Joining list. Calendar reforms.

[Karl Palmen]

Dear Mike (and Calendar People)

This note was mucked up!
Please resend in a correct format.

Karl

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of MIKE OSSIPOFF
Sent: 28 July 2009 00:57
To: CALNDR-L@...
Subject: Declination calendar details


 
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Calendarists=2C
=20
I've posted the details of my fixed terrestrial-seasonal calendar
proposal.=
 I'd also like to post similar details for a fixed
declination-calendar=2C =
and then for non-fixed terrestrial-seasonal and declination calendars.
Four=
 proposals=2C four postings. Then I'll repost them all together in one
post=
ing=2C so=2C then=2C my proposals will be posted all in one place=2C
approp=
riately-titled.
=20
I've chosen for the fixed declination-calendar to be next=2C for this
posti=
ng=2C because I feel that people here prefer a fixed calendar=2C even
thoug=
h its requirement for a new leapyear rule=2C a leapweek rule=2C could
compl=
icate the proposal. And I know that some here don't like the idea of a
terr=
estrial-seasonal calendar=2C and so=2C for those two reasons=2C I'm
posting=
=2C here=2C the details of my proposal for a fixed declination-calendar.
=20
By "declination-calendar"=2C I mean a calendar whose largest
year-divisions=
=2C the seasonal-divisions=2C are based directly on the amount of solar
dec=
lination. Not on equinoxes and solstices and not directly ultimately
based =
on solar ecliptic longitude. And not with seaston starting-dates
intended t=
o approximiate the perceived terrestrial-seasons' starting dates.
=20
Goals:
=20
There are two extreme-declination seasonal periods=2C North and South=2C
in=
tended to be the periods when (as nearly as possible=2C given other
constra=
ints) the north or south solar declination is in the top half of its
range.
=20
Because this is a fixed calendar=2C and because a fixed calendar offers
max=
imum convenience only if all of the year divisions consist of whole
numbers=
 of weeks=2C this need places a constraint on the lengths of North and
Sout=
h--but they still are periods when the north or south solar declination
is =
very nearly in the top half of its range.
=20
As a result of these goals and constraints=2C  32.5 degrees is chosen as
th=
e solar ecliptic longitude at which for North to begin.
=20
Year-divisions:
=20
Four declination-seasonal year-divisions:
=20
South=2C Northward=2C North=2C and Southward.
=20
North and South each have 17 weeks
=20
Northward and Southward each have 9 weeks=2C for a total of 52 weeks.
=20
Each of those four year-divisions is divided into months=2C of 4 or 5
weeks=
.
=20
The seasonal year-divisions have these month-lengths (in weeks)=2C in
this =
order:
=20
North and South: 5=2C4=2C4=2C4
=20
Northward and Southward: 5=2C4
=20
(I call those "Mike-months". Karl has suggested a different ordering of
the=
 5 & 4 week months=2C to distribute them more uniformely=2C even if less
si=
mply. I have no objection to Karl-months)
=20
Months are named by number. For example=2C NorthI=2C NorthII=2C NorthIII
an=
d NorthIV.
=20
Leapyear rule:
=20
Leapweeks are used=2C with the intent to minimize the distance=2C on the
ec=
liptic=2C between 32.5 degrees and the solar ecliptic longitude at
midnight=
=2C UT=2C NorthI/1=2C with this 364-day-year calendar.
=20
Definition of "initial d"=2C for the purpose of specifying starting date
an=
d leapyear rule:
=20
"Initial d" is defined for the new calendar's first 365 days in use. For
th=
e new calendar's first 365 days in use:=20
=20
d2 =3D 32.5 minus the solar ecliptic longitude at midnight=2C UT=2C
NorthI/=
1.
=20
=20
If the solar ecliptic longitude =3D 32.5 degrees after midnight=2C UT=2C
No=
rthI/1=2C then the "Outside Date" is the midnight=2C UT directly after
the =
time when the solar ecliptic longitude equals 32.5 degrees.
=20
If the solar ecliptic longitude =3D 32.5 degrees before midnight=2C
UT=2C N=
orthI/1=2C then the "Outside date" is the midnight=2C UT=2C directly
before=
 the time when the solar ecliptic longitude equals 32.5 degrees.
=20
Divide (days between midnight=2C UT=2C NorthI/1 and the Outside Date) by
(3=
2.5 degrees minus the solar ecliptic longitude on the Outside Date).
Take t=
he absolute value of the result of that division.
=20
That gives "days per degree".
=20
Multiply d2 by days per degree. That gives the initial d. The starting
valu=
e of d=2C used in the leapyear rule and the starting-date rule.
=20
Starting date:
=20
The new calendar comes into use on the beginning (midnight) of the day
afte=
r the old calendar's December 31.
=20
Every year and every year-division begins on a Monday. The new
calendar's f=
irst year in use starts on a Monday. That Monday can be the first day in
wh=
ich the new calendar comes into use (the day after the old December
31)=2C =
if that is a Monday=2C or it can be any Monday during the 365 days
previous=
 to that.
=20
The Monday on which the new calendar starts is chosen so as to minimize
the=
 magnitude of initial d.
=20
Leapyear rule:
=20
The initial value of d is the "initial d" determined as described above.
=20
If=2C for any year=2C d> 7/2 - 1.24219=2C then that year is a leapyear.
=20
(I've intended to write=2C here=2C the better implementatin described by
Mi=
chael Deckers. If this is different from what Michael Deckers wrote=2C
then=
 Deckers' rule is what I intend).
=20
Immediately when a non-leapyear ends=2C d + 1.24219 becomes the new
value o=
f d.
=20
Immediately when a leapyear ends=2C d + 1.24219 - 7 becomes the new
valule =
of d.
=20
Mike Ossipoff
=20
=20
=20
=20
=20
=20
=20
=20
_________________________________________________________________
Windows Live=99 Hotmail=AE: Search=2C add=2C and share the web=92s
latest s=
ports videos. Check it out.
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AGL=
M_WL_QA_HM_sports_videos_072009&cat=3Dsports=

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[MIKE OSSIPOFF]

 
Karl,
 
You wrote:

> This note was mucked up!
> Please resend in a correct format.
 
Ok. Most likely I forgot to change to "plain-text". Can you tell, was the messed-up posting in plain-text or rich text? I'm sending this quick note in plain-text.
 
I've heard it said that plain-text is well-received by all systems, but that format-compatibility problems can arise with rich-text.
 
So, tomorrow (There isn't enough time available on the computer today) I'll re-posts my message in plain-text.
 
But,if it was already in plain-text, when it didn't post well, and if it's my _rich-text_ postings that post better, please let me know, because it's important for me to know which format works on the mailing list.
 
