Everything Is Logarithms: A Mathematical Framework
Original: Everything is logarithms
Why This Matters
Presents novel conceptual framework for understanding fundamental mathematical operations with potential pedagogical and theoretical implications.
Alex Kritchevsky proposes a novel mathematical interpretation of logarithms through the concept of baseless logarithms, presenting connections between logarithmic functions and abstract algebraic objects without explicit numerical bases.
In a technical blog post dated May 25, 2026, Alex Kritchevsky introduces the concept of baseless logarithms as a framework for understanding logarithmic mathematics more intuitively. The author argues that conventional notation for logarithms with bases obscures their fundamental meaning. Kritchevsky proposes treating logarithms as abstract objects independent of a specific base, written simply as log N, and then expressing standard based logarithms as ratios of these baseless logarithms: log_2 N = (log N)/(log 2). This approach frames different logarithmic bases as different units of measurement—bits when using base 2, and nats when using base e. The author draws an analogy to vectors in geometry, distinguishing between points and displacement vectors. Just as displacement vectors result from the difference between two points, baseless logarithms function as the multiplicative analog, where selecting a specific base corresponds to choosing a coordinate system. The framework shows that logarithmic change-of-base formulas emerge naturally from converting between different units rather than as separate algebraic rules. Kritchevsky suggests this perspective may reveal deeper mathematical connections not previously recognized in standard logarithmic notation.