The “Compendium” of Antonius Lilius

The “Compendium” of Antonius Lilius:
Blueprint for the Calender Reform of Pope Gregory XIII

Our hypothesis of precession jolts, proposed by Ilya Topper and the author in 2004, brings a new solution to the problems of how our calendar and modern chronology developed; it has to be regarded as a first sketch needing continuous research and revision.
In Ilya Topper’s article “Kalender und Präzessionssprung” (2009), the “Compendium” of Antonius Lilius was mentioned briefly; I’ll elaborate now on this subject.

Previously we stated: The date in the Julian Calendar jumped by seven days due to a hypothetical precession jolt and in addition had moved steadily over three days due to regular precession, until the distance to the traditional vernal equinox (21st March) by late 16th century amounted to around ten days. Gregory XIII eliminated these ten days in 1582, putting the equinox back to where it had been “in the time of the Fathers at the Council of Nicæa”.

The correction of the Calendar announced in the papal bull Inter Gravissimas was based on the Compendium novae rationis of Antonius Lilius, written in 1577 as an abstract of a longer book supposedly authored by Antonius’ brother Aloysius Lilius, an Italian astronomer and mathematician working with the Calendar Commission until his death in 1576. This book was never printed and remains unpublished. The abridged version by his brother Antonio, which summarizes the content in 11 pages, was sent “to the Christian princes, famous academics … and competent mathematicians” (“ad principes christianos et celeberrimas quasque academias… peritis mathematicis“). It is a well-known but little-studied text.

The content of this introduction into the method of the planned Calendar Reform brings some surprises to any unaware reader, so I need to go into details.

The original handwritten book of Aloysius is described as an easy reading in the Compendium, which mentiones that it “was brought” to Pontiff Gregory XIII, stating that “a book written by Aloysius Lilius was brought to him [Gregory], which seems to propose neither an inconvenient nor difficult way and method to accomplish this matter. (“… dum Gregorio XIII pontifex … allatus est illi liber ab Aloysio Lilio conscriptus, que neque incommodam, neque dificilem viam ac rationem eius rei perficiendae proponere videbatur.”) : But the book remained unprinted, because preparing a printed edition, says the Compendium, would be laborious and difficult, and perhaps unnecessary for expert astronomers (“astrologers” in latin), to whom the matter should be explained (“sed cum liber nondum typis excusus sit, operosum id atque impeditum futurum erat et peritis astrologis, cum quibus ea ratio communicanda est, minus fortasse necessarium.”)

Antonius speaks throughout the Compendium in a somewhat distant way, explaining that the Pope did not intend to act without the consent of Christiandom, instead wishing to consult with the learned men of his time. His aim, he says, must be reached by concord and if objections – even possible improvements- arise, these will be taken into account. (“visum est prudentissimo pontifici de ea re peritissimos quosque huius scientiæ viros consulendos esse, ut res, quæ omnium communis est, communi etiam omnium consilio perficiatur. Cogitarat itaque eum librum cunctis christianis principibus mittere ut ipsi, adhibitis peritioribus mathematicis, illum aut sua sententia comprobarent, aut si quid deesse videretur, id omne absolverent atque perpolirent. Simul ut si qui modus aptior alicubi (quod non desperat) repertus foret, eo communicato, illum potius ipse sequeretur.”)

When the reform by the Pope was finally adopted, but rejected by the Protestants, we are excused to think that a publication of the full book by Aloysius might have proven helpful to persuade them. But this was never undertaken and as far as I could find out, Aloysius original text remains unknown today. Perhaps it contained material deemed heretical to the Catholic dogma and therefore it was deemed preferable to make public only the most relevant parts about the proposed calender reform, leaving the rest aside, as the Compendium says. (“Quare satis esse putavit, reliquis omnibus prætermissis, summa tantum capita, quæ maxime rem causamque contineant, breviter indicare.“)

And so Antonius enters in medias res, explaining the following:

Holy Easter is the highest feast (“feast of feasts”) for Christians, celebrated unanimously on the date the Holy Fathers of the Council of Nicæa prescribed, between the 14th and 21st days after the first full moon following the spring equinox . The Fathers had to fix the date of the spring equinox in the calendar to avoid disputes. (Antonius considers also the problem of adjusting the moon tables, but as this is not of interest for our question, I shall leave aside all references to the moon and concentrate on the sun).

