of the sidedness being higher than 

the one of the pointedness. 

Similarly, the numerosity illusion of Fig. 5 can be considered as related to the 

shape attribute that defines the number of elements in the octagon. We suggest 

that this figure, similarly to the other polygons, is mostly defined by the sidedness 

and thus by the number of sides. More specifically, to answer a question like 

“what polygon is this?” spontaneously we count at a glance the number of sides 

but not the number of vertices. The importance of the two properties in defining 

the shape appears in fact asymmetrical. Therefore, because in the pointed octagon 

of Fig. 5 the sidedness is weakened while the vertices are perceived with a stronger 

vividness, the numerosity of the sides is determined taking into account or starting 

from the angles or vertices, which induce an increasing of number of sides or a 

summation effect due to the numerosity fuzziness of the sides together with the 

angles. The calculation at a glance of the number of sides can include also some 

vertices that pop out more strongly than the sides. 

These phenomenal reports suggest that, all else being equal, the perceived shape 

can change or switch from one shape to another by accentuating the sidedness 

or the pointedness independently from the vertical/horizontal and gravitational 

axes. A demonstration of this expectation is illustrated in Fig. 6, where, despite 

the configural orientation effects (i.e. the perception of local spatial orientation 

determined by the global spatial orientational structure) studied by Attneave 

(1968) and Palmer (1980), rows of figures are perceived as rotated squares or as 

diamonds according to the position of the small circle placed near the sides or 

near the angles of the figures (see also Pinna, 2010a, 2010b; Pinna & Albertazzi, 

2011). While in Figs. 6a and 6c, the geometrical diamonds are phenomenally 

perceived as rotated squares, in Figs. 6b and 6d, the geometrical diamonds are 

perceived more strongly than in the control (Fig. 6e) as diamonds. 

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Fig. 6 Rotated squares or diamonds? 

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5.2. On the Difference between a Square and a Rotated Square 

It is worthwhile clarifying that a diamond and a square rotated by 45 deg as shown 

in Fig. 6 are different shapes, not only because they have two different names, but, 

mostly, because they show opposite phenomenal properties: pointedness in the 

diamonds and sidedness in the rotated squares. This shape switch is not a minor 

difference but a variation of the perceptual meaning of shape (see Pinna, 2010b). 

Pointedness and sidedness are like the underlying shapes of the shape, a second 

level shape (meta-shape), i.e. the meanings of the perceived shapes, and, more 

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particularly, of the diamond and square or of the two octagons illustrated in Fig. 

5. These phenomenal remarks are corroborated by the results of Fig. 7, where the 

inner rectangles accentuate the sidedness or the pointedness of both the checks 

and the whole checkerboards, thus eliciting respectively the perception of rotated 

squares or diamonds in the same geometrical figures. This result demonstrates 

local and global effects of the accentuation. 

Fig. 7 Rotated squares or diamonds in both the checks and the whole checkerboards 

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Sidedness and pointedness can also be accentuated in the two grids with the 

same geometrical shape as shown in Fig. 8. Again, the single elements of the grid 

(each single inner diamond shape) and the global shape of the grid are perceived 

as rotated squares or diamonds by virtue of the accentuation of sidedness or 

pointedness. 

Fig. 8 Rotated squares or diamonds in both the components and the whole grids 

These results suggest that the shape of an object depends on its inner properties, 

on their accentuation due to other elements (disk or empty circles) present in 

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the visual field. Therefore, shape perception is the result of the organization of its 

inner attributes, whose gradient of visibility can be changed according to accents 

placed in a spatial position that enhances the vividness of one shape attribute 

against the other. 

It is worthwhile showing Kopfermann’s effect demonstrating the dependence of 

an object shape on the frame of reference (Kopfermann, 1930; see also Antonucci 

et al., 1995; Gibson, 1937; Wikin & Asch, 1948). The effect is shown in Fig. 9 in 

the four classical versions. Under these conditions, the square and the diamond 

of Figs. 9a-b, when included within a rectangle obliquely oriented are perceived 

respectively as a diamond and as a rotated square (see Figs. 9c-d). 

Fig. 9 Kopfermann’s effect 

Figs. 10a and 10b demonstrate the stronger role of the accentuation of the 

sidedness or the pointedness over the larger reference frame. Due to the black 

dot and to the inner small rectangle, the geometrical shapes are now restored, 

i.e. the diamond and the rotated square perceived in Figs. 9c-d are switched into 

a rotated square and a diamond demonstrating the ineffectiveness of the larger 

frame of reference. 

!"#$%&'()''!"#$%#&'(#$$" 

!"#$%&'%$"(%)(#*&*+%,-%'"#.(/ 

# 0 

1 2 

400

Fig. 10 Kopfermann’s effect annulled 

# 

0 

401 


5.3. On the Accentuation of Shape Properties 

Sidedness and pointedness can be accentuated in many ways (see Pinna, 2010a, 

2010b; Pinna & Albertazzi, 2011). A powerful accentuation factor is the reversed 

contrast shown in Fig. 11. Due to this factor, the same geometrical octagons 

appear rotated in opposite directions, clockwise or anticlockwise (Figs. 11a-b). 

