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
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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.
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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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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
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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
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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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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
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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
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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
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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,
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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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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
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in Fig. 6 are different shapes, not only because they have two different names, but,
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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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Pinna, What is the Meaning of Shape?
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).
#
0
1
2
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.
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400
Pinna, What is the Meaning of Shape?
#
0
Fig. 10 Kopfermann’s effect annulled
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
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the figures depending on the position of the white components (Figs. 11c-d).
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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.
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GESTALT THEORY, Vol. 33, No.3/4
#
1
0
2
(
-
Fig. 11 Accentuation of sidedness and pointedness in octagons
In
Fig. 12, the accentuation of the sidedness and pointedness through the
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reversed
contrast induces diamond-shaped (Fig. 12a) or grand piano-like (Fig.
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12b) figures in the same geometrical objects.
402
Pinna, What is the Meaning of Shape?
#
0
Fig. 12 Diamond-shaped or grand piano-like figures in the same geometrical objects
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
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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 &
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GESTALT THEORY, Vol. 33, No.3/4
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.
#
0
1
2
Fig. 13 The accentuation, due to black sides, produces a directional symmetry and manifests
vectorial properties
404
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Pinna, What is the Meaning of Shape?
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.
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GESTALT THEORY, Vol. 33, No.3/4
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.
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406
Pinna, What is the Meaning of Shape?
Fig. 16 The vertical organization weakens the 3D appearance of the cubes
5.4. Other
Shape Properties: The Pointing
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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
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GESTALT THEORY, Vol. 33, No.3/4
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
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Fig. 17 The pointing and the shape of triangles can be influenced by the accentuation
408
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Pinna, What is the Meaning of Shape?
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.
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GESTALT THEORY, Vol. 33, No.3/4
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
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an
amoeba or to some kind of living creature with a head and upper and lower
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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
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Pinna, What is the Meaning of Shape?
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.
#
1
0
2
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-
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Fig. 19 Different organic segmentations of undulated figures
411
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!"#$%&'%$"(%)(#*&*+%,-%'"#.(/
GESTALT THEORY, Vol. 33, No.3/4
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).
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Pinna, What is the Meaning of Shape?
0
#
1
2
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-
+
Fig. 20 The positions of the small circle and the different shapes of the accentuation change the
headedness of the undulated figures
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worthwhile noticing that this kind of segmentation is related to those
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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.
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GESTALT THEORY, Vol. 33, No.3/4
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).
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Pinna, What is the Meaning of Shape?
6. Discussion and Conclusions
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.
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GESTALT THEORY, Vol. 33, No.3/4
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
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Pinna, What is the Meaning of Shape?
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
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GESTALT THEORY, Vol. 33, No.3/4
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
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Pinna, What is the Meaning of Shape?
phänomenaler Eigenschaften enthält, nämlich den Zustand der Organisation der inneren
Meta-Formen.
Schlüsselwörter: Formwahrnehmung, Gestaltpsychologie, Wahrnehmungsorganisation,
visuelle Bedeutung, Wahrnehmungstäuschung.
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Pinna, What is the Meaning of Shape?
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 421
Announcements - Ankündigungen
On the occasion of the 100th 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, 24th to 27th 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-MetzgerPreis: 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