Lilius tells us something very peculiar about the movement of the sun. First he states that the ‘Fathers were quite convinced’ that the date of the equinox (March 21st) was correct and would stay fixed (“Et quidem æquinoctii sedes in eo concilio ad XII Kalendas Aprilis collocata et constituta est; quam fore stabilem et certam propemodum sibi persuaserunt“). But this is not the case, he observes. To the contrary, the equinox has moved by unequal steps and travelled to the 11th or even 10th of March, and if nothing was done about this, it might move into winter and still go further, with no end in sight. („verum æquinoctium locum suum non facile tenuit, sed statione deserta, incertis passibus, ad ante diem quintum iam aut etiam sextum Idus Martii errans usque pervenit. Cui errori nisi mature obviam eatur, ad id tempus quo nunc bruma conficitur, accedet aliquando; neque tamen ibi terminus statuetur, quin in infinitum procedat.”)

The strange expression “the Fathers were quite convinced” —but not completely sure, it seems— hints at an unmentioned but rather obvious fact: The lengths of the solar year and the Julian Year are unequal, the latter being a fraction longer. As commonly known, Hipparchus noticed this discrepancy, and Ptolemy pointed to it clearly in the Almagest, the most important book used in astronomy from classical times till Renaissance. The Fathers must have known that by fixing the equinox to the Julian Calendar it would wander, if left uncorrected. But Lilius adds to this that the length of the tropical year was unsteady – contained in the words “incertis passibus“”(unequal steps) and “errans” (erring) – and variable. Therefore, he continues, no rule had been found to fix the date.

The Compendium then becomes explicit: Since Pope Nicolaus V, when science and liberal arts lying neglected for long were resuscitated, popes were trying to find a remedy for the uncorrect dating and a method that would avoid further troubles. (“atque equidem ea iam inde a felicis recordationis Nicolao Quinto, cuius ætate meliores literæ et liberalium artium studia, quæ diu neglecta iacuerant, reviviscere et recreari cœperunt, magna summorum pontificum cura atque studio tentata est, sed nihil constitui posse videbatur, quod non in magnam aliquam difficultatem incurreret“.)

The mentioned Nicolaus V (1447-1455) is the pope who cleansed Rome from the ruins and debris, resettling the nearly deserted town, clearing the pavements, reconstructing the aquæducts, and searching out old books to restore the knowledge from past times. It is since his time, says Lilius, that the church desires to reform the calendar. The thought comes to mind that Nicolaus might have been the first bishop of Rome after the collapse and thus did not reign 800 years after the destruction by barbaric peoples like Goths, Huns, or Vandals (as commonly taught), but only a generation or two after a general catastrophe.

It was also around this time (around 1440) that the Persian prince Ulugh Beg measured the length of the year  in his magnificient observatory, perhaps due to the need to verify the new value after a catastrophe. His calculations were accepted by European astronomers, including Copernicus. But when Nicolaus of Cusa proposed a correction of the calendar at the Council of Basle (1431–1449), the exact value of Ulugh Beg’s measurements was still not generally known, and so Nicolaus of Cusa’s proposal to eliminate seven days from the calendar was rejected, with good reasons, we might add.

The text of the Compendium describes very well the situation of its time, namely general uncertainty of all astronomical dates in regard to traditional ones: The tropical year is variable, and therefore the equinox moves. So it was not the fault of ancient Julius Cæsar —the last authority who had reformed the calendar— but this continued irregularity of the movement of the sun which hindered and prevented reliable methods of updating the calendar, considers Lilius.

As far as astronomy is concerned, Lilius goes on, one sees two huge difficulties. Firstly, the length of the year is inconstant, as found out by learned mathematicians of different epochs, who had been convinced that they remain unequal for all time; so it remained impossible to install rules fixing the date of the equinox forever in the calendar. (“nam quod ad astrologiam attinet, duæ potissimum res obstare atque officere videbantur. Primum ipsius anni vertentis iusta certaque mensura, quæ quoniam a doctissimis ac diligentissimis mathematicis diversis temporibus alia atque alia reperta est, non eadem semperque sui similis esse convincitur. Cum ergo sol tam vaga et mutabili ratione labatur, difficillimum factu erat intercalationes ita dispensare ut æquinoctia ævo perpetuo certas ac fixas habeant in calendario sedes“).

The second difficulty concerns the full moon problem and is left out of our article, as explained above.

