as of present time, is it still true that 4000 A.D. will NOT be a leap year?

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as of present time, is it still true that 4000 A.D. will NOT be a leap year?

gerry lowry +1 705 429-7550 wasaga beach ontario canada
Hello ... I can not find an authoritative source.

I have been under the impression that 4000 A.D. is an exception
to the divisible by 400 rule and therefore 4000 will NOT be a leap year.

Unfortunately Wikipedia is not authoritative.  A number of sources
I've found via Google seem to be quoting each other.

Will 4000 be a leap year?

(If yes, then we have a year 4000 problem ~~ not that that will affect all of us alive today;
 with advances in modern science, if we do not destroy each other and/or the planet,
 it may be a problem for some of us, or at least some of our descendants.)

Thank you.

Regards,
Gerry (Lowry)

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Re: as of present time, is it still true that 4000 A.D. will NOT be a leap year?

Victor Engel
The 4000 year exception is a proposal by people who are trying to
bring the mean year closer to their target tropical year. But the
Gregorian calendar is meant to follow not the tropical year, but the
northward equinox year, and that adjustment makes it less, not more
accurate. Additionally, adding another adjustment like that increases
the jitter of the calendar, thus lessening the value of such an
adjustment.

Victor

On Mon, Apr 6, 2009 at 7:39 AM, gerry_lowry (alliston ontario canada)
<[hidden email]> wrote:

> Hello ... I can not find an authoritative source.
>
> I have been under the impression that 4000 A.D. is an exception
> to the divisible by 400 rule and therefore 4000 will NOT be a leap year.
>
> Unfortunately Wikipedia is not authoritative.  A number of sources
> I've found via Google seem to be quoting each other.
>
> Will 4000 be a leap year?
>
> (If yes, then we have a year 4000 problem ~~ not that that will affect all of us alive today;
>  with advances in modern science, if we do not destroy each other and/or the planet,
>  it may be a problem for some of us, or at least some of our descendants.)
>
> Thank you.
>
> Regards,
> Gerry (Lowry)
>
>

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Re: as of present time, is it still true that 4000 A.D. will NOT be a leap year?

HR-CALNDR-L
According to the Gregorian Calendar, 4000 A.D. WILL be a leap year, but who
knows what people in the next 1991 years will decide about the calendar?
Nobody can predict.

_________________________________________________
Kind regards / met vriendelijke groeten,

Henk Reints



Oorspronkelijke tekst Victor Engel

> The 4000 year exception is a proposal by people who are trying to
> bring the mean year closer to their target tropical year. But the
> Gregorian calendar is meant to follow not the tropical year, but the
> northward equinox year, and that adjustment makes it less, not more
> accurate. Additionally, adding another adjustment like that increases
> the jitter of the calendar, thus lessening the value of such an
> adjustment.
>
> Victor
>
> On Mon, Apr 6, 2009 at 7:39 AM, gerry_lowry (alliston ontario canada)
> <[hidden email]> wrote:
>> Hello ... I can not find an authoritative source.
>>
>> I have been under the impression that 4000 A.D. is an exception
>> to the divisible by 400 rule and therefore 4000 will NOT be a leap year.
>>
>> Unfortunately Wikipedia is not authoritative.  A number of sources
>> I've found via Google seem to be quoting each other.
>>
>> Will 4000 be a leap year?
>>
>> (If yes, then we have a year 4000 problem ~~ not that that will affect all
>> of us alive today;
>>  with advances in modern science, if we do not destroy each other and/or the
>> planet,
>>  it may be a problem for some of us, or at least some of our descendants.)
>>
>> Thank you.
>>
>> Regards,
>> Gerry (Lowry)
>>
>>
>

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Re: as of present time, is it still true that 4000 A.D. will NOT be a leap year?

Gerard Ashton
In reply to this post by gerry lowry +1 705 429-7550 wasaga beach ontario canada
Since Mr. Lowry is from Canada, let me point him to the
goverment council responsible for measurement in Candada,
http://inms-ienm.nrc-cnrc.gc.ca/faq_time_e.html

Gerry Ashton

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:[hidden email]] On Behalf Of gerry_lowry (alliston
ontario canada)
Sent: Monday, April 06, 2009 8:39 AM
To: [hidden email]
Subject: as of present time, is it still true that 4000 A.D. will NOT be a
leap year?