They are also perceived pointed with different strength and at different locations 

of the figures depending on the position of the white components (Figs. 11c-d). 

!"#$%&'()*''!"#$%#&'(#$$" 

By !"#$%&'%$"(%)(#*&*+%,-%'"#.(/ 

comparing Figs. 11a-b and 11c-d, the visual differences between the sidedness 

and the pointedness emerge very clearly. The difference in salience of sides and 

angles is seen very clearly also in Figs. 11e-f, where a slightly concave and convex 

effect of the sides can be perceived. 

These differences are also accompanied by the illusion of numerosity described 

in section 4.2. It is worthwhile noticing that it is not the geometrical orientation 

which defines the numerosity, in fact it is kept constant, but the emergence of the 

sidedness or of the pointedness due to their accentuation.


# 1 

0 

( 

Fig. 11 Accentuation of sidedness and pointedness in octagons 

In Fig. 12, the accentuation of the sidedness and pointedness through the 

!"#$%&'(()''!"#$%#&'(#$$" 

reversed !"#$%&'%$"(%)(#*&*+%,-%'"#.(/ 

contrast induces diamond-shaped (Fig. 12a) or grand piano-like (Fig. 

12b) figures in the same geometrical objects. 

402 

2 

-

403 


Fig. 12 Diamond-shaped or grand piano-like figures in the same geometrical objects 

# 

0 

In Fig. 13, the accentuation, due to the arrangement of black and white sides of each 

square, !"#$%&'()*''!"#$%#&'(#$$" 

produces a directional symmetry and elicits several phenomena: (i) a global 

!"#$%&'%$"(%)(#*&*+%,-%'"#.(/ 

and local rectangle illusion, i.e. the geometrical squares, both locally (each single 

square) and globally (the square made up of squares), are perceived like rectangles 

elongated in the direction perpendicular to the black sides; (ii) the orientation of 

each element appears polarized (upwards in Fig. 13a and downwards in Fig. 13b); 

(iii) the elements are grouped in columns and rows and a global waving (up &


down or left & right) apparent motion is clearly perceived when the gaze follows 

the tip of a pen moved across the patterns illustrated in Figs. 13c and 13d. 

These results are likely related to the fact that the black side not only enhances 

the salience of the sidedness, but also defines the base of each check. This suggests 

that the phenomenal accentuation of one shape property manifests vectorial 

properties. More particularly, the accent placed on the black side appears, under 

these conditions, as the starting point of the oriented direction. The white side 

of each check, opposite to the black one, is perceived as the tip of the arrow or 

as the terminal point of the oriented direction induced by the accent. Finally. 

the magnitude of the vector depends on the magnitude of the accent, here kept 

constant. Briefly, the accents behave like Euclidean vectors considered in the 

same acceptation used in physics. 

Fig. 13 The accentuation, due to black sides, produces a directional symmetry and manifests 

vectorial properties 

!"#$%&'()*''!"#$%#&'(#$$" 

!"#$%&'%$"(%)(#*&*+%,-%'"#.(/ 

# 0 

1 2 

404

405 


These results demonstrate that the accentuation of one shape property against 

the other can induce different kinds of dimensional, direction and even motion 

effects, which suggest a theory of shape, considered like an overall holder 

containing many shape attributes that compete or cooperate and whose strength 

can be changed or accentuated in many ways. 

Other effects induced by the accentuation and by its vectorial properties are the 

tilt and straighten up effects of Fig. 14. The dot seems to tilt further the shape 

by pulling the top left-hand corner of the parallelogram in Fig. 14-left and to 

push the whole figure in the right-vertical direction, thus, straightening up the 

parallelogram in Fig. 14-right. 

Fig. 14 Tilt and straighten up effects 

Another kind of accentuation is induced by the missing parts or cuts of sides 

and angles shown in Fig. 15, thus inducing the switch from the diamond to the 

rotated square shape both in the 2D and 3D conditions. It is worthwhile noticing 

that the 3D appearance of the cube with the missing corner is weaker than the 

one of the cube with the cut side (see also Fig. 16). This is likely due to the 

directional symmetry induced by the cut, which favors the vertical organization 

of lines that camouflages the whole 3D perception. 

!"#$%&'()*''!"#$%#&'(#$$" 

!"#$%&'%$"(%)(#*&*+%,-%'"#.(/


Fig . 15 Diamond and the rotated square shapes both in the 2D and 3D conditions 

By introducing white sides or white dots within the same shape near the corner 

or next to one side, the cube appearance can be either weakened or optimized (cf. 

the control at the bottom) as shown in Fig. 16. 

!"#$%&'()*''!"#$%#&'(#$$" 

!"#$%&'%$"(%)(#*&*+%,-%'"#.(/ 

406

Fig. 16 The vertical organization weakens the 3D appearance of the cubes 

407 


5.4. Other !"#$%&'()*''!"#$%#&'(#$$" Shape Properties: The Pointing 

!"#$%&'%$"(%)(#*&*+%,-%'"#.(/ 

The shape properties are not restricted to the sidedness and pointedness. Given 

the vectorial attributes previously described and the relations between sides and 

angles and also between what appears as the base of a shape and its height, the 

pointing is another significant shape property, which can be strongly influenced 

by the accentuation. If the pointing is a shape attribute, then it is expected to 

create and define the perceived shape. 

