Proceedings 1982 Vatican Conference online

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Proceedings 1982 Vatican Conference online

Gent van R.H.
Hi,  

A new feature of the NASA-ADS website (http://www.adsabs.harvard.edu/) is
the possibility to do a full text search in the hundreds of volumes of
digitized journals and other astronomical publications.

Go to

http://adsabs.harvard.edu/fulltext_service.html

and enter appropriate search words such as Easter, Gregorian calendar,
Islamic calendar, etc. to find numerous references to online articles
discussing calendars.

One of the nice surprises is the following link

http://articles.adsabs.harvard.edu//full/book/grc../1983//0000001,001.html

to the complete proceedings of the 1982 Vatican conference on the 400th
anniversary to the Gregorian reform of the calendar.

Best wishes to all for the New Year,

=======================================================
* Robert H. van Gent                                  *
* E-mail: [hidden email]                     *
* Homepage: http://www.phys.uu.nl/~vgent/homepage.htm *
=======================================================
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Re: Proceedings 1982 Vatican Conference online

Joan Griffith
Dear Robert,

This is a wonderful resource!! I have been wanting to read
http://articles.adsabs.harvard.edu//full/book/grc../1983//0000001,001.html
and I had no idea how I would ever find it. (It might be in the US
Library of Congress, which is a hop & a skip and at least one day off
from work to get anything...)

Thanks so much for being such a marvelous person. (Once, one of my
aims in life was to know everything, something I am far, far, far
from, but it's a fine thing to know somebody who does!
Happy New Year to you & your family.

Joan



On 12/30/05, Gent van R.H. <[hidden email]> wrote:

> Hi,
>
> A new feature of the NASA-ADS website (http://www.adsabs.harvard.edu/) is
> the possibility to do a full text search in the hundreds of volumes of
> digitized journals and other astronomical publications.
>
> Go to
>
> http://adsabs.harvard.edu/fulltext_service.html
>
> and enter appropriate search words such as Easter, Gregorian calendar,
> Islamic calendar, etc. to find numerous references to online articles
> discussing calendars.
>
> One of the nice surprises is the following link
>
> http://articles.adsabs.harvard.edu//full/book/grc../1983//0000001,001.html
>
> to the complete proceedings of the 1982 Vatican conference on the 400th
> anniversary to the Gregorian reform of the calendar.
>
> Best wishes to all for the New Year,
>
> =======================================================
> * Robert H. van Gent                                  *
> * E-mail: [hidden email]                     *
> * Homepage: http://www.phys.uu.nl/~vgent/homepage.htm *
> =======================================================
>


--
Joan
A single person, sitting
alone reading a book one evening, suddenly stands up and strides to the
phöne. "I feel nervous about calling you up out of the blue, but I'd
really like to spend some time with you." In such moments destinies shift,
new pathways open up.
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Re: Proceedings 1982 Vatican Conference online

Gent van R.H.
Joan Griffith wrote:

> Once, one of my aims in life was to know everything, something I am
> far, far, far from, but it's a fine thing to know somebody who does!

Sadly, the more one knows, the more evident the gaps in one's knowledge
become.

=======================================================
* Robert H. van Gent                                  *
* E-mail: [hidden email]                     *
* Homepage: http://www.phys.uu.nl/~vgent/homepage.htm *
=======================================================
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Re: Proceedings 1982 Vatican Conference online

Joan Griffith
Hi,
I just read *somewhere* that your mind holds on to only 70% of what
you read AND hear (which explains why I remember only things I take
notes on...)  It's very daunting to see those gaps, but it's very
encouraging to know there is someone who can help to fill them in from
time to time.
Joan

On 12/30/05, Gent van R.H. <[hidden email]> wrote:

> Joan Griffith wrote:
>
> > Once, one of my aims in life was to know everything, something I am
> > far, far, far from, but it's a fine thing to know somebody who does!
>
> Sadly, the more one knows, the more evident the gaps in one's knowledge
> become.
>
> =======================================================
> * Robert H. van Gent                                  *
> * E-mail: [hidden email]                     *
> * Homepage: http://www.phys.uu.nl/~vgent/homepage.htm *
> =======================================================
>


--
Joan
A single person, sitting
alone reading a book one evening, suddenly stands up and strides to the
phöne. "I feel nervous about calling you up out of the blue, but I'd
really like to spend some time with you." In such moments destinies shift,
new pathways open up.
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Re: Proceedings 1982 Vatican Conference online

Irv Bromberg
In reply to this post by Gent van R.H.
On Dec 30, 2005, at 10:00, Gent van R.H. wrote:
> http://adsabs.harvard.edu/fulltext_service.html

BROMBERG says:  That is great -- THANKS!

> One of the nice surprises is the following link
> http://articles.adsabs.harvard.edu//full/book/grc../1983// 
> 0000001,001.html
>
> to the complete proceedings of the 1982 Vatican conference on the  
> 400th anniversary to the Gregorian reform of the calendar.

BROMBERG says:

They found a reason to print 323 pages??  (Silly me, I was looking for  
a way to download all of it as one PDF...)
I hope that somebody who is a much faster reader than I might highlight  
some of the interesting pages!
Is there any hint of calendar reform being needed mentioned in the  
proceedings?

-- Irv Bromberg, Toronto, Canada

<http://www.sym454.org/>
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Re: Proceedings 1982 Vatican Conference online

Joan Griffith
You can compare Owen Gingrich's comments on Robert Newton's "Crime of
Claudius Ptolemy"  with the article in Dio (August 1994, DIO 4.1).

