Impossible Figures

This essay examines three documentary depictions of gay Palestinians in Israel and the West Bank. These documentaries often problematically assume a fundamental incompatibility between gay identities and Arab and Palestinian cultures, thereby, first, placing their subjects in the position of choosing between living in Palestine/Israel and living as openly gay; and second, producing a narrative of impossibility, in which Palestinian and gay identities can only exist in irresolvable conflict. However, Paul also argues that critical reactions to these films, as well as some broader scholarly debates over sexual identities and practices in the Arab world, also reinforce this narrative of impossibility in a way that makes little room for the diverse lived experiences of gay Palestinians. In order to move beyond this narrative, Paul rereads these documentaries with an emphasis on the quotidian experiences of the films’ gay Palestinian subjects. Through attention to queerness as a spatial experience, he analyzes the ways in which these characters inhabit urban spaces in Israel and Palestine in ways that contest and disorient dominant narratives about these spaces. Paul concludes that a focus on such experiential moments reveals queer lives that are exuberant and subversive, and he shows the necessity of moving beyond narratives of impossibility in studies of sexuality in the Middle East.

“Impossible” Somatosensation and the (Ir)rationality of Perception

Impossible figures represent the world in ways it cannot be. From the work of M. C. Escher to any popular perception textbook, such experiences show how some principles of mental processing can be so entrenched and inflexible as to produce absurd and even incoherent outcomes that could not occur in reality. Surprisingly, however, such impossible experiences are mostly limited to visual perception; are there “impossible figures” for other sensory modalities? Here, we import a known magic trick into the laboratory to report and investigate an impossible somatosensory experience—one that can be physically felt. We show that, even under full-cue conditions with objects that can be freely inspected, subjects can be made to experience a single object alone as feeling heavier than a group of objects that includes the single object as a member—an impossible and phenomenologically striking experience of weight. Moreover, we suggest that this phenomenon—a special case of the size-weight illusion—reflects a kind of “anti-Bayesian” perceptual updating that amplifies a challenge to rational models of perception and cognition. Impossibility can not only be seen, but also felt—and in ways that matter for accounts of (ir)rational mental processing.

Illusory Planes in Fred Sandback’s Sculpture

A remarkable feature of artist Fred Sandback’s string constructions has often been noted: that the geometrical forms created with string have a strong planar feel. Phenomenologically, the spaces between the strings are perceived as planes with some substance. The illusion is amodally completed, as in the famous Kanizsa triangle, by minimal prompts, but in three dimensions. Instead of an illusory figure, then, Sandback creates illusory planes. By noting how the constructions are like “impossible” figures, we can see how bottom up and top down effects combine to complicate the illusion and the works become about the construction of space rather than its reification.

Contextuality Analysis of Impossible Figures

This paper has two purposes. One is to demonstrate contextuality analysis of systems of epistemic random variables. The other is to evaluate the performance of a new, hierarchical version of the measure of (non)contextuality introduced in earlier publications. As objects of analysis we use impossible figures of the kind created by the Penroses and Escher. We make no assumptions as to how an impossible figure is perceived, taking it instead as a fixed physical object allowing one of several deterministic descriptions. Systems of epistemic random variables are obtained by probabilistically mixing these deterministic systems. This probabilistic mixture reflects our uncertainty or lack of knowledge rather than random variability in the frequentist sense.

Principles of Three-Dimensional Computer Design for Understanding Impossible Figures

For a better understanding of the impossible figures, it is advisable to use modern technological means by which the design of the geometry of the models gives a complete understanding of how they are made. Computer-aided 3D design completely solves this problem. That is, on the one hand, the ultimate visual variant of impossible figures is created, on the other hand, there is the possibility for real manipulation, movement, rotation and other models of space. In this study, 3D models of impossible figures are fully constructed, which are applied in the educational process in order to develop logical thinking. The steps of creating 3D geometry using open source software Blender 3D are described in details.

Unveiling the Secrets of Escher’s Lithographs

An impossible structure gives us the impression of looking at a three-dimensional object, even though this object cannot exist, since it possesses parts that are spatially non-connectable, and are characterized by misleading geometrical properties not instantly evident. Therefore, impossible artworks appeal to our intellect and challenge our perceptive capacities. We analyzed lithographs containing impossible structures (e.g., the Necker cube), created by the famous Dutch painter Maurits Cornelis Escher (1898–1972), and used one of them (The Belvedere, 1958) to unveil the artist’s hidden secrets by means of a discrete model of the human retina based on a non-uniform distribution of receptive fields. We demonstrated that the ability of Escher in composing his lithographs by connecting spatial coherent details into an impossible whole lies in drawing these incoherent fragments just outside the zone in which 3D coherence can be perceived during a single fixation pause. The main aspects of our paper from the point of view of image processing and image understanding are the following: (1) the peculiar and original digital filter to process the image, which simulates the human vision process, by producing a space-variant sampling of the image; (2) the software for the filter, which is homemade and created for our purposes. The filtered images resulting from the processing are used to understand impossible figures. As an example, we demonstrate how the impossible figures hidden in Escher’s paintings can be understood.

Architectural Perspective in Italian paintings of the 14th century

This paper discusses the system of the pictorial depth representation, typical for Giotto and other Italian artists of 14th century. Differing from the linear perspective, this system has a number of peculiar features, and its own consistent logic for the formation of pictorial space. The paper is especially focused on the contradictions of such a system, which lead to the appearance of impossible figures, and the ways in which the artists solved these difficulties.

Impossible Somatosensation

Impossible figures represent the world in ways it cannot be. From the work of M.C. Escher to any popular perception textbook, such experiences show how some principles of mental processing can be so entrenched and inflexible as to produce absurd and even incoherent outcomes that the perceiver knows cannot occur in reality. Surprisingly, however, such experiences have been conspicuously limited to visual perception; are there impossible experiences in other sensory modalities? Here, we modify a known conjurer’s trick to report the first impossible somatosensory experience — one that can be physically felt. We show that, even in full-cue conditions with objects that can be freely inspected, subjects can be made to experience a single object alone as feeling heavier than a group of objects that includes the single object as a member — an impossible and phenomenologically striking experience of weight. Impossibility can not only be seen, but also felt.