Tuesday, September 30, 2014


A company at which I once worked had to solve the "Y2K problem" where comparing year 99 with year 00 gives you the wrong result.  The comparison yields "99 is greater (later) than 00" and that's wrong because it's really [19]99 vs [20]00.  The solution they implemented was to subtract 28 from every year they had to process so that "99 v 00" became "71 v 72" which yields the correct result: '71 is smaller (earlier) than 72".  Why 28?  Because every 28 years the calendar repeats itself and days-of-the-week exactly match date-of-the-year.

Of course, this only works because 2000 was a leap year.  "Of course, 2000 was a leap year!" I hear you exclaim. "It's evenly divisible by 4!"  Well, actually, no, that's not the whole rule.  A year is a leap year if it's evenly divisble by 4, but not if it's evenly divisible by 100 — unless it's also evenly divisible by 400.  1900 was not a leap year, and 2100 won't be, either.  Wait;  you'll see.  1600 was a leap year, and 2400 will be, too, although I doubt very much that you care.

This got me to thinking about why our calendars repeat, and why every 28 years and not every 14 years.  Here's why:

There are only 14 unique yearly calendars.  There are seven for "January 1st is sUnday, Monday, Tuesday, Wednesday, thuRsday, Friday, and sAturday.  We'll call these calendars U, M, T, W, R, F, and A.  There are seven more for "this is a leap year"; we'll call those U*, M*, T*, etc.

If a year were 364 days long (52 x 7), every year would begin on the same day of the week.  Since the typical year is 365 days long, succeeding years begin on succeeding days of the week: if this year began on a Tuesday, next year will begin on Wednesday.  When it's a leap year (366 days), next year will skip a day;  instead of beginning on Wednesday, it will begin on thuRsday.  Every 4th year will be a leap year.  So, let's see how they line up.

Let's assume a starting point where January 1st is sUnday, and it's a leap year.  The first calendar is U* and it's 366 days long.  The next calendars will be T, W, R, and F*.  Next is U, M, T, and W*, then F, A, U, and M*, then W, R, F, and A*, then M, T, W, and R*, then A, U, M,and T*, then R, F, A, and U*.  We are now back where we started, at a calendar with January 1st on sUnday, and it's a leap year.  Let's see how we got there.

U* T W R F*
U M T W* F A
U M* W R F A*
M T W R* A
U M T* R F A

In 28 years, each day of the week gets to be associated with 'starting a leap year' once and 'not starting a leap year' thrice.  Neat, but it only works if every 4th year is leap.  As long as you don't cross a non-leap-century-boundary (and that only happens three times every four hundred years) you're okay.

While we're on the topic...  Every once in a while I see some nonsense either on FaceBook or via e-mail that says something like "This May has five Fridays and five Saturdays and five Sundays! That only happens once every 42 bazillion years!"  Well, as a matter of fact, no.  It happens four times every 28 years and now you know why.

Wednesday, July 23, 2014

Heidelberg, 23 July

The boat docks on the Neckar River somewhat downstream from Heidelberg and buses take us the rest of the way.  It's a time-saving gimmick: the boat is slow compared to buses; while we're touring Heidelberg castle and its town, the boat can complete the trip to Speyer and we'll be that much further along.

Heidelberg is impressive, but much less so than I had expected.  In that sense, I guess, it was a disappointment for someone who has watched The Student Prince once too often.

No pictures here, alas.  Viking River Cruises' free Wi-fi is worth every penny I paid for it -- uploading anything is next-to-impossible.

Koblenz and Marksburg Castle, 22 July

Great weather again.  Temps in the high-70s and bright sun. The boat docks at Koblenz, a name which derives from 'confluence' because here the Main River flows into the Rhine.  

Buses take us up to Marksburg castle, the only German castle never successfully attacked.  As a result, it is in pristine condition.  "Pristine", in this case, means it looks and feels like something out of the Middle Ages.  There are few, if any, alterations beyond basic creature comforts like toilets.  I'd show you images, but I've already spent nearly an hour unsuccessfully trying to upload two using Viking's 'free Wi-fi'.  You'll just have to take my word for it.

Cologne, 21 July

(Posted from Speyer DE.)

It's raining in Cologne, but not heavily, and our guide is a hoot!  He's got a Masters in History, so he knows where all the bodies are buried.  We avoid the cathedral (which is closed, anyway, thank heaven) and prowl the downtown area, finally settling on a tractor-driven tram that gets us back to our ship.

At dinner, the waiter looks at our table and whispers in my ear: "I've seen tables of six with only one man, but never a table of eight with only one man.  How did you do that?"  If I ever find out, I may sell the secret to him, but he won't get it for free.  At 'my' table is Norene, Patricia, Cathy, Gail, Carolyn, and Marcia 1 and Marcia 2.

Post-dinner entertainment is a cello-piano combo performing (excellently) selected short pieces.

Monday, July 21, 2014

Kinderdijk, 20 July

(Posted from Cologne) 

Windmills don't grind grain; they pump water to keep The Netherlands dry. 

They were going to demolish the windmills at Kinderdijk because the newer pumps are so much more efficient, but a Dutch princess pointed out that the rest of the world knows only a few things about Holland: tulips, dikes, wooden shoes... and windmills.  They kept these 19.  Now they can't pull them down because it's a UNESCO World Heritage site.  

There is a message told by the way the vanes are parked: horizontal is 'taking a break'; 11:00 is happiness (births, weddings); 1:00 sadness (sickness, death); 9:30/1:30 is 'permanent stop'. These vanes mark the loss of many Dutch aboard MH17.  (You're seeing them from the back.) 

Re-board and we're outahere for Cologne. Internet service will be spotty the whole trip.

Amsterdam, 19 July

(Posted from Cologne.)  

Our hotel is close to the Viking docks, but far from everything else.  Tram 26 to Central Station and bus 48 to the Maritime Museum and suddenly we're in the 17th century, when the VOC, the Dutch East-India Company, ruled the world. 

The cannons are an interactive exhibit designed to teach children and adults to work a warship.  In the cargo hold is a jungle gym made of ropes and barrels.  Norene remarks that in the US, all this would be marked "Do Not Touch". 

We board the Var in time for dinner.  At 11:30 the boat departs for Kinderdijk.  

Amsterdam, 18 July

(Posted from Cologne DE.)  

Viking says they have 'free Wi-Fi', but it only works in port.  When you're in port, you're on a tour.  When you get back from the tour, you're under way.  Catch-22.)

The best laid plans of mice and men gang aft agley, and mine are no exception.  The Rijksmuseum... out.  The VanGogh museum... out.  Anne Frank's house... out.  A walking tour of Amsterdam has shown us that the Red Light district is far more confusing than shocking, but we are better for the experience. 

At least we know where the shopping is best, and we now have a 24-hour tram/bus pass.  It will serve us well tomorrow.