Joan


On 12/30/05, Irv Bromberg <[hidden email]> wrote:

> On Dec 30, 2005, at 10:00, Gent van R.H. wrote:
> > http://adsabs.harvard.edu/fulltext_service.html
>
> BROMBERG says:  That is great -- THANKS!
>
> > One of the nice surprises is the following link
> > http://articles.adsabs.harvard.edu//full/book/grc../1983//
> > 0000001,001.html
> >
> > to the complete proceedings of the 1982 Vatican conference on the
> > 400th anniversary to the Gregorian reform of the calendar.
>
> BROMBERG says:
>
> They found a reason to print 323 pages??  (Silly me, I was looking for
> a way to download all of it as one PDF...)
> I hope that somebody who is a much faster reader than I might highlight
> some of the interesting pages!
> Is there any hint of calendar reform being needed mentioned in the
> proceedings?
>
> -- Irv Bromberg, Toronto, Canada
>
> <http://www.sym454.org/>
>


--
Joan
A single person, sitting
alone reading a book one evening, suddenly stands up and strides to the
phöne. "I feel nervous about calling you up out of the blue, but I'd
really like to spend some time with you." In such moments destinies shift,
new pathways open up.
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Re: Proceedings 1982 Vatican Conference online

Victor Engel
In reply to this post by Irv Bromberg
Dear Irv, and Calendar People,

On Fri, 30 Dec 2005 12:15:54 -0500, you wrote:

>They found a reason to print 323 pages??  (Silly me, I was looking for  
>a way to download all of it as one PDF...)

It looks like such is possible. I don't remember exactly how I navigated here,
but here is a page with various retrieval options, including generation of PDF
documents.

http://tinyurl.com/clyxy

Victor
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Re: Proceedings 1982 Vatican Conference online

Brij Bhushan Vij
In reply to this post by Joan Griffith
Joan & all:
True, the more you learn and THINK you know - your SELF want to complete its
emptyness and STRIVES for more. Truth is 'How little we really urge to KNOW
more? One may achieve godliness BUT cannot become HE HIMSELF. Har-ki-pauri
Haridwaar is a site in (UP, India) where occasionally a Kumbh Mela is held,
where Hindus take a holy dip in memory of Shiva.
The more you distribute YOUR knowledge; the more you attain and COMES to you
in return. So distribute, share and share.....
A VERY HAPPY YEAR 2006 AHEAD INDEED.
Regards,
Brij Bhushan Vij
(Saturday – Kali 5106-W37-06)/D-001 (Sunday, 2006 January 01H0571(decimal)
IST
Aa Nau Bhadra Kritvo Yantu Vishwatah -Rg Veda
Jan:31; Feb:29; Mar:31; Apr:30; May:31; Jun:30
Jul:30; Aug:31; Sep:30; Oct:31; Nov:30; Dec:30
(365th day of Year is World Day)
******As per Kali V-GRhymeCalendar******
2108 Henry Court, MAHWAH  NJ  07430 (USA)
Telephone: +001(201)684-0191/ext6696


>From: "Gent van R.H." <[hidden email]>
>Reply-To: East Carolina University Calendar discussion List              
><[hidden email]>
>To: [hidden email]
>Subject: Re: Proceedings 1982 Vatican Conference online
>Date: Fri, 30 Dec 2005 17:01:25 +0100
>
>Joan Griffith wrote:
>
> > Once, one of my aims in life was to know everything, something I am
> > far, far, far from, but it's a fine thing to know somebody who does!
>
>Sadly, the more one knows, the more evident the gaps in one's knowledge
>become.
>
>=======================================================
>* Robert H. van Gent                                  *
>* E-mail: [hidden email]                     *
>* Homepage: http://www.phys.uu.nl/~vgent/homepage.htm *
>=======================================================


Har-Ki-Pauri.JPG (52K) Download Attachment
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Re: Proceedings 1982 Vatican Conference online

Tom Peters-2
In reply to this post by Gent van R.H.
Op 30-dec-2005, om 16:00 heeft Gent van R.H. het volgende geschreven:

> One of the nice surprises is the following link
>
> http://articles.adsabs.harvard.edu//full/book/grc../ 
> 1983//0000001,001.html
>
> to the complete proceedings of the 1982 Vatican conference on the  
> 400th
> anniversary to the Gregorian reform of the calendar.

Thanx!  I've been trying to get a copy of that book for years.
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Re: Proceedings 1982 Vatican Conference online

Tom Peters-2
In reply to this post by Irv Bromberg
Op 30-dec-2005, om 18:15 heeft Irv Bromberg het volgende geschreven:

> On Dec 30, 2005, at 10:00, Gent van R.H. wrote:
>> http://adsabs.harvard.edu/fulltext_service.html

>> One of the nice surprises is the following link
>> http://articles.adsabs.harvard.edu//full/book/grc../ 
>> 1983//0000001,001.html
>>
>> to the complete proceedings of the 1982 Vatican conference on the  
>> 400th anniversary to the Gregorian reform of the calendar.
>
> BROMBERG says:
>
> They found a reason to print 323 pages??  (Silly me, I was looking  
> for a way to download all of it as one PDF...)
> I hope that somebody who is a much faster reader than I might  
> highlight some of the interesting pages!
> Is there any hint of calendar reform being needed mentioned in the  
> proceedings?

Yup: the last contribution (pp.287..297).  The UN abandoned the  
efforts in 1955, the Vatican in its 2nd concilium in 1963.

I finally read the whole book - I found it very interesting.  Here  
are my thoughts, comments, and notes.

########################################################################
##############################################

Notes to "Gregorian Reform of the Calendar" A.R. (Tom) Peters dd.
20060304
Proceedings of the Vatican conference to commemorate its 400th  
anniversary 1582 - 1982

Introduction
----------------
   The book is a conference report containing papers on various  
subjects by international experts, covering most (but not all)  
aspects of calendars, the related astronomy and history, computus,  
and reception of the Gregorian reform.

   I find the book both intriguing and disappointing.  The historical  
background, procedures and politics, and reception of the calendar  
are described in detail.  The contributions concentrate on the solar  
calendar.  What I find disappointing is that the lunar calendar is  
hardly addressed: there is no comprehensive description of its  
workings, not to mention its shortcomings.  Contemporary and later  
criticisms are addressed but not in much detail.

Reasons and result of the reform
------------------------------------------------
   The innovation of the solar calendar involved a jump of 10 days in  
the calendar and dropping 3 leap days in 4 centuries.  These rather  
trivial innovations do not merit a 300+ page book.  What was new to  
me was that at the time it was not trivial to decide on the proper  
length of the calendar year.  There were several complications.  The  
driving motive for the reform was celebrating Easter at the proper  
time, rather than the circumstance that the Julian calendar was  
slowly drifting through the seasons (which was not a problem in  
practice).

