The average error is in fact 0! The average absolute error is reduced but not 0.
That may technically be correct, but it is incorrect in the real world. I submit that error is error in the real world. Mathematics can go jump off a cliff unless it wants to be helpful. :)
Re:All clocks are 30 seconds late
by roywiggins on Monday January 06, 2025 @01:25PM
(#42613491)
Zero average error conveys something important though: the error that there is, isn't biased positive or negative.
That's language failing us, not maths :-)
What are you talking about? Error is a metric.
By this logic, a broken 24 hour clock stuck at mid day has 0 error.
The average of its errors is 0- ie it is not biased. Ofc, the average absolute error, which in English one could very reasonably refer to as "average error" is much greater than 0.
Re:All clocks are 30 seconds late
by fouronnes3 on Monday January 06, 2025 @01:03PM
(#42613191)
That's a very fair nitpick, but even with a more rigorous error function the point still stands, I think.
Agreed. There will be less error, just not zero. I thought it was a silly error that detracted from the point, rather than defeated the point.
It depends on the application. Are you summing times (as with a pay clock at a job), or are you paying for error in both directions for some reason?
Re:All clocks are 30 seconds late
by lavelganzu on Tuesday January 07, 2025 @12:30PM
(#42624968)
Good catch. RMS (root mean square) error is typical in signal processing to avoid this undesirable cancellation.
"If clocks rounded to the nearest minute instead of truncating, the average error would be 0.”
The negative and the positive error don’t cancel each other out. They are both error. The absolute value needs to be used.