Wednesday, December 31, 2014

Calendar Reform

"It all started on the thirteenth hour, of the thirteenth day, of the thirteenth month.  We were there to discuss the misprinted calendars the school had purchased."



-- Marge Simpson, The Simpsons, "Treehouse of Horror VI"


One of my more esoteric hobbies is Calendar Reform. Sometimes I wonder, what would our lives be like if we had a different calendar -- one with, say, a thirteenth month, like Homer's "Smarch." I often like to think about Calendar Reform around this time of year -- New Year's Eve -- since after all, it's the day when we take our old calendars down and put up new ones.

In particular, since this is a school blog, I would like to point out how certain problems in the school year could be solved via Calendar Reform:

-- The Early Start Calendar. Many people, students and teachers alike, don't like the idea of starting school in August, and would rather wait until after Labor Day in September. But the reason for the Early Start Calendar is so that the semester can end before Christmas. That way, students don't have to try to remember what they learned before winter break in order to pass their January finals.

Even schools that start in August seldom start early enough so that exactly 90 days, or one-half of the school year, are completed before winter break. Originally, I counted backwards 90 days from winter break and started Day 1 so that Day 90 would be the last day before the holiday. But then I switched so that my dates matched the actual calendar for a local school district. As you can see, the first semester was only 84 days, so there are 96 days during the second semester.

(As an aside, notice that since the second semester is 96 days, this would make each quarter exactly 48 days, each quaver exactly 24 days, and each hemidemisemiquaver exactly three days.)

There are only two ways to get a full semester in before Christmas -- either make the first day of school earlier, or make Christmas later. Schools do the former and start school in August, since Christmas can't be changed -- at least, not without Calendar Reform.

-- Block Schedules. Many high schools have an A/B Block Schedule, where students have half of their classes on A Days and the other half on B Days. The problem is, with a Monday-Friday school week, if two days are A Days and the other two are B Days, what about the fifth day? Different schools do different things, including all classes meeting on the fifth day, the fifth day alternating between A and B, or even a pure block schedule alternating between A and B with no relationship between A/B and day of the week,

All of this could be avoided if there were an even number of days in the week. But the only way to accomplish this is Calendar Reform.

-- Veteran's Day Weekend. I mentioned earlier how, with Veteran's Day on a Tuesday this year, many students and teachers unofficially took Monday off -- and many schools and districts officially closed that day as well. This problem also occurs at offices, where workers want to take off last Friday and this Friday because Christmas and New Year's Day are on Thursdays this year. Independence Day, on the Fourth of July, also suffers when the holiday falls on an inconvenient day of the week.

When a holiday is tied to a particular day of the week, such as Thanksgiving on Thursday, its date must necessarily change. In 2012 Thanksgiving was on its earliest possible date, November 22nd, while in 2013 it was on its latest possible date, November 28th. I believe that much of Christmas creep -- where stores seem to be advertising for the holidays earlier every year -- is caused by this problem with the calendar. In the year when Thanksgiving moves from the 22nd back to the 28th, many stores who might have waited until after Turkey Day for a sale start it before the holiday instead, and it remains before the holiday even the next time Thanksgiving is on the 22nd again. A local radio station that switched to Christmas music the week before Thanksgiving in 2012 made the switch two weeks before Turkey Day last year, and so on. The accumulation of such changes over the years and decades means that Christmas ads are now earlier than ever before. ("Franksgiving" refers to President FDR, who changed the date of Thanksgiving in 1939, a year when Thanksgiving would have moved from November 24th the previous year to November 30th, for this very reason.)

(This happens with other holidays as well. Some stores felt the need to advertise for Easter early in 2008 when the holiday fell on March 23rd -- and kept on doing so ever since, even in 2011 when it fell on April 24th.)

Of course, even if Thanksgiving or Easter were fixed to a certain date, many retailers might decide to start the sales earlier one year anyway -- but they wouldn't feel as pressured to do so as they are when the holidays are early one year and late the next.