   Canonically, Easter should be celebrated on the first Sunday after  
the 14th day of the first lunar month of spring.  It had been  
established practice to define "spring" as the aequinox: and the  
calendar should fix it at a specific date, therefore the calendar  
year should follow the tropical year.  There was some discussion  
whether the aequinox date should be 21 March (which most believed was  
the proper traditional date), or 25 March as advocated by some.  But  
more importantly, there was no universally accepted astronomical  
theory to find the moment of aequinox over long periods of time.  The  
theory of precession, which defines the difference between sidereal  
and tropical years, was in disarray.  This goes back to the Almagest  
of Claudius Ptolemaeus, who fixed the precession to the value of 1  
deg./cy, which is too small.  Later Arab and European astronomers  
could not match this with their own observations, so they introduced  
the "trepidation of the aequinoxes", a long-period oscillation that  
would be driven by an additional (ninth) celestial sphere and made  
the tropical year variable.
   But even if there were an adequate description of the astronomical  
events (aequinoxes and syzygies), and even while most experts held  
the opinion that Easter should be determined from the most accurate  
calculations available, some others preferred to use mean motions.  
The committee probably did not want to take position (p.149) in  
controversies on the best astronomical theory and tables (not the  
least involving Copernicus' system): so they chose to use a mean  
tropical year, and its value was the rounded value consistent with  
the most popular tables in use.  This happened to be 365;14:33 days  
(sexagesimal) = 365.2425 (decimal) (p.99).

Ptolemy's erroneous precession value
---------------------------------------------------
   Moesgaard in the first contribution to this book proposes a very  
interesting explanation for Ptolemy's error: I had not been aware of  
it and I have not seen it elsewhere, so I wonder if this is now  
received theory among scholars.  Babylonian astronomy (which was a  
major source for Hipparchus and Ptolemy) used the lunation as a unit  
of time, and used fractional period relations to the lunation for  
computing ephemerides.  The most relevant here is the Metonic ratio  
of 19 years in 235 lunations.  Moesgaard argues that originally this  
referred to sidereal years.  The relation is not perfect, and the 235  
positions in 19 years of the Full Moons among the stars drift about 1  
degree per century.  When later the Metonic relation was applied to  
the tropical year, Ptolemy applied this Babylonian parameter to the  
difference between the sidereal and tropical year, i.e. the  
precession of the aequinox.  This confusion was perpetuated to modern  
times.

Mean and mean mean tropical years
--------------------------------------------------
   There is a difference between the length of the mean mean tropical  
year (about 365.2422 days) and the mean vernal aequinox year  
(365.2424 days), as has been much discussed in the CALNDR-L mailing  
list.  The cause is a second-order effect of the drift of the  
aequinox with respect to the perigee.  The speed of the Earth in its  
orbit is variable (because of the elliptic motion).  The drift of the  
aequinox w.r.t. the perigee changes the average orbital speed of the  
Earth over the arc between two such events, which changes the time  
interval, i.e. the length of the tropical year from one instance of  
the vernal aequinox to the next.  I found it striking that all of the  
authors of the conference equate (sometimes explicitly) the vernal  
equinox year with a (mean) mean tropical year of 365.2422 days.  
Apparently this distinction has not become generally known before  
Jean Meeus published expressions for the times of aequinoxes and  
solstices in his Astronomical Algorithms in 1991 (Chapter 26).  
However anyone looking for regularity or predicting of these events  
could have known.  Indeed John Dee is quoted (p.103) to have  
discussed this (ca. 1583).  Even Clavius c.s. knew that the perigee  
is moving (p.211, p.217), and could have inferred that it would have  
an effect on the length of the tropical year even within the  
geocentric model with excentric spheres (indeed it had been known  
since Babylonian times that the seasons have unequal length, and at  
least since Hipparchus this has been explained by an excentric  
orbit).  But they are excused from taking this into account in the  
calendar because they tried to get rid of all variations (p.123).  I  
myself found out all this around 1983 when making least square fits  
of different order to the computed times of the events, although I  
did not understand the exact cause until much later (and learned how  
to derive the expressions from the polynomials for the mean  
parameters of the VSOP).
   Moreover, the first-order effect of elliptic motion is that the  
instances of aequinoxes or solstices are offset from those computed  
for a steady circular motion.  Ziggelaar's conference reports says  
(pp.221..222) that Clavius realized that they were not using the real  
mean position and motion of the Sun for fixing the date of the  
aequinox, which implies that he understood that they kept a constant  
offset caused by the excentricity.  The jump of 10 days would cause  
the adjusted mean aequinoxes to fall on average around the selected  
date of 21 March.  However, in fact at present it is the mean mean  
aequinox (once every 365d5h48m45s = 365.24219d) rather than the true  
aequinox (once every 365d5h49m1s = 365.24237d, elliptic offset of  
around -21h09m28s = -0.88157d from the mean mean aequinox in  
2000..2003, plus small planetary corrections) that seems to fall on  
21 March in the Gregorian calendar.  Of course on Cassidy's magic  
meridian of Washington (77:02:11 W) these instances would fall even  
earlier by 5h7m5s on the local clock (UT=ET-0:01:04 in 2000).

[The following table shows the dates (in March) in ET that the mean  
mean, the mean, and the true longitude of the Sun was 0 in 2000..2003 .
The mean mean aequinox occurs when the polynomial (from the VSOP-87  
theory) for the mean mean longitude of the Sun w.r.t. the mean  
aequinox of date is 0; its period is about 365.24219 days.
The mean aequinox comes from a polynomial that is fitted to the true  
aequinoxes over several centuries: it contains the fairly constant  
correction for the elliptic terms in the Earth's orbit, but all short-
periodic perturbation terms from Moon and planets, as well as  
nutation terms in the motion of the aequinox, are averaged out; its  
period is about 365.24237 days for the northward aequinox, which is  
different from the mean mean tropical year and from the tropical  
years for the solstices and the other aequinox.  Notice the drift of  
+16s/year on the offset between the mean and mean mean aequinox in  
the table below.
The true aequinox is when the Sun is at the instantaneous aequator of  
the date, as computed from the full theory.
All expressions are derived from Meeus' Astronomical Algorithms  
(based on the VSOP-87).