In Fig. 17a, the horizontal alignment of equilateral triangles induces the pointing


of the triangles in the direction of their alignment. This is due to the configural 

orientation effect studied by Attneave (1968), Palmer (1980, 1989) and Palmer 

& Bucher (1981). 

Figs. 17b-c demonstrate that the pointing of the triangles can be deviated or 

redirected by the small rectangles and circles placed inside each triangle, 

respectively in the top left and bottom left-hand directions. These results are 

unexpected on the basis of the configural orientation effect (see also Pinna, 

2010a, 2010b). 

# 

2 

0 

1 

( 

Fig. 17 The pointing and the shape of triangles can be influenced by the accentuation 

!"#$%&'()*''!"#$%#&'(#$$" 

!"#$%&'%$"(%)(#*&*+%,-%'"#.(/ 

408

409 


More important than these conditions are the following ones of Figs. 17d-e, where 

the pointing clearly influences the shape of the triangles, thus demonstrating 

that the pointing is a shape property. Geometrically the triangles are isosceles, 

nevertheless due to the pointing induced by the two kinds of accentuation 

(rectangles and circles), they are perceived like scalene triangles. More in details, 

because the perceived pointing is not in the direction of the angle created by 

the two longer sides, this induces an asymmetrical effect that propagates and 

determines the whole shape of each triangle making it appear as scalene. 

These results suggest that the pointing and all the other meta-shape attributes 

here studied are the main attributes responsible for the shape formation. They 

can explain what a shape is. 

Variations in the pointing of sides or vertices, due to the accentuation, clearly 

influence the shape of figures as shown in Fig. 18. Under these conditions, the 

rows of irregular quadrilaterals are perceived as different shapes, difficult to 

recognize as the same figures. By determining the shape, the accent determines 

also the orientation of each specific shape and therefore the shape-related 

information about its rigidity and surface bending in the 3D space. The bending 

region is easily and immediately perceivable and its location changes in relation 

to the accent position within the figure. These results suggest the kind of visual 

organization and the new conditions illustrated in the following section.


Fig. 18 Rows of irregular quadrilaterals are perceived as different shapes 

5.5. The Headedness and the Organic Segmentation 

There is a special kind of shape formation never studied before, which subsumes 

a meta-shape property that we call “headedness”. This property is shown in the 

irregular !"#$%&'()*''!"#$%#&'(#$$" wiggly object of Fig. 19a that assumes an organic appearance similar to 

an !"#$%&'%$"(%)(#*&*+%,-%'"#.(/ 

amoeba or to some kind of living creature with a head and upper and lower 

limbs, moving in the direction defined by the shape component perceived as the 

head of the organism. The object shapes up slowly and appears reversible, i.e. 

the same component can assume different roles (head, limb), therefore changing 

the whole organic segmentation and, as a consequence, the direction of the 

perceived motion, the structure, the weight and all the other static and dynamic 

characteristics of the organism. 

This organic segmentation can be reshaped, similarly to the ways previously 

410

411 


shown in the case of the squares, through the accentuation of one component 

against the others in the function of head, thus favoring the emergence of the 

headedness shape property. Figs. 19b-e demonstrate that by changing the spatial 

position of the small circle the organism changes its shape, appearing each time 

as a different creature. The component defined by the circle becomes the head. 

As such, all the organic properties change accordingly to what is perceived as the 

head, i.e. to the headedness property. For instance, the organisms of Figs. 19bc 

or 19d-e are perceived moving in opposite directions. The limbs appear also 

totally different and so on. 

0 

Fig. 19 Different organic segmentations of undulated figures 

!"#$%&'()*''!"#$%#&'(#$$" 

!"#$%&'%$"(%)(#*&*+%,-%'"#.(/ 

# 

2 ( 

- + 

1


Figs. 19f-c demonstrate that not all the components can assume the function of 

head. The accentuation of the bottom components cannot induce so strongly as 

in Figs. 19b-e the headedness property. This likely depends on the position of the 

head, usually placed sideways or at the top of a living being. However, the term 

“usually” does not necessarily mean that the position of the head is totally due to 

past experience, but that the head should be structurally located in certain spatial 

components and not in others in order to show the strongest headedness property 

necessary to influence at best the entire shape. 

Against the headedness and organic segmentation, it can be argued that these 

results are due to the fact that the filled circle behaves or is reminiscent of an 

eye, thus eliciting cognitive processes that have nothing to do with the shape 

formation within the visual domain. The counter-arguments to this issue are 

illustrated in the conditions of Fig. 20, where the positions of the small circle 

and the different shapes of the accentuation reject this objection in favor of the 

spontaneous organic segmentation as part of the problem of shape formation 

within the perceptual domain and depending on the headedness property. Figs. 

20f-g shows how different shapes of the inner components can create organic 

segmentation by putting together different wiggly components that create not 

only a head within a body but also a face with different components (nose, mouth 

and so on). 

