Thursday, December 29, 2016

The School Year on Various Reform Calendars

It's still winter break, but I did something related to school today. No, I don't expect a pat on the back from teacher critic Floyd Thursby for doing so, since all I did today was pick up my paycheck. (Even Thursby would come in to work on an off day to get his check!) Our monthly paycheck comes at the end of every month, and with the school locked up for the holiday, we actually pick up our checks at the house of our director (or principal, were this a public school).

If you recall, the Quinter Calendar I mentioned in last week's post is not a Calendar Reform. An academic year divided into five quinters can work on the Gregorian Calendar.

On the other hand, in my last post I mentioned several actual versions of Calendar Reform. Since I'm a teacher, it's especially important to me to see what the school year might look like on each proposed Calendar Reform. For the less radical reform calendars, we'll use the LAUSD Calendar as a basis.

Table of Contents
1. The World Calendar
2. Hanke-Henry Calendar
3. Aristean Calendar
4. Usher Calendar
5. Thirteen Month Calendar
6. Six-Day Calendars
7. Introduction to Longer Week Calendars
8. Eight-Day Calendars
9. Nine-Day Calendars
10. Ten-Day Calendars
11. Eleven-Day Calendars

The World Calendar

We know that New Year's Day is always on Sunday on the World Calendar. Notice that this upcoming year 2017 starts on a Sunday, Because of this, advocates of the World Calendar have proposed 2017 as the year when we should convert to the World Calendar:

Since 2017 is almost here and no one is about to convert to the World Calendar, we see 2023 -- the next year beginning on Sunday -- as a possible alternate starting date. I admit that of all proposed calendars, the World Calendar is one of my favorites. To me, the 13-month calendar is monotonous -- I don't mind different months within the same year starting on different days of the week. Calendar Reformers simply want the same date to fall on the same day of the week from year to year.

Here's what the LAUSD Calendar looks like on the World Calendar:

Monday, August 13th -- Teacher Prep Day
Tuesday, August 14th -- First Day of School
Friday, September 1st -- Admission Day
Monday, September 4th -- Labor Day
Friday, November 10th -- Veteran's Day
November 20th-24th -- Thanksgiving Break
December 18th-January 6th -- Winter Break
Monday, January 16th -- MLK Jr. Day
Monday, February 20th -- President's Day
Monday, May 27th -- Memorial Day
Friday, June 8th -- Last Day of School

Obviously, not every holiday is listed here. Of course I can't give Rosh Hashanah or Yom Kippur -- I assume that the Hebrew Calendar would still exist even if the Gregorian Calendar is replaced by the World Calendar. Of course, it's unsatisfying to have a perpetual calendar yet have to have two holidays that aren't perpetual included in the school year.

Another holiday missing from the list is spring break, Most Calendar Reforms state that if the Gregorian Calendar is replaced, Easter would be fixed. The current Easter range is March 22nd to April 25th -- Sundays on the World Calendar in this range are March 24th, April 1st, April 8th, April 15th, and April 22nd. For simplicity, let's say that spring break is always the first week in April. This results in a breakdown of 17 weeks before winter break, 12 weeks between winter and spring breaks, and nine weeks after spring break.

It's possible to use quinters on the World Calendar, If we start school the week before Labor Day as was proposed by the LAUSD, this would entail pushing the year two weeks back. If we push spring break back two weeks as well, then the breakdown would be 15 weeks before winter break, 14 between the breaks, and nine after. It's natural to push spring break yet another week back (to April 23rd to 27th), so that the breakdown would be 15-15-8. Then spring break can divide the fourth and fifth quinters, just as winter break divides the second and third quinters.

One might even wish to push the first day of school to completely after Labor Day. If we were to do this, then first semester finals would have to go all the way up to December 22nd if we want there to be 15 weeks before Christmas, We could either shorten winter break to two weeks or push the rest of the year back as well -- spring break would be very late, April 30th to May 4th, but students would still return in time for the first AP on May 7th, The last day of school would also be late, June 29th.

When I was young, I often wondered why winter break was two weeks long. I always figured it was because Christmas could fall on any day of the week, so we had to take the whole week off in order to guarantee that Christmas would fall during the break. And the same was true for New Year's Day, hence the second week of break.

With the weekday of Christmas now predictable on the World Calendar, winter break doesn't need to be as long, and some schools might switch to a New York-style break, with Friday, December 22nd and Tuesday, January 3rd being school days. Notice that this is one day longer than the current New York break due to the World Calendar's blank day.

But as we've seen, people like having the extra days off at the holidays no matter what day of the week Christmas happens to fall. So it's possible that LAUSD might still take three weeks off for winter break, even on the World Calendar.

