November 3, 2025
Angles vs axes cage match
Geonum – geometric number library for unlimited dimensions with O(1) complexity
Geonum claims super‑fast math in any dimension — commenters ask if it’s a prank
TLDR: A new Rust library, Geonum, says numbers should include angles to avoid matrices and work in any dimension. Commenters split between intrigue and ridicule, asking for a real paper and pointing out a quaternion example that fails, turning big claims into bigger skepticism.
Geonum dropped with a wild promise: numbers that carry their own angle, so you skip coordinates, matrices, and tensors, and get O(1) speed even in “unlimited” dimensions. The project says you can “rotate by quarter turns” instead of stacking axes, and even claims it reduces mind‑melting math from n^k·2^n to just 2. Cue the crowd: confusion, skepticism, and comedy. One reader begged, “Is there a joke I’m not getting, or a paper I can read?” linking the author’s manifesto‑style write‑up here. Another didn’t mince words: “It’s slop.” The biggest splash came from someone testing quaternions (the 3D rotation math) and noting that Geonum’s own example says k*i gives the wrong result — a polite way of screaming, “Your rotation math broke.”
Fans think it’s a bold rethink: numbers with built‑in direction instead of “scalar prisons.” Critics say it reads like metaphysics with Rust syntax. The tone whipsawed between curiosity (“show the proof!”) and meme mode (“scalar chain gang” jokes, angle amputations, and the quaternion police flashing badges). The drama: audacious claims, zero citations, and a demo that trips on a basic rotation. Tech theater at its finest.
Key Points
- •Geonum proposes a geometric number representation storing length and a bladed angle to enable dimension-free computations with claimed O(1) complexity.
- •The article asserts that conventional scalar-centric linear algebra causes dimensional explosion, sparsity, and expensive matrix/tensor operations to recover direction.
- •It claims Geonum reduces component complexity from n^k and 2^n (for geometric algebra multivectors) to 2 by dualizing components and setting metrics via a quadrature’s bivector.
- •Core operations include project (cosine of angle difference), dual (π rotation with grade mapping), grade (blade % 4), and differentiate (using sin(θ+π/2)=cos(θ)).
- •A Rust example installs via cargo, computes projections equivalent to cos and sin, verifies px²+py²=L², and demonstrates results independent of blade (dimension) count.