The explanation by owencb is what I was trying to address. To be explicit about when the offset is being added, I’m suggesting replacing your log1p(x) ≣ log(1 + x)
transformation with log(c + x)
for c
=10 or c
=100.
If the choice of log-dollars is just for presentation, it doesn’t matter too much. But in a lesswrong-ish context, log-dollars also have connotations of things like the Kelly criterion, where it is taken completely seriously that there’s more of a difference between $0 and $1 than between $1 and $3^^^3.
Seconding all of gjm’s criticisms, and adding another point.
The sostenuto (middle) pedal was invented in 1844. The sustain (right) pedal has been around roughly as long as the piano itself, since piano technique is pretty much unthinkable without it.