[keskival]

It's not really about flooring or rounding, but whether one thinks of time indices as ranges or moments.

Days, as the author points out, are though of with "flooring", but more accurately it could be said that a date is thought of as a range between the times belonging to the date.

Minutes one can consider as ranges or time indices. There the error comes, in switching the interpretation of a start of a duration to an actual estimate of a point of time index.

[ASalazarMX]

A minute is an insignificant period for most daily tasks, so the convention "show me when the minute changes" is simple and pragmatic. If your task needs precise count of seconds, you get a clock that shows when the second changes, and now you are half a second late on average.

You can keep playing with increasingly smaller time units until you conclude, like Zeno's arrow paradox, that you're always infinitely late.

[msm_]

Pointless remark about myself, but I always set my phone's clock to second precision (I think this setting is hidden somewhere, or even needs a third-party app to unlock), and I am annoyed there's no way to do this on the lockscreen. How is it possible that nobody else (apparently) wants it, and it's not the Android default? Why would I want a clock that is, on average, a half minute off?

[derbOac]

I think that's about right.

Another way of thinking about this is that the author is confusing time as measurement (how much time) with time as rule (what time is it). If you wanted to measure the duration as a difference in clock times, yes, there would be a certain amount of measurement error incurred by the way clocks are displayed. But if you want to know the time, in the sense of whether a certain time has been reached, or a certain graduation has been crossed, it doesn't make sense to round to the nearest minute.

The question of "how much is this clock off?" is only meaningful with reference to a certain use or interpretation of the numbers being displayed. If you say it's "8:56" people know it could be anything up to but not including 8:57, but greater than or equal to 8:56. The number means a threshold in time, not a quantity.