By the way, one last thing I like about the World Calendar is that April 31st exists. In Great Britain or Australia, this would be written 31/4 -- so these in the Commonwealth get a Pi Day, just as we Americans get March 14th, 3/14.

Hanke-Henry Calendar

The Hanke-Henry Calendar, unlike the World Calendar, uses Leap Weeks. But notice that these Leap Weeks are irrelevant to determining when the holidays are. In fact, because the World Calendar starts on Sunday with a 31-30-30 pattern and the H-H Calendar starts on Monday with a 30-30-31 pattern, all of the World Calendar and H-H months are identical except January, April, July, and October!

Thus the LAUSD calendar under H-H looks very similar to that under the World Calendar:

Monday, August 13th -- Teacher Prep Day
Tuesday, August 14th -- First Day of School
Friday, September 1st -- Admission Day
Monday, September 4th -- Labor Day
Friday, November 10th -- Veteran's Day
November 20th-24th -- Thanksgiving Break
December 18th-January 5th -- Winter Break
Monday, January 15th -- MLK Jr. Day
Monday, February 20th -- President's Day
April 1st-5th -- Spring Break
Monday, May 27th -- Memorial Day
Friday, June 8th -- Last Day of School

You may ask, what happens during Leap Week (which Henry calls "Xtr Week")? It's easiest just to include Xtr Week as part of winter break. This means that winter break would be four weeks long in years with an Xtr Week. This is why UCLA this year has a four-week break -- the university is essentially following a Leap Week Calendar, even if they don't call it "Xtr Week."

Because the H-H Calendar now begins on a Monday, Henry now proposes 2018 (a year starting on Monday) to be the first year of the new calendar, just as World Calendar fans propose 2017. So Henry has an extra year to convince people to use his calendar.

Aristean Calendar

The Aristean Calendar, like the World Calendar, uses blank days:

In fact, the Aristean Calendar is essentially the World Calendar with New Year's Day shifted from Sunday to Monday, just as the new Hanke-Henry Calendar is just the old H-H Calendar with New Year's Day shifted from Sunday to Monday.

Because of this, you may think that it's easy to write the LAUSD year under the Aristean Calendar -- just shift all of the World Calendar dates one day. For example, December 25th is on Sunday on the World Calendar and Tuesday on the Aristean Calendar.

There's just one problem -- on the Aristean Calendar, December 25th is not Christmas!

Aristeo is the Australian who invented the Aristean Calendar. According to him, the traditional dates for both Christmas and Easter don't match the actual birth and death dates of Christ. He came to this conclusion by figuring that the Hebrew Calendar back then wasn't lunisolar, as it is now, but purely lunar, like the modern Islamic Calendar (that is, with no Leap Months). The Bible states that Christ was killed at the Passover -- but in that year, Passover on the pure lunar calendar fell in August rather than the spring. On the Aristean Calendar, Easter is Tuesday, August 20th and Christmas falls on Friday, May 23rd.

This, of course, has a very interesting effect on the school calendar, In deference to Aristeo's home country, let's look at the Australian school calendar. Notice that the Australian school year under the Aristean Calendar can be made to look like the Northern Hemisphere school year under the Gregorian Calendar. The autumn term is from February to May, then Christmas break in May. Then the second term is from June to August, followed by Easter break in August, and then the last term is from September to December.

In the Northern Hemisphere, things are more complicated. Notice that Easter, on August 20th, is very close to the first day of school in the LAUSD. It seems logical to incorporate both Easter break and Christmas break into the summer break, as these dates are so close. But is this possible?

If we start school the first full week after Easter and end it the last full week before Christmas, then there are 38 weeks of school in between these holidays. The current LAUSD school year contains 38 weeks, not counting holiday breaks -- and we don't need a Christmas or Easter break, since these are part of summer break!

So it is possible, but is it desirable? This calendar would have us go 38 straight weeks of school without vacations of a week or more -- just long three- and four-day weekends. Most people would like there to be at least one full week off during the school year.

Since Easter is on a Tuesday, we can actually squeeze in extra school days the Wednesday through Friday after the holiday. This may allow us to take a full week off -- and since Christmas isn't on December 25th, we can place the break so that the semesters are actually equal, with 19 weeks of school before and after the holiday.

Before we attempt to write the Aristean LAUSD calendar, notice that Aristeo actually incorporates the Jewish holidays into his calendar. He accomplishes this by using October as a surrogate for Tishri, the first month of the Jewish year. Then Rosh Hashanah is always on Monday, October 1st, and Yom Kippur is always on Wednesday, October 10th.

By the way, since Hanukkah starts on the 25th of Kislev, Aristeo starts it on the 25th of December -- that is, the first candle is lit the previous sunset (as days start at sunset). This means that the Aristean Hanukkah is identical to the actual Hanukkah in 2016. The seventh day of Hanukkah is the blank day (which Aristeo calls "World Peace Day") and the eighth day is New Year's Day.

