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Re: Symmetry Statement and Divide-by-Six RE: using Primary cycles of 11,15,19&33-years RE:
by Karl Palmen
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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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