The Grand Si11iness of 11/11/11 11:11:11

Matt Strassler 11/11/11

Today is a special day — at least if you are fond of the numeral 1, or the number 11, and especially so if you’re willing to buy in to one of the oldest human pseudo-scientific pursuits: numerology.  Oh, don’t get me wrong, I love numbers and I always have.  When I was five years old I was mesmerized when my parents’ car reached 99,999.9 miles, and I think 12:34:56 on 7/8/90 is just a cool a time as anybody else does. But I do this with a sense of humor.

Unfortunately it happens that a few influential people attempt serious and consequential numerology involving the calendar — predicting disaster and convincing people to sell their homes and give away their belongings.  Now that makes me mad.  Outraged, in fact — because it’s often obvious from the way these predictions are generated that those who made them don’t understand much about the calendar, about time, about history and about astronomy or physics… and yet they speak with authority, an authority they haven’t earned and don’t deserve.

Of course the movies play this up too, making money off of people’s fear: we have an 11/11/11 horror film in store.  The prophet intones: “On the eleventh hour of the eleventh day of the eleventh month…” Well.  By the end of this article I hope you’ll wonder what he’s even talking about.  [Note added: I should have emphasized, for non-European readers, that the phrase “on the eleventh hour…” refers to the moment that it was decided, arbitrarily, that the Armistice ending the First World War should be signed. Is it not ironic that this tragically modern war was concluded at a time chosen by an ancient form of calendar numerology? Perhaps more enlightened leadership could have avoided future disasters.]

Meanwhile, we should most certainly drink to this one-one-of-a-kind moment, and as we do, let’s also remember, and enjoy, just how absurd it really is.  Let us even count the ways.

Cycles and Compromise

Let’s look at our string of elevens: we are 11 years after the year 2000; 11 months and 11 days after the start of the year; 11 hours, 11 minutes and 11 seconds since midnight.

Each of the first three 11’s has something to do with astronomy — but if we look closely, something’s a little off.

First we need to count years, and a year is the time it takes the earth to orbit the sun.  Almost.  Not quite. An astronomical year is the time it takes the earth to orbit the sun. A calendar year? that’s something else.

Then we need to count months. A month, of course, is roughly a “moon”, the time between two full moons … and a full moon occurs at the moment that the sun is on one side of the earth and the moon is on the exact other side.  In some calendars around the world and throughout history, a month is a moon — but not in ours.

Then there’s the day: the time it takes for the sun to go from overhead to setting and rising and back to overhead again.

The problem with all of these astronomical cycles is that they are not well-synchronized.  The number of moons in an astronomical year isn’t a nice number; nor is the number of days in an astronomical year, or in a moon.

The number of days in an astronomical year is close to 365 and a quarter, not 365 or 366.  That’s why at some point it was decided (by whom? and when? and on whose authority? our democratic society keeps track of its dates under the decree of a Roman emperor) that we would have three years in a row of 365 days, and then a fourth year of 366 years — a “leap” year.  That way, the number of days in four years is just about 1461.   But even this isn’t exactly right, so thanks to Pope Gregory, 3 of every 400 years (most recently the years 1700, 1800, and 1900, but not 2000) we skip a leap year, to get back on track.  More or less.  It’s still not perfect.

Of course this way of doing things is completely arbitrary!  We could just as well have 19 years of 365 days, and then in the 20th year have an extra five days.  Or we could go 99 years of 365 days, with an extra month of 25 days at the turn of the century.  Indeed some calendar systems around the world do something just like that.  If we’d decided to do either of those things, there wouldn’t have been a leap year in 2004 or 2008, and today wouldn’t be 11/11 at all! It would be 11/13.

Or if Pope Gregory had chosen to put the leap years not in 2004, 2008 and 2012 but instead in 2001, 2005 and 2009, again it wouldn’t be 11/11 today.  It would be 11/10, because of the leap year in 2009.  And so forth.

So let’s celebrate 11/11 — an accident of the leap year decisions of a Roman emperor and a Roman pope.

