Subject: Implementing a correct 33-year calendar reform
Date: Wednesday, 09 Oct 1996 (finalised)
From: Simon Cassidy <simoncas@pacbell.net>
To: East Carolina University Calendar Discussion ListI wll take up from where I left off, (answering Rick McCarty's query about how I think a 33-year calendar could work), by repeating the relevant significant paragraph at the end of my "Thirty-three year calendars" message:
>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..That scheme (the only one that I feel is appropriate for our time), which has appeal for christians and non-christians alike, since it embodies many different traditions of human knowledge into a perfect christian solar (and solunar) penitential reform, is simplicity itself, and has been in effect since March 1st. 1980 on a probationary trial period of 36 years!
All we HAVE to do (before the trial period granted to us ends, on February 28th. 2016) is to decide, whether we wish to continue having leap years in A.D. years with numbers divisible by 4, except century years not divisible by 400 (the simplest expression of Pope Gregory's rule); or whether instead TO CONTINUE WITH A CYCLIC REPETITION OF THE EIGHT NOMINAL LEAP-YEARS IN THE 33-YEAR TRADITIONAL LIFE OF JESUS!
The above statement, in terms of the life of Jesus is an elegant and totally sufficient and determinative definition of the proposed new way to insert leap years, but is not prescriptive in a simple numerical fashion like the Gregorian rule (which requires no math. beyond the 4-times-table up to 100).
Fortunately, this years-of-Jesus rule (henceforth referred to as the "Anni- Domini" rule) is exactly equivalent to a mathematical statement which requires no more arithmetic than the 4-times-table up to 32 (and the simple shopper and shopkeeper's, price-totalling and change-making skill, needed for a couple of double-digit additions or subtractions).
In mathematical language we can say "February will have 29 days whenever the A.D. year-number, reduced modulo 33, is non-zero and divisible by 4."
But, in its simplest layman's formulation, here, finally, is the Anni-Domini Leap-Year Decision Procedure, which will (initially) triple the current accuracy with which the calendar follows the Vernal Equinox.**
Start with the Anno Domini year-number to be tested.
Get a new year-number by adding the number of centuries in it to the remaining number of years (beyond whole centuries). E.G. for 2012 A.D. add 20 to 12 to get 32 A.D.
If possible repeat the first step until it can no longer reduce the year. E.G. for 1996 A.D. add 19 to 96 to get 115 A.D. then repeat and add 1 to 15 to get 16 A.D.
If the result is greater than 33 A.D. then subtract 33 or 66 to finish. E.G. for 2016 A.D. add 20 to 16 to get 36 A.D. then subtract 33 from 36 to get 3 A.D.
We now have a year-number guaranteed to be between 1 and 33 A.D. inclusive. If it is 4,8,12,16,20,24,28 or 32 A.D. then the tested year is a leap-year.
So, 2012 reduces to 32 and thus is a leap-year, and 1996 reduces to 115, then to 16 and thus is a leap-year, but 2016 reduces to 36, then to 3, so is not leap in the Anni-Domini system.
One or two, double-digit additions, or, one addition and one subtraction, will suffice for all year-numbers until 3498 A.D. Then, two additions and one subtraction, or three additions, may be necessary (but three additions and one subtraction will not be necessary until 340,099 A.D.).
Note that this, current, millenial transition period, in which both the Gregorian and Anni-Domini leap-years are the same (from 1981-2015) is like the similar period around 1600 (1585-1619). This explains how John Dee's friends in parliament (Raleigh's group), were able to submit, in his absence, a concrete proposal for his calendar reform in 1585 and yet not reveal its leap-year rule. They did not have to specify any new leap-year rule until 1620! They just had to specify the number of days to apply as the special julian-discontinuity-correction.
