Non-Euclidean Doom: what happens to a game when pi is not 3.14159 (2022) [video]

Original Article ↗ Hacker News Discussion ↗

What Changing π in Doom Actually Does

  • Changing π mainly breaks graphics and movement, leading to warped FOV, sliding motions, texture popping, and eventual unplayability.
  • Effects come from Doom’s heavy use of radians in movement and rendering; lookup tables appear to assume a fixed π, and extreme changes cause out-of-bounds accesses and crashes.
  • Some wished for smaller incremental changes to see how space “deviates” rather than jumping straight to wildly distorted values.

Is This Really “Non-Euclidean”?

  • Several argue this isn’t true non-Euclidean geometry, just “messing with constants” causing glitches.
  • Others accept a looser use of “non-Euclidean” for any space that violates ordinary geometric intuitions, including portal-based worlds.
  • One perspective notes that Euclidean geometry plus portals breaks several Euclidean axioms, making it “non-Euclidean” in a broad sense, though not a formal geometry.

Game Engines, Portals, and Non-Euclidean Spaces

  • Discussion compares Doom’s BSP-based, mostly-2.5D engine to portal-based engines (e.g., Build engine, Marathon, Descent).
  • Doom originally disallowed overlapping sectors; later source ports add portals and tricks enabling room-over-room and “impossible” spaces (e.g., MyHouse.wad).
  • Portal-style rendering is contrasted with true non-Euclidean manifolds; collision and spatial reasoning through portals are noted as harder than rendering.

Related Games and Media

  • Many games are cited as better demonstrations of non-Euclidean or perception-bending spaces: Antichamber, HyperRogue, Hyperbolica, Superliminal, Viewfinder, Manifold Garden, and various portal-based titles.
  • Classic examples from other engines include Duke Nukem 3D’s “Lunatic Fringe”, Marathon’s “5D space”, and earlier work like Descent.

Mathematics and Geometry Discussion

  • Some commenters clarify that in differential geometry, π itself does not change; curvature affects circle circumference but not the derivative that defines π.
  • The talk’s premise is contrasted with more rigorous non-Euclidean constructions (hyperbolic, spherical, Nil geometry, etc.).

Bugs, Constants, and Programming Lessons

  • Doom famously uses a slightly wrong 10-digit approximation of π, traced to a misremembered digit.
  • Broader lesson: hardcoding constants (e.g., seconds in a day) is error-prone; several real-world codebases are cited as having such typos.

Overall Reception

  • Some viewers find the talk fun, playful, and a good curiosity-inducing demo.
  • Others dismiss it as clickbait or trivial “garbage in, garbage out” behavior, preferring deeper exploration of actual non-Euclidean geometry.