We’ve hardly begun.  Let’s talk about those months.  The number of days in a moon is about 29 and a half, so a moon is neither 29 nor 30 days, which is sort of inconvenient.  And worse, it also doesn’t divide 365 (or 366) very conveniently; a year is quite a bit more than 12 moons and quite a bit less than 13.  So how did we end up with 12 months of 30 or 31 days (except for February)?  Well, you can blame the Roman emperors for that too: we’ve inherited our calendar mainly from Julius Caesar (who got a month named after himself — a long one with 31 days) with adjustments by Augustus (who had another month named after himself and made sure it too was one with 31 days).  And so the days per month are all funny.  Why not, you might ask, have 12 months alternating between 29 days and 30 days, and 1 extra mini-month of 11 days?

Or why not have the last month of the year be the short one, making February a month of 30 days and December a month of 29, instead of our current odd arrangement?  That would be more sensible — and if we did that, then today would be 11/09, not 11/11.

Or how about this?  What about 13 months of 28 days each, with the last month being 29?  That’s 365 days.  Wouldn’t that be simpler? Each month would be four weeks, with just one extra day tacked on at the end of the year. No muss, no fuss, no having to remember which months have 30 days and which have 31.  Ah, but that would mean 13 (ooooooooo! scary!) months… which we all know would be terrible.  (And today would be 12/7, not 11/11.)

So let’s drink another toast to 11/11 — an accident of how a Roman military dictator chose the days of our calendar’s months — and perhaps also a consequence of the fear of the number 13.

I’ll get back to years, months and days in a minute and a second, but first let’s talk about 11:11:11 as a time.

An Ancient Obsession with Twelve

How did we end up dividing our day into 24 hours, each of which has 60 minutes, each of which has 60 seconds?  Well, not everybody has counted on their ten fingers the way we do; some have calculated the joints on their fingers (not including the thumb), of which we have 12 on each hand.  Probably some have counted in other ways, but the fact that 12 was a special number for the Sumerians, Babylonians and Egyptians has resulted (through what appears to be a rather torturous history that I don’t claim to understand at all) in our having 12 hours for daytime and 12 for night, with 60 (which is 12 times 5) being the number of minutes in an hour and the number of seconds in a minute.

Our western culture does not share this obsession with 12.  Our obsessions are with 10, and indeed that’s why Europeans worked to convince most of the world (except for the stubborn United States) to go over to a metric system, which is all based on 10s, 100s, 1000s, etc., in analogy to the way we in Europe and its former colonies (and many other human cultures) count.  There are 1000 meters in a kilometer, 100 centimeters in a meter, 10 millimeters in a centimeter, and so forth.  So how did we avoid ending up with a metric clock, and find ourselves stuck with timekeeping that harkens back to numerical preferences over 4000 years old?

The French actually tried a metric clock after their revolution, and indeed it would have worked rather well.  With 24 hours, 60 minutes and 60 seconds, our day has a total of 86,400 seconds and 1440 minutes.  If instead we made the second just about 15 percent shorter and the minute just about 15 percent longer, we could have 100,000 seconds per day, organized as 10 hours of 100 minutes, each with 100 seconds.  Now wouldn’t that make more sense?  No more having to figure out that a 140 minute movie is two hours and twenty minutes.  No more making that silly mistake that we’ve all made, forgetting that 1 minute and 30 seconds is shorter than 100 seconds.  Noon occurs at 5:00, Midnight at 10:00.  All very simple.

Sadly, with that arrangement, no time during the day would be 11:11:11.  So much for that.  You’d have to reserve your excitement for 9:99:99.  (Which actually sounds just as exciting to me — the last second before midnight.)

Of course we’d have to give up many other things.  Those beautiful European clock towers would become anachronistic (pardon the pun.)  No more “eleventh-hour solutions,” either.  And we’d have to get used to the fact that a quarter of an hour — 0.25 hours — would be a sensible 25 minutes, not 15.  Well, it’s certainly a little late for this change, reasonable as it would have been; we should have done it before the digital age.

So let’s enjoy 11:11:11 by drinking to the health of the Sumerians and Babylonians who made it all possible, and to those who successfully defeated the French Revolution and prevented the metric system from taking over timekeeping.

