Thursday, December 31, 2015

Leap Years & Leap Seconds


Introduction

Tomorrow is the start of a leap year.  What does this mean, besides the obvious bit about there being a February 29?  Why do we observe leap year?  What folk traditions surround this?  What is a bissextile year?  What practical matters does the leap year introduce?  Is “Leap Year” a good movie?  What is a leap second?  I will answer all these questions, and more, in this post.

A helpful mnemonic

You probably already know this by heart, but here’s a handy mnemonic for keeping track of the number of days in each month: 
30 days hath September, April, June, and November.  All the rest have 31, except for February, which usually has 28 but has 29 on leap years, which occur every four years unless the year is divisible by 100 but not by 400, a distinction we make to account for the slight rounding error that occurs by counting each year as 365.25 days when it’s actually 36.24; by skipping leap years on turns of the century that are not divisible by 400, the Gregorian calendar is able to compensate for the 11 minute loss of accuracy each year.
From a completely self-serving standpoint, we could probably dispense with leap years, since the drift in the calendar would take several generations to really foul things up.  But is that really the kind of world we want to leave to our grandchildren’s grandchildren?

Are you looking for an easy way to tell if it’s a leap year?  They tend to coincide with Presidential elections.  But you have to be a bit careful:  even though 2000 was a leap year (being divisible by 400), 2100 won’t be.  If you’re lucky enough to be alive in 2100, you’ll have to keep that in mind.

Folk traditions around leap year

According to Wikipedia, “In Ireland and Britain, it is a tradition that women may propose marriage only in leap years....  Supposedly, a 1288 law by Queen Margaret of Scotland (then age five and living in Norway), required that fines be levied if a marriage proposal was refused by the man; compensation was deemed to be a pair of leather gloves, a single rose, £1 and a kiss.”

There’s just so much to react to here!  First of all, it puts me at ease about the upcoming American Presidential election.  Scotland is in pretty decent shape, as far as I can tell, despite having once been ruled by a five-year-old who wasn’t shy about pushing through sweeping legislation.  So, whoever wins our next election, how badly could he or she really screw things up?

Personally, I’d like to bring back this leap year marriage proposal law.  Don’t get me wrong, I’m not suggesting that men are the only ones allowed to propose marriage in this day and age.  Yes, the prevailing tradition is still for the man to pop the question and present the ring, but he wouldn’t do so without some kind of tacit advance consent, unless he’s a fool.  In other words, the thinking man won’t propose to his sweetheart unless he’s quite sure she’ll say yes.  In this way, the woman is actually holding the cards.  (Of course you could mix & match the pronouns around all you want here.)

The part of that law I like, though, is the compensation the man must provide when turning down a proposal.  To bring back that law would create jobs, or at least create income for a daring woman.  She could find some schmuck who doesn’t seem her type, then do everything in her power to alienate him, and then propose, just so she could collect her gloves, flower, money, and kiss.  Sure, £1 isn’t much money today, but adjusting for the inflation since 1288, it would be a considerable sum.

You may be wondering:  is courtship the aspect of leap year that introduces the term “bissextile”?  Well, I hate to break it to you, but this term isn’t nearly as racy as you’d think.  “Bissextile year” is just another term for leap year.

Is “Leap Year” a good movie?

I’ll be honest with you, I never much cared for doing research, but this blog sometimes demands it.  When that happens, I’ll always prefer a popular video over some thick book.  Thus, I was pleased to see that the third Google hit on “leap year” was a movie by the same name.  Better yet, “Leap Year” stars Amy Adams, whom I enjoyed watching in “Junebug,” “American Hustle,” and “Big Eyes.” 

Alas, my hopes fell when I went to IMDb and saw the Metascore for “Leap Year” ... 33 out of 100, one of the lowest scores I’ve ever seen.  (Consider that “Star Wars:  Episode I – The Phantom Menace” got a 51.)  I scanned the highlights from various critics:  “A by-the-numbers romantic comedy as predictable as it is cloying,” “Virtually every word and plot turn is insincere, manufactured, unfelt and dishonest,” “Mostly awful,” “It’s unclear what Amy Adams did to deserve Leap Year,” “Using Love to Shed Pounds and Boost Confidence in School,” “A retread of just about every rom-com cliché ever turned,” and—wait!  What was that bit about using love to shed pounds?  Oh, an ad crept in there.  Geez.