Meantime, if I don't hear any other information, I'll try plain-text tomorrow. (I don't remember whether or not I switched to plain-text before I posted my message yesterday. Anyway, please let me know which format messed-up yesterday, and whether this plain-text posting works ok.
 
Mike Ossipoff


 
_________________________________________________________________
NEW mobile Hotmail. Optimized for YOUR phone.  Click here.
http://windowslive.com/Mobile?ocid=TXT_TAGLM_WL_CS_MB_new_hotmail_072009

[Mark J. Reed]

Once again, Mike, the problem is an extra blank line in your headers.
It doesn't matter whether it's rich-text or plain-text in that case,
all we get is gobbledygook.  What mail client are you using?
Hotmail's web interface, Outlook Express, Microsoft Mail, or something
else?

On Tue, Jul 28, 2009 at 7:50 PM, MIKE OSSIPOFF<nkklrp@...> wrote:

>
> Karl,
>
> You wrote:
>
>> This note was mucked up!
>> Please resend in a correct format.
>
> Ok. Most likely I forgot to change to "plain-text". Can you tell, was the messed-up posting in plain-text or rich text? I'm sending this quick note in plain-text.
>
> I've heard it said that plain-text is well-received by all systems, but that format-compatibility problems can arise with rich-text.
>
> So, tomorrow (There isn't enough time available on the computer today) I'll re-posts my message in plain-text.
>
> But,if it was already in plain-text, when it didn't post well, and if it's my _rich-text_ postings that post better, please let me know, because it's important for me to know which format works on the mailing list.
>
> Meantime, if I don't hear any other information, I'll try plain-text tomorrow. (I don't remember whether or not I switched to plain-text before I posted my message yesterday. Anyway, please let me know which format messed-up yesterday, and whether this plain-text posting works ok.
>
> Mike Ossipoff
>
>
>
> _________________________________________________________________
> NEW mobile Hotmail. Optimized for YOUR phone.  Click here.
> http://windowslive.com/Mobile?ocid=TXT_TAGLM_WL_CS_MB_new_hotmail_072009
>

--
Mark J. Reed <markjreed@...>

[Karl Palmen]

Dear Mark and Calendar People

This E-mail was not affected by the problem. It is not mucked up.

The mucked up E-mails have a corrupted header with a blank line in it.

Karl

10(11(07 till noon

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of MIKE OSSIPOFF
Sent: 29 July 2009 00:51
To: CALNDR-L@...
Subject: Re: Declination calendar details

 
Karl,
 
You wrote:

> This note was mucked up!
> Please resend in a correct format.
 
Ok. Most likely I forgot to change to "plain-text". Can you tell, was
the messed-up posting in plain-text or rich text? I'm sending this quick
note in plain-text.
 
I've heard it said that plain-text is well-received by all systems, but
that format-compatibility problems can arise with rich-text.
 
So, tomorrow (There isn't enough time available on the computer today)
I'll re-posts my message in plain-text.
 
But,if it was already in plain-text, when it didn't post well, and if
it's my _rich-text_ postings that post better, please let me know,
because it's important for me to know which format works on the mailing
list.
 
Meantime, if I don't hear any other information, I'll try plain-text
tomorrow. (I don't remember whether or not I switched to plain-text
before I posted my message yesterday. Anyway, please let me know which
format messed-up yesterday, and whether this plain-text posting works
ok.
 
Mike Ossipoff


 
_________________________________________________________________
NEW mobile Hotmail. Optimized for YOUR phone.  Click here.
http://windowslive.com/Mobile?ocid=TXT_TAGLM_WL_CS_MB_new_hotmail_072009
--
Scanned by iCritical.

[Mark J. Reed]

True, the note Mike sent in plaintext was uncorrupted.  So maybe the
blank-line bug is triggered by richtext format.  I was perhaps too
hasty in claiming that format was unrelated.  I"m still curious what
MUA Mike is using..

On Wed, Jul 29, 2009 at 3:57 AM, Palmen, KEV
(Karl)<karl.palmen@...> wrote:

> Dear Mark and Calendar People
>
> This E-mail was not affected by the problem. It is not mucked up.
>
> The mucked up E-mails have a corrupted header with a blank line in it.
>
> Karl
>
> 10(11(07 till noon
>
> -----Original Message-----
> From: East Carolina University Calendar discussion List
> [mailto:CALNDR-L@...] On Behalf Of MIKE OSSIPOFF
> Sent: 29 July 2009 00:51
> To: CALNDR-L@...
> Subject: Re: Declination calendar details
>
>
> Karl,
>
> You wrote:
>
>> This note was mucked up!
>> Please resend in a correct format.
>
> Ok. Most likely I forgot to change to "plain-text". Can you tell, was
> the messed-up posting in plain-text or rich text? I'm sending this quick
> note in plain-text.
>
> I've heard it said that plain-text is well-received by all systems, but
> that format-compatibility problems can arise with rich-text.
>
> So, tomorrow (There isn't enough time available on the computer today)
> I'll re-posts my message in plain-text.
>
> But,if it was already in plain-text, when it didn't post well, and if
> it's my _rich-text_ postings that post better, please let me know,
> because it's important for me to know which format works on the mailing
> list.
>
> Meantime, if I don't hear any other information, I'll try plain-text
> tomorrow. (I don't remember whether or not I switched to plain-text
> before I posted my message yesterday. Anyway, please let me know which
> format messed-up yesterday, and whether this plain-text posting works
> ok.
>
> Mike Ossipoff
>
>
>
> _________________________________________________________________
> NEW mobile Hotmail. Optimized for YOUR phone.  Click here.
> http://windowslive.com/Mobile?ocid=TXT_TAGLM_WL_CS_MB_new_hotmail_072009
> --
> Scanned by iCritical.
>
>

--
Mark J. Reed <markjreed@...>

[MIKE OSSIPOFF]

Some parts of this message have been removed. Learn more about Nabble's security policy.

 
You wrote:
 
> True, the note Mike sent in plaintext was uncorrupted. So maybe the
> blank-line bug is triggered by richtext format.
 
Ok, I'll make sure to change to plaintext in all my future postings. (Richtext is the default, and so that's what happens if I forget)
 
>I'm still curious what
> MUA Mike is using..
 
All I know is that I'm using an msn e-mail account.
 
Now I'll re-post my Declination calendar details posting in plaintext.
 
Mike Ossipoff

 

---

Windows Live™ Hotmail®: Celebrate the moment with your favorite sports pics. Check it out.

[Mark J. Reed]

On Wed, Jul 29, 2009 at 7:04 PM, MIKE OSSIPOFF<nkklrp@...> wrote:
> All I know is that I'm using an msn e-mail account.

We know that too. But what do you do when you want to read/send email?
 Do you start Internet Explorer?  Or Outlook?  Or what?