-- Paydays. Many districts in this area follow one of two payday schedules. One is quadriweekly, where payday comes every four weeks, on Friday. Notice that since there are 52 weeks in a year, there are actually 13 quadriweekly paychecks per year. Therefore, there is no relationship between the date of the month and payday -- some checks occur early in the month, while others occur late in the month. The problem is that rent and mortgage payments are typically due on the first of the month, so the checks don't line up exactly with the bills.

The other payday schedule is monthly -- many schools pay on the fifth of the month, since the first four days are ostensibly for processing the checks. But this still often means that bills are due four days before teachers get the money to pay them. Unfortunately, no Calendar Reform can make that four-day processing window disappear.

Still, we see some problems that teachers have that can be solved with Calendar Reform. There are many proposals for Calendar Reform floating around. The best way for me to state them is to observe the following link:

http://qntm.org/calendar

Notice that the author of this site is actually criticizing Calendar Reform -- he is saying that all calendar reform is bad and that we should just leave the calendar the way it is. The link contains a list of reasons why a particular proposal won't work. Every proposal will cause at least one of the boxes to be checked, so that every proposal would be rejected.

In the comments, someone joked that one should try to make a calendar proposal for which every box is checked. This is likely impossible, since many of the boxes are actually opposite solutions to the same problem. For example, the box:

no, we don't know what year the Big Bang happened

refers to a proposal where someone lets Year 0 be the year of the Big Bang. But then we have:

BC and AD aren't
that is, BC and AD aren't actually before Christ and anno Domini, in the year of the Lord, since according to scholars, Christ was most likely born around 5 BC. But a calendar that sets Year 0 to the year of the Big Bang probably wouldn't have BC or AD to begin with. Similarly:

nobody cares what year you were born

refers to a calendar whose author sets Year 0 to the year of his or her own birth. Such a calendar would reference neither the Big Bang nor the birth of Christ. So it would be difficult to create a calendar for which all three boxes are checked.

Still, an excellent way for me to introduce you to the various Calendar Reform proposals is to look at each item on the list and for me to give a proposal which would cause that item to be checked -- in other words, the calendar that inspired the author of the list to include that item.

So let's begin with the third item on the list, since it's an important one:

the solar year cannot be evenly divided into solar days

The length of the solar (or tropical) year is 365.2421897 days, so this is true. What this means is a calendar with only 365 days with fail to sync with solar years (which is, after all, the first item on the list) after several years have passed.

This problem has been known since the days of Julius Caesar. And so the ancient Roman emperor created a new calendar, the Julian Calendar, in which an extra day is added to the calendar once every four years. This leap day occurred as a doubled February 24th -- six days before the first (or kalends) of March, and so such a year became known as a bissextile, or "double sixth," year. In 1970, the Roman Catholic Church changed it so that February 29th is now Leap Day.

Because of Leap Day, someone may be either 365 or 366 days old on one's first birthday, either 730 or 731 days on one's second birthday, and either 1095 or 1096 days old on one's third birthday. But on one's fourth birthday in the Julian calendar, one must be exactly 1461 days old. Because of this, I sometimes refer to one's fourth birthday as one's "first Julian birthday," so that one's eighth birthday becomes the "second Julian birthday," and so on. Notice that someone born on Leap Day itself can be described as celebrating only the Julian birthdays.

So any calendar with Leap Days, such as the Julian calendar, would check this box. The reason for leap days is that the solar year cannot be evenly divided into solar days.

the solar day cannot be evenly divided into SI seconds
the length of the solar day is not constant

These two go together. Even though we think of days as being divided into 24 hours, hours into 60 minutes, and minutes into 60 seconds, the length of the day is not constant. It's always changing -- indeed, it's slowing down. After all, if you spin a globe, it eventually slows down and stops. And so it is with the earth.

Even though it takes a very long time for the earth to slow down appreciably -- for example, the dinosaurs experienced 22-hour days -- it has been slowing down noticeably. In particular, every few years, the clock is one second off. To make up for this, a Leap Second is added. The most recent Leap Second was added on June 30, 2012. No one knows when the next Leap Second will be, since it's based on actually observing the rotation of the earth.

