Mathematics

The {7/2} heptagram is not only a symbol. It is a traversal algorithm over seven beat positions. Because 7 is prime, that traversal never gets trapped in a sub-orbit.

In October 2024, the largest known prime was discovered — 41 million digits, found by a GPU cluster. But the deepest prime story is not about record-breaking numbers. It is about a 1972 teatime conversation at the Institute for Advanced Study, a pair correlation formula, and the suspicion — numerically confirmed to extraordinary precision — that the zeros of the Riemann zeta function are the energy levels of an undiscovered quantum system.

Danny Carey calls it sacred geometry. Gauss proved it non-constructible. They are, unexpectedly, describing the same object.

Why does the octave divide into twelve? The answer lies not in aesthetics but in the continued-fraction convergents of log₂(3/2) — and the same group structure that gives Messiaen his modes.

Alongside physics and astronomy, two other things have occupied an unreasonable share of my attention since adolescence: mathematics and music. Lateralus by Tool — released 2001, still in rotation — is the piece that most conspicuously occupies the intersection. The song is structurally built around the Fibonacci sequence, from the syllable counts in Maynard Keenan’s vocals to the time signature pattern that concatenates to F(16). This post works through the mathematics in some detail and asks why it works musically.