A Calendar for the Third Millennium
WARNING: Mathematical reasoning and simple arithmetic ahead!
Thirty days hath Septober,
August, May, and no wonder
All the rest is peanut butter . . .
[NOTE: Parts of this article refer specifically to the United States holiday calendar, but the principle is universal. Readers elsewhere in the world, feel free to substitute your own favorite holidays.]
Quick, now…what day of the week does the Fourth of July fall on this year? What about your birthday? What’s the exact date of Thanksgiving? You probably don’t know off the top of your head, because the answers to all those questions change from one year to the next. Wouldn’t life be easier if every date always fell on the same day of the week from year to year?
The problem is that the year doesn’t divide evenly into a whole number of weeks. Fifty-two weeks times seven days in a week comes to 364 days, one short of a full year. That one extra day is what makes the next year begin on a different day of the week, causing the whole calendar to shift from one year to the next.
From time to time, people have come up with various suggestions for reforming the calendar. Most of these proposals are based on the idea of fixing the year at exactly 52 weeks and treating that extra, 365th day as a special holiday falling outside the normal seven-day cycle. In effect, the extra day has no date and no day of the week. If the last day of December falls on a Saturday, the next day is New Year’s Day, followed by Sunday, January 1. Fifty-two weeks later, December again ends on a Saturday, followed again by New Year’s Day and then Sunday, January 1. By removing that one extra day from the cycle of weeks and months, the calendar stays exactly the same from year to year. In leap years another extra day is added, either between February and March, the way it is now, or perhaps at midyear, between June and July. This Leap Day, like New Year’s Day, is likewise exempt from the ordinary cycles of weeks and months.
One such reform proposal would divide the year into thirteen months instead of twelve, with each month consisting of exactly four weeks, or 28 days. This has the advantage that any given date falls on the same day of the week every month. No more “thirty days hath September”: If the 4th of this month is a Wednesday, then the 4th of next month will also be a Wednesday, and the month after that, and the month after that. The only calendar you’ll ever need is a single page, because every month is exactly the same as every other.
But thirteen months is kind of an awkward number. A thirteen-month year doesn’t divide evenly into halves or quarters. Some people get spooked at the very thought of thirteen of anything. So an alternate suggestion is to keep the current twelve months, but even them out into a repeating three-month cycle of 31, 30, and 30 days. That divides the year into neat, convenient quarters of 91 days (13 weeks) each, but the months don’t all start on the same day of the week and none of them have an exact, whole number of weeks. If January 1 is a Sunday, then February 1 will be a Wednesday and March 1 a Friday. Not nearly as convenient as having every month begin on the same day of the week.
Perhaps the best suggestion is to have the months alternate 35, 28, and 28 days instead of 31, 30, and 30. This combines the best features of the other two plans: every month begins on the same day of the week and contains a whole number of weeks (four or five, depending on the month), and the year still splits neatly into 13-week (91-day) quarters. That one-page calendar will still work for every month; all you need to do is ignore the bottom (fifth) row in eight of the twelve months.
But all of these reform schemes suffer from one serious problem, which makes them unacceptable to many people. Religiously committed Jews and Christians observe their sabbath every seventh day (Jews on Saturday and Christians on Sunday), and observant Muslims attend weekly Jumu’ah prayers every Friday. Inserting an extra day between weeks would interfere with these seven-day cycles, causing them to shift to a different day of the week each year. Jews, for instance, would find themselves observing the sabbath on Fridays instead of Saturdays, then on Thursdays the following year, and so on; leap years would shift the cycle two days instead of only one. For adherents of these religious practices, the new calendar would clearly make life extremely difficult.
Luckily, there is a solution: instead of adding an extra day (or two) every year, simply save them up for a few years and then add them in a whole week at a time. The present calendar loses about a quarter of a day per year relative to the solar seasons, which is why we add back an extra leap day every fourth year. Shortening the year to 364 days (exactly 52 weeks) would increase that “solar deficit” to a day and a quarter per year. After five years, the accrued deficit would amount to six-and-a-quarter days. So instead of adding an extra leap day every four years, make every fifth year a leap year of 53 weeks (371 days), by adding a leap week to one of the normally short months (say, February or June), lengthening it to 35 days instead of 28.
