Exploring Mondrian Compositions in Three-Dimensional Space

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ABSTRACT (CC BY4.0) license neering) and decorative (crafts) aspects into a genuine art art genuine a into aspects (crafts) decorative and neering) developarchitectureto was (engi - goal technical itsbeyond howonpainting relates architecture.focused to crucial The nature. aesthetic that was no longer restricted by formsin observed Stijl journal the in published was warped—manifesto and lofty first—somewhat The equilibrium.constant achieve to ofuse cardinal orientations for lines and rectangular shapes the prescribes which of one [3], Art” Pictorial in plasticism “Neo essay his in aesthetics oflaws” “neoplastic six posed pro Mondrian relationship” [2]. “pure in colors basic and lines of use the by beauty” “pure capture to aspired which abstraction”“neo-plastic[1], of style characteristic own his developed Mondrian avant-garde. Russian the and many Ger in movement art Bauhaus the with closely interacted ment. Thisgroup ofpainters, sculptors, architects andpoets the founding members of the Amsterdam De Stijl art move- of one was (1872–1944) Mondrian Piet painter Dutch The standards ofbeauty. the essentialroleofperceptualprocessesinreachingneoplastic highlights elicited bya“reverspective”Mondrian-likespacefurther couldbeminimizedinacylinder.distortions Theparadoxicalpercept challenges withperspectiveprojectionsandshowhowsuch modelsofthesalon,authorsdemonstrate physical andvirtual and perceptualfactorsthatconflictwithneoplasticideals.Using Dresden” wasnotexecuted.Theauthorsdiscussphysicalconstraints and hisuniqueinteriordesignof“SalondeMadameB. à to 3Dstructures.Mondrianrarelyventuredintoarchitecturaldesign, initiated adiscourseabouttranslatingaestheticidealsfrompaintings The dogmaticnatureofPietMondrian’s neoplasticismmanifesto in Three-DimensionalSpace Exploring MondrianCompositions l a r e n e G ©2020 ISAST. Published underaCreativeCommons Attribution 4.0International with thisissue. See www.mitpressjournals.org/toc/leon/53/1 forsupplementalfilesassociated University of London, U.K. Email: [email protected]. Johannes M. Zanker (neuroscientist), Department of Psychology, Royal Holloway University of London, U.K. Email: [email protected]. Jasmina Stevanov (researcher), Department of Psychology, Royal Holloway A key debate about universality of neoplastic aesthetics aesthetics neoplastic of universality about debate key A in 1918 [4], proclaiming a new, universal and abstract abstract and universal new, a proclaiming [4], 1918 in J M S A A e l c i t r https://doi.org/10.1162/leon_a_01583 n i a S E T v a v o n d n a

h o J De De - - -

a “Salona Madamede . B for drawings axonometric and plan box exploded an is his studio in1926 1b). [12](Fig. ofaustere model this scale A proscenium found couldbe in and exchangeable backdrop scenes painted in his iconic style. stage set with a frame facing the audience in the foreground by Seuphor’s Dada play Inspired [11]. occluders placing by wall oblique an around worked even he studio Paris his In 1a). (Fig. viewpoint era cam specific a to locked studios, his in furniture of pieces and life, he purposefully arranged paintings, color plates and art of aesthetics towardinseparable goals manifestolowing Fol- [10]. studios his in paintings his of stagingintentional Mondrian’s passing interest in interior design is shown by the 1920 and 1941, many as variants of the same between basic design [9]. artist the by created abstraction distinctive pure of 83 patterns shows [8] works his of catalogue 1998 The arts. twentieth-century of icons the with belong doubtedly colors, un- with primary whiteground filled andrectangles inherent to architecture [7]. the need to overcome the dependence on perspective that is Many of these ideas are presented as intuitive claims, such as principles to create equilibrium, putting beauty above utility. “pure”same the follow should that object artistic an space, limitations [5]. Mondrian [6] saw the interior as an enclosed statement aesthetic longer the no isconstrained byphysical term Dutch the in encapsulated form, promptedquestions as to why plans the were never realized York,this New and Gallery, Pace the in reconstructed was museum.Collections nert’s estate [14], held in the archives of the Dresden State Art [13].Figure shows2 color the version ofplans the from Bie - instructions coloring with drawing black-and-white a was and study. The initial version ofthis plan, kept by Mondrian, her for nert (Fig. 2). He was commissioned in 1925 by his patron Ida Bie- n n A unique example of Mondrian’s architectural thinking thinking Mondrian’s architectural of example unique A on lines blackMondrian’s of grids rectangular paintings, Mondrian never did see the salon completed. In 1970 it 1970 In completed. salon the see did never Mondrian S E Z . M in Dresden to become a library library a become to Dresden Damenzimmerin LEONARDO, Vol. 53, No.1,pp.63–69, 2020 a . L’Ephémère est éternel, he designed a . à Dresden”à . “salon”) (the from 1926 k n R E bouwkunst , where where , -

