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Re: Brief addendum and reply
On 2009-05-23, Amos Shapir wrote on the length
of months in the Gregorian calendar:
> It's even simpler if January is appended as month 13 of
> the previous year:
>
> Month_Length = 30 + { [ (month - 2) MOD 5 ] MOD 2 } days
>
Hm, I suppose you mean, for 3 <= M <= 13:
length of month( M ) = ( 31 - (M - 3) mod 5 mod 2 ) d
Michael Deckers.
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Re: Brief addendum and reply
Dear Mike and Calendar People, On Sun, May 24, 2009 at 3:22 PM, MIKE OSSIPOFF <nkklrp@...> wrote:
I'd said:
> > someone pointed out today, no one really knows why Julius chose it. That
> > isn't a good enough reason for us to copy it from him!
>
Mark replied:
> What we need is a good reason not to.
How about so that we'll have a civil calendar that explicitly relates to the natural year, the seasons in particular?
That's not really possible. For one thing, the seasons are opposite in the northern hemisphere compared to the southern hemisphere, but even within a hemisphere, the seasons vary hugely by location. I'm a photographer, and I sometimes participate in what we call challenges. Someone chooses a challenge, which is essentially a theme, and we're supposed to take photos according to the theme. Invariable, someone will choose a season-specific theme, like fall color. It never really works out, because it's highly location specific. Fall color, for example, here in central Texas, generally comes one or two months later than it does in New England.
Then you have tropical parts of the world where you have separate rainy and dry seasons, which are more important than winter vs. summer. But it's not a definite part of the year that is always rainy or dry.
Victor
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Lunar Themelion
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In
its calendar calculations, the Orthodox Church uses something called the
"Lunar Themelion". For example, according to http://www.goarch.org/chapel/kanonion/2009_kanonion-en.pdf,
the Lunar Themelion for 2009 is 15.
I
found the values for the years 2000-2009 and I have listed them here together
with the Epact for each year:
|
Year
|
Lunar Themelion
|
Epact
|
Difference
(mod 30)
|
|
2000
|
24
|
24
|
0
|
|
2001
|
5
|
5
|
0
|
|
2002
|
16
|
16
|
0
|
|
2003
|
27
|
27
|
0
|
|
2004
|
8
|
8
|
0
|
|
2005
|
19
|
19
|
0
|
|
2006
|
12
|
0
|
12
|
|
2007
|
23
|
11
|
12
|
|
2008
|
4
|
22
|
12
|
|
2009
|
15
|
3
|
12
|
What
is the Lunar Themelion? (The Greek word "themelion" means
"basis" or "foundation". ) It obviously has some
relationship to the Epact, but why did it change in 2006?
Cheers,
Claus
Tøndering
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5 Months of 153 days RE: Brief addendum and reply
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Dear Amos and Calendar People
Amos said The
curious fact is that any sequence of 5 consecutive months which does not
include the Feb.-March boundary, contains exactly 153 days.
The five consecutive months Oct, Nov, Dec, Jan and Feb do not
have 153 days.
I’d say “The curious fact is that any sequence of 5
consecutive months which does not include the end of February, contains exactly
153 days.”
Note that Mar, Apr, May, Jun, Jul do have 153 days.
One could be more precise and state “The curious fact is
that any sequence of 5 consecutive months which does not include the end of
February used as a month end, contains exactly 153 days.” to allow 29 September
to 28 February inclusive to be included (which does have 153 days).
Karl
10(09(03
From: East Carolina University Calendar
discussion List [mailto:CALNDR-L@...] On Behalf Of Amos
Shapir
Sent: 23 May 2009 17:12
To: CALNDR-L@...
Subject: Re: Brief addendum and reply
It's
even simpler if January is appended as month 13 of the previous year:
Month_Length = 30 + { [ (month - 2) MOD 5 ]
MOD 2 } days
The curious fact is that any sequence of 5 consecutive months which does not
include the Feb.-March boundary, contains exactly 153 days.
Amos Shapir
Date: Fri, 22 May 2009 18:03:45 -0400
From: irv.bromberg@...
Subject: Re: Brief addendum and reply
To: CALNDR-L@...
On 2009 May 22, at 15:39 , MIKE OSSIPOFF
wrote:
any calendar with a rational,
un-arbitrary month-system would be an improvement over the Roman Calendar.
Irv replies: The Gregorian month
lengths are not arbitrary, they follow a consistent pattern, which is given by:
Month_Length = 30 + { [ month + FLOOR(month
/ 8) ] MOD 2 } days
where month is an integer from 1 to 12 where
January = 1 ... December = 12.
If month = 2 (February) then subtract 2 days
and if Leap Year then add 1 day.
-- Irv Bromberg, Toronto, Canada
What
can you do with the new Windows Live? Find
out
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Re: Brief addendum and reply
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Dear Mike
Please make the subject more informative (rather than “Brief
addendum and reply”).
Karl
From: East Carolina University Calendar
discussion List [mailto:CALNDR-L@...] On Behalf Of MIKE
OSSIPOFF
Sent: 22 May 2009 20:39
To: CALNDR-L@...
Subject: Brief addendum and reply
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Coptic Calendar New Year too RE: Brief addendum and reply
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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: 22 May 2009 20:39
To: CALNDR-L@...
Subject: Brief addendum and reply
.
Of course there's ample historical precedent for starting the year at a
solstice or equinox.
