Jitter Reduction from Offsetting Additional Leap Weeks in Divide-by-7 & Divide-By-6 Leap Week Rules

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Jitter Reduction from Offsetting Additional Leap Weeks in Divide-by-7 & Divide-By-6 Leap Week Rules

Karl Palmen - UKRI STFC

Dear Brij and Calendar People

 

In his Divide-by-Seven and Divide-by-Seven leap week rules Brij offsets the leap weeks that are in addition to the regular leap weeks every seven or six years to reduce the jitter rather than have two leap weeks in some years as Marcus Wong has proposed.

 

I’ve thought about how much this would reduce the jitter by and I came to the conclusion that it would reduce the jitter by exactly the same amount as the drift of the calendar year against the mean year over one cycle of the regular leap weeks without any additional leap week.  I leave it to other calendar people how I came to this conclusion about the jitter reduction.  Next I give it in more detail.

 

For Divide-by-Seven, and offset of two or three years would reduce the jitter by the difference between seven mean years and a seven years with one leap week. This works out as

7*365.2421875 – 7*365 = 1.6953125 days for a mean year of 365.2421875 days and

7*365.2425 – 7*365 = 1.6975 days for a mean year of 365.2425 days.

This applies regardless of the intervals between the additional leap weeks, provided of course they are divisible by seven years.

 

For Divide-by-Six, and offset of one, two or three years would reduce the jitter by the difference between six mean years and a six years with one leap week. This works out as

6*365.2421875 – (6*364 + 7) = 0.453125 days for a mean year of 365.2421875 days and

6*365.2425 – (6*364 + 7) =  0.455 days for a mean year of 365.2425 days.

This applies regardless of the intervals between the additional leap weeks, provided of course they are divisible by six years. It may also apply if the offset is varied so the intervals are no longer divisible by six years.

 

The fewer additional leap weeks there are to offset, the less the reduction in jitter arising from this offset.

 

 

Karl

 

11(08(28

 

 

 


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Re: Jitter Reduction from Offsetting Additional Leap Weeks in Divide-by-7 & Divide-By-6 Leap Week Rules

Willy Juul Krogh
Dear Brij, Karl Palmen and Calendar People
 
Interesting readings, but far too complicating in my opinion.
 
Willy





 

Date: Wed, 6 Oct 2010 13:10:48 +0100
From: [hidden email]
Subject: Jitter Reduction from Offsetting Additional Leap Weeks in Divide-by-7 & Divide-By-6 Leap Week Rules
To: [hidden email]

Dear Brij and Calendar People

 

In his Divide-by-Seven and Divide-by-Seven leap week rules Brij offsets the leap weeks that are in addition to the regular leap weeks every seven or six years to reduce the jitter rather than have two leap weeks in some years as Marcus Wong has proposed.

 

I’ve thought about how much this would reduce the jitter by and I came to the conclusion that it would reduce the jitter by exactly the same amount as the drift of the calendar year against the mean year over one cycle of the regular leap weeks without any additional leap week.  I leave it to other calendar people how I came to this conclusion about the jitter reduction.  Next I give it in more detail.

 

For Divide-by-Seven, and offset of two or three years would reduce the jitter by the difference between seven mean years and a seven years with one leap week. This works out as

7*365.2421875 – 7*365 = 1.6953125 days for a mean year of 365.2421875 days and

7*365.2425 – 7*365 = 1.6975 days for a mean year of 365.2425 days.

This applies regardless of the intervals between the additional leap weeks, provided of course they are divisible by seven years.

 

For Divide-by-Six, and offset of one, two or three years would reduce the jitter by the difference between six mean years and a six years with one leap week. This works out as

6*365.2421875 – (6*364 + 7) = 0.453125 days for a mean year of 365.2421875 days and

6*365.2425 – (6*364 + 7) =  0.455 days for a mean year of 365.2425 days.

This applies regardless of the intervals between the additional leap weeks, provided of course they are divisible by six years. It may also apply if the offset is varied so the intervals are no longer divisible by six years.

 

The fewer additional leap weeks there are to offset, the less the reduction in jitter arising from this offset.