--
Mark J. Reed <markjreed@...>

[MIKE OSSIPOFF]

             <677CE4DD24B12C4B9FA138534E29FB1D06929A3A@...>
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Content-Type: text/plain; charset="Windows-1252"
Content-Transfer-Encoding: quoted-printable
MIME-Version: 1.0
X-OriginalArrivalTime: 29 Jul 2009 23:28:03.0575 (UTC) FILETIME=[381F8070:01CA10A4]


Calendarists=2C=20
=20
I've posted the details of my fixed terrestrial-seasonal calendar proposal.=
 I'd also like to post similar details for a fixed declination-calendar=2C =
and then for non-fixed terrestrial-seasonal and declination calendars. Four=
 proposals=2C four postings. Then I'll repost them all together in one post=
ing=2C so=2C then=2C my proposals will be posted all in one place=2C approp=
riately-titled.=20
=20
I've chosen for the fixed declination-calendar to be next=2C for this posti=
ng=2C because I feel that people here prefer a fixed calendar=2C even thoug=
h its requirement for a new leapyear rule=2C a leapweek rule=2C could compl=
icate the proposal. And I know that some here don't like the idea of a terr=
estrial-seasonal calendar=2C and so=2C for those two reasons=2C I'm posting=
=2C here=2C the details of my proposal for a fixed declination-calendar.=20
=20
By "declination-calendar"=2C I mean a calendar whose largest year-divisions=
=2C the seasonal-divisions=2C are based directly on the amount of solar dec=
lination. Not on equinoxes and solstices and not directly ultimately based =
on solar ecliptic longitude. And not with season starting-dates intended to=
 approximiate the perceived terrestrial-seasons' starting dates.=20
=20
Goals:=20
=20
There are two extreme-declination seasonal periods=2C North and South=2C in=
tended to be the periods when (as nearly as possible=2C given other constra=
ints) the north or south solar declination is in the top half of its range.=
 Because this is a fixed calendar=2C and because a fixed calendar offers ma=
ximum convenience only if all of the year divisions consist of whole number=
s of weeks=2C this need places a constraint on the lengths of North and Sou=
th--but they still are periods when the north or south solar declination is=
 very nearly in the top half of its range.=20
=20
As a result of these goals and constraints=2C 32.5 degrees is chosen as the=
 solar ecliptic longitude at which for North to begin.=20
=20
Year-divisions: Four declination-seasonal year-divisions: Northward=2C Nort=
h=2C Southward=2C and South. North and South each have 17 weeks Northward a=
nd Southward each have 9 weeks=2C for a total of 52 weeks.
=20
I think the declination calendar's year should start with NorthwardI/1=2C a=
nd so that's what I'm proposing=2C unless & until others advocate otherwise=
. For my=2C previously-posted=2C terrestrial-seasonal calendar=2C that cale=
ndar's year starts with SouthI/1.=20
=20
Each of those four year-divisions is divided into months=2C of 4 or 5 weeks=
. The seasonal year-divisions have these month-lengths (in weeks)=2C in thi=
s order: North and South: 5=2C4=2C4=2C4 Northward and Southward: 5=2C4 (I c=
all those "Mike-months". Karl has suggested a different ordering of the 5 &=
 4 week months=2C to distribute them more uniformely=2C even if less simply=
. I have no objection to Karl-months).=20
=20
Months are named by number. For example=2C NorthI=2C NorthII=2C NorthIII an=
d NorthIV.=20
=20
Leapyear rule: Leapweeks are used=2C with the intent to minimize the distan=
ce=2C on the ecliptic=2C between 32.5 degrees and the solar ecliptic longit=
ude at midnight=2C UT=2C NorthI/1=2C with this 364-day-year calendar.
=20
Definition of "initial d"=2C for the purpose of specifying starting date an=
d leapyear rule:=20
=20
"Initial d" is defined for the new calendar's first 365 days in use. For th=
e new calendar's first 365 days in use: =20
=20
d2 =3D 32.5 minus the solar ecliptic longitude at midnight=2C UT=2C NorthI/=
1. =20
=20
If the solar ecliptic longitude =3D 32.5 degrees at a time that is after mi=
dnight=2C UT=2C NorthI/1=2C then the "Outside Date" is the midnight=2C UT d=
irectly after the time when the solar ecliptic longitude equals 32.5 degree=
s.=20
=20
If the solar ecliptic longitude =3D 32.5 degrees at a time that is before m=
idnight=2C UT=2C NorthI/1=2C then the "Outside date" is the midnight=2C UT=
=2C directly before the time when the solar ecliptic longitude equals 32.5 =
degrees.=20
=20
Divide (days between midnight=2C UT=2C NorthI/1 and the Outside Date) by (3=
2.5 degrees minus the solar ecliptic longitude on the Outside Date). Take t=
he absolute value of the result of that division. That gives "days per degr=
ee".=20
=20
Multiply d2 by days per degree. That gives the initial d. That's the starti=
ng value of d=2C used in the leapyear rule and the starting-date rule.=20
=20
Starting date:=20
=20
The new calendar comes into use on the beginning (midnight) of the day afte=
r the old calendar's December 31. Every year and every year-division begins=
 on a Monday. For the new calendar's first year in use=2C the beginning of =
that first calendar year of the new calendar can be at a day (a Monday) bef=
ore the calendar actually comes into use. That Monday could be the first da=
y in which the new calendar comes into use (the day after the old December =
31)=2C if that is a Monday=2C or it could be any Monday during the 365 days=
 previous to that. The Monday on which the new calendar starts is chosen so=
 as to minimize the magnitude of initial d.=20
=20
Leapyear rule:=20
=20
The initial value of d is the "initial d" determined as described above.=20
=20
If=2C for any year=2C d> 7/2 - 1.24219=2C then that year is a leapyear.=20
=20
(I've intended to write=2C here=2C the better implementatin described by Mi=
chael Deckers. If this is different from what Michael Deckers wrote=2C then=
 Deckers' rule is what I intend).=20
=20
Immediately when a non-leapyear ends=2C d + 1.24219 becomes the new value o=
f d.=20
=20
Immediately when a leapyear ends=2C d + 1.24219 - 7 becomes the new valule =
of d.=20
=20
Mike Ossipoff =20
=20
_________________________________________________________________
Windows Live=99 SkyDrive=99: Store=2C access=2C and share your photos. See =
how.
http://windowslive.com/Online/SkyDrive?ocid=3DTXT_TAGLM_WL_CS_SD_photos_072=
009=

[MIKE OSSIPOFF]

 
Mark,
 
You wrote:
 
> But what do you do when you want to read/send email?
> Do you start Internet Explorer? Or Outlook? Or what?

