1. Introduction
2. Pappas Question of the Day
3. Definition of Decade
4. A Mild Implementation of the Eleven Calendar
5. A Radical Implementation of the Eleven Calendar
6. A Compromise That Respects Sabbaths
7. One Last Compromise
8. Loose Ends with the Eleven Calendar
9. Conclusion
Introduction
This is my second of three winter break posts. It's also my final post of the calendar year 2019 -- thus making it the last post of the calendar decade of the 2010's.
There has been much discussion this month regarding the end of the decade. In addition to "Year in Review" news stories, there have also been "Decade in Review" stories. Even though today's post is mainly about the Eleven Calendar, I'll also be retrospective about the past ten years of my own life.
Pappas Question of the Day
Today on her Mathematics Calendar 2019, Theoni Pappas writes:
What is the perimeter of this square?
(Here is the given info from the diagram: the diagonal is sqrt(91.125).)
Well, since the diagonal divides a square into two 45-45-90 triangles with that same diagonal as the hypotenuse, the leg of the triangle -- the side of the square -- is sqrt(91.125)/sqrt(2), which we can simplify as sqrt(45.5625) = 6.75. The square's sides add up to four times this, or 27. Therefore the desired perimeter is 27 -- and of course, today's date is the 27th.
Last week, we studied perimeter in Lesson 8-1 of the U of Chicago text. But 45-45-90 triangles -- used to get from diagonal length to side length -- don't appear until Chapter 14. (It's possible to get the side length using only the Pythagorean Theorem, studied later in Chapter 8.)
At some point we probably used a calculator to find a square root. It's possible to avoid a calculator if we cleverly eliminate the decimal under the square root. If s is the desired side length, then:
s sqrt(2) = sqrt(91.125)
s sqrt(2)sqrt(2) = sqrt(91.125)sqrt(2)
2s = sqrt(182.25)
2s sqrt(4) = sqrt(182.25)sqrt(4)
4s = sqrt(729)
Notice that 4s is the desired perimeter. Some teachers have their students memorize their perfect squares up to 30^2, and so we might even get sqrt(729) = 27 without a calculator. Otherwise, we might guess sqrt(729) = 27 and find 27^2 to verify it.
Once again, there is no 2020 Pappas calendar. This is my final post of the year, and thus it's my last mention of a Pappas problem on the blog. It's not her last Geometry problem, though -- next week she asks how many edges a dodecahedron has (given it has 20 vertices and 12 faces). We can use Euler's formula to find that it has 20 + 12 - 2 or 30 edges -- and the date of that problem is the thirtieth.
Her final problem on New Year's Eve isn't Geometry, but probability (which might be taught in a California Geometry class anyway). She asks for the probability of choosing two successive red marbles from a bag with six red, 21 blue, and four green marbles. Since there are 31 total marbles, the desired probability is 6/31 * 5/30 = 1/31 -- and the date of that problem is the 31st.
That wraps up the Theoni Pappas calendar for this year. I've enjoyed reading her calendar and answering questions on the calendar all year -- as well as during all eight years during the decade when she published her calendar. The only years this decade when she didn't have a calendar were 2013 (the year before I started this blog) and 2017.
And we already know that the new decade will begin without a 2020 calendar. Once again, I just hope that 2019 won't turn out to be the final Pappas calendar.
Definition of Decade
Twenty years ago, there was much discussion about whether 1999 or 2000 was the last year of the century and millennium. The nonexistence of the year 0 means that the twentieth century and second millennium didn't end until 2000, with the 21st century and third millennium starting in 2001.
But this seems to clash with our definition of decades. Indeed, the QNTM website, which critiques all versions of Calendar Reform, includes the following item on its list:
https://qntm.org/calendar
by that logic, 2000 was the final year of the Nineties
In other words, if 2000 was the final year of the twentieth century and third millennium, why shouldn't we consider it to be the last year of the 1990's.
The answer is that there's a difference between the "nth unit" (millennium, century, decade) and the unit (millennium, century, decade) of the x's. For example, the century of the 1900's was 1900-1999 -- the years with 1900 in their names. But the 20th century was 1901-2000. Thus the 1900's and the 20th century shared 99 out of 100 years.
Following this pattern, the millennium of the 1000's spanned 1000-1999, but the second millennium was years 1001-2000. They share 999 out of 1000 years.
And by the same pattern, the decade of the 1990's spanned 1990-1999, but the two hundredth decade was years 1991-2000. They share nine out of ten years.
The point here is that no one ever uses the phrase "200th decade." The only names given to the decade are 1990's or just '90's. Both of these names imply the digit 9 in the tens place, and so 1999 was the last year of that decade.
Both "1900's" and "20th century" are commonly used to refer to a century. I suspect that "20th century" is much more common, hence the insistence that the century didn't end until 2000. In particular, Google reveals 866 million results for 20th century and only 14 million for 1900's -- and the first result refers to the decade of the 1900's (that is, 1900-1909). Likewise, 2000's is most likely to refer to a decade, not a century or millennium.
In fact, the millennium doesn't appear to have a commonly used name at all. Neither "millennium of the 2000's" nor "third millennium" is often used. The insistence that "the millennium" didn't end until 2000 is likely in analogy with centuries (not decades), since a millennium is closer in length to a century than a decade.
The QNTM author makes his opinion clear with another item in the list:
there needs to be a year 0 and negative year numbers
With a year 0, the century and millennium ended in 1999. This eliminates the problem with "the decade" ending in 1999, one year before "the century" and "the millennium" ending. Instead, they would all end in 1999.
Here's a link where this issue is discussed:
https://www.npr.org/2019/12/27/791546842/people-cant-even-agree-on-when-the-decade-ends
Since I labeled this post "Last Post of the Old Decade," I'm taking the "Team Zero" side. I agree that the 203rd decade doesn't start until 2021, but we don't use "nth decade" to name decades. The decade that starts next week is the 2020's, or just the '20's.
This leads to one more related question -- on this blog, I've defined the "Millennial Generation" as consisting of those individuals who were born in the old millennium and graduated high school in the new millennium. If 2000 was the last year of the old millennium, does this make someone born in that year a Millennial? For that matter, is someone born in 1982 and graduated in 2000 a member of the Millennial Generation?
