Everything is logarithms
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Logarithms are structurally identical to vectors in coordinate systems.
The author proposes thinking of the logarithm as a base-free abstract object, "log N", analogous to a geometric vector. Writing log₂ N = log N / log 2 is then like measuring a vector in different units. The change-of-base formula becomes a unit conversion, similar to rewriting a vector v as vₓ x = vₓ' x'. The analogy extends to partial derivatives: p-adic valuation νₚ(n) extracts the coefficient of log p in the prime factorization of n, just as a partial derivative extracts a component of a differential. Complex analysis uses a similar limit to extract the order of vanishing of a meromorphic function.
What commenters are saying
Commenters split into two camps. One group appreciates the structural insight but warns against overgeneralization: saying "everything is a logarithm" flattens important differences between mathematical tools, just as a hammer and a meat mallet are both metal hitting tools with different uses. The other camp critiques the essay's lack of a type system: every use of "log" needs a clear signature (from what, to what, preserving which operation). Several commenters emphasize that you cannot take a logarithm of a quantity with units, you must normalize by a scaling unit first, which is why dB systems always have an implicit reference.