I'm using Internet Explorer.
 
Mike Ossipoff
 
_________________________________________________________________
NEW mobile Hotmail. Optimized for YOUR phone.  Click here.
http://windowslive.com/Mobile?ocid=TXT_TAGLM_WL_CS_MB_new_hotmail_072009

[Deckers, Michael-2]

Calendarists,

I've posted the details of my fixed terrestrial-seasonal calendar proposal. I'd
also like to post similar details for a fixed declination-calendar, and then for
non-fixed terrestrial-seasonal and declination calendars. Four proposals, four
postings. Then I'll repost them all together in one posting, so, then, my
proposals will be posted all in one place, appropriately-titled.

I've chosen for the fixed declination-calendar to be next, for this posting,
because I feel that people here prefer a fixed calendar, even though its
requirement for a new leapyear rule, a leapweek rule, could complicate the
proposal. And I know that some here don't like the idea of a terrestrial-
seasonal calendar, and so, for those two reasons, I'm posting, here, the details
of my proposal for a fixed declination-calendar.

By "declination-calendar", I mean a calendar whose largest year-divisions, the
seasonal-divisions, are based directly on the amount of solar declination. Not
on equinoxes and solstices and not directly ultimately based on solar ecliptic
longitude. And not with season starting-dates intended to approximiate the
perceived terrestrial-seasons' starting dates.

Goals:

There are two extreme-declination seasonal periods, North and South, intended to
be the periods when (as nearly as possible, given other constraints) the north
or south solar declination is in the top half of its range. Because this is a
fixed calendar, and because a fixed calendar offers maximum convenience only if
all of the year divisions consist of whole numbers of weeks, this need places a
constraint on the lengths of North and South--but they still are periods when
the north or south solar declination is very nearly in the top half of its
range.

As a result of these goals and constraints, 32.5 degrees is chosen as the solar
ecliptic longitude at which for North to begin.

Year-divisions: Four declination-seasonal year-divisions: Northward, North,
Southward, and South. North and South each have 17 weeks Northward and Southward
each have 9 weeks, for a total of 52 weeks.

I think the declination calendar's year should start with NorthwardI/1, and so
that's what I'm proposing, unless & until others advocate otherwise. For my,
previously-posted, terrestrial-seasonal calendar, that calendar's year starts
with SouthI/1.

Each of those four year-divisions is divided into months, of 4 or 5 weeks. The
seasonal year-divisions have these month-lengths (in weeks), in this order:
North and South: 5,4,4,4 Northward and Southward: 5,4 (I call those "Mike-
months". Karl has suggested a different ordering of the 5 & 4 week months, to
distribute them more uniformely, even if less simply. I have no objection to
Karl-months).

Months are named by number. For example, NorthI, NorthII, NorthIII and NorthIV.

Leapyear rule: Leapweeks are used, with the intent to minimize the distance, on
the ecliptic, between 32.5 degrees and the solar ecliptic longitude at midnight,
UT, NorthI/1, with this 364-day-year calendar.

Definition of "initial d", for the purpose of specifying starting date and
leapyear rule:

"Initial d" is defined for the new calendar's first 365 days in use. For the new
calendar's first 365 days in use:  

d2 32.5 minus the solar ecliptic longitude at midnight, UT, NorthI/1.  

If the solar ecliptic longitude 32.5 degrees at a time that is after midnight,
UT, NorthI/1, then the "Outside Date" is the midnight, UT directly after the
time when the solar ecliptic longitude equals 32.5 degrees.

If the solar ecliptic longitude 32.5 degrees at a time that is before midnight,
UT, NorthI/1, then the "Outside date" is the midnight, UT, directly before the
time when the solar ecliptic longitude equals 32.5 degrees.

Divide (days between midnight, UT, NorthI/1 and the Outside Date) by (32.5
degrees minus the solar ecliptic longitude on the Outside Date). Take the
absolute value of the result of that division. That gives "days per degree".

Multiply d2 by days per degree. That gives the initial d. That's the starting
value of d, used in the leapyear rule and the starting-date rule.

Starting date:

The new calendar comes into use on the beginning (midnight) of the day after the
old calendar's December 31. Every year and every year-division begins on a
Monday. For the new calendar's first year in use, the beginning of that first
calendar year of the new calendar can be at a day (a Monday) before the calendar
actually comes into use. That Monday could be the first day in which the new
calendar comes into use (the day after the old December 31), if that is a
Monday, or it could be any Monday during the 365 days previous to that. The
Monday on which the new calendar starts is chosen so as to minimize the
magnitude of initial d.

Leapyear rule:

The initial value of d is the "initial d" determined as described above.

If, for any year, d> 7/2 - 1.24219, then that year is a leapyear.

(I've intended to write, here, the better implementatin described by Michael
Deckers. If this is different from what Michael Deckers wrote, then Deckers'
rule is what I intend).

Immediately when a non-leapyear ends, d + 1.24219 becomes the new value of d.

Immediately when a leapyear ends, d + 1.24219 - 7 becomes the new valule of d.

Mike Ossipoff

 

[Deckers, Michael-2]

.oops, I missed three = signs:

d2 = 32.5 minus the solar ecliptic longitude at midnight, UT, NorthI/1.

If the solar ecliptic longitude = 32.5 degrees at a time that is after midnight,..

If the solar ecliptic longitude = 32.5 degrees at a time that is before midnight,...

   

[Karl Palmen]

Dear Mike, Michael and Calendar People

I take that this is a valid fix of Mike Ossipof's note, having restored
the missing equal signs.
Can Mike confirm this?

I add some comments below:

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Deckers, Michael
Sent: 30 July 2009 08:26
To: CALNDR-L@...
Subject: Re: Declination calendar details without escapes

Calendarists,

I've posted the details of my fixed terrestrial-seasonal calendar
proposal. I'd
also like to post similar details for a fixed declination-calendar, and
then for
non-fixed terrestrial-seasonal and declination calendars. Four
proposals, four
postings. Then I'll repost them all together in one posting, so, then,
my
proposals will be posted all in one place, appropriately-titled.

I've chosen for the fixed declination-calendar to be next, for this
posting,
because I feel that people here prefer a fixed calendar, even though its

requirement for a new leapyear rule, a leapweek rule, could complicate
the
proposal. And I know that some here don't like the idea of a
terrestrial-
seasonal calendar, and so, for those two reasons, I'm posting, here, the
details
of my proposal for a fixed declination-calendar.

By "declination-calendar", I mean a calendar whose largest
year-divisions, the
seasonal-divisions, are based directly on the amount of solar
declination. Not
on equinoxes and solstices and not directly ultimately based on solar
ecliptic
longitude. And not with season starting-dates intended to approximiate
the
perceived terrestrial-seasons' starting dates.

