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Re: Never Before RE: 400-yrs,834-yrs & 896-yrs RE: Symmetry Statement and Divide-by-Six RE:

by Karl Palmen :: Rate this Message:

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Dear Brij and Calendar People

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Brij Bhushan Vij
Sent: 27 April 2009 20:22
To: CALNDR-L@...
Subject: Never Before RE: 400-yrs,834-yrs & 896-yrs RE: Symmetry Statement and Divide-by-Six RE:

Karl, sir & CC:

>….. The intervals between the successive Kepler's leap weeks are either 90 or 96 years, including

>the interval over the end of the cycle…..

Placing of Keplers’ Leap Weeks is left best to judgments of ‘astronomers, mathematicians & software engineers’ like yourself. I have tried to be as symmetrical as I could possibly be. My point of suggesting *CENTRAL YEAR* (Y2000-80)+417 =Y2337, in separation of 84-years all through; as 0081, 0165, 0249, 0333, 0417, 0501, 0585, 0669, 0753.... that I had been shown long ago. Does extending the gaps to 90 & 96-yr intervals present EXTRA benefits.

Yes. Less jitter. Each date varies no more than 2 weeks with respect to the seasons (rather than almost 3 weeks for Brij’s suggestion). Note that ALL the gaps including the gap across the end of the cycle are 90 or 96 years usually alternating.

It is the cyclic repetition of 834-year cycle that I considered i.e. in cycle (1920 thro 2754), 1^st KLWk to be at Y2001 (2004 being divisible by six) and then every 84-years to have Keplers’ Leap Week as shown. Why do we want to count distance between TWO KLWks (unless there is a specific advantage), while 1^st cycle ends at Y2754^th year. ERA start at YEAR ZERO could be formed, as shown at: http://www.brijvij.com/bbv_417-year-div.6.pdf

0000, 0834, 1668, 2502, 3336, 4170, 5004…..and repeating.

Having the Kepler’s leap weeks once every 84 years is equivalent to having a Julian Calendar mean year of 365.25 days.

In the suggested 834-year cycle its like running the Julian calendar for 834 years before correcting it.

It has a huge gap of 162 years between year 0753 and year 834+81=0915. Brij’s suggestion would have the dates moving back and forth almost three weeks with respect to the seasons rather than two weeks that is possible by a divide-by-six rule.

I feel, as shown, central year 417^th i.e. *Y0417^th or Y2337^th is of significance* with repetition at 834-year cyclic interval. This shall be more conducive to software designers!

I am not allergic to placing extra NINE Keplers’ LWks as Karl has shown: 45^th, 141^st, 231^st, 327^th 417^th, 507^th, 603^rd, 693^rd, 789^th years, BUT why ‘wider & alternate placing’ 96, 90 years interval and call them symmetrical? It is the start that has been delayed/enhanced by 45 years. I see this as: 45-96-90-96-90-90-96-90-96-45 =834-years; whereas I place KLWk every 84-years, starting 3-yaers earlier for 1st KLWk i.e. Y0081 or Y2001.

Brij must pay attention to the interval between the last Kepler’s leap week of one cycle and the first Kepler’s leap week of the next cycle and so the two 45s add together to form an interval of 90 years.

If the middle year (417) is a Kepler’s leap week year and there are an odd number (9) of Kepler’s leap weeks, then the last year (834) must occur half way between two Kepler’s leap week years. This is possible for an interval of 90 (but not 96) making the first Kepler’s leap week year the 45^th year.

The cycle is symmetrical thus:

045+789=834

141+693=834

231+603=834

327+507=834

417+417=834.

Brij’s suggestion is also symmetrical, but the two 81s in his 81-84-84-84-84-84-84-84-84-81 add to form a huge interval of 162 years between Kepler’s leap weeks.

> “Even the simple 57^th, 147^th, 237^th, 327^th, 417^th, 507^th, 597^th, 687^th, 777^th is better with a gap of 114

>years”

This is 90-years from 417th…..shifts the start of next cycle from 57^th to 33^rd year [(777+90=(867 - 834) =33] for next cycle.. I therefore leave THIS for software designers to choose, so long as there are 9 KLWks between 834-years & repeating every 834-years.

I see that Brij did pay attention to this interval across the end of the cycle!