Hello ... I can not find an authoritative source.

I have been under the impression that 4000 A.D. is an exception
to the divisible by 400 rule and therefore 4000 will NOT be a leap year.

Unfortunately Wikipedia is not authoritative.  A number of sources
I've found via Google seem to be quoting each other.

Will 4000 be a leap year?

(If yes, then we have a year 4000 problem ~~ not that that will affect all
of us alive today;
 with advances in modern science, if we do not destroy each other and/or the
planet,
 it may be a problem for some of us, or at least some of our descendants.)

Thank you.

Regards,
Gerry (Lowry)

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Re: as of present time, is it still true that 4000 A.D. will NOT be a leap year?

Mark J. Reed
In reply to this post by Victor Engel
The year 4000 is a leap year in the Gregorian calendar, and that has
been true since the calendar's inception.  There have been proposals
to add a rule that would make the year 4000 common, but such proposals
have never been widely adopted.  Of course, calendars including such a
rule are perforce no longer the Gregorian calendar, just as the
Gregorian calendar is not the same as the Julian.
    However, I do believe some Eastern European countries officially
adopted such a derivative calendar rather than the Gregorian... So as
it stands now, whether or not 4000 is a leap year may depend on your
location.

On 4/6/09, Victor Engel <[hidden email]> wrote:

> The 4000 year exception is a proposal by people who are trying to
> bring the mean year closer to their target tropical year. But the
> Gregorian calendar is meant to follow not the tropical year, but the
> northward equinox year, and that adjustment makes it less, not more
> accurate. Additionally, adding another adjustment like that increases
> the jitter of the calendar, thus lessening the value of such an
> adjustment.
>
> Victor
>
> On Mon, Apr 6, 2009 at 7:39 AM, gerry_lowry (alliston ontario canada)
> <[hidden email]> wrote:
>> Hello ... I can not find an authoritative source.
>>
>> I have been under the impression that 4000 A.D. is an exception
>> to the divisible by 400 rule and therefore 4000 will NOT be a leap year.
>>
>> Unfortunately Wikipedia is not authoritative.  A number of sources
>> I've found via Google seem to be quoting each other.
>>
>> Will 4000 be a leap year?
>>
>> (If yes, then we have a year 4000 problem ~~ not that that will affect all
>> of us alive today;
>>  with advances in modern science, if we do not destroy each other and/or
>> the planet,
>>  it may be a problem for some of us, or at least some of our descendants.)
>>
>> Thank you.
>>
>> Regards,
>> Gerry (Lowry)
>>
>>
>
>

--
Sent from my mobile device

Mark J. Reed <[hidden email]>

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Re: as of present time, is it still true that 4000 A.D. will NOT be a leap year?

Irv Bromberg
In reply to this post by gerry lowry +1 705 429-7550 wasaga beach ontario canada
On 2009 Apr 6, at 08:39 , gerry_lowry (alliston ontario canada) wrote:
I have been under the impression that 4000 A.D. is an exception
to the divisible by 400 rule and therefore 4000 will NOT be a leap year.

That was not part of the Gregorian reform, nor was it adopted at the recent 400th anniversary of the Gregorian calendar reform.

With the Gregorian mean year of 365+97/400 days = 365d 5h 49m 12s the calendar season is at about March 3rd, or nearly 18 days before the northward equinox.  The Gregorian calendar mean year will "expire" around 4500 AD, that is when it will be longer than all points in the solar cycle.

Calendar seasons are explained under the topic heading "Calendar Seasons:  Stable points in the solar cycle" at <http://www.sym454.org/leap/>.

Omitting year 4000 as a leap year would greatly increase the long-term equinox jitter as others have mentioned, and it also changes the calendar mean year to 365+969/4000 days = 365d 5h 48m 50.4s (exact), thereby shifting the calendar season to a position that is 10 days beyond the northward equinox, about March 31st.