Dee's treatise written in 1582, specified an eleven-day correction. But it is followed by a note allowing a ten day correction for the year 1583. This is usually interpreted as Dee capitulating to the Gregorian correction so that e.g. commerce with France would not be affected by differing calendars. But actually, in the Anni-Domini calendar, 1583 should be a leap year not 1584. Thus a ten-day correction in 1583 combined with NO LEAP DAY in 1584 adds up to an 11 day correction for the years 1585-1619. Similarily an eleven day correction if applied in 1582 (when Dee apparently wrote the main body of his treatise) would be synchronous with the Gregorian calendar (with its ten day correction in 1582) only for the period March 1583 to February 28th. 1584. The Anni-Domini cycle required a February 29th. 1583, which would pull Dee's correction back to a temporary synchrony with the Gregorian calendar, just until February 28th. 1584, when, as already stated, the Gregorian calendar's leap day would pull it back, to being one day behind the Anni-Domini calendar, again.
This is just to forewarn you that other historians will insist that there is proof, in Dee's own handwriting, that he proposed that England follow the Pope's calendar reform (an otherwise most unlikely assertion, given what I have already narrated to you, about the attitude of his circle to the Catholic League, Pope Gregory himself, and the jesuits). The secrecy around the whole project has confused all historians to date. And note that when I talk about February 1583 or February 1584 I am using the modern convention which begins the year with January; NOT the convention used by many Englishmen of the time which started the year in March. The confusion over which convention Dee used has not helped clarify matters either!
The secrecy was required by Dee's anti-Spanish colleagues (who needed time to first break King Phillip's monopoly on the calendrical longitude) and this kept postponing official implementation. Dee left for Germany, in September of 1583, to confer with William "the wise" and feel out the alchemical Emperor Rudolph. Dee was irenic at heart and probably hoped to be able to persuade the Holy Roman Emperor and thus all his Catholic subjects, to desert the corrupt Papal calendar for the perfect Nicene version which he had entrusted to Raleigh's "Atlantical" venture and parliament.
In light of the apparently implausible nature of my "conspiracy theory", it is instructive to examine the wonderful double meaning in a little piece of verse (perhaps inspired by Dee's spritely adviser Uriel) which appears to be, as intended for insertion, in that particular reform proposal of Dee's, which planned for a 1583 10-day correction by Queen Elizabeth (I will attempt authentication to confirm Dee's authorship.)
ELIZABETH our Empress bright, Who in the yere of eighty three, Thus made the truth to come to light, And civile yere with heaven agree. But eighty foure, the Pattern is Of Christ's birth yere: and so for ay Eche Bissext shall fall little mys, To shew the sun of Christ birth day. Three hundred yeres, shall not remove The sun, one day, from this new match: Nature, no more shall us reprove Her golden tyme, so yll to watch.The second of these three consecutive verses from the piece (as it appears in Robert Poole's web-page essay on Dee's reform, which can be found at http://ihr.sas.ac.uk/ihr/esh/jdee.html) is usually, as here by Poole, interpreted to simply repeat the statement, in the body of the treatise, that the birth year of Jesus is commonly held to be a leap-year ("Bissext") and that 1584 will be like it in this respect and the Sun will be in the same point of the zodiac (on Christmas day or New Years) for Jesus' anniversary.
However, from the point of view of the Anni-Domini calendar rule, a whole other meaning springs to light. The 33-year "Pattern" of the rule makes the year 1584 (0 modulo 33) equivalent to 1 B.C. (traditionally Christs birth year) AND 33 A.D. (traditionally the year of the Passion), thus marking the beginning and end of a cyclic repetition of the life of Jesus. "And so for ay", thus, using this "Pattern", we can from now on, place each leap year ("Eche bissext") with almost no error ("shall fall little mys"), repeating the solar behaviour over and over, in a cycle begun at the birth of Christ.
Note also that, as Dee was certainly aware, it was not at all clear that the year now known as 1 B.C. really was a leap-year; that is, officially, and as actually observed, in the then Roman, Civil Calendar (when of course it was not known as the year 1 B.C. but as some year of Augustus or his consuls). Dee's young friend, Thomas Harriot, who went to Roanoke and did the survey, with John White in 1585-6, of the area necessary to stake England's claim to the Calendrical meridian (its there on their map!), apparently collected the various theories, about this ambiguity in the way leap years were assigned from 45 B.C. (1 Julius Caesar) to 8 A.D. (53 Julius Caesar). These theories can be found set out in columns, in BM MS ADD. 6788 (Thomas Harriot Mathematical Papers) at folio 499 (Recto), written after Dee and Clavius were both dead. Harriot was apparently concerned abut Christoph. Clavius' and Joseph Justus Scaliger's claim that neither 1 B.C. nor 4 A.D. were "actually" leap years (this theory is labelled as theirs in his column 7). Such claims would tend to undercut the elegance of the "years-of-Jesus" appeal of the Anni-Domini 33-year leap-day cycle. At columns 2 and 3 of his table, Harriot posits unnamed theories which probably represent the two alternatives that our spritely verse holds out.