With Christmas now in May -- and Aristeo wants his Christmas to be a purely religious festival -- I wonder whether the secular part of Christmas (Santa and all that) would simply attach itself to Hanukkah, since it would start on the old Christmas.

OK, so let's look at the Aristean LAUSD calendar:

Tuesday, August 20th -- Easter
Wednesday, August 21st -- First Day of School
Monday, September 3rd -- Labor Day
Monday, October 1st -- Rosh Hashanah
Wednesday, October 10th -- Yom Kippur
Monday, November 12th -- Veteran's Day
November 22nd-23rd -- Thanksgiving
January 1st-5th -- Winter Break
Monday, January 15th -- MLK Jr. Day
Monday, February 19th -- President's Day
Friday, May 16th -- Last Day of School

Notice that even though Christmas is no longer December 25th, New Year's Day is still January 1st -- and it just happens that taking off the first week of January for winter break gives us a 19-19 week split -- though with more holidays in the first semester, the day split is 87-93. This calendar is a bit tough to follow, as there are no holidays from President's Day until the last day of school.

If we decide to squeeze in a few extra days before Christmas in May -- Monday, Tuesday, and Wednesday before the holiday -- then we can take a second week off before the holiday. We may now attempt to divide the year equally into trimesters:

Tuesday, August 20th -- Easter
Wednesday, August 21st -- First Day of School
Monday, September 3rd -- Labor Day
Monday, October 1st -- Rosh Hashanah
Wednesday, October 10th -- Yom Kippur
Monday, November 12th -- Veteran's Day
November 19th-23rd -- Thanksgiving Break
Monday, January 1st -- New Year's Day
Monday, January 15th -- MLK Jr. Day
February 19th-23rd -- President's Break
Wednesday, May 21st -- Last Day of School
Friday, May 25th -- Christmas

We see that instead of New Year's Day, the holiday breaks now line up with Thanksgiving (when LAUSD currently takes a week off) and President's Day (when some schools in other states take a week off). The distribution of days within the trimesters is 59-58-63.

By the way, here's how I might write the schedule, if we don't mind having slightly fewer than 180 days in a school year: we observe that Easter week is August 19th-23rd, Thanksgiving week is November 19th-23rd, President's week is February 19th-23rd, and Christmas week is May 19th-23rd.

In between these breaks are three 12-week trimesters. If we're going to have a calendar based on equal quarters (like the Aristean or World Calendars), why not try to make the quarters equal? With three 12-week trimesters we have exactly 180 days if there are no other holidays -- but of course, a dozen weeks without a break is brutal.

So we add in holidays to make the schedule palatable, even though this drops us below 180. The three Mondays October 1st (Rosh Hashanah), January 1st (New Year's Day), and April 1st are a good starting point, and the three trimesters remain identical. I'd add at least one more holiday to each trimester to obtain a year of 174 days.

By the way, we may wonder whether it's possible to create a calendar similar to the World or Aristean Calendars, yet with Christmas on either of the popular days Wednesday or Friday. (Of course, by "Christmas" here I mean December 25th.)

Suppose we want Christmas to be on a Friday. Then the last day of school before winter break will be a full week before Christmas. (New Yorkers might prefer a Wednesday Christmas, in order to avoid school on the Monday, Tuesday, and Wednesday before Christmas.)

If we want New Year's to be a week later, also on Friday, then December should have 31 days, which gives us a 30-30-31 pattern. (We'll worry about the blank day later.) January starts on a Friday, February starts on Sunday, and March starts on Tuesday, and the pattern repeats each quarter.

Now let's place the blank day. We could put the blank day between December 31st and January 1st, but it's awkward to place it between Thursday and Friday, even if Friday's a holiday. We should put the day between a month ending on Saturday and one starting on Sunday instead -- for example, between January and February, or between April and May, and so on.

I choose between April and May, and here's why. Recall in my March 11th post about how some people don't like losing an hour of sleep on the day that Daylight Saving Time begins. So if we place the blank day in the spring, we'd have an extra day to adjust to the time change! The end of April may seem a bit late, but from the 1960's to the 1980's this was when the spring time change occurred.

This is convenient for the Northern Hemisphere. For Australians, we throw them a bone and give them a blank day every four years on Leap Day. It will occur during their spring time change -- between October and November.

Usher Calendar

Recall that the Usher Calendar is, on the surface, a Gregorian Calendar with a different rule to determine Leap Days, but underneath, it's actually a Leap Week Calendar.