year mean mean aequinox     mean aequinox   true aequinox  
2000 21 Mar 2000 04:36:02 ET 20 Mar 2000 07:26:10 ET 20 Mar 2000  
07:36:12 ET
2001 21 Mar 2001 10:24:47 ET 20 Mar 2001 13:15:11 ET 20 Mar 2001  
13:31:43 ET
2002 21 Mar 2002 16:13:32 ET 20 Mar 2002 19:04:12 ET 20 Mar 2002  
19:17:10 ET
2003 21 Mar 2003 22:02:17 ET 21 Mar 2003 00:53:14 ET 21 Mar 2003  
01:01:17 ET

year diff. true - mean mean diff. mean - mean mean diff. true - mean
2000 -0d20:59:50     -0d21:09:52     +0d00:10:02
2001 -0d20:53:04     -0d21:09:36     +0d00:16:32
2002 -0d20:56:22     -0d21:09:20     +0d00:12:58
2003 -0d21:01:00     -0d21:09:03     +0d00:08:03
]

Looking for the best solution: politics and integrity
------------------------------------------------------------------
   Interesting tales of the reform cover who were appointed or  
admitted to the committee making the final proposal; to what extent  
that group was open to external input; and how and why their proposal  
finally became universally accepted: about which I believe much is  
still poorly understood.
   I found it striking that Luigi Giglio, committee president Tomasso  
Gigli, and his successor Gulielmo Sirleto, all came from Calabria: it  
gives the impression that the a gang of the N'drangheta had taken  
over the reform.
   Clavius was a late addition, and he had little scientific record  
to show: it seems that he was assigned because he was one of the few  
people in Rome who had any expertise on the subject.  His name has  
stuck to the reform because he finally wrote the Explicatio, 3  
decades later (after failing to publish his theories of planetary  
motion) at which time all others involved were long dead.
   The main other published document was the 8-page excerpt  
"Compendium" based on Lillius manuscript (which is lost).  Even this  
Compendium had very limited distribution - that it had been printed  
at all was news at this conference - and was only sent to Catholic  
rulers and their scientists.  Protestants were ignored, Orthodox only  
diplomatically massaged after the final proposal had been made: maybe  
because of this the Orthodox never accepted the new Easter rules.
   On the other hand I have the impression that the committee was  
open to external criticism and committed to find the best and  
universally acceptable solution.  But the people who sent in comments  
on the Compendium misunderstood the issues, or proposed their own pet  
calendar reform of more or less radical ideas: there was no  
consensus.  The committee waited another year for an alternative by  
van Zeelst from Leuven (p.219), but his proposals were a  
disappointment.  They then rushed their proposal, with supposedly  
only minor modifications to the Compendium (I think they were  
substantial for the lunar calendar).
   One striking example of the open-mindedness was that they had no  
dogmatic prejudice against the Copernican heliocentric system.  
Although e.g. Clavius never accepted the heliocentric system and  
initially opposed the models of "De Revolutionibus", he later became  
to appreciate Copernicus (p.151), and Reinhold's Prutenic tables were  
treated as a reliable source and basis for computations.  This looks  
much different from the circumstances that Galilei had to deal with  
half a century later.  I don't know whether the Catholic church and  
especially the Jesuits became more dogmatic, or that Galilei  
irritated them too much in another way and they just found an excuse  
to teach him a lesson.
   Another fascinating example is the reception of patriarch Ignatius  
(e.g. p.215).  He came at the scene late when the Compendium was  
already disseminated (1578); he apparently was member of a Nestorian  
church so not even in communion with Rome; and he shared no common  
language with the other people involved, so communication must have  
been tedious and costly.  It would have been easy to ignore him.  Yet  
the pope received him in audience within a few months, and documents  
were translated for him.  The Roman clergy apparently regarded the  
books he brought with much respect for tradition.  Again it appears  
that the reformers really wanted to make the best possible calendar  
and valued all authorative input.  So unlike many other commentators,  
Na'amatallah's points were addressed and some adopted in the final  
proposal.  Most notably, at the time astronomers reckoned New Moon in  
the astronomical way: from the conjunction.  Na'amatallah convinced  
them (p.217) that the traditional start was at the observation of the  
lunar crescent, and that this tradition should be followed.  Clavius  
had to re-compute the epact table accordingly.  To the eternal  
chagrin of Simon Cassidy, Na'amatallah's proposal to adopt the  
Persian 8/33 intercalation scheme for the solar calendar was  
rejected.  I suppose the rest of the committee did not want to  
consider yet another solar theory at that point (p.149).  I wonder  
what else became of this stranger.

Next reform
---------------
   As we at CALNDR-L know, the Gregorian calendar does have its  
shortcomings, and there is no lack of alternatives.  The Universal  
Calendar has been the most serious contester.  Personally, I find it  
totally unacceptable for two reasons:
1) It is A Big Mistake to put the leap day somewhere in the middle of  
the year.  We make it ourselves so much easier in computation and  
algorithms if we put it after a year.
2) It unnecessarily breaks the 7-day week.
   Personally, I prefer a leap week calendar; the ISO calendar is one  
(although its leap rule is not formalized, but it rides on the  
Gregorian calendar), and is "de facto" a calendar that is used  
alongside the Gregorian calendar.  Annually I do suffer from the  
disjunction between the two when I have to make consistent accounts  
of worked hours and free days in different systems that use either  
the one or the other.  Still the ISO calendar suffers from some of  
the shortcomings of the Gregorian calendar (like the astronomically  
arbitrary begin of the year), for its definition it depends on the  
Gregorian calendar, and it lacks a "month" as intermediate between  
week and quarter.