63 a b

Fig. 1. (a) Mondrian in his studio, 1933. (Photo: Charles Karsten. Collection Het Nieuwe Instituut/KARS, E3.238-2.) Note that the lines on the diamond-shaped painting in the center of this photograph show an arrangement of horizontal and vertical lines, creating the outline of a truncated square shape as an emphatic statement supporting the ideal of cardinal lines. (b) Scale model of the stage set for L’Ephémère est éternel, 1926. (©2017 Mondrian/Holtzman Trust)

a b

Fig. 2. Piet Mondrian, Color Design for the Salon of Ida Bienert, 1926. (a) Exploded box plan. (b) Axonometric plot: The floor and two walls are assembled such that they can be seen in a perspective from 30° from the left wall and 30° from above; no perspective foreshortening. (Image source: Staatliche Kunstsammlungen Dresden)

[15]. The original drawings show some rudimentary pieces in such space and an alternative configuration that would of furniture [16], and there is no indication how paintings avoid corner effects; and (3) a physical model of a space in from Bienert’s art collection would be placed. These details Mondrian-like patterns that create surprising depth illusions, might indicate fundamental issues with the translation of demonstrating perceptual conflict of these patterns with the these drawings into three-dimensional space. Mondrian’s geometry of surfaces. firm commitment to cardinal line orientations on planar surfaces would create issues with decorating a cuboid while A Physical Model allowing multiple viewpoints. of Bienert’s Salon The purpose of this article is to explore the role of per- Although Mondrian mentioned in letters that he was ex- ceptual mechanisms in an attempt to resolve the apparent perimenting with the design for Ida Bienert and might even conflict between neoplastic dogmatic ideals and projective build a scale model [17], the project was not realized during geometry. To this end, we present three demonstrations: (1) his lifetime. In order to get a better idea about how this sa- a scale model of the salon that highlights how the corners lon might have looked, we constructed a “shoebox” model of the room affect the picture projected on the observers’ (Fig. 3) by following Mondrian’s drawings (Fig. 2a). eyes; (2) a computer graphics (CG) simulation of being It is obvious that in the image plane, horizontal lines on the

64 Stevanov and Zanker, Exploring Mondrian Compositions in Three-Dimensional Space

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Fig. 3. The Salon scale model: (a) Bird’s-eye view into the “shoebox,” 289 × 304 × 125 mm (L × W × H), ceiling removed, with fisheye lens. (b) Diagonal view into the “shoebox” with standard camera lens (“shoebox” rotated by 45° relative to left image), two exterior walls removed. (© Jasmina Stevanov and Johannes M. Zanker)