(In fact, our quirky Roman calendar seems to be almost unique in not doing
that)
The Coptic calendar also does not do that. It starts the year on
August 29th in the Julian calendar or August 30th before
a Julian leap year.
Karl
10(09(03
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Re: Coptic Calendar New Year too RE: Brief addendum and reply
On 2009 May 26, at 09:01 , Palmen, KEV (Karl) wrote: From: MIKE OSSIPOFF
Sent: 22 May 2009 20:39 . Of course there's ample historical precedent for starting the year at a solstice or equinox.
(In fact, our quirky Roman calendar seems to be almost unique in not doing that)
Karl wrote: The Coptic calendar also does not do that. It starts the year on August 29th in the Julian calendar or August 30th before a Julian leap year.
Irv adds:
The eastern asian traditional lunisolar calendars (Chinese, Korean, Vietnamese, Japanese) are another example. Although they use accurate astronomical algorithms to reckon the moment of the south solstice, the calendar year starts more than a month later (normally up to almost two months later, but can be up to almost 3 months later if there is a leap 11th or leap 12th month). If I recall correctly, the solstice is required to land in the 11th month, reckoned according to the reference meridian of the respective calendar (Beijing, Seoul, Hanoi, or Tokyo, respectively).
The traditional fixed arithmetic Hebrew calendar also has no direct relationship to any equinox or solstice, having a calendar mean year that is much longer than any point in the astronomical solar cycle, but in particular is about 6 minutes and 25 seconds longer than the mean northward equinoctial year. According to the widely held but misguided opinion that the Hebrew calendar is regulated according to the traditional spring equinox reckoning of Rav Adda bar Ahavah, those equinox moments fall on average 1 day 3 hours 42 minutes 7 parts and 72 moments after the molad of Nisan (occurs exactly in the 12th year of each traditional 19-year cycle), Nisan being the month that is enumerated as month #1.
-- Irv Bromberg, Toronto, Canada
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Hebrew Equinox RE: Coptic Calendar New Year too RE: Brief addendum and reply
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Dear Irv and Calendar People
Irv said According to the widely held but misguided opinion
that the Hebrew calendar is regulated according to the traditional spring
equinox reckoning of Rav Adda bar Ahavah, those equinox moments fall on average
1 day 3 hours 42 minutes 7 parts and 72 moments after the molad of Nisan
(occurs exactly in the 12th year of each traditional 19-year cycle), Nisan
being the month that is enumerated as month #1
The 12th year of the Hebrew Metonic cycle is the year
with an average end and the end point matters because Nisan occurs after the
intercalary month’s place.
This is so, because if you start the Hebrew Metonic Cycle from the
13th year, you get leap month years so:
2 (14th), 5(17th), 7(19th),
10(3rd), 13(6th), 15(8th), 18(11th),
which is the Helios cycle for the 19-year cycle.
Consequently, the average supposed equinox would be exactly as
in the 12th year.
Karl
10(09(03
From: East Carolina University Calendar
discussion List [mailto:CALNDR-L@...] On Behalf Of Irv
Bromberg
Sent: 26 May 2009 15:23
To: CALNDR-L@...
Subject: Re: Coptic Calendar New Year too RE: Brief addendum and reply
On
2009 May 26, at 09:01 , Palmen, KEV (Karl) wrote:
From: MIKE OSSIPOFF
Sent: 22 May 2009 20:39
. Of course there's ample
historical precedent for starting the year at a solstice or equinox.
(In fact, our quirky Roman calendar seems to be
almost unique in not doing that)
Karl wrote: The Coptic
calendar also does not do that. It starts the year on August 29th in
the Julian calendar or August 30th before a Julian leap year.
The
eastern asian traditional lunisolar calendars (Chinese, Korean, Vietnamese,
Japanese) are another example. Although they use accurate astronomical
algorithms to reckon the moment of the south solstice, the calendar year starts
more than a month later (normally up to almost two months later, but can be up
to almost 3 months later if there is a leap 11th or leap 12th month). If
I recall correctly, the solstice is required to land in the 11th month,
reckoned according to the reference meridian of the respective calendar
(Beijing, Seoul, Hanoi, or Tokyo, respectively).
The
traditional fixed arithmetic Hebrew calendar also has no direct relationship to
any equinox or solstice, having a calendar mean year that is much longer than
any point in the astronomical solar cycle, but in particular is about 6 minutes
and 25 seconds longer than the mean northward equinoctial year.
According to the widely held but misguided opinion that the Hebrew
calendar is regulated according to the traditional spring equinox reckoning of
Rav Adda bar Ahavah, those equinox moments fall on average 1 day 3 hours 42
minutes 7 parts and 72 moments after the molad of Nisan (occurs exactly in the
12th year of each traditional 19-year cycle), Nisan being the month that is
enumerated as month #1.
-- Irv Bromberg, Toronto,
Canada
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Re: Lunar Themelion
Claus Tøndering wrote:
In its calendar calculations, the Orthodox Church uses something called the
"Lunar Themelion". For example, according to
http://www.goarch.org/chapel/kanonion/2009_kanonion-en.pdf, the Lunar
Themelion for 2009 is 15.
What is the Lunar Themelion? (The Greek word "themelion" means "basis" or
"foundation". ) It obviously has some relationship to the Epact, but why did
it change in 2006?
