Digital Culture & AudioVisual Challenges

Summary:
This article provides an overview of ten case-studies of videogames, examining the relation between non-Euclidean geometric representation and the embodied spatial perception. Videogames, through the use of non-Euclidean geometries propose a new posture towards a more dynamic and interactive perception of the space, where dissociations and cognitive interpretations operate as generators of imaginative spaces.


During the last decades, with the aid of digital design, many examples of non-Euclidean geometries have overflowed the architectural imaginary. It has been a common concern in nearly every major modern art movement of the twentieth century, as an avant-garde expression of the space: Analytical and Synthetic Cubists -as well as Duchamp-; Italian Futurists; Russian Futurists; Supremacists, and Constructivists. Also, non-Euclidean geometries have been very popular among American modernists in the Stieglitz and Arensberg circles; Dadaists; and members of De Stijl. French Surrealism and Andrés Bretón have devoted a great amount of energies in abstract, absurd geometries and fantasies, resulting in exceptional artworks.
Nevertheless, it seems that non-Euclidean geometry has never achieved the popularity of the fourth dimension in its representation in the field of artistic expression, nor has approximated enough other nongeometric associations. The projective geometry has not changed broadly the principles and understanding of linear perspective till almost the dawn of the twenty-first century; from the early 30´s, mathematicians have established some characteristics of the non-Euclidean geometries that have been demonstrated or illustrated quite recently with the aid of computers and the representative abilities of 3D computer graphics.
In a creative combination between videogames and non-Euclidean geometries, an interesting number of examples can be found. Inside the spatial constructions of these games, non-Euclidean characteristics are fused with traditional Euclidean geometries, in order to create endless places in motion, spatiotemporal loops, teleportation abilities/opportunities, perspective illusions and other mind-boggling elements that provide innovative and unique experiences of spatial representation and navigation. Non-Euclidean geometry in videogames has presented another interesting spatial aspect: the sense of multistable perception (or bistable perception). That means a kind of mixed sensation between stable worlds and temporal instability that alters the spatial perception continuously. Navigation and movement in non-Euclidean spaces are not considered isomorphic according to the perceived environment, both due to geometric representations and traditional Euclidean projective abstractions.
The space conceived in Euclidean geometry is a space of neutrality, stability and unity. It is a static container where geometric forms are perfect and unalterable. On the other hand, non-Euclidean forms are produced by curved surfaces, in elliptic, spherical, or hyperbolic projections, where spaces deviate the principal laws of Euclidean geometry. In videogames, a list of different mechanics is deployed to facilitate navigation and spatial narration in order to simulate the spatial experience of the real world. Videogames rely heavily on spatial structure and arrangements to implement a detailed world. Most virtual environments represent an aspect of reality, as an illusion or as a symbolic and allegoric representation of space itself. The spatial representation and the illusion of reality can often achieve higher levels of immersion, even though these techniques are obscure to the player. This element can provide abstract and surrealistic narrations based on a spatiality disconnected from the strict rules and the barriers of the physical realm.
Non-Euclidean spaces in digital environments invent a special primordial form that raises interesting cognitive spatial challenges. The forms are ontologically different from the traditional Euclidean knowledge; they are similar to our unconscious experience of space. Their utilisation in videogames undermines players´ ability to make conscious use of the fundamental spatial epistemologies, encrusted in early school years. Thus, videogames challenge the cognitive gap between experience and theoretical knowledge, creating a kind of disorientation and some cognitive dissonance that could result to be even an imaginative or visionary space, linking non-Euclidean videogames with artistic surrealistic abstraction.
Active participation in these worlds is not a suspension of disbelief but rather a creation of a new belief. The spatial dissociation of non-Euclidean environments lies in-between the architectural theory of the space and the empirical navigation modes of everyday life. Although, navigation has been integrated as a fundamental action/experience in videogames, in non-Euclidean examples this element increments even more the feeling of uncertainty of perception. The impairment of objects´ perception is not strict, and even a greater amount of components are characterised by semiotic contingency. This leads the players to use hermeneutic cognitive tools to interpret and understand the ambiguity of the non-Euclidean videogames.
This powerful aesthetic strategy has the potential to provide more pleasure, immersion, and engagement. In this context, the classification of ten examples of non-Euclidean videogames according to their spatial characteristics and properties is a revealing task as it can outline their relation to embodied spatial perception. Furthermore, recognising differences and similarities between the navigational methods that these games use, can produce an interesting association between spatial movement and main gameplay features.

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3 Some quite interesting examples of videogames created with non-Euclidean geometries are: Manifold Garden https://store.steampowered.com/app/473950/Manifold_Garden, Antichamber https://store.steampowered.com/app/219890/Antichamber/, The bridge https://store.steampowered.com/app/204240/The_Bridge/ , FEZ, Portal, Monument Valley, 4D Toys, EleVR, FORM, Superliminal, HyperRogue, Tea For God, Marathon 5D space, Non-Euclidean Room, Fragments of Euclid, Hyperbolica, Splitgate, Spherical Geometry, Non-Euclidean Chess, Parallelia, Glitchphobia, Sokyokuban – most of them can be found in STEAM platform - [visited 15.03.2022]
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