Goals:

KARL SAYS: The end of the Goals section and the start of the Rules
section is not clearly marked

There are two extreme-declination seasonal periods, North and South,
intended to
be the periods when (as nearly as possible, given other constraints) the
north
or south solar declination is in the top half of its range. Because this
is a
fixed calendar, and because a fixed calendar offers maximum convenience
only if
all of the year divisions consist of whole numbers of weeks, this need
places a
constraint on the lengths of North and South--but they still are periods
when
the north or south solar declination is very nearly in the top half of
its
range.

As a result of these goals and constraints, 32.5 degrees is chosen as
the solar
ecliptic longitude at which for North to begin.

Year-divisions: Four declination-seasonal year-divisions: Northward,
North,
Southward, and South. North and South each have 17 weeks Northward and
Southward
each have 9 weeks, for a total of 52 weeks.

I think the declination calendar's year should start with NorthwardI/1,
and so
that's what I'm proposing, unless & until others advocate otherwise. For
my,
previously-posted, terrestrial-seasonal calendar, that calendar's year
starts
with SouthI/1.

Each of those four year-divisions is divided into months, of 4 or 5
weeks. The
seasonal year-divisions have these month-lengths (in weeks), in this
order:
North and South: 5,4,4,4 Northward and Southward: 5,4 (I call those
"Mike-
months". Karl has suggested a different ordering of the 5 & 4 week
months, to
distribute them more uniformely, even if less simply. I have no
objection to
Karl-months).

KARL SAYS: I suggested 4,4,5,4 and 4,5 (or 4,5,4,4 and 5,4). This makes
them less simple with respect to the unequal seasons but simpler with
respect to the whole year (beginning NorthI 4,4,5,4,4,5,4,4,5,4,4,5).
We now seem to be talking about calendar rules rather than goals.

MIKE CONTINUES:
Months are named by number. For example, NorthI, NorthII, NorthIII and
NorthIV.

Leapyear rule: Leapweeks are used, with the intent to minimize the
distance, on
the ecliptic, between 32.5 degrees and the solar ecliptic longitude at
midnight,
UT, NorthI/1, with this 364-day-year calendar.

Definition of "initial d", for the purpose of specifying starting date
and
leapyear rule:

"Initial d" is defined for the new calendar's first 365 days in use. For
the new
calendar's first 365 days in use:  

d2 32.5 minus the solar ecliptic longitude at midnight, UT, NorthI/1.

KARL SAYS: I don't understand d2.
 
If the solar ecliptic longitude = 32.5 degrees at a time that is after
midnight,
UT, NorthI/1, then the "Outside Date" is the midnight, UT directly after
the
time when the solar ecliptic longitude equals 32.5 degrees.

If the solar ecliptic longitude = 32.5 degrees at a time that is before
midnight,
UT, NorthI/1, then the "Outside date" is the midnight, UT, directly
before the
time when the solar ecliptic longitude equals 32.5 degrees.

KARL SAYS:
I'm trying to get my head round this one. It seems to be a definition of
"Outside date" which is not a date at all but an instant that occurs at
midnight UT. It seems to be equivalent to this:

"Outside date" is 24 hours before the UT start (at midnight) of NorthI,
if NorthI starts after the moment the solar longitude equals 32.5
degrees else it 24 hours after the UT start of NorthI.

MIKE CONITUNES:
Divide (days between midnight, UT, NorthI/1 and the Outside Date) by
(32.5
degrees minus the solar ecliptic longitude on the Outside Date). Take
the
absolute value of the result of that division. That gives "days per
degree".

Multiply d2 by days per degree. That gives the initial d. That's the
starting
value of d, used in the leapyear rule and the starting-date rule.

KARL SAYS:
I think Mike is estimating when the ecliptic longitude is 32.5 degrees
by linear extrapolation or interpolation based on the ecliptic
longitudes at the UT starts of two dates NorthI 1, and one of its two
neighbouring dates (the date that begins with "Outside date"). This he
does to calculate the initial d, which he refers to later on.


MIKE CONTINUES:
Starting date:

The new calendar comes into use on the beginning (midnight) of the day
after the
old calendar's December 31. Every year and every year-division begins on
a
Monday. For the new calendar's first year in use, the beginning of that
first
calendar year of the new calendar can be at a day (a Monday) before the
calendar
actually comes into use. That Monday could be the first day in which the
new
calendar comes into use (the day after the old December 31), if that is
a
Monday, or it could be any Monday during the 365 days previous to that.
The
Monday on which the new calendar starts is chosen so as to minimize the
magnitude of initial d.

KARL SAYS:
This is utterly confusing!

It would be wise to make the calendar independent of the choice of
starting date.

For example Irv fixed this Symmetry454 293-cycle rule so that year 1
would begin on Monday January 1, AD 1 proleptic Gregorian calendar,
while the calendar could be started on any day, but preferably one in
which the Gregorian and Symmetry454 dates would match as I believe is
the case for most months that begin on a Monday in the Gregorian
calendar.
A leap week calendar needs no legislation to start it (unlike the World
Calendar).

I suggest Mike finds an ideal year when 32.5 degrees ecliptic longitude
occurs very close to the start of a Monday (or whatever day of the week
he wishes to start the seasons). Let's call it the ideal year. Then set
it's value of d to 3.5.

MIKE CONTINUES:
Leapyear rule:

The initial value of d is the "initial d" determined as described above.


If, for any year, d> 7/2 - 1.24219, then that year is a leapyear.

(I've intended to write, here, the better implementatin described by
Michael
Deckers. If this is different from what Michael Deckers wrote, then
Deckers'
rule is what I intend).

Immediately when a non-leapyear ends, d + 1.24219 becomes the new value
of d.

Immediately when a leapyear ends, d + 1.24219 - 7 becomes the new value
of d.

KARL SAYS: I'd expect the calendar rule to explicitly state a value and
year for initial d.

It would then be equivalent to year Y is a leap year if and only if
(124,219*Y + K) mod (700,000) < 124,219, where K is determined by
initial d and its year.

If year 1 is the ideal year in which NorthI begins very close in UT to
when the ecliptic longitude is 32.5 degrees, then K can be chosen to be
350,000. If then you want some other year to be year 1, the resulting K
can be worked out by algebraic manipulation.

The accumulator ( (124,219*Y + K) mod (700,000)) tells you when, in the
calendar year, the calendar reckons the ecliptic longitude for year Y+1
is 32.5 degrees within its 7-day (168-hour) range in units of 1/100,000
day. I expect Mike wants the start of NorthI to occur in the centre of
this range. This can be achieved by selecting K as suggested.