Lilius proposes a remedy to provide a long-sought rule for the future, proposing a so called ‘Alfonsine year’ to be used as basic, an “average measure” which would keep the error minimal. The spring equinox,he states, arrives one day early every 134 years.
(“proponit enim sibi anni Alfonsini mensuram, quæ inter varias media est, atque ideo errori minus obnoxia; ex qua subductis calculis efficitur ut in annis plus minus CXXXIIII æquinoctiorum loca integrum antevertant diem.”)

The spring equinox date has moved by 13 days since Julius Cæsar, says Lilius, and therefore, thirteen days should be eliminated from the calendar. Or rather, he suggests, ten days, representing the difference since the Council of  Nicæa, because this would be better for the dignity of the Church. This would be done either by omitting the intercalary day over the next forty years so by 1620 the calendar return into line; or as others proposed, the ten days would be corrected all at once the next year (1582).

This latter proposal was finally adopted, as we know.

In addition, an omission of the intercalary day every 134 years was introduced for the future, suppressing the intercalary day in every full century whose basic number was indivisible by four (i.e. 1700, 1800 and 1900). Using this procedure the calendar would remain correct forever — if nothing else happens. This is the Gregorian calendar we still use today, and so far, nothing has happened.

It should be noted that the Compendium – just like the papal bull – mentions no dates nor chronographical information for the ‘historical’ events of reform by Julius Cæsar and the Council of Nicæa. It only gives relative distances for the amount in error: thirteen days for the first one, ten days for the second. The problem of chronology remained unsolved and the impossibility to retro-calculate such faraway dates into the past was known. To introduce any wrong dates into this so important process would have made it generally unacceptable, we must conclude.

Between the ‘historical’ Julius Cæsar’s solstice date (at December 25th, sol invictus) and the Nicæan Father’s equinox (March 21st corresponding to December 21st), not three but four days should have elapsed, a fact that which was noticed by the Calendar Commission and remained unexplained by the simple fluctuation of the date which the intercalary day causes. Jesus’ passion is adjusted to March 24th while his incarnation lies on March 25th, corresponding to his birth on December 25th: 130 years had to pass to account for this one day discrepency.

With all this ponderous discussion by the calendar makers, it is difficult to ascertain why March 24th or 25th was not chosen for a corrected equinox. Possibly the time elapsed between these two events supposedly having historical reality, Cæsar and Nicæa, was really unknown. Finally the Church adopted the Council of Nicæa as starting point, with a reason neatly expressed in the Compendium: The dignity of the Church —not that of God— would thus be restored, (‘ex ecclesiastica dignitate‘).

From what we read we can conclude one obvious fact: Lilius did not believe in a steady precession allowing retrocalculation over any amount of time. He mentions no dates for Cæsar nor Nicæa, indicating that fixing the equinox over longer times was incalculable. This idea is repeated in the Compendium, and its reason is clearly expressed, too: Since the sun is moving in irregular way, it is impossible to introduce any rule to keep the equinox steady. The length of the tropical year is variable, which has been found out by the greatest astronomers, as Lilius himself says.

Those “greatest and most diligent astronomers” mentioned are probably the ones known in his time, such as the Greeks (Hipparchus and Ptolemy among others) or the Arabs (for example al-Battani, i.e. Albategnius, whose works were even translated into Spanish and widely published). They all gave differing results for the tropical year length: Hipparchus measured 365 ¼ days minus 1/300 part of a day, which meant six minutes longer than today, while Battani’s year was two minutes shorter than today, and eight minutes shorter than Hipparchus’.

Lilius projects a “medium value” and called it ‘Alfonsine year’, an incorrect designation (it is Ulugh Beg’s year value) but it served his purpose. The year became known as that of Alfonso X, the astronomer king of Castilia, only 27 seconds longer than today’s, which was exact enough. The designation probably was impelled by the Church because it was much better to mention a Spanish Catholic king rather than a Persian prince as an authority.

[Note: In my latest book on the subject, Das Jahrkreuz (2016, p. 180 and 240), I explain that Alfonse stands for the Spanish astronomer Alonso de Córdoba whose tables from 1503 were named in honour of Isabella of Castille (reigning till 1504). He is the same Alfons Hispalensis whose measure of the year length was used by Copernicus]

The precession is understood to be the difference between the sidereal and the tropical year, the first measured against the background of the stars, the second as distance from one spring equinox to the next averaged over a long time: Only knowing both values can the amount of precession be measured. Battani (880 AD) calculated a precession value of 66,4 years per degree and his contemporaries had similar results (sometimes one year more or less) after painstaking observations: Kushair gives 66,25, Sufi 65,4, Biruni (1031 AD) 68,7, Haraqi (around 1112 AD) 65,7 years. This was the value used by Alfonso X (1270) in books ascribed to him.