If this interval were 90 years, then the next Kepler’s year would be the 33^rd year of the next cycle, but it is a 114-year (twice 57) interval to make it into a symmetrical 834-year cycle. For a symmetrical cycle the interval over the end is always twice the first Kepler’s year. That why the 45^th year is a good choice.

If all intervals were 90 years we’d have a mean year of 365.2444444444 days.

> Perhaps, Brij intends to omit one of these 10 Kepler’s leap weeks once every third 896-year cycle.

>This would correct the number of leap weeks, but produce extra jitter by leaving a gap of 180 or 186

>years between two of the Kepler’s leap weeks.

YES sir, this was an exercise that I undertook to see if I could achieve cyclic placing of 896-year cycles around 448^th year (CENTRAL) to fulfill: Mean Year =7*(52+159/896), since there are EXACTLY 159 LWks in 896-year cycle. I agree, as earlier discussed 3*896 =2688-years make better sense, to get MY =7*[(52+1/6+29/2688)] days - since 896 is NOT divisible by six BUT 10 KLWks are needed every 896-year cycle.

Wrong! I’ve shown this many times before!

BASICALLY, the point I make is that DIVIDE six(6) plan that had NEVER been attempted has a solution; additionally resolving the ZERO YEAR riddle. Likewise, the 400-year cycle, using div. six(6) for LWks has Mean Year =7*[52+1/6+13/1200)] =365.2524 days.

The 400-year cycle does not work with divide-by-six for the same reason that 896-year cycle does not work. The number of years must be divisible by six. The 400-year becomes a 1200-year cycle with 71*3-200=13 Kepler’s leap weeks. Because 1200 is not twice an odd number, the Kepler’s leap weeks cannot be arranged symmetrically like the 834-year cycle. Making the first Kepler’s leap week year the 45^th year and using intervals of 96 and 90 years, we can get an almost symmetrical cycle of

45^th, 141^st 231^st, 321^st, 417^th, 507^th, 597^th, 693^rd, 783^rd, 879^th, 969^th, 1059^th and 1155^th years. This cycle would be symmetrical if the 597^th year were moved to the 600^th year. It has eight intervals of 90 years (including the interval between the 1155^th year and the 1200+45^th year) and five intervals of 96 years.

Karl

10(08(04

Regards,
Brij Bhushan Vij
Today:

(MJD 2454950)/1361+D-128W18-01 (G. Monday, 2009 April 27H15:36 (decimal) EST
Aa Nau Bhadra Kritvo Yantu Vishwatah -Rg Veda
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)
My Profile:http://www.brijvij.com/bbv_2col-vipBrief.pdf
HOME PAGE: http://www.brijvij.com/
******As per Kali V-GRhymeCalendaar*****
"Koi bhi cheshtha vayarth nahin hoti, purshaarth karne mein hai"
Contact # 001 (201) 675-8548

Date: Mon, 27 Apr 2009 12:42:29 +0100
From: karl.palmen@...
Subject: Re: 400-yrs,834-yrs & 896-yrs RE: Symmetry Statement and Divide-by-Six RE:
To: CALNDR-L@...

Dear Brij and Calendar People

The Kepler’s leap week years of the 834-year cycle can be arranged symmetrically thus:

45^th, 141^st, 231^st, 327^th 417^th, 507^th, 603^rd, 693^rd, 789^th years. The intervals between the successive Kepler's leap weeks are either 90 or 96 years, including the interval over the end of the cycle.

This is much better than Brij’s suggestion of

81^st, 165^th, 249^th, 333^rd, 417^th, 501^st, 855^th, 669^th 753^rd years, which suffers from a huge gap of 162 years over the end of the cycle. Even the simple 57^th, 147^th, 237^th, 327^th, 417^th, 507^th, 597^th, 687^th, 777^th is better with a gap of 114 years.

Brij seems to be unaware of the importance of having the all the intervals between Kepler's leap weeks with either 90 or 96 years to avoid excessive jitter. Also the intervals of 90 and 96 years need to be roughly equal in proportion with slightly more 90s than 96s.

The cycles listed although symmetrical do not have the same symmetry in the symmetry statement, which requires the first year to be of the same type as the last year. In this case year 1 has no leap week, but year 834 does has a leap week. So the statement that Irv and I have made does not apply to them.

What the symmetry of the 834-year cycle does tell you is that the middle of year 417 and 834 is time at the average of middles of all years.