_______________________________________________________________
The determination of Easter (Pascha) in the Orthodox Church derives directly from the Coptic Calendar. It is based on a 19-year Metonic Cycle. Year One of the Metonic Cycle was Year One of the Coptic Calendar, which is the (northern) Spring of Year 285 AD. In this year the Epact (or "offset" of lunar to solar calendars) was Zero. In each successive year of the Cycle the Epact increases by 11 (meaning that the lunar dates come 11 days earlier each year relative to the solar dates), but any time the number is greater than 30, reduce it by 30. (This is equivalent to adding a 30-day intercalary month to keep the lunar dates in phase with the northern Spring Equinox.)
For the Years 2000 through 2009 AD, this gives a (Julian) Epact as follows:
2000 25
2001 6
2002 17
2003 28
2004 9
2005 20
2006 1
2007 12
2008 23
2009 4
Note that these are not the same as the Gregorian Epacts which you cited in your table.
The Julian Epact gives the date of the Paschal Full Moon (Luna XIV) on the Coptic Calendar, as follows: Lunar Date is 40 minus the Epact; if greater than 30, then subtract 30. This gives the day of the Month for the Pascal Full Moon, in the APPROPRIATE Month of the Coptic Calendar, being Month 8 (Pharmuthi) unless the date is equal to or greater than 25, in which case it refers to Month 7 (Phamenoth). This gives the proper limits for Easter on the Julian Calendar, with the earliest Luna XIV being 25 Phamenoth which is always March 21 Julian.
The Tables as commonly published obscure somewhat this direct derivation. They use a number called the "Lunar Foundation" (in Greek, Themelion tis selenis. In Slavonic, Osnovanie), which is always 11 more than the Julian Epact. This gives the lunar dates as 51 minus the Themelion; if greater than 30, then subtract 30. Results will be same as above.
The Slavonic Tables (found online at http://www.liturgy.ru/grafics/tipicon/page.php?p=1141&cd=&k= ) give this number Osnovanie for every year in the 532-year combined cycle (19-year Metonic Cycle times 28-year Solar Cycle). They also list the Coptic Lunar Date as discussed above, unfortunately under the misleading title of "Epakta". (But everybody knows that an Epact should Increase by 11 days from year to year, whereas these number Decrease by 11 days from year to year.)
The Greek Tables (which I have studied in a Book of the Canons, published by the Church of Greece in Athens, 1859, are consistent with the above understanding.
The references you give show an unfortunate confusion. For the years 2000 through 2005, they listed the Gregorian Epact, falsely labelling it as the Themelion. For the years 2006 through 2009, they got it right, properly listing the Julian Themelion as discussed above. This accounts for the discontinuity you observed.
-- Robert H. Douglass
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Re: Coptic Calendar New Year too RE: Brief addendum and reply
Irv Bromberg wrote:
> According to the widely held but misguided opinion that the Hebrew calendar is
> regulated according to the traditional spring equinox reckoning of Rav Adda...
Not misguided at all. Take the moment of the Tekufah (northern Spring Equinox) of Rav Adda, and subtract exactly 16 days. The first Molad occurring after that instant will be the Molad of Nissan, according to the Traditional Fixed Arithmetic Hebrew Calendar. This allows the Hebrew Calendar to be correctly computed with no explicit regard whatsoever for the 19-year Metonic Cycle. Everything just follows naturally from the simple relationship cited here.
-- Robert H. Douglass
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Re: Coptic Calendar New Year too RE: Brief addendum and reply
On 2009 May 26, at 12:43 , RDoug wrote: According to the widely held but misguided opinion that the Hebrew calendar is regulated according to the traditional spring equinox reckoning of Rav Adda...
Not misguided at all. Take the moment of the Tekufah (northern Spring
Equinox) of Rav Adda, and subtract exactly 16 days. The first Molad
occurring after that instant will be the Molad of Nissan, according to the
Traditional Fixed Arithmetic Hebrew Calendar.
Irv replies: Hah! You took the bait!
The mean year according to Adda = 235 x molad interval / 19, which is exactly the same as that of the Hebrew calendar. Therefore they appear to have a relationship.
The latest equinox moments, regardless of how the equinox is reckoned, occur in the 16th year of each 19-year cycle.
According to Adda's reckoning, in that year the equinox is 15d 3h 25m 7 parts and 36 moments after the molad of Nisan. (This is based on Maimonides' description of the arithmetic, in chapter 10 of "Sanctification of the Month", because I am aware of no earlier non-ambiguous traditional source for Adda's arithmetic, although Maimonides didn't cite Rav Adda by name.)
The latest equinox moments according to Adda's method expressed in terms of the time and traditional fixed arithmetic Hebrew calendar date is just shy of an hour before noon on the 16th of Nisan. In this case the reference meridian is undefined. (Most people assume it refers to Jerusalem, but I am aware of no primary traditional source that says so. Astronomically it is impossible to determine where the reference meridian is, because the mean year by this method is far in excess of the actual astronomical mean northward equinoctial year, about 6m 25s as I stated previously.) Such late equinox moments only occur about once or twice per century, but the equinox according to Adda occurred just shy of 2 hours before noon on the 16th of Nisan in Hebrew year 4120, the very next year after it is believed that Hillel ben Yehudah fixed the Hebrew calendar.