The calendar season concept is not too realistic in the context of such a long leap cycle with such high jitter.  It works best with smoothly spread leap cycles that are under 1000 years long.  Nevertheless this analysis of the calendar mean years serves to make the point that that proposed reform of the Gregorian calendar would not be particularly helpful.

Furthermore, by the time that the next year 4000 leap day would be omitted in 8000 AD the northward equinoctial year will be appreciably shorter than it is today, so there will not be any point in the solar cycle that has a mean year as long as even this shorter 365+369/4000 mean year.  The 4000-year cycle will thus "expire" around the year 6000.  Thus it is rather silly to even consider a reform proposal for a leap rule modification that most likely would be invoked only once in the far future.

On the other hand, if the 4000-year cycle were implemented as a cycle having its leap years as smoothly spread as possible then numerical integration (SOLEX) shows that relative to the Gregorian epoch the northward equinox will reach a maximum of about 1/2 day late around year 5000 AD, and by around 8000 AD it will have close to zero drift, but will already drift >1/2 day early by year 9000 AD, by which time the drift will be exponentially migrating towards earlier dates.  Overall, this is not bad at all, but would require that leap years be as smoothly spread as possible, a very different situation from the present Gregorian leap rule or this proposed year 4000 modification.

A reasonably short and smoothly spread leap cycle would greatly reduce the calendar equinox jitter and would also greatly reduce the long-term equinox drift, particularly if an appropriate calendar mean year is selected.

Although the mean northward equinoctial year is presently just a fraction of a second shorter than 365+127/524 days = 365d 5h 49m 60/131s, which accordingly has its calendar season just a fraction of a day before the northward equinox, for calendrical purposes the 524-year leap cycle is not as good as a cycle with a slightly shorter calendar mean year because:

1.  Traditionally dates are calculated relative to the Gregorian epoch, and for the past 2000 years the northward equinoctial year has been shorter than it is today.

2.  The present era mean northward equinoctial year is near its maximum and in about 1000 years will start to get progressively shorter, which will make the 524-year cycle mean year too long for future dates.  The northward equinoctial year will never again be as long as it will be around the year 3000 AD.

For further information see my "Lengths of the Seasons" web page at <http://www.sym454.org/seasons/>, especially the row #6 figures.

That is why I prefer the 293-year leap cycle with either 71 leap days or 52 leap weeks per cycle.


-- Irv Bromberg, Toronto, Canada

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Re: as of present time, is it still true that 4000 A.D. will NOT be a leap year?

Ryan Provost-2
Friendly Greetings calendar people!
 
So why does the 400-year cycle (also known as the Gregorian calendar) is put in place? There are 97 leap days in the Gregorian calendar. The ISO week calendar system uses the 400-year cycle as with the Gregorian Calendar, and there are 71 leap weeks in that calendar system. So, there are 97 leap days or 71 leap weeks in the 400-year cycle that we use today.
 
So for now, the year 4000 will be a leap year in the leap-day Gregorian Calendar and the leap-week ISO week calendar. That's 1,991 years from now. We would be way dead by then. On my Elite Measurement and time system (EMTS) (in which you can find it on my website, http://rynprov.ueuo.com/emts.php), The year 4000 AD will be EY (EliteYear) 3000 EE. EY 3000 EE will occur from 4000/01/01 Fri to 4000/12/30 Sat.

Sent: Monday, April 06, 2009 1:50 PM
Subject: Re: as of present time, is it still true that 4000 A.D. will NOT be a leap year?

On 2009 Apr 6, at 08:39 , gerry_lowry (alliston ontario canada) wrote:
I have been under the impression that 4000 A.D. is an exception
to the divisible by 400 rule and therefore 4000 will NOT be a leap year.

That was not part of the Gregorian reform, nor was it adopted at the recent 400th anniversary of the Gregorian calendar reform.

With the Gregorian mean year of 365+97/400 days = 365d 5h 49m 12s the calendar season is at about March 3rd, or nearly 18 days before the northward equinox.  The Gregorian calendar mean year will "expire" around 4500 AD, that is when it will be longer than all points in the solar cycle.

Calendar seasons are explained under the topic heading "Calendar Seasons:  Stable points in the solar cycle" at <http://www.sym454.org/leap/>.