Looking for any shred of silver lining, I consulted the IMDb Parents Guide:  “No sex scenes. A woman is briefly seen in her underwear.  There is a short fight scene, but it is not very frightening, and could even be considered comical.”  I think when the viewer can’t tell for sure if a movie scene was meant to be funny, that movie is automatically in trouble.

What does leap year mean to me?

At first glance, it would seem that as long as we avoid the movie “Leap Year,” we won’t be materially affected by there being 366 days in 2016.  That said, the following leap year, 2020, is going to cause me some heartbreak.  You see, I have this great wall calendar commemorating the 50th anniversary of my dearly departed favorite restaurant of all time, and though it’s a 2009 calendar, all the days of the week are the same between 2009 and 2015.  Thus, I got to enjoy the use of it all year long (it’s hanging out in the garage).  I was hoping to use it again six years from now, but leap year gets in the way.


How does leap year interfere?  Well, here’s the thing.  Normally, the day of the week on which January 1 falls will change by one day each year.  The year 2013 started on a Tuesday, 2014 started on a Wednesday, 2015 started on a Thursday, 2016 will start on a Friday, etc.  The term “leap year” derives from the fact that a day of the week is “leapt over” during a leap year.  That is, instead of 2017 starting on a Saturday, it will leap over Saturday and start on Sunday (owing to the extra day in February).

If it weren’t for leap year, we could reuse our wall calendars every seven years, meaning I could re-hang my La Fiesta calendar in 2022.  Leap years make it more complicated.  Because 2012 was a leap year, and skipped over a weekday, I got to use my 2009 calendar again this year (2015 instead of 2016)—so I saved a year.  Does that mean I’ll get to use it again in another six years?  Well, 2016 being a leap year will speed things along, like 2012 did.  But 2020 is also a leap year, so 2021 will leap over Thursday and land on Friday.  That means I won’t get to use this calendar again until 2026!



Not only will this require me to be more organized, but for a whole decade I’ll have to keep that calendar from being “disappeared” by my wife.  This will be a bit like secreting a war refugee in my attic, because my wife is the polar opposite of a hoarder.  For example, if my younger daughter stops playing with a stuffed animal or toy for any period of time, it goes to this purgatory area in the closet for a few weeks before being given to the Goodwill.  Whenever I’m at home I have to be careful to keep moving, lest my wife drag me out to the curb with the garbage and recycling.

What is a leap second?

My family, I’m proud to say, is a bunch of nerds.  Tonight, for example, my brother Bryan will entertain guests at a New Year’s gathering by giving a short lecture, including a demo, on the slide rule.  Similarly, on Christmas Eve, my wife gathered the kids and me in the living room to hear her read aloud from a speech titled “Pericles, in a Deathless Funeral Oration, Sums Up the Glory That Was Athens,” written in 430 B.C.  (I found the speech enjoyable, even the part where my kids burst out laughing because I was snoring.  Later in the speech I got confused about whether I’d heard the word “turban” or “turbine,” and apparently I talked in my sleep because this got another big laugh.  Neither word actually appears in the speech; I’d dreamt it.)

Furthering my family’s nerd cred is the exchange of e-mails we’ve had about leap years. I sent out the handy mnemonic that started this blog post, and my older daughter offhandedly asked, in reference to the rounding error that makes leap year necessary, “Yikes... couldn’t they just fix the rounding error in the first place?”  This question may have been rhetorical, but my dad provided a very thorough answer, explaining that it isn’t exactly right to say we make a rounding error by calling a year 365.25 days when it’s actually 365.24.  The truth is more complicated than that:  
“The mnemonic has 97 leap days per 400 years, so instead of a simple 365.25 days per year (which it would be if there were 100 every 400) the current calendar gives 365 97/400 or 365.2425.  The actual number of days per one year, from measurements, is a bit different, and wanders a little from year to year, unpredictably [due to tides slowing down the earth’s rotation, and the cycle of water freezing and thawing, which brings about changes related to conservation of angular momentum].  So to keep our civil clocks in match with the much more regular rhythm of the standard atomic clocks, ‘they’ add a leap second sometimes.  This has been necessary 26 times since 1972, the most recent being at time 23 hours, 59 minutes, and 60 seconds on June 30 of this year.  That minute had 61 seconds!”