Scientific revolution
--------------------------
   Finally, I found in this book much interesting information on the  
scientific revolution from geocentric to heliocentric world view: how  
a paradigm shift takes place, and scientific progress in general.  
The general attitude since the age of Enlightenment has been that the  
Middle Ages were backward and superstitious.  However, I've come to  
appreciate that in all ages there have been smart and inquisitive  
people, who dedicated themselves for a big part of their lives to  
understanding and describing some aspect of their natural experiences.
   Babylonian astronomy was mostly numeric, concentrating on cycles  
of recurrence in time; in addition they positioned the events in a  
reference frame on the celestial sphere.  The Greek changed this to a  
geometric model that worked in 3 dimensions.  I have the impression  
that overall, the Greek were more concerned with the geometry than  
with the mechanics and the physical reality of revolving crystal  
spheres.  This seems to have reversed somewhat in the Middle Ages  
(e.g. p.148).
   Apparently only at the time of the reform, astronomers came to  
appreciate that their theories should match observed phenomena, so  
explanations should not only make sense qualitatively in a physical  
or geometrical model (p.151), but also "ad numeros" (p.145).  For  
instance, Ptolemy's lunar epicycles over-estimate the variation in  
lunar distance (and variation in apparent size) by a dactor of 2, but  
for 14 centuries no-one seemed to care.
   Reading this book it occurred to me that the big leap in the  
scientific revolution from Copernicus to Newton was not the change  
from geocentric to heliocentric, whatever its philosophical  
implications and change in world view may have been.  Rather, it was  
letting go of the geometrical or even mechanical world view of nested  
spheres.  Copernicus still stuck to spheres and epicycles: he just  
shifted the origin of his reference frame, which is pretty trivial in  
our post-relativistic world view.  Kepler dared to give preference to  
an alternative geometry that better fitted the observations, even  
though there was no obvious mechanical construction that would make  
such a theory work in the physical world.  Finally Newton dared to  
have the planets float in a void driven by an invisible, non-
mechanical force.  The new theories gave a better description, but  
not an explanation, of the world in the way that the revolving nested  
spheres did: I can fully understand that most bright minds elaborated  
on the established model, and it took real genius to think out of  
this box and come up with a completely different paradigm.  So I  
think the scientific revolution was an evolution along these mile posts:
1) theory should match observations
2) quantitative match is more important than qualitative: the model  
must provide numerically correct results
3) move from geocentric to heliocentric (Copernicus)
4) drop the mechanical concept of rotating spheres
5) adopt better fitting geometries than just circles (Kepler)
6) new understanding of motion and impulse (Galilei)
7) new understanding or introduction of new concepts such as force,  
acceleration, energy (Newton)
8) mathematical formulation of theories
9) development of new mathematical techniques: algebraization of  
geometry, calculus (Descartes, Leibniz, Newton)
   I think the first two and last two innovations are fundamental  
characteristics of science.  The others are peculiar to particular  
fields.

Mysterious date of the Bul
-----------------------------------
   One thing that remains a mystery to me is the date of the Bull: 24  
February 1581 (see e.g. http://www.bluewaterarts.com/calendar/ 
NewInterGravissimas.htm).  It is generally accepted that it was  
actually signed and issued only in 1582, the year that the reform was  
brought to effect (in October).  The usual explanation is that Rome  
would start the year on 25 March (the traditional date of the  
incarnation, i.e. conception, of Jesus: Dionysius Exiguus started his  
Christian era with the incarnation of Christ).  However, this is  
contested in the Wikipedia article on the Gregorian calendar (http://
en.wikipedia.org/wiki/Gregorian_calendar#Beginning_of_the_year).  
Indeed, the reprint in band V of Clavius' Opera Mathematicorum that  
is shown in the figure on p.204 in this book, carries the year 1582.  
Can anybody resolve this issue?



Notes to conference contributions:
==================================

1) Kristian Peder Moesgaard: Basic Units in Chronology and Chronometry.
p.5: Babylonian independent variable for ephemerides ("Ephemeris  
Time") was the synodic month: divided into 30 tithis (O.N.: HAMA  
358;395;1069).
Also Metonic year = 235/19 synodic months: 14 min. short of sidereal  
(known), 6 min. longer than tropical year (probably unnoticed).
Metonic cycle is an eclipse cycle: beat of 235 synodic = 255  
draconitic months leads to 35 knots on the ecliptic where Full Moons  
may eclipse.
p.8: "eternal" cycle, attributed to Oppolzer and Stockwell, is better  
known as van den Bergh's InEx.
p.8: synodic month constant, day length variable? cf. variable  
seasonal hours.
p.9: idem Full Moon positions fixed ==> stars drift (not precession!)  
~1 deg./cy .
   Sidereal year = (100*360)/(100*360-1)*235/19 = 12;22:07:33 synodic  
months is 1/2911 synodic month  = 14.6 min. longer than a Metonic year.
N.B. Standard Babylonian sidereal year was 12;22:08 syn.months;
   hellenistic astronomy used 1 deg./cy precession and Metonic year  
of (235 - 1/12000)/19 = 12;22:06:18 syn.months.
N.B. all this independent of count of days (calendars) or tropical  
(seasonal) years.
pp.10..11: Ancient stated or derivable year lengths in days are  
either sidereal or "Metonic"; no tropical years!
pp.11..13: Hipparchus measured tropical solar longitudes (i.e. w.r.t.  
aequinox) but according to Moesgaard he reverted to the Metonic year.
   Later Ptolemy confused the matter by explicitly using ecliptic  
longitudes w.r.t. the aequinox but implicitly still using Metonic  
concepts and values.
   Even later astronomers (Thabit ibn Qurra, Copernicus) were forced  
to assume a varying tropical year and trepidation of the aequinoxes,  
but found a constant sidereal year.

2) Olaf Pedersen: The Ecclesiastical Calendar and the Life of the  
Church.
Very long (pp.17..69 and notes pp.70..74) and detailed description of  
the history and development of in particular the computus in the  
Middle Ages.
p.17: confuses (mean) mean tropical year with vernal aequinox year.
Adequate description of historical calendars and their astronomical  
basis.
Good description of background of Christian calendars and chronology  
(or lack thereof).
Interesting description of the early Easter problems. "Solved" by  
defining in the Julian (not Jewish)
calendar and using period relations (starting with octaetris),  
ignoring the preciser astronomy of the Almagest
(2*18=16 year canon on statue of Hippolytus; 3*28=84 year laterculus  
of Augustalis: epactae and saltus lunae; 19-year cycle by Anatolius  
from Alexandria (and Laodicea) since 277).
At Nicaea (325) it was decided that Christians should celebrate  
Easter on the same date everywhere, following Alexandria and Rome;  
but these differed in details.
Alexandrians put the aequionox at 21 March in the Julian calendar,  
Romans kept 25 March; Romans used the 84-year cycle, Alexandrians the  
Metonic cycle.
Dissemination of Alexandrian system in the West.  Victorius of  
Aquitaine.  Dionysius Exiguus.  Isidor of Sevilla.  Bede.  Later  
Middle Ages.