Omitting year 4000 as a leap year would greatly increase the long-term equinox jitter as others have mentioned, and it also changes the calendar mean year to 365+969/4000 days = 365d 5h 48m 50.4s (exact), thereby shifting the calendar season to a position that is 10 days beyond the northward equinox, about March 31st.

The calendar season concept is not too realistic in the context of such a long leap cycle with such high jitter.  It works best with smoothly spread leap cycles that are under 1000 years long.  Nevertheless this analysis of the calendar mean years serves to make the point that that proposed reform of the Gregorian calendar would not be particularly helpful.

Furthermore, by the time that the next year 4000 leap day would be omitted in 8000 AD the northward equinoctial year will be appreciably shorter than it is today, so there will not be any point in the solar cycle that has a mean year as long as even this shorter 365+369/4000 mean year.  The 4000-year cycle will thus "expire" around the year 6000.  Thus it is rather silly to even consider a reform proposal for a leap rule modification that most likely would be invoked only once in the far future.

On the other hand, if the 4000-year cycle were implemented as a cycle having its leap years as smoothly spread as possible then numerical integration (SOLEX) shows that relative to the Gregorian epoch the northward equinox will reach a maximum of about 1/2 day late around year 5000 AD, and by around 8000 AD it will have close to zero drift, but will already drift >1/2 day early by year 9000 AD, by which time the drift will be exponentially migrating towards earlier dates.  Overall, this is not bad at all, but would require that leap years be as smoothly spread as possible, a very different situation from the present Gregorian leap rule or this proposed year 4000 modification.

A reasonably short and smoothly spread leap cycle would greatly reduce the calendar equinox jitter and would also greatly reduce the long-term equinox drift, particularly if an appropriate calendar mean year is selected.

Although the mean northward equinoctial year is presently just a fraction of a second shorter than 365+127/524 days = 365d 5h 49m 60/131s, which accordingly has its calendar season just a fraction of a day before the northward equinox, for calendrical purposes the 524-year leap cycle is not as good as a cycle with a slightly shorter calendar mean year because:

1.  Traditionally dates are calculated relative to the Gregorian epoch, and for the past 2000 years the northward equinoctial year has been shorter than it is today.

2.  The present era mean northward equinoctial year is near its maximum and in about 1000 years will start to get progressively shorter, which will make the 524-year cycle mean year too long for future dates.  The northward equinoctial year will never again be as long as it will be around the year 3000 AD.

For further information see my "Lengths of the Seasons" web page at <http://www.sym454.org/seasons/>, especially the row #6 figures.

That is why I prefer the 293-year leap cycle with either 71 leap days or 52 leap weeks per cycle.


-- Irv Bromberg, Toronto, Canada

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Re: as of present time, is it still true that 4000 A.D. will NOT be a leap year?

Mark J. Reed
The ISO leap week calendar is defined in terms of the Gregorian
calendar, so saying that they both have the same number of leap days
in their largest cycle is a tautology.  (Computationally, you can of
course  treat it as a separate calendar, but it's hardly valid to cite
it as an example of a different calendar that independently arrived at
the Gregorian scheme... )

Naturally, with full-week intercalation, the ISO calendar is jitterier.

On 4/6/09, ELITE 3000 <[hidden email]> wrote:

> Friendly Greetings calendar people!
>
> So why does the 400-year cycle (also known as the Gregorian calendar) is put
> in place? There are 97 leap days in the Gregorian calendar. The ISO week
> calendar system uses the 400-year cycle as with the Gregorian Calendar, and
> there are 71 leap weeks in that calendar system. So, there are 97 leap days
> or 71 leap weeks in the 400-year cycle that we use today.
>
> So for now, the year 4000 will be a leap year in the leap-day Gregorian
> Calendar and the leap-week ISO week calendar. That's 1,991 years from now.
> We would be way dead by then. On my Elite Measurement and time system (EMTS)
> (in which you can find it on my website, http://rynprov.ueuo.com/emts.php),
> The year 4000 AD will be EY (EliteYear) 3000 EE. EY 3000 EE will occur from
> 4000/01/01 Fri to 4000/12/30 Sat.
>
>
> From: Irv Bromberg
> Sent: Monday, April 06, 2009 1:50 PM
> To: [hidden email]
> Subject: Re: as of present time, is it still true that 4000 A.D. will NOT be
> a leap year?
>
>
> On 2009 Apr 6, at 08:39 , gerry_lowry (alliston ontario canada) wrote:
>   I have been under the impression that 4000 A.D. is an exception
>   to the divisible by 400 rule and therefore 4000 will NOT be a leap year.
>
>
>
> That was not part of the Gregorian reform, nor was it adopted at the recent
> 400th anniversary of the Gregorian calendar reform.
>
>
> With the Gregorian mean year of 365+97/400 days = 365d 5h 49m 12s the
> calendar season is at about March 3rd, or nearly 18 days before the
> northward equinox.  The Gregorian calendar mean year will "expire" around
> 4500 AD, that is when it will be longer than all points in the solar cycle.
>
>
> Calendar seasons are explained under the topic heading "Calendar Seasons:
> Stable points in the solar cycle" at <http://www.sym454.org/leap/>.
>
>
> Omitting year 4000 as a leap year would greatly increase the long-term
> equinox jitter as others have mentioned, and it also changes the calendar
> mean year to 365+969/4000 days = 365d 5h 48m 50.4s (exact), thereby shifting
> the calendar season to a position that is 10 days beyond the northward
> equinox, about March 31st.
>
>
> The calendar season concept is not too realistic in the context of such a
> long leap cycle with such high jitter.  It works best with smoothly spread
> leap cycles that are under 1000 years long.  Nevertheless this analysis of
> the calendar mean years serves to make the point that that proposed reform
> of the Gregorian calendar would not be particularly helpful.
>
>
> Furthermore, by the time that the next year 4000 leap day would be omitted
> in 8000 AD the northward equinoctial year will be appreciably shorter than
> it is today, so there will not be any point in the solar cycle that has a
> mean year as long as even this shorter 365+369/4000 mean year.  The
> 4000-year cycle will thus "expire" around the year 6000.  Thus it is rather
> silly to even consider a reform proposal for a leap rule modification that
> most likely would be invoked only once in the far future.
>
>
> On the other hand, if the 4000-year cycle were implemented as a cycle having
> its leap years as smoothly spread as possible then numerical integration
> (SOLEX) shows that relative to the Gregorian epoch the northward equinox
> will reach a maximum of about 1/2 day late around year 5000 AD, and by
> around 8000 AD it will have close to zero drift, but will already drift >1/2
> day early by year 9000 AD, by which time the drift will be exponentially
> migrating towards earlier dates.  Overall, this is not bad at all, but would
> require that leap years be as smoothly spread as possible, a very different
> situation from the present Gregorian leap rule or this proposed year 4000
> modification.
>
>
> A reasonably short and smoothly spread leap cycle would greatly reduce the
> calendar equinox jitter and would also greatly reduce the long-term equinox
> drift, particularly if an appropriate calendar mean year is selected.
>
>
> Although the mean northward equinoctial year is presently just a fraction of
> a second shorter than 365+127/524 days = 365d 5h 49m 60/131s, which
> accordingly has its calendar season just a fraction of a day before the
> northward equinox, for calendrical purposes the 524-year leap cycle is not
> as good as a cycle with a slightly shorter calendar mean year because:
>
>
> 1.  Traditionally dates are calculated relative to the Gregorian epoch, and
> for the past 2000 years the northward equinoctial year has been shorter than
> it is today.
>
>
> 2.  The present era mean northward equinoctial year is near its maximum and
> in about 1000 years will start to get progressively shorter, which will make
> the 524-year cycle mean year too long for future dates.  The northward
> equinoctial year will never again be as long as it will be around the year
> 3000 AD.
>
>
> For further information see my "Lengths of the Seasons" web page at
> <http://www.sym454.org/seasons/>, especially the row #6 figures.
>
>
> That is why I prefer the 293-year leap cycle with either 71 leap days or 52
> leap weeks per cycle.
>
>
>
>
> -- Irv Bromberg, Toronto, Canada
>
>
> <http://www.sym454.org/>

--
Sent from my mobile device

Mark J. Reed <[hidden email]>

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Pray we live RE: as of present time, is it still true that 4000 A.D. will NOT be a leap year?

