Time intervals aren't floors or rounds but thresholds.
This is most evident above the level of hours, minutes, or seconds: we speak of a new day beginning (though the time at which this occurs has varied culturally and regionally), or a new year, decade, century, or millennium (with their own threshold arguments courtesy the AWOL Year Nil in the Julian/Gregorian calendrical system).
Birthdates are an interesting example. In Western/European cultures, it's typical to count by full years elapsed, such that an infant within its first 12 months is 0 years old. In Asian cultures, the age is given as "1", which is reflected in an occasionally-used Western notion of "being in my nth year". That is, a 49 year old is in their 50th year.
What a clock (or calendar) indicates generally is what time period you are presently in, that is, the second of a minute, the minute of an hour, the hour of a day, day of a month, etc., etc. And what's relevant from this point of view is that the threshold is what matters.
The other problem touched on in this essay is of estimating time remaining to a future threshold, and here, rounding is indeed useful. If you have a 10am meeting and the time presently reads 9:55 am, you have fewer than five minutes to arrive punctually. But that is planning and not timekeeping issue, strictly.
This is most evident above the level of hours, minutes, or seconds: we speak of a new day beginning (though the time at which this occurs has varied culturally and regionally), or a new year, decade, century, or millennium (with their own threshold arguments courtesy the AWOL Year Nil in the Julian/Gregorian calendrical system).
Birthdates are an interesting example. In Western/European cultures, it's typical to count by full years elapsed, such that an infant within its first 12 months is 0 years old. In Asian cultures, the age is given as "1", which is reflected in an occasionally-used Western notion of "being in my nth year". That is, a 49 year old is in their 50th year.
What a clock (or calendar) indicates generally is what time period you are presently in, that is, the second of a minute, the minute of an hour, the hour of a day, day of a month, etc., etc. And what's relevant from this point of view is that the threshold is what matters.
The other problem touched on in this essay is of estimating time remaining to a future threshold, and here, rounding is indeed useful. If you have a 10am meeting and the time presently reads 9:55 am, you have fewer than five minutes to arrive punctually. But that is planning and not timekeeping issue, strictly.