Actually, generation boundaries (or cusps) are much fuzzier than this. Not only is it uncertain whether a 2000 baby is a Millennial, but going a year or two either way (1998, 1999, 2001, 2002) keeps us in the gray area. Likewise, 1980-1984 is a cusp regarding the start of the generation. The in-between birth years of 1985-1997 are nearly always included in the Millennial Generation.
I myself was born in 1980, which is a part of the generational cusp. Lately, I've been hearing a new term, "X-ennial," to refer to the cusp between Generation X and the Millennial Generation. Similarly, the 1998-2002 cusp might be called "Z-ennial." This suggests that the Millennial Generation itself should be "Generation Y" -- a former name for this generation before the millennium caught on.
The Z-ennials were born just as we X-ennials were graduating high school. This suggests that we are currently on the cusp of a new generation after Gen Z (that is, something like 2016-2020). Of course, it remains to be seen what the next named generation after Z will be.
A Mild Implementation of the Eleven Calendar
At this point I will attempt to give a full implementation of the Eleven Calendar. So far, we know that this calendar contains 11 days per week, three weeks per month, and 11 months per year. But I have yet to give the days or months any names.
(Of course, this only adds up to 363 days. It's possible to add two or three blank days per year, or a Leap Week every five years or so. But this is beyond the scope of today's post. Here I'm only concerned with what the main part of the calendar, with its 363 days, looks like.)
There are several ways to implement the Eleven Calendar. One way is a mild approach -- keep as much of the Gregorian Calendar as possible. This includes some of its day and month names, as well as some holidays. More ambitious approaches destroy familiar aspects of our calendar.
Let's start with the mild approach. We can characterize this approach as requiring as few boxes checked on the QNTM list as possible. Every version of the Eleven Calendar needs the following box to be checked:
(x) every civilisation in the world is settled on a seven-day weeksince there are obviously eleven days per week, not seven.
In our mild approach, we could keep the seven old day names and add four new names. But instead, let's divide our 11-day week into two part-weeks -- one with five and one with six days. This allows us to reuse our old day names and maintain some familiarity. We can also refer to previous Calendar Reforms that have five- or six-day weeks, such as:
Five-Day Examples:
https://calendars.wikia.org/wiki/Long_Summer_Modified_Gregorian_Calendar
https://calendars.wikia.org/wiki/Luni-solar_Modified_Gregorian_Calendar
Six-Day Examples:
https://calendars.wikia.org/wiki/60-Week_Calendar
https://calendars.wikia.org/wiki/6-Day_Week_Solar_Calendar_with_common_Muslim/Christian_weekend
Notice that the last calendar listed here keeps the Muslim (Friday) and Christian (Sunday) sabbaths (as its name implies), but drops the Jewish sabbath (Saturday). Instead, I take the suggestion that other Calendar Reformers make -- drop the most unpopular day of the week, Monday (which isn't the sabbath of any religion).
For the five-day part of the week, we drop Monday and Tuesday. Thus every 11-day week contains one Tuesday and two each of the days from Wednesday-Sunday.
Note that it might be preferable to drop Tuesday and keep Monday in order to avoid having two days starting with T -- so that TF can unambiguously mean "every Thursday and Friday," not "every Tuesday and Friday." Here I drop Monday instead only because "everyone hates Mondays."
Let's look at the months next. There are 12 Gregorian months and we need only 11, so the easiest thing to do is drop a month. Which month should we drop?
Some Calendar Reformers state that their least favorite month is February, and so this is the month they'd wish to drop in an 11-month calendar. Why is February hated so much? Well for one thing, most Calendar Reformers live in North America or Europe, where February is winter -- this isn't so terrible in California, but further north, Februaries are freezing. But for Australians and other in the south, February means summer.
Also, most Calendar Reformers are male. February means Valentine's Day -- a holiday when women are the main recipients of gifts and men are the main givers. So Valentine's Day is a holiday that many men can't afford. But in Japan and some other Asian countries, men are the main recipients of Valentine's Day gifts. Women receive gifts a month later, on White Day (same as Pi Day). And singles receive gifts two months later, on Black Day.
So I don't necessarily wish to skip February just because Western men hate Valentine's Day, ignoring the Asian men and Australian outdoor lovers who enjoy it. Of course, skipping any month of the year has its advantages and disadvantages. As teachers, for example, we might prefer to skip March in order to eliminate the Big March.
I don't wish to commit to which month to skip in this post. Instead, I will blog two possible calendars, each with its own skipped month. I randomly select January as the month to skip in the first version and October in the second version.
In the no-January version of the calendar, February is the first month of the year, and every month needs to be renumbered. I suggest starting with February as zero rather than one. This allows September-December to be numbered as months 7-10, in line with their Latin names. On the other hand, in the no-October version, let's keep January as month 1 with no month 0. Without October, there's no hope of matching the Latin names anyway, and keeping January as 1 allows Months 1-9 to match the Gregorian calendar.
Notice that New Year's Day in the new calendar doesn't necessarily have to match January 1st in the old calendar. Indeed, if we were to insist that the Eleven Calendar start on the same day as the Gregorian Calendar, then in the no-January version, 31 of February's 33 days would correspond to old January, with only the last two days corresponding to old February.
It's often desirable to make as many days as possible land in the same month on both calendars. For example, in the International Fixed Calendar (with 13 months), New Year's Day is the same, and the new month (Sol) is placed as far away New Year's Day as possible -- between June and July. Then all of new January and new December land in the corresponding old months, as do most of new February and new November. New March and new October have slightly fewer days in the old months of the same name, and progressively less until only about half of new June and new July land in old June and old July. The other halves of old June and old July are part of new Sol. This scheme allows the maximum overlap between old and new months of the same name.
For an 11-month calendar, we do the opposite. Instead of adding new Sol to take half of old June's and old July's days, the dropped month's days should be given half to the month before and half to the month after. Thus in the no-January version, new February should start near old January 16th. This also allows the month directly opposite the skipped month -- in this case July -- to be nearly aligned with the old month (depending on how the blank days are assigned). Then July 1st would be the same as the Gregorian Calendar, as would the Fourth of July, Independence Day.