Brij Bhushan Vij
In reply to this post by HR-CALNDR-L
Sirs:
>If yes, then we have a year 4000 problem ~~ not that that will affect all of us alive ....
We perhaps lived in earlier incarnations and shall do so if.....birth, rebirth cycles existed!
Please see: http://www.brijvij.com/bb_metro-contrbn.2007.pdf
and http://www.brijvij.com/bb1920_caL-harappa.pdf
Regards,
Brij Bhushan Vij 

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> Date: Mon, 6 Apr 2009 16:00:44 +0200

> From: [hidden email]
> Subject: Re: as of present time, is it still true that 4000 A.D. will NOT be a leap year?
> To: [hidden email]
>
> According to the Gregorian Calendar, 4000 A.D. WILL be a leap year, but who
> knows what people in the next 1991 years will decide about the calendar?
> Nobody can predict.
>
> _________________________________________________
> Kind regards / met vriendelijke groeten,
>
> Henk Reints
>
>
>
> Oorspronkelijke tekst Victor Engel
> > The 4000 year exception is a proposal by people who are trying to
> > bring the mean year closer to their target tropical year. But the
> > Gregorian calendar is meant to follow not the tropical year, but the
> > northward equinox year, and that adjustment makes it less, not more
> > accurate. Additionally, adding another adjustment like that increases
> > the jitter of the calendar, thus lessening the value of such an
> > adjustment.
> >
> > Victor
> >
> > On Mon, Apr 6, 2009 at 7:39 AM, gerry_lowry (alliston ontario canada)
> > <[hidden email]> wrote:
> >> Hello ... I can not find an authoritative source.
> >>
> >> I have been under the impression that 4000 A.D. is an exception
> >> to the divisible by 400 rule and therefore 4000 will NOT be a leap year.
> >>
> >> Unfortunately Wikipedia is not authoritative.  A number of sources
> >> I've found via Google seem to be quoting each other.
> >>
> >> Will 4000 be a leap year?
> >>
> >> (If yes, then we have a year 4000 problem ~~ not that that will affect all
> >> of us alive today;
> >>  with advances in modern science, if we do not destroy each other and/or the
> >> planet,
> >>  it may be a problem for some of us, or at least some of our descendants.)
> >>
> >> Thank you.
> >>
> >> Regards,
> >> Gerry (Lowry)
> >>
> >>
> >
>


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Re: as of present time, is it still true that 4000 A.D. will NOT be a leap year?

gerry lowry +1 705 429-7550 wasaga beach ontario canada
In reply to this post by Ryan Provost-2
http://rynprov.ueuo.com/emts.php appears to be broken.

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Re: as of present time, is it still true that 4000 A.D. will NOT be a leap year?

Irv Bromberg
I just noticed that of all fixed-arithmetic Symmetry454 leap cycles built into the most recent public beta of Kalendis the only one that makes the year 4000 a leap year is the symmetrically spread 69/389 leap cycle.

Note that 4000 is not a leap year according to ISO, nor according to the almost symmetrical 71/400 cycle.

-- Irv Bromberg, Toronto, Canada

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Re: as of present time, is it still true that 4000 A.D. will NOT be a leap year?

Karl Palmen - UKRI STFC

Dear Irv and Calendar People

 

I’d expect this (i.e. whether a given year has a leap week in a Symmetry454 calendar)  to depend on (but not be completely determined by)  on the day of week of a the northward equinox (or any other given equinox or solstice).

 

Assuming an equinox on 20 March 4000, this day of week is Monday for the year 4000.

The 69/389 leap week cycle has an extremely low mean year of 365.241645 days.

This suggests that Monday is on the edge of the range of days of week of the Northward equinox, whose year may have a leap week.

 

Karl

 

10(07(13

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Irv Bromberg
Sent: 07 April 2009 15:09
To: [hidden email]
Subject: Re: as of present time, is it still true that 4000 A.D. will NOT be a leap year?

