Testing the aesthetic significance of the golden-section rectangle

The aesthetic significance of the golden-section rectangle was tested in two studies designed to obviate some of the criticisms of earlier experiments. In the first, employing the method of use, the mean sides-ratios of samples of paintings from five subject-matter categories (landscape, still life, head-and-shoulders portrait, upper-body portrait, full-length portrait) provided no evidence for the significance of the golden section. However, the sides ratio of portraits varied between categories in ways that were consistent with the requirements of the proportions of the subject matter. In the second study, using the method of production, participants produced the most pleasing four-sided shape, under four instruction conditions. Under a 'portrait painting' condition and a 'landscape painting' condition, the mean sides-ratios differed significantly from the golden section. Under two 'context free' geometric shape conditions--horizontal rectangle and vertical rectangle--the mean sides-ratio approximated the golden section. The results are discussed in terms of the methodological requirements for a valid test of the aesthetic significance of the golden section and the possibility that this ratio may indeed have special significance.     

Aesthetic preferences for the unity ratio resist the influence of color illusions

The addition of color produces an extension of previous research examining aesthetic preferences for proportional relationships. To date, most favored preferences have been for the unity (1:1) and golden section (1.618:1) ratios. Two experiments examined preferences in and assessed the accuracy of areajudgments for divided figures that varied in saturation contrast and were presumed to present a complementary color illusion. Regardless of colors, saturation contrast, direction of division, or area-to-area ratio, participants were accurate in locating the boundary between the two areas of the divided figure, and preferences for the unity ratio dominated as the most preferred ratio. There was no notable interest in the golden section ratio. Looking at the world through colored glasses seems not to interfere with a preference for symmetry, as produced by the unity ratio.     

Letters of Galileo's Daughter: A Historical Application of the Golden Section Hypothesis

The golden section has been shown to be a robust feature of the connotative structure of repertory grids. This article extends the research with repertory grids by providing an analysis of the connotative structure of a historical collection of 124 letters written to Galileo by his eldest daughter, Suor Maria Celeste. I found that the mean level of positive connotation in the letters is quite close to the golden section. This result suggests that the golden section is an underlying connotative feature of the letters Maria Celeste wrote to Galileo, and it provides further support for the golden section hypothesis that the construing person strikes a balance between negative and positive experiences in which negative experiences are focal relative to a background of positive experiences.     

On Runco's Problem Finding,Problem Solving,and Creativity

The relative significance of the "golden section" (? 0.618) and other notable proportions was investigated using a new unobtrusive methodology, a modified Fechnerian method of production. Fourteen professional painters each sketched under controlled conditions--"veridically, accurately, and realistically" (but without there being any mention of proportions)--27 complex stimuli presented as slides, thus producing a total of 378 sketches. The stimuli in the slides were (a) vase cutouts of various proportions placed in a mantelpiece context and (b) paintings by Kodama, Mondrian, and Whistler. The golden section and other significant and control proportions (a total of 120 occurrences) were identified beforehand by the researcher in the 27 stimuli. The 378 painters' sketches were subsequently measured by the researcher and two assistants to determine the accuracy with which the various proportions had been reproduced by the painters (a grand total of 1680--14 x 120--possible occurrences). The overall accuracy of rendering the proportions was found to be low for the vases and Kodama's paintings, but increased considerably for the Whistlers and Mondrians. As predicted, the accuracy of rendering the golden section increased from the vases to the Kodamas to the Whistlers and Mondrians. For the latter two, the golden section was in fact the most accurately rendered proportion, followed by 1.00 (found, for example, in the square and circle). The golden section is clearly important in art and to artists, but both its use and detection are subtle and must be pursued with great analytic care. The use of professional artists as informants and research participants may be of considerable help.     

The grammar of aesthetic intuition: on Ernst Cassirer’s concept of symbolic form in the visual arts

This paper provides a précis of Ernst Cassirer’s concept of art as a symbolic form. It does so, though, in a specific respect. It points to the fact that Cassirer’s concept of “symbolic form” is two-sided. On the one hand, the concept captures general cultural phenomena that are not only meaningful but also manifest the way man makes sense of the world; thus myth, religion, and art are considered general symbolic forms. On the other hand, it captures the formal structures and semiotic tools thanks to which meaning is constructed within each general symbolic form (Cassirer called these structures “modes of objectivation”); thus, in art, perspective or the golden section are well-known examples of symbolic forms, now in a narrow sense, i.e. they are means to configure parts into an organized, meaningful whole. The paper will comment on art along both these two dimensions, but its main goal is to provide with concrete examples of aesthetic symbolic forms in the narrow sense in order to show how conceptual meaning can be inscribed in the space of aesthetic intuition.     

Affective Balance in the Construal of Activities

This study serves to extend the range of convenience of the golden section hypothesis by applying it to the construal of activities. Participants rated a set of leisure, work, and personal care activities on the basis of a series of bipolar constructs. The mean level of positive affect in participants’ construal of activities was remarkably close to the golden section. This finding is interpreted in light of Kelly's sociality corollary.     