The point is that most people believe / argue that the cutoff limit for reckoning the leap status of the Hebrew year is somewhere prior to the 16th of Nisan, but in actuality the only way to perfectly reproduce the fixed dates of the traditional Hebrew calendar is to use a cutoff time of 1h before noon on the 16th of Nisan. Nobody does that. Hebrew calendar dates are instead reckoned by finding the molad of Tishrei (implicit in this is the 19-year leap cycle), applying the Rosh HaShanah postponement rules, determining the length of the year (which gives us the length of Cheshvan and Kislev and if it is a leap year then Adar 1 has 30 days and there is a 29-day Adar 2), and all other features of the calendar year are fixed. Nowhere in there is there any reckoning of any equinox by any method.
All this was explained by Maimonides -- the arithmetic procedures that he outlined in chapters 6 to 8 of his book are exactly the way the calendar used today works. Variations of calendrical arithmetic can reproduce the same dates, but if any dates differ then Maimonides' method is de facto the correct one. For example, the arithmetic of Dershowitz & Reingold differs substantially from Maimonides' procedure, but when properly implemented using an arbitrary precision calculation engine (exact arithmetic) their method exactly matches all dates obtained by Maimonides' method. (Interestingly, Maimonides' method requires more computer code to implement but executes about 2 orders of magnitude faster than the seemingly tight but highly recursive code of D&R.)
My own implementation of Hebrew calendar arithmetic, as documented on my Rectified Hebrew calendar web page at <http://individual.utoronto.ca/kalendis/hebrew/rect.htm>, is a novel, non-recursive algorithm that also reproduces the dates of Maimonides' method and similarly contains no reckoning of any equinox moments, but has the advantage that of those mentioned it is the only method that is also compatible with alternative leap cycles, such as the 353-year cycle, and with progressively shorter molad intervals. In the "traditional mode", it employs the 19-year cycle with traditional molad intervals, and reproduces all traditional dates.
It makes perfect sense to have the latest allowable equinox moment land an hour before noon on the 16th of Nisan, because that would ensure that the omer (new spring barley) offering could be brought at the earliest possible moment in the spring season. The omer offering took place after the morning services in the Temple in Jerusalem, so earliest possible time for that offering would have been an hour before noon, but in practice probably almost always after noon.
RDoug continued: This allows the Hebrew Calendar to be correctly computed with no explicit regard whatsoever for the
19-year Metonic Cycle. Everything just follows naturally from the simple relationship cited here.
Irv continues: So the way that Hebrew calendar arithmetic is actually carried out (if done properly), it is correctly computed with no explicit regard whatsoever for the equinox moment (regardless of how such a moment might be reckoned). The 19-year cycle is all-important in the reckoning of the molad of Tishrei. (In this case the molad method suggested by D&R is exceptionally simple and efficient, whereas it is their handling of the postponement rules that is highly recursive.)
As I mentioned, it is theoretically possible to reproduce Hebrew dates by using 1h before Noon on the 16th of Nisan as an equinox cutoff time. It would be sensible to actually use that cutoff if the actual astronomical equinox were being used, especially if the new Sanhedrin re-establishes the annual omer offering. The calendrical arithmetic required to make an equinox-based calendar that otherwise works like the traditional fixed Hebrew calendar is considerably more cumbersome when approached from that starting point. I have only succeeded in implementing it with a Rosh HaShanah advance/postpone rule (as described in the Talmud tractate Rosh HaShanah) instead of the traditional postpone/double-postpone rule (not documented in the Talmud), but I have no reason to believe that it is impossible to implement the latter.
For more information, see the following web pages:
-- Irv Bromberg, Toronto, Canada
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Re: Coptic Calendar New Year too RE: Brief addendum and reply
Irv replies: > Hah! You took the bait!
Not so fast. Consider the discussion posted below:
> The point is that most people believe / argue that the cutoff limit for reckoning the leap status of the Hebrew year is somewhere prior to the 16th of Nisan, but in actuality the only way to perfectly reproduce the fixed dates of the traditional Hebrew calendar is to use a cutoff time of 1h before noon on the 16th of Nisan. Nobody does that.
I do. It works just fine. Or rather, my cutoff for the Molad is exactly 16 days before the moment of the Tekufah, which gives identical results in all cases. When combined with the Molad Zakein rule applied to the First of Tishrei, it assures that the Tekufah never occurs later than the 16th of Nissan on the Hebrew Calendar. Thus the Day of the Omer (16th of Nissan) never takes place before the first day of Spring.
> Irv continues: So the way that Hebrew calendar arithmetic is actually carried out (if done properly)...
This statement is too limiting. I have several independent ways of "actually carrying out" the Calendar arithmetic. Since they all give identical results in all cases, they CANNOT be considered "improper" in any sense.
> As I mentioned, it is theoretically possible to reproduce Hebrew dates by using 1h before Noon on the 16th of Nisan as an equinox cutoff time.
Yes, this works just fine. So your post is Confirming, Not Refuting, my own.
> The calendrical arithmetic required to make an equinox-based calendar that otherwise works like the traditional fixed Hebrew calendar is considerably more cumbersome when approached from that starting point.
I find it quite simple, actually. First, we need a convenient reference point for the Tekufah. Two of these exist. The first is in Hebrew Year 1, when the Tekufah occurred at exactly Zero Hours at the start of Hebrew Wednesday, April 2, -3759 Julian which is Day 179 of the Hebrew Calendar, labelled as 29 Adar.
