Part2, Joining list. Calendar reforms.

[MIKE OSSIPOFF]

Starting Days and Month systems:  
 
As I was saying, for a fixed calendar, if we want the easiest day-of-week determinations, then we want year-divisions of 28 days, 14 days or 91 days. The proposals with a 28-day month have 13 months. Ok, but are the public going to accept a year with 13 months? I'm not so sure. I don't think I'd try proposing it. Fourteen days sounds a bit short for a year-division, but landlords, and others who do billing, could bill every other year-division. But I prefer Asimov's 91-day year-division. His World Season Calendar.  
 
Though I'd like a new calendar, a more rational one than our current Roman Calendar, and would help promote any promising calendar proposal that doeesn't use blank days, it seems to me that, to get the full benefit of a new calendar, it would be best to try for a seasonal calendar--a calendar intended to at least make some effort to represent the seasons.  I fully understand that the seasons aren't necessarily four equal time-periods, and that the seasonal time-lag varies from place to place, and even varies during the year. But it doesn't seem so unreasonable to define a "season" as a quarter of a year. And the idea is just to make a good _attempt_ to represent the seasons. If you know that the season-time-lag where you live is different from 38 days, than you know where you currently are, in the seasonal year, by correcting the date of the Improved Seasonal Calendar appropriately for your locale.
 
I suggest the "Improved Seasonal Calendar" as a fixed calendar and also as a non-fixed calendar.
 
I'd make these changes in Asimov's World Season Calendar, and I'd call it the "Improved Seasonal Calendar":
 
I'd change the starting date. He goes by the conventional notion that the seasons start on the equinoxes and solstices. Winter, for instance, starts on the winter solstice. That assumes that the seasons lag a month-and-a-half behind the sun's declination. I've read estimates that typically the lag varies from a month to a month-annd-a-half, for different places. So then, for a seasonal calendar, intended to at least make some effort to represent the seasons, I'd assume a lag of 1.25 months. 38 days. Actually, for Santa Cruz, California, on the West Coast, temperature records for various years consistently showed January 28th as the middle of winter (when there wasn't an "El Nino")--a seasonal time-lag of 38 days. So that's what I'd assume for my seasonal calendar proposal.
 
Since the middle of winter is then on January 28 (in terms of our Roman Calendar), that would be the day of mid-winter in my "Improved Seasonal Calendar". So Winter would start about 45.5 days before that, on, say, December 14th. My Improved Seasonal Calendar would start Winter on December 14th. Each season would be 91 days. But, if the calendar is not a fixed calendar, then the last season, Autumn, would be 92 days.  
 
If the calendar is not fixed, then leapyear would be Winter 92nd. If the calendar is fixed, then of course there would be a leap-week instead of a leap-day. The leap-week would occur as needed to minimize the drift-from-center, correcting for the calendar's drift of 1.24219 days per year.
 
By the way, as Asimov pointed out, the season-designations would be wrong for places in the Southern Hemisphere. So, for international use, when people in both southern and northern hemispheres are communicating, of course I'd call the seasons 1, 2, 3 and 4. Or A, B, C, & D. Or maybe I, II, III & IV. For local or national use, there's no reason to not say "Winter, Spring, Summer & Fall (or Autumn)"
 
If the calendar is non-fixed, then I'd add subdivisions of the seasons. Either two, three, or four subdivisions per season. The most familiar proposal would be three. It would closely resemble the months of the World Calendar, except, of course it would be displaced from the World Calendar, season-wise. Other possibilities, for the non-fixed version would be to divide each season into a 45-day division and a 46-day division; or three 23-day divisions and a 22-day division. Of course, in the non-fixed version, Autumn would have three 31-day divisions, two 46-day divisions, or three 23-day divisons, to bring the year up to 365 days. Leap-day would then be added to Winter's last division.
 
The divisions would have names such as Winter 1, Spring 3, etc. Their purpose would be to have the relatively short payment-periods we're used to, while using the seasons as a medium for locating and naming the months with respect to the seasons. For a fixed calendar, I'd just number the seasons' days from 1 to 91, without the divisions. Then, landlords and companies that do billing could just bill every 30 days, and that would be easy, with the seasons' day-numbering.
 
It would be easy to determine what day of the week any date falls on.
 