 

 

Karl

 

11(08(28

 

 

 


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Re: Jitter Reduction from Offsetting Additional Leap Weeks in Divide-by-7 & Divide-By-6 Leap Week Rules

Willy Juul Krogh
In reply to this post by Karl Palmen - UKRI STFC
Dear Brij and Karl Palmen and Calendar People

 

For better or for worse, the Gregorian Calender after Pope Gregor XIII, is what we have chosen in the near and farther future.

Here are som thoughts that are far too simple.

 

Once the idea of leaving every 128 Years with only 365 days was abandoned, every (sic) now and then, 128th years should change

down to every and once 100th Year.

 Instead it was chosen to

give ordinary 100-years 365 days. And here comes the question, when each and every year divideable by 100, only get

365 days. What could be done next, some years to decide what to do, 1 and 2 days off course.

 

Years divideable with 80 now gets only 365 days. And in the beginning, or what should it be called, years that are

divideable with 400 will get 366 days. Somewhere in a distant future every 80th Year only have 365 days, all and everybody are long gone.

 

Another question is, will this " Be a legal Calendar or a legal Calendar change ?"

 

A Calendar with "Leap weeks" seems too far a guesswork. One thought who could bring me down, or more severe punishment, is making Easter the

Last Week in March, here I must abstain.

 

 

 

Name of the Calendar?  

 

Of course good ol' Pope Gregor XIII

 

Kind Regards  Willy

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History HackDay in London

John Dalziel
  There's a History HackDay happening in London 22nd-23rd Jan 2011

http://historyhackday.org/
http://historyhackday.pbworks.com/
http://twitter.com/#!/historyhackday

could be interesting.
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Re: Jitter Reduction from Offsetting Additional Leap Weeks in Divide-by-7 & Divide-By-6 Leap Week Rules

Karl Palmen - UKRI STFC
In reply to this post by Willy Juul Krogh

Dear Willy and Calendar people

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Willy Juul Krogh
Sent: 06 October 2010 14:37
To: [hidden email]
Subject: Re: Jitter Reduction from Offsetting Additional Leap Weeks in Divide-by-7 & Divide-By-6 Leap Week Rules

 

Dear Brij and Karl Palmen and Calendar People

 

For better or for worse, the Gregorian Calender after Pope Gregor XIII, is what we have chosen in the near and farther future.

The Gregorian calendar has a jitter of 2.1975 days, which can be seen by comparing the actual number of leap days in the 193-year interval 1903 to 2196 inclusive with the average number of leap days in 193 years.

 

Here are som thoughts that are far too simple.

 

Once the idea of leaving every 128 Years with only 365 days was abandoned, every (sic) now and then, 128th years should change

down to every and once 100th Year.

The 128-year cycle calendar has a jitter of 1.6953215 days got by comparing the number of leap days in the seven-year interval 125 to 131 inclusive (which is zero) with the mean number of leap days in seven years, which is (31/128)*7 = 1.6953125.

 Instead it was chosen to

give ordinary 100-years 365 days. And here comes the question, when each and every year divideable by 100, only get

365 days. What could be done next, some years to decide what to do, 1 and 2 days off course.

 

Years divideable with 80 now gets only 365 days. And in the beginning, or what should it be called, years that are

divideable with 400 will get 366 days. Somewhere in a distant future every 80th Year only have 365 days, all and everybody are long gone.

This is beyond me. It may refer to the distant future when the tropical year is less than 365.24 days.

 

Another question is, will this " Be a legal Calendar or a legal Calendar change ?"

 

A Calendar with "Leap weeks" seems too far a guesswork.

See more about leap week calendars at

http://www.hermetic.ch/cal_stud/palmen/lweek1.htm

 

The note you have been replying to is about a particular class of leap week calendars that are in my opinion not the best. It says the a particular feature of these calendars (the offsetting) gives just a small benefit in reducing jitter. The reduction of jitter by about 1.7 or 0.45 days is small compared with the jitter of such calendars which is about 14 days at best.

 

A similar issue applies to some sidereal leap day calendars. For example, one could have a leap day every four year plus an additional leap day every 160 years (mean year 365.25625 days). Such a calendar would have a jitter of 1.74375 days (over the one-year interval of year 160). If the extra leap day that occurs once every 160 years were offset two years, then the jitter would be reduced by the error over 4 years, which is 4*(1/160) = 0.025 days to 1.71875 days; not a big improvement.