The second is exactly 4104 years later... the Wednesday in question is March 20, 345 AD Julian, which is 29 Adar of Hebrew Year 4105. This was the day of the Astronomical Equinox and of the Astronomical New Moon. The Tekufah occurred exactly one hour before the Zero hour of this date. This is because 4104 = 216 x 19 years = 50760 lunations = 1498973 days less exactly one hour.
From one year to the next, the Tekufah advances by 365.2468222 days (which over 19 years totals 6939.6896 days, identical by definition to the duration of 235 Hebrew Lunations).
This can be adapted to a handy technique to accurately calculate the Hebrew Calendar for any year, using a pocket calculator, independent of the traditional methods.
-- Robert H. Douglass
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Re: Coptic Calendar New Year too RE: Brief addendum and reply
On 2009 May 26, at 15:17 , RDoug wrote: Irv Bromberg wrote:
The point is that most people believe / argue that the cutoff limit for
reckoning the leap status of the Hebrew year is somewhere prior to the
16th of Nisan, but in actuality the only way to perfectly reproduce the
fixed dates of the traditional Hebrew calendar is to use a cutoff time of
1h before noon on the 16th of Nisan. Nobody does that.
RDoug says: I do. It works just fine. Or rather, my cutoff for the Molad is exactly 16
days before the moment of the Tekufah, which gives identical results in all cases.
Irv replies: That's impossible, although it may seem to work for extended periods of times. The mismatches will happen when the Tekufah according to Adda is supposed to land on the 16th of Nisan. Since this occurs only once or twice per century, a cutoff of 16 days will seem to work most of the time.
Note that the beginning of the 16th of Nisan equals 15 elapsed days within the month of Nisan, exactly halfway through the 30-day month.
RDoug: When combined with the Molad Zakein rule applied to the First of
Tishrei, it assures that the Tekufah never occurs later than the 16th of
Nissan on the Hebrew Calendar. Thus the Day of the Omer (16th of Nissan)
never takes place before the first day of Spring.
Irv replies: Right, but my point was that a later limit could be used and still ensure that the bringing of the omer offering would be within the spring season. This has the advantage that the omer can be brought at the earliest possible moment. What is implied? If the tekufah is on the 16th of Nisan but before an hour before noon, your rule would make it a leap year, so the omer would not be brought until 30 days later, but the traditional rule would not make it a leap year. The choice is always between being "in its proper time" or "30 days late" (due to the length of the inserted leap month).
The molad zakein rule implicitly includes the 3rd and 4th Rosh HaShanah postponement rules, since they are just molad zakein postponements affecting the year after or the year before, causing an illegal year length if the present year is not postponed, but are you including the rule that Rosh HaShanah can't fall on Sunday, Wednesday, or Friday? That rule is responsible, together the the molad zakein rule, for causing double-day postponements, which are quite common. It is the double-day postponements that I found to be the "real killer" when attempting to implement a Hebrew calendar based on an equinox reckoning, and I suspect that that is the reason why standard Hebrew calendar arithmetic doesn't work that way.
Irv continues: So the way that Hebrew calendar arithmetic is actually
carried out (if done properly)...
RDoug continued: This statement is too limiting. I have several independent ways of
"actually carrying out" the Calendar arithmetic. Since they all give
identical results in all cases, they CANNOT be considered "improper" in any
sense.
Irv replies: Specifically what I meant is that to validate any algorithm purported to calculate Hebrew calendar dates correctly, it is necessary to verify date identity between a known proper algorithm and the algorithm being evaluated for every calendar date from the calendar epoch until the beginning of the next full repeat of the Hebrew calendar (same weekdays, same moladot, etc.). That is the "first" 689472 years of the Hebrew calendar! Don't panic, a modern computer can carry this out in a few moments. If there is not perfect agreement on every date in this full repeat cycle, then at least one of the algorithms is defective.
Another aspect of the validation is as recommended by Dershowitz & Reingold: verify that every Hebrew date can be converted to a fixed day number and back again without change, and from a fixed day number to a Hebrew date and back again without change. This ensures that the calendar implementation / conversion routines are logically consistent.
A defective algorithm may yield mismatches in either of the above evaluations, or may simply crash.
Irv wrote: As I mentioned, it is theoretically possible to reproduce Hebrew dates by
using 1h before Noon on the 16th of Nisan as an equinox cutoff time.
RDoug: Yes, this works just fine. So your post is Confirming, Not Refuting, my own.
Irv replies: Right, but if one uses the sunset at the beginning of the 16th of Nisan as the equinox cutoff time then dates won't match for cases where the equinox would otherwise land between that sunset and 1h before noon on the 16th of Nisan. There will be a one month difference in such cases, and sometimes the Rosh HaShanah postponement rules will be affected for the prior or next year.
Irv wrote: The calendrical arithmetic required to make an equinox-based calendar that
otherwise works like the traditional fixed Hebrew calendar is considerably
more cumbersome when approached from that starting point.
RDoug replied: I find it quite simple, actually. <remaining details snipped out>
Irv replies: Calculation of the moment of the Tekufah is not the cumbersome part, it just requires the epoch, the number of elapsed years, and the mean year length (or alternatively the number of elapsed seasons and the mean season length which is 1/4 of the mean year length). The cumbersome part is the multi-step procedure required to then find the prior and next Rosh HaShanah, apply the postponement rules, check for illegal year lengths, and I dunno what else because I could never get it to work that way except using the traditionally unacceptable advance/postpone logic.