In the no-October version, new November should start around old October 16th. Depending on how blank days are set up, April Fool's Day should be aligned with the Gregorian date. Also, notice that new January 1st, New Year's Day, now lies near the winter solstice. (In the no-January version, we can instead place April 1st near the spring equinox.) Some Calendar Reformers like starting months or years near solstices and equinoxes. To me, this is only desirable if the number of months is a multiple of four. In calendars with an odd number of months (like 11 or 13), at most one month can start at a solstice or equinox anyway, so why even bother?
We now wish to place holidays on the calendar. It's easiest to allow most holidays to remain in their previously-defined months, keeping their old definitions if possible. This means that holidays in the skipped months would no longer exist.
Well, we can't make New Year's Day disappear, since new years would still exist. In the no-January version, New Year's Day would now be February 1st.
In the Gregorian Calendar, most holidays are always on a Monday. In our new calendar, it might be easiest just to place those holidays on a Tuesday (assuming the no-Monday version), since every eleven-day week contains only one Tuesday anyway. This can include New Year's Day -- thus each week and month should begin on a Tuesday. The three Tuesdays in a 33-day month are the 1st, 12th, and 23rd, so these are when we should place most holidays.
Here's what the US Federal Holidays would look like on the new calendar:
New Year's Day: January 1st (February 1st in no-January version)
MLK Day: January 12th or 23rd (disappears in no-January version)
President's Day: February 12th or 23rd. Note that the 12th is an actual president's birthday (Lincoln), but the official name of President's Day is "Washington's Birthday," not Lincoln's. The 23rd is closer to Washington's actual birthday on the 22nd.
Memorial Day: May 23rd
Independence Day: July 4th is a Friday in the new calendar, so let's keep it there.
Labor Day: September 1st
Columbus Day: October 12th (disappears in no-October version). This is the actual day that the explorer and his ships landed in the New World.
Veteran's Day: November 12th
Thanksgiving Day: This is a tricky one. If we keep the definition "fourth Thursday in November," then this would be November 19th. We might prefer the next Thursday, the 25th, to be Thanksgiving instead since this is within Gregorian Thanksgiving range.
If we keep Thanksgiving on the 19th, then not only is Black Friday on the 20th a no-work day, but so would Wednesday the 18th, as this is the day after Sunday the 17th (in order to avoid having a week with a lone workday). This is one of the weeks that doesn't have a Tuesday. On the other hand, with Thanksgiving on the 25th, there can theoretically be both work and school on Tuesday the 23rd and Wednesday the 24th. But many schools already close the day before Turkey Day, and once we take Wednesday off, then we must also take Tuesday off to avoid a lone workday.
It's also possible just to change Thanksgiving to Tuesday the 23rd and drop the need to have Turkey Day on Thursday. (But this would ruin Black Friday sales the day after Thanksgiving.)
If we keep Christmas on December 25th, then this is also a Thursday. Many of the arguments about Thanksgiving on November 25th also apply to Xmas on December 25th. Since there is never school on Christmas Eve, there can't be any school on Christmas Adam either (to avoid a lone day). It's also likely that more offices will take Friday off for Boxing Day, to avoid a lone day.
Let's now try to make a 180-day school year out of this. Notice that every 11-day week contains exactly seven school days. We might consider having 27 weeks of school -- since 27 * 7 = 189, this allows nine extra days for holidays (including the Tuesday holidays mentioned above).
Since the whole year has 11 * 3 = 33 weeks, this leaves six weeks for vacations (including winter, spring, and summer breaks). We might wish to take a week off for the Thanksgiving, winter, and spring breaks. Notice that winter break only needs to be one week long (the whole week of Christmas plus New Year's Day, return on the 2nd). And Thanksgiving only a half-week (recall that a week consists of 11-days, so taking Wednesday-Friday November 23rd-25th is only a half-week). We might choose to add an extra half-week to winter break (Tuesday-Friday the 2nd-5th).
Regarding spring break -- I haven't defined an Easter yet. If we choose to keep the lunar definition, notice that in the no-January version, April 1st is the spring equinox. Thus Easter would be always in April in this version. (Possible Sundays are 6th, 11th, 17th, 22nd, 28th, and 33rd.) In the no-October version, April is aligned with the Gregorian Calendar, and so Easter in March is possible (with about the same frequency as a Gregorian March Easter.)
This leaves three full weeks for the summer break -- that is, one full month. Let's keep July as the month with no school. That completes our mild implementation of the Eleven Calendar, except for a few loose ends.
(For example, in the no-October version, can there be a Halloween? This holiday is popular enough for us to keep. We might argue that Halloween really means "All Hallows' Eve" or the day before All Saint's Day, which remains as November 1st. Thus Halloween is Sunday, September 33rd.)
This implementation keeps the Eleven Calendar as close to the Gregorian as possible. It's good for those who want to make fewer changes, but it suffers some of the same problems. Thanksgiving, Christmas, and other holidays still exist, so we still have problems with airline travel, the need to take extra days off to accommodate travel, and so on.
A Radical Implementation of the Eleven Calendar
The most radical version of the calendar eliminates holidays completely. The days are simply numbered 1-11, as are the months.
I like the version of the workweek that I mentioned in yesterday's post -- three workdays, a midweek day off, three more workdays, and a four-day weekend. But which days are off days, and which ones aren't, can be different for each person.
With six workdays per week, we need 30 weeks of school, so there's only three weeks off. We combine this to a single month off -- and for each student and worker, the month off is the one containing that person's birthday. (For example, my birthday is late in the year, so assuming that the first month lines up with the Gregorian Calendar, my birthday would be in Month 11. Thus I would get Month 11 off.)
Now here's what the workweek looks like -- the midweek day off matches the number of the month that is taken off. (So I would get Day 11 off.) This completely determines the rest of the week. (For me, I'd work Days 8-10 and 1-3, leaving Days 4-7 as my four-day weekend.)
This version solves some of the problems with the Gregorian calendar. Because different people have different holidays, there's no holiday period when demand exceeds supply at the airports, so airlines can't jack up the prices. The same is true for amusement parks, with their blackout dates close to major holidays. At schools, it also solves the redshirt problem -- every student starts kindergarten the first full month after he or she turns five, and is scheduled to graduate high school during the last month before he or she turns eighteen.
