From M.C. Escher to Mass Effect: Impossible Spaces and Hyper-Real Worlds in Video Games

This peer-reviewed article by Athanasios Petrovits and Alessandro Canossa examines how impossible spaces and hyper-real worlds can be designed, interpreted, and implemented across 2D, 2.5D, and 3D video game environments, and what this means for the future of stereoscopic 3D games. The authors trace a lineage from early text-based MUDs, which used teleportation to create non-Euclidean connections between rooms, through arcade titles such as Pac-Man and Asteroids, whose screen-wrapping mechanics shared the same spatial logic. They draw on the artistic precedents of Oscar Reutersvärd, M.C. Escher, Salvador Dalí, and Giorgio De Chirico, and on research into human visual perception, including the role of the visual cortex, left-right asymmetries in interface design, and the distinction between aperture, ambient, and ambulatory vision.

The central argument concerns the mathematical constraints on impossible geometry in computer graphics. Because game engines represent objects as meshes positioned in Cartesian coordinates, the authors contend that a shape such as the Penrose triangle cannot be consistently constructed in three dimensions, and that a true four-dimensional coordinate system cannot exist within a three-dimensional rendering space. Their practical solution is to fix the object at a single viewing angle, which preserves the illusion as long as the player cannot move around it. Isometric and axonometric projections, used in titles such as Zaxxon, Populous, Diablo, and Civilization II, are presented as the most natural vehicles for this technique.

The authors conclude that stereoscopy, despite offering enhanced depth, does not overcome these limits. Systems such as CAVE environments and future virtual reality may extend the experience, but impossible objects will remain impossible once the viewer is free to move, since virtual space is ultimately defined by coordinates. The study's sources are primarily theoretical and historical, drawing on art history, mathematics, and media studies, rather than on empirical user testing or survey data.