Subject: Re 4-1/8 yr. Leap Rule responses of Richard, Jim and Amos
Date:Sun, 06 Oct 1996 23:09:04 -0700
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 [now http://www.hermetic.ch/cal_stud/cassidy/err_trop.htm]. 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:
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.