But of course, there are lots of problems with this calendar. Indeed, previous nations such as the French (ten-day week) and Soviets (five-day week) tried something similar to this, where holidays and weekends are replaced with workers on different "shifts" like this. One problem faced was that the new systems didn't respect religious sabbaths.
Another problem was that family members might end up on different shifts. In some cases, this might be desirable (for example, if a father and mother are on different shifts, then there's more likely to be someone home to take care of the children). But it also means that the family members can't be together when they want to (for example, to go on vacation). Actually, the Eleven Calendar is designed to minimize this problem -- everyone has a four-day weekend and no one ever works more than three consecutive days, so every pair of individuals is guaranteed a common day off. But still, the vacation months will be different for people born in different months.
It's possible to reduce some of this by using last names as the basis for determining off-days. (This isn't easy with the Eleven Calendar, but I once saw a calendar with 14 months of 26 days each, with the days lettered A-Z. The letters can be used to determine the off-days.) Then people with the same last name (that is, family members) get the same days off.
But then again, this isn't my favorite version of the Eleven Calendar week anyway. I like the week layout (3 on, 1 off, 3 on, 4 off), but there are better ways to implement it.
A Compromise That Respects Sabbaths
Let's begin by trying to respect religious sabbaths. These are Friday for Muslims, Saturday for Jews, and Sunday for Christians. (Only the Abrahamic religions have anything resembling a weekly sabbath, so I'm not intentionally leaving out non-Abrahamic religions here.)
Just as important as the sabbath are the days of preparation for the sabbaths. This is especially important in traditions where the day starts at sunset rather than midnight -- for example, a Jew who works 9-5 Monday-Friday will often have the sabbath begin before work ends on Friday, especially in the winter when sunset is so early.
So the period Thursday-Sunday includes sabbaths for all three Abrahamic religions along with their preparation days. My ideal 11-day week contains a four-day weekend anyway, so we might as well let those four days be Thursday-Sunday to accommodate the religions.
As for the other seven days, we'll just number them as Days 1-7. Then Day 4 becomes the midweek day off. Schools are thus open Days 1-3, closed Day 4, open Days 5-7, and closed Thursday-Sunday.
Once again, there are six days per school week, so we need 30 school weeks with only three potential vacation weeks. But this time, we won't have a single month of no school. Instead, we'll divide the vacation into three separate weeks -- one each for winter, spring, and summer breaks
If we assume that the winter break is near Gregorian Christmas, and if we wish to space the three holiday weeks equally around the year, then spring break is in late April (Gregorian -- that is, a bit later than Easter, approaching International Labor Day) and the summer break is in late August (Gregorian, approaching American Labor Day).
With four-day weekends every week, the hope is that this will reduce the need to take extra days off during the year. But this doesn't avoid the airline/amusement park problem -- the holiday weeks are well-defined, allowing businesses to jack up prices around those holidays. We might trying adding some flexibility -- for example, if we define Easter as the Sunday near (Gregorian) April 25th, then schools may choose to take the week before or the week after Easter off. The same is true for Christmas (if defined to be on a weekend, especially if New Year's is no longer defined to be a week after Christmas). But that just means that businesses can raise prices for two weeks. And of course, the four-day weekends are also set up perfectly for price gouging.
One Last Compromise
Is it possible to compromise one final way so that sabbaths are respected, yet there are different shifts available in order to beat businesses and get lower ticket prices for airlines and amusement parks?
Suppose within each country, we designate only one day to be the sabbath. Christian nations (including the US) might choose Sunday, Israel might select Saturday, and Muslim nations might choose Friday. (To keep the rest of this post simple, assume that the US chooses Sunday.)
Now instead of considering all 11 shifts (as given under the "Radical Implementation" above), we only look at those with Sunday as an off-day. There are five such shifts, whose weekends are:
Thursday-Sunday
Friday-Day 1
Saturday-Day 2
Sunday-Day 3
Days 4-7 (with Sunday as the midweek day off)
Now we assign students and workers to these five shifts. Some might be more desirable than others -- for example, those for whom a preparation day is important might choose one of the shifts with Saturday included in the weekend. Religious minorities might choose shifts with Friday off (as either a preparation day for Jews or the sabbath itself for Muslims). Still others might prefer Day 1 off.
This instantly beats amusement park blackout plans. Parks can't blackout everyday -- even if they blackout seven days (Sunday and the three days before and after Sunday -- that is, every possible four-day weekend including Sunday), then everyone's midweek days off are white. (The exception is the shift that chooses Sunday as the midweek day off -- but then their entire four-day weekend ends up white.)
Airlines and other travel-related businesses are trickier to beat -- trips last multiple days, and as long as there are holidays, there will be price gouging near those holidays. There are four-day weekends and so less need to wait until a holiday to travel, but airlines can still raise prices on the days surrounding Sunday.
One simple version of the Eleven Calendar simply starts the new year on Gregorian March 1st and places the blank days at the end of the year -- February 27th, 28th, and possibly the 29th. If we simply named each month after the Gregorian month in which it begins, then February (the month which many Western men hate) is dropped, and September-December are months 7-10 to fit their Latin number names. (The alternative is to drop January, in order to maintain the Latin names.)
December, the tenth month, now begins on Gregorian December 23rd. If we decide to transfer all holidays so that they remain close to their Gregorian equivalents, then Christmas now becomes the third day of December. If we declare this date to be Sunday (the Christian sabbath) to guarantee that it's an off day, then the first of December (and hence of every month) becomes a Friday. (If you prefer, we might call the numbered days 4-10 instead of 1-7.) Then it's now possible to take either the week before or the week after Christmas off, allowing for some flexibility. (Recall that New Year's is now March.) Some schools might even choose to take off weeks far away from Christmas, just as they often now ignore Easter.
(It's also possible to declare the 25th of December to be Christmas, even if this is much later than Gregorian December 25th. This is 22 days or two weeks later, hence it's still good to start all months on Friday if we wish to keep Christmas on the sabbath.)
Loose Ends with the Eleven Calendar
We're essentially done with our Calendar Reform posts for the year. But there are a few more things I'd like to say about the Eleven Calendar before we leave it.
So I've stated that for now, my favorite version of the calendar has weeks beginning with the three Abrahamic Sabbaths (Friday, Saturday, Sunday) followed by generic number names -- Day 4, Day 5, and so on to Day 11. I should probably make these names look more like weekdays -- Fourday, Fiveday, up to Elevenday.