Calendar people are likely to dispute the choice of 1.24219. The simpler
alternative of 77/62 would better achieve the goal of keeping NorthI
starting close to the time of ecliptic longitude 32.5 degrees and Irv
could come up with a less simple but still more accurate value.
Different values would suit the starts of other seasons. The fraction of
1.2425 (= 497/400) would keep the calendar in step with the Gregorian
calendar.

Karl

10(11(09

 

--
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[Mark J. Reed]

On Wed, Jul 29, 2009 at 7:29 PM, MIKE OSSIPOFF<nkklrp@...> wrote:
> I'm using Internet Explorer.

So you're using MSN's webmail interface.  That at least tells us
what's broken...


--
Mark J. Reed <markjreed@...>

[MIKE OSSIPOFF]

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Mark,
 
You wrote:
 
 > So you're using MSN's webmail interface. That at least tells us
> what's broken...
 
I know what you mean, though I get by ok with it as long as I learn to avoid the worst problems. And I think I know how to avoid this one: My two attempts, so far, to post "Declination calendar details" had one thing in common: I copied the message and then pasted it into a reply to the list. That happened the first time because I didn't finish in time to send, so I sent it to myself, and then later copied it and pasted it into e-mail. Then, when that posted messed-up, I copied it from my "sent" folder and again pasted it (plaintext) into e-mail to the list. Same result.
 
Each time I did that, all the "carriage-returns" were lost, and I had to put them back in. What I didn't realize was that there was an additional problem, that the message would post full of spurious garbage.
 
So now I'm going to try one more thing: I'll try forwarding the message to the list, from my "sent" folder. That will probably make the left margin full of ">", but removing those won't be a big deal.
 
And if, when I check the forum website, I find that it's still posting messed-up, then I'll just print the message out from my "sent" folder, set it on the desk, and then copy it the old-fashioned way--at the keyboard.
 
Anyway, I just want to assure you that I'm not going to keep posting the same spurious garbage indefinitely. Starting over at the keyboard will surely avoid the garbage problem.
 
Mike Ossipoff
 

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[MIKE OSSIPOFF]

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Thanks to Michael Deckers for fixing my posting for me--and of course for earlier pointing out a much more economical way to write the leapyear rule.
 
Mike Ossipoff
 

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[MIKE OSSIPOFF]

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Dear Karl and Calendar People,
 
Karl, you wrote:
 
> I take that this is a valid fix of Mike Ossipof's note, having restored
> the missing equal signs.
> Can Mike confirm this?
 
Yes, with the restoral of the three equals signs, I didn't find any other differences. The version posted below is the same as my original posting, in the form in which I sent it.
 
 
You wrote:
 
> The end of the Goals section and the start of the Rules
> section is not clearly marked
 
Yes that's true. The broad heading of "Goals" calls for a similarly broad "Rules" heading, rather than just starting with a heading for a particular rules topic. Additionally, I neglected to give the heading after "Goals" a line of its own, which further made it look as if everlything that followed was under the "Goals" heading.
 
> KARL SAYS: I don't understand d2.
 
The restoral of the equals sign in that line clarified the matter: d2 = 32.5 minus the solar ecliptic longitude at midnight, UT, NorthI/1.
(I'd earlier specified that this definition refers only to the first 365 days of the actual use of the new calendar)

I'd written:
 
>

> If the solar ecliptic longitude = 32.5 degrees at a time that is after
> midnight,
> UT, NorthI/1, then the "Outside Date" is the midnight, UT directly after
> the
> time when the solar ecliptic longitude equals 32.5 degrees.
>
> If the solar ecliptic longitude = 32.5 degrees at a time that is before
> midnight,
> UT, NorthI/1, then the "Outside date" is the midnight, UT, directly
> before the
> time when the solar ecliptic longitude equals 32.5 degrees.
> 

You replied:
 
> I'm trying to get my head round this one. It seems to be a definition of
> "Outside date" which is not a date at all but an instant that occurs at
> midnight UT.
 
Yes, and I did feel a little bit incorrect when I named it as a date. Yes, it refers to an instant at midnight UT.
 
You continued:
 
> It seems to be equivalent to this: ...
 
I'm sticking to my original wording, though I'll change the name from "outside date" to "outside midnight".

You continued:
 
>
> "Outside date" is 24 hours before the UT start (at midnight) of NorthI,
> if NorthI starts after the moment the solar longitude equals 32.5
> degrees else it 24 hours after the UT start of NorthI.
 
But the start of NorthI/1 can be days away from the time at which the solar ecliptic longitude equals 32.5 degrees, because of the amount of jitter of the leapweek rule. My specification, later, about the starting-date is very poorly worded, but I did okay with the outside date (except for giving it an unfortunate name).
 
I'd written:
 

>
> MIKE CONITUNES:
> Divide (days between midnight, UT, NorthI/1 and the Outside Date) by
> (32.5
> degrees minus the solar ecliptic longitude on the Outside Date). Take
> the
> absolute value of the result of that division. That gives "days per
> degree".
>
> Multiply d2 by days per degree. That gives the initial d. That's the
> starting
> value of d, used in the leapyear rule and the starting-date rule.
>

You wrote:

> I think Mike is estimating when the ecliptic longitude is 32.5 degrees
> by linear extrapolation or interpolation based on the ecliptic
> longitudes at the UT starts of two dates NorthI 1, and one of its two
> neighbouring dates (the date that begins with "Outside date"). This he
> does to calculate the initial d, which he refers to later on.
 
Yes. I determine the average days per degree between the "Outside Date" and midnight UT, NorthI/1, and then I use that days per degree estimate to convert d2 from degrees to days.

 
I'd written:
 
> The new calendar comes into use on the beginning (midnight) of the day

> after the
> old calendar's December 31. Every year and every year-division begins on
> a
> Monday. For the new calendar's first year in use, the beginning of that
> first
> calendar year of the new calendar can be at a day (a Monday) before the
> calendar
> actually comes into use. That Monday could be the first day in which the
> new
> calendar comes into use (the day after the old December 31), if that is
> a
> Monday, or it could be any Monday during the 365 days previous to that.
> The
> Monday on which the new calendar starts is chosen so as to minimize the
> magnitude of initial d.
>

You wrote:

> This is utterly confusing!
 
Yes, it is a bit of a mess. It's a difficult thing to word, and I therefore should take the necessary care to word it much more clearly than I did.
 
I was going to do that, but then, from what you said below, I realize that the approach that I was using isn't favored by calendarists anyway. So it would be better if I instead specified a definite date for the calendar's first NorthwardI/1 (sometime before the present date), which is independent of when the calendar comes into use. --and then specified the starting value of d in that year. So that's what I'll do. (The calendar's "New Year's Day" is NorthwardI/1, though its relation to solar ecliptic longitude is based on NorthI/1)

>
> It would be wise to make the calendar independent of the choice of
> starting date.
 