3) J.D. North: The Western calendar - "intolerabilis, horribilis, et  
derisibilis"; Four Centuries of Discontent.
p.78: Again mean mean tropical year...
pp.79,98 : Copernican extremes 365d5h55m37.7s and 365d5h42m55.1s :  
mean 365d5h49m16.4s is accepted value for Gregorian reform (according  
to Clavius).
p.93: Richard Monk (1434) appears to have used al-Khayyami's (1079)  
33-year cycle (discussed here), a century before John Dee.
p.99: Values for tropical year from Alfonsine, Revolutionibus,  
Prutenic, can all be rounded to 365;14:33 (sexagesimal) days is  
exactly the Gregorian mean.
p.102 ff.: John Dee:
p.103: Dee explains that the VE year not equal to AE year (using  
Prutenic Tables).  Used mainly calculated positions, not observations!
P.104: 11 days, not 10, for correcting the aequinox.

4) Jerzy Dobrzycki: Astronomical Aspects of the Calendar Reform.
Addresses solar calendar only...
p.118: Again mean mean tropical year, but:
p.123: reformers used mean solar year, i.e. without trepidation of  
the aequinoxes (mainly from Prutenic Tables).
p.124: "Gregorian meridian"(for solar calendar): 5 deg. W. of Frombork.

5) Edoardo Proverbio: Copernicus and the Determination of the Length  
of the Tropical Year.
p.132: still confusues VE year with mean tropical year?

6) Ugo Baldini: Christoph Clavius and the scientific scene in Rome.
Clavius had not published any theoretical (and certainly no  
observational) astronomical work when asked for the reform committee.
Mathematics was in low esteem and standard at the young Collegio  
Romano of the Jesuits at that time; Clavius was mostly an autodidact.
He never published his intended magnus opus Theoricae Planetarum.
Main problem for the determination of the tropical year was that  
there was no generally accepted theory (model as well as numerical)  
of precession at the time:
mostly because Ptolemy's erroneous constant precession rate was  
incompatible with those found by later observers,
so most (including Copernicus) suspected trepidation of the  
aequinoxes: but that concept was being abandoned again later in the  
16th century.
This probably was one of the reasons why the committee continued  
using mean motion instead of astronomically accurate events,
so that they would not fix themselves on a particular and disputed  
model.
Clavius changed his opinions in successive editions of his work  
during the decades around and after the reform.

7) Gordon Moyer: Aloisius Lilius and the "Compendium Novae Rationis  
Restituendi Kalendarium"
p.181: again computation on basis of the mean mean tropical year.
Biggest point made is that the Compendium indeed was printed and  
distributed albeit in limited edition.
Again almost nothing on Lilian epacts; except that Clavius made  
several minor changes.

8) Juan Casanovas: The Vatican Tower of the Winds and the Calendar  
Reform.
   The Tower of the Winds was built during the reform, and decorated  
and instrumented by design of Ignazio Danti: especially an anemometer  
and a "gnomon" or meridian instrument (pinhole camera obscura).
   Despite popular tradition, it can not have been used to determine  
the length of the tropical year,
but maybe to demonstrate the relevance of the reform afterwards.

9) August Ziggelaar: The Papal Bull of 1582 Promulgating a Reform of  
the Calendar.
   Multiple proposals since 1575: Juan SalÛn, Giovanni Carlo Octavio  
Lauro, Luigi Giglio (from CirÚ in Calabria ; later Naples, Verona)  
supported by brother Antonio.  Commision president Tomasso Gigli,  
bishop of Sora in Calabria and papal treasurer, was undecided;  
successor cardinal Gulielmo Sirleto (also from Calabria) chose  
Giglio's solution.
   Main innovation is abandonment of the Golden Numbers, use 30  
possible epacts instead.
   Several responses to the Compendium, most proposing alternatives.
   Arab-speaking ex-patriarch Ignatius of Antioch (Na'amatallah)  
arrived only in Rome begin 1578, but was taken seriously and became  
part of the committee; he criticised misunderstanding of Jewish  
calendar reckoning.  Notably astronomically-minded reformers counted  
New Moon from the conjunction, while the Jews used to count from  
first visibility (p.217).  This and some of his other points were  
taken account of in the final calendar (or at least the Explicatio).
   Ziggelaar gives a reasonably accurate account of the Lillian and  
Clavian epacts.
   The committee waited a year for a promised improved proposal by  
van Zeelst from Leuven, but the result was disappointing (p.219).  
Funny to read how, after centuries of discussion, the introduction of  
the new calendar was rushed through the committee, despite lack of  
consensus among external experts.
pp.211,217: motion of perigee known.
pp.221..222: difference between real and mean Sun: season lengths not  
equal because of excentricity.

10) H.M. Nobis: The Reaction of Astronomers to the Gregorian Calendar.
   Deals with various factors, little on technical arguments.  
Attitude of Protestants and Catholics was different: former  
considered it a worldly (emperial) task, not a papal; latter stressed  
connection of the calendar with liturgy.  Concentrates on Germany.
p.247: apparently it was believed that at the time of the Council of  
Nicaea, the aequinox should have been at 21 March.
   Michael Maestlin appears to have been the most influential  
commentator; Clavius rebuked him in an Apologia.  Also long & harsh  
disputes between Clavius and Scaliger.
p.250: reference to Kepler's famous statement: "Easter is feast and  
not a planet" (note 49).

