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

Original Article ↗ Hacker News Discussion ↗

Altering the value of π in the classic game Doom produces increasingly broken graphics and movement, prompting debate over whether this really counts as “non‑Euclidean” geometry or is simply what happens when you corrupt a fundamental constant in an engine. Commenters contrast the experiment with games and engines that implement genuine non‑Euclidean spaces or portal-based level design, from HyperRogue and Antichamber to Duke Nukem 3D’s Build engine and modern Doom mods like MyHouse.wad. The thread branches into how game engines represent space, what “non‑Euclidean” means mathematically, and how small numerical mistakes in constants (like π or seconds per day) can have outsized and sometimes surprising effects in software.

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.