 

One thought who could bring me down, or more severe punishment, is making Easter the

Last Week in March, here I must abstain.

Or the first week in April, or whatever.

 

 

 

Name of the Calendar?  

 

Of course good ol' Pope Gregor XIII

 

Kind Regards  Willy

 

Karl

 

11(08(29


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Re: Jitter Reduction from Offsetting Additional Leap Weeks in Divide-by-7 & Divide-By-6 Leap Week Rules

Brij Bhushan Vij
In reply to this post by Willy Juul Krogh
WILLY, Karl, sirs:
>Dear Brij and Karl Palmen and Calendar People
>Once the idea of leaving every 128 Years with only 365 days was abandoned,.....
When was this? Surely, this must have happened after the Papal Bull of 1582! Does this mean NO correction to 'calendar format be considered - for improving the Mean Year value; the very purpose of Pope Gregory's work that caused deleting 10-days out of calendar. Please see the formats I have been discussing and placed at my Home Page: http://www.brijvij.com/  and  my Leap Weeks plan using 896-year/159 LWks on div.6; div.7 or even div.8 to give IMPROVED mean year =365.2421875 days instead of 365.2425 days.
Please see: http://www.brijvij.com/bb_DIV_7plan.pdf
I shall be temporarily out of doing any calculations since I shall be away attending to my my wife who has undergone surgery. I shall, however, read occasional reactions.
Regards,
Brij Bhushan Vij
20101008H00:21(decimal) EST
Aa Nau Bhadra Kritvo Yantu Vishwatah -Rg Veda
The Astronomical Poem (revised number of days in any month)
"30 days has July,September,
April, June, November and December
all the rest have 31 except February which has 29
except on years divisible evenly by 4;
except when YEAR divisible by 128 and 3200 -
as long as you remember that
"October (meaning 8) is the 10th month; and
December (meaning 10) is the 12th BUT has 30 days & ONE
OUTSIDE of calendar-format"
Jan:31; Feb:29; Mar:31; Apr:30; May:31; Jun:30
Jul:30; Aug:31; Sep:30; Oct:31; Nov:30; Dec:30
(365th day of Year is World Day)
******As per Kali V-GRhymeCalendaar*****
"Koi bhi cheshtha vayarth nahin hoti, purshaarth karne mein hai"
My Profile - http://www.brijvij.com/bbv_2col-vipBrief.pdf
Author had NO interaction with The World Calendar Association
except via Media & Organisations to who I contributed for A
Possible World Calendar, since 1971.
HOME PAGE: http://www.brijvij.com/
Contact via E-mail: [hidden email]


 

Date: Wed, 6 Oct 2010 15:36:57 +0200
From: [hidden email]
Subject: Re: Jitter Reduction from Offsetting Additional Leap Weeks in Divide-by-7 & Divide-By-6 Leap Week Rules
To: [hidden email]

Dear Brij and Karl Palmen and Calendar People  

For better or for worse, the Gregorian Calender after Pope Gregor XIII, is what we have chosen in the near and farther future.

Here are som thoughts that are far too simple.

 

Once the idea of leaving every 128 Years with only 365 days was abandoned, every (sic) now and then, 128th years should change

down to every and once 100th Year.

 Instead it was chosen to

give ordinary 100-years 365 days. And here comes the question, when each and every year divideable by 100, only get

365 days. What could be done next, some years to decide what to do, 1 and 2 days off course.

 

Years divideable with 80 now gets only 365 days. And in the beginning, or what should it be called, years that are

divideable with 400 will get 366 days. Somewhere in a distant future every 80th Year only have 365 days, all and everybody are long gone.

 

Another question is, will this " Be a legal Calendar or a legal Calendar change ?"

 

A Calendar with "Leap weeks" seems too far a guesswork. One thought who could bring me down, or more severe punishment, is making Easter the

Last Week in March, here I must abstain.

 

 

 

Name of the Calendar?  

 

Of course good ol' Pope Gregor XIII

 

Kind Regards  Willy