Counting from 0, 2019 would still be the 19th year of the 21st century. I'm puzzled why you completely changed grammar to make it seem like counting from zero also solved the century mismatch. If anything it suggests that counting from 1 is more consistent. Then 2020 is year 20 of century 20.
But then 2000 becomes year 0 of century 20, which is confusing English. But "century 20" isn't great English anyway. Calendars should be 0-based like any other measuring tool. The 3rd minute of the 2nd hour of a marathon is 1:02. The 3rd day of the 2nd month of my marathon is 1/02. If that happens to be the 3rd day of the second month of the year, it's 2/03?
> Counting from 0, 2019 would still be the 19th year of the 21st century.
I think you meant to say the "20th" year (off-by-one error!), since 2000 would be the "1st" year under your grammatical assumptions.
I think it's safe to assume that if we conventionally counted from 0 instead of 1, we wouldn't refer to the initial thing as "first" (or "1st"). If we did maintain that construction, we would probably just refer to the initial century as the "0th century" and then 2019 would be the "19th year of the 20th century".
> But then 2000 becomes year 0 of century 20, which is confusing English.
I think it's only confusing because it's unconventional, not because there's something inherently more confusing about it. There have been plenty of languages that haven't even had counting systems that do anything more than "alone, pair, many" .. sure, you can find contexts where counting in general is confusing.
> The 3rd minute of the 2nd hour of a marathon is 1:02.
Right, under current 1-based counting convention, but the point of this discussion is that this inconsistency exists for basically no reason (or rather, historical reasons—look up the history of "0"). When people want to do arithmetic on ordinal numbers, they end up subtracting 1 to turn them into a zero-based natural number, then add 1 again to turn them back into an ordinal:
I suspect most off-by-one errors can indeed be seen as due to this inconsistency between conventional ordinals and the more arithmetic-friendly zero-based naturals. Again, since the former is simply convention, I claim it would be better if our convention were different.
It doesn't go from -1 to 1, it goes from 1 BCE to 1 CE. Negatives aren't used at all. Personally I think we should use zero and negative CE to extend backwards instead. So the year we currently refer to as 1 BCE becomes 0 CE, 2 BCE becomes -1 CE and N BCE becomes -N+1 CE.
But then 2000 becomes year 0 of century 20, which is confusing English. But "century 20" isn't great English anyway. Calendars should be 0-based like any other measuring tool. The 3rd minute of the 2nd hour of a marathon is 1:02. The 3rd day of the 2nd month of my marathon is 1/02. If that happens to be the 3rd day of the second month of the year, it's 2/03?