This could make for an easy upgrade path to use of nepers or centinepers instead of percents in comparatives involving rates, which would reduce semantic confusion. “50% faster” can mean “gets 150% as far” (so .41Np faster, or 41 cNp, or perhaps 41Np%) or “takes 50% as much time” (so .69Np faster, or 69cNp, or 69Np%). That’s an argument for using nepers as a standard base outside communications of probability.
(trivia: Nepers and radians are each other turned sideways, being respectively the real and imaginary parts of eigenvalues of linear differential equation systems.)
The natural unit of ratio, the neper (Np), is easier to interpret for small ratio contributions, where the derivative of exp(x) is ≈1:
0.1Np = exp( 0.1) ∶ 1 ≈ 1.1 ∶ 1
-0.1Np = exp(-0.1) ∶ 1 ≈ 0.9 ∶ 1
This could make for an easy upgrade path to use of nepers or centinepers instead of percents in comparatives involving rates, which would reduce semantic confusion. “50% faster” can mean “gets 150% as far” (so .41Np faster, or 41 cNp, or perhaps 41Np%) or “takes 50% as much time” (so .69Np faster, or 69cNp, or 69Np%). That’s an argument for using nepers as a standard base outside communications of probability.
(trivia: Nepers and radians are each other turned sideways, being respectively the real and imaginary parts of eigenvalues of linear differential equation systems.)