From this we deduce that real observations were involved, so any difference to the modern value (roughly 72) implies a sudden leap caused by the irregularity of the sun. just as Lilius argues. We also surmise that this was general knowledge in his time. Between the Council of Nicæa and Pope Gregory XIII, a sudden rupture must have taken place, changing the smooth flow of the calendar. We call this the ‘precession jolt’ and place it somewhere from six to seven centuries before present.

In our first model (2004) we describe it in this way:

The axis of the Earth usually retroceding by a tiny fraction every year (precession), once in a while jumps —in the same direction— by a bigger leap or jolt. After some decades of irregular movement (called ‘trepidation’), the precession adjusts to a new regular speed nearly equal to that prior to the leap but measurably slightly different. On account of these unknown amounts, from the jolt itself and the swaying movement after a jolt (trepidation), it is impossible to tell by astronomical calculation the exact amount of years that have elapsed between two events before and after the jolt, only by measuring astronomical data. If this last jolt corresponded to a week in the calendar, (as we think we have reasonably shown, see our article in 2004) and the intercalational error amounts to two days (as it would from 1300 AD to Pope Gregory), there remains one more day to be reckoned with, possibly hidden owing to the uncalculable time span of the trepidation.

Our first draft (2004) included two jolts near each other, about 650 and 740 years ago. We have come to the conclusion that we had confused two traditions; they refer to one and the same jolt, no more than 700 years before present, between the reform of Pope Gregory and the Council of Nicæa, the latter one being the starting point for Gregory. By using archaeological results we might get closer to a definite dating but for the moment we have to leave it open.

The remaining parts of the Compendium are concerned with the moon, giving final tables for calculating the Easter dates on the ground of the new reform. Although the year for the introduction of the reform 1582 is already proposed, the month is still open to discussion and had to be chosen according to suitability. For the future there are tables presented which run until 2199 ( more than six centuries!) while for the past they only go back until 1500 AD. Here’s another hint that retro-calculation was not regarded as providing sensible results if the time span exceeded certain limits.

Our hypothesis remains that counting in AD years was only introduced after 1500.

At the end of the Compendium, Lilius makes a generous move towards Protestants and all professional astronomers/astrologers by proposing: If anyone thinks the calculations of Alfonso are unreliable and prefers other values, this method using the cycle of ‘epacts’ invented by Lilius can be easily adapted to the calculations of Copernicus —or any other— simply substituting those of Copernicus,  which were added here, too. (“quod si alicui Alfonsi calculi incertiores esse videbuntur quam ut illis fidendum putet, potiusque recentioribus adhærendum existimet, is profecto intelliget eam esse huius artificiosi cycli tabulæque epactarum a Lilio excogitatæ dispositionem ac digestionem, ut nullo negotio sive Copernici, sive cuiusvis alterius calculis possit aptari, si tabella æquationis ex illis confecta, pro ea, quam ad marginem scripsimus, substituatur veluti hæc, quam exempli gratia a Copernici ratione non multum distantem apposuimus.”)

The tables of Copernicus are included in the Compendium; we know, that he, too, regarded the length of the tropical year as not always the same. In this he coincides with Lilius, and this was the general conviction. In his Comentariolus, Copernicus says:
“As the cornerpoints of the year such as the equinox are wandering considerably, everyone who thinks that the seasons are uniformely constant, is in error. By many observations at different epochs they have been found different.” He then brings the known examples of the Greek and Arab astronomers, and goes on: “These differences do not seem to be due to errors in observation because if one regards the observations more closely one finds that their differences are coherent to the movement of the equinoxes”.

The possibility that the Compendium was fabricated at some time later and could be a clerical fiction (like the aforementioned script of Nicholas Cusanus) should be considered. But after thorough deliberation I came to the conclusion that this cannot be the case. It contains elements running counter to Catholic dogma, and this is an argument for its authenticity. Had it been written later, it would not have been so favourable to the Copernican tables, and much less to the basic idea of a differing year throughout history which opposes the later teachings of the Vatican. In addition, a considerable amount of documents refer to the Compendium and its reception before 1582, as stated by the Catholic Encyclopedia. (Protestant testimonies so far I could not find.)