 

I just noticed that of all fixed-arithmetic Symmetry454 leap cycles built into the most recent public beta of Kalendis the only one that makes the year 4000 a leap year is the symmetrically spread 69/389 leap cycle.

 

Note that 4000 is not a leap year according to ISO, nor according to the almost symmetrical 71/400 cycle.

-- Irv Bromberg, Toronto, Canada

 




Scanned by iCritical.


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Re: as of present time, is it still true that 4000 A.D. will NOT be a leap year?

Irv Bromberg
On 2009 Apr 7, at 10:50 , Palmen, KEV (Karl) wrote:
The 69/389 leap week cycle has an extremely low mean year of 365.241645 days.

The mean year is 365+94/389 days  365d 5h 47m 58+58/389s and is just a few seconds longer than the shortest solar year length that presently exists at aphelion, which I have reckoned using the Find Calendar Seasons spreadsheet at approximately 365 days 5 hours 47 minutes 52 seconds or about 365+43/178 days.  This means that it has recently (within the past millennium) become a stable calendar season starting at aphelion, and its calendar season is now migrating towards perihelion at the same time that perihelion is migrating towards it, keeping it quite stable and very near to the north solstice.  It is actually slightly too long for the present era mean north solstitial year (calendar season slightly before the north solstice), but in the future the mean north solstitial year will spend quite a few millennia at an even longer mean year, so overall the 389-year cycle will remain an excellent average approximation for the next 10-11 millennia, as shown as the dashed orange horizontal line on this chart:


Because of the expected near-maximal longevity of this cycle and the fact that the stability of the mean northward equinoctial year is about 2/3 of the way towards its expiration era, I have been very seriously considering switching Symmetry454 to use the 389-year cycle with 69 leap weeks as the preferred leap cycle.  If adopted then a fixed arithmetic Easter computus would be out of the question due to the cycle tracking the north solstice rather than the northward equinox.  Therefore it would have to use either the astronomical Uniform Easter as recommended by the World Council of Churches, or the proposed fixed Easter date of Sunday April 7th on the Symmetry454 calendar.  Yesterday I checked and found that Symmetry454 Sunday April 7th remains the median astronomical Easter date with this 389-year leap cycle even for thousands of years into the future, despite the cycle's comparatively short calendar mean year.

This chart shows the predicted long-term drift of the cycle relative to the north solstice, based on the numerical integration of SOLEX:


(The drift chart depicts the cycle performance before adopting the K value that makes this cycle fully symmetrical, but the only difference is the vertical alignment.  Since the north solstice at the epoch occurred at about 3/4 hour before midnight Jerusalem local time at the end of Symmetry454 Friday, June 19, 1 AD, therefore with the fully symmetrical cycle the green line average would shift later by about 2+1/2 days.  This doesn't affect the interpretation of the calendar drift performance.)


-- Irv Bromberg, Toronto, Canada


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Cal-Reform, are we serious RE: as of present time, is it still true that 4000 A.D. will NOT be a leap year?

Brij Bhushan Vij
In reply to this post by Irv Bromberg
Irv, Karl and friends:
>Omitting year 4000 as a leap year would greatly increase the long-term equinox jitter as others have mentioned, and it also >changes the calendar mean year to 365+969/4000 days = 365d 5h 48m 50.4s (exact), thereby shifting the calendar >season to a position that is 10 days beyond the northward equinox, about March 31st.
There must be good reasons for astraying & exporing 'other options' that achievable Mean Year of 365+31/128 days.
As far Y4000 AD to be a Leap Year, none among us shall be living to see unless we come and experience during our next cycles of re-birth. Yes, (it most likely) will not be a Leap Year if our intention is to find the best option and settle the Calendar Reform ISSUE within or outside of UNITED NATIONS. Also plese see:  http://www.brijvij.com/bb_IndianContri..pdfand
http://www.brijvij.com/bbv_cal-reform_brij.view.pdf
From another mail: 

The mean year is 365+94/389 days ≡ 365d 5h 47m 58+58/389s and is just a few seconds longer than the shortest solar year length that presently exists at aphelion, which I have reckoned using the Find Calendar Seasons spreadsheet at approximately 365 days 5 hours 47 minutes 52 seconds or about 365+43/178 days”

    What is the objection with MeanYear =365 31/128 =365.2421875 days (365d5h48m45s)? This mean year can be obtained with or without using Leap Days or Leap weeks, as has remained under discussion.