My niece chimed in, recalling how excited her dad (i.e., my brother Bryan), had gotten about the last leap second.  She asked the other e-mail recipients, “I’m curious, ‘mathletes,’ how you’d calculate when to add the next leap second.”  This, too, elicited a very detailed and math-infused answer from her grandpa, which began, “Interestingly, it is not just a question of math, but one of exacting observational astronomy.  Oh, there is some math involved, but it is quite straightforward.  And there is a decision to make:  what is a ‘socially acceptable’ time to insert (or delete?) the second.  Midnight on June 30 is the very middle of the calendar year, a seemingly reasonable time to adjust the clocks.”

The explanation went on from here and involved meridian transit telescopes, measurements taken at a very  specific time of day, the effect of the Earth’s rotational precession (i.e., of the fact that it wobbles) on when equinoxes occur, and a bunch of other stuff I don’t really understand.  I wasn’t about to tackle the math involved, but was intrigued by the “socially acceptable” aspect of the leap second, and the friction that inevitably results when scientists present their findings to those who turn them into public policy.

Reading up on the leap second on Wikipedia, I discovered (not surprisingly) that politics does influence the leap second’s implementation (more on that in a minute).  I also discovered some other interesting tidbits, such as this:  “Muslim scholars, including al-Biruni in 1000, subdivided the mean solar day into 24 equinoctial hours, each of which was subdivided sexagesimally, that is into the units of minute, second, third, fourth and fifth, creating the modern second as 1⁄60 of 1⁄60 of 1⁄24 = 1⁄86400 of the mean solar day in the process.”  

I’m guessing that if Donald Trump were to become President, some cabinet member who happened to read up on leap seconds could approach him with the fact that it was Muslim scholars who defined the method by which we subdivide our days, and drop the name “al-Biruni” a bunch of times, and Trump would immediately want to take the USA off of the 24-hour, 60-minute, 60-second standard.  (Never mind that the sexagesimal system originated with the Sumerians and Babylonians.) 

Why would anybody want to open this can of worms?  Well, if we were to adopt a decimal basis for measuring time (as feasible an alternative to the current scheme as any, and probably easy to sell to The Donald), this might be a nifty back-door into finally getting the US into the metric system, albeit a modified version that uses base-10 for everything, including time.

I was also interested to read, on the Wikipedia leap second page, about problems that the leap second has caused with computer systems, due to its six-month notification not being enough time for developers to prepare:  “A number of organizations reported problems caused by flawed software following the June 30, 2012 leap second....  Despite the publicity given to the 2015 leap second, Internet network failures occurred due to the vulnerability of at least one class of router.  Also, interruptions of around 40 minutes duration occurred with Twitter, Instagram, Pinterest, Netflix, Amazon, and Apple’s music streaming series Beats 1.” 

That list reads like a “who’s who” of needless time-wasting Internet social media and passive entertainment platforms, doesn’t it?  I think that instead of abolishing the leap second, or getting developers to step up their game in preparing, we should create a national holiday around the post-leap-second outage, where for forty minutes after each leap second, people engage in offline, timeless activities like face-to-face socializing, reading books, and maybe venturing outdoors.  (Presumably this interruption will begin at 23:59:60 UTC, which would be 15:59:60 Pacific, a perfect time for a stroll.)

I was similarly intrigued to learn that Google, never one to be pushed around by governing bodies or consortiums like the International Earth Rotation and Reference Systems Service, has their own scheme for handling the leap second:  “Instead of inserting a leap second at the end of the day, Google servers implement a leap smear, extending seconds slightly over a time window prior to the leap second.”  I’m not sure exactly what to make of this workaround, other than to note that “leap smear” would be a good name for a rock band.

And on that note, I wish you a happy, healthy, and rockin’ 2016!
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