Ok

>
> For example Irv fixed this Symmetry454 293-cycle rule so that year 1
> would begin on Monday January 1, AD 1 proleptic Gregorian calendar,

But if the calendar's first year were specified for a time so long ago, wouldn't that cause problems due to changes in the number of days per calendar year over the time since 1 AD?
 
So maybe the calendar's first NorthwardI/1 should be only a few years ago. Because calendar's "distance" (between 32.5 degrees and the solar ecliptic longitude on NorthI/1) in 2000 doesn't really matter, I'd probably choose a Monday in 2000 for the new calendar's first NorthwardI/1, because of the appeal of using a millenium year, and because I want it to be a fairly recent year, to avoid problems due to changes in days per mean tropical year. So I'll determine which Monday in 2000 A.D. minimizes the initial value of d, and will specify that date and that initial value of d.
 
 
You wrote:
 
> I'd expect the calendar rule to explicitly state a value and
> year for initial d.
 
Sure, I see the merits of that. I just didn't know how calendarists prefer to do such things, and maybe hadn't given the matter enough consideration. But I can see now that asking people to calculate the day of the first NorthwardI/1, and the value of d for that year, isn't such a good idea. Better for the proposal to specify both of those things.
 
Yes, I want the solar ecliptic longitude on NorthI/1 to be as close as possible to 32.5 degrees.
 
You wrote:
 
 
> Calendar people are likely to dispute the choice of 1.24219. The simpler
> alternative of 77/62 would better achieve the goal of keeping NorthI
> starting close to the time of ecliptic longitude 32.5 degrees...
 
But isn't 77/62 only an approximation to 1.242190, where 365.242190 is the number of days per mean tropical near, to the nearest 1/100,000 of a day? So wouldn't 1.24219 be more accurate than 77/62 (at least for now?)  Or is it that, because the number of days per mean tropical year is gradually decreasing, the lower value of 77/62 will soon be more accurate than 1.24219? But won't that be not until something like 6000 years from now? And, disregarding change in the number of days per mean tropical year, wouldn't the 77/62 approximation cause a unidirectional drift of about a quarter day in the next millenium?
 
It seems to me that a 1955 book said that there were 365.242191 days in a mean tropical year. I've seen more current books that said that there are 365.242190 days per mean tropical year.
 
Mike Ossipoff
 

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[Karl Palmen]

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Dear Mike and Calendar People

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of MIKE OSSIPOFF
Sent: 30 July 2009 22:32
To: CALNDR-L@...
Subject: Re: Declination calendar details

 

 
Mark,
 
You wrote:
 
 > So you're using MSN's webmail interface. That at least tells us
> what's broken...
 
I know what you mean, though I get by ok with it as long as I learn to avoid the worst problems. And I think I know how to avoid this one: My two attempts, so far, to post "Declination calendar details" had one thing in common: I copied the message and then pasted it into a reply to the list.

I suspected that might be the case, because ALL previous mucked-up messages were replies.

Karl

10(11(09 till noon

 

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[Karl Palmen]

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Dear Mike

 

Thank you for your reply.

 

More comments towards the end of the note.

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of MIKE OSSIPOFF
Sent: 31 July 2009 00:45
To: CALNDR-L@...
Subject: Re: Declination calendar details without escapes

 

 
Dear Karl and Calendar People,
 
Karl, you wrote:
 
> I take that this is a valid fix of Mike Ossipof's note, having restored
> the missing equal signs.
> Can Mike confirm this?
 
Yes, with the restoral of the three equals signs, I didn't find any other differences. The version posted below is the same as my original posting, in the form in which I sent it.
 
 
You wrote:
 
> The end of the Goals section and the start of the Rules
> section is not clearly marked
 
Yes that's true. The broad heading of "Goals" calls for a similarly broad "Rules" heading, rather than just starting with a heading for a particular rules topic. Additionally, I neglected to give the heading after "Goals" a line of its own, which further made it look as if everlything that followed was under the "Goals" heading.
 
> KARL SAYS: I don't understand d2.
 
The restoral of the equals sign in that line clarified the matter: d2 = 32.5 minus the solar ecliptic longitude at midnight, UT, NorthI/1.
(I'd earlier specified that this definition refers only to the first 365 days of the actual use of the new calendar)

I'd written:
 
>
> If the solar ecliptic longitude = 32.5 degrees at a time that is after
> midnight,
> UT, NorthI/1, then the "Outside Date" is the midnight, UT directly after
> the
> time when the solar ecliptic longitude equals 32.5 degrees.
>
> If the solar ecliptic longitude = 32.5 degrees at a time that is before
> midnight,
> UT, NorthI/1, then the "Outside date" is the midnight, UT, directly
> before the
> time when the solar ecliptic longitude equals 32.5 degrees.
> 

You replied:
 
> I'm trying to get my head round this one. It seems to be a definition of
> "Outside date" which is not a date at all but an instant that occurs at
> midnight UT.
 
Yes, and I did feel a little bit incorrect when I named it as a date. Yes, it refers to an instant at midnight UT.
 
You continued:
 
> It seems to be equivalent to this: ...
 
I'm sticking to my original wording, though I'll change the name from "outside date" to "outside midnight".

You continued:
 
>
> "Outside date" is 24 hours before the UT start (at midnight) of NorthI,
> if NorthI starts after the moment the solar longitude equals 32.5
> degrees else it 24 hours after the UT start of NorthI.
 
But the start of NorthI/1 can be days away from the time at which the solar ecliptic longitude equals 32.5 degrees, because of the amount of jitter of the leapweek rule. My specification, later, about the starting-date is very poorly worded, but I did okay with the outside date (except for giving it an unfortunate name).
 
I'd written:
 
>
> MIKE CONITUNES:
> Divide (days between midnight, UT, NorthI/1 and the Outside Date) by
> (32.5
> degrees minus the solar ecliptic longitude on the Outside Date). Take
> the
> absolute value of the result of that division. That gives "days per
> degree".
>
> Multiply d2 by days per degree. That gives the initial d. That's the
> starting
> value of d, used in the leapyear rule and the starting-date rule.
>

You wrote:

> I think Mike is estimating when the ecliptic longitude is 32.5 degrees
> by linear extrapolation or interpolation based on the ecliptic
> longitudes at the UT starts of two dates NorthI 1, and one of its two
> neighbouring dates (the date that begins with "Outside date"). This he
> does to calculate the initial d, which he refers to later on.
 
Yes. I determine the average days per degree between the "Outside Date" and midnight UT, NorthI/1, and then I use that days per degree estimate to convert d2 from degrees to days.