The first alternative (Harriot's column 2; column 1 being the years numbered from the calendars inauguration, by Julius Caesar in 45 B.C.) is the banal unthinking assumption that the Romans had a leap year every four years from Julius Caesar on. This meaning would hold if Dee's calendar reform were not carried out properly after he left for Germany, and 1584 were deemed a leap year in contradiction to the Anni-Domini prescription. The second alternative (Harriot's column 3) however, has 1 B.C. a common year and has the four-year leap-days starting with 4 A.D., precisely in accord with the Anni-Domini rule, and with the hidden meaning of the verse. This second hidden meaning would only become apparent if parliament deemed 1584 a common non-leap year while Dee was to be away in Germany, or if posterity were to see Dee's "plat for the meanes".
The third verse is usually held to predict that the accuracy of the new calendar will match the sun's behaviour (every Christmas day?) to an accuracy of one day in three hundred years. This is not much of a claim to accuracy since it implies a possible error of up to 0.0033 days between the real solar year (based on Christmas or New Year?) and the proposed Elizabethan reform's average year (despite the fact that this putative average calendar-year or the procedure for maintaining an average year different from the julian one, is never actually stated anywhere in the extant works credited to Dee!!). If Dee really meant to follow the Gregorian year-length and leap-year rule, then he would have known that the accuracy (for any point in the tropical zodiac) was much better than this apparent 0.0033 days/year claim.
On the other hand, in terms of the accuracy of the Anni-Domini leap-year rule, this verse can be claiming that the Vernal Equinox will always occur on the same calendar day for at least three hundred years (at some calendrical prime meridian). This claim is much more in line with what we know of the accuracy of astronomy in Dee's time (both claimed and in retrospect). It is claiming an inaccuracy of no more than one ten thousandth of a day between the (unmentioned) average year of the proposed Elizabethan calendar and the true tropical year (true "Vernal Equinox" flavour, not the modern tropical Newcomb-style year, wrongly characterised as the mean year between V.E.s).
In retrospect this claim is uncannily accurate, in that, from 1580 until 1880, for calendar days beginning and ending at midnight local apparent time (the most unambiguous rule available in Dee's time), the Vernal equinox would indeed have occured always on March 21st. at the longitude that Sir Walter tried to plant his city of Raleigh in "Old Virginia" (i.e. White's "50 miles into the main" from Roanoke Island, under the one meridian drawn, on his and Harriot's, map of the area, which also shows its relation to the Bahamas). That is, of course, if the full calendar reform with the ten-day correction in 1583 and NO LEAP DAY in 1584 using the Anni-Domini leap-year rule had been properly implemented!
I invite those of you mathematically competent, to do the detailed calculations and also check the history of time-conventions in effect at the dates involved. I personally am left amazed at the prophetic quality of this verse. If the calendrical meridian is calculated based on local mean time rather than apparent time (versions of mean time were in use by some astronomers in Dee's era) then "White's Ralegh longitude" seems good to this day, but if apparent local time is adhered to then "White's lost city of Ralegh" was saved from experiencing March 20th. Vernal Equinoxes (under the 11-day julian-corrected Anni-Domini calendar) in the nick of time by Railway Time-zone time of the 1880s becoming standardised to the mean-time under the meridian which lies exactly 5 hours behind Greenwich (75 degrees of longitude West of Greenwich meridian).