Year 4000 AD is not a multiple of 128-block nor is divisible by six to have the Leap Week, as such will NOT have the Leap adjustment.

Brij Bhushan Vij 

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Date: Mon, 6 Apr 2009 13:50:31 -0400
From: [hidden email]
Subject: Re: as of present time, is it still true that 4000 A.D. will NOT be a leap year?
To: [hidden email]

On 2009 Apr 6, at 08:39 , gerry_lowry (alliston ontario canada) wrote:
I have been under the impression that 4000 A.D. is an exception
to the divisible by 400 rule and therefore 4000 will NOT be a leap year.

That was not part of the Gregorian reform, nor was it adopted at the recent 400th anniversary of the Gregorian calendar reform.

With the Gregorian mean year of 365+97/400 days = 365d 5h 49m 12s the calendar season is at about March 3rd, or nearly 18 days before the northward equinox.  The Gregorian calendar mean year will "expire" around 4500 AD, that is when it will be longer than all points in the solar cycle.

Calendar seasons are explained under the topic heading "Calendar Seasons:  Stable points in the solar cycle" at <http://www.sym454.org/leap/>.

Omitting year 4000 as a leap year would greatly increase the long-term equinox jitter as others have mentioned, and it also changes the calendar mean year to 365+969/4000 days = 365d 5h 48m 50.4s (exact), thereby shifting the calendar season to a position that is 10 days beyond the northward equinox, about March 31st.

The calendar season concept is not too realistic in the context of such a long leap cycle with such high jitter.  It works best with smoothly spread leap cycles that are under 1000 years long.  Nevertheless this analysis of the calendar mean years serves to make the point that that proposed reform of the Gregorian calendar would not be particularly helpful.

Furthermore, by the time that the next year 4000 leap day would be omitted in 8000 AD the northward equinoctial year will be appreciably shorter than it is today, so there will not be any point in the solar cycle that has a mean year as long as even this shorter 365+369/4000 mean year.  The 4000-year cycle will thus "expire" around the year 6000.  Thus it is rather silly to even consider a reform proposal for a leap rule modification that most likely would be invoked only once in the far future.

On the other hand, if the 4000-year cycle were implemented as a cycle having its leap years as smoothly spread as possible then numerical integration (SOLEX) shows that relative to the Gregorian epoch the northward equinox will reach a maximum of about 1/2 day late around year 5000 AD, and by around 8000 AD it will have close to zero drift, but will already drift >1/2 day early by year 9000 AD, by which time the drift will be exponentially migrating towards earlier dates.  Overall, this is not bad at all, but would require that leap years be as smoothly spread as possible, a very different situation from the present Gregorian leap rule or this proposed year 4000 modification.

A reasonably short and smoothly spread leap cycle would greatly reduce the calendar equinox jitter and would also greatly reduce the long-term equinox drift, particularly if an appropriate calendar mean year is selected.

Although the mean northward equinoctial year is presently just a fraction of a second shorter than 365+127/524 days = 365d 5h 49m 60/131s, which accordingly has its calendar season just a fraction of a day before the northward equinox, for calendrical purposes the 524-year leap cycle is not as good as a cycle with a slightly shorter calendar mean year because:

1.  Traditionally dates are calculated relative to the Gregorian epoch, and for the past 2000 years the northward equinoctial year has been shorter than it is today.

2.  The present era mean northward equinoctial year is near its maximum and in about 1000 years will start to get progressively shorter, which will make the 524-year cycle mean year too long for future dates.  The northward equinoctial year will never again be as long as it will be around the year 3000 AD.

For further information see my "Lengths of the Seasons" web page at <http://www.sym454.org/seasons/>, especially the row #6 figures.

That is why I prefer the 293-year leap cycle with either 71 leap days or 52 leap weeks per cycle.


-- Irv Bromberg, Toronto, Canada



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