Hyperbolic Space & Negative Curvature

✦Description

Reports that DMT space is not merely full of shapes but is itself curved the 'wrong' way — saddle-shaped, warped, with far more surface area packed into it than ordinary Euclidean space could hold. Travelers describe scenes riddled with saddles, joints, twists, knots, double-helixes and curved alleys, where a small movement of attention produces enormous changes in the scene, and where surfaces seem to expand faster than they should as you look 'into' them (area growing exponentially with distance rather than proportionally). This is the felt substrate beneath many other effects: the 'impossible' packing of infinite detail, the sense of rooms folding around and behind you, and the Escher-like objects that cannot be embedded in a flat 3D world.

✦What the sources say

'Phenomenal space... has an overall geometry that can accurately be described as hyperbolic'; scenes dominated by 'the omnipresence of saddles' with 'joints, twists, bifurcations, curved alleys, knots, and double helixes'; small movements 'lead to huge changes in the scene.'

Lexicon 'Folding Rooms' — multidimensional spaces where architecture is 'reaching behind and around one,' a lay description of non-Euclidean enclosure.