A fancier version of the Improved Seasonal Calendar would have two refinements:
 
1) It would take into account the variation during the year of the average seasonal timelag. If we can find a figure for that average lag for summer and for winter, then I'd assume that one applies at the winter solstice and the other at the summer solstice. I'd use some interpolating function to get an estimate of what the lag is at other times of year. Unless there were reason to do otherwise, I'd use a linear interpolating function.
 
2) The Babylonians did something interesting: They'd made very precise measurements of the Sun's movement along the ecliptic, and they knew that it moved faster during the winter than during the summer. They had a calendar that took this into account. They had a 12 month calendar, which started on an equinox, and in which each month represented the Sun's time in a particular sign of the zodiac, a particular 30 degrees along the ecliptic. I'd borrow that idea from them. The lengths of the seasons would be equal to the number of days that the sun spends in the corresponding quarters of the ecliptic. From when I checked, for instance, it seems to me that Winter would be 89 days long, and Summer would be 94 days long. If the calendar is non-fixed, then the _divisions_ of the seasons, too, would represent equal distances along the ecliptic, and their length, again, would be equal to the time that the sun spends in each division of the ecliptic.
 
I don't know what to call this version. For now, I'll call it the "Fancy Improved Seasonal Calendar".
 
It seems to me that, very likely, the Fancy Improved Seasonal Calendar is too complicated to explain, and too lacking in simplicity and regularity, to be popular with the public. So, most likely, I'd instead propose the Improved Seasonal Calendar in the simpler version, the non-Fancy version I described first.
 
The Improved Seasonal Calendar, whether fixed or non-fixed, is my favorite calendar-reform proposal. Though I like the Fancy version of it, I'd instead probably propose the simpler non-Fancy version for better public acceptance.
 
Again this posting is getting long, so I'll post it now.
 
Mike Ossipoff
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[Irv Bromberg]

On 2009 May 20, at 16:58 , MIKE OSSIPOFF wrote:

2) The Babylonians did something interesting: They'd made very precise measurements of the Sun's movement along the ecliptic, and they knew that it moved faster during the winter than during the summer. They had a calendar that took this into account. They had a 12 month calendar, which started on an equinox, and in which each month represented the Sun's time in a particular sign of the zodiac, a particular 30 degrees along the ecliptic. I'd borrow that idea from them. The lengths of the seasons would be equal to the number of days that the sun spends in the corresponding quarters of the ecliptic. From when I checked, for instance, it seems to me that Winter would be 89 days long, and Summer would be 94 days long. If the calendar is non-fixed, then the _divisions_ of the seasons, too, would represent equal distances along the ecliptic, and their length, again, would be equal to the time that the sun spends in each division of the ecliptic.

That proposal is similar to the modern Persian astronomical calendar, which starts the year at the northward equinox with 6 x 31-day months, then the rest of the months have 30 days except for the last which has 29 days in a regular year or 30 days in a leap year.  It is a good idea to have the leap day (or week or month, whatever the leap unit is) at the end of the year so that its insertion doesn't affect the ordinal numbering of any prior date in the year -- that simplifies calendrical arithmetic.  The Persian scheme, even though it is an astronomical calendar for the equinox, doesn't include any rule for progressively advancing which months have 31 days in parallel with the advance of perihelion, and the 6 longer months are not centered with respect to the present or recent past position of perihelion, in fact at present perihelion is nearly 3 months before the Persian New Year Day (Norouz).

If you look in the archives of this CALNDR LISTSERV you will see some threads about Shriramana Sharma's STAY calendar, which was proposed as an astronomical calendar that would have a rule for advancing which 6 months would have 31 days.  The proposal proved problematic to actually implement in calendar arithmetic, Shriramana never got it working.  I also tried and gave up.  It is difficult to avoid oscillations of the 31-day months from year-to-year unless special rules are adopted to prevent such oscillations.  Such rules could include using the mean perihelion instead of the actual perihelion, and probably not changing the month lengths more frequently than at century boundaries.

Another problem is that the Earth orbital eccentricity is declining and will continue to decline for tens of millennia into the future.  This will gradually reduce the seasonal length differences, making it harder to justify having 6 x 31-day months in a row, at least until the orbital eccentricity goes back on the increase.

If months are constrained to contain only a whole number of weeks then that precludes any possibility of making month lengths correspond to the position of perihelion.

