Symmetry Is Not a Universal Law of Beauty

Abstract

Scientific disciplines as diverse as biology, physics, and psychological aesthetics regard symmetry as one of the most important principles in nature and one of the most powerful determinants of beauty. However, symmetry has a low standing in the arts and humanities. This difference in the valuation of symmetry is a remarkable illustration of the gap between the two cultures. To close this gap, we conducted an interdisciplinary, empirical study to directly demonstrate the effects of art expertise on symmetry appreciation. Two groups of art experts—artists and art historians—and a group of non-experts provided spontaneous beauty ratings of visual stimuli that varied in symmetry and complexity. In complete contrast to responses typically found in non-art experts, art experts found asymmetrical and simple stimuli as most beautiful. This is evidence of the effects of specific education and training on aesthetic appreciation and a direct challenge to the universality of symmetry.

Full text

Brief Reports
Symmetry Is Not a
Universal Law of Beauty
Helmut Leder
1,2
, Pablo P. L. Tinio
3
,
David Brieber
1,2
, Tonio Kr€
oner
2
,
Thomas Jacobsen
4
, and
Raphael Rosenberg
2
Abstract
Scientific disciplines as diverse as biology, physics, and psychological aesthetics regard
symmetry as one of the most important principles in nature and one of the most
powerful determinants of beauty. However, symmetry has a low standing in the arts
and humanities. This difference in the valuation of symmetry is a remarkable illus-
tration of the gap between the two cultures. To close this gap, we conducted an
interdisciplinary, empirical study to directly demonstrate the effects of art expertise
on symmetry appreciation. Two groups of art experts—artists and art historians—
and a group of non-experts provided spontaneous beauty ratings of visual stimuli
that varied in symmetry and complexity. In complete contrast to responses typically
found in non-art experts, art experts found asymmetrical and simple stimuli as most
beautiful. This is evidence of the effects of specific education and training on aesthetic
appreciation and a direct challenge to the universality of symmetry.
Keywords
expertise, aesthetics, symmetry, preference
1
Department of Basic Psychological Research and Research Methods, and Cognitive Science Research
Platform, University of Vienna, Vienna, Austria
2
Department of Art History, and Cognitive Science Research Platform, University of Vienna,
Vienna, Austria
3
Department of Educational Foundations, Montclair State University, NJ, USA
4
Department of Psychology, Helmut-Schmidt University, Hamburg, Germany
Corresponding Author:
Helmut Leder, University of Vienna, Liebiggasse 5, Vienna 1010, Austria.
Email: helmut.leder@univie.ac.at
Empirical Studies of the Arts
0(0) 1–11
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DOI: 10.1177/0276237418777941
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Disciplines as diverse as biology, chemistry, physics, and psychological aes-
thetics regard symmetry as one of the most important principles in nature and
as one of the most powerful determinants of beauty. The influence of symmetry
seems so universal (Weyl, 1952) that it has even been discussed as a super prin-
ciple (Voloshinov, 1996). Researchers have repeatedly shown symmetry’s central
role in preference and beauty judgments of visual stimuli, including biological
entities such as faces (Rhodes, 2006; Tinio, Gerger, & Leder, 2013) and also as a
quantifiable dimension underlying pattern preference (al-Rifaie et al., 2017).
The preference for symmetry in faces and bodies (Grammer & Thornhill,
1994) has been associated with advantages regarding mate choice, as there is
some evidence that symmetry indicates good health, stable development, and
good genes (Thornhill & Møller, 1997). The importance of symmetry has been
further supported by evidence that symmetry is a strong determinant of aesthetic
judgments of meaningless, abstract patterns (Gartus & Leder, 2013; Jacobsen &
H€
ofel, 2002; Tinio & Leder, 2009). Beyond the relation to mate choice (i.e.,
symmetry signals health and fitness; Rhodes, 2006), the preference for symmetry
is also often explained with reference to the functioning of the human visual
system: Symmetrical stimuli are processed fluently and efficiently (Reber,
Schwarz, & Winkielman, 2004).
Contrary to the high esteem that symmetry has in the sciences, symmetry has
a rather low standing in the arts and humanities. For art historians, symmetry is
just one of many features used to characterize specific works of art and specific
art styles. Art historians, for instance, will state that Classicism has an affinity
towards symmetry, whereas Japonism does not. In fact, the 34 volumes of the
Dictionary of Art only include a very short article on Symmetry (Summers,
1996), which argues that since Greek antiquity, symmetria has mainly referred
to pleasing proportions (e.g., between parts of depicted bodies in paintings and
sculptures). It was not until the 17th century that symmetry was considered in
the sense of geometrical bilateral axial balance. In Barck et al.’s (2003) presti-
gious seven-volume encyclopedia of key concepts in aesthetics, symmetry is not
even included as a keyword.
The difference in the valuation of symmetry between the two disciplines is a
remarkable illustration of the gap between the two cultures (Snow, 1963) of
humanities and science. Although this gap has been discussed for years
(Wille, 1986), it has rarely been adequately characterized (for a notable excep-
tion, see McManus, 2006) but surely not tested with regard to aesthetic percep-
tion. Could it be that art experts are wrong about the role of symmetry, because
they are at variance with hard empirical data? Or could it be that the expertise
that they develop through many years of art-specific training and education lead
them to perceive symmetry in a different manner? Through their training, art
experts are able to more deeply process works of art, for example, by placing
them within the historical contexts during which they were created (Leder &
Nadal, 2014; Parsons, 1987).
2Empirical Studies of the Arts 0(0)