412

# 

1 2 

( - 

+ 

413 


Fig. 20 The positions of the small circle and the different shapes of the accentuation change the 

headedness of the undulated figures 

It is !"#$%&'()*''!"#$%#&'(#$$" 

worthwhile noticing that this kind of segmentation is related to those 

!"#$%&'%$"(%)(#*&*+%,-%'"#.(/ 

previously described, where the accentuation popped out some inner meta-shape 

attributes. Furthermore, like in the previous conditions, these attributes can 

be spontaneously highlighted through our own gaze and the focus of attention 

without the need of external accents. This free and subjective visual highlight can 

be easily demonstrated in Fig. 19a by switching spontaneously the headedness 

from one wiggly component to another, therefore addressing the organic 

segmentation in different ways. 

0


5.6. The Happening as a Further Shape Property 

In the light of these results, we can now go back to the conditions illustrated in 

Fig. 1, by reviewing the phenomenal notion of “happening”. It can, in fact, be 

considered as another meta-shape attribute among the others. Every happening 

is a discontinuity that accentuates one or more properties of the main shape. 

This discontinuity gives a meaning to the shape in the same way as we have 

shown in the previous sections, or like, for example, in the diamond and the 

rotated squares of Fig. 15. The missing portion of the side or of the angle imparts 

different meanings to the shape by eliciting a diamond or a rotated square shape. 

Furthermore, in the same way as the happening (the geometrical discontinuity) 

imparts a meaning to the shape, the shape imparts a meaning to the discontinuity. 

For instance, the object illustrated in Fig. 1c is the result of a complex kind 

of shape formation and meaning assignment that we spontaneously define “a 

beveled square”. Geometrically, there is neither a “square”, nor a “beveling”, or 

an “a” but two vertical, two horizontal and one oblique segment forming a closed 

figure with the oblique segment placed in the top right-hand portion of the figure 

connecting the horizontal and vertical segments, shorter than the other two. This 

complex geometrical description is strongly simplified by giving a visual meaning 

to that shape, i.e. a beveled square. Differently from these phenomenal results, 

good continuation, prägnanz and closure principles group the sides of the figure 

to form a pentagon. The discontinuous component, i.e. the oblique segment, 

gives a meaning to the other sides, that become a square, and, at the same time, 

the square assigns a meaning to the discontinuity that appear like a beveling (see 

also Pinna, 2010a, 2010b). 

The notion of happening also suggests a more interesting aspect of the meaning 

of shape. Shape not only implies boundary contour formation or geometrical 

organization like square vs. diamond. It also contains more complex properties 

as suggested by Rubin introducing depth and chromatic attributes (see section 

1.2). Figs. 1c-i clearly demonstrate that there are also material properties that 

can influence and assign different meanings to the shape. In fact, when, for 

example, it is broken, the material properties strongly determine its shape. If a 

square is made up of glass, when its shape is broken, it will be different from a 

square made up of pottery or fabric. The shape of the break changes according 

to the material property. Conversely, the shape of the broken square suggests its 

material properties. The beveled square indicates only a small number of material 

attributes (paper, metal, etc.) and, at the same time excludes many others. They 

are reciprocally determined in the same way we have seen in the case of the 

diamond and the rotated square. 

For a more exhaustive analysis of the notion of “happening” see Pinna (2010a, 

2010b) and Pinna & Albertazzi (2011). 

414

6. Discussion and Conclusions 

415 


In the previous sections, following the methods traced by Gestalt psychologists, 

we studied the meaning of shape perception starting from the square/diamond 

illusion, which represents a problem for the invariant features hypothesis and for 

any model of shape formation. Theories based on the role of frame of reference in 

determining shape perception were discussed and largely weakened or refuted in 

the light of a high number of new effects, demonstrating the basic phenomenal 

role of inner properties in defining the meaning of shape. 

On the basis of these effects, several shape properties were demonstrated. They 

are: (i) the sidedness and the pointedness, related to the sides and angles in the 

case of squares, diamonds and polygons; (ii) the pointing involved mostly in 

the triangles; (iii) the headedness, i.e. the appearance like a head of a particular 

component within an irregular shape, in the case of a new kind of visual 

organization that we called “organic segmentation”; finally, (iv) the happening, 

i.e. the something that happens to a figure. Many other shape properties remain 

to be studied. 

These shape properties were demonstrated to underlie the whole notion of shape 

and to appear like second level shape meanings. They can be considered like 

transversal or elemental meta-shapes common to a large number of shapes both 

regular and irregular. They are like meaningful primitives, phenomenally relevant, 

of the language of shape perception. 

This suggests that the meaning of shape can be understood on the basis of a 

multiplicity of meta-shape attributes. Therefore, the notion of shape can be 

phenomenally represented like a whole visual “thing” that contains a specific set 

of phenomenal primitive properties. In other words, the shape can be considered 

like the holder of shape attributes. As a holder it expresses and manifests the state 

of organization of the inner meta-shapes. 

