One wrinkle here is the choice of signed error instead of eg. RMSE; absolute error metrics don't care about rounding vs. flooring. Since the conclusion of the analysis hinges on this choice of error metric, I think some justification or discussion of that choice adds interesting context.
Signed error implies that clock-imprecision "cancels"; that being 20 seconds late to your meeting will be undone by being 20 seconds early to lunch afterwards. I'm not sure if this is quite how people reason about 'lateness' though. Obviously in some applications it makes sense (ex. recording event times of some phenomenon of interest), but in scheduling my daily life that's not really how I think about things.
I think RMSE is closer to how people evaluate scheduling of stuff; it doesn't matter if I'm late or early, both will have notable consequences in unique ways. The ambivalence of the RMSE error to rounding vs. flooring is the intuition I would put behind the counterargument fielded by the author:
> But this is just a convention! Truncating, rounding or even ceiling are all valid, as long as we pick one and stick to it.
I think you can also squeeze some juice out of playing with the error metric further. If you want a 'just-in-time' schedule (ie. you want to never be early to anything) then the flooring clock is superior to the rounding clock. If you want the opposite then a ceiling-ing clock would be the best choice.
> Personally, I would never say that it's 10 if the clock shows anything past 10:30
I like to floor my times to the nearest 15-minute interval (10, quarter-past, half-past, quarter-to), only rounding once I've reached ~10:55
Signed error implies that clock-imprecision "cancels"; that being 20 seconds late to your meeting will be undone by being 20 seconds early to lunch afterwards. I'm not sure if this is quite how people reason about 'lateness' though. Obviously in some applications it makes sense (ex. recording event times of some phenomenon of interest), but in scheduling my daily life that's not really how I think about things.
I think RMSE is closer to how people evaluate scheduling of stuff; it doesn't matter if I'm late or early, both will have notable consequences in unique ways. The ambivalence of the RMSE error to rounding vs. flooring is the intuition I would put behind the counterargument fielded by the author:
> But this is just a convention! Truncating, rounding or even ceiling are all valid, as long as we pick one and stick to it.
I think you can also squeeze some juice out of playing with the error metric further. If you want a 'just-in-time' schedule (ie. you want to never be early to anything) then the flooring clock is superior to the rounding clock. If you want the opposite then a ceiling-ing clock would be the best choice.
> Personally, I would never say that it's 10 if the clock shows anything past 10:30
I like to floor my times to the nearest 15-minute interval (10, quarter-past, half-past, quarter-to), only rounding once I've reached ~10:55