It is, however, unclear how this kind of expertise affects aesthetic preferences
made quickly and spontaneously, when there is limited opportunity for one’s
vast knowledge base to enter the picture. Experts might have a different set of
criteria that guide their preferences. If this is indeed the case, it could serve as
evidence that the preference for symmetry is not as universal as has been
claimed. It could even be that art experts prefer asymmetry.
After close consideration of the above issues, and drawing on knowledge
from each of our respective disciplines, we decided to test this hypothesis
within an interdisciplinary study, which combined the methodological precision
of empirical aesthetics and the theoretical rigor of art history within a
straightforward design. The study involved two groups of art experts—artists
and art historians—and a group of non-expert participants as a control group.
All participants evaluated 160 meaningless, abstract patterns for their beauty.
We decided to use such patterns, as they had been used in several behavioral
studies that have produced evidence that symmetry is strongly preferred.
The patterns primarily varied along symmetry (symmetrical or asymmetrical)
and complexity (simple or complex) dimensions (Jacobsen & H€
ofel, 2002).
Complexity was included as a dimension because previous research has shown
that it is related to symmetry—asymmetrical objects are more complex and
more demanding to process than their symmetrical counterparts. In addition,
people generally prefer complex over simple stimuli. These pattern had been
used in several studies with non-art experts and revealed remarkably consistent
preferences for symmetry (Gartus & Leder, 2013; H€
ofel & Jacobsen, 2007;
Jacobsen & H€
ofel, 2002; Tinio, Gerger, & Leder, 2013; Tinio & Leder, 2009).
Method
Participants
A group of 27 art experts (12 advanced students of art from an art academy in
Vienna, Austria, and 15 advanced students from the Art History Department of
the University of Vienna) and 26 non-art experts (from the Psychology
Department of the University of Vienna) were tested in a quasi-experimental
design. Informed consent was obtained from each participant prior to data
collection, and all participants had normal or corrected-to-normal vision.
Materials and Procedure
The stimuli systematically varied according to symmetry and complexity
(40 symmetrical and simple, 40 symmetrical and complex, 40 asymmetrical
and simple, and 40 asymmetrical and complex). As in Tinio and Leder (2009),
stimuli were derived from the larger, original set by Jacobsen and H€
ofel (2002).
Each stimulus consisted of a solid black circle (8.8 cm in diameter) featuring a
Leder et al. 3