11) Michael A. Hoskin: The Reception of the Calendar by Other Churches.
p.255: Again equinox on 21 March at the time of Nicene Council  
thought to be the proper adjustment.
        Change of computus hardest to accept by non-catholics.
p.256: John Dee main proponent for acceptance of the reformed  
calendar in England.  Mentions that in England, New Year began on 25  
March, in contrast with the catholics; indeed (p.257) the year count  
differed for 3 months between England and the continent.
p.260: German protestants used Rudolphine Tables for astronomically  
computing Easter, but that too was sometimes in error.
pp.261..: Diplomatic negotiation with Orthodox church difficult  
because of Turkish sensitivities; patriarch Jeremiah II Tranos seemed  
in favour, but the unilateral emission of the Inter Gravissimas bul  
fell badly: synods in Constantinople in November 1582 and 1593  
rejected the reform.
p.263: opposition to reform because of hate of the papacy: but only  
monarchical power like from the pope could enforce such a reform.

12) Owen Gingerich: The Civil Reception of the Gregorian Calendar.
pp.265..266: Christmas skipped over when the reform was introduced in  
Southern Netherlands at the end of 1582!
p.267: Meastlin against; Kepler and Leibniz later in favour.
p.268: Sweden skipped a leap day in 1700, added one as 30 February!  
in 1712 when going back to Julian (accepted Gregorian calendar only  
in 1753, 1 year after England and as last of Western Europe).
p.268..270: advise of John Dee: skip 11 days to get calendar in sync  
with time of jesus; OTOH fierst skip only 10 to stay in sync with  
catholic countries.
p.276: Gregorian calendar adopted by Bolsheviks in 1918 as anti-
clerical act against the orthodox church.
pp.276..277: brief mention of (proposed) reform on congress of  
Eastern Orthodox Church in Constantinople in 1923.

13) Karl Fischer: Appended Note: On the Calendar Reform in Bohemia  
and Moravia.
   In these countries, Catholic prelates introduced the new calendar  
in 1582..1584 against some opposition in their dominions; but  
protestants retained the old calendar for a long time.

14) FranÁois Russo: Contemporary Discussions on the Reform of the  
Calendar.
   Discusses period 1834..1963; only astronomy-based solar calendar;  
specifically the Universal Calendar which has been most seriously  
considered as a successor to the Gregorian calendar.  But there came  
no universal agreement on using either 12 or 13 months.  Also the  
date of Easter was an issue, and of course the discontinuous week.
p.290: erroneously states that U.C. has 4 months of 30 days and 8 of  
31 .
p.292: U.C. was proposed in essence already in 1834 (by Mastrofoni in  
Rome).
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Re: Proceedings 1982 Vatican Conference online

Irv Bromberg
On Mar 4, 2006, at 13:46, Tom Peters wrote:
> There was some discussion whether the aequinox date should be 21 March
> (which most believed was the proper traditional date), or 25 March as
> advocated by some.

> Alexandrians put the aequionox at 21 March in the Julian calendar,
> Romans kept 25 March; Romans used the 84-year cycle, Alexandrians the
> Metonic cycle.

> p.247: apparently it was believed that at the time of the Council of
> Nicaea, the aequinox should have been at 21 March.

> p.255: Again equinox on 21 March at the time of Nicene Council thought
> to be the proper adjustment.

Bromberg says:

I recently revised my web page entitled "Why March 21st", after finding
the solar azimuth at sunset in Alexandria was consistent with the
reckoning of the Alexandrians that Julian March 21st as the day of the
equinox in 325 AD.

<http://www.sym454.org/mar21/>

-- Irv Bromberg, Toronto, Canada
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Re: Proceedings 1982 Vatican Conference online

Gent van R.H.
In reply to this post by Gent van R.H.
Irv Bromberg wrote:

> I recently revised my web page entitled "Why March 21st",
> after finding the solar azimuth at sunset in Alexandria was
> consistent with the reckoning of the Alexandrians that Julian
> March 21st as the day of the equinox in 325 AD.
>
> <http://www.sym454.org/mar21/>

According to Ptolemy's _Almagest_, which Alexandrian astronomers are more
likely to have used than AA or CC, the solar longitude at mean noon in
Alexandria for the years 325-328 were the following:

                         325     326     327     328

20 March [24 Phamenoth] 358;24  358;10  357;55  358;39
21 March [25 Phamenoth] 359;22  359;08  358:53  359;37
22 March [26 Phamenoth]   0;20    0;06  359:52    0;35

Reckoning from noon to noon (as astronomers usually did until 1925) the
spring equinox would have been placed on the 21st of March three times in
every four years.

This would easily give rise to a tradition that the spring equinox fell
around the 21st of March in that period. No "observations" would have been
necessary for arriving at such a date.

=========================================================
*                                                       *
*  Robert H. van Gent                                   *
*  E-mail: [hidden email]                      *
*  Homepage: http://www.phys.uu.nl/~vgent/homepage.htm  *
*                                                       *
=========================================================
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Re: Proceedings 1982 Vatican Conference online

Irv Bromberg
On Mar 10, 2006, at 11:31, Gent van R.H. wrote:

> Irv Bromberg wrote:
>> I recently revised my web page entitled "Why March 21st", after
>> finding the solar azimuth at sunset in Alexandria was
>> consistent with the reckoning of the Alexandrians that Julian March
>> 21st as the day of the equinox in 325 AD.
>>
>> <http://www.sym454.org/mar21/>
>
> According to Ptolemy's _Almagest_, which Alexandrian astronomers are
> more likely to have used than AA or CC,...

Bromberg inserts:
In case anybody doesn't follow the non-standard abbreviations:
AA=Astronomical Algorithms, by Jean Meeus
CC=Calendrical Calculations, by Reingold & Dershowitz.
(both published at the end of the 20th century)

> ...the solar longitude at mean noon in
> Alexandria for the years 325-328 were the following:
>
>                          325     326     327     328
>
> 20 March [24 Phamenoth] 358;24  358;10  357;55  358;39
> 21 March [25 Phamenoth] 359;22  359;08  358:53  359;37
> 22 March [26 Phamenoth]   0;20    0;06  359:52    0;35
>
> Reckoning from noon to noon (as astronomers usually did until 1925) the
> spring equinox would have been placed on the 21st of March three times
> in
> every four years.
>
> This would easily give rise to a tradition that the spring equinox fell
> around the 21st of March in that period. No "observations" would have
> been
> necessary for arriving at such a date.