"At noon or before on Sunday 18 November 1883 public clocks all over North America were altered to the 'new standard of time agreed upon, first by the railroads, for the sake of the uniformity of their schedules, but since generally adopted by the community through the action of various officials and corporate bodies as an obvious convenience in all social and business matters'" (Derek Howse in "Greenwich Time" 1980, quoting the New York Herald newspaper of that date?). November 1883 is 300 years to the month, from Dee's mysterious "secrett" deadline for implementation of his Calendar Reform, (see Poole http://ihr.sas.ac.uk/ihr/esh/jdee.html note#7 re this "deadline").
As we all probably know, Ralegh's American colonisation attempts failed, the last being John White's "Lost Colony" in 1587. Most everything but the Spanish Armada was forgotten about, in the following year of 1588. Dee's calendar has languished in secret ghostly committee ever since! Although some thought the ghost of Dee exorcised, when the British parliament implemented an eleven-day correction in 1752, we should note, that Queen Elizabeth herself, at the prompting of her new favorite Walter Raleigh, had reassured Dee, in April of 1583, that "Quod defertur non aufertur" (What is deferred, SHALL NOT BE ABORTED!).
And mow we can see why Dee insisted, on an eleven day correction in contrast to the Gregorian ten day correction (though his extant treatise diguises the reasons), before leaving, in 1583, to attempt to convert the Holy Roman Emperor to his calendar. With a ten-day correction, his Anni-Domini leap-year cycle would have kept the Vernal Equinox always on the 20th. of March (at longitudes through Ralegh's Virginia), but, with an eleven day correction, the Vernal equinox would have always fallen on 21st. March, the stated Nicene goal of the Gregorian reform! He certainly had a wonderfully seductive proposal for a Holy Roman Emperor who might feel miffed at the Pope, for not allowing the calendar reform pronouncement to emanate from the proper Imperial quarters. Dee could hand the Emperor a proposal even more Catholic and Orthodox than the Pope's! As it turned out, Dee fell foul of Vatican agents in Prague, and may never have felt secure enough to confide in any of Rudolph's experts.
Though I doubt that there will be any calendar reform before the turn of the century, I propose that, if and when it is decided, to adopt the Anni- -Domini leap-year rule, then we ought to ritually expunge Pope Gregory XIII from our calendar, by finally applying Dee's extra day of correction.
In this way, the Nicene tradition will finally be fulfilled and the Equinox will occur on March 21st.** for as long as Gaia (Earth's rotation) allows. This symbolic changing of the guard could conveniently, and with all solemnity, be achieved with no requirement for any special activity on the actual date affected by the proclamation. The ritual would consist of an act of government(s) naming February 29th 2000AD "Pope Gregory XIII Day" and then immediately thereupon, consigning his name and calendar to perdition by passing the act of discontinuity, which will leap one day ahead of the Gregorian calendar by declaring the year 2000 A.D. to be (or have been) a regular non-leap year! (as were 1800 and 1900 A.D.).
In this fashion no planet need be offended ever again by having its day of the week associated with Pope Gregory XIII's leap-days (pardon my levity).
After the Vatican recovers from high dudgeon, it will find that its Easter and metonic solunar tables will work readily and more accurately in the new Anni-Domini leap-year system, by the simple expedient of applying their lunar correction every 231 years (e.g. whenever Monday the 29th. February is followed, five years later, by Sunday 29th. February) instead of the current application of lunar corrections at some of the century years.
** The increasing solar accuracy will actually keep the Vernal Equinox within the same twenty-four calendar-hour period, every year for many centuries (probably for millenia) to come. This 24-hour period will be always on the same calendar date (for local, apparent or mean time) at longitudes such as Bermuda (Where Shakespeare's "The Tempest" envisages Dee with his spiritual adviser Uriel, as Prospero and the spirit Ariel, surrendering his magic staff into the earth and his book into the water). If, however, we consider calendar dates to be CIVILLY separated, by the stroke of midnight ZONE-TIME, then the Eastern Standard Time-zone (5 hours behind Greenwich) is still currently the place where the Vernal Equinox can stay on the same date, but a new time-zone (4 and 1/2 hours behind Greenwich) may succeed it, in some future century. (Math. based on Meeus '83 & '91).
Yrs, Simon Cassidy, 1053 47th.St. Emeryville Ca.94608, .ph.510-547-0684.