Of course, since the actual five-year solar deficit is only six-and-a-quarter days instead of seven, adding a full week puts the calendar ahead of the sun by three-quarters of a day every five years. That amounts to a solar surplus of 15 days per century (three-quarters of a day times 20 leap years in a century). So to keep the calendar synchronized with the seasons, we’ll have to drop two of the extra leap weeks each century by reducing, say, the 25th and 75th years of the century (which would otherwise be leap years, since they’re divisible by 5) to ordinary common years of 364 days. That reduces the solar surplus to only a day per century, which can be resolved by dropping a week every seventh century, making all years divisible by 700 common rather than leap years.
There’s still one more detail to take care of, and that’s the Gregorian adjustment. It turns out that the true length of the solar year is not exactly 365.25 days but approximately 365.24218967, or a little more than 11 minutes shorter. That may not sound like much, but over the course of centuries it adds up. By the year 1582, the old Julian calendar, which had been running since the time of Julius Cæsar in the first century BCE, had fallen 11 days behind the solar seasons, with the vernal equinox (the first day of spring) falling on the 10th of March instead of the 21st. To correct the discrepancy, Pope Gregory XIII ordered 10 days dropped from the calendar. (It should have been 11, but he got it slightly wrong. So much for papal infallibility.) By papal decree, Thursday, September 4, 1582 was followed immediately by Friday, September 15. Then, to keep it from starting to drift again, the calendar was reformed by making all “centurial years” (those divisible by 100) common instead of leap years unless they’re also divisible by 400. (In other words, the years 1600 and 2000 were leap years, but 1700, 1800, and 1900 were not, even though they’re divisible by 4.)
So how do we incorporate this “Gregorian adjustment” into our new calendar? Well, the adjustment subtracts three days from the calendar every 400 years, or three-quarters of a day per century. Over our 700-year cycle, we would have to subtract three-quarters of 7 days, or five-and-a-quarter days. So suppose we shorten one more of our leap years — say, the 350th year of the 700-year cycle — to a common year instead. That subtracts one-and-three-quarters days too many, or a quarter of a day per century. Over four cycles, the deficit amounts to exactly seven days. So we just add back one more leap week in the 2800th year (if humanity is still around and our calendar is still running by then), and we’re done. To summarize:
• A common year is 52 weeks (364 days) long, divided into four quarters of 13 weeks (91 days) each. Each quarter consists of one month of 5 weeks (35 days) and two months of 4 weeks (28 days).
• Except as noted below, all years divisible by 5 are leap years of 53 weeks (371 days), in which one of the normally short months is extended from 28 days to 35.
• Years ending in 25 or 75 are common rather than leap years, even though they’re divisible by 5.
• Years divisible by 350 are common rather than leap years, with the exception stated in the next rule.
• Years divisible by 2800 are leap years, even though they’re divisible by 350.
Now that we’ve got the general scheme worked out, there are still a few details to nail down. If every month begins on the same day of the week, which day should that be? The generally established convention is that the week starts on Sunday and ends on Saturday. But starting every month on a Sunday would mean that the thirteenth of the month would always fall on a Friday. The thought of having a Friday the 13th every month would leave some people quivering with fright. So to accommodate those superstitious souls, let’s start the month on a Monday instead. To most people, Monday feels like the start of the week anyway, and if Saturday and Sunday are the “weekend,” shouldn’t they come at the end of the week? So let’s agree that every month of our calendar will start on a Monday and end on a Sunday.
Next, there’s the question of which months should be lengthened to 35 days and which shortened to 28. Should the long month be the first, second, or third of each three-month quarter? Since February already has just 28 days, it seems only natural to leave it that way — so let’s rule out the second month of each quarter as the long month. That leaves the first month or the third. If we lengthen the third month of each quarter (March, June, September, and December) to 35 days, that stretches the December holiday season between Christmas and New Year’s from the present 8 days to 12: from Thursday, December 25, all the way to Sunday, December 35, and Monday, January 1. Some people might welcome this prospect — the more the merrier, after all — but others may well feel that it’s too much of a good thing. Why not shorten December to 28 days and combine the two holidays into one long, festive, five-day weekend from Thursday to Monday? That leaves us with the first month of each quarter (January, April, July, and October) as the long, 5-week months. In leap years (every fifth year, remember), we can add the extra 53rd week at the middle of the year, lengthening June from 28 days to 35.