Bromberg says:

My point was NOT that the Alexandrians used sunset azimuth, or any
observational method, but rather that the tradition was CONSISTENT with
a modern estimate of what the sunset azimuth was then and there,
whereas modern estimates of the solar longitude (as per Meeus in
Astronomical Algorithms, can see the same in Kalendis choosing built-in
Alexandria locale) place the moment of solar longitude = 0 degrees on
Julian March 20th very close to Noon in 325 AD, Alexandria mean solar
time.

Do you have direct access to a copy of the Almagest?  The UofT
Astronomy Library has ceased regular hours of operation.  The Almagest
is in there, but I would have to make an appointment with the Dean's
Office just to see it!  Is the text on-line anywhere?

I gather that it was written in Greek -- do you read and understand
that?  Are translations to English available?  My department has
numerous Greek graduate students.  I see that there are a few online
resources derived from it linked into the Wiki page on it.

I had believed that Maimonides' astronomical algorithms were based on
Ptolemy's algorithms, because he was living in Egypt at the time that
he wrote his treatise on the calendar calculations of the Hebrew
calendar. However, he did not cite Ptolemy by name nor did he reference
the Almagest, and he wrote his treatise approximately a millennium
after Ptolemy, so his work may very well have been based on further
advances from later sources, especially Arabic, which was his daily
spoken language.  My implementation of Maimonides' "true solar
longitude" algorithm yields slightly different values compared to the
figures quoted above.  Besides possible algorithmic differences, this
may be related to differences of locale (Alexandria vs. Jerusalem)
and/or timing relative to sunset vs. noon.

-- Irv Bromberg, Toronto, Canada

<http://www.sym454.org/>
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Re: Proceedings 1982 Vatican Conference online

Palmen, KEV (Karl)
In reply to this post by Gent van R.H.
Dear Robert, Irv and Calendar People

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:[hidden email]]On Behalf Of Gent van R.H.
Sent: 10 March 2006 16:32
To: [hidden email]
Subject: Re: Proceedings 1982 Vatican Conference online


Irv Bromberg wrote:

> I recently revised my web page entitled "Why March 21st",
> after finding the solar azimuth at sunset in Alexandria was
> consistent with the reckoning of the Alexandrians that Julian
> March 21st as the day of the equinox in 325 AD.
>
> <http://www.sym454.org/mar21/>

According to Ptolemy's _Almagest_, which Alexandrian astronomers are more
likely to have used than AA or CC, the solar longitude at mean noon in
Alexandria for the years 325-328 were the following:

                         325     326     327     328

20 March [24 Phamenoth] 358;24  358;10  357;55  358;39
21 March [25 Phamenoth] 359;22  359;08  358:53  359;37
22 March [26 Phamenoth]   0;20    0;06  359:52    0;35

Reckoning from noon to noon (as astronomers usually did until 1925) the
spring equinox would have been placed on the 21st of March three times in
every four years.

This would easily give rise to a tradition that the spring equinox fell
around the 21st of March in that period. No "observations" would have been
necessary for arriving at such a date.

KARL SAYS:
I recall from an earlier e-mail that these calculations assume that each Vernal equinox occurs exactly 1/300 day short of 365.25 days after the previous (rather than about 1/132 day short). This would explain the error in reckoning the date of the equinox in AD 325.

Also I note that this value (exactly 365 days 5 hours 55 minutes and 12 seconds) gives rise to a fairly accurate mean month (29.53058156... days) with the Metonic cycle.

Karl

08(01(12 till noon
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Re: Proceedings 1982 Vatican Conference online

Lance Latham
In reply to this post by Irv Bromberg
RE:

> Do you have direct access to a copy of the Almagest?
>  The UofT
> Astronomy Library has ceased regular hours of
> operation.  The Almagest
> is in there, but I would have to make an appointment
> with the Dean's
> Office just to see it!  Is the text on-line
> anywhere?
>
> I gather that it was written in Greek -- do you read
> and understand
> that?  Are translations to English available?

Lance replies:
I recall seeing a copy of the 'Almagest' in the
Fredericksburg, TX public library, where it was
included as a hard-bound volume among numerous other
'Great Books'. It was in English. I've seen similar
purchasing strategies pursued in other small libraries
as well, so I doubt that a copy should be difficult to
obtain. In the worst case, Inter Library Loan, which I
assume operates in Canada.

That's an interesting policy at the University, Irv.
'Own resource, but deny access'. Hopefully, they'll
either re-open the collection or move it to another
library that's actually open.

-Lance
 

Lance Latham
[hidden email]
Phone:    (518) 274-0570
Address: 78 Hudson Avenue/1st Floor, Green Island, NY 12183
 




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Re: Proceedings 1982 Vatican Conference online

Irv Bromberg
On Mar 13, 2006, at 12:24, Lance Latham wrote:
> That's an interesting policy at the University, Irv.
> 'Own resource, but deny access'. Hopefully, they'll
> either re-open the collection or move it to another
> library that's actually open.

People infrequently went to the UofT astronomy library, so they decided
to save two salaries (librarian, assistant).

Having the Astronomy Library on the 13th floor of the Physics Tower
(with a slow old elevator) may have had something to do with the low
usage rate, as well as the fact that it opened late in the morning,
closed early in the afternoon, and they took 2-hour lunch breaks!  
Sheesh!

Another factor was that increasingly the journals in particular have
been available in PDF format.

Also, much of the collection is reference material that can't be
borrowed anyway, so if one needed the material the choices were lots of
photocopying, or buy a personal copy, if not available in PDF.

I recently sent my son there to borrow a book on celestial mechanics,
which they do allow to be borrowed, but they refused to let him borrow
the book, even though he is a UofT student, but he is not in the
faculty of science.  He does take several science courses, but not
physics or astronomy.  They weren't impressed with his "this is for my
Dad" objection, because I'm in the faculty of medicine!  Yep, another
example of 'own resource, but deny access'.  I'll bet that book just
collects dust...  Anyhow I just wanted to borrow it briefly to decide
whether or not to buy it.

Part of the collection was moved to the undergraduate science library,
which is actually closer to me, but I haven't found where they stashed
it yet, don't know how much got moved.

-- Irv Bromberg, Toronto, Canada

<http://www.sym454.org/>