Symmetry Is Not a Universal Law of Beauty

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 Empirical Studies of the Arts 2019, Vol. 37(1) 104 114! The Author(s) 2018 Article reuse guidelines: sagepub.com/journals-permissions DOI: 10.1177/0276237418777941 journals.sagepub.com/home/art 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. 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

Leder et al. 105 Disciplines as diverse as biology, chemistry, physics, and psychological aesthetics 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 principle (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) prestigious 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 exception, see McManus, 2006) but surely not tested with regard to aesthetic perception. 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).

106 Empirical Studies of the Arts 37(1) 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. 107 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) preceded 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 complexity as within-subjects factors and group as a between-subjects factor revealed a significant main effect of complexity, F(1, 50) ¼ 16.126, p <.01, etasquared ¼.244. There was no main effect of symmetry, F(1, 50) ¼ 1.844. 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) ¼ 6.711, 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 distribution 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

108 Empirical Studies of the Arts 37(1) Figure 1. Mean beauty ratings for all conditions and three groups. (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

Leder et al. 109 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. 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 (approximately 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 (n ¼ 37) ¼.901, Factor 2 (n ¼ 8) ¼.311, and Factor 3 (n ¼ 8) ¼.413 as the dependent variable. The analyses revealed a main effect of factor, F(2, 52)¼ 5.101, 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 systematically from each other, as they are not represented by different factors of the PCA.

110 Empirical Studies of the Arts 37(1) Figure 3. Scattergrams of means between non-expert ratings for the four classes of stimuli, in relation to the two groups of experts. 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 symmetry. 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.

Leder et al. 111 General Discussion The results showed that non-art experts evaluated the symmetrical complex stimuli as most beautiful, followed in descending order by symmetrical simple, asymmetrical complex, and asymmetrical simple stimuli. This was an expected pattern of responses that has been previously shown to be largely stable, that is for nonart expert participants. What was surprising, however, was that both groups of experts showed a contrasting, even reversed, pattern of responses: Unlike the nonart 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, asymmetry), and complexity (complex, simple). To further illustrate the dramatic differences 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., education 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 science 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

112 Empirical Studies of the Arts 37(1) 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 compared 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 primitives. 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 perception 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, authorship, 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). References al-rifaie, M., Ursyn, A., Zimmer, R., & Javid, M. A. J. (2017). On symmetry, aesthetics, and quantifying symmetrical complexity. Lecture Notes in Computer Science, 10198. doi: 10.1007/978-3-319-55750-2 Barck, K., Fontius, M., Schlenstedt, D., Steinwachs, B., & Wolfzettel, F. (2003). Asthetische Grundbegriffe [Fundamental Terms in Aesthetics]. Frankfurt, German: Band XX, J.B. Melzer Verlag. Belke, B., Leder, H., Harsanyi, G., & Carbon, C. C. (2010). When a Picasso is a Picasso : The entry point in the identification of visual art. Acta Psychologica, 133(2), 191 202. Gartus, A., & Leder, H. (2013). The small step towards asymmetry: Aesthetic judgment of broken symmetries. i-perception, 4, 361 364. Grammer, K., & Thornhill, R. (1994). Human (Homo sapiens) facial attractiveness and sexual selection: The role of symmetry and averageness. Journal of Comparative Psychology, 108(3), 233 242.

Leder et al. 113 H ofel, L., & Jacobsen, T. (2007). Electrophysiological indices of processing symmetry and aesthetics: A result of judgment categorization or judgment report? Journal of Psychophysiology, 21(1), 9 21. Jacobsen, T., & H ofel, L. (2002). Aesthetic judgments of novel graphic patterns: Analyses of individual judgments. Perceptual and Motor Skills, 95, 755 766. Leder, H., & Nadal, M. (2014). Ten years of a model of aesthetic appreciation and aesthetic judgments: The aesthetic episode Developments and challenges in empirical aesthetics. British Journal of Psychology, 105, 443 464. McManus, I. C. (2006). Measuring the culture of C.P. Snows two cultures. Empirical Studies of the Arts, 24(2), 219 228. Parsons, M. J. (1987). How we understand art. New York, NY: Cambridge University Press. Reber, R., Schwarz, N., & Winkielman, P. (2004). Processing fluency and aesthetic pleasure: Is beauty in the perceiver s processing experience? Personality and Social Psychology Review, 8, 364 382. Rhodes, G. (2006). The evolutionary psychology of facial beauty. Annual Review of Psychology, 57, 199 226. Snow, C. P. (1963). The two cultures: A second look. Cambridge: Cambridge University Press. Summers, D. (1996). Symmetry. In J. Turner (ed.), The dictionary of art (London) (Vol. XXX, p. 171). London: Macmillan. Thornhill, R., & Møller, A. P. (1997). Developmental stability, disease and medicine. Biological Reviews of the Cambridge Philosophical Society, 72(4), 497 548. Tinio, P. P. L., & Leder, H. (2009). Just how stable are aesthetic features? Symmetry, complexity and the jaws of massive familiarization. Acta Psychologica, 130, 241 250. Tinio, P. P. L., Gerger, G., & Leder, H. (2013). Birds of a feather... Generalization of facial structures following massive familiarization. Acta Psychologica, l 144(3), 463 471. doi: 10.1016/j.actpsy.2013.08.003. Voloshinov, A. (1996). Symmetry as a superprinciple of science and art. Leonardo, 29(2), 109 113. Weyl, H. (1952). Symmetry. Princeton, NJ: Princeton University Press. 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 institutions. 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.

114 Empirical Studies of the Arts 37(1) 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 (neurocognitive) psychology, including auditory processing, language, empirical aesthetics, 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.