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« Return to Thread: as of present time, is it still true that 4000 A.D. will NOT be a leap year?
Re: as of present time, is it still true that 4000 A.D. will NOT be a leap year?
by Mark J. Reed
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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 <rw8000@...> 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: CALNDR-L@...
> 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 <markjreed@...>
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 <rw8000@...> 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: CALNDR-L@...
> 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 <markjreed@...>
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