Golden section: Preferred figural orientationI

A hypothesis that the shape of the binocular visual field determines the supposed preference for rectangles possessing dimensions similar to those of the golden section was tested by having Ss draw pleasing rectangles. The results indicated that rectangles were oriented in correspondence with the shape of the visual field but there was, generally, a failure to obtain ratios approximating the golden section.     

Golden section: Preferred figural orientation

A hypothesis that the shape of the binocular visual field determines the supposed preference for rectangles possessing dimensions similar to those of the golden section was tested by havltlg Ss draw pleasing rectangles. The results iudicated that rectangles were oriented in correspondence with the shape of the visual field but there was, generally, a failure to obtain ratios approximating the golden section.     

The golden section and American psychology, 1892–1938

The golden section has been said by many to be the most beautiful proportion. Fechner was the first to investigate it experimentally, and several late‐nineteenth‐ and early‐twentieth‐century American psychologists followed up on his work. Among these were four prominent names: Lightner Witmer (1867–1956), Edward L. Thorndike (1874–1949), Robert S. Woodworth (1869–1962), and Robert M. Ogden (1877–1959). Why did such well‐known psychologists bother with the golden section? In attempting to answer this question we discovered that the golden section was surprisingly well known during this period, not only in psychology but also in advertising and design. It would have been entirely congruent with their stature for prominent psychologists to take an interest in it. © 2010 Wiley Periodicals, Inc.     

Documenting and explaining the common AAB pattern in music and humor: establishing and breaking expectations

The AAB pattern consists of two similar events followed by a third dissimilar event. The prevalence of this pattern in the aesthetic domain may be explained as violation of expectation: A minimum of two iterations is required to establish a repetitive pattern; once established, it is most efficient to promptly violate the expected continuance of the pattern to produce the maximal aesthetic effect. We demonstrate the prevalence of this pattern (in comparison to AB or AAAB) in a representative sample of a variety of musical genres and in a representative sample of repetitive genre of jokes. We also provide experimental evidence that the AAB pattern in jokes is maximally effective in producing a humor response in participants.     

Figural preference and the visual field

Three experiments tested a hypothesis that the shape and relative dimensions of the binocular visual field determine a preference for rectangles possessing dimensions similar to those of the golden section. The results were that Ss horizontally oriented the rectangles they had drawn in correspondence with the shape of the binocular visual field but when Ss chose the most pleasing rectangles there was no significant preference for rectangles whose long side was horizontal. For all experiments there was little preference for rectangles whose ratio of short to long side approximated the golden section. There was some evidence that the placement of the rectangles with respect to the background affects preference.     

Narrative Representation and Phenomenological Knowledge

The purpose of this paper is to demonstrate that narrative representations can provide knowledge in virtue of their narrativity, regardless of their truth value. I set out the question in section 1, distinguishing narrative cognitivism from aesthetic cognitivism and narrative representations from non-narrative representations. Sections 2 and 3 argue that exemplary narratives can provide lucid phenomenological knowledge, which appears to meet both the epistemic and narrativity criteria for the narrative cognitivist thesis. In section 4, I turn to non-narrative representation, focusing on lyric poetry as presenting a disjunctive objection: either lucid phenomenological knowledge can be reduced to identification and fails to meet the epistemic criterion, or lucid phenomenological knowledge is provided in virtue of aesthetic properties and fails to meet the narrativity criterion. I address both of these problems in sections 5 and 6, and I close with a tentative suggestion as to how my argument for narrative cognitivism could be employed as an argument for aesthetic cognitivism.     

Note on the golden section

Abstract.— Lines of different lengths were offered to subjects. One half of ten lines were presented horizontally; the other vertically. It was found that two groups of subjects, graduate and undergraduate psychologists and art students at the average produced a ratio close to the ratio the "golden section", which is a controversy in aesthetics.     

From “Einfühlung” to empathy: exploring the relationship between aesthetic and interpersonal experience

Is there a relationship between aesthetic and interpersonal experience? This question is motivated not only by the fact that historically experiences of both kinds have often been accounted for in terms of “empathy”, the English translation of the German term “Einfühlung”, but also by the fact that some contemporary theories refer to mechanisms underlying both aesthetic and interpersonal experience. In this Editorial introducing the special section titled “From ‘Einfühlung’ to empathy: exploring the relationship between aesthetic and interpersonal experience”, we briefly sketch these two motivations and the relationship between the different mechanisms that have been associated with both aesthetic and interpersonal experience.     

