The golden ratio as an ecological affordance leading to aesthetic attractiveness

The golden ratio as an ecological affordance leading to aesthetic attractiveness. Daniela De Bartolo,Maria De Luca,Gabriella Antonucci,Stefan Schuster,Giovanni Morone,Stefano Paolucci,Marco Iosa. PsyCh Journal, December 23 2021. https://doi.org/10.1002/pchj.505

Abstract: The golden ratio (GR) is an irrational number (close to 1.618) that repeatedly occurs in nature as well as in masterpieces of art. The GR has been considered a proportion perfectly representing beauty since ancient times, and it was investigated in several scientific fields, but with conflicting results. This study aims at investigating if this proportion is associated with a judgment of beauty independently of the type of the stimulus, and the factors that may affect this aesthetic preference. In Experiment 1, an online psychophysical questionnaire was administered to 256 volunteers asked to choose among three possible proportions between the parts of the same stimulus (GR, 1.5, and 1.8). In Experiment 2, we recorded eye movements in 15 participants who had to express an aesthetic judgment on the same stimuli of Experiment 1. The results revealed a slight overall preference for GR (53%, p < .001), with higher preferences for stimuli representing humans, anthropomorphic sculptures, and paintings, regardless of the cultural level. In Experiment 2, a shorter dwell time was significantly associated with a better aesthetic judgment (p = .005), suggesting the possibility that GR could be associated with easier visual processing, and it could be hence considered as a visual affordance.

DISCUSSION

The main purpose of this study was to establish whether the presence of the GR may favor the perception of beauty in aesthetic judgments and which factors might influence it, clarifying the main controversies found in previous studies (Benjafield & Adams-Webber, 1976; Berlyne, 1970; Boselie, 1984; Davis & Jahnke, 1991; Di Dio et al., 2007; Fechner, 1865; Green, 1995; Witmer, 1893; Zeising, 1855).

First of all, we found a slight but significant preference for GR, but its entity depended on the category of the stimulus. This preference was statistically significant for human photographs, in both the experiments, and for sculptures and paintings in Experiment 1 (being only close to a significant threshold for virtual humanoid figures).

Conversely, we did not find a significant preference for GR in geometric stimuli. These findings are in line with some previous results (Di Dio et al., 2007; Di Dio et al., 2011) but in contrast with other studies finding a preference for GR also for geometric figures (Fechner, 1865; Russell, 2000). There are many possible explanations for the high variability among studies related to the possible preference for golden rectangles. First of all, it could be related to different methodologies related to how central tendency was computed: by means of mean, median, or modal values, with the GR that could emerge as mean value even if it was not the most frequent choice, as also previously suggested (Green, 1995). Indeed, in contrast to previous research on lines and geometric shapes' aesthetic preference, recent studies used more ecological experimental paradigms including natural and anthropomorphic figures, highlighting that geometric simple stimuli could be poorly attractive for our culture (Di Dio et al., 2007; Di Dio et al., 2011). Furthermore, with respect to the study of Fechner (1865) and successive ones, subjects are now more often exposed to rectangular shapes different from GR, such as those of television screens, monitors, or smartphones having proportions closer to 1.8 (16:9 = 1.78, or 1980:1020 pixels = 1.78), or also paper sheets closer to 1.5 (A4: 1.41).

The GR is often present in many natural stimuli (Iosa et al., 2018). Indeed, subjects might prefer stimuli recognized as original, as in our study occurred for human photographs, with GR preferred for stimuli originally in GR (oGR vs. noGR), despite participants not knowing which was the original stimuli.

The golden section was conceivably identified by anatomical Greek investigations in the 5th century BCE (as in the canon of Protagoras) with the idea to reproduce the harmony of the human body in the anthropomorphic sculptures and then in other artworks (Haines & Davies, 1904; Iosa et al., 2018). It should be considered that anthropomorphic stimuli have their own symmetry given by the right–left relationship along the horizontal axis, whereas the golden section defines the vertical harmony of a standing human being. Hence, the GR preference could occur more frequently on the vertical than horizontal axis. Despite our studies not investigating this aspect, it should be noted that the rectangles of Fechner (1890) had the longer segment along the vertical axis, whereas in our and other studies (McManus, 1980; Russell, 2000) the longer dimension of rectangles and that of the bisected line was the horizontal one.