The key difference between the Usher and Hanke-Henry Leep Week Calendars is that the Usher Leap Week (which he calls Week 1) occurs in August. It makes sense for the school year to start during Week 2, as this week occurs every year. This means that school can't start more than two weeks before Labor Day. The current calendar for 2016-2017 starts three weeks before Labor Day, but the calendar that was proposed for 2017-2018 starts at Usher's Week 2. So the final week of school would be one week later as well, which is Usher's Week 44.

Other than that, holidays are set to a fixed week in the Usher Calendar. Thanksgiving, for example, is always Week 15, so there are thirteen weeks from the first day of school and three weeks between Thanksgiving and winter break, for a 16-week first semester. This may be considered close enough to two quinters to justify using a quinter calendar as well.

By the way, the following link mentions a proposal similar to the Usher Calendar:

The weeks begin on Monday and Leap Week at this link is at the end of the year, so this calendar is actually more like Hanke-Henry than Usher. Still, we see some similarities to Usher. For example, the NAWHA President's Day agrees with the Gregorian date 86% of the time -- and the other 14% is when the NAWHA date is February 22nd -- so it agrees with Usher 100% of the time. And Memorial Day agrees with the Gregorian date 96% of the time. The other 4% is when there's a year with a Leap Day beginning on Thursday -- which the Usher Leap Day rule cleverly avoids!

Thirteen Month Calendar

So far, all of the calendars we've seen are similar to the Gregorian -- seven days, twelve months. Let's look at some thirteen month calendars. We'll start with the International Fixed Calendar (Cotsworth Calendar) -- on this calendar, the new month is called Sol and is placed between June and July. We can now convert all of the LAUSD dates we found on the World Calendar to the Cotsworth Calendar:

Monday, August 2nd -- Teacher Prep Day
Tuesday, August 3rd -- First Day of School
Friday, August 20th -- Admission Day
Monday, August 23rd -- Labor Day
Friday, November 6th -- Veteran's Day
November 16th-20th -- Thanksgiving Break
December 16th-January 6th -- Winter Break
Monday, January 16th -- MLK Jr. Day
Monday, February 23rd -- President's Day
April 9th-13th -- Spring Break
Monday, June 9th -- Memorial Day
Friday, June 20th -- Last Day of School

All of this assumes that holidays in the new calendar are found by converting their respective dates from the Gregorian Calendar. For example, Labor Day is now in August and Memorial Day has moved to June. We see that there are now two school-free months (Sol and July), while there's only one such Gregorian month (July),

It's also possible that the new calendar could have all of the holidays in the same named months, even if this means moving them with respect to the seasons. So Labor Day would be on the first Monday in September, namely the 2nd, even though this places it a week closer to the equinox than the Gregorian Labor Day. Likewise, Memorial Day would be on May 23rd -- the last Monday in May.

Another 13-month calendar is the Pax Calendar. This is a Leap Week calendar. The new month is called Columbus and placed between November and December. We can obtain a calendar similar to that for Cotsworth simply by renaming the months above:

Monday, September 2nd -- Teacher Prep Day
Tuesday, September 3rd -- First Day of School
Friday, September 20th -- Admission Day
Monday, September 23rd -- Labor Day
Friday, Columbus 6th -- Veteran's Day
Columbus 16th-20th -- Thanksgiving Break
December 16th-January 6th -- Winter Break
Monday, January 16th -- MLK Jr. Day
Monday, February 23rd -- President's Day
April 9th-13th -- Spring Break
Monday, June 9th -- Memorial Day
Friday, June 20th -- Last Day of School

Notice that now school doesn't begin until the named month September. It's now appealing to think about what would happen if we kept the holidays on the same named dates, so that Labor Day is still the first Monday in September, namely the 2nd. Then we can actually have a calendar that starts after Labor Day and have a first semester that's both the same length as the current LAUSD semester and end before Christmas!

In fact, if we assume that Christmas is on the named date December 25th, this is a Wednesday, so we can have school all the way up to Friday, December 20th, without any problems. The dates December 25th and January 1st are just four days apart since all months have 28 days, With Christmas and New Year's closer to each other, a shorter winter break can be used. Then the first semester can be made a week longer -- making it closer to the ideal 90 days.

For this calendar, I'm dropping Admission Day. Let's replace it with a new holiday. We see that there's a new month between Thanksgiving and Christmas. Since this month is called "Columbus," let's place Columbus Day in this month (instead of October). We could put it on the 12th (since the explorer landed on this date in October 1492), but this is a Thursday, so maybe the 13th is better.

Actually, I prefer placing the holiday as late as possible -- Friday, Columbus 27th. Not only is this closer to the midpoint between Thanksgiving and Christmas, but with the Leap Week (Pax) right after Columbus, the three-day weekend can extend to a full week vacation in Pax years.

