Subject: Re 4-1/8 yr. Leap Rule responses of Richard, Jim and Amos
Date:Sun, 06 Oct 1996 23:09:04 -0700
To:East Carolina

Richard McCarty wrote:
>On 4-Oct-1996 Simon Cassidy wrote:
>----------------
>An old tradition of 8 leap-days* in 33 years (probably handed down by
>oral tradition, from a pre-Druidic time when both the summer solstice year
>and the vernal equinox year followed this rule)could have been most easily
>applied by adding a 366th. day every four and one-eighth years.
>----------------
>
>Simon, this is fascinating; you've made my week.  But please help
>me get the concepts to mesh.
>
>The idea seems to be that a solar calendar more accurate
>than the Gregorian results by adding leap-day every 33/8 year.  If
>my math is right, this yeilds 96.96 leaps in 400 years, compared to
>the Greogrian's 97 in 400.

actually 96.96969696... recurring (i.e. 96.97 to the nearest 1/100 th.)
leap days every 400 years.
As Amos understands, this is an average year (in decimal notation) of
365.24242424..recurring days.

The current VE-year (interval between vernal equinoxes smoothed over
several decades) is 365.24238 days (by my calculations, and from the work
of Jean Meeus) and thus, the current error in keeping the VE steady, in
Gregorian average year (365.24250 days), is three times that of calendars
using the "8 leap-days in 33 years" rule. Over the centuries to come this
comparative accuracy factor (currently three) should get larger and larger,
(in fits and starts) and eventually rise towards infinity!

Amos, please note, that while you are right, that the mean tropical year
(averaged over all points in the tropical zodiac) is 365.2422 days (to the
nearest ten-thousandth of a day) and decreasing, this kind of tropical year
is not the correct one to use in judging the accuracy of the Gregorian
calendar or 33-year calendars (like the "Khayyam"-style calendars or my
hypothetical eight-fold implementation) which all seek to (or can only,
in this epoch) KEEP THE VERNAL EQUINOX STEADY.

This confusion about the true length of the vernal-equinox year is
acknowledged by the jesuit-run Vatican Observatory itself (see J. De Kort
S.J. in "Astronomical Appreciation of the Gregorian Calendar" vol.2 #6
of Richerche Astronomiche Specola Vaticana, 1949), but even the jesuit
astronomer De Kort could not get his math quite straight (he came up with
365.2423 days as the current VE-year). Please let us clear up this matter
before proceeding with the discussion.

The source of the confusion appears, to me, to be in publications of
institutions such as the United States Naval Observatory and the Greenwich
Royal Observatory which (in the context of celestial mechanics) define
the "tropical year" as a mean over all points of the tropical zodiac, but
then turn around and (in the context of calendars) define it as "the (mean)
interval between vernal equinoxes". Scholars of calendars and historians
of astronomy such as Gordon Moyer ("The Gregorian Calendar" Scientific
American, May 1982) are thus understandably led completely astray when
trying to explain to the layman how well or ill, the Gregorian calendar
suceeds in keeping the Vernal Equinox on the 21st. of March. This is
because he uses the formulae of these institutions, as they do, (which
formulae are designed to model the celestial mechanics of the whole of
the earth's orbit) as though these formulae were the right way to model
the actual varying average interval between real instants of vernal
equinox! Simon Newcomb can never have intended his formulae to be
adapted for use in this deceptive manner!

On this read my page(http://serendipity.magnet.ch/cassidy/err_trop.html).
I do not expect you to take my word on this, but please do believe me, that
resolving this issue (either ourselves or by bringing in further qualified
consultants) may be the one true positive contribution that we can make to
Calendar Reform and its body of expert lore.

Consider, for instance, that the Greek Orthodox Church (whose decisions are
also determininative for the newly liberated Russian Orthodox Church) has
made (early this century) a decision to diverge from the Roman Catholic
Gregorian Calendar by one leap-day come 2800 A.D.. This was apparently done
to have a calendar more accurate than their competitior but to postpone
the confusion into the indefinite future. Their belief in their correctness
must be based on the misleading statements of astronomical institutions,
so imagine the stir if it is revealed that they have been suckered into
adopting a calendar which is less accurate than the Gregorian by the
standards of their very own revered Nicene council!

Further to Amos' clarification of how a Celtic-style 4-1/8 year leap-cycle
might NOT require 8 equal periods, I supply an example like his below:

Samhian-45days-WinterSolstice-45days-Imbolc-45days-V.E.-46days-Beltane-
-46days-SummerSolstice-46days-Lughnasa-46days-FallEquinox-46days-Samhain

My choice of starting the 3 short eighths at Samhain is merely conditioned
by my knowledge that the sun (earth) currently travels fastest (when at the
perihelion) in January (between WinterSolstice and Imbolc). Such a scheme
is thus unlikely to correspond exactly to any supposed lost prehistoric
tradition.