And the eleven months go March, April, May, and so on up to January. March 1st, New Year's Day, is on the same named day in the Gregorian Calendar. The last 2-3 days (February 27th, 28th, 29th) are blank days so that every week starts on Friday, March 1st. Each month begins in the Gregorian month with the same name, which is why there is no February -- no month starts in Gregorian February.
At this point, you may wonder about the rule for Leap Days. When I first posted the Eleven Calendar, I mentioned a 33-year cycle with eight Leap Days per cycle -- yet today, I state that each year begins on Gregorian March 1st (thus implying the Gregorian leap cycle). Anyway, the intended leap cycle is indeed the 33-year cycle. But since I can't implement the Eleven Calendar single-handed in the real world, in reality I must convert from the actual calendar in use (the Gregorian Calendar) to my own Eleven Calendar. Hence in reality I have to use the Gregorian leap rules. (It would certainly be desirable to start my calendar on March 1st on an established calendar that actually use a 33-year cycle, such as the Dee-Cecil Calendar.)
The school week in each 11-day week goes 3 on, 1 off, 3 on, 4 off. But each school operates on a different shift (in order to beat airlines, amusement parks, etc., raising prices on the weekend). As I've explained, all shifts will have a day off on the sabbath of the majority religion in a given country -- thus in the majority-Christian US, all shifts will be closed on Sunday. This leaves five logically possible shifts. Let's label each of these five shifts in a way so that members of each religion can be off on its respective sabbath, with the weekend starting on its respective Day of Preparation:
Muslim shift: on Fourday-Sixday, off Sevenday, on Eightday-Tenday, off Elevenday-Sunday
Jewish shift: on Fiveday-Sevenday, off Eightday, on Nineday-Elevenday, off Friday-Fourday
Christian shift: on Sixday-Eightday, off Nineday, on Tenday-Friday, off Saturday-Fiveday
Librarian shift: on Sevenday-Nineday, off Tenday, on Elevenday-Saturday, off Sunday-Sixday
Atheist shift: on Elevenday-Saturday, off Sunday, on Fourday-Sixday, off Sevenday-Tenday
The "Librarian shift" is so-called because many libraries are closed on Sundays and Mondays, so this is the equivalent in my calendar. The "Atheist shift" is off on Sundays because all shifts are, but for this shift, Sunday is the midweek day off. The assumption is that this shift is less interested in religion (hence no extra days off surrounding Sunday) and perhaps even more interested in avoiding weekend prices at businesses (hence observing the Sevenday-Tenday weekend, far away from Sunday).
Now the school year will be divided into three trimesters of ten weeks each (to give the usual total of 180 school days), each followed by a week off (33 total 11-day weeks in the calendar year). We place Christmas on Sunday, December 3rd, since this corresponds to Gregorian December 25th. Since New Year's is on March 1st (far away from Christmas), schools now have the option of taking the week before Christmas or the week after Christmas off (similar to Easter and spring break). Again, the idea is for there to be shifts rather than having every school take its breaks at the same time.
In fact, Easter should now be eleven weeks after Christmas, which works out to be April 25th in my calendar (April 27th Gregorian). Even though this is a bit later than Gregorian Easter, it works out so that schools that take the week before or week after Christmas off can also take the corresponding week of Easter off, and thus fit exactly one trimester between the holidays.
Notice that it's possible to take a week off that's not adjacent to Christmas, just as many schools do now with Easter. Thus it's possible for there to be four vacation shifts:
Penultimate week before Christmas/Easter
Week before Christmas/Easter
Week after Christmas/Easter
Second week after Christmas/Easter
And just as there's a fifth weekly shift (the "Atheist shift"), we might even have a fifth annual shift that takes no week near Christmas nor Easter off, but the week halfway in between instead. This week turns out to be close to March 1st, New Year's Day, so those who would prefer to take New Year's off than Christmas/Easter might choose this fifth shift.
Thus there are 25 possible shift combos, five for the weekly cycle and five for the annual cycle. But we might reduce this to five, since some weekly/annual cycles might go together. For example, the Librarian shift might choose the week before Christmas off to avoid working on Christmas Eve. (It's also possible for the shift that's off Elevenday-Sunday likewise to choose the week after Christmas off to avoid working on Boxing Day, but some workers on this shift might be Muslims for whom Christmas/Boxing Day aren't important holidays.)
Those on the "Christian shift" are off Saturday-Fiveday, and thus they are automatically off from Christmas Eve to the second day after Christmas. I'm not sure which they would prefer -- to take the week before Christmas off (to avoid working on Christmas Adam, as well as Good Friday in spring), or the week after off (to avoid the actual 12 Days of Christmas, and Bright Week in spring).
If I were to choose a shift, which one would I personally choose? This is an interesting one. Recall that in my "radical version" of the calendar, everyone gets the birthday month off. It's possible for me to take my birthday into consideration and choose a shift which will allow me to get my birthday off.
Notice that while only the March dates are aligned with their Gregorian counterparts, the first eleven days in Gregorian December likewise fit into an 11-day week starting with Friday (although these dates are now labeled November 12th-22nd). Thus I know that my December 7th birthday will fall on Sevenday in the new calendar.
I can get Sevenday off as my midweek day off if I take the "Muslim shift" above. (Disclaimer: I am not Muslim.) Moreover, if I take the penultimate week before Christmas off as my vacation week, that week includes my birthday, so I'd get my entire birthday week off. I'm actually torn here between taking my birthday week off and taking the week after Christmas off. (Since this shift is off from Elevenday-Sunday, I'd get the days leading up to Christmas off anyway, so it's more important to get the days after Christmas, including the day after the holiday, off.)
Another choice for me is the "Atheist shift," since it has Sevenday-Tenday off. It thus gives me my birthday and the next three days off. My assumption is that the "Atheist shift" is also the one that takes New Year's off instead of any week near Christmas (or my birthday).
