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When Y2K was a hot topic, I was surprised to learn that the church (at least the protestant ones, but I assume that catholic ones agree, and then the other (Christian) ones follow suit) have a discontinuous time line: Year 1 BC is immediately followed by year 1 AD, with no intermediate year 0. So the question is if the time format used here has a year 0. We must assume that value 1 is AD (or if you like: CE), but is a value of 0 then 1 BC, and a value of -1 consequently 2 BC? Or is value 0 illegal?
I was surprised to read in Wikipedia that the numerical value of AD/BC and CE are identical, with "400 BCE corresponds to 400 BC" explicitly given as an example. So the CE concept has adopted a discontinuous number line for labeling years. It is kind of curious that in an attempt to mark an independence from religion defined time scales, still we stick to a highly religion defined number line, rather than a mathematical one.
Maybe it has to do with the zero being invented by the Arabs, and as we all know, their culture is not quite as we want it to be, so we reject it. What I am now waiting for is some (secular) standard that requires 1 = 3.
(for Americans, that's the logical order of day-month--year).
That's the typical Eurocentric ass-backwards mindset.
YYYYMMDD, with whatever delimiters float you boat.
As for the US Vernacular, most conversations would say something like October 25th or June 2nd. The year is only necessary, in conversations, a fraction of the time. So - the dates are written as they are said. But, as far as it goes, it's no worse for sorting (even when numeric) than the crappy Euro-convention. At least, if all in the same year, the US convention MM-DD would sort correctly (small consolation).
Usually, Americans consider every single NIH standard "crappy". If an ISO standard does not exactly and without modifications specify established US traditions and conventions down to the last detail, then the standard is not invented here, and is crappy. ISO standards are great if they state that the way Americans always have done it is The Right Way to do it. Otherwise: Forget ISO standards!
ISO 8601[^] has been rapidly growing as The date format in all formal and technical application. It has not taken completely over yet, but every year you see increased usage, in all sorts of paper and electronic forms, in automatically formatted printouts etc. The yyyy-mm-dd format is consistent, all details of the format is strictly defined, and the textual representation can be sorted correctly as text. (8601 convers time as well as dates.)
In informal speech, we still say "twentysecond of October, 2018", we never say "October twentysecond, 2018". Funny enough: When I talk with native English speakers, they use the "twentysecond of October" form more often than "October twentysecond" in their speech, but they all insist on writing "Oct. 22nd". I guess that Europeans will continue to say it the same way as before, that is the most common way for English speakers, but just like the English speakers, we will gradually change to use the ISO 8601 even when writing with a quill, because that is what we see every day where dates are formatted (or consumed) by a computer. Most information today is.
For the discussion about which is the "natural" order - from smaller to larger, or larger to smaller (forget the mixed-order alternative!): Isn't it funny that for DNS names, smaller to larger is "natural", but for IP addresses, larger to smaller is "natural".
Also: Our numerals are Arabic, and we write the digits in the same order in Latin based scripts as the Arabs do - but we read them in the opposite order! In Arabic, "24 blackbirds" (or "sdribkcalb 24" if you like) is read like "four-and-twenty blackbirds" (or German: "vierundzwanzig Amseln"). The right-to-left reading of numbers is gradually disappearing; it was far more common earlier. Nowadays, left-to-right reading is the standard in both English, Norwegian, Swedish and several other European languages that earlier used the Arabic / German reading order.