-- Irv Bromberg, Toronto, Canada

<http://www.sym454.org/seasons/>

[Amos Shapir]

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A tropical calendar may be difficult, but this can be made simpler by defining the calendar along the sidereal year.  A convenient cycle is 366 years with 95 leap (year Y is leap if (Y mod 27) mod 4 == 3); it can be started on apphelion or perihelion day, with 5 or 6 long months around the apphelion, the same way the Iranian calendar does.
 
To make it into a tropical calendar, just shift the starting day by 1 day every 57 years (that may change in the future), but keep month lengths the same as the overlapping sidereal months.
 
A lunar calendar of 122 years, 1509 months, can be superimposed on the same cycle.  Longer lunar months should be concentrated around the perihelion, by keeping leap months and days closer to that point.
 
(Perl source is available if anyone wants the gory details)

Amos Shapir
 



 

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Date: Sat, 23 May 2009 23:34:25 -0400
From: irv.bromberg@...
Subject: Re: Part2, Joining list. Calendar reforms.
To: CALNDR-L@...

...

If you look in the archives of this CALNDR LISTSERV you will see some threads about Shriramana Sharma's STAY calendar, which was proposed as an astronomical calendar that would have a rule for advancing which 6 months would have 31 days.  The proposal proved problematic to actually implement in calendar arithmetic, Shriramana never got it working.  I also tried and gave up.  It is difficult to avoid oscillations of the 31-day months from year-to-year unless special rules are adopted to prevent such oscillations.  Such rules could include using the mean perihelion instead of the actual perihelion, and probably not changing the month lengths more frequently than at century boundaries.

 

 

 

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[Irv Bromberg]

On 2009 May 24, at 10:14 , Amos Shapir wrote:

A tropical calendar may be difficult, but this can be made simpler by defining the calendar along the sidereal year.  A convenient cycle is 366 years with 95 leap (year Y is leap if (Y mod 27) mod 4 == 3); it can be started on apphelion or perihelion day, with 5 or 6 long months around the apphelion, the same way the Iranian calendar does.

Irv replies:  A mean year of 365+95/366 = 365d 6h 13m 46.2s is quite a bit longer than the usually quoted length for the mean sidereal year of about 365.256363051 days = 365d 6h 9m 9.7676s, but nevertheless that excess should more closely approximate the advance of aphelion.

If a fixed cycle is going to be employed, doesn't the optimal year length have to be a good approximation to the mean anomalistic year, which is slightly longer?

365.259635864 days = 365d 6h 13min 52s = 365+701/2700 days is exact (for the given length, which I presume is in atomic time), or other close approximations are 365+182/701 days or 365+155/597 days.  Also there is 365+27/104 days whose mean year is a tad short = 365d 6h 13m 50+10/13s but should be better than the 366-year cycle.  Making it a tad short should prolong its useful duration of good accuracy, by better approximating mean solar time over future centuries.

To make it into a tropical calendar, just shift the starting day by 1 day every 57 years (that may change in the future), but keep month lengths the same as the overlapping sidereal months.

If astronomical algorithms are employed to determine the New Year Day, as is done for the modern Persian calendar, then the anomalistic year approximation cycle will only be used to determine which months have 31 days, although I'm not clear on what the criteria would be.  If the criteria are defined then I see little advantage in using a fixed cycle for the aphelion approximation, assuming that astronomical algorithms (solar longitude) are being employed for the northward equinox anyway, because it would be simple enough to use a mean aphelion polynomial to find the target ecliptic longitude and then use the same solar longitude astronomical algorithms to find the moment when Sun reaches that target, then apply the defined 31-day month numbering criteria.

However, to avoid oscillations around leap years it will be necessary to pre-calculate switchover points, or have a complicated scheme that analyses a series of years and statistically decides what to do.  If such a list is defined then there is no need to reckon the position of aphelion at all, except that the list would need re-verification from time-to-time as knowledge of celestial mechanics etc. advances sufficiently to justify re-evaluating the list.

-- Irv Bromberg, Toronto, Canada

<http://www.sym454.org/>

[Irv Bromberg]

On 2009 May 23, at 23:34 , Irv Bromberg wrote:

The Persian scheme, even though it is an astronomical calendar for the equinox, doesn't include any rule for progressively advancing which months have 31 days in parallel with the advance of perihelion, and the 6 longer months are not centered with respect to the present or recent past position of perihelion, in fact at present perihelion is nearly 3 months before the Persian New Year Day (Norouz).

Irv adds:  Oops, my mistake.  The longer months should be centered on aphelion, as Amos correctly pointed out.