Oh, and speaking of New Year's, there are some anomalies around that week. On most calendars with blank days, we expect those blank days to be days off for everyone. But notice that on my calendar, the blank days appear at the end of the week (between Elevenday and Friday). Thus someone on the "Christian shift" would have 3 on (Sixday-Eightday), 1 off (Nineday), 3 on (Tenday-Elevenday), 2-3 days off (blank days), 1 on (Friday), and then 4 days off. That lone workday on Friday sticks out like a sore thumb (especially when it's New Year's Day itself, which should be a holiday).
Instead, we should treat the first blank day like Friday, and the second blank day like Saturday, for those shifts that work on Fridays or Saturdays. The third blank day (Leap Day) is truly a day off for everyone, as are the first three days of the New Year, Friday-Sunday. (This affects the Librarian shift, but not the Atheist shift if we assume that they get the entire week surrounding New Year's off.)
So far, we moved Christmas to Sunday since it's the one day of the week that everyone gets off. If we wish to observe US federal holidays as common days off, then they must also be moved to Sunday (as there are no weeks off other than the three vacation weeks and first three days in March). We'll find each federal holiday in the Gregorian Calendar and then convert it to the nearest Sunday in the new Eleven Calendar. (All Sundays are on the 3rd, 14th, 25th in my calendar.)
MLK Day: January 16th (Gregorian), December 25th (Eleven Calendar)
President's Day: February 18th (Gregorian), January 25th (Eleven Calendar)
Memorial Day: May 30th (Gregorian), May 25th (Eleven Calendar)
Independence Day: July 2nd (Gregorian), June 25th (Eleven Calendar)
Columbus Day: October 9th (Gregorian), September 25th (Eleven Calendar)
Veteran's Day: November 11th (Gregorian), October 25th (Eleven Calendar)
Thanksgiving: November 22nd (Gregorian), November 3rd (Eleven Calendar)
It's actually interesting that so many of these holidays land on the 25th. (This is actually something I once noticed about the distribution of US federal holidays.)
Holidays when businesses don't close thus can fall on days other than Sunday. For example, we can convert Valentine's Day (February 14th Gregorian) to January 21st, a Tenday. (That's right, even though February no longer exists in my calendar, Valentine's Day still does.) St. Patrick's Day is easier, since dates in March are aligned. March 17th is a Sixday in my calendar. We might wish to keep Mother's Day and Father's Day on Sundays anyway -- the closest dates that fall on Sundays are May 3rd (May 8th Gregorian) and June 14th (June 21st Gregorian).
Halloween is an interesting one. October 31st Gregorian converts to October 14th, a Sunday. But Halloween on Sunday isn't necessarily desirable -- indeed, we might prefer to have All Saints' Day on that Sunday instead, and move Halloween to the previous day (a Saturday, plus it's the 13th -- a fearful day that's fitting for Halloween). So we might make this change anyway, even though it places Halloween on October 30th Gregorian.
You might notice that I haven't placed Labor Day yet, even though it's a federal holiday. We see that August 25th on the new calendar corresponds to September 6th Gregorian -- and it even fits the pattern that most federal holidays land on the 25th.
But here's the problem -- I haven't placed the third holiday break (in addition to Christmas/winter break and Easter/spring break) yet. In order for the trimesters to be equal, there can be a holiday near August 14th on the new calendar (August 26th Gregorian). Then schools can close the week before or week after this day for a short summer break (depending on which week before and after Christmas and Easter is the vacation week at that school).
We might even place a Christian holiday on that date -- perhaps the Assumption of Mary (which is also used as an anchor in the Andrew Usher Calendar). Then Christmas, Easter, and Assumption divide the year into equal thirds, and these are used to determine the trimesters and vacations).
But if we place Assumption on August 14th and Labor Day on August 25th, then schools will be tempted to take the week after Assumption off, which then forces the weeks after Christmas and Easter to be vacations as well (thus taking away the flexibility to take the weeks before off instead).
My solution is to define both Assumption and Labor Day to be August 14th, but this isn't necessarily the best solution. (Also, notice that Assumption on August 14th is awkward, only because the actual Assumption -- August 15th Gregorian -- becomes August 3rd, which is already a Sunday anyway!)
Finally, I wonder where to place Pi Day on the new Calendar. We might keep wish to keep March 14th as Pi Day, but 3/14 now means May 14th (since March is the first month, May now becomes the third month). In any case, the 14th of any month is a Sunday, so there can never be school on Pi Day.
Conclusion
This last version of the Eleven Calendar is my favorite. It's a compromise of all the different versions that I previously mentioned. Celebrating the third of December (in this calendar) as Christmas also addresses the reality that no one is really going to implement this calendar. So I can't just pretend to the rest of the world that my own December 25th (Gregorian January 16th) is Christmas.
Anyway, this concludes my Calendar Reform posts for the year. I wish you a Merry Christmas, Happy Hanukkah, New Year, or whatever you celebrate. And I'll see you next decade!
One Last Compromise
Is it possible to compromise one final way so that sabbaths are respected, yet there are different shifts available in order to beat businesses and get lower ticket prices for airlines and amusement parks?
Suppose within each country, we designate only one day to be the sabbath. Christian nations (including the US) might choose Sunday, Israel might select Saturday, and Muslim nations might choose Friday. (To keep the rest of this post simple, assume that the US chooses Sunday.)
Now instead of considering all 11 shifts (as given under the "Radical Implementation" above), we only look at those with Sunday as an off-day. There are five such shifts, whose weekends are:
Thursday-Sunday
Friday-Day 1
Saturday-Day 2
Sunday-Day 3
Days 4-7 (with Sunday as the midweek day off)
Now we assign students and workers to these five shifts. Some might be more desirable than others -- for example, those for whom a preparation day is important might choose one of the shifts with Saturday included in the weekend. Religious minorities might choose shifts with Friday off (as either a preparation day for Jews or the sabbath itself for Muslims). Still others might prefer Day 1 off.
This instantly beats amusement park blackout plans. Parks can't blackout everyday -- even if they blackout seven days (Sunday and the three days before and after Sunday -- that is, every possible four-day weekend including Sunday), then everyone's midweek days off are white. (The exception is the shift that chooses Sunday as the midweek day off -- but then their entire four-day weekend ends up white.)
Airlines and other travel-related businesses are trickier to beat -- trips last multiple days, and as long as there are holidays, there will be price gouging near those holidays. There are four-day weekends and so less need to wait until a holiday to travel, but airlines can still raise prices on the days surrounding Sunday.