Monday, September 2nd -- Labor Day
Tuesday, September 3rd -- Teacher Prep Day
Wednesday, September 4th -- First Day of School
Wednesday, November 11th -- Veteran's Day
November 23rd-27th -- Thanksgiving Break
Columbus 27th -- Columbus Day
December 23rd-January 6th -- Winter Break
Monday, January 16th -- MLK Jr. Day
Monday, February 16th -- President's Day
April 9th-13th -- Spring Break
Monday, May 23rd -- Memorial Day
Friday, June 13th -- Last Day of School

Finally, suppose the new month is called "Smarch" (as on The Simpsons) and placed, just as the show implies, after December, We can either rename the months on the Cotsworth Calendar to reflect the new order or simply place the holidays in the same named months. Then there would be a whole month between Christmas and New Year's. We could make winter break a full month long -- but then again, the Simpsons episode mentioning "Smarch" takes place at the school, so we'd better just convert the dates.

By the way, with today being my payday, recall what I wrote in my last post about quadriweekly pay every four weeks at some districts. The LAUSD used to have quadriweekly paydays, but now it is monthly, on the fifth of the month. (As you can see, my charter school pays on the last or penultimate weekday of the month.) I mentioned in that post how the New Earth Calendar has thirteen months with each beginning on a Monday, so on that calendar, "quadriweekly" and "monthly on the fifth" are in fact identical! (The school year for New Earth would be the same as Cotsworth shifted one day.)

Six Day Weeks

Now let's start looking at the calendars which change the number of days in a week. We'll start with a six day calendar:

On this calendar, Saturday is dropped. The weekend is now Friday and Sunday (that is, the Muslim and Christian Sabbaths), and the school week is now Monday to Thursday.

The 6 Day Week Solar Calendar contains 60 weeks of six days each, or 360 days. This calendar then places five extra days at the end of the months May through September. This is because the calendar is trying to have months end on equinoxes and solstices -- March 30th is the spring equinox, June 31st the summer solstice, and so on. There are more days from summer solstice to fall equinox than there are from winter solstice to spring equinox, so this is how the extra 31st dates are placed. We can consider the 31st dates to be blank days or "Saturdays."

There used to be a six day calendar called the Raenbo Calendar, which was nice because its author included the dates of the holidays. Unfortunately, that calendar is no longer posted on the web, so we must go through the legwork of determining when the holidays should be on a six day calendar.

With the spring equinox on March 30th instead of March 20th, we'll convert the dates by starting the LAUSD calendar the first week in September. On the other hand, I keep Labor Day the first Monday in September -- I know workers will want to take advantage of the blank day August 31st to make Labor Day into a four-day weekend. Like the Pax Calendar, school can start after Labor Day. At this point, we might as well convert all holidays to the same named month, except for Memorial Day, which I place on the first Monday in June to take advantage of the blank day May 31st:

Monday, September 2nd -- Labor Day
Tuesday, September 3rd -- Teacher Prep Day
Wednesday, September 4th -- First Day of School
Thursday, November 11th -- Veteran's Day
November 20th-23rd -- Thanksgiving Break
December 26th-29th -- Winter Break
Monday, January 20th -- MLK Jr. Day
Monday, February 20th -- President's Day
April 2nd-5th -- Spring Break
Monday, June 2nd -- Memorial Day
Thursday, June 29th -- Last Day of School

With four days per school week, we need more weeks to reach 180 days. Still, we can make July and August both school-free (which places the first and last days of school near their current LAUSD dates) if we squeeze out weeks during the holiday breaks. We can take advantage of the fact that New Year's Day is April 1st on this calendar rather than January 1st. We may also define April 1st to be either Easter Sunday or Palm Sunday, to make it easier on the schools. As we can see, the calendar is scheduled tightly on both the Aristean and 6 Day Week Solar Calendars.

Recall that April Fool's Day was created as a reaction to the new year being switched from spring to winter, so this calendar reverses that tradition. So on this calendar, we might define a new holiday, January Fool's Day, on January 1st.

Introduction to Longer Week Calendars

Our goal is to define the school week and year for my original calendar, the Eleven Calendar. But before we tackle an eleven-day week, we should try out calendars with week lengths that are in between the Gregorian seven days and my eleven days.

So we want to look at 8-10 day calendars. There are several issues with longer week calendars:

-- How many days should there be during the week?
-- How many days should there be on the weekend?

My preference is for weeks to contain an even number of days during the week This makes A/B block schedules more convenient for high schools. The six-day week given above has four weekdays, and so block schedules work out well.

Eight Day Weeks

Here is a link to a typical eight day calendar:

The new day is simply called Newday and placed between Saturday and Sunday. So the obvious intent is for there to be five school days and three weekend days.