Within the shape like a holder, the shape attributes are not placed all at the 

same height within the gradient of visibility, i.e. some emerge more strongly 

than others depending on a number of factors that can influence their vividness 

and thus their visibility. Among them, we studied some known factors like the 

horizontal/vertical axes, the gravitational orientation, the configural orientation 

and the large reference frame. We also demonstrated their limits and showed the 

reason of their effectiveness under specific conditions. Within the hypothesis of 

the shape like a holder, their effectiveness depends on the accentuation of one 

specific meta-shape attribute. Therefore, in the case of a square, the horizontal/ 

vertical organization of the sides accentuates the sidedness, while in the case of 

the diamond the pointedness is accentuated by the same factor. This entails that 

a rotated square is perceived when the sidedness is stronger than the pointedness; 

otherwise we would have perceived a rotated diamond.


This suggests that all the shape attributes are present at the same time but some 

or only one emerges, due to specific factors, as the winner that imparts the basic 

meaning to the shape. It follows that the shape attributes can compete and 

cooperate and, above all, they are all present at the same time, placed along the 

gradient of visibility and in a dynamic state of equilibrium that can be changed by 

accentuating the opposite or competing attribute. Several ways to accentuate the 

shape attributes were demonstrated in most of the figures illustrated. It was also 

demonstrated that the accentuation operates like Euclidean vectors. 

The organization of the shape attributes can create conditions of singularity 

where one specific attribute emerges much more than others. This is the case 

of the square of Fig. 2a and of the diamond of 2c. Under these conditions, the 

perceived shape manifests a unique and a special meaning similar to the one 

assumed by the term “Prägnanz” within the Gestalt literature. This term was 

related to a special phenomenal property belonging to certain gestalts but not to 

others. This property makes some objects appear as unique, preferred, singular 

and distinguished (Ausgezeichnet). This is the case of the circle and the square 

(Metzger, 1963; 1975a; 1975b; Wertheimer, 1912a; 1912b; 1922, 1923). 

Wertheimer (1923) introduced a second interesting meaning, aimed at describing 

not only a property but also a process: Prägnanz refers to a process bringing to a 

stable result and with the maximum of equilibrium. This is the case of Prägnanz 

as a grouping principle (see also Metzger, 1963) directed to create the best Gestalt 

(Tendenz zur Resultierung in guter Gestalt; gute Fortsetzung) with an inner necessity 

and with the minimum of requiredness (innere Notwendigkeit, Köhler, 1938). As 

regards the need to distinguish between the two meanings see Hüppe (1984) and 

Kanizsa and Luccio (1986, 1989). The third meaning of the term “Prägnanz” 

is the most controversial and states that Prägnanz refers to self-organization 

processes aimed at the formation of an ordered, singular (Einzigartigkeit), and 

distinguished (Ausgezeichnet) outcome (Goldmeier, 1937; Köhler, 1920; Metzger, 

1963; 1982; Rausch, 1952, 1966; Wertheimer, 1912a, 1912b, 1922). 

For an interesting discussion on the meanings of Prägnanz see Kanizsa (1975, 

1991) and Kanizsa & Luccio (1986, 1989), who criticized and rejected the third 

meaning as part of perception and suggested distinguishing sharply the first two 

meanings to avoid any possible confusion. Pinna (1993, 1996, 2005) introduced 

a fourth meaning going beyond and solving Kanizsa and Luccio’s critiques to the 

third meaning. It states that a tendency toward Prägnanz does not necessarily 

concern the modal realization of a singular perceptual result but it usually implies 

the amodal formation of the most distinguished and singular result (amodal 

prägnanz). 

This idea is in agreement with the meaning of shape introduced in this work. In 

fact, the perception of a rotated square implies the amodal prägnanz. This is all 

416

417 


the more reason for the notion of happening. In fact, in the case of the beveled 

square, the square appears as the amodal whole object and the beveling as the 

modal part of it. The square is the result of the amodal wholeness completion of 

something perceived as its visible modal portion. The square is perceived and not 

perceived at the same time and its amodal whole completion occurs “beyond” the 

beveling. This implies that the amodal completion can be considered as a subset 

or as an instance of the more general problem of amodal wholeness. In the case of 

the beveled square, the amodal wholeness corresponds to the amodal prägnanz. 

This suggests that every shape manifests an ideal condition where one meta-shape 

attribute emerges much more than others. In other words, each shape indicates 

amodally its starting or converging point of singularity. Therefore, we are able to 

perceive how a figure can be changed or accentuated to obtain the best condition 

under which the shape becomes a singularity. It is worthwhile noticing that, on 

the basis of our results, the gradient of visibility of the shape attributes indicates 

that, when one attribute emerges, the others remain invisible or in a second plane 

of visibility. 

In conclusion, the meaning of shape, here suggested, allows its extension to 

conditions never included in the notion of shape so far. They are, for example, 

the material properties, previously considered as shape attributes (see section 

5.6), but also figures like those illustrated in Fig. 21, known as “Maluma-Takete” 

(Köhler, 1929, 1947; see also Ramachandran & Hubbard; 2001), where two 

opposite attributes are perceived, curviness and pointedness, and where a large 

set of further opposite properties – smoothness and sharpness, jaggedness and 

roundedness – are related to these ones. 