One simple version of the Eleven Calendar simply starts the new year on Gregorian March 1st and places the blank days at the end of the year -- February 27th, 28th, and possibly the 29th. If we simply named each month after the Gregorian month in which it begins, then February (the month which many Western men hate) is dropped, and September-December are months 7-10 to fit their Latin number names. (The alternative is to drop January, in order to maintain the Latin names.)
December, the tenth month, now begins on Gregorian December 23rd. If we decide to transfer all holidays so that they remain close to their Gregorian equivalents, then Christmas now becomes the third day of December. If we declare this date to be Sunday (the Christian sabbath) to guarantee that it's an off day, then the first of December (and hence of every month) becomes a Friday. (If you prefer, we might call the numbered days 4-10 instead of 1-7.) Then it's now possible to take either the week before or the week after Christmas off, allowing for some flexibility. (Recall that New Year's is now March.) Some schools might even choose to take off weeks far away from Christmas, just as they often now ignore Easter.
(It's also possible to declare the 25th of December to be Christmas, even if this is much later than Gregorian December 25th. This is 22 days or two weeks later, hence it's still good to start all months on Friday if we wish to keep Christmas on the sabbath.)
Loose Ends with the Eleven Calendar
We're essentially done with our Calendar Reform posts for the year. But there are a few more things I'd like to say about the Eleven Calendar before we leave it.
So I've stated that for now, my favorite version of the calendar has weeks beginning with the three Abrahamic Sabbaths (Friday, Saturday, Sunday) followed by generic number names -- Day 4, Day 5, and so on to Day 11. I should probably make these names look more like weekdays -- Fourday, Fiveday, up to Elevenday.
And the eleven months go March, April, May, and so on up to January. March 1st, New Year's Day, is on the same named day in the Gregorian Calendar. The last 2-3 days (February 27th, 28th, 29th) are blank days so that every week starts on Friday, March 1st. Each month begins in the Gregorian month with the same name, which is why there is no February -- no month starts in Gregorian February.
At this point, you may wonder about the rule for Leap Days. When I first posted the Eleven Calendar, I mentioned a 33-year cycle with eight Leap Days per cycle -- yet today, I state that each year begins on Gregorian March 1st (thus implying the Gregorian leap cycle). Anyway, the intended leap cycle is indeed the 33-year cycle. But since I can't implement the Eleven Calendar single-handed in the real world, in reality I must convert from the actual calendar in use (the Gregorian Calendar) to my own Eleven Calendar. Hence in reality I have to use the Gregorian leap rules. (It would certainly be desirable to start my calendar on March 1st on an established calendar that actually use a 33-year cycle, such as the Dee-Cecil Calendar.)
The school week in each 11-day week goes 3 on, 1 off, 3 on, 4 off. But each school operates on a different shift (in order to beat airlines, amusement parks, etc., raising prices on the weekend). As I've explained, all shifts will have a day off on the sabbath of the majority religion in a given country -- thus in the majority-Christian US, all shifts will be closed on Sunday. This leaves five logically possible shifts. Let's label each of these five shifts in a way so that members of each religion can be off on its respective sabbath, with the weekend starting on its respective Day of Preparation:
Muslim shift: on Fourday-Sixday, off Sevenday, on Eightday-Tenday, off Elevenday-Sunday
Jewish shift: on Fiveday-Sevenday, off Eightday, on Nineday-Elevenday, off Friday-Fourday
Christian shift: on Sixday-Eightday, off Nineday, on Tenday-Friday, off Saturday-Fiveday
Librarian shift: on Sevenday-Nineday, off Tenday, on Elevenday-Saturday, off Sunday-Sixday
Atheist shift: on Elevenday-Saturday, off Sunday, on Fourday-Sixday, off Sevenday-Tenday
The "Librarian shift" is so-called because many libraries are closed on Sundays and Mondays, so this is the equivalent in my calendar. The "Atheist shift" is off on Sundays because all shifts are, but for this shift, Sunday is the midweek day off. The assumption is that this shift is less interested in religion (hence no extra days off surrounding Sunday) and perhaps even more interested in avoiding weekend prices at businesses (hence observing the Sevenday-Tenday weekend, far away from Sunday).
Now the school year will be divided into three trimesters of ten weeks each (to give the usual total of 180 school days), each followed by a week off (33 total 11-day weeks in the calendar year). We place Christmas on Sunday, December 3rd, since this corresponds to Gregorian December 25th. Since New Year's is on March 1st (far away from Christmas), schools now have the option of taking the week before Christmas or the week after Christmas off (similar to Easter and spring break). Again, the idea is for there to be shifts rather than having every school take its breaks at the same time.
In fact, Easter should now be eleven weeks after Christmas, which works out to be April 25th in my calendar (April 27th Gregorian). Even though this is a bit later than Gregorian Easter, it works out so that schools that take the week before or week after Christmas off can also take the corresponding week of Easter off, and thus fit exactly one trimester between the holidays.
Notice that it's possible to take a week off that's not adjacent to Christmas, just as many schools do now with Easter. Thus it's possible for there to be four vacation shifts:
Penultimate week before Christmas/Easter
Week before Christmas/Easter
Week after Christmas/Easter
Second week after Christmas/Easter
And just as there's a fifth weekly shift (the "Atheist shift"), we might even have a fifth annual shift that takes no week near Christmas nor Easter off, but the week halfway in between instead. This week turns out to be close to March 1st, New Year's Day, so those who would prefer to take New Year's off than Christmas/Easter might choose this fifth shift.
Thus there are 25 possible shift combos, five for the weekly cycle and five for the annual cycle. But we might reduce this to five, since some weekly/annual cycles might go together. For example, the Librarian shift might choose the week before Christmas off to avoid working on Christmas Eve. (It's also possible for the shift that's off Elevenday-Sunday likewise to choose the week after Christmas off to avoid working on Boxing Day, but some workers on this shift might be Muslims for whom Christmas/Boxing Day aren't important holidays.)
Those on the "Christian shift" are off Saturday-Fiveday, and thus they are automatically off from Christmas Eve to the second day after Christmas. I'm not sure which they would prefer -- to take the week before Christmas off (to avoid working on Christmas Adam, as well as Good Friday in spring), or the week after off (to avoid the actual 12 Days of Christmas, and Bright Week in spring).