Despite this, Renaissance artists provided a horizontal division of their paintings according to the golden section, such as in The Flagellation of Christ and The Creation of Adam (de Campos et al., 2015), with these stimuli that can be mentally divided into two parts and visually explored horizontally. A slight preference for GR was found in our paintings (54.6%), quite independent if the original stimuli was or not in golden proportion. Wölfflin (1994) questioned the preference for GR when observing an abstract rectangle because it should be related to a mental comparison of the lengths of basis, height, and their sum, again claiming that GR may “present an average measure conforming to man”.

This hypothesis put in relationship the GR with “objective beauty”, because it was related to a harmonic property intrinsic to the stimuli, but there is also an alternative hypothesis, reported in the so-called constructal theory, referring to “perceptual beauty” suggesting that the preference for GR was related to the hypothesis that visual system scans the world approximatively in golden proportion (Bejan, 2009). Di Dio et al. (2007) identified also the “subjective beauty” driven by one's own emotional experiences and related to the activation of the amygdala, whereas the objective beauty related to the intrinsic properties of the stimulus is based on a joint activation of sets of cortical neurons of lateral occipital cortex, parietal cortex, and anterior insula. All these processes could be not mutually exclusive and cohabit, forming our sense of beauty.

This integrated approach works even better considering GR as an affordance, and hence a property intrinsic to the stimulus that is recognized by our visual system and favoring the visual process. In fact, Gibson proposed the theory of affordances, suggesting that subjects noted the features of a stimulus that may constitute functional relations between the stimulus and the perceiver (Gibson, 2014; Lobo et al., 2018). The abstraction of geometric figures and even of virtual humanoids might hence have mitigated this preference, in accordance with the ecological approach suggested by Gibson for the visual system (Gibson, 2014). The cultural level of subjects did not seem to influence the general preference for GR. This result could be read in conjunction with previous findings that the aesthetic judgment of beauty was mainly independent by sociocultural factors, intelligence, personality, and age (Eysenck & Tunstall, 1968). However, in our study, culture was assessed in terms of scholarly level, but different cultures were not analyzed, and further studies could investigate the preferences for GR comparing subjects of Western versus Eastern Countries.

When we analyzed single categories of stimuli, the preference for GR in human photographs and sculptures was related to art knowledge. These two types of stimuli have in common the same criterion for GR: the ratio between the distance of the navel from the ground and that between the navel and the top of the head. Virtual humanoids had the same proportion, but the judgments about them seemed to be not affected by cultural level. Probably, this judgment mainly depended on the realism of their faces, as shown by the long time spent by observers looking at the virtual faces in Experiment 2. Furthermore, being human bodies on average in GR, humans might have reflected this proportion in the concept of beauty, and it led to the adoption of this parameter also in some classical artistic masterpieces, starting from anthropomorphic sculptures (Hernández-Castro, 2007).

Human beings may associate, more or less consciously, the concept of beauty to their own body proportions (Burrell, 1932), as is the case with the preference of symmetric figures that could be related to the symmetry of the human body (Evans et al., 2012; Huang et al., 2018; Mühlenbeck et al., 2016). As well as symmetry being considered as an affordance in accordance with the ecological approach suggested by Gibson for vision (2014), the GR that can be considered as a symmetry of higher order (Liu & Sumpter, 2018) could also be another visual natural affordance, preferred by humans and put in artworks by artists.

In our study, the proposed paintings have the longest dimension horizontal; indeed, the golden ideal division was along the horizontal axis. A slight preference (54.6%) was found for GR, quite independently if the stimulus was or not originally in GR. With respect to the geometric figures, participants could perceive the harmony of a scene ideally divided in two parts according to the GR, even if this scene is represented with the horizontal length longer than the vertical. Considering that for symmetry there is a perceptual sensitivity to the orientation of the stimulus (1905; Fisher & Bornstein, 1982; Mach, 1883), and that there are no studies that directly investigated the relationship between GR and the orientation of the stimulus, future studies should investigate whether there is a dependence on the orientation with which it is presented the stimuli and the possible preference for GR.