About the 895-year cycle, Brij stated

During use of 896-Years Cycle (Div.6 Plan), In addition to Div.six(6) Leap Weeks, following Kepler's Leap Weeks are ADDED every896-year cycle.

First KLWk is added during 87^{th-year, while rest nine are added ONCE every 90-years
and then repeating every 896-year cycle ; to give Mean Year of 7*(52+159/896)
=365.2421875 days.}

1920 thro 2816 AD: 2007, 2097, 2187, 2277, 2367, 2457, 2547, 2637, 2727 & 2817th years

I hope this clarify my approach, to place Kepler's Leap Weeks in 400-year, 834-year & 896-years cycle. Multiples of these cycles could be used, in necessary to achieve better placing/results.

The 896-year cycle as stated is here erroneous. If he were to add 10 Kepler’s leap week years like this every 896-year cycle, then in three 896-year cycles, he have 3*896/6 = 448 leap weeks in years divisible by six and 30 Kepler’s leap weeks adding to 478 in total. But three 896-year cycle require just 3*159=477 leap weeks and so such a 896-year cycle would be one week out every 3 cycles of 2688 years. Perhaps, Brij intends to omit one of these 10 Kepler’s leap weeks once every third 896-year cycle. This would correct the number of leap weeks, but produce extra jitter by leaving a gap of 180 or 186 years between two of the Kepler’s leap weeks.

Instead one can use a 2688-year cycle (equal to three 896-year cycles) made up of two 834-year cycles and one 1020-year cycle. The Kepler’s leap years can be as stated above on the 45^th, 141^st, 231^st, 327^th 417^th, 507^th, 603^rd, 693^rd and 789^th year of each 834-year cycle and also the 879^th and 975^th years of each 1020-year cycle. This gives rise to 9+9+11=29 Kepler’s leap weeks in a whole 2688-year cycle, which added to the 448 divide-by-six leap weeks gives the required 477=3*159 leap weeks. The 1020-year cycle cannot be made symmetrical in the same way as the 834-year cycle, because the number of years is not twice an odd number. The same applies to the entire 2688-year cycle.

However, the 462-year cycle of 5 Kepler’s leap weeks and same mean year as 33-year cycle can have this symmetry with Kepler’s leap weeks on the 45^th, 141^st, 231^st, 321^st and 417^th year of each 462-year cycle.

Karl

10(08(03

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Brij Bhushan Vij
Sent: 24 April 2009 19:58
To: CALNDR-L@...
Subject: 400-yrs,834-yrs & 896-yrs RE: Symmetry Statement and Divide-by-Six RE: using Primary cycles of 11,15,19&33-years RE:

Karl, Irv & CC:
>I now realise that if the 148 leap years were arranged in two identical cycles of 417 years and 79 leap years, then an odd number of
>moves would be needed to change this into the 834-year cycle described, where one move is a shift of one leap week by one year.
I had shown such distribution in my: http://www.brijvij.com/bbv_417-year-div.6.pdf

Thus 5^{th KLWk is placed at midway between 2*417-years
i.e. 834 years.}

0081, 0165, 0249, 0333, 0417, 0501, 0585, 0669, 0753.....

Distribution shown now in http://www.brijvij.com/bb_harappaTithi-Cycles.pdf is aslo (Y1920+417 =Y2337) as the mid year for symmetry.
During my discussion with list earlier (some 2 years ago), I had shown that Mean Year for Gregorian calendar could be attained using (3*400)-year cycle, with 13 Keplers' Leap Weeks. There, however, was difference of opinion for 896-year cycle (896/6 not being excatly divisible, and 3*896=2688 years cycle was considered). I believe, since 896-years are a little over 159 weeks (as pointed earlier) I attempted to charp cut close to 448th year and shown distribution as:

During use of 896-Years Cycle (Div.6 Plan), In addition to Div.six(6) Leap Weeks, following Keplers Leap Weeks are ADDED every896-year cycle.

