alt Hacker NewsThis essay needs a type system. Every time it says “log” it should say: log of what, into what?
It’s like audio where people say "dB" as if it answers the next question. Relative to what, measured how, and weighted for whom?
Author should brush up on https://en.wikipedia.org/wiki/Lie_theory
Replies
jfengel • today at 2:14 AM
I still don't understand why audio dB are negative. That's relative to what? What happens at 0dB?
➕ show 3 replies
jmyeet • yesterday at 10:54 PM
The first section details how the author thinks of "log N" with no base as an abstract object rather than a number. Or what are you referring to?
➕ show 1 reply
The important properties of the logarithm are structural: we usually do not care about units or bases, except when carrying out an actual numerical computation.
As developed in the article, informally, but somewhat sufficiently, the change of base formula shows that the choice of base is largely irrelevant: different bases give equivalent logarithms up to a constant factor.
The Taylor expansion of exp gives a more intrinsic and general definition of the exponential function. This allows exp to be generalised structurally to many algebraic settings, provided the relevant convergence conditions are met: for example, the complex exponential and its many possible logs, the matrix exponential, and so on…