walls intersect in the corners at oblique angles, as would be later paintings). Interestingly, lines were largely reduced to expected in projective geometry. Mondrian’s dogmatic proc- boundaries between rectangles, nothing like the thick black lamations [18] to use cardinal lines exclusively in 2D contexts lines in his paintings [21]. We created a CG salon without (paintings) could be challenged when his patterns are placed rectangle outlines as in Mondrian’s original drawings (Fig. 4). in a 3D context; his L’Ephémère est éternel stage set could The other variant has heavy lines, truer to his iconic style (see be regarded as the only viable solution where the observer’s the online supplemental video A). We assumed the height viewpoint is restricted to a frontoparallel inspection. In a of doors to be 2 m; using proportional scaling, the salon di- cubic room, however, the observer is allowed to look from mensions approximate 4 × 3.6 × 3 m (L × W × H). The key a wide range of viewpoints at the patterns on the walls. Al- observations are illustrated with five still frames showing the though the room is faithfully constructed to doctrine, in the view captured in 45° rotation intervals (Fig. 4c). static retinal image—comparable to a snapshot—the lines The salon with prominent cardinal lines demonstrates that on the walls would deviate from cardinal orientations. For oblique converging lines are very strong cues to depth per- demonstration purposes, this is shown as the projection onto ception and facilitate shape constancy; the latter is difficult to the camera lens in a photograph of the shoebox model (see maintain under high uncertainty about the shape, perspec- Fig. 3b; cf. to Fig. 2b). tive and inclination of surfaces in linear perspective [22]. A Mondrian created axonometric drawings of the salon as trapezoidal shape can be seen both as a trapezoid on a fronto- seen from 30° above floor level and from the left. These show parallel plane or as a slanted rectangle (Fig. 5). However, the a clear deviation from the rectangular doctrine: oblique lines correct perspective interpretation of the room is enhanced in the vertexes of the room. In the axonometric plot (Fig. 2b), by the motion parallax information provided in animations. horizontal lines on the wall remain parallel, whereas they are Mondrian patterns can be unambiguously perceived only oblique in the realistic photograph (Fig. 3b), as a result of if the line of sight is perpendicular to the walls of the salon natural perspective [19]. In G. Vantongerloo’s representation (Fig. 4, panels c1, c3, c5). The strongest perceptual ambiguity, of a similar room [20], there are signs of foreshortening—it distortions of rectangular shapes and noncardinal orienta- appears that these artists were struggling with the attempt to tions, can be seen in the static retinal image of vertexes of the preserve parallel lines. Salon (Fig. 4, panel c4). Prominent black lines would facilitate shape constancy of rectangles from a range of vantage points, CG Visualizations of while at the same time more robustly violate the neoplastic Mondrian’s Interior Design dogma. On the other hand, distortions of rectangles in ver- Mondrian’s axonometric plots assume an observer position texes are more pronounced without thick black lines, as they outside the room. We created a 3D model of the salon in are more likely to be interpreted both as trapezoids and rect- LightWave3D (NewTek Inc. 2013) to simulate experiencing angles (Fig. 4, panels c2, c4; see online supplemental video A). the real salon and also to remove walls to render an inside Noncardinal orientations and distortions of rectangular look for any given viewpoint. shapes can be avoided in a room without corners, such as Mondrian’s original drawings show that the space was in a cylinder. We created a CG model of a cylindrical room divided into rectangles filled with primary colors, white with the same overall dimensions as the salon (Color Plate B, and several shades of gray (which were abolished in his online supplemental video B). The four walls of Mondrian’s

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c 1 2 3

4 5

Fig. 4. CG model of Mondrian’s Salon using patterns without prominent cardinal lines: (a) Geometry in top view: Field of view (FoV) was 90° horizontally and 53° vertically; viewing distance D set to the length of the longer diagonal of the floor area. (b) A perspective view of the scene layout. (c) Camera view of three walls (C: steps 1, 3, 5) and two corners (C: steps 2, 4); C2 corresponds to the viewing angle in Fig. 3b. (© Jasmina Stevanov and Johannes M. Zanker)

a b

Fig. 5. Ambiguity of converging lines: (a) Without oblique converging lines suggesting perspective planes, a trapezoid can be seen both as trapezoid in the frontoparallel plane and as a slanted rectangle belonging to another perspective plane (picture adapted from Kitaoka [45]); (b) Joint ambiguity of shape and perspective: shape constancy is difficult to maintain if estimated from inclination in linear perspective. (Image adapted from Howard [46]. Used by permission of Oxford University Press, U.S.A.)

