Digital Culture & AudioVisual Challenges

Summary
This work aims to develop a Virtual Reality application that attempts to train our brain to comprehend a colour-coded 4D hypersphere intersecting 3D space.

Objective
Man can perceive 3D geometry; however, the question arises whether can be trained to perceive hyper dimensions. According to the definitions of Topology, we need four different coordinates to distinguish any point within the 4D space. (Thurston 1997: 32) However, our brain cannot perceive this information since our sensory system neither has 3D nor 4D transducers to measure the fourth coordinate at the physical level. Is it possible to train our brain in a suitable way to perceive 4D visual information, the same way it is trained to perceive 3D visual information? There are three ways of perceiving hyper-solids: projection, intersection and development. For the implementation of the above mentioned VR interactive application the intersection method is proposed, which is using the color-coded Hypersphere designed by TecnArtists (Traperas, Gounaropoulos, Kanellopoulos, 2021).

Methodology
Color-Coded Hypersphere application
To create an educational process to perceive the 4D hyperspace via training, we propose to employ the color-coded hypersphere intersection representation method (Traperas and Kanellopoulos 2018), which codes the 4D space with R, G, B & W colors. We develop an interactive application in a VR environment that will train the viewer to interact with the hypersphere intersection by rotating it, as well as increasing and decreasing its size and to study the hypersphere at various stages of its evolution as it enters or exits the 3D space.

A. The software
The software used for the interactive visualization of the hypersphere intersection is the Unity virtual reality environment, a program suitable for developing interactive games, which contains a very rich library equipped with the necessary tools for creating VR environments. The programming language used is the C#.

B. The Application
The application created depicts an empty 3D space, where there is a point from which the color-coded hypersphere begins to enter-intersect the 3D space. The user is able to use buttons to interact with the color-coded hypersphere as it intersects with the 3D space (enters, exits and rotates). As the hypersphere intersects and enters the 3D space, its mass increases receiving different colors from invisible monochromatic projectors that illuminate it in every dimension x΄x, y΄y, z΄z, w'w. As the sphere changes size, the color mix and different combinations emerge indicating to us the steps of its evolution into 3D space.

Figure 1. A screenshot of the Hypersphere Intersection Application (© 2023 Gounaropoulos and Kanellopoulos)
C. The purpose
The purpose of this implementation is to attempt to train the brain to perceive higher dimensions using the color-coded Hypersphere Intersection method. The great advantage of this application is the easy use of the educational tool by anyone, since it can be used employing either a computer or a mobile phone screen. In addition, by using a VR phone case, one can achieve isolation from the natural environment and experience immersion.

Conclusions
The creation of the color-coded Hypersphere VR educational tool for training the brain to perceive higher dimensions is a pioneering method. The use and exploitation of new digital applications and technologies may speed up the process of this particular experimental training. Our approach is based on the idea of displaying the color-coded Hypersphere Intersection, while retaining the ability to manually control its transit through 3D space. In the future, we may improve this application by increasing the interaction; e.g., by employing hand tracking features and mobile phone VR frame. With such features, the user may have a better control of the color-coded hypersphere interaction in all stages of its transit through the 3 D space.

References
Traperas, D., Gounaropoulos C., Kanellopoulos, N., (2021). 4D Hypersphere perception via a holographic art installation. International Conference on Digital Culture & AudioVisual Challenges, Ionian University, Corfu, Greece, 28–29 May.
Hinton, C.H. (1904). The fourth dimension. Swan Sonnenschein & Co; John Lane.
Thurston, W.P. (1997) “Three-Dimensional Geometry and Topology”, Vol.1. New Jersey: Princeton University Press.
Traperas, D. & Kanellopoulos, N. (2018a). Visualizing the hypersphere using Hinton’s method. Technoetic Arts: A Journal of Speculative Research 16, No.2, 163–178. https://doi.org/10.1386/tear.16.2.165_1