The link above doesn't state how to divide the 365-day year into 8-day weeks. It's possible to do the same as with the six day calendar -- have five blank days and divide the other 360 days into the various weeks, The number 360 is divisible by not only 6, but 8, 9, and 10 as well. So the five blank day model works for all week lengths off 8-10 days.

But there is a more efficient way to obtain weeks of 8-10 days with few blank days. Here's how: instead of looking at one year, we consider two years. Now twice 360 is 720, which of course is also divisible by 8, 9, and 10 (indeed it's the product of all three). But if we insert one extra week of each respective week length, we obtain 728, 729, or 730 days -- and these are much closer to the actual length of two tropical years than 720, so we have fewer blank days.

For eight day weeks, we note that 728 is double 364. Therefore our calendar only requires one or two blank days a year, just like the World Calendar. We are now looking at a two-year cycle -- if New Year's Day for, say 2017, falls on a Sunday, then 2018 will start on a Thursday, but 2019 will start on a Sunday once again. Each year contains 45 1/2 weeks of 8 days each.

This means that the calendar isn't completely perpetual, But then again, I once mentioned a drawback of perpetual calendars -- the birthday problem. Most people want their birthdays on the weekend, but more people are actually born on a given weekday than a weekend day (since C-sections are scheduled on weekdays). So people will be stuck with their birthdays on the weekend every year.

Let's think about the seven day calendar for a second. If you could choose any day of the week to have your birthday, which day would you choose? I assume Saturday would be most popular. Some people might choose Sunday as it's also a weekend day, and Friday is popular for parties since even though there's work or school that day, at least people are off the next day. So assume that there are three desirable days for birthdays (Friday-Sunday) and four undesirable days (Monday-Thursday).

On the eight day calendar, Newday is placed on the weekend. So now there are four desirable days for birthdays. Again, there are only three weekend days, but we include Friday as a desirable birthday for the same reason as we would on the seven day calendar.

Now we note that with our two-year cycle, each date on the eight day calendar alternates between two days of the week:

Monday -- Friday
Tuesday -- Saturday
Wednesday -- Newday
Thursday -- Sunday

So each date alternates between a desirable party day and an undesirable party day! And if we schedule a C-section for Monday through Thursday, the baby will grow up to celebrate all odd birthdays on the weekend.

Let's think about it for a moment. The birthdays that we look forward to the most are mostly the odd year birthdays. For example, Jewish males celebrate their 13th birthdays with a bar mitzvah, Latina females celebrate their 15th birthdays with a quinceanera, and of course everyone looks forward to the 21st birthday. On the other hand, the birthdays we dread the most are all even birthdays -- like 30, 40, 50, and so on. The calendar allows people to celebrate the good birthdays like 13, 15, and 21 on the weekend, and buries the dreadful birthdays like 30, 40, and 50 in the middle of the week where we can avoid talking about them.

I know -- I know! The real difference between good and dreadful birthdays is young vs. old and not odd vs. even. Still, I claim that 65 is a good birthday -- the beginning of retirement and entry into the golden years. And soon 65 will be replaced with 67 -- hey, another odd number! So certainly odd birthdays like 65 and 67 are more worthy of celebration than the dreaded 60 and 70.

So far, I haven't mentioned how to divide the year into months. Based on the eight day link above, the intention is just to keep the Gregorian month lengths -- 31 in January, 28 or 29 in February, and so on, just with eight days a week instead of seven. But I'm sure we can do better than that -- especially since 31 days in many months is so tantalizingly close to 32, which is a multiple of the eight.

If every month had 32 days, then twelve months would have 384 days, which is too many. So we can reduce some months, say April and August, to three weeks, or 24 days. Recall that the total number of weeks needs to be 45 1/2, so let's make December 3 1/2 weeks, or 28 days.

Then again, if we're going to have half-weeks, let's have more 28 day months so that we can avoid all 24 day months altogether. We'll need five such months. Well, February is already 28 days, and we can reduce all Gregorian 30 day months -- April, June, September, and November -- to 28 days, while extending all 31 day months to 32 days.

Then again, if we're going to have 28 day months, let's make all months 28 days long -- and have 13 months instead of 12. The International Fixed Calendar is surprisingly compatible with the 8 day week, despite being created to fit a 7 day week.

Now let's look at the holidays. Some people who create weeks of eight days (or longer) point out that every weekend is a three-day weekend, so we don't need any holidays. On the other hand, if we want to include some holidays anyway, notice that if a holiday such as New Year's Day falls on a Monday one year, it will fall on Friday the next -- and both Monday and Friday are convenient for extending the three-day weekend into a four-day weekend.