By the way, this raises another issue: how we get ’11 from 2011.  It happens we count years by 10s. 2011 is two thousand plus zero hundred plus ten plus one years.  And when we write the year using two digits, we just strip off the “20”.  But of course that’s arbitrary: we don’t count hours, minutes or seconds by 10s, and we don’t write the 1011th minute of the day by stripping off the 10.  Instead, the 1011th minute of the day is what we call 5:51 in the afternoon, or 17:51 on a 24-hour clock.  And we could have done the same thing with years: we could count 60 years as a cycle, and then 2011 would be the 31st year in the 34th cycle, which would then make today more naturally 11/11/31.  In fact, that’s exactly what the Chinese do.  However, their calendar doesn’t share our year 1; their last 60 year cycle started in 1984, so they refer to this year not as ’11 or ’31, but as ’28.

The Arbitrary Starting Points

And why is it 2011 anyway?  That’s 2011 years from when?  Of course it is from when the Christian (or “Common”) Era began, ostensibly from the year of the date of birth of Jesus of Nazareth.  But Jesus was born during or just after the reign of Herod the Great (so say two of the Gospels rather clearly).  Herod is well-known from other non-religious historical sources, too.  These sources also have dates, and it is clear, comparing them, that Herod died in what we now call 4 B.C.  In other words, our calendar is wrong; it starts at the wrong year.  The original estimate of when to set the year 1, made around the year 525, was simply mistaken; the historical knowledge available back then was not sufficient to make a correct estimate.  And we can’t precisely fix the mistake now, because even today the historical data doesn’t make it clear exactly which year is the right one.  So.  Is it 2011?  Or 2015?  Or 2016?  Or 2013?

Of course there are other cultures out there who might not agree that it is anywhere close to 2011.  The Jewish calendar says it is 5772. The Chinese calendar says it is 4709.  There are Buddhist calendars used in large portions of Asia that put the year at 2555; in Tibet the year is 2138.  From the astronomical or the philosophical point of view, the setting of year 1 is arbitrary, and throughout human history there have been many calendars setting the starting year in different ways.

Ok, that’s one 11 down; now what about the fact that November is the 11th month?  Hmm.  November.  What does that mean?  Well, let’s see.  September, October, November, December… oh, right!  Seventh-month, Eight-month, Ninth-month, Tenth-month… wait a second!  How did November end up with this name when it is the 11th month in our calendar?

Well, go back to early Roman republican times, and you’ll find November was the ninth month — the year started in the spring, in March.  There was a change made for political convenience during the Roman republic, back in what we now call 153 B.C.E. (of course they didn’t call it that), putting January at the start of the year. Were it not for this change, today would be… 9/11.  Of course, were that the case, it would then be 7/11 that was now the darkest of dates for Americans, which would have a certain ironic sound to it, given that 7/11 is supposed in some circles to be the luckiest of number pairs.  So thank the Roman republic that we avoided that dark twist of fate.

Then there is still a question of which day is to be denoted the first of the year: the first day of the first month.  Why is the first day of January the day when we start the year?  It’s not the solstice (December 21st typically) — the shortest day of the year in the northern hemisphere and the longest in the southern — which would seem to be a natural day on which to mark the beginning of the year.  And it’s not the equinox, the start of spring in the northern hemisphere, when day and night are of equal length across the globe.  It’s a completely arbitrary day, and the position of the earth in its orbit on what we call January 1st has even shifted as adjustments have been made to our calendar.  If we had put the start of the year on the solstice, but kept the months laid out the same way, we’d be at 11/22 by now, not 11/11.

Indeed, the arbitrariness of the date has been noticed before.  For many centuries, different parts of Europe celebrated the new year on various days other than January 1st.   And today many other cultures around the world start the year on another day.  The Chinese start the year toward the end of February; for them we are not in the 11th month yet.  The Jewish calendar has its New Year sometime in September; we’re not even into the 3rd month.  And so on.  In short, there’s nothing intrinsically special about starting the year where we do, and so only for societies using Pope Gregory’s calendar (a minority of the world’s population) is today the eleventh day of the eleventh month.