Since any rule must be rooted in observational results collected at some
period earlier in the tradition, you might want to study the article I
cited (Archaeoastronomy suppl.#13 of JHA) to see how McCluskey fared when
testing for several different ways of dividing the tropical year into
eighths (by different mixtures of observation and geometry).

My point is that rule-based calendars inevitably develop out of
observationally based calendars when patterns (in numbers of days) are
noticed by the record-keepers. If the lost folk tradition, that McCluskey
tests for, is as old as Alexander Thom's evidence for PRE-Celtic eight-fold
calendars (McCluskey tests specifically for Thom's reconstruction of an
eight-fold year), then, I suggest that, by Christian times, patterns in the
numbers were bound to have been noticed. The one pattern that would have
stayed most constant over such a long period of time (waiting to be
noticed) would have been the pattern of days between Vernal Equinoxes which
would show up as requiring a 366th. day, every four years for twenty-eight
years, and then a gap of five years before requiring the next 366th. day.

Of course this would not be an absolutely consistent pattern (though
inconsistencies would probably have been more due to observational errors
than to discrepancies between the solar behaviour and the ideal 365 + 8/33
pattern). But, the Vernal equinox pattern would stand out as much more
consistent than any of the other seven possible years in an eight-fold
calendar. Note also that all proposed observational methods are more
accurate (and therefore also more consistent) at the equinoxes. A Fall
Equinox marker would benefit as much as a Vernal Equinox marker from this
greater observational precision (in locating its actual day of occurence),
but the Fall Equinox has been, in the millenia under discussion, the
fastest changing of the tropical years.

However this is not quite my favorite scenario for explaining McCluskey's
findings. My thoughts are conditioned by my own field research
and measurements at Stonehenge, which supplement the findings of Alexander
Thom, Gerald Hawkins and Fred Hoyle as well as the dating by the
archaeologists. Briefly, I propose that the rule, of seven four-year leap
-days followed by one five-year leap-day, was known and built into the
central sarsen structure of Stonehenge. This suggests that the observations
and records for establishing confidence in this pattern (for either the
vernal equinox or the summer solstice) actually predate that structure
(currently estimated at ca. 2300 BC calibrated radiocarbon) and thus
predate the preponderance of the evidence for Alexander Thom's eightfold
(or sixteen-fold) calendar.

This suggests that an eight-fold calendar may have been constructed to
take advantage of this Stonehenge-memorialised leap-day scheme, at about
that same time (3rd. millenium BC). If asked where and when I suppose,
that the pre-Stonehenge observing, recording and pattern-recognition could
have occured, I would point to Old-Kingdom Egypt. I will not go into my
reasons, for that, here.

Let me be clear that I am not proposing that such a scheme (of moving the
leap-day around the year by stepping it through some eight stations in the
calendar scheme) is an appropriate scheme for reforming our current
calendar (though neo-pagans may get very enthusiastic about the idea) nor
should you suppose that this was the secret scheme and perfect rival, to
the Gregorian calendar reform which I have discovered was contemplated, and
suppressed, in both Vatican and English circles ca. 1600 A.D..

As to Jim's concerns:

>All deny that they have (a la ideologically) enshrined one consideration
>above all others.  All proceed as if they were enlightened only by
>numbers, processions, intersections and fuzzy circumferances.  None
>speak of the social objectives they pursue, if any.
>
>What I'm saying here is that it all has the smack of ideology, that
>oh so familiar licorice smack of arguing for an unstated interest.
>I want to cry "But whose interest does it serve?" but dare not since
>I have only a very partial grasp of the details.  Anybody can say,
>What do you know; you can't even do the Calculus?"

I have tried to be honest about all the factors that brought me to this
discussion (see my message "Why I Do bash the Gregorian Calendar") and
I will admit that part of my current personal agenda is to remove the
name of Pope Gregory XIII from humanity's major method of ordering its days
and rhythms. This may seem petty, but I pursue it also in the belief that
the pursuit of this cause may also demonstrate the folly of unquestioning
belief even in modern scientific institutions. I am not a UNABOMBER but
there was something in what he wrote. Modern science and technology
worshippers need to be jolted out of their hypnotised march to planetary
doom! I will continue with my specific calendric proposal for a non-violent
stab at such a jolt, in a separate message. But lets not get too serious!
This is fun too!

--
Yrs, Simon Cassidy, 1053 47th.St.EmeryvilleCa.94608,USA.ph.510-547-0684.