tl;dr: The author argues that logarithms should be thought of as "baseless" objects analogous to coordinate-free geometric vectors, where writing log_b(x) is just choosing units (like "bits" or "nats") much like projecting a vector onto a basis. From this lens, many seemingly unrelated math operations—p-adic valuations, orders of vanishing in complex analysis, vector space dimension, and even translation operators in differential geometry—are all essentially logarithms or logarithm-like projections. The piece is speculative numerology aimed at uncovering a unifying coordinate-free framework that the author suspects underlies these scattered notations.