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:**

http://www.theworldcalendarin2017.org/

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:**

http://aristean.org/calendaridx.htm

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!

http://aristean.org/holydays.htm

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:

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

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:**

http://calendars.wikia.com/wiki/International_Fixed_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:**

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

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:**

http://calendars.wikia.com/wiki/8-days_a_week_simple_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:

Tuesday

Wednesday

Thursday

Friday

T____day

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:

Saturday

_____day

Sunday

Tuesday

S____day

Thursday

Friday

T____day

_____day

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:

Saturday

F____day

Sunday

Tuesday

S____day

Thursday

Friday

T____day

F____day

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:

T____day

F____day

Saturday

Fourday

Sunday

Tuesday

Sevenday

Thursday

Friday

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:

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

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

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:

http://zapatopi.net/metrictime/week.html

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!