monogate.dev · lab · equation genome

Do equations cluster by field or by math?

265 scientific equations embedded in a 25-dimensional fingerprint space (operator counts + pattern hits + structural metrics), projected to 2-D via PCA and partitioned by k-means (K = 5). Toggle the colouring to see the punchline.

265 equations5 clusterspair-purity 0.1808random baseline 0.1546excess +0.0262

hover to inspect · click to lock a cluster · click empty to release

Domains

unknown · 76Chemistry · 40Biology · 34Electromagnetism · 25Geology · 23Astrophysics · 22Economics · 20Neuroscience · 16Information Theory · 5Probability / Game Theory · 1Economics (Finance) · 1Chemistry (Thermodynamics) · 1Chemistry (Acid-Base) · 1

Pair-purity — the probability that two equations in the same cluster share a domain — lands at 0.1808, compared with a random baseline of 0.1546. Excess over random: +0.0262. Beer-Lambert, radioactive decay, RC discharge, drug elimination, and compound interest all share a single cluster; the NFL passer rating sits next to neural activation models; sigmoid growth laws cross biology, engineering, and economics. Domain is decorative. Structure is fundamental.