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c 1 2 3

Fig. 6. “Reverspective” Mondrian space: two square frustums with morphed Mondrian patterns made of four paintings; catalogue numbers and years (from Mondrian et al. [47]): 129 [1921], 142 [1922], 210 [1929], 216 [1929]. Square frustums are (a) perceived as two concave corridors when seen from above and (b) seen as two capped pyramids from a side. (c) Three still images from the animation showing illusory rotation in 9° steps. The camera was at 90 cm from the model and captured 12 frames, each displaced by 2 cm. (© Jasmina Stevanov and Johannes M. Zanker)

salon were mounted on the circular wall next to each other. how perspective cues from static images and dynamic cues Instead of modifying the ceiling and floor of the salon to fit from motion parallax [26] interact in 3D perception. These onto the circular base of the cylinder, we simulated a mirror mechanisms have a long evolutionary history—they can even surface to perceptually expand wall patterns across the ridge enable insects to discriminate between 3D shapes [27], sug- of the cylinder (Color Plate Bb). gesting that no high-level cognitive processing is needed to In the cylindrical room, there are no vertexes; thus the interpret the shapes of objects in space. In the following sec- most obvious conflict with neoplastic composition rules is tion, we will demonstrate how the same mechanisms that en- removed. Throughout the field of view (FoV), vertical lines force shape constancy and veridical space perception cannot on the cylinder appear strictly vertical. With half of the cyl- always resolve perceptual ambiguity of static (pictorial) and inder being in the FoV, however, horizontal lines appear dynamic (motion-parallax) depth information. horizontal only in the center, but bend upward and down- ward in the periphery, deviating from orthogonality. These Mondrian Composition in Reverse Perspective peripheral distortions are further enhanced by more promi- Trapezoidal shapes seen in photographs at the corners of ob- nent black lines and persist in conflict with Mondrian’s ideal jects are typically perceived as representations of rectangles, (see online supplemental video B). due to shape constancy; in an extreme case this creates a The sense of a rectilinear composition could be enhanced conflict with motion parallax information that generates the by restricting the FoV—for instance, by getting closer to the paradoxical experience of a room following the observer wall ahead. Within a smaller region of the wall, the number sidewise [28]. Following the work of Patrick Hughes [29], of visible rectangles and lines is reduced, raising the question we constructed a model in “reverspective” space: Mondrian- whether the remaining pattern would still be compatible with like patterns were morphed onto the surfaces of two capped the typical Mondrian composition. The analysis of his paint- pyramids with a square base (square frustums), so that the ing layouts [23] for works created between 1925 and 1935 re- original pattern rectangle was stretched to fit into the four veals that in images having the average size of 52 × 58 cm, the isosceles trapezoids of the frustums (Fig. 6b). average number of lines was 5.2, while the average number of Seen from the apex at a distance (reducing binocular rectangles was 5.5. This means that the number of elements depth cues), the frustums are perceived as concave boxes or on the wall pattern would need to be inversely proportional corridors (Fig. 6a, online supplemental video C). Based on to the FoV, by reducing the size of rectangles and increasing perspective cues, the shorter lines at the apex appear more the number of elements on the wall. Our hypothetical pattern distant than the longer lines at the base. However, if the ob- in a narrow FoV may be alternatively considered in terms of server moves their head laterally, closer regions at the apex neoplastic doctrine, although it is clear that aesthetic ten- move more quickly across the retina than more distant re- sions cannot be completely resolved. gions at the base, which creates the paradoxical illusion of a Using CG models and animations was useful to demon- rectangular corridor following the observer [30,31]. Percep- strate possible issues with neoplastic aesthetic rules arising tion is biased toward the most likely interpretation by shape from different viewpoints [24] and geometry [25] of the real constancy mechanisms. Lines can be perceived as parallel world. Most importantly, these animations demonstrated and orthogonal when they are part of slanted trapezoids—

