What's this whole "28 year cycle" anyway?

Why did I start thinking about this?       Oh, remember way back when we were all worried about the Y2K thing (now wait .. I'm not knocking the issue .. we spent alot of money, yes .. but I believe it to be well-spent .. but there was some unnecessary and weird hype). One of the "issues" that people discussed was whether VCR's would be compliant. There is a solution if you happen to have a non compliant VCR - set it to 1972! Since we have a 28 year calendar, that will give a day to date exact copy - that is, April 5th, 1972 and April 5th of the year 2000 will both be on a Wednesday). But, I was thinking about this and decided there is more to this than we thought (or maybe less?).

Why the 28 year cycle?       Well, take 365.25 (the quarter day is for the leap year) and multiply by 28 years ... you get the number 10227 {the first time a whole number is reached in multiples of 365.25 that is divisible by the number 7 (as in 7 days in a week)}. Thus, the calendar day-vs-date can cycle through the whole week and come back in synch. But, what about those pesky leap days? Take a deep breath ... If we say that all the days of 1972 are the same as 2000, I wonder how many leap years are included in that? The rule is that if the year is divisible by 4, it's a leap year ... except if it is divisible by 100 ... but it is again if it is divisible by 400! Thus, 1900 was not a leap year, but 2000 will be! [There has be some controversy over this, but this is the correct rubric.]

What about the leap days .. does that mess things up?       Sort of .. let's take a look. For the 1972-2000 cycle, we will add a day in the year 1972, 76, 80, 84, 88, 92, 96 and 2000 = 8 leap days added overall (since both ends are leap years). What about starting with the year 1973? we would have 76, 80, 84, 88, 92, 96 and 2000 = 7 leap days added overall!! But, checking my calendar program, 1973 and 2001 *ARE* identical day-to-date-wise. So, if both end years are leap years, there would be 8 days, and if not, seven days ... are there years that it won't work? Hmm, oh, what about 1899 to 1927? - Bingo! Doesn't work .. that pesky 1900 didn't have the leap day, so it throws things off! 1904, 1908, 1912, 1916, 1920, 1924 = 6 days! (So at least part of the year is out of joint). So, it seems that any 28 year cycle that includes one of those "strange" leap years won't work .. thus, starting with the 1901+1929 pair .. we are good-to-go up through 2071+2099 .. 2100 is one of those pesky years that doesn't give us a leap day, so it throws everything off. When does the trouble start? The companions 2071+2099 are fine for the whole year .. but 2072+2100 are only good from Jan 1st to Feb 28th (see, 2072 has a leap day, but 2100 does not, so there will be a Feb 29th, 2072 but no Feb 29th 2100, thus the day of the week gets skewed!) ... since 2100 "should have been" a leap year, but is not, it throws off the rest of the year. Then 2073+2101 (first year fully out of synch) on up to 2099+2127 will be completely out of synch. (By that, I mean that there isn't a single day and date that matches for both years - if you think about it, aside from the leap day, that has to be true ... if March 10th matched, then March 11th would also, etc. The leap days then serve to partially bring you back in synch, or keep you out!) Then, for 2100+2128, only from March 1st through Dec 31st will they be in synch (the leap day in 2128 can bring the cycle back in synch), then in 2101 and farther, we will repeat the 28 year cycle up until 2200 (doh! another weird non-leap year!) (actually the 2171+2199 pair is the last good one). If you vcr can hold out until 2400, no problem, that will act like the 2000 crossover, and we will have smooth sailing! What's the bottom line here ... you better get a Y2K complient VCR by the year 2071, or you'll be a some big trouble, you will - that's all I'm saying! (Ok, someone needs to point out that you could just keep resetting the year back to 1972 each time 28 years have passed .. that's true, but then I wouldn't need to create this program and put stuff up on the Astro-wall on the Second floor of the Science building!) And, Melissa, in answer to your as-yet-unasked question .. "Why do this?" ... "Because we can!" [ By the way .. here is Version 1.0 of my year28.exe program (runs under any version of Windows) The program will let you investigate the synchronization of the days in the 28 year cycle, and see which years mess it up (such as 1900 and 2100). Also, there is some information on the second floor of the Science building on the "Astro Wall"!]

Still reading this? .. how about some more obsessive-compulsive stuff about the calendar?      The above info is about the calendar year cycles (Jan 1st - Dec 31st) - that are caused by (aided by?) leap days. What about a 'wrap around' cycle .. say March 1st to Feb 28th (since the leap days shift the cycles)? First, how many times does 7 fit into 365? 7*52=364 .. therefore each normal year we would add one weekday (thus, if March 1st, 1992 is a Sunday, then March 1st, 1993 is a Monday). But during the leap year transition, we would add two days. All we need is seven weekdays to shift until we are back on track again, but with the leap days, it would seem that less than 7 years are needed. Let's look : March 1st, 1992 is a Sunday (and that was a leap year) - for successive years we add one weekday (or two if a leap year transition has occured) .. 1993=Monday (+1) .. 1994=Tuesday (+1) .. 1995=Wednesday (+1) .. 1996=Friday (+2 because of leap year) .. 1997=Saturday (+1) .. 1998=Sunday (+1) Hey, we came back around again ... a 6 year-cycle pair (for the Mar1-Feb28 timeframe). What about 1993? March 1st, 1993=Monday - 1994=T - 1995=W - 1996=F (L.Y.) - 1997=Sa - 1998=Su - 1999=M (6 year cycle .. cool!) What about 1994? 1994=T - 1995=W - 1996=F (L.Y.) - 1997=Sa - 1998=Su - 1999=M - 2000=W (L.Y.) Yikes! .. keep going .. 2001=Th - 2002=F - 2003=Sa - 2004=M (L.Y.) - 2005=T hey it is an 11 year cycle Ok, here is the "rule": The March1st-Feb28th(of the next year) will line up again in : 6 years if March1st is in a leap year, or in the year after; 11 years if March1st is two years before or after a leap year; 5 years if March1st is in a year before a leap year.

Closing thoughts.      Is this useful? (I can't imagine how...) Is this fun to figure out? (It was for me ...) Are you intrigued? (I can't answer that ...) Have I exhausted this inquiry? (Don't bet on it ...) But, for now, I will leave you alone to contemplate the Calendar and the Universe in which it lives.

See how the moon fits into all of this at the Blue Moon page!

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