If January 1st is a Monday, then the 5th, 9th, 13th, 17th, 21st, 25th, and 29th are all on either Monday or Friday every year. The 25th -- hey, that's convenient for Christmas! The other holidays must all be shifted to fit these dates -- maybe MLK Jr. day is January 17th, President's Day February 21st, and so on throughout the year.

Suppose January 1st, 2017, is on a Monday. Then all months in 2017 start on Monday, but all months in 2018 start on Friday. If we use thirteen months instead, then a month starts on Monday if the year number and month number are both odd or both even. If the month and year are of opposite parity, then the month begins on Friday.

Let's set up the school calendar now. Notice that if we don't have any holidays at all (because we already have three-day weekends), then our task becomes much easier. We need 180 days and every week has five days, so we need 36 weeks. If we assume the 24-32 calendar where every month has 32 days except April (24), August (24), and December (28), then we start counting:

August -- 3 weeks (3 weeks so far)
September -- 4 weeks (7 weeks so far)
October -- 4 weeks (11 weeks so far)
November -- 3 weeks (skip Thanksgiving week, 14 weeks so far)
December -- 2 weeks (skip the last week and half, 16 weeks so far)
January -- 4 weeks (20 weeks so far)
February -- 4 weeks (24 weeks so far)
March -- 4 weeks (28 weeks so far)
April -- 2 weeks (skip Easter week, 30 weeks so far)
May -- 4 weeks (34 weeks so far)
June -- 2 weeks (36 weeks)

Nine Day Weeks

I've already alluded to a nine day "week" here on the blog. Recall the guards at the Tomb of the Unknown Soldier -- I wrote about their 24 hour shifts in trying to compare them to middle school students who claim they need to go to the restroom every 24 minutes! I wrote that they follow a nine day rotation in which they work three of the nine days. So this implies that a nine day calendar already exists!

So let's try to create a nine day Calendar Reform based on the tomb guards' rotation. First of all, it's convenient if the days of the week indicate which guard is on duty. Recall that the pattern is:

1 day on
1 day off
1 day on
1 day off
1 day on
4 days off

So let's try to create our nine day week:


Do you see what I've done here? If we have a third day starting with T, then the first guard knows that he always works on days starting with T. In fact, let's try to do the same thing with the letter S:


Well, our third guard works on the day after Thursday, so let's call that day "Friday" and let his other shift days begin with the letter F:


I lack the imagination to come up with the new day names. If we let Friday be the last day of the week, then two of the names come up automatically:


But then we're still stuck with two more names to figure out.

Recall that our plan was to take advantage of 729 being a multiple of nine. We would need blank days less often than once a year -- in fact, three blank days in four years creates a calendar that's as accurate as the Julian Calendar.

But we can't leave the tomb unguarded on blank days. So we'd need Leap Weeks instead. Here are links to two existing Nine Day Calendars:

Notice that both of these calendars note that 729 isn't merely a multiple of nine -- it's a power of nine as well as of three. Even though both have nine day units (and Kalentris even calls it a "week"), the Leap Unit added every four years has only three days (Kalentris calls this a "tierce").

If we really want a full nine day Leap Week, we should add it only once every 12 years in order to attain Julian accuracy.

Of course, tomb guards work only three out of nine days, but that's not acceptable for students. The Kalentris link above implies that every weekend should last for one "tierce" or three days, which implies that we should have a six day workweek. To me, six day weeks are convenient for high school block schedules, since they fits both A/B and A/B/C schedules. But six straight days of work might be too tough on students.

With six day weeks, we need 30 weeks of school. There are 40 1/2 weeks available, leaving us 10 1/2 weeks for winter, spring, and summer breaks. We can have six weeks for summer break, three weeks for winter break, and a week and a half for spring, so that summer break is double the length of winter break, which in turn is double the length of spring break.

Ten Day Weeks

With ten day weeks, we would need 36 1/2 weeks per year. Notice that 730 days is already so close to two years that the only blank days we'd need are the Leap Days!

Unlike the 40 1/2 nine day week calendar, the 36 1/2 ten day week calendar already exists:

This link suggests that we should have seven weekdays and three-day weekends. But I prefer having six weekdays and four-day weekends. The six weekdays are convenient for block schedules, and with four-day weekends, people can celebrate odd-numbered birthdays just as with the 45 1/2 eight day week calendar.

Again 30 weeks of school are needed, so there are 6 1/2 weeks left over for vacations.

Eleven Day Weeks

Finally we'll look at my own Eleven Calendar. Again, I like having six weekdays as this works well with block schedules. So there are now five days off from school.

But I don't propose having a five-day weekend. Instead, there will be four-day weekends -- and the fifth off day is used to break up the six-day week! So we have three days of school, a midweek break, three more school days, and then the four-day weekend.