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Downloaded from http://direct.mit.edu/leon/article-pdf/53/1/63/1579552/leon_a_01583.pdf by guest on 01 October 2021 and equally when they are part of a tilted rectangle as in the Bauhaus [38], and although Mondrian interacted with the salon. Because the retinal images would appear equal, the Bauhaus [39], he seems not to have taken particular interest interpretations of the retinal images are equal: Lines are seen in scientific evidence [40]. as parallel and orthogonal. The reverspective model demon- The conflict between the neoplastic ideal of beauty and strates the robustness of the shape constancy mechanism. the human interpretation of the 3D world results from a di- Similarly, different viewpoints for Mondrian patterns would rect interpretation of static retinal images. However, oblique hardly disrupt our stable perception of cardinal lines in the distortions in the retinal images are corrected by perceptual salon. Could this demonstration cast new light on Mondri- mechanisms (e.g. shape constancy), generating veridical an’s design of the salon? perceptual representations of space [41]: The characteristic relationship between physical space, the rules of perspective Discussion for a given viewpoint and their effortless 3D interpretation from projections on a single plane are well understood. We The Problem used a reverspective object here to demonstrate how the In his discourse with De Stijl, Mondrian [32] published his mind makes sense of the outside world in the presence of plan for a salon to illustrate his vision of neoplasticist architec- conflicting depth cues. ture: a fusion of many simultaneous planes into a balanced 3D Five years after publishing the neoplasticism manifesto, object. The fact that the salon was never realized could have Mondrian pointed at a mysterious way for the mind to de- been due to logistic and financial reasons but also could reflect tach from the physical body: “Man’s eye is not yet free from his dissatisfaction with dependence on perspective and laws his body . . . only the mind knows anything of the fourth of projective geometry. We have demonstrated that vertexes dimension and detaches itself from our poor physical bod- in the salon might be in conflict with Mondrian’s ideal of car- ies” [42,43]. Could this be a hidden or unintended hint at dinal lines, and we have suggested that unwanted distortion relaxing the composition rules, taking into account men- could be reduced in a hypothetical cylindrical room. Such a tal representation? A scientific framework can put some of room could provide a partial workaround but would remain Mondrian’s comments about the future of architecture into far from a universal guidance for neoplastic architecture. a new perspective. Mondrian strictly believed that universal beauty could be A Proposition defined solely by the properties of objects. A century later we In the nineteenth century, scientific understanding of subjec- think that aesthetic judgement arises from the interaction tive human experience emerged with the advance of experi- between object features, properties of our visual system and mental psychology and the new discipline of psychophysics processes of value attribution [44]. While the corners of the [33]. An idea to study beauty by focusing on basic forms and salon might have frustrated Mondrian’s appetite to work on relations had already been pioneered by Fechner and his re- perspective challenges, we propose a simple solution: Aes- ductionist “aesthetics from below” [34], studying colors and thetic judgment should be based on our perceptual represen- simple geometrical shapes as stimuli that could be precisely tation rather than static retinal images. Another rather crude controlled and manipulated. In the twentieth century, Gestalt alternative would be to accept that the Mondrian-type space psychology provided comprehensive insight in perceptual is just not beautiful, as it falls short of strict neoplastic ide- representation [35], which has influenced the development als of beauty. Although Mondrian-type space may not have of a “vocabulary of pictorial representation” in art [36]. Early been considered beautiful at the beginning of the twentieth claims about the relevance of psychophysics for aesthetics century, we should not easily adopt that verdict in the 21st [37], however, attracted surprisingly little attention. The century—after all, the beauty is not in the eye, but in the scientific approach was embraced by some members of the mind of the beholder.