Fig. 21 Maluma and Takete


Summary 

The aim of this work is to answer the following questions: what is shape? What is its 

meaning? Shape perception and its meaning were studied starting from the square/ 

diamond illusion and according to the phenomenological approach traced by gestalt 

psychologists. The role of frame of reference in determining shape perception was 

discussed and largely weakened or refuted in the light of a high number of new effects, 

based on some phenomenal meta-shape properties useful and necessary to define the 

meaning of shape. The new effects studied are based on the accentuation of the following 

meta-shape attributes: sidedness and pointedness (in the case of squares, diamonds 

and polygons); the pointing (in the triangles); the headedness (in irregular shapes); the 

happening (in deformed shapes), i.e. the something that happens to a figure. Every 

happening is a discontinuity that accentuates one or more properties of the main shape 

and gives a meaning to the shape. 

The phenomenal results demonstrated that the accentuation of the meta-shape properties 

operates like Euclidean vectors. On the basis of these results we suggested that the meaning 

of shape could be understood on the basis of a multiplicity of meta-shape attributes 

that operate like meaningful primitives of the complex language of shape perception. 

Therefore, the notion of shape can be represented like a whole visual “thing/holder” that 

contains a specific organized set of phenomenal primitive properties, i.e. the state of 

organization of the inner meta-shapes. 

Keywords: Shape perception, Gestalt psychology, perceptual organization, visual 

meaning, visual illusions. 

Zusammenfassung 

Ziel der vorliegenden Arbeit ist die Beantwortung folgender Fragen: Was ist Form 

und was ist deren Bedeutung? Die Wahrnehmung von Form und Bedeutung wurde 

erstmals anhand einer Quadrat-Rauten-Täuschung (Pinna) mit Hilfe der von der 

Gestaltpsychologie entwickelten phänomenologischen Methode untersucht. Die 

Rolle des Bezugssystems für die Wahrnehmung einer Form wird diskutiert, jedoch 

angesichts zahlreicher neuer Effekte größtenteils herabgestuft oder gar widerlegt. Diese 

neuen Effekte gehen auf einige für die Definition der Form-Bedeutung förderliche 

und notwendige phänomenale Meta-Form-Eigenschaften zurück. Sie beruhen auf der 

Akzentuierung folgender Eigenschaften: anschauliche Erstreckung von Kanten und 

Ecken (im Fall von Quadraten, Rauten und Polygonen); anschauliche Ausrichtung (bei 

Dreiecken); anschauliche Gerichtetheit (bei unregelmäßigen Formen); Bezogenheit auf 

ein dynamisches Ereignis (bei deformierten Formen), also auf das Etwas, das mit einer 

Form geschieht. Jedes Ereignis stellt eine Störung dar, die eine oder mehrere (implizite) 

Eigenschaften der zugrunde liegenden Form isoliert und verstärkt und dadurch der Form 

eine Bedeutung zuweist. 

Die Beobachtungen zeigen, dass die Meta-Form-Eigenschaften sich wie euklidische 

Vektoren verhalten. Aufgrund der Ergebnisse vertreten wir die Auffassung, dass man die 

Bedeutung einer Form auf der Grundlage einer Vielzahl von Meta-Form-Eigenschaften 

verstehen kann, die sich ihrerseits wie bedeutungshaltige Primitiva der komplexen Sprache 

der Formwahrnehmung verhalten. Der Begriff der Form kann daher wie ein holistischer 

“Ding-Träger” aufgefasst werden, der eine spezifisch organisierte Anzahl grundlegender 

418

419 


phänomenaler Eigenschaften enthält, nämlich den Zustand der Organisation der inneren 

Meta-Formen. 

Schlüsselwörter: Formwahrnehmung, Gestaltpsychologie, Wahrnehmungsorganisation, 

visuelle Bedeutung, Wahrnehmungstäuschung. 

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420

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Acknowledgments 

Supported by Finanziamento della Regione Autonoma della Sardegna, ai sensi della L.R. 7 agosto 2007, n. 7, 

Fondo d’Ateneo (ex 60%) and Alexander von Humboldt Foundation. 

Baingio Pinna, born 1962, since 2002 Professor of Experimental Psychology and Visual Perception at 

the University of Sassari. 2001/02 Research Fellow at the Alexander Humboldt Foundation, Freiburg, 

Germany. 2007 winner of a scientific productivity prize at the University of Sassari, 2009 winner of the 

International “Wolfgang Metzger Award to eminent people in Gestalt science and research for outstanding 

achievements”. His main resaerch interests concern Gestalt psychology, visual illusions, psychophysics 

of perception of shape, motion, color and light, and vision science of art. 

Address: Facoltà di Lingue e Letterature Straniere, Dipartimento di Scienze dei Linguaggi, University of 

Sassari, via Roma 151, I-07100 Sassari, Italy. 

E-Mail: baingio@uniss.it

Announcements - Ankündigungen 

On the occasion of the 100 th anniversary of the pivotal publication by 

Max Wertheimer on the phi-phenomenon in 1912, 

Wertheimer’s symposium 

at the convention of the German Society of Psychology 

Bielefeld, 24 th to 27 th September 2012 

will take place. 

