Non-euclidean virtual reality I: explorations of $\mathbb{H}^3$

Abstract

We describe our initial explorations in simulating non-euclidean geometries in virtual reality. Our simulations of three-dimensional hyperbolic space are available at h3.hypernom.com. 1 Figure 1: A view from H 3 .We are used to living in three-dimensional euclidean space, and our day-to-day experiences of curvature centre around surfaces embedded in E 3 . In the study of topology, the closed two-dimensional surfaces are the sphere, the torus, the two-holed torus, the three-holed torus, and so on. Thinking of these surfaces topologically, they don't come with a particular choice of geometry -that is, we can think about a surface as if they were made from plasticine -without knowing what lengths and angles mean on the surface. There are however particularly nice geometries for these surfaces: isotropic geometries, meaning that the geometry is the same everywhere in the space, facing in every direction. We have spherical geometry for the sphere, euclidean geometry for the torus, and hyperbolic geometry for all of the others. In three dimensions, the story is more complicated. Thurston's geometrization conjecture, proved by Perelman [5], gives eight geometries 1 The code is available at github.com/hawksley/hypVR.

Isness: Using Multi-Person VR to Design Peak Mystical Type Experiences Comparable to Psychedelics

“…VR is particularly well suited to exploring alterations in our experience of space and time. [31,32] Isness included specific states that challenged participants' conventional understandings of space and time. For example, as they sculpted the dynamics of the energetic thread, they were invited to become aware that whilst their own bodies were subject to normal space constraints and unable to pass through the floor, the same was not true for the energetic essences cohabiting the simulated VR space with them.…”