So any calendar with Leap Seconds would check this box. The reason for leap seconds is that the solar day cannot be evenly divided into SI seconds.

the lunar month cannot be evenly divided into solar days
the solar year cannot be evenly divided into lunar months
These two go together. They refer to calendars such as the Chinese and Hebrew calendars, in which new months and years begin at the new moon. This is why we have Jewish holidays such as Hanukkah, which occurred very early in 2013 ("Thanksgivukkah") but later this year (not ending until Christmas Eve) and Chinese holidays such as Lunar New Year, which will occur very late in 2015 (February 19th, making the current Year of the Horse a "double spring, double rain" year).

A lunar calendar normally has twelve months, but once in a blue moon there is a thirteenth month, a Leap Month. It occurs about seven times every 19 years (the Metonic cycle, named for the Greek astronomer Meton, who calculated it). In particular, we know that a Leap Month in the Hebrew calendar occurred between Hanukkah 2013 and 2014, and a Leap Month in the Chinese Calendar occurred during the Year of the Horse.

(One personal note about the Metonic Cycle. Back when I was 18, I was curious as how to find the date of Easter -- which is influenced by Passover and thus the lunisolar Hebrew calendar. I was also curious as to what the phase of the moon was on the day I was born. As it turned out, it was easy. I only had to look ahead on the calendar for my next birthday, which happened to be my 19th -- that is, my first Metonic birthday -- and saw that it was a new moon. Therefore, I was born at new moon.)

So any calendar with Leap Months would check this box. The reason for leap months is that the solar year cannot be evenly divided into lunar months.

(Notice that the Islamic calendar would not check this box, as there are no leap months. But its twelve months are short of a full year. So the Islamic calendar would check the first box instead, since its lunar years don't sync up with the solar year.)

having months of different lengths is irritating
having months which vary in length from year to year is maddening

These two go together. Notice that these refer to our current calendar -- the three links in the second item link to "February," "Common year," and "Leap year." So our current calendar is one which would check these boxes!

But our current calendar is not the Julian calendar. February has a Leap Day every four years in the Julian Calendar. But why is it every four years? It's because the length of the tropical year is nearly 365.25 days, and .25 is equal to one-fourth. Yet, as I mentioned earlier, the length of the tropical year is not 365.25 but 365.2421897 days. That difference was noticeable enough that by the 16th century, the first day of spring was around March 10th or 11th, and not March 20th or 21st as it was when the Julian Calendar was created.

So the Catholic Church decided to reform the calendar. Pope Gregory XIII dropped ten days so that the seasons would begin when they were supposed to, and then added more rules to determine which years would have leap days. In particular, years that are divisible of 100 do not have Leap Days (even though 100 is divisible by 4) unless they are also divisible by 400. So 1600 had a Leap Day, but not 1700, 1800, or 1900. The year 2000 had a Leap Day, but 2100 won't.

Most of the readers of this blog weren't born yet in 1900, and most of us will be long dead by the time 2100 comes around. And so these Gregorian Exceptional Years don't affect any of us -- for our lifetimes, the Julian leap rule suffices. But still, the calendar we actually use is the Gregorian, not the Julian -- because of the skipped days, the date is different in both calendars. In the Julian Calendar, today is December 18th, not 31st as in the Gregorian. Many churches still use the Julian Calendar to determine Christmas and Easter -- most noticeably the Orthodox churches. These churches have no loyalty to the pope, so why would they follow Pope Gregory's calendar?

So far, the only calendars I've mentioned are existing calendars. By doing so, I've described the history of Calendar Reform thus far. The next boxes definitely refer to proposed calendars -- indeed, some of the most common proposals will check these boxes.

the solar year cannot be evenly divided into seven-day weeks
having one or two days per year which are part of no month is stupid
having one or two days per year with no day of the week is asinine
This is the big one, and the cause of many of the problems that I listed above. The solar year cannot be evenly divided into seven-day weeks -- seven divides neither 365 nor 366 evenly. The closest number that seven does divide is 364. It's because of that extra day or two that Christmas must change its day of the week every year, and why Thanksgiving must change its day of the month every year, and so on.