centered quadratic rhombic cutout and 86 to 88 basic graphic elements arranged
within the rhomb according to a grid and resulting in an abstract pattern. The
overall luminance was identical for all stimuli. The basic elements included
geometric figures such as triangles, squares, rhombuses, and horizontal, vertical,
or oblique bars. A maximum of two mirroring operations giving four possible
symmetry axes were permitted. One half of the patterns were symmetrical, while
the other half were asymmetrical. Stimulus complexity was manipulated by
varying the number of elements composing a pattern (see Jacobsen & H€
ofel,
2002, for more details).
Participants were tested individually. E-Prime 2.0.8.90 was used to present a
fixation cross for 200 ms followed by the stimulus for 3,000 ms on a gray
background. The presentation of the stimuli was randomized, and participants
rated each stimulus while the stimulus was presented on the screen. Ratings were
provided using a 7-point scale with “1” representing least beautiful and “7”
representing most beautiful. Twelve practice trials (three per stimulus type) pre-
ceded the main experiment, and none of these practice stimuli was included in
the experiment. Afterwards, to verify their expertise, the experts were asked
questions regarding their expertise and the study.
Results
The mean beauty ratings for the stimuli were sampled across participants for
each stimulus type (Figure 1). An analysis of variance with symmetry and com-
plexity as within-subjects factors and group as a between-subjects factor revealed
a significant main effect of complexity,F(1, 50) ¼16.126, p<.01, eta-
squared ¼.244. There was no main effect of symmetry,F(1, 50) ¼1.844.
There were significant interactions between complexity and group,F(1, 50) ¼
9.247, p<.001, eta-squared ¼.270, and symmetry and group,F(1, 50) ¼
27.271, p<.001, eta-squared ¼.522, as well as between complexity and symmetry,
F(1, 50) ¼6.711, p<.05, eta-squared ¼.118. No other effects were significant.
This is convincing evidence that expertise—in art or art history—had a major
impact on the aesthetic appreciation of two principles of visual design that are
often assumed to be universally preferred.
In order to demonstrate that the two groups of experts indeed showed a very
different pattern of preferences, in Figure 2, we show a depiction of the distri-
bution of the four different types of stimuli (40 stimuli for each type) and their
rankings (between 1 and 160) within each of the three groups of participants.
Also depicted are the three stimuli judged as most beautiful and the three stimuli
judged as least beautiful by each group of participants.
To show how the different groups of participants differ, in Figure 3, we
present three scattergrams of the mean score for each image with art historians
on one axis and artists or non-art experts on the other; and likewise for the two
groups of experts against each other. This figure clearly shows how much closer
4Empirical Studies of the Arts 0(0)

(less spread) the preferences are between the two expert groups as compared
with the non-experts for whom the means are much higher for the symmetric
than the nonsymmetric stimuli.
We also analyzed the underlying structure of the interindividual differences.
We took the standard data matrix of P rows (each being a participant) and
S columns (each being a stimulus), transposed it, and then conducted factor
analyses (parallel analysis, Monte Carlo, 1,000 iterations), which revealed a
three-factor solution. A subsequent principal component analysis (PCA) with
direct oblimin rotation (as it allows the data to be orthogonal or oblique
Figure 1. Mean beauty ratings for all conditions and three groups.
Leder et al. 5

depending on the best solution) revealed that the first three components
accounted for 47% of the cumulative variance. Mostly non-expert participants
loaded positively and all experts loaded negatively on the first factor (approx-
imately 30% of the variance). A few non-experts loaded on Factors 2 and 3
(approximately 10% of the variance).
We also conducted an analysis of variance in which we included the three
factors revealed by the PCA as levels of the independent variable, and an index
(for each participant) of preference for symmetry—mean liking of symmetry
minus mean preference for asymmetry; mean values were Factor 1 (n¼37) ¼
.901, Factor 2 (n¼8) ¼.311, and Factor 3 (n¼8) ¼.413—as the dependent
variable. The analyses revealed a main effect of factor, F(2, 52)¼5.101, p¼.01,
with differences between Factor 1 and Factors 2 and 3, but not between the
latter two factors. This indicates that non-art experts differ in their preference
for symmetry from artist and art historians, who in turn, do not differ system-
atically from each other, as they are not represented by different factors of
the PCA.
Figure 2. Distribution of ranks of the four different types of stimuli (40 stimuli for each type;
between 1 and 160) for each of the three groups of participants.
6Empirical Studies of the Arts 0(0)

The results indicate that people untrained in the visual arts did show the
often-claimed preference for symmetrical and complex stimuli. In contrast,
experts seemed to completely disregard these design principles and showed
stronger and more consistent preferences for stimuli that deviated from symme-
try. The experts also showed more variability in their preference for complexity.
Future studies must, however, determine the level of processing within which
such differences are manifested, although the present results illustrate what
could result from the convergence of art and science.
Figure 3. Scattergrams of means between non-expert ratings for the four classes of stimuli,
in relation to the two groups of experts.
Leder et al. 7