In the present year, Sun will reach mean aphelion, at a solar longitude of about 103.1°, at about 02:54h Tehran standard time on the 14th of Tir (4th month) in the modern astronomical Persian calendar.  So actually, aphelion is currently as well-centered as is possible with respect to the 31-day months of the year (first 6 months).

This reminds me of another oscillation problem for a calendar that is intended to keep the 31-day months centered with respect to aphelion:  each time that there is a leap day and the position of aphelion is near the cutoff, that can cause the 31-day months to shift one way during the leap year, and then back during non-leap years.  It seems to me that the rules of such a calendar ought to prevent any such short-term shifts.

-- Irv Bromberg, Toronto, Canada

<http://www.sym454.org/seasons/>

[Karl Palmen]

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Dear Amos and Calendar People

 

365 95/366 days = 365.25956284 days, which is quite close to the anomalistic year, but not the sidereal year as stated by Amos, but the anomalistic year is the year that Amos requires. A calendar with the same years, but with one day removed once every 57 of its years, would have a mean year of 365.24201898 days.

 

The mean month resulting from dividing the 336-year cycle into three 122-year cycles of 1509 months is 29.5305942125 days, which is remarkably close to the Hebrew mean month.  The 122-year cycle can for formed from six 19-year cycles and an Octaeteris (6*19+8=122 & 6*235+99=1509).

 

For the suggested 366-year cycle leap year rule, I think Amos meant (year Y is leap if ((Y mod 366) mod 27) mod 4 == 3);.  This gives 14 27-year cycles with a total of 98 leap years from which 12 years of 3 leap years have been cut from the end. These leap years are not spaced as evenly as possible.

 

Karl

 

10(09(03

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Amos Shapir
Sent: 24 May 2009 15:15
To: CALNDR-L@...
Subject: Astronomical sidereal calendar (was: Part2, Joining list. Calendar reforms)

 

A tropical calendar may be difficult, but this can be made simpler by defining the calendar along the sidereal year.  A convenient cycle is 366 years with 95 leap (year Y is leap if (Y mod 27) mod 4 == 3); it can be started on apphelion or perihelion day, with 5 or 6 long months around the apphelion, the same way the Iranian calendar does.
 
To make it into a tropical calendar, just shift the starting day by 1 day every 57 years (that may change in the future), but keep month lengths the same as the overlapping sidereal months.
 
A lunar calendar of 122 years, 1509 months, can be superimposed on the same cycle.  Longer lunar months should be concentrated around the perihelion, by keeping leap months and days closer to that point.
 
(Perl source is available if anyone wants the gory details)

Amos Shapir
 



 

---

Date: Sat, 23 May 2009 23:34:25 -0400
From: irv.bromberg@...
Subject: Re: Part2, Joining list. Calendar reforms.
To: CALNDR-L@...

...

If you look in the archives of this CALNDR LISTSERV you will see some threads about Shriramana Sharma's STAY calendar, which was proposed as an astronomical calendar that would have a rule for advancing which 6 months would have 31 days.  The proposal proved problematic to actually implement in calendar arithmetic, Shriramana never got it working.  I also tried and gave up.  It is difficult to avoid oscillations of the 31-day months from year-to-year unless special rules are adopted to prevent such oscillations.  Such rules could include using the mean perihelion instead of the actual perihelion, and probably not changing the month lengths more frequently than at century boundaries.

 

 

 

 

 

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[MIKE OSSIPOFF]

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Irv--
 
That's interesting that others in modern times (including you)  have looked into a calendar that divides equally the eclliptic, instead of the year's days.
 
I hadn't considered the motion of perihelion, and the changing eccentricity, and I'm disappointed to hear that that would mess  up an ecliptic-measured calendar. But ok--an ecliptic-meassured calendar would be more difficult to explain anyway, and wouldn't have the nice neat regularity that would otherwise be possible. So my "Fancy" version might not be a good proposal after-all.
 
Yes, using an ecliptic-measured calendar would mean giving up having the months &/or quarters have whole numbers of weeks. I probably wouldn't suggests (but wouldn't oppose) an exliptic-measured calendar being a fixed calendar. Such a fixed calendar would still have the advantage of no need to reschedule annualy due to different calendar each year. But of course it would lose the advantage of easy day-of-week determinations.
 
Yes, I'd always add the leapweek to the last month or quarter.
 
Mike Ossipoff
 
 
 
 

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