The first attempt to solve this problem is known as the World Calendar:

http://www.theworldcalendar.org/

A full description of the calendar comes from this link:

http://www.theworldcalendar.org/TWCandDescription_HTML.html

In this improved calendar every year is the same. 
• The quarters are equal: each has exactly 
91 days, 13 weeks or 3 months. 
• The four quarters are identical in form with an 
ordered variation within the three months. 
• The three months have 31,30, 30 days respectively. 
• Each month has 26 weekdays, plus Sundays. 
• Each year begins on Sunday, 1 January; 
each working year begins on Monday, 2 January. 
• Each quarter begins on Sunday, ends on Saturday. 
• The calendar is stabilized and made perpetual 
by ending the year with a 365th day following 
30 December each year.  This additional day is  
       
   dated ‘W’, which equals 31 December, and 
called Worldsday, a year-end world holiday. 
• Leapyear Day is similarly added at the end of 
the second quarter.  It is likewise dated ‘W’, 
which equals 31 June, and called Leapyear Day, 
another world holiday in leap years.


In this case, it's these blank days -- the days dated 'W,' that make every year the same. Christmas in the World Calendar is always on Monday, and Thanksgiving is always on the 23rd. But it's these blank days that lead to checks on our checklist. They definitely have no day of the week -- the 'W' dates occur between Saturday and Sunday. Whether they are part of no month is debatable, since the link above does refer to them as the 31st days of June and December. So the World Calendar gets at least one and possibly two checks here.

Notice that the World Calendar does not get a check for "the solar year cannot be evenly divided into seven-day weeks," since the calendar doesn't attempt to divide them evenly (that's what the blank days are for). What sort of calendar gets a check here? Let's think about it. Consider what we've discussed in this blog entry so far:

The solar year can't be evenly divided into solar days -- that's why some years have Leap Days.
The solar day can't be evenly divided into SI seconds -- that's why some days have Leap Seconds.
The solar year can't be evenly divided into lunar months -- that's why some years have Leap Months.

Following this pattern, we should have:

The solar year can't be evenly divided into 7-day weeks -- that's why some years have Leap Weeks.

And that's the calendar that gets a check here -- a Leap Week calendar. There are several Leap Week calendars around. One that gained a little publicity about three years ago is the Hanke-Henry Permanent Calendar, posted at the following site:

http://henry.pha.jhu.edu/calendar.html

Like the World Calendar, the Hanke-Henry Calendar begins on a Sunday, but the latter's months follow a 30-30-31 pattern while the former's go 31-30-30. This means that Christmas will always be on Sunday, and Thanksgiving will always be on the 24th. But the main difference is, instead of blank days, it has a Leap Week, called Xtr Week, at the end of December.

How often does Xtr Week occur? It occurs every six or five years. Henry writes:

I am indebted to Irv Bromberg for pointing out that a simple way exists to test whether a year contains a Xtr (or Extra) month: if the corresponding Gregorian year either starts on a Thursday, or ends on a Thursday, that year contains a Xtr (or Extra).

According to this rule, 2015 will contain a Xtr, since the Gregorian year 2015 both starts and ends on
a Thursday. Henry writes a program in Fortran that calculates whether a year has a Xtr. Let me rewrite it in TI-BASIC:

PROGRAM:XTR
:Input Y
:0->N
:For(I,Y-1,Y)
:I*365+int(I/4)-
int(I/100)+int(I
/400)->D
:int(D/7)->W
:D-W*7->R
:If (R=4 and I=Y
) or (R=3 and I=
Y-1)
:1->N
:End
:N

Entering 2015 outputs 1, indicating that there will be an Xtr Week. Entering 2016, 2017, 2018, and 2019 all output 0. The next Xtr Week will be in 2020.

When Henry posted his calendar three years ago, many news sites picked up the story. The following website, IO9, is typical. It's interesting to read the comments:

http://io9.com/5871546/the-hanke-henry-permanent-calendar-would-put-us-all-in-one-big-happy-timezone

Many of the comments involve other proposed changes that will be covered in other items on our calendar checklist. Of those relevant to the calendar itself, many people weren't enamored with the idea of Christmas always being on Sunday. When given a choice, posters tend to choose days like Wednesday or Friday for Christmas, rather than Sunday. I tend to agree -- when Christmas is on Sunday, some schools don't break until December 23rd, so that kids actually have to go to school two days before Christmas! Other schools break on the 16th, but then have to take an extra day off on Monday, January 2nd. So Christmas on Sunday wreaks havoc on the school schedule as well.