The symposium will be hosted by Viktor Sarris (University of Frankfurt) 

and Horst Gundlach (University of Würzburg) in cooperation with the GTA 

– Society for Gestalt theory and its applications. 

The preliminary agenda contains contributions by Michael Wertheimer 

(University of Colorado at Boulder), Lothar Spillmann (Neurocentrum, 

University medical center Freiburg), Riccardo Luccio (University of Trieste), 

and Jürgen Kriz (University of Osnabrück). 

eeeee 

Aus Anlass des 100jährigen Jubiläums der entscheidenden Publikation 

von Max Wertheimer zum Phi-Phänomen im Jahre 1912 findet ein 

Wertheimer-Symposium 

auf dem Kongress der Deutschen Gesellschaft für Psychologie 

Bielefeld, 24. – 27. September 2012 

statt. 

Das Symposium wird in Kooperation mit der GTA - Gesellschaft für 

Gestalttheorie und ihre Anwendungen, von Viktor Sarris (Universität 

Frankfurt) und Horst Gundlach (Universität Würzburg) veranstaltet. 

Vorgesehen sind Beiträge von Michael Wertheimer (University of Colorado 

at Boulder), Lothar Spillmann (Neurocentrum, Universitätsklinikum 

Freiburg), Riccardo Luccio (University of Trieste) und Jürgen Kriz 

(Universität Osnabrück). 

422

GTA – Symposium 

Helsinki 

29. September 2012 

In the anniversary year of Gestalt Theory, the GTA – Society for Gestalt 

Theory and its Applications – hosts a scientific symposium in Finland for 

the first time. 

Interacting with Finnish academics, various topics focusing on Gestalt 

Theory will be covered. 

Contributions on the following topics are planned: Gestalt Theory - 

History and Modern, Gestalt Theory in Finland, Gestalt Theory in Art and 

Culture, Gestalt Theory in Education, Gestalt Theory in Psychotherapy, 

Gestalt Theory and Design. 

eeeee 

Im Jubiläumsjahr der Gestalttheorie veranstaltet die GTA - Gesellschaft für 

Gestalttheorie und ihre Anwendungen, erstmals ein wissenschaftliches 

Symposium in Finnland. 

Gestalttheoretische Schwerpunkte aus verschiedenen Themenbereichen 

werden in Interaktion mit finnischen Wissenschaftlern behandelt. 

Geplant sind Beiträge u.a. zu folgenden Themen: 

Gestalttheorie - Geschichte und Aktualität, Gestalttheorie in Finnland, 

Gestalttheorie in Kunst und Kultur, Gestalttheorie in Bildung und 

Erziehung, Gestalttheoretische Psychotherapie, Gestalttheorie und 

Design. 

423

The International 

SOCIETY FOR GESTALT THEORY AND ITS APPLICATIONS 

invites submissions for the 

WOLFGANG METZGER AWARD 2013 

This award is named after Wolfgang Metzger, a student of Max Wertheimer and one of 

the leading members of the second generation of the Berlin Gestalt School. 

In the first period of this award it was granted by decision of the board of directors of the 

GTA to eminent people in Gestalt science and research for outstanding achievements. 

In 1987, the award went to Gaetano Kanizsa and Riccardo Luccio (Italy), in 1989 to 

Gunnar Johansson (Sweden). 

Since 1999 the award has been granted every second or third year by the board of 

directors of the GTA based on an international public award contest and a screening 

and review of the submittals by an international scientific Award Committee. The first 

prize winners since 1999 were: Giovanni Bruno Vicario, Italy, and Yoshie Kiritani, 

Japan; Peter Ulric Tse, USA; Fredrik Sundqvist, Sweden; Cees van Leeuwen, NL/Japan; 

Baingio Pinna, Italy. 

Applicants for the Metzger Award 2013 must submit a scientific paper (in English 

or German) inspired by Gestalt theory and that contributes to the research or the 

application of Gestalt theory in the physical sciences, the humanities, the social sciences, 

the economic sciences, or any other field of human studies. Hence, the paper could deal 

with a subject from psychology, philosophy, medicine, arts, architecture, linguistics, 

musicology or other fields of research or application of research as long as it is inspired 

by a Gestalt theoretical approach. 

The first prize winner will receive € 1000, will be invited as the award speaker to the 18th 

international Scientific Convention of the GTA in 2013, and the paper will be published 

in the international multidisciplinary journal Gestalt Theory (www.gestalttheory.net/ 

gth/) in the submitted version or in an adapted form. 

Members of the Award Committee for the 2013 contest are: Geert-Jan Boudewijnse 

(Montreal/Canada; chair), Silvia Bonacchi (Warsaw/Poland), Hellmuth Metz-Göckel 

(Dortmund/FRG), Baingio Pinna (Sassari/Italy), Fiorenza Toccafondi (Parma/Italy), N.N. 

Submittals for the Metzger Award 2013 are due by September 2012. 