-- Irv Bromberg, Toronto, Canada
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Re: Coptic Calendar New Year too RE: Brief addendum and reply
> Irv replies: That's impossible, although it may seem to work for extended periods of times. The mismatches will happen when the Tekufah according to Adda is supposed to land on the 16th of Nisan. Since this occurs only once or twice per century, a cutoff of 16 days will seem to work most of the time.
Impossible or not, it does work (in all cases).
> If the tekufah is on the 16th of Nisan but before an hour before noon, your rule would make it a leap year, so the omer would not be brought until 30 days later, but the traditional rule would not make it a leap year.
Not at all. I said that the 16th of Nissan would never occur before the DAY of the Tekufah, REGARDLESS of what time of day that event should occur.
> The molad zakein rule implicitly includes the 3rd and 4th Rosh HaShanah postponement rules, since they are just molad zakein postponements affecting the year after or the year before, causing an illegal year length if the present year is not postponed, but are you including the rule that Rosh HaShanah can't fall on Sunday, Wednesday, or Friday?
I am not ignoring any of the standard postponement rules. Rather, the application of Molad Zakein to the First of Tishrei carries with it implicitly an additional postponement rule, which is as follows: The Molad of Nissan shall be the first Molad following the instant which is exactly 16 days before the instant of the Tekufah of Rav Adda. And if in any case the Tekufah should seem to land sometime on the 17th day of Nissan (measuring from the day of the Molad as Day 1), this will no longer be the case when a delay of (at least) one day is made to the First of Tishrei (using the Molad occurring six lunations after the Molad of Nissan as just determined), based on Molad Zakein for the First of Tishrei, then re-computing the First of Nissan accordingly (always 177 days before the First of Tishrei as corrected).
> Irv replies: Specifically what I meant is that to validate any algorithm purported to calculate Hebrew calendar dates correctly, it is necessary to verify date identity between a known proper algorithm and the algorithm being evaluated for every calendar date from the calendar epoch until the beginning of the next full repeat of the Hebrew calendar (same weekdays, same moladot, etc.). That is the "first" 689472 years of the Hebrew calendar! Don't panic, a modern computer can carry this out in a few moments.
Been there, done that.
> Another aspect of the validation is as recommended by Dershowitz & Reingold: verify that every Hebrew date can be converted to a fixed day number and back again without change, and from a fixed day number to a Hebrew date and back again without change. This ensures that the calendar implementation / conversion routines are logically consistent.
Been there, done that.
> A defective algorithm may yield mismatches in either of the above evaluations, or may simply crash.
Been there, done that.
> Irv replies: Right, but if one uses the sunset at the beginning of the 16th of Nisan as the equinox cutoff time then dates won't match for cases where the equinox would otherwise land between that sunset and 1h before noon on the 16th of Nisan.
That's why we do NOT use "sunset at the beginning of the 16th", because it doesn't work that way. Like I said.
> Irv replies: Calculation of the moment of the Tekufah is not the cumbersome part, it just requires the epoch, the number of elapsed years, and the mean year length (or alternatively the number of elapsed seasons and the mean season length which is 1/4 of the mean year length). The **cumbersome** part is the multi-step procedure required to then find the prior and next Rosh HaShanah, apply the postponement rules, check for illegal year lengths, and I dunno what else because I could never get it to work that way except using the traditionally unacceptable advance/postpone logic.
Sorry, I thought that was the easy part. I guess it just depends how you implement the Algorithms. The reason I thought working with the Tekufah might be the tricky part is that nobody else (including yourself) seems to have got it to work. Of course, that does not indicate any degree of intrinsic difficulty at all, once the proper approach has been conceived of.
-- Robert H. Douglass
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Re: Brief addendum and reply
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I'd said:
> > What? The book _365 Days_ says that Julius Caesar's year perfectly > > alternated the 31-day months throughout the year.
Mark replied:
> No. The original Julian calendar, from day 1, had the same structure > it has today, complete with February weirdness. It was all inherited > from the Republican calendar, with only the lengths of the months > adjusted. It's true that Quintilis and Sextilius were renamed in > honor of Julius and Augustus Caesar, but in each case it wasn't the > ruler's own idea, and there was no shifting of days to make them > longer.
I never said it was the Augustus's idea, though of course it's impossible to know that he didn't originate the suggestion. Julius had died before a month was named for him.
This is another instance in which Mark disagrees with Professor Emiritus Irvin, of Colorado State. Sure maybe the professor is wrong...or maybe not.
If the re-named Sextilius/Augustus wasn't augmented with a day taken from February, then it isn't just Prof. Irvin who was wrong--it was all the authors that I've read on the subject. Is everyone else wrong, Mark?
And, Mark, if you could be mistaken on that point, might you also be mistaken in your claim that, by all reasonable estimates, January 1, 46 B.C. couldn't have been a new moon? After all, you later said that, on that matter, the only thing you were sure of is that you weren't sure of anything. I'm not saying that you're necessarily mistaken on that, only that it's a possibility. Anyway, the new moon is the only explanation that I've ever heard, for why Julius began his year when he did.
Mike Ossipoff
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Re: Brief addendum and reply
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Victor--
I'd said:
> > someone pointed out today, no one really knows why Julius chose it. That > > isn't a good enough reason for us to copy it from him! >
Mark replied:
> What we need is a good reason not to.
I then said:
How about so that we'll have a civil calendar that explicitly relates to the natural year, the seasons in particular?