One of the advantages of the new calendar is that holidays always fall on the same date and day of the week. With the month always starting on a Monday, it’s surprising how many holidays can return to their traditional dates without needing to be artificially moved to create a three-day weekend:
• New Year’s Day: Monday, January 1. End of a five-day holiday weekend beginning on Thursday, December 25.
• Martin Luther King Day: Monday, January 15. The actual date of King’s birth.
• Valentine’s Day: Sunday, February 14. Spend the whole day with your sweetie.
• George Washington’s Birthday: Monday, February 22. Washington’s actual date of birth; no more artificial “Presidents’ Day.” States that are so inclined can also celebrate Lincoln’s birthday on Friday, February 12 — another three-day weekend.
• Cinco de Mayo: Friday, May 5. A three-day weekend for those who celebrate it.
• Mothers’ Day: Sunday, May 14. The second Sunday in May, just as always.
• Memorial Day: Monday, June 1. Traditionally observed on May 30, but that date no longer exists. June 1 is easy to remember and creates another extended weekend.
• Juneteenth: Friday, June 19. Our newest Federal holiday.
• Fathers’ Day: Sunday, June 21. The third Sunday in June, just as always.
• Independence Day: Thursday, July 4. Give everybody Friday off too, and make it a nice four-day break at midyear.
• Labor Day: Monday, September 1. Easy to remember.
• Columbus (or Indigenous Peoples’) Day: Friday, October 12. Back to the actual historical date.
• Halloween: Wednesday, October 31. Or, to preserve its traditional meaning as the eve of All Hallows’ Day (All Saints’ Day, November 1), make it Sunday, October 35, instead. Those who insist on wearing their costumes to school or work can do it on Monday, November 1.
• Election Day: Tuesday, November 2. Always the same date; no more confusion or uncertainty.
• Veterans’ Day: Thursday, November 11. Give it back its historical meaning commemorating the armistice ending World War I.
• Thanksgiving: Thursday, November 25. Another easy date to remember, and the start of the traditional four-day weekend.
• Christmas: Thursday, December 25. Start of a five-day holiday weekend through Monday, January 1.
Religious and cultural holidays that are “movable feasts” based on the lunar cycle — such as Mardi Gras, Ash Wednesday, Good Friday, Easter Sunday, all Jewish and Muslim religious festivals, Asian New Year, and so forth — would, of course, continue to shift from year to year as they always have. The Moon goes her own way.
One last question is what becomes of people’s birthdays? Most people would have a choice: either keep the same nominal date or convert it to the new calendar by counting the days from the beginning of the year. If, for instance, you were born on February 16, that was the 47th day of the year under the old system. But because in the new calendar January has 35 days instead of 31, the 47th day of the year falls back to February 12 instead of the 16th. It’s up to you whether to keep on celebrating on the 16th or convert it to the 12th instead. But some people would see the nominal date of their birth disappear under the new system. If you happened to be born on, say, March 31 of the old calendar, what do you do when March gets shortened to only 28 days? Well, you could either do the conversion just described, moving your birthday from March 31 (the 90th day of the old calendar) to Saturday, March 27 (the 90th day of the new one); or you could do what February 29 “leaplings” have always done and just celebrate on the nearest existing date (in this case, Sunday, March 28, or Monday, April 1). The choice is yours. Of course, if you were born on December 31, the 365th day of the year under the old calendar, you couldn’t do the conversion, because common years in the new calendar don’t have a 365th day. But then you’ve always thought of your birthday as New Year’s Eve anyway, so just celebrate it on the new New Year’s Eve (Sunday, December 28), and may you have many happy returns of the day.
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“A Calendar for the Third Millennium” by Stephen Chernicoff is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