 
I'd written:
 
> The new calendar comes into use on the beginning (midnight) of the day
> after the
> old calendar's December 31. Every year and every year-division begins on
> a
> Monday. For the new calendar's first year in use, the beginning of that
> first
> calendar year of the new calendar can be at a day (a Monday) before the
> calendar
> actually comes into use. That Monday could be the first day in which the
> new
> calendar comes into use (the day after the old December 31), if that is
> a
> Monday, or it could be any Monday during the 365 days previous to that.
> The
> Monday on which the new calendar starts is chosen so as to minimize the
> magnitude of initial d.
>

You wrote:

> This is utterly confusing!
 
Yes, it is a bit of a mess. It's a difficult thing to word, and I therefore should take the necessary care to word it much more clearly than I did.
 
I was going to do that, but then, from what you said below, I realize that the approach that I was using isn't favored by calendarists anyway. So it would be better if I instead specified a definite date for the calendar's first NorthwardI/1 (sometime before the present date), which is independent of when the calendar comes into use. --and then specified the starting value of d in that year. So that's what I'll do. (The calendar's "New Year's Day" is NorthwardI/1, though its relation to solar ecliptic longitude is based on NorthI/1)

>
> It would be wise to make the calendar independent of the choice of
> starting date.
 
Ok

>
> For example Irv fixed this Symmetry454 293-cycle rule so that year 1
> would begin on Monday January 1, AD 1 proleptic Gregorian calendar,

But if the calendar's first year were specified for a time so long ago, wouldn't that cause problems due to changes in the number of days per calendar year over the time since 1 AD?

KARL SAYS: You could derive your d for a nearby year and work the leap year rule backwards to work out the d for year 1 AD.

 
So maybe the calendar's first NorthwardI/1 should be only a few years ago. Because calendar's "distance" (between 32.5 degrees and the solar ecliptic longitude on NorthI/1) in 2000 doesn't really matter, I'd probably choose a Monday in 2000 for the new calendar's first NorthwardI/1, because of the appeal of using a millenium year, and because I want it to be a fairly recent year, to avoid problems due to changes in days per mean tropical year. So I'll determine which Monday in 2000 A.D. minimizes the initial value of d, and will specify that date and that initial value of d.
 
 
You wrote:
 
> I'd expect the calendar rule to explicitly state a value and
> year for initial d.
 
Sure, I see the merits of that. I just didn't know how calendarists prefer to do such things, and maybe hadn't given the matter enough consideration. But I can see now that asking people to calculate the day of the first NorthwardI/1, and the value of d for that year, isn't such a good idea. Better for the proposal to specify both of those things.

The proposal can have an explanation of the choice of the initial d and also the 32.5 degrees, but neither form a part of the calendar rules.

 
Yes, I want the solar ecliptic longitude on NorthI/1 to be as close as possible to 32.5 degrees.
 
You wrote:
 
 
> Calendar people are likely to dispute the choice of 1.24219. The simpler
> alternative of 77/62 would better achieve the goal of keeping NorthI
> starting close to the time of ecliptic longitude 32.5 degrees...
 
But isn't 77/62 only an approximation to 1.242190, where 365.242190 is the number of days per mean tropical near, to the nearest 1/100,000 of a day?

77/62 would cause the leap years to follow a cycle of just 62 years of which 11 are leap years. The resulting mean year would be 365.241936.. days.

 So wouldn't 1.24219 be more accurate than 77/62 (at least for now?) 

Not for the 32.5 degree solar longitude. 1.2418 would be more accurate for  now.

Or is it that, because the number of days per mean tropical year is gradually decreasing, the lower value of 77/62 will soon be more accurate than 1.24219? But won't that be not until something like 6000 years from now?

Nor will 1.24219.

And, disregarding change in the number of days per mean tropical year, wouldn't the 77/62 approximation cause a unidirectional drift of about a quarter day in the next millennium?

No. It would have a bi-directional drift where different quarter days drift in different directions. This is a good thing, because there are two times of year, when there is no drift. These are what Irv and I call the calendar seasons. The calendar season after the perihelion and before aphelion is stable (moves little over the years).

I don’t think Mike is aware that the length of the tropical year depends on when in the year it starts. The figure of 365.24219 is just the mean for all starting points. Please read http://en.wikipedia.org/wiki/Tropical_year . You see that a tropical year beginning at the Southern Solstice currently has about 365.24274 days, while a tropical year beginning at the Northern Solstice currently has about 354.24163 days. The tropical years beginning at each equinox have lengths in between.

The 77/62 gives the shortest cycle whose mean year lies in between and hence has the bi-directional drift. The Gregorian 497/400 also has bi-directional drift.

 
It seems to me that a 1955 book said that there were 365.242191 days in a mean tropical year. I've seen more current books that said that there are 365.242190 days per mean tropical year.

Please read the above-mentioned Wikipedia article on the tropical year.

Karl

10(11(10

 

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[Karl Palmen]

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Dear Mike and Calendar People

 

I noticed something rather interesting about Mike’s Declination Calendar and the ISO-week based calendar.

 

I assume that Mike chose the ecliptic longitude of 32.5 degrees, because the mean ecliptic longitude of June 1, 00:00 UT is close to that value.

I also assume Mike starts his Seasons on a Monday (like the ISO week).

 

This implies that those Gregorian years when June 1 in a Monday will nearly always have NorthI 1 on the same day. Also such years would occur about half way between leap years. All such years however have 53 ISO weeks. Hence the ISO week leap years lie about half way between the Ossipof leap years and vice versa.

 

Karl

 

10(11(10

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[Karl Palmen]

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Dear Calendar People

 

Mike’s d is equivalent to the accumulator ( (L*Y + K) mod ( C )) for a C-year cycle with L leap years. Mike uses C=700,000 and L=124,219.

 

A year is a leap year if its accumulator is less than L. Also a year is a leap if d is less than 1.24219 more than its minimum permitted value.

However converting d to the accumulator or back is not quite as simple as hinted by the previous sentence.

 

To find the accumulator corresponding to d, subtract d from the maximum permitted value of d, then multiply by the denominator of the fraction used to increment d (for 1.24219 this is 100,000). If the result is not an integer, ignore the fractional part. It will make no difference. Then you have the accumulator of the previous year. Add L mod C to get the accumulator of this year.

 

L is simply the numerator of the fraction used to increment d. C is seven times the denominator of this fraction. If the numerator is divisible by seven, then L, C and the resulting accumulator can be divided by seven (and still be an integer). This would be the case for 1.2425 or 1.24215.

 

This conversion can be reversed to find the d value corresponding to a given accumulator.

 

If you do the same to the d for year 1, you get the accumulator of year 0, which is simply K. So if K=C/2, then d of year 1 is halfway between the minimum and maximum permitted values of d.

 

Karl

 

 

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