Newsgroups: comp.misc Path: utzoo!sq!msb From: msb@sq.sq.com (Mark Brader) Subject: Re: Gregorian Calendar start (was:Re: Leap Year Checker.) Message-ID: <1990Oct13.101434.21356@sq.sq.com> Organization: SoftQuad Inc., Toronto, Canada References: <1002@nlsun1.oracle.nl> <2188@ukc> <2457@root44.co.uk> <18359@haddock.ima.isc.com> Date: Sat, 13 Oct 90 10:14:34 GMT Lines: 98 I've waited a few days before responding to this in the hope that either (1) I'd find the old Usenet article on the topic that I printed off some years ago, or (2) the person who posted it, or someone else who knows, would see this thread and follow up. However, the details in that old article were interesting enough that I believe I have remembered them accurately. Well, Bjorn Engsig (bengsig@oracle.nl) writes: > Here are a few of the ways different European countries changed from 'old' > Julian Calendar to 'new' Gregorian Calendar: > ... > Sweden: Gradual change over 40 years (February 1712 had 30 days!). In fact, if I am remembering the old article correctly, what happened in Sweden was even more interesting than that. In the year 1700 or 1704, Sweden *decided* to gradually change calendars by omitting 11 leap years, and that year was made a common (non-leap) year. But 4 years later, with more pressing matters demanding attention, they simply forgot about it and had a leap year after all. So Sweden remained one day out of step with its Old Style neighbors. This state of affairs persisted until 1712, when it was felt that this was getting pretty silly, and the calendar was put *back* to the Old Style by having a double leap year (a very uncommon year!), with, as noted, 30 days in February. Much later, in the late 18th or the 19th century, Sweden converted in the usual fashion by omitting 11 or 12 days (respectively). Now, Tim Goodwin (tlg@ukc.ac.uk) writes: > Aha, but the Russian system (where the year is a leap year iff the > remainder on division by 7 is 2 or 6) is actually more accurate* than > the Gregorian system, as well as not having the confusion at the end of > a century. which Geoff Clare (gwc@root.co.uk) notes can't be right: > There are approx. 365.242191 mean solar days in the tropical year. > The Gregorian system gives 365 + 1/4 - 1/100 + 1/400 = 365.2425 days. > The Russian system (as described by Tim, I don't know if he's right) > gives 365 + 2/7 ~= 365.285714 days. Even the Julian system (365.25 days) > was more accurate than that! Geoff is right, of course. I believe the actual Russian system is to have leap years every 4 years except in century years where the *century number* (or is it the year?) has to meet the criteria given by Tim. *This* gives a year of 365 + 1/4 - 1/100 + 2/700 = 365.242857+ days, which is indeed more accurate than the Gregorian system. But we'll see how *they* like being one day out of step, beginning on March 1 (Gregorian), 2200... An interesting point in all this is that when the Gregorian system was first proclaimed in the 16th century, only 10 days were dropped. This means that, extrapolating backwards, the Julian and Gregorian calendars would agree not in the 1st century BC, when the Julian calendar was started, nor in the 1st century AD, which might be thought especially significant to the Roman Catholic Church, but rather in the *3rd* century AD, or more precisely, from March 1, 200, through to February 28, 300. Finally, Karl Heuer (karl@haddock.ima.isc.com) notes: > Interestingly, the approximation 365 + 1/4 - 1/128 is simpler, better suited > to binary computation, and over four times more accurate. He's right; it yields 365.2421875 days. Supposing that this calendar was made to agree with the Julian calendar beginning in the year 256 (to keep with the above), then the subsequent omitted leap years since then would be 384, 512, 640, 768, 896, 1024, 1152, 1280, 1408, 1536, 1664, 1792, and 1920... numbers much easier for anyone to remember than the silly 1700, 1800, 1900 stuff! Note incidentally that there were 13 years in that list, and the Julian and Gregorian calendars are now 13 days apart. This means that the Gregorian and Heuerian calenders are currently in agreement. This alignment would change in 2048, when the Heuerian (Lintian?) calendar omits a leap year, but it and the Gregorian then come back into line in 2100, only to separate again in 2176, come together again in 2200... A further advantage of the Heuerian system is that the total number of days in its overall cycle, 128*365 + 31 = 46751, is not a multiple of 7 as is the corresponding number in the Gregorian system, 400*365 + 97 = 146097 = 7*20871. This means that in the Heuerian system a particular date is equally likely to be any day of the week. In the Gregorian system, Christmas occurs on a Monday only 7/50 of the time; in the Heuerian system, this event gets its proper probability of 1/7. I think Karl has a great idea. Let's adopt it in Canada at once! :-) -- Mark Brader, SoftQuad Inc., Toronto, utzoo!sq!msb, msb@sq.com A standard is established on sure bases, not capriciously but with the surety of something intentional and of a logic controlled by analysis and experiment. ... A standard is necessary for order in human effort. -- Le Corbusier This article is in the public domain.