General Discussion
The results showed that non-art experts evaluated the symmetrical–complex stim-
uli as most beautiful, followed in descending order by symmetrical–simple, asym-
metrical–complex, and asymmetrical–simple stimuli. This was an expected pattern
of responses that has been previously shown to be largely stable, that is for non-
art expert participants. What was surprising, however, was that both groups of
experts showed a contrasting, even reversed, pattern of responses: Unlike the non-
art experts who found symmetrical and complex stimuli to be most beautiful, the
art experts found asymmetrical and simple stimuli to be most beautiful. The
results are depicted in Figure 2 where each color-coded bar represents one type
of stimulus. The distribution of the bars reflects the average set of most beautiful
to least beautiful judgments within each of the three participant groups. These
findings are supported by statistical analyses that revealed interactions amongst
the factors participant group (experts, non-experts), symmetry (symmetry, asym-
metry), and complexity (complex, simple). To further illustrate the dramatic dif-
ferences between the groups, Figure 2 shows examples of the three stimuli that
were judged as most and least beautiful by each participant group.
Although we did not find any statistically significant difference between the
two groups of experts—artists and art historians—the stimuli judged as most
beautiful shown in Figure 2 suggest that when art historians look at the stimuli,
they could have thought of them as constructivist abstractions—such as those
by Malevich or Mondrian. Artists did not show this bias. Post hoc questions
given to the experts, that were included as a check on expertise indeed revealed
their status of experience and interest in art. However, only two experts (one art
historian and one artist) mentioned that the pattern reminded them of artworks,
or artists, without being more specific. Therefore, this explanation of specific art
associations could be tested further in future studies and would provide evidence
for the influence of specific education and training within the arts (e.g., educa-
tion in art history vs. art making).
Future studies might also more systematically study different kinds of symmetry
and test more specificly whether different participants prefer different kinds of
symmetry. Moreover, current methods in quantifying symmetry might help to
identify even finer grades of preferences for symmetry and its relation to
other image properties (al-Rifaie et al., 2017). Also, in order to better understand
differences between experts and non-experts, a much broader approach could
combine various perceptual tasks with a battery of personality measures (see
McManus, 2006).
Our results demonstrate that the gap between the two cultures—art and sci-
ence—in terms of the evaluation of symmetry corresponds to, and might be
rooted in, basic differences in aesthetic responses. Those differences could be
the result of extensive training (or lack thereof) in the arts (see Belke, Leder,
Harsanyi, & Carbon, 2010). In the present study, to test our expertise-related
8Empirical Studies of the Arts 0(0)

hypotheses in a straightforward research design, we used meaningless patterns
that had no biological or artistic significance. In a recent study, Little (2014) had
shown that there are different levels of preferences for different classes of object.
He found that symmetry preferences were much weaker for artworks as com-
pared to faces. An interesting issue to test in future studies is whether the use of
symmetry in artworks for experts would show similar results.
Symmetry is often considered as the most fundamental of aesthetic primi-
tives. Now, the assumed biologically hard-wired response to symmetry has to be
put into perspective. Altogether, these results challenge the concept of universal
aesthetic principles and demand more in-depth examination of how factors—
such as knowledge, expertise, culture, and context—influence the aesthetic per-
ception of our world.
Acknowledgments
The authors thank Ju
¨rgen Goller and Matthew Pelowski for their support.
Declaration of Conflicting Interests
The authors declared no potential conflicts of interest with respect to the research,
authorship, and/or publication of this article.
Funding
The authors disclosed receipt of the following financial support for the research, author-
ship, and/or publication of this article: This work was sponsored by two interdisciplinary
WWTF Vienna Science and Technology Fund projects awarded H. L. and R. R. (LedRos
CS11–023 and RosLed CS15–036).
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Author Biographies
Helmut Leder is a professor of Cognitive Psychology at the University of
Vienna, where he is the head of a research focus in Empirical Visual
Aesthetics. He is the head of an interdisciplinary research platform in cognitive
science and current president of the International Association of
Empirical Aesthetics.
Pablo P. L. Tinio is an associate professor at Montclair State University. His
research is focused on the psychology of aesthetics, creativity, and the arts; arts
and aesthetics in education; and learning and engagement in cultural institu-
tions. He is an editor of the APA journal, Psychology of Aesthetics, Creativity,
and the Arts. He is also a coeditor of the Cambridge Handbook of the Psychology
of Aesthetics and the Arts.
10 Empirical Studies of the Arts 0(0)

David Brieber is a senior test and training consultant at Schuhfried Inc. He
received his doctoral degree in psychology from the University of Vienna. His
research interests are in the area of scientific aesthetics, neuropsychology, and
psychological assessment.
Tonio Kr€
oner is an artist and curator in Munich, where he works at the
museum Brandhorst.
Thomas Jacobsen is a professor of Experimental and Biological Psychology at
Helmut Schmidt University/University of the Federal Armed Forces Hamburg,
Hamburg, Germany. He is the author of publications in the area of (neuro-
cognitive) psychology, including auditory processing, language, empirical aes-
thetics, and executive function. He was a visiting professor at the University of
Vienna and the Freie Universit€
at Berlin.
Raphael Rosenberg is a professor of Art History at the University of Vienna
where he founded the Lab for Cognitive Research in Art History. He is a
member of the Heidelberg Academy of Sciences and Humanities and of the
Academia Europaea.
Leder et al. 11