Acknowledgments References and Notes This work received financial support from JGU (8393084) and JSPS 1 P. Mondrian (1920), “Neo-Plasticism: The General Principle of Plas- Grants-in-Aid for Scientific Research (No. 25.13011) to J. Stevanov and tic Equivalence,” in H. Holtzman, ed., The New Art, the New Life : ESRC (ES/K000187/1) to J.M. Zanker. We thank Željko Šešum for his The Collected Writings of Piet Mondrian (New York: Da Capo, 1993) help in creating CG models and Thomas Papathomas for his plan for pp. 134–147. the reverse perspective box. We are grateful to Sabine Zanker for ex- tensively researching original De Stijl documents and scrutinizing the 2 H. Holtzman, “Piet Mondrian’s Environment,” in Mondrian: The manuscript. We also thank Thomas Papathomas, Nick Wade, László Process Works (New York: Pace Gallery, 1970) pp. 4–5. Tálas and Chris McManus for their insightful comments on an earlier 3 P. Mondrian, “Le Home, La Rue, La Cité,” in B. Léal and C.G. Pom- version of this manuscript. pidou, eds., Écrits français (Paris: Centre Pompidou, 2010). Original publication in Vouloir, No. 25 (1927). 4 T. Van Doesburg et al., “Manifest I van ‘De Stijl,’ ” De Stijl 1 (1918) pp. 2–3.

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Downloaded from http://direct.mit.edu/leon/article-pdf/53/1/63/1579552/leon_a_01583.pdf by guest on 01 October 2021 5 Y.A. Bois, “Mondrian and the Theory of Architecture,” Assemblage 31 Papathomas [28]. No. 4 (1987) pp. 103–130: www.doi.org/10.2307/3171039. 32 Mondrian [3]. 6 Mondrian [3]. 33 H. von Helmholtz, Handbuch der physiologischen Optik (Hamburg; 7 P. Mondrian (1922), “The Realization of Neoplasticism in the Distant Voss, 1866); in English: N. Wade, ed., and J.P.C. Southall, trans., Future and in Architecture Today: Architecture, Conceived as Our Helmholtz’s Treatise on Physiological Optics (New York: Dover, 1962). Total [Non-Natural] Environment,” in Holtzman [1] pp. 166–172. 34 G.T. Fechner, Vorschule Der Ästhetik (Leipzig: Breitkopf, 1876). 8 P. Mondrian et al., Piet Mondrian: Catalogue Raisonné of the Work of 1911–1944 (New York: Harry N. Abrams, 1998). 35 K. Koffka,Principles of Gestalt Psychology (London: Routledge, 1935). 9 J.M. Zanker, J. Kalpadakis-Smith and S. Durant, “ ‘Natural’ Image 36 J. Willats, Art and Representation: New Principles in the Analysis of Statistics and ‘Neoplasticism’—What Could Be the Formula to Com- Pictures (Princeton, NJ: Princeton Univ. Press, 1997). pose a Mondrian?” Journal of Vision 14, No. 10, 653–653 (2014). 37 Fechner [34]. 10 Holtzman [2]. 38 J. Albers, Interaction of Color (New Haven, CT: Yale Univ. Press, 11 B. Léal, “Das Atelier als Kunstwerk: Kurt Schwitters, PietMondrian 1975). und Constantin Brancuși,” in I. Conzen, ed., Mythos Atelier. Künstler- räume von Carl Spitzweg bis Bruce Nauman (Munich: Hirmer Verlag, 39 P. Mondrian, Neue Gestaltung. Neoplastizismus (Munich: Langen, 2012) pp. 156–166. 1925). 12 Mondrian et al. [8]. 40 It is interesting to note that some of the transformations that Mon- 13 Holtzman [2]. drian made on his paintings can be interpreted as an introspective experimentation with his composition scheme, which resembles the 14 Mondrian et al. [8]. manipulations in an experimental study of his style half a century later. See H. Cooper and R. Spronk, Mondrian: The Transatlantic 15 Holtzman [2]. Paintings (Cambridge MA: Harvard Art Museums, 2001); and I.C. 16 N.J. Troy, “Mondrian’s Designs for the Salon de Madame B . . ., à McManus, B. Cheema and J. Stoker, “The Aesthetics of Composition: Dresden,” The Art Bulletin 62, No. 4, 640–647 (1980). A Study of Mondrian,” Empirical Studies of the Arts 11, No. 2, 83–94 (1993). 17 Holtzman [2]. 41 Gregory [25]. 18 Mondrian [1]. 42 Mondrian [3]. 19 I. Carlbom and J. Paciorek, “Planar Geometric Projections and View- ing Transformations,” ACM Computing Surveys 10, No. 4, 465–502 43 Holtzman [2] p. 13. (1978): www.doi.org/10.1145/356744.356750. 44 J.P. Huston et al., Art, Aesthetics, and the Brain (Oxford: Oxford Univ. 20 Troy [16]. Press, 2015). 21 Troy [16]. 45 A. Kitaoka, “Ambiguous or Reversible Figures” (18 September 2014): 22 I.P. Howard, Perceiving in Depth, Vol. 3 (Oxford: Oxford Univ. Press, www.psy.ritsumei.ac.jp/~akitaoka/tagi7e.html (accessed 21 March 2012): www.dx.doi.org/10.1093/acprof:oso/9780199764167.001.0001. 2017). 23 Zanker et al. [9]. 46 Howard [22] p. 139. 24 J.J. Gibson, The Ecological Approach to Visual Perception (Boston: 47 Mondrian et al. [8]. Houghton Mifflin, 1979).

