RMSE of current digital clocks rounding down is roughly 34.5 seconds.
RMSE of proposed rounding to closest is 17.5 seconds.
The new method is roughly 17 seconds more accurate on average.
Does this reduced error make a significant difference? Probably not. There are very annoying practical issues with this proposal though.
Rounding down makes it clear what minute has already passed. If your clock says 3:00, you know the current time is definitely some point after 3:00. If something needs to happen at 3:00, and your clock says 3:00, it is time to start.
With this proposed method, 3:00 could mean anywhere from 2:29:30 to 3:00:30. When do you start? Do you start as soon as your clock says 3:00? Then you're starting 30 seconds early. Do you wait until your clock says 3:01? Then you're starting 30 seconds late.
And how do you set a clock that uses this scheme? If I want to set the clock to 3:00, do I wait until 2:59:30 and then set the clock to 3:00?
The headaches that arise from this scheme are not worth the trivial error reduction.
RMSE of proposed rounding to closest is 17.5 seconds.
The new method is roughly 17 seconds more accurate on average.
Does this reduced error make a significant difference? Probably not. There are very annoying practical issues with this proposal though.
Rounding down makes it clear what minute has already passed. If your clock says 3:00, you know the current time is definitely some point after 3:00. If something needs to happen at 3:00, and your clock says 3:00, it is time to start.
With this proposed method, 3:00 could mean anywhere from 2:29:30 to 3:00:30. When do you start? Do you start as soon as your clock says 3:00? Then you're starting 30 seconds early. Do you wait until your clock says 3:01? Then you're starting 30 seconds late.
And how do you set a clock that uses this scheme? If I want to set the clock to 3:00, do I wait until 2:59:30 and then set the clock to 3:00?
The headaches that arise from this scheme are not worth the trivial error reduction.