The submission must be sent as a Word or a PDF document to the Metzger Award committee 

at: metzger-award@gestalttheory.net. More information about the international Society 

for Gestalt Theory and its Applications as well as the Wolfgang Metzger Award 2013 can 

be found on the website of the Society: www.gestalttheory. net/ 

424

Die internationale 

GESELLSCHAFT FÜR GESTALTTHEORIE UND IHRE ANWENDUNGEN 

lädt ein zu Einreichungen für den 

WOLFGANG-METZGER-PREIS 2013 

Dieser Preis ist nach Wolfgang Metzger benannt, Schüler von Max Wertheimer und 

führendem Vertreter der zweiten Generation der Berliner Schule der Gestalttheorie. 

In einer ersten Periode wurde der Preis über Beschluss des Vorstandes der GTA an 

verdiente Persönlichkeiten für herausragende Beiträge zur Anwendung der Gestalttheorie 

in Wissenschaft und Forschung verliehen: 1987 ging der Metzger-Preis in diesem 

Sinn an Gaetano Kanizsa und Riccardo Luccio (Italien), 1989 an Gunnar Johansson 

(Schweden). 

Seit 1999 wird der Preis international öffentlich ausgeschrieben und vom GTA-Vorstand 

auf Grundlage der Begutachtungsergebnisse und Empfehlungen eines internationalen 

wissenschaftlichen Preis-Komitees vergeben. Die ersten Preise gingen seither an 

Giovanni Bruno Vicario (Italien) und Yoshie Kiritani (Japan), Peter Ulric Tse (USA), 

Fredrik Sundqvist (Schweden), Cees van Leeuwen (NL/Japan), Baingio Pinna (Italien). 

Für Bewerbungen um den Metzger-Preis 2013 ist ein wissenschaftlicher Beitrag (in 

Englisch oder Deutsch) einzureichen, der zur Überprüfung und Weiterentwicklung 

der Gestalttheorie in Forschung oder Anwendung in den Naturwissenschaften, 

den Humanwissenschaften, den Sozial- und Wirtschaftswissenschaften oder auf 

einem anderen Gebiet beiträgt. Einreichungen können also beispielsweise aus der 

Psychologie, Philosophie, Medizin, Kunst, Architektur, den Sprachwissenschaften, der 

Musikwissenschaft oder auch aus anderen Fachgebieten kommen, solange sie sich in der 

Behandlung ihres Themas kompetent auf die Gestalttheorie beziehen. 

Die Gewinnerin bzw. der Gewinner des Metzger-Preises 2013 erhält ein Preisgeld von 

€ 1000 und wird zum Preisträgervortrag bei der 18. internationalen Wissenschaftlichen 

Arbeitstagung der GTA im Jahr 2013 eingeladen. Die eingereichte Arbeit oder der 

Preisträgervortrag wird in der internationalen multidisziplinären Zeitschrift Gestalt 

Theory (www.gestalttheory.net/gth/) veröffentlicht. 

Mitglieder des Metzger-Preis-Komitees 2013 sind: Geert-Jan Boudewijnse (Montreal/ 

Kanada; Vorsitz), Silvia Bonacchi (Warschau/Polen), Hellmuth Metz-Göckel (Dortmund 

/D), Baingio Pinna (Sassari/Italien), Fiorenza Toccafondi (Parma/Italien), N.N. 

Einsendeschluss für den Metzger-Preis 2013 ist September 2012. 

Einreichung als Word- oder PDF-Dokument an das Preis-Komitee: metzger-award@ 

gestalttheory.net. Weitere Informationen über die GTA und den Wolfgang-Metzger- 

Preis: www.gestalttheory.net/ 

425

Gestaltpsychologie und Person 

Entwicklungen der Gestaltpsychologie 

Herausgegeben von Giuseppe Galli 

154 Seiten, € 18,-- 

ISBN 978 3 901811 43 2 

Das vorliegende Buch beschreibt die Beziehungen zwischen Gestalttheorie 

und Person und ist die Frucht der Arbeit einer Gruppe von Psychologen, die 

sich mit folgenden Aspekten der Person befassten: die Person und ihr Ich; 

die Person in Aktion; die Person in Beziehung; die Entstehung der Person; 

die Person in Dialog; die Person und die Zentrierung. Der hauptsächliche 

Zugang zur Untersuchung dieser Aspekte ist ein relationaler oder feldtheoretischer, 

dem zufolge die Faktoren, die das Verhalten bestimmen, nicht 

nur aus dem innerpersonalen System abgeleitet werden können, sondern 

auch von den Beziehungen zwischen Individuum und der konkreten Situation, 

in das es eingebettet ist, abhängen. In der Person-Umwelt-Beziehung 

haben die Gestalttheoretiker besonders die Ausdrucks- und Wesensqualitäten 

aufgewertet, die aus dem Objekt-Pol das Ego anzielen. Die Theorie 

des psychischen Feldes konnte seine Fruchtbarkeit sowohl in den Untersuchungen 

zur Allgemeinen und Sozial-Psychologie zeigen, als auch in jenen 

zur Entwicklungspsychologie. In den letzten Jahrzehnten setzte sich das 

Feldmodell auch im psychoanalytischen Umfeld durch. 

Das Buch ist sowohl für Studierende als auch für Forschende und Therapeuten 

von Interesse. 

Fax: + 43 1 985 21 19-15 | Mail: verlag@krammerbuch.at

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