Whitehead,Confucius, and the aesthetics of virtue

The most constructive response to the crisis in moral theory has been the revival of virtue ethics, an ethics that has the advantages of being personal, contextual, and, as this paper will argue, normative as well. The first section offers a general comparative analysis of Confucian and Whiteheadian philosophies, showing their common process orientation and their views of a somatic self united in reason and passion. The second section contrasts rational with aesthetic order, demonstrating a parallel with analytic and synthetic reason, and showing that rule‐based ethics comes under the former and virtue ethics under the latter. The third and final section discusses a Confucian–Whiteheadian aesthetics of virtue, focusing on love as the comprehensive virtue. The principal goal of the paper is to propose that an appropriation of Confucian virtue ethics will enhance the otherwise slow development of a Euro–American process ethics.     

The golden section and an algebraic model of ethical cognition

In experimental investigations related to Kelly's theory of constructs (1955. The psychology of personal constructs. New York: Norton) a special constant was discovered. It was found that subjects on the average choose a positive over a negative pole with the probability 0.62. (Adams-Webber and Benjafield 1973. Canadian Journal of Behavioral Science5, 234–241). The same constant was also found in other experiments related to the choice of elements marked “good” and “bad.” Benjafield and Adams-Webber (1976. British Journal of Psychology67, 11–15) hypothesized that the precise value of this constant coincides with “golden section” ≈0.6180. In this paper it is shown that if we suppose that the subjects actualize mechanisms of choice described by the algebraic model of ethical cognition (which was constructed without any relation to the constant 0.62), then the existence of this constant is mathematically explained. Under very broad assumptions its value is 0.625, and under more constrained conditions it is equal to the golden section ratio precisely.     

The Relationship Between Visual Illusion and Aesthetic Preference – an Attempt to Unify Experimental Phenomenology and Empirical Aesthetics

Experimental phenomenology has demonstrated that perception is much richer than stimulus. As is seen in color perception, one and the same stimulus provides more than several modes of appearance or perceptual dimensions. Similarly, there are various perceptual dimensions in form perception. Even a simple geometrical figure inducing visual illusion gives not only perceptual impressions of size, shape, slant, depth, and orientation, but also affective or aesthetic impressions. The present study reviews our experimental phenomenological work on visual illusion and experimental aesthetics, and examines how aesthetic preference is influenced by stimulus factors determining visual illusions including anomalous surface and transparency as well as geometrical illusion. Along with line figures producing geometrical illusions, illusory surface figures inducing neon color spreading and transparency effects were used as test patterns. Participants made both of psychophysical judgments and of aesthetic judgments for the same test pattern. Both of geometrical illusions and aesthetic preferences were found to change similarly as a function of stimulus variables such as the number of filling lines and the size ratio of the inner and outer figural components. Also, following specific stimulus variables such as lightness contrast ratio and spatial interval between inducing figural elements (so called ``packmen''), strong effects of color spreading and transparency were accompanied with strong preferences. It seems that the paradigm to investigate aesthetic phenomena along with perceptual dimensions is useful to bridge the gap between experimental phenomenology and experimental aesthetics.     

Physical and spiritual education within the framework of pure life

This paper aims at showing the dimensions of spirituality in childhood education by suggesting a new analysis of the concept of ‘pure life’ used in the Qur’an. Putting spirituality in the framework of the pure life provides us with a rich framework in dealing with spirituality as the latter will be extended to all dimensions of a life. In the first section of the paper, the pure life is analysed in terms of different dimensions of body, thought, inclinations, will, action and aesthetic taste. Then, the requirements of this framework are discussed for spirituality. In the final section of the paper, the implications for spiritual education in the childhood are derived.     

The Aesthetic Preference for Nature Sounds Depends on Sound Object Recognition

People across the world seek out beautiful sounds in nature, such as a babbling brook or a nightingale song, for positive human experiences. However, it is unclear whether this positive aesthetic response is driven by a preference for the perceptual features typical of nature sounds versus a higher‐order association of nature with beauty. To test these hypotheses, participants provided aesthetic judgments for nature and urban soundscapes that varied on ease of recognition. Results demonstrated that the aesthetic preference for nature soundscapes was eliminated for the sounds hardest to recognize, and moreover the relationship between aesthetic ratings and several measured acoustic features significantly changed as a function of recognition. In a follow‐up experiment, requiring participants to classify these difficult‐to‐identify sounds into nature or urban categories resulted in a robust preference for nature sounds and a relationship between aesthetic ratings and our measured acoustic features that was more typical of easy‐to‐identify sounds. This pattern of results was replicated with computer‐generated artificial noises, which acoustically shared properties with the nature and urban soundscapes but by definition did not come from these environments. Taken together, these results support the conclusion that the recognition of a sound as either natural or urban dynamically organizes the relationship between aesthetic preference and perceptual features and that these preferences are not inherent to the acoustic features. Implications for nature's role in cognitive and affective restoration are discussed.     

Interpreting nature

We assume that knowledge arises through an interpretation of phenomena and ask what type of process is involved. To this end, on the basis of a theory of cognition and a Peircean theory of signs, we introduce a process model of interpretation and show the existence of a relation of our model with Platonic solids and the golden section. The model’s relation with syllogistic, hence the possibility of a relation between phenomena and reasoning, implies that knowledge can be inevitable.