If I were to choose a shift, which one would I personally choose? This is an interesting one. Recall that in my "radical version" of the calendar, everyone gets the birthday month off. It's possible for me to take my birthday into consideration and choose a shift which will allow me to get my birthday off.
Notice that while only the March dates are aligned with their Gregorian counterparts, the first eleven days in Gregorian December likewise fit into an 11-day week starting with Friday (although these dates are now labeled November 12th-22nd). Thus I know that my December 7th birthday will fall on Sevenday in the new calendar.
I can get Sevenday off as my midweek day off if I take the "Muslim shift" above. (Disclaimer: I am not Muslim.) Moreover, if I take the penultimate week before Christmas off as my vacation week, that week includes my birthday, so I'd get my entire birthday week off. I'm actually torn here between taking my birthday week off and taking the week after Christmas off. (Since this shift is off from Elevenday-Sunday, I'd get the days leading up to Christmas off anyway, so it's more important to get the days after Christmas, including the day after the holiday, off.)
Another choice for me is the "Atheist shift," since it has Sevenday-Tenday off. It thus gives me my birthday and the next three days off. My assumption is that the "Atheist shift" is also the one that takes New Year's off instead of any week near Christmas (or my birthday).
Oh, and speaking of New Year's, there are some anomalies around that week. On most calendars with blank days, we expect those blank days to be days off for everyone. But notice that on my calendar, the blank days appear at the end of the week (between Elevenday and Friday). Thus someone on the "Christian shift" would have 3 on (Sixday-Eightday), 1 off (Nineday), 3 on (Tenday-Elevenday), 2-3 days off (blank days), 1 on (Friday), and then 4 days off. That lone workday on Friday sticks out like a sore thumb (especially when it's New Year's Day itself, which should be a holiday).
Instead, we should treat the first blank day like Friday, and the second blank day like Saturday, for those shifts that work on Fridays or Saturdays. The third blank day (Leap Day) is truly a day off for everyone, as are the first three days of the New Year, Friday-Sunday. (This affects the Librarian shift, but not the Atheist shift if we assume that they get the entire week surrounding New Year's off.)
So far, we moved Christmas to Sunday since it's the one day of the week that everyone gets off. If we wish to observe US federal holidays as common days off, then they must also be moved to Sunday (as there are no weeks off other than the three vacation weeks and first three days in March). We'll find each federal holiday in the Gregorian Calendar and then convert it to the nearest Sunday in the new Eleven Calendar. (All Sundays are on the 3rd, 14th, 25th in my calendar.)
MLK Day: January 16th (Gregorian), December 25th (Eleven Calendar)
President's Day: February 18th (Gregorian), January 25th (Eleven Calendar)
Memorial Day: May 30th (Gregorian), May 25th (Eleven Calendar)
Independence Day: July 2nd (Gregorian), June 25th (Eleven Calendar)
Columbus Day: October 9th (Gregorian), September 25th (Eleven Calendar)
Veteran's Day: November 11th (Gregorian), October 25th (Eleven Calendar)
Thanksgiving: November 22nd (Gregorian), November 3rd (Eleven Calendar)
It's actually interesting that so many of these holidays land on the 25th. (This is actually something I once noticed about the distribution of US federal holidays.)
Holidays when businesses don't close thus can fall on days other than Sunday. For example, we can convert Valentine's Day (February 14th Gregorian) to January 21st, a Tenday. (That's right, even though February no longer exists in my calendar, Valentine's Day still does.) St. Patrick's Day is easier, since dates in March are aligned. March 17th is a Sixday in my calendar. We might wish to keep Mother's Day and Father's Day on Sundays anyway -- the closest dates that fall on Sundays are May 3rd (May 8th Gregorian) and June 14th (June 21st Gregorian).
Halloween is an interesting one. October 31st Gregorian converts to October 14th, a Sunday. But Halloween on Sunday isn't necessarily desirable -- indeed, we might prefer to have All Saints' Day on that Sunday instead, and move Halloween to the previous day (a Saturday, plus it's the 13th -- a fearful day that's fitting for Halloween). So we might make this change anyway, even though it places Halloween on October 30th Gregorian.
You might notice that I haven't placed Labor Day yet, even though it's a federal holiday. We see that August 25th on the new calendar corresponds to September 6th Gregorian -- and it even fits the pattern that most federal holidays land on the 25th.
But here's the problem -- I haven't placed the third holiday break (in addition to Christmas/winter break and Easter/spring break) yet. In order for the trimesters to be equal, there can be a holiday near August 14th on the new calendar (August 26th Gregorian). Then schools can close the week before or week after this day for a short summer break (depending on which week before and after Christmas and Easter is the vacation week at that school).
We might even place a Christian holiday on that date -- perhaps the Assumption of Mary (which is also used as an anchor in the Andrew Usher Calendar). Then Christmas, Easter, and Assumption divide the year into equal thirds, and these are used to determine the trimesters and vacations).
But if we place Assumption on August 14th and Labor Day on August 25th, then schools will be tempted to take the week after Assumption off, which then forces the weeks after Christmas and Easter to be vacations as well (thus taking away the flexibility to take the weeks before off instead).
My solution is to define both Assumption and Labor Day to be August 14th, but this isn't necessarily the best solution. (Also, notice that Assumption on August 14th is awkward, only because the actual Assumption -- August 15th Gregorian -- becomes August 3rd, which is already a Sunday anyway!)
Finally, I wonder where to place Pi Day on the new Calendar. We might keep wish to keep March 14th as Pi Day, but 3/14 now means May 14th (since March is the first month, May now becomes the third month). In any case, the 14th of any month is a Sunday, so there can never be school on Pi Day.
Conclusion
This last version of the Eleven Calendar is my favorite. It's a compromise of all the different versions that I previously mentioned. Celebrating the third of December (in this calendar) as Christmas also addresses the reality that no one is really going to implement this calendar. So I can't just pretend to the rest of the world that my own December 25th (Gregorian January 16th) is Christmas.
Anyway, this concludes my Calendar Reform posts for the year. I wish you a Merry Christmas, Happy Hanukkah, New Year, or whatever you celebrate. And I'll see you next decade!
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