You commented:
That's not really possible. [You then gave reasons why it isn't possible for the calendar to exactly model our seasons]
...But please note that I said "explicitly relates to...", not "exactly models..."
You continue:
For one thing, the seasons are opposite in the northern hemisphere compared to the southern hemisphere
I reply:
This anti-hemisphere-ism can be taken too far. Should colleges stop referring to their "Spring break", and their "Fall quarter"?
No, because people of the other hemisphere are unlikely to show up and think that they're referring to Australian spring or fall.
For local use, then, there is no reason not to call the season-quarters by the local names of the seasons.
Asimov suggested numbering the quarters, to avoid hemisphere-ism. I suggest doing so only when communicating with people of both hemispheres.
You continued:
, but even within a hemisphere, the seasons vary hugely by location.
Of course. I've read estimates that typically the seasons' timelag behind the sun's declination varies from place to place, from a month to a month and a half. And that some places it's less than a month or more than a month and a half.
That's why I suggested, as one possibilitly, using an estimated average seasonal timelag. I tentatively suggested averaging the typical extremes of 1 and 1.5 months, and using 1.25 months. Thirty-eight days. As I mentioned, in Santa Cruz., California, the seasonal-lag is typically 38 days. I looked at temperature records for a few years, and added up the "cold" before and after various winter days. I added up the temperatures before and after various winter days, and found that the middle of winter determined in that way was typically January 28th. It was a quite stable measurement. The only time it differed from January 28th was in an El Nino year. Of course I only check a few years, but it was enough to show that the date was pretty stable.
It isn't a matter of precisely modeling the seasons. It's a matter of explicitly referring to them, and making the effort.
I have no objection to just starting the year on the winter solstice, or even the summer solstice or an equinox, because, as I said, that amounts to assuming a seasonal-lag of 1.5 months. If the lag is different where you live, then you can easily correct for the difference between your local seasonal-lag and that assumed by the calendar (whether that's 1.5 months, 1.25 months, or something else).
You continued:
Invariable, someone will choose a season-specific theme, like fall color. It never really works out, because it's highly location specific. Fall color, for example, here in central Texas, generally comes one or two months later than it does in New England.
I reply:
So then an explicitly seasonal calendar would need to be corrected for your area, as it would for most places. The point is that at least the calendar would be making the effort. If we're going to name times of year in some way, doesn't it make the most sense to explicitly refer to the seasons, even if it isn't possible to do so with great accuracy?
You continued:
Then you have tropical parts of the world where you have separate rainy and dry seasons, which are more important than winter vs. summer. But it's not a definite part of the year that is always rainy or dry.
I reply:
Ok, I admit that's a problem. Completely different kinds of seasons in the tripics. But still, a calendar that at least tries in some way to roughly match the seasonal timelag, that calendar is a better basis for comparison to any local seasons than is the Roman Calendar, which, by its starting date, is completely irrelevant to the seasons.
So, ask not how perfectly a seasonal calendar can model the seasons. Ask instead whether the Roman calendar has any relevence to them at all.
Mike Ossipoff
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Sorry Brij--I confused you with someone else
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It was Mikail Petin, not Brij, who suggested eliminating the 7-day week, and so, my apologies, Brij.
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Re: Brief addendum and reply
On Tue, May 26, 2009 at 6:30 PM, MIKE OSSIPOFF < nkklrp@...> wrote:
>> No. The original Julian calendar, from day 1, had the same structure
>> it has today, complete with February weirdness.
> This is another instance in which Mark disagrees with Professor Emiritus
> Irvin, of Colorado State. Sure maybe the professor is wrong...or maybe not.
Well, let's look at some sources that agree with me:
1. The Oxford Book of the Year
2. Calendrical Calculations
3. Wikipedia
None of those is primary, of course. One good primary source: in the
first book of the Saturnalia, Macrobius's introduction of the god
Janus leads to a discussion of the history of the Roman calendar,
which agrees with the above.
The story about the emperors stealing days from February to augment
their eponymous months originated with Sacrobosco in the 13th century.
It has been debunked, but it is still widely believed. Even by
professors emeriti, apparently. :)
--
Mark J. Reed < markjreed@...>
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Re: Brief addendum and reply
Dear Mike, On Tue, May 26, 2009 at 5:56 PM, MIKE OSSIPOFF <nkklrp@...> wrote:
That's not really possible. [You then gave reasons why it isn't possible for the calendar to exactly model our seasons]
...But please note that I said "explicitly relates to...", not "exactly models..."
OK.
Of course. I've read estimates that typically the seasons' timelag behind the sun's declination varies from place to place, from a month to a month and a half. And that some places it's less than a month or more than a month and a half.
I would go further than that. Here in central Texas, winter is almost like a conglomeration of fall, winter, and spring. Live oaks, for example, shed their leaves in the end of what is normally considered winter and the start of spring. Redbuds begin blooming in early February. Loquats bloom in December. Summer typically seems to last from mid-May to mid-October, nearly half the year.
That's why I suggested, as one possibilitly, using an estimated average seasonal timelag. I tentatively suggested averaging the typical extremes of 1 and 1.5 months, and using 1.25 months. Thirty-eight days. As I mentioned, in Santa Cruz., California, the seasonal-lag is typically 38 days. I looked at temperature records for a few years, and added up the "cold" before and after various winter days. I added up the temperatures before and after various winter days, and found that the middle of winter determined in that way was typically January 28th. It was a quite stable measurement. The only time it differed from January 28th was in an El Nino year. Of course I only check a few years, but it was enough to show that the date was pretty stable.