25 R.L. Gregory, “Knowledge in Perception and Illusion,” Philosophi- Manuscript received 2 December 2016. cal Transactions of the Royal Society of London, Series B, Biologi- cal Sciences 352, No. 1358, 1121–1127 (1997): www.doi.org/10.1098 /rstb.1997.0095. Jasmina Stevanov, trained as a painter and an experi- 26 J.J. Koenderink and A.J. van Doorn, “Invariant Properties of the Mo- mental psychologist, completed her doctoral training under the tion Parallax Field Due to the Movement of Rigid Bodies Relative to an Observer,” Optica Acta: International Journal of Optics 22, No. 9, supervision of Akiyoshi Kitaoka, the world-renowned researcher 773–791 (1975): www.doi.org/10.1080/713819112. of visual illusions. Her main research focuses on investigating 27 A. Werner, W. Stürzl and J. Zanker, “Object Recognition in Flight: neural correlates of insight, visual ambiguity and aesthetic How Do Bees Distinguish between 3D Shapes?” PLoS ONE 11, No. 2 appreciation. (2016): www.doi.org/10.1371/journal.pone.0147106. 28 T.V. Papathomas, “Art Pieces That ‘Move’ in Our Minds—An Expla- Johannes M. Zanker, trained as a biologist with a focus nation of Illusory Motion Based on Depth Reversal,” Spatial Vision on cybernetics, has held various positions at research institutes 21, No. 1–2, 79–95 (2007): www.doi.org/10.1163/156856807782753958. and universities in Germany, Italy, Australia and the United 29 J. Slyce, Patrick Hughes: Perverspective (London: Momentum, 1998). Kingdom, now being professor of neuroscience at Royal Hol- loway, University of London. His research covers a wide range 30 G. Sperling and B.A. Dosher, “Depth from Motion,” in T.V. Papatho- mas et al., eds., Early Vision and Beyond (Cambridge, MA: MIT of topics in perceptual, behavioral and computational aspects Press, 1994) pp. 133–142. of vision.

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