What is the Meaning of Shape? - Gestalt Theory

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Pinna, What is the Meaning of Shape?
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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