First KLWk is added during 87^{th-year, while rest nine are added ONCE every 90-years
and then repeating every 896-year cycle ; to give Mean Year of 7*(52+159/896)
=365.2421875 days.}

1920 thro 2816 AD: 2007, 2097, 2187, 2277, 2367, 2457, 2547, 2637, 2727 & 2817th years

I hope this clarify my approach, to place Keplers' Leap Weeks in 400-year, 834-year & 896-years cycle. Multiples of these cycles could be used, in necessary to achieve better placing/results.
Regards,
Brij Bhushan Vij
Today: (MJD 2454947)/1361+D-125W17-05 (G. Friday, 2009 April 24H14:93 (decimal) EST
Aa Nau Bhadra Kritvo Yantu Vishwatah -Rg Veda
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)
My Profile:http://www.brijvij.com/bbv_2col-vipBrief.pdf
HOME PAGE: http://www.brijvij.com/
******As per Kali V-GRhymeCalendaar*****
"Koi bhi cheshtha vayarth nahin hoti, purshaarth karne mein hai"
Contact # 001 (201) 675-8548

Date: Fri, 24 Apr 2009 14:38:15 +0100
From: karl.palmen@...
Subject: Re: Symmetry Statement and Divide-by-Six RE: using Primary cycles of 11,15,19&33-years RE:
To: CALNDR-L@...

Dear Brij, Irv and Calendar People

What I says applies to Irv’s statement too.

I thought there might be one or two years in the 834-year divide-by-six cycle that have an average start, but this is not the case. I show this next.

The 834 -year cycles has every year whose number is divisible by six has a leap week (139 years) along with nine Kepler years 87, 183, 273, 369, 459, 555, 645, 741, 831, whose intervals alternate between 90 and 96 years, except for year 831, which is 90 years from both its neighbours. The cycle is symmetrical about year 831, but this symmetry does not allow any year to be the year after its mirror image so be the first year of a symmetrical cycle to which the statement applies.

Because the cycle is symmetrical about year 831, its middle coincides with the middle of the mean years and so its start is 3.5*(53 - (52 + 148/834)) = 2401/834 days earlier than average. Now we can work out how early or late other years start compared with average.

831: 2401/834 days early

832: 2401/834 days late

833: 1365/834 days late

834: 329/834 days late

001: 5131/834 days late

002: 4095/834 days late

etc..

Because steps are of 4802/834 for a 53-week year or 1036/834, every year must start an odd multiple of 1/834 days from average and so no year starts exactly on average.

I now realise that if the 148 leap years were arranged in two identical cycles of 417 years and 79 leap years, then an odd number of moves would be needed to change this into the 834-year cycle described, where one move is a shift of one leap week by one year.

Karl

10(07(30

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Brij Bhushan Vij
Sent: 23 April 2009 19:56
To: CALNDR-L@...
Subject: Revision RE: Symmetry Statement and Divide-by-Six RE: using Primary cycles of 11,15,19&33-years RE:

Karl, sir:
>.....the symmetry to which I refer to in the statement I made and Brij quoted and so the statement does not apply to....
I picked the 'bold quote (below) statement' from: http://individual.utoronto.ca/kalendis/leap/index.htm#CS and have not intended to hurt any sentiments of professionals like yourself or Dr. Irv Bromberg or for that matter any member on the list, since I my self have shown a way of reaching results that I felt could have something worth 'a thought'.
Year start statement for either 896-years/159 LWks or 834-year/148 LWks in seperation of odd multiple of 1/256 from average; or odd multiple of 1/800 from average, of day for 'symmetry' can be examined independently and compared with the presently used data. My tabulated display of YEAR blocks http://www.brijvij.com/bb_harappaTithi-Cycles.pdf and their possible distribution is subject to re-adjustments where desired, to get optimised Mean Year & Mean Lunation!
My regards,
Brij Bhushan Vij
Today: (MJD 2454946)/1361+D-124W17-04 (G. Thursday, 2009 April 23H14:93 (decimal) EST
Aa Nau Bhadra Kritvo Yantu Vishwatah -Rg Veda
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)
My Profile:http://www.brijvij.com/bbv_2col-vipBrief.pdf
HOME PAGE: http://www.brijvij.com/
******As per Kali V-GRhymeCalendaar*****
"Koi bhi cheshtha vayarth nahin hoti, purshaarth karne mein hai"
Contact # 001 (201) 675-8548

Date: Thu, 23 Apr 2009 08:57:51 +0100
From: karl.palmen@...
Subject: Symmetry Statement and Divide-by-Six RE: using Primary cycles of 11,15,19&33-years RE:
To: CALNDR-L@...