So any calendar with Leap Weeks would check this box. The reason for leap weeks is that the solar year cannot be evenly divided into seven-day weeks. But most calendars won't check both this box and the box for days without a month or day of the week (blank days), since these are opposite solutions to the same problem.

your name for the thirteenth month is questionable

Aha, so there's our "Smarch"! Actually, there's a reason for having 13 months in a year. Recall how some schools pay teachers quadriweekly, so there are 13 paychecks in a year. So a 13-month calendar would have months exactly four weeks each.

One 13-month plan is the International Fixed Calendar:

http://www.citylab.com/work/2014/12/the-world-almost-had-a-13-month-calendar/383610/

The new month here is called "Sol" and occurs between June and July. Like the World Calendar, every month begins on Sunday and ends on Saturday. (Notice that Homer Simpson's "Smarch" also begins on Sunday and ends on Saturday. Presumably "Smarch" occurs after December, since Homer notes how lousy the weather is.)

I assume that any 13-month plan will result in a check for this box. Supposedly, this box is checked only if the name of the 13th month is questionable, but since the author of the list is opposed to all Calendar Reform, this box would be checked for any 13-month plan. (It might have been more honest for this item to read, "thirteen is an unlucky number of months" or something like that.)

The link on this item is to the name "Undecimber." I agree that it's a questionable name, since its name actually means eleventh month. But if we're going to criticize "Undecimber" as questionable, then we should similarly attack September, October, November, and December. An octagon in geometry has eight sides, so why is October the tenth month? Before Julius Caesar, the first month of the year was March, not January.

One day when I was in a local library, there was a display where someone posted a 13-month Calendar Reform plan. This plan drops July and August so that September through December are no longer misnomers. So now there are three new months to name -- Humanus, Sanctus, and Spiritus.

All of the calendars mentioned so far have blank days, just like the World Calendar. It's possible to have a 13-month plan with a Leap Week instead. One such calendar is the Pax Calendar:

http://myweb.ecu.edu/mccartyr/colligan.html

Here the new month is called Columbus and occurs between November and December. The Leap Week is called Pax and occurs after Columbus.

With the new month of Columbus, notice that there's an extra month between Labor Day in September and Christmas in December. This means that we can fit the whole first semester between these two holidays and solve the Early Start problem! The five months September, October, November, Columbus, December make up 20 weeks, and let's declare the last week in December to be winter break. (Notice that December 25th occurs, much to the delight of the posters in the Henry thread, on Wednesday.)

This gives us 19 weeks, or 95 school days. So we can afford five more days off. Of course, Labor Day is one of these days. Many schools reserve the day after Labor Day for teacher preparation, so there's our second day. And of course we take off Thursday and Friday for Thanksgiving. These are November 26th and 27th in this calendar. The last day off could be another day for teacher preparation (as many schools start on Thursday after Labor Day). Or the extra day could be Wednesday, November 11th for Veteran's Day. This would actually divide the quarters evenly as there are 45 days from Labor Day to Veteran's Day and 45 more from Veteran's Day to Christmas.

Another calendar similar to the Pax Calendar is the New Earth Calendar:

http://calendars.wikia.com/wiki/New_Earth_Calendar

The extra month occurs between June and July, except that it's called Luna, not Sol. Also, its months begin on Monday, not Sunday. Notice that this would put the 5th of the month on Friday -- meaning that the both payday schedules (quadriweekly and monthly) coincide in this calendar.

the lunar month cannot be evenly divided into seven-day weeks
Despite the New Earth Calendar having a month called Luna, it's not a lunar calendar. I don't know of any Calendar Reform proposal where there are months with 28 or 35 days, but designed to fit into a lunar calendar.

every civilisation in the world is settled on a seven-day week
This is a big one. Some Calendar Reformers propose weeks longer or shorter than seven days. One of the most common week-lengths, instead of seven, is six days. Here is a typical six-day calendar:

http://calendars.wikia.com/wiki/6-Day_Week_Solar_Calendar_with_common_Muslim/Christian_weekend

Six-day calendars tend to have twelve months with five weeks each. This gives us 360 days, so there must be five blank days. Different calendars distribute the five blank days differently.