January is typically the coldest month in the northern hemisphere.
It isn't a matter of precisely modeling the seasons. It's a matter of explicitly referring to them, and making the effort.
So how is it any different than what we do now? Typically, I hear winter described as the three months starting on the winter solstice. Spring is the three months starting on the vernal equinox, etc. That makes for a good match with your suggested scheme I think.
I have no objection to just starting the year on the winter solstice, or even the summer solstice or an equinox, because, as I said, that amounts to assuming a seasonal-lag of 1.5 months. If the lag is different where you live, then you can easily correct for the difference between your local seasonal-lag and that assumed by the calendar (whether that's 1.5 months, 1.25 months, or something else).
OK. But I thought you were proposing a formal calendar change designed to align with the seasons. My main point is that you can't align with the seasons because they're too variable. They're already about as aligned as they can be, I think.
You continued:
Invariable, someone will choose a season-specific theme, like fall color. It never really works out, because it's highly location specific. Fall color, for example, here in central Texas, generally comes one or two months later than it does in New England.
I reply:
So then an explicitly seasonal calendar would need to be corrected for your area, as it would for most places. The point is that at least the calendar would be making the effort. If we're going to name times of year in some way, doesn't it make the most sense to explicitly refer to the seasons, even if it isn't possible to do so with great accuracy?
If it's not possible to peg the seasons with any specificity, why is it helpful to construct a calendar with such specificity?
You continued:
Then you have tropical parts of the world where you have separate rainy and dry seasons, which are more important than winter vs. summer. But it's not a definite part of the year that is always rainy or dry.
I reply:
Ok, I admit that's a problem. Completely different kinds of seasons in the tripics. But still, a calendar that at least tries in some way to roughly match the seasonal timelag, that calendar is a better basis for comparison to any local seasons than is the Roman Calendar, which, by its starting date, is completely irrelevant to the seasons.
So, ask not how perfectly a seasonal calendar can model the seasons. Ask instead whether the Roman calendar has any relevence to them at all.
It does. Dividing the year in what I'll term the Gregorian calendar by quarters, starting with January, serves to mark the seasons just as well as what you suggest, in my opinion.
Victor
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Re: Coptic Calendar New Year too RE: Brief addendum and reply
Dear Robert and Calendarists:
Robert's procedure is, if I understand correctly:
To find the date of Rosh HaShanah for a given Hebrew year...
Compute the Tekufat Nisan according to Rav Adda for the previous spring. The molad of that month of Nisan is the molad that is not more than 16 days earlier if it exists, otherwise the following molad (in which case the tekufah is before the molad). The molad of Tishrei for the given Hebrew year is 6 x (molad interval) later. Apply the standard Rosh HaShanah postponement rules.
To determine if the given year is a leap year, find the Tekufat Nisan according to Rav Adda for the spring in the given year. The molad of the month of Nisan in the given year is the molad that is not more than 16 days earlier if it exists, otherwise the following molad. Subtract this molad from the one computed for the previous month of Nisan. If that difference is 13 x (molad interval) then the given year is a leap year.
For this algorithm, a crude cutoff time of 16 days works because the latest allowable tekufah is 15d 3h 25m 7 parts 36 moments after the molad and the next possible tekufah timing relative to the molad would be 1/19 of a molad interval = 1+272953/492480 days = 1d 13h 18m 1 part 72 moments later, which at 16 days 16 hours 43 minutes 9 parts 32 moments would put it well past Robert's 16-day cutoff.
My cutoff time of 1h before noon on the 16th of Nisan referred to the time of day on the calendar date 16th of Nisan.
Robert's method of calculating relative to the molad is much simpler, and is perfectly valid for reproducing traditional fixed arithmetic Hebrew calendar dates. Although the 19-year cycle is not explicitly used, it is implicit in that Adda's tekufah mean year is a multiple of 19 and a multiple of the molad interval and a multiple of 235, which is the number of months in 19 years.
Robert's method does allow the tekufah to land on the 16th of Nisan, when it occasionally ought to.
Can it be adapted to more accurate Hebrew calendar arithmetic, for example using a 353-year cycle with 4366 months per cycle, still using the traditional molad? In such a case the time of day of tekufah moments (reckoned with a mean year of 4366 x molad interval / 353 = 365 days 5 hours 49 minutes 1 part 39 moments) can occur at 1/353 day increments relative to the molad, so the cutoff time would have to be specified to higher precision. Is it possible that exactly 16 days will always work?
How about when a progressively shorter molad interval is used? In that case the tekufah moments can occur at any time of day relative to the progressive molad (or actual mean lunar conjunction for some specified reference meridian), so the cutoff would have to be specified to some acceptable level of precision. Again, is it possible that exactly 16 days will always work?
By "will always work", I mean that the tekufah, however it is reckoned, shall not land later than 1h before noon on the 16th of Nisan, for the omer offering to be as early as possible on that day within the spring season. If exactly 16 days doesn't yield that, then the molad-relative cutoff limit can be incrementally adjusted to quantify the relationship between molad-relative cutoff limit and the latest moment of the tekufah on the 16th of Nisan, to allow the optimum to be selected.
-- Irv Bromberg, Toronto, Canada
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