Dear Brij, Irv, Tom and Calendar People

Brij said (quoting me in bold type):

>If a leap cycle is arranged such that the list of leap years is symmetrical, so that year n of each cycle has the same leap status as >the symmetrical year occurring n years before the first year of the next cycle, then the start of the first year of every cycle will >always be at the average for that cycle.
I have been attempting to build table of my Div. six(6) approach to place Leap Weeks and Keplers' Leap Weeks in my 7*128=896-year cycle using 159 Leap Weeks or 834-years/148 Leap Weeks

Brij refers to his idea of having a leap week on each year whose number is divisible by 6 plus some additional years referred to as Kepler’s Leap Week years. No such cycle can have the symmetry to which I refer to in the statement I made and Brij quoted and so the statement does not apply to any such cycle (i.e. the first year of such a cycle need not have an average start).

However the 834-year cycle may have one or two years that do have an average start, but they are not easy to find.

The 896-year cycle, has no year with an average start no matter how the 159 leap weeks are arranged, because each year has a start that is an odd multiple of 1/256 days from average. The same applies to the 400-year cycle with 71 leap weeks, because each year has a start that is an odd multiple of 1/800 days from average.

Karl

10(07(28

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Brij Bhushan Vij
Sent: 21 April 2009 21:30
To: CALNDR-L@...
Subject: using Primary cycles of 11,15,19&33-years RE: solar year range

Irv, Tom Peters, Karl & CC:
>If a leap cycle is arranged such that the list of leap years is symmetrical, so that year n of each cycle has the same leap status as >the symmetrical year occurring n years before the first year of the next cycle, then the start of the first year of every cycle will >always be at the average for that cycle.
I have been attempting to build table of my Div. six(6) approach to place Leap Weeks and Keplers' Leap Weeks in my 7*128=896-year cycle using 159 Leap Weeks or 834-years/148 Leap Weeks & see combination for other cycles like 9405-years. From what I place at:
http://www.brijvij.com/bb_harappaTithi-Cycles.pdf
it may be seen that ANY cycle could be built using 11,19 & 33-years. I have tried to re-check my results and there could have been some typographic mistakes. I shall be grateful for pointing these. Karl's previous mail suggested to use larger PRIMARY cycles which, to my mind, can be made from my smaller cycle approach - especially the 19-year Lunar-Tithi cycle (in 6932.5 Tithi).
During this International Astronomy Year (2009) my inputs for A possible World Calendar http://www.brijvij.com/bb_IndianContri..pdf and
http://www.brijvij.com/bb_metro-contrbn.2007.pdf can become the cause for initaiating corrective actions for Reform of the Gregorian calendar.
In my 896-year cycle, I place the start Era at [(Y2000 - 80) +/- 128] i.e. Y1920 [as also Year 0000 CE] and first Keplers LWk year at Year 2007 i.e. 87th year, followed by 9 more KLWs at intervals of 90-years; and likewise Era start for 834-year cycle remain at Y1920 but the First Keplers' Leap Week would be at Y2001 i.e. 81st year followed by 8 more KLWks at intervals of 84-years and repeating every 834-years.
I am aware that Karl has a point suggesting (3*896)=2688-years to give Mean Year =365.2421875 days, while this distribution that I place has (149+10) 159 LWks, since 896-years have EACTLY 159 LWks to account. Karl's suggestion of (3*834)=2502-years is like saying (2*417)-years =834-years/(139+9)149 LWks.
Most cycles can be constructed from a combination of base cycles: 19-year Lunar (5*47=235 lunation) cycles, 33-year (12053-days) Solar cycle & 15-year cycle of indiction. What is the 'significance/importance' of this 15-year cycle of indiction, I am unaware? 11-year cycle does make some sense (being 3*11 of 33-solar cycle) that I have used in examining some break-ups for larger cycles!
Regards,
Brij Bhushan Vij
Today:

(MJD 2454944)/1361+D-122W17-02 (G. Tuesday, 2009 April 21H16:49 (decimal) EST
Aa Nau Bhadra Kritvo Yantu Vishwatah -Rg Veda
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)
My Profile:http://www.brijvij.com/bbv_2col-vipBrief.pdf
HOME PAGE: http://www.brijvij.com/
******As per Kali V-GRhymeCalendaar*****
"Koi bhi cheshtha vayarth nahin hoti, purshaarth karne mein hai"
Contact # 001 (201) 675-8548

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