This is very convenient for the A/B/C block schedule. It also works with the A/B block schedule, though we now have A/B/A/off/B/A/B.

It's also possible to have midweek breaks with the ten day calendar -- for example, we can have school on Zeroday to Twoday, an off day on Threeday, school from Fourday to Sixday, and then the weekend from Sevenday to Nineday (as intended at the Zapatopi link above). But then someone born on Zeroday will have odd birthdays on Fiveday -- and neither Zeroday nor Fiveday is a desirable birthday on this calendar. (Of course, the Eleven Calendar is fully perpetual, so anyone born on a weekday must celebrate all birthdays on the weekday.)

The Eleven Calendar contains 33 weeks, and we need 30 weeks of school. This is what we expect -- with longer weekends and midweek breaks, the vacations must be shorter. I propose simply having one week off each for summer, winter, and spring breaks. The week is 11 days, and combining it with an adjoining four-day weekend provides a 15-day break. This is just one day shorter than the usual Gregorian two-week winter break (16 days counting the adjoining weekend). It's longer than the old spring break, but of course much shorter than the old summer break.

My next post will be in 3-5 days. As this is my final post of 2016, I wish you a Happy New Year! So enjoy 2017, no matter what calendar you use!

Monday, December 26, 2016

Calendar Reform

I hope you had a wonderful Christmas. But now it's the day after Christmas, often called Boxing Day in many English-speaking countries. Beginning today, my thoughts start turning towards New Year's Day, calendars -- and Calendar Reform.

As I wrote last year, calendars and Calendar Reform have always fascinated me. Notice that last week, I wrote a post about the Quinter Calendar for high schools. But the Quinter Calendar is not a Calendar Reform. A true Calendar Reform changes our actual calendar -- the one that starts on January 1st and ends December 31st -- not just a local school calendar. 

Is it possible to create a brand-new calendar, one on which Christmas always falls on a full moon date? Or, perhaps an easier task is one on which Christmas always falls on the same day of the week. This year, it fell on a Sunday, which is why post offices and banks observe today as the federal holiday. Last year, it fell on a Friday, which is nice as it also leads to a three-day weekend.

Today I will repeat the post I wrote last year, when I mentioned several calendar proposals (with a few updates for the current year). But first, let's start with a video clip from my favorite TV show, The Simpsons:

"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"

The video clip I posted last year no longer works, so here's a new link:

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 -- Boxing Day -- since after all, it's the week 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.

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 in years when Veteran's Day falls on a Tuesday, many students and teachers unofficially take Monday off -- and many schools and districts officially close that day as well. This problem also occurs at offices, where, as I said at the start of this post, workers want to take off two extra Fridays when Christmas and New Year's Day are on Thursdays. 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:

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. A Leap Second will be added this year, on December 31st, 2016. 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 very late this year (not ending until January 1st) and Chinese holidays such as Lunar New Year, which occurred very late in 2015 but very early in 2017.

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 will occur during the upcoming Year of the Rooster.

(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:

A full description of the calendar comes from this link:

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 four years ago is the Hanke-Henry Permanent Calendar, posted at the following site:

This calendar has been changed since I wrote abut it last year. The Hanke-Henry Calendar now begins on a Monday, and its months follow a 30-30-31 pattern while the World Calendar's months follow a 31-30-30 pattern. This means that in both calendars, Christmas will always be on Monday, and Thanksgiving will always be on the 23rd. But the main difference is, instead of blank days, the Hanke-Henry Calendar 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 contained 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:

:Input Y
:If (R=4 and I=Y
) or (R=3 and I=

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 four years ago, many news sites picked up the story. The following website, IO9, is typical. It's interesting to read the comments:

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, as it was on the original version. 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, as it was this year, 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. Christmas on Monday is a slight improvement, but some people may still find Friday, December 22nd to be too late.

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:

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 SeptemberOctoberNovember, 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 --HumanusSanctus, 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:

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:

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:

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.

Last year, I invented my own Calendar Reform proposal -- a calendar with eleven-day weeks. The main reason for the proposal is that I wanted my calendar to be original. All other week lengths from six to ten days were already taken, so I created a 11-day calendar.  I invented this calendar over eleven months ago, back in my January 1st post.

I also wrote about another calendar, the Usher Calendar, in my February 29th post. The Usher Calendar has two parts -- a visible regular calendar and a hidden leap-week calendar.
"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:

This simply places a 1 in front of all the dates. So this year is 12016, to be followed by 12017.

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 02016, to be followed by 02017.

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:

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 three years ago mentions this calendar.

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

Happy New Year, and have a wonderful Gregorian year 2017. My next post will be in 3-5 days -- and I'll be writing more about Calendar Reform in that post.