From Thales and Pythagoras to companion rectangles

In empirical art research, understanding how viewers judge visual artworks as beautiful is often explored through the study of attributes—specific inherent characteristics or artwork features such as color, complexity, and emotional expressiveness. These attributes form the basis for subjective evaluations, including the judgment of beauty. Building on this conceptual framework, our study examines the beauty judgments of 54 Western artworks made by native Japanese and German speakers, utilizing an extreme randomized trees model—a data-driven machine learning approach—to investigate cross-cultural differences in evaluation behavior. Our analysis of 17 attributes revealed that visual harmony, color variety, valence, and complexity significantly influenced beauty judgments across both cultural cohorts. Notably, preferences for complexity diverged significantly: while the native Japanese speakers found simpler artworks as more beautiful, the native German speakers evaluated more complex artworks as more beautiful. Further cultural distinctions were observed: for the native German speakers, emotional expressiveness was a significant factor, whereas for the native Japanese speakers, attributes such as brushwork, color world, and saturation were more impactful. Our findings illuminate the nuanced role that cultural context plays in shaping aesthetic judgments and demonstrate the utility of machine learning in unravelling these complex dynamics. This research not only advances our understanding of how beauty is judged in visual art—considering self-evaluated attributes—across different cultures but also underscores the potential of machine learning to enhance our comprehension of the aesthetic evaluation of visual artworks.

Silicon-based materials still dominate the current semiconductor industry for the foreseeable years such that it is needed in continuously developing the related advanced manufacturing technologies. For the abrasive precision lapping of single-crystal silicon wafers, the surface form accuracy is very important which can significantly improve its efficiency and reduce the cost in the following ultra-precision polishing process. In this study, a novel driving system is proposed in the single-side planetary lapping process that could realize the irrational rotation speed ratio of the lapping plate to the workpiece, and it is found from the numerical qualitative and quantitative analysis that the uniformity of the particle trajectories moving on the target surface has been significantly improved using the irrational rotation speed ratio and hence resulting in the higher surface form accuracy than that driven by the rational rotation speed ratio. Moreover, an in-house developed irrational rotation speed ratio driving system has been designed for the experimental study, and it is found that the effect of the rational and irrational rotation speed ratios on surface roughness is not significant, while all the five essential values related to the surface form accuracy are better under the rotation speed ratio of i = 1.0772… than that under the rotation speed ratio of i = 1, which demonstrates that the irrational rotation speed ratio driving system has the advantage of being able to obtain a good surface form accuracy and agrees well with the numerical simulation results.

Using structural geometric arguments, Whiteley showed that a line drawing is a correct projection of a spherical polyhedron if and only if it has a cross-section compatible with it. We here enlarge the class of drawings to which this test applies, including those of polyhedral disks, possibly with perforations. This extension is helpful, as it makes the test applicable to verify and reconstruct drawings from usual scenes with opaque objects.The presented results rely on geometric constructions, thus offering an alternativeapproach to line drawing interpretation, complementary to the algebraic-combinatorial treatment given in the classic work by Sugihara.

Through the manipulation of color and form, visual abstract art is often used to convey feelings and emotions. Here, we explored how colors and lines are used to express basic emotions and whether non-artists express emotions through art in similar ways as trained artists. Both artists and non-artists created abstract color drawings and line drawings depicting six emotions (i.e., anger, disgust, fear, joy, sadness, and wonder). To test whether people represented basic emotions in similar ways, we computationally predicted the emotion of a given drawing by comparing it to a set of references created by averaging across all other participants’ drawings within each emotion category. We found that prediction accuracy was higher for color drawings than line drawings and higher for color drawings by non-artists than by artists. In a behavioral experiment, we found that people (N = 242) could also accurately infer emotions, showing the same pattern of results as our computational predictions. Further computational analyses of the drawings revealed systematic use of certain colors and line features to depict each basic emotion (e.g., anger is generally redder and more densely drawn than other emotions, sadness is more blue and contains more vertical lines). Taken together, these results imply that abstract color and line drawings are able to convey certain emotions based on their visual features, which are also used by human observers to understand the intended emotional connotation of abstract artworks.

Abstracts from the Spectra 2018 Symposium Part 3: <i>Nano-Optics</i>

A driven quantum system was recently studied in the context of nonequilibrium phase transitions and their responses. In particular, for a periodically driven system, its dynamics are described in terms of the multidimensional Floquet lattice with a lattice size depending on the number of driving frequencies and their rational or irrational ratio. So far, for a multifrequency driving system, the energy pumping between the sources of frequencies has been widely discussed as a signature of topologically nontrivial Floquet bands. However, the unique edge modes emerging in the Floquet lattice have not been explored yet. Here, we discuss how the edge modes in the Floquet lattice are controlled and result in the localization at particular frequencies, when multiple frequencies are present and their magnitudes are commensurate values. First, we construct the minimal model to exemplify our argument, focusing on a two-level system with two driving frequencies. For the strong frequency limit, one can describe the system as a quasi-one-dimensional Floquet lattice where the effective hopping between the neighboring sites depends on the relative magnitudes of the potential for two frequency modes. With multiple driving modes, nontrivial Floquet lattice boundaries always exist from controlling the frequencies, and this gives rise to states that are mostly localized at such Floquet lattice boundaries, i.e., particular frequencies. We suggest the time-dependent Creutz ladder model as a realization of our theoretical Hamiltonian and show the emergence of controllable Floquet edge modes.