Despite our study lacking this direct comparison, the bimodal distribution of dwell time found in Experiment 2 for human figures for which the golden section regards the vertical axis, are similarly replicated for the paintings in which it regards the horizontal axis. In general, the results of Experiment 2 were found in accordance with those of Experiment 1 and seem to confirm the hypothesis of GR as an affordance. In Experiment 2, we found no significant differences between the three proportions related to the total exploration time, but also some significant differences with respect to specific areas of interest. Further, analyzing the dwell times, significant differences among GR, R1.5, and R1.8 were found regarding the exploration of the AOIm, that is, the specific AOI where the image modification was performed. A significant negative correlation was found between the AOIm dwell time and the aesthetic judgment only for GR stimuli. This could indicate that the subject does not need to observe that area for too long to judge it as beautiful if it is in golden proportion.

Despite previous studies showing that the aesthetic appreciation of beauty is not based on an “immediate” response and may even require more time to discriminate the main characteristics of the stimuli (Bar et al., 2006; Evans et al., 2012; Huang et al., 2018; Liu & Sumpter, 2018; Mühlenbeck et al., 2016), the presence of GR may have reduced this time because it was quickly recognized and preferred by the observers. So, hypothesizing GR as an affordance, it may be implicitly recognized, facilitating the processing of visual information relating to a stimulus, making aesthetic experience more fluent, in accordance with the “processing fluency theory” for which that fluency could contribute to the pleasantness of the experience associated with the perception of beauty (Witmer, 1893).

It is noteworthy that the GR divides the human stature in a region roughly close to the body center of mass and could even play an important role in human motor behavior (Iosa et al., 2018). It should be noted that the exposition to GR does not regard only the visual system: GR was recently found as a harmonic feature of voluntary and involuntary rhythmic human movements, such as cardiac (Yetkin et al., 2013), respiratory (Iared et al., 2016), and walking rhythms (Iosa et al., 2013; Iosa et al., 2016; Iosa et al., 2019; Serrao et al., 2017). In fact, walking performed with GR between gait phases allows humans to harmonize locomotor acts (Iosa et al., 2016; Iosa et al., 2019), thus reducing energy expenditure (Serrao et al., 2017). Furthermore, it has been demonstrated that perception of internal gait rhythm may be modulated (De Bartolo, Belluscio, et al., 2020a) and that the harmonic structure of music can ameliorate harmony of walking in patients with Parkinson's disease (De Bartolo, Morone, et al., 2020b), especially if acoustic stimulation presents GR harmony (Belluscio et al., 2021), confirming the possibility to consider GR as an affordance to exploit by the observer/listener/acting subject.

However, we must bracket this proposal with some caveats. The main limitation of Experiment 1 was the online administration of the questionnaire that did not allow for controlling some variables such as the eyes' positions with respect to the screen, the response time of the subjects, or their attention level. For example, the questionnaire was formed by 51 items, and it might have led to a progressive physiological decline in the participants' attention due to fatigue.

However, the online administration allowed for enrolling a wide sample of subjects (N = 256) that could have attenuated the above-mentioned limits. Experiment 2 was performed in more controlled conditions, and its results confirmed those obtained in Experiment 1. Subjects were required to judge the most liked stimulus, without any investigations related to the judgment of naturalness, so caution is needed in discussing the role of naturalness of stimuli and its relationship to the preference for stimuli originally or not in GR.

Finally, in our study we did not manipulate canonical orientation of stimuli, so we included only vertical stimuli for anthropomorphic figures and horizontal for images of artworks. Further studies should investigate the possible differences in the GR preferences for vertical versus horizontal stimuli, and these results could contribute to understand the relationship between GR and visual scan process.