The members of the Calendar Commission are mostly known and named, some remain obscure or uncertain while there was a remarkably mobile membership. Even the year of Aloysius Lilius death (1576) has been doubted, and it is somewhat awkward that his book has never been published, as it would be a veritable treasure trove, as we have tried to show here.

There are two other texts similar to the Compendium. One is a handwritten report of the Commission to Pope Gregory, the other pne being the Compendium of Ciaconus, printed by Clavius, the later chief of the Commission and its last survivor. Those two texts remain unknown to me and are still to be scrutinised.

The following phrase in the Encyclopedia is doubtful:
“Certain it is that Aloisius Lilius commenced his work before the accession of Gregory XIII to the throne and even before the publication of the new Breviary, spending ten years on it.” This may be true, but when someone starts his phrase with “Certain it is …” it’s a definite red flag and severe scepticism must be observed. The mentioned Breviary is that of Gregory’s predecessor Paul V.

The following books should be consulted:

That of Alexander Piccolomini, co-adjutor Bishop of Siena who supposedly was not a member of the commission but requested to express an opinion, which he did in his “Libellus on the new form of the ecclesiastical calendar” (Rome, 1578).
Two books of Teofilus Martius from Siena: “Treatise on the Reform of the Calendar” (after 1578) and “Short Narration of the Controversy in the Congregation of the Calendar”. This influential person accuses the Commission of innovation and a lack of reverence towards the Council of Nicæa, yet the date of the equinox at Nicæa was not really known. It is conventional to believe it on March 21st, even Oriental Christians hold to this date. The proposal of Martius to put it on March 24th, or of the Veronese mathematician Petrus Pitatus, to put it on March 25th and delete 14 days, was unsuccessful.
The last date corresponds to the usual date of the winter solstice at Cæsar’s time and seems to be a very ancient tradition because the church celebrates the annunciation to Mary on March 25th .

According to the cited Catholic Encyclopedia, “responses to the Compendium are on record from Emperor Rudolf, from the Kings of France, Spain, Portugal, from the Dukes of Ferrara, Mantua, Savoy, Tuscany, Urbino, from the Republics of Venice and Genoa, from the Universities or Academies of Paris, Vienna, Salamanca, Alcalá, Cologne, Louvain, from several bishops and a number of mathematicians.”

The article continues that the Catholic princes approved of the proposed reform. Although many mathematicians had objections on scientific grounds, they were too different as to condensed in one solid argument, and most rulers thought that any new research would be time-consuming and finally lead nowhere. Therefore it was considered a better political move to accept all at once the new calendar in 1582, as proposed.

The answers included basically three suggestions from which the final solution had to be selected: The Humanists wished that the date of the equinox should be March 25th, where Julius Cæsar had put it. The University of Salamanca suggested March 24th, where it was at the time of Christ’s resurrection. Others insisted on March 21st, where the Council of Nicæa had put it, and finally they were also proposals to fix it definitely on March 11th, where it was at the time of the Commission.

Several letters to this effect are said to be extant. Those questions are said to have postponed the introduction of the reform by one year, which must be a mistake since the intended year 1582 is mentioned in the Compendium itself. Some replies reached Rome after this date.

Pope Gregory signed the bull on February 24th 1581 and published it on March 1st 1582, (New Years Day) in the Vatican. In October of the same year it was put into action and the ten days were eliminated.

Reading the Compendium this way, it delivers a sequence of arguments for our hypothesis.

Lilius and his contemporaries knew what could be said without violating currently valid knowledge. The Compendium addressed all Europe and therefore was above any foul play. Only when the Protestants clearly would not follow suit, the Catholic church then swept scientific standards aside, hiding all ideas contrary to their dogma. The Compendium can be regarded as one of the last open-minded documents of the Church after the Council of Trent.

From 1700 the Protestant churches mostly implemented the Gregorian Calendar, thus safeguarding the dogma of the uniformity and invariability of the planetary system.

The Orthodox churches have so far not joined this ‘plot’ ; some like the Greek, have indicated a willingness to comply in the near future.

Uwe Topper 25. 11. 2009

BIBLIOGRAPHY:

Cusanus, Nicolaus: De emendatione Kalendarii (Latin and German by Victor Stegemann, Heidelberg 1955)
Copernicus, Nikolaus (around 1514): Commentariolus (German transl. by F. Rossmann, Darmstadt 1986)
Lilius, Antonius (1577): Compendium, as edited by Clavius, Christopherus (1603): Romani calendarii … restituti explicatio (Rome)