Adriaan van Roomen published an outline of what he called a Mathesis Universalis in 1597. This earned him a well-deserved place in the history of early modern ideas about a universal mathematics which was intended to encompass both geometry and arithmetic and to provide general rules valid for operations involving numbers, geometrical magnitudes, and all other quantities amenable to measurement and calculation. ‘Mathesis Universalis’ (MU) became the most common (though not the only) term for mathematical theories developed with that aim. At some time around 1600 van Roomen composed a new version of his MU, considerably different from the earlier one. This second version was never effectively published and it has not been discussed in detail in the secondary literature before. The text has, however, survived and the two versions are presented and compared in the present article. Sections 1–6 are about the first version of van Roomen’s MU the occasion of its publication (a controversy about Archimedes’ treatise on the circle, Sect. 2), its conceptual context (Sect. 3), its structure (with an overview of its definitions, axioms, and theorems) and its dependence on Clavius’ use of numbers in dealing with both rational and irrational ratios (Sect. 4), the geometrical interpretation of arithmetical operations multiplication and division (Sect. 5), and an analysis of its content in modern terms. In his second version of a MU van Roomen took algebra into account, inspired by Viete’s early treatises; he planned to publish it as part of a new edition of Al-Khwarizmi’s treatise on algebra (Sect. 7). Section 8 describes the conceptual background and the difficulties involved in the merging of algebra and geometry; Sect. 9 summarizes and analyzes the definitions, axioms and theorems of the second version, noting the differences with the first version and tracing the influence of Viete. Section 10 deals with the influence of van Roomen on later discussions of MU, and briefly sketches Descartes’ ideas about MU as expressed in the latter’s Regulae.

Re: Rational and irrational ratios.

Rational and irrational ratios.

Treats ray geometry of microwave antenna and optical systems through a unique approach using geometrical constructions. Discusses mirrors, lenses, and rays in non-uniform media. Develops two new geometrical methods that avoid the usual ray tracing formula for the development of ray patterns, and explains a new theorem of rays in non-uniform media. Extensively illustrated with line drawings.

Impossible objects, geometric constructions that humans can perceive but that cannot exist in real life, have been a topic of intrigue in visual arts, perception, and graphics, yet no satisfying computer representation of such objects exists. Previous work embeds impossible objects in 3D, cutting them or twisting/bending them in the depth axis. Cutting an impossible object changes its local geometry at the cut, which can hamper downstream graphics applications, such as smoothing, while bending makes it difficult to relight the object. Both of these can invalidate geometry operations, such as distance computation. As an alternative, we introduce Meschers, meshes capable of representing impossible constructions akin to those found in M.C. Escher's woodcuts. Our representation has a theoretical foundation in discrete exterior calculus and supports the use-cases above, as we demonstrate in a number of example applications. Moreover, because we can do discrete geometry processing on our representation, we can inverse-render impossible objects. We also compare our representation to cut and bend representations of impossible objects.

This article challenges the assumption in a classical sociology of art that artworks are created in the artist’s studio as independent and self-sufficient objects. Given that artistic production merges with exhibition making in contemporary art, I argue that the production of artworks needs to be situated in the exhibition space. In this institutional and physical environment, a set of scenographic principles dominate. Scenography is an ideology and method for exhibition making that emphasises the audience’s experience of the exhibition as a coherent entity. In the exhibition context, therefore, artworks are produced as an integral part of the scenography. Drawing upon six cases of solo exhibitions in museums and galleries, I reveal how the material, conceptual, and experiential features of artworks are shaped by scenographic considerations. The six cases also demonstrate the variations in the production of contemporary art. This article further develops the sociology of art in three ways. First, I show a middle way between the classical sociology of art and the recent material turn in cultural sociology. While the former explains artworks as social products but often fails to show the direct impact of social factors on features of artworks, the latter prioritises the agency of artworks qua artistic features but take these as given. Through the concept of scenography, I explain the social genesis of artistic features without prioritising human or non-human actors. Second, I call more attention to the dialogue with art history, especially its turns towards exhibitions for apprehending new developments in art. Third, the hybrid practices in visual art extend our understanding of artistic mediation as art itself, which becomes more applicable to different genres of art.

The Aboriginal Story of Burke and Wills is the first major study of Aboriginal associations with the Burke and Wills expedition of 1860–61. A main theme of the book is the contrast between the skills, perceptions and knowledge of the Indigenous people and those of the new arrivals, and the extent to which this affected the outcome of the expedition. The book offers a reinterpretation of the literature surrounding Burke and Wills, using official correspondence, expedition journals and diaries, visual art, and archaeological and linguistic research – and then complements this with references to Aboriginal oral histories and social memory. It highlights the interaction of expedition members with Aboriginal people and their subsequent contribution to Aboriginal studies. The book also considers contemporary and multi-disciplinary critiques that the expedition members were, on the whole, deficient in bush craft, especially in light of the expedition’s failure to use Aboriginal guides in any systematic way. Generously illustrated with historical photographs and line drawings, The Aboriginal Story of Burke and Wills is an important resource for Indigenous people, Burke and Wills history enthusiasts and the wider community. This book is the outcome of an Australian Research Council project.

After a long and brave battle with a serious illness, our dear friend and colleague Slavik Jablan passed away on 26 February 2015. [...]

A novel approach to the analysis of modulation processes in power convertors is developed. The single harmonic components of the modulator output spectrum are given in terms of series with fast convergence rate. The method set forth is based on the theory of the Kapteyn series. Both the cases of rational and irrational frequency ratio are treated and some typical peculiarities of the modulation processes are stressed.