The calendar I chose to link above drops Saturday. It declares Friday and Sunday to be the weekend, so that both Muslims and Christians can have their respective Sabbaths off. For schools, notice that this provides a four-day school week, from Monday to Thursday. This is convenient for A/B block schedules, where there can be two A days and two B days every week.

"daylight saving" doesn't

that is, daylight saving doesn't save daylight. I've already discussed DST back in November, in my first post after the time change.

Many of the items in this section refer to the biannual clock change, to which this author of this list is apparently opposed. But notice that my preferred alternatives -- year-round DST and the Sheila Danzig plan -- don't necessarily avoid checks either. Year-round DST results in the following box being checked:

local "midnight" should be the middle of the local night

because year-round DST puts the middle of the local night at 1 AM, not midnight. Also, the Danzig plan, which puts some time zones at year-round DST and others at year-round standard time, would result in a check here:

nobody would agree to pick your time zone over theirs

since those whom Danzig places in year-round standard time might prefer year-round DST instead, and vice versa.

Notice that the Hanke-Henry calendar places the entire world in a single time zone -- the Greenwich time zone. Naturally, this would place checks in both of the above boxes.

no, we don't know what year the Big Bang happened

Someone actually mentioned this on one of the comment threads! But I assume that it's actually a parody of the Holocene Calendar, where Year 0 is set to the Ice Age:

http://calendars.wikia.com/wiki/Holocene_calendar

This simply places a 1 in front of all the dates. So today is New Year's Eve 12014, to be followed by New Year's Day 12015.

a leading zero on the year number only delays the inevitable

This refers to the Long Now, which is similar to the Holocene Calendar except that a 0 is placed in front of all dates instead of a 1. So today is New Year's Eve 02014, to be followed by New Year's Day 02015.

http://longnow.org/

planetary-scale engineering is impractical

This one may sound weird, but it actually appeared in the comments at the International Fixed Calendar link above -- emcourtney posted:

Why don't we just boost the Earth into a slightly lower 336 day orbit around the sun, That way we can have 12 * 4 * 7 calendar with no sloppy leftovers! Why tinker with the calendar when you can tinker with orbital mechanics instead.

On the TV show Futurama (created by the Simpsons creator), a group of robots pushed the earth slightly farther from the sun in order to prevent global warming. This made the year a week longer, and this extra week was declared "Robot Party Week."

not every part of the world has four recognisable seasons

This refers to a calendar which seeks to put New Year's Day at a solstice or equinox. For example, the six-day-a-week calendar above begins at the spring equinox, and other months begin at the fall equinox and the solstices.

"sunrise" and "sunset" are meaningless terms at the poles

This refers to a calendar where days begin at sunrise or sunset. Notice that the Jewish and Islamic calendars have days beginning at sunset. As it turns out, these calendars do cause problems near the poles, where observers of fasts such as Yom Kippur and Ramadan don't know when to break the fast when the sun doesn't set.

Greenwich is not unambiguously inferior to any other possible prime meridian

This refers to a calendar where another prime meridian is chosen. For example, the Florence, Italy, meridian is chosen because it would put its opposite meridian, the International Date Line, out in the in the Bering Strait so that it no longer intersects Russia.

everybody in the world is already used to sexagesimal time divisions

This refers to changing the time to metric time rather than time based on 60 -- which goes back to the ancient Babylonians. Principal Skinner on the Simpsons once tried to introduce metric time. The following calendar proposes metric time:

http://calendars.wikia.com/wiki/Denary_system_of_measurement

This calendar also proposes the Florence-Bering prime meridian as mentioned above.

they tried that in France once and it didn't take

This refers to the French Revolutionary Calendar of the late 18th century. It contains ten-day weeks, with five blank days, and starts at the fall equinox -- so several other boxes are checked as well.

A Slate article from last year mentions this calendar.

http://www.slate.com/blogs/moneybox/2013/12/30/republican_calendar_worthwhile_jacobin_initiative.html

I could go on forever about calendars, but this post is already bloated enough.

Happy New Year, and have a wonderful Gregorian year 2015.

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