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« Return to Thread: Gregorian calendar jitter and lunar calendar in Wikipedia computus
Re: Gregorian calendar jitter and lunar calendar in Wikipedia computus
by Karl Palmen
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Dear Tom and Calendar People
On the Wikipedia talk page of Computus
http://en.wikipedia.org/wiki/Talk:Computus#Unified_system_of_corrections
Mockingbird said:
"I have always held that the Gregorian scheme is more accurate than a
unified scheme. See my post at the beginning of this section. What I
disagree with is the claim that "jitter" from the solar side is being
"transmitted" to the lunar side by a unified scheme. The "jitter" on the
solar side is the motion of the mean and true equinoxes relative to
midnight (beginning of day) March 21 Gregorian. On the lunar side the
difference between a fixed date and a fixed annual event is of no
consequence. The important difference is between the beginning of a
lunation and the mean and true conjunctions. So nothing is "transmitted"
from one side to the other."
The first two sentences are clear and important.
Tom later gave a reply that did not seem to address these two sentences,
but got bogged down in the unclear terminology that followed.
Mockingbird seems to be unaware that the lunar calendar piggy backs on
the solar calendar and that the scheduling of the tabular lunar months
and the tabular conjunctions does depend on the scheduling of the solar
year. If the solar year is a day late, so are the lunar months (which
Mockingbird refers to as Tabular lunations or lunations). Therefore the
difference between a fixed date and an annual event such as an equinox
is of consequence to the lunar calendar. It does affect the difference
between the beginning of a lunar month and a mean or true conjunction.
So the jitter is transmitted.
Such a transmission does not occur completely, if there is any
correlation between the leap years in the solar calendar and the
corrections in the lunar calendar. The corrections in the lunar calendar
include the saltus lunae corrections, but these follow a strict 19-year
cycle so have no correlation with the leap years and so only the
correlations of corrections to the 19-year cycle need be considered. The
examples of the uniform corrections systems that Mockingbird provided do
have considerable correlation. This results in only a partial
transmission of the jitter and can make it appear that no transmission
occurs at all.
We do not seem to know which uniform correction computus was proposed by
Lichtenberg. It may have been one that has the 43 correction centuries
spaced as evenly as possible. If so, the correlation would be low (but
never completely absent) and so transmission of jitter would be evident.
Also I want to make it clear that the jitter that is transmitted if the
motion of a mean equinox placed exactly once every mean calendar year
and (beginning of day) March 21 in the solar calendar. This is only
slightly different from the jitter defined by Mockingbird above.
Karl
10(07(01
-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Tom Peters
Sent: 20 March 2009 00:20
To: CALNDR-L@...
Subject: Re: Gregorian calendar jitter and lunar calendar in Wikipedia
computus
Op 19-mrt-2009, om 16:26 heeft Palmen, KEV (Karl) het volgende
geschreven:
> Dear Tom and Calendar People
>
> I've found a weakness that occurs in EVERY uniform correction
> system. It
> is three consecutive common century years with only one correction.
> The
> Gregorian System makes at least two corrections in any three
> consecutive
> common century years.
> This causes the minimum number of days in 11 consecutive Metonic
> cycles
> (of 235 lunar months equal to 19 lunisolar years) to be one less than
> for the Gregorian system.
>
Karl,
thank you for your investigations. I do not have the time now to
study this issue as thorough as is necessary. Maybe at some later time.
--
Tom Peters
--
Scanned by iCritical.
On the Wikipedia talk page of Computus
http://en.wikipedia.org/wiki/Talk:Computus#Unified_system_of_corrections
Mockingbird said:
"I have always held that the Gregorian scheme is more accurate than a
unified scheme. See my post at the beginning of this section. What I
disagree with is the claim that "jitter" from the solar side is being
"transmitted" to the lunar side by a unified scheme. The "jitter" on the
solar side is the motion of the mean and true equinoxes relative to
midnight (beginning of day) March 21 Gregorian. On the lunar side the
difference between a fixed date and a fixed annual event is of no
consequence. The important difference is between the beginning of a
lunation and the mean and true conjunctions. So nothing is "transmitted"
from one side to the other."
The first two sentences are clear and important.
Tom later gave a reply that did not seem to address these two sentences,
but got bogged down in the unclear terminology that followed.
Mockingbird seems to be unaware that the lunar calendar piggy backs on
the solar calendar and that the scheduling of the tabular lunar months
and the tabular conjunctions does depend on the scheduling of the solar
year. If the solar year is a day late, so are the lunar months (which
Mockingbird refers to as Tabular lunations or lunations). Therefore the
difference between a fixed date and an annual event such as an equinox
is of consequence to the lunar calendar. It does affect the difference
between the beginning of a lunar month and a mean or true conjunction.
So the jitter is transmitted.
Such a transmission does not occur completely, if there is any
correlation between the leap years in the solar calendar and the
corrections in the lunar calendar. The corrections in the lunar calendar
include the saltus lunae corrections, but these follow a strict 19-year
cycle so have no correlation with the leap years and so only the
correlations of corrections to the 19-year cycle need be considered. The
examples of the uniform corrections systems that Mockingbird provided do
have considerable correlation. This results in only a partial
transmission of the jitter and can make it appear that no transmission
occurs at all.
We do not seem to know which uniform correction computus was proposed by
Lichtenberg. It may have been one that has the 43 correction centuries
spaced as evenly as possible. If so, the correlation would be low (but
never completely absent) and so transmission of jitter would be evident.
Also I want to make it clear that the jitter that is transmitted if the
motion of a mean equinox placed exactly once every mean calendar year
and (beginning of day) March 21 in the solar calendar. This is only
slightly different from the jitter defined by Mockingbird above.
Karl
10(07(01
-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Tom Peters
Sent: 20 March 2009 00:20
To: CALNDR-L@...
Subject: Re: Gregorian calendar jitter and lunar calendar in Wikipedia
computus
Op 19-mrt-2009, om 16:26 heeft Palmen, KEV (Karl) het volgende
geschreven:
> Dear Tom and Calendar People
>
> I've found a weakness that occurs in EVERY uniform correction
> system. It
> is three consecutive common century years with only one correction.
> The
> Gregorian System makes at least two corrections in any three
> consecutive
> common century years.
> This causes the minimum number of days in 11 consecutive Metonic
> cycles
> (of 235 lunar months equal to 19 lunisolar years) to be one less than
> for the Gregorian system.
>
Karl,
thank you for your investigations. I do not have the time now to
study this issue as thorough as is necessary. Maybe at some later time.
--
Tom Peters
--
Scanned by iCritical.
« Return to Thread: Gregorian calendar jitter and lunar calendar in Wikipedia computus
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