So let’s drink yet another toast: this one to the Roman republic, without which we’d be in the wrong month.  And also to Pope Gregory, who from the Vatican in Rome repaired Julius Caesar’s legacy with a one-time removal of 10 days from the calendar; without him we’d be on the wrong day.  And finally to the Roman monk Dionysius Exiguus, who was perhaps worshiping Dionysus when he calculated the year 1; without him, it wouldn’t be ’11.  We should definitely be drinking these toasts with Italian wine.

Time After Time

Let’s set the date aside again and go back to the time. 11:11:11 — 11 hours, 11 minutes, 11 seconds — after what?  After midnight of course.  Ah.  Which midnight?

There’s astronomical midnight — the moment when your particular point on earth is exactly opposite the sun.  And then there’s clock midnight — the moment when your time zone celebrates the start of a new day.  These aren’t, generally, the same.  In fact, astronomical midnight occurs (obviously, if you think about it) about an hour earlier at the east edge of a time zone that it does at the west edge.

I say “about an hour earlier” because the time zones that we use around the world aren’t exact divisions of the earth into 24 equal slices, like an orange cut into equal wedges.  In principle they should be, but they’re adjusted for a very non-astronomical reason — political concerns and societal convenience.  It was judged inconvenient for the US state of Texas to be in two time zones, so the time zone dividing line was adjusted to put the entire state in the same zone.  The union of Europe has led most of western and central continental Europe, from Spain to Poland, to join a single time zone; the United Kingdom, due north of France, remains in a different zone, even though, as Paris is almost due south of London, astronomical time in London and Paris are only about 10 minutes apart.  In some parts of Europe, 11:11:11 occurs well before astronomical 10 o’clock!  And then there’s China, a country the width of the continental United States.  China uses a single time zone, while the continental US uses four.  The time 11:11:11 occurs all at once across China, while it happens at four different hours across the United States.

There’s even more arbitrariness hidden here.  Astronomical midnight in Washington D.C. occurs fifteen minutes or so after astronomical midnight in New York, but then again, neither city’s astronomical midnight is the same as clock midnight within their shared time zone.  In a given time zone, whose astronomical midnight determines the clock midnight?  Due to a historical accident, the time zones were set in the 1880s as follows: astronomical midnight in the English town of Greenwich is set as clock midnight in the London time zone, and then all other time zones worldwide differ by one hour, two hours, three hours, and so on.  (There are exceptions, where the shift involves an additional half hour [e.g., all of India], or an additional fifteen minutes.)  If human history had played out a little differently, and astronomical midnight in the London time zone had been set by astronomical midnight in the Swiss city of Geneva, then what we call 11:11:11 in New York would instead be called 10:45:32, or something like that.  (I didn’t actually calculate the precise time shift; that’s an exercise for the reader.)

In short, if we want to measure 11:11:11 from astronomical midnight, the problem is that it doesn’t occur when the clock says 11:11:11; it may happen when the clock says 10:58:34, or 11:24:06, depending on eactly where we are located within our time zone.  And if instead we do want to use clock time, we should remember that if it weren’t for the historical progression that set the London time zone on Greenwich astronomical time, then again our clocks would be shifted away from where we find them today.

Drink, then, to 11:11:11 — a time that, but for the grace of history and the strength and scientific prowess of the British Empire, might easily have been shifted by as much as half an hour in either direction — and in some countries with extended time zones by as much as two or three hours!

Today and Tomorrow

Before we all keel over in a drunken stupor, we have one more great accident to thank for today being 11/11/11 here in North and South America.  I refer to the location of the International Date Line.  It’s one thing to set all the time zones — starting from midnight in one time zone, around through noon, and back to midnight as you go round the world — so that they give roughly the same clock time as astronomical time.  But you still have to decide what day it is.  And it can’t be the same day everywhere on the earth at the same time!  For instance, if it is midnight in London, it is after midnight in Moscow and before midnight in New York… so if London’s calendar says it is July 2nd, then so does Moscow’s, while in New York you would think it is July 1st.  But then in San Francisco it is a few hours earlier on July 1st, and in Tokyo it is even earlier on July 1st; still earlier in Beijing and in New Delhi on July 1st; and back we come to Moscow very early on … July 1st???  Whoops!  A contradiction.  Somewhere around the earth we have to make the day jump.  And that’s what the International Date Line is for.  When you cross that line, the calendar day has to jump by one.  That line is completely arbitrary too.  It was placed at a convenient value of longitude, right down the middle of the Pacific Ocean, where it intersects no continents except for a corner of Siberia, and affects rather few people, mainly on small islands.   So when it is before midnight on July 1st in New York and San Francisco, it is midday on July 2nd in Tokyo.  And when it is 11/11/11 at 11:11 in the morning in New York, it is 11/12/11 in Tokyo already; Tokyo is not 11 hours behind New York, it is 24 – 11 = 13 hours ahead.

