created 2025-06-28, & modified, =this.modified
tags:y2025computersvrvirtual-spaces
rel: Poché of the Mind Palace, Virtual Architectures
Exploration of
We describe our initial explorations in simulating non-euclidean geometries in virtual reality. Our simulation of the product of two-dimensional hyperbolic space with one-dimensional euclidean space is available at h2xe.hypernom.com.
The properties of euclidean space seem natural and obvious to us, to the point that it took mathematicians over two thousand years to see an alternative to Euclid’s parallel postulate. The eventual discovery of hyperbolic geometry in the 19th century shook our assumptions, revealing just how strongly our native experience of the world blinded us from consistent alternatives, even in a field that many see as purely theoretical. Non-euclidean spaces are still seen as unintuitive and exotic, but we believe that with direct immersive experience we can get a better “feel” for them.
Curved Space by Jeff Weeks
Curved Spaces is a flight simulator for multi-connected universes. Because light itself wraps around such a space, inhabitants see their universe’s contents repeating in a crystalline pattern, like a hall of mirrors but with no reflection.
One of the more disconcerting experiences of VR simulators is watching the floor fall out from beneath your feet as you walk forward.
Thought
Typical traversal is done here. What if stuck in an a manner where other biology was tied to movement or vision. Movement tied to heartbeat, or time of day etc. Or minute thing we might control but only with practice.
Eventually, we plan to put recognisable, human scale objects in our simulation of H^2 × E, for people to interact with
In our simulations so far, the user never actually leaves the central cube of the tiling: as they attempt to they are teleported from one side of it to the other, and the colours of the cells updated appropriately. We would not be able to use this trick for objects left in the world.