I got a couple of inquiries, which I answered in email, about this -- but that suggests a

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I got a couple of inquiries, which I answered in email, about this -- but that suggests a possibly more general interest in the Roman oddities of counting days. There is a tabular conversion, and some discussion, in the _Explanatory Supplement to the Astronomical Almanac_ (the current edition) on page 602, and I will expand on that a bit here. This source prompted my earlier question about the earliest date of a *our* counting convention: "By the eleventh century, consecutive counting of days from the beginning of the month came into use." which suggests to me that no such usage is known before 1000 CE. The Roman method involved two things which seem odd to us -- counting back- wards, and a somewhat counter-intuitive numbering scheme. Plus a wildly arbitrary placement of the mid-month "Ides" that are central to the scheme. Basically, each month has a "Calends" which is its first day; that we under- stand without problem. There is also an "Ides" in the midst of the month. Back in the mists of time, this may have been a kind of "fortnight" or half-month division. But classically, the Ides were on the 15th of the months March, May, July and October and on the 13th of all other months (I speculate that a 15th versus 13th Ides originated in 30 versus 29 day lunar months and originally located the full moon; but direct observation of the moon was irrelevant to the Roman calendar in *all* historical eras.) Just to complicate matters, there is a Nones 9-days (by Roman counting :-)) before the Ides. This is entirely algorithmic and causes no boggling of minds beyond that caused by the rest of the system (though it is of some interest that the Babylonian lunar observances noted new moon, full moon and first quarter but had no special 3rd quarter observance.) The Roman system doesn't really respect lunar phases, but it seems to have a memory of once having done so :-) [From our perspective, if the Ides represented the full moon conventionally taken as the 15th, then the Nones was 8 days earlier on the 7th which is a good match for the 1st quarter.] The end result is that in Roman calendar notation, all counting is *back- wards*, and one has to memorize what it is backwards *from.* And Roman counting is inclusive, so that the Ides of March is 15th March, and this counts as "1st" Ides (but is *not* written so) and the day before the Ides of March is "2nd Ides Martius." And so on down to "9th Ides", which is not so named, but called Nones Martius. What follows is a C function to print the Roman date, given one of ours. For full Roman obfuscation, one should use a function to print out Roman numerals for the integer n below (and probably do something like output the year as n+753 AUC in Roman numerals as well :-)) I have given in to the urge to present a Gregorian leap year reckoning, so that obscurantists amongst us can "use" this for current dates. ---- int ides[] = { 0, 13, 13, 15, 13, 15, 13, 15, 13, 13, 15, 13, 13 }; int mlen[] = { 0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 }; char *mnam[] = { "Jan", "Feb", "Mar", "Apr", "May", "Jun", "Jul", "Aug", "Sep", "Oct", "Nov", "Dec" }; roman(month, day, year) int month; int day; int year; { char *mark, *ref; int n; mark = "Calends"; ref = mnam[month-1]; if (day > ides[month]) { ref = mnam[month%12]; mark = "Calends"; n = mlen[month]-day+2; if (month == 2 && leap(year) && n < 6) n += 1; } else if (day > ides[month] - 8) { mark = "Ides"; n = ides[month] - day + 1; } else if (day > 1) { mark = "Nones"; n = ides[month] - day - 7; } else n = 1; if (n > 1) printf("%d %s %s %d\n", n, mark, ref, year); else printf("%s %s %d\n", mark, ref, year); } leap(year) int year; { if (year%4) return 0; else if (year%400) return 1; else if (year%100) return 0; return 1; } -- Michael L. Siemon "We honour founders of these starving cities mls@panix.com Whose honour is the image of our sorrow ... - or - They built by rivers and at night the water mls@ulysses.att.com Running past the windows comforted their sorrow."


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