Well, there’s another place where the International Date Line could have been conveniently placed: down the middle of the Atlantic.  There’s just enough room between the continents to squeeze it in.  And if that were the case, instead of New York being 5 hours behind London time, it would be 24 – 5 = 19 hours ahead of London time.  In other words, it would already be 11/12/11 here in North and South America.

So fill the glasses again!  We celebrate 11/11/11 here in New York today because of the location of the continents and the oceans, and because of the arbitrary choice to locate the International Date Line on the ocean between the Americas and Asia, and not on the ocean that separates the Americas from Europe and Africa.

Rant

By now I’ve had enough to drink that I feel comfortable venting about people like Harold Camping, former head of Family Radio Stations, whose ludicrous prophesies of the end of the world led many of his followers to give their money to his ministry and to dispense with all their worldly belongings.  Yet it was completely obvious he was a solatic.  (A lunatic is a person who becomes crazy when in the presence of the moon; but Camping was obviously nuts in broad daylight.)  This became clear when not only did he predict a date — May 21, 2011 — of the earth’s destruction, but also a time: 6 p.m.

Ummm.. that’s 6 p.m. where? according to whose clock?

Camping’s answer: local time.

Is that astronomical time or clock time?

The answer wasn’t very sharp, but seemed to be: clock time.

Is that Standard Time or Daylight Savings Time?   (A chunk of the Northern Hemisphere, heading into its summer, was on Daylight Savings time.  The Southern Hemisphere, heading into its winter, was not.)

I don’t think we ever got an answer to that.

So: we were asked to believe that Camping was brilliant enough to carry out the numerology necessary to determine, from a document written down and unchanged for more than 1600 years, that divine forces would begin to destroy the earth on a particular date this year.  And yet we learned, from his own predictions, that he was silly enough to infer from this ancient document that the destruction would start at the International Date Line (an arbitrary human convention that dates back only 125 years) and at 6 pm (using a method of timekeeping that is a human convention that did not exist even 200 years ago) working its way time zone by time zone (even though time zones are a human convention that dates back 125 years, and the time zones are heavily modified from astronomical time by political redrawings of their boundaries) and would perhaps even destroy the Southern and Northern hemispheres at slightly different rates because of the use of Daylight Savings Time in some northern regions.

In short, we learned Harold Camping doesn’t know too much about the real world.

It might be worth mentioning that when the New Testament was written down, the mistake of getting year 1 of the Christian era in the wrong place hadn’t happened yet.  And of course Pope Gregory hadn’t removed his 10 days from the calendar yet either.  I’m not sure, of course, but I’m willing to bet Camping didn’t know about these issues and probably didn’t correct for them.

So since Camping clearly didn’t understand some basic issues in timekeeping, why in heaven’s name did anyone give him the time of day, much less millions of dollars?  And why couldn’t we stop him from damaging the lives of so many innocent people?  It is too late for Camping’s followers, but perhaps we can be better prepared for the next round. At least, we should bring justifiable discredit on this type of numerology, pointing out its many logical flaws.

End of rant

There; I’m finally done.  So glasses up, and let’s make a final drunken toast to 11/11/11 11:11:11 — a one-derfu11y si11y consequence of misaligned astronomical orbital periods, calculational errors, ancient political decisions, Western hegemony, human physiology, historical anachronisms, religious doctrine, and Babylon.  On the absurdity scale from one to ten, it surely scores an eleven.

[This article was posted on 11/11/11 at 11:11:11 …  Greenwich Mean Time.]