Millennium Mistake
© 2003 Jan Zuidhoek 2010
www.millenniummistake.net
1 introduction
On
When people hear someone assert that the year 2000 was the last year of the previous millennium then they often react by saying something like: “oh no, the year 2000 was the first year of the new millennium, because the year zero was the first year of our era”. At first sight it possibly looks as if the logic of such a reaction leaves little to be desired, for a millennium is by definition a period of one thousand years. But what is meant by “the year zero”? To be able to answer that question, and with this the tricky question when exactly the third millennium began, we have to find out which is exactly the structure of our era (the term ‘era’ here of course in the meaning of a linear system of numbered calendar years). For that purpose we will enter the field of historical chronology, which, as the science of locating historical events in time, is part of the discipline of history (chronology is the backbone of history).
After having taken note of the history of the coming into existence of our era (in section 2 and section 5) we will establish that there is no year zero in our era (in section 5) and explore why there is no year zero in our era (in section 6). After having established thus which is the connection between the moment zero (i.e. the beginning moment) of our era and the millennium question (see also e.g. www.janzuidhoek.net) the solution to this question (see section 8), as well as the justification of the term ‘millennium mistake’ (see section 10), is there for the taking. Not surprisingly it is the sections 2, 5, 6, 8 and 10 which together stand for the original core of this website. Clarifying remarks in reply to the standpoint with regard to the millennium question taken in this website and sceptical reactions to it led to reformulation of passages or were included among the deductions of section 7 or incorporated into the objections of section 9.
Besides the millennium question still some other subjects related to the beginning of our era (but not being of vital importance for the solution of the millennium question) are treated in this essay, e.g. in section 3 calendars, in section 4 Easter tables, in section 11 Anni Domini. A table obtained at my investigation into Anni Domini provides us not only with the most probable two possible dates of Jesus’ dying day (see section 11), but also with a first indication that the ultimate replacement of (not exactly calculable) dates of the fourteenth day of Nisan (see section 3) with dates of Alexandrian Paschal full moon (see section 4), which the church of Alexandria (Egypt) applied around the year 320 to make possible the construction of the first generation of the classical Alexandrian Easter tables (see section 4) so important for the history of Christianity, must have gone hand in hand with rather substantial changes of position with respect to Nisan (not particularly in accordance with the centuries old Christian tradition which says that “Paschal full moon = 14 Nisan”), which changes of position are examined more closely in section 12 (which is the newest version of the very first publication devoted to this subject). After an addition to our result with regard to Jesus’ dying day (see section 13), an explanatory scenario with regard to the provenance of those changes of position (see section 14), an analysis of the meaning of certain remarks of Beda Venerabilis (see section 4) leading to remarkable conclusions which only can be explained in terms of those changes of position (see section 15) and a consideration devoted to possible coincidences of the date of the fourteenth day of Nisan with the date of Easter Sunday in the fourth century (see section 16) this essay is ended with an epilogue in which the reasons are summarized why this website exists (see section 17) and a concise profile of the author (see section 18).
This website is provided with an index and a concise bibliography.
2 incomplete era
Our era is the complete Christian era (see also section 5), nowadays in combination with the Gregorian calendar (see also section 3) the most widespread dating system on earth. The founder of that era is the learned monk Dionysius Exiguus, who, originating from a region in or near the Danube delta area, settled in Rome around the year 500. In the year 525 he finished his Easter table (see table 1), which forms a continuation of the Easter table which is attributed to bishop Cyril of Alexandria (in Egypt) but was composed by an assistant of this bishop (around het jaar 440). The most important detail of Dionysius Exiguus’ Easter table (see also section 4) is that the calendar years (Roman calendar) herein (see column A) are not numbered according to the era of the emperor Diocletianus, as still was the case in the Easter table attributed to Cyril, but according to his new era, which was intended to have begun with Jesus’ incarnation.
Now the dating of Jesus’ birth is an impossible task, even for modern historians (see also section 11). So it is not so surprising that Dionysius Exiguus was not able to that either. Be that as it may, he chose indirectly (via the era of the emperor Diocletianus) the Roman year 754, i.e. the year 754 of the Anno Urbis Conditae (literaly ‘in the Year of the Foundation of the City’) era, as the starting year of his new era, on the basis of rational and intuitive considerations (see also section 11). Then he took the successive Roman calendar years from and including that starting year and numbered them 1, 2, 3, ……. With the duration of a year as unit of time, the incomplete Christian era, better known as Anno Domini (literaly ‘in the Year of the Lord’) era, thus obtained, boils down to our first timeline (figure 1):
* year 1 1 year 2 2 year 3 3 …… time (in years)
in which (modern) picture the moment * = the moment zero (i.e.
the beginning moment) of our era, i.e. the midnight point in time at which the
first day of our era began, and year 1
= the year 1 (of our era) = the
Roman year 754 and e.g. year 10 = the year 10 (of our era) = the Roman year 763
(this calendar year began at moment 9
and ended at moment 10). The
first day of our era is not the day of Jesus’ birth, but simply
About a moment zero or about a year zero Dionysius Exiguus, who used no other numerals than Roman ones in his Easter table and in his calculations, never worried. Though he understood very well that dividing (which in this case boiled down to repeated subtraction, for in his time in Europe division algorithms were not available yet) a positive integer by e.g. 19 sometimes produces no remainder, the number zero, being an (extremely important) mathematical concept, was not known to him. That is the reason why in our first timeline (see figure 1) the place of the moment zero of our era has been marked by means of an asterisk (*).
Zero is a name of our tenth digit as well as of the number 0 with the unique property that x + 0 = x for any number x. The digit zero in our decimal positional system as well as the number zero is usually indicated with the symbol 0. For centuries before the invention of the number zero (see also section 5) precursors of the number zero were used (e.g. in Egypt and in Mesopotamia), i.e. words or symbols which represented an empty spot in a positional system or literally ‘nothing’ and were not considered by their users as (abstract) numbers with which abstract calculations could be carried out actively.
Why must the digit 0 be considered (historically seen) as our tenth digit? Counting precedes calculating, personally as well as (pre)historically. From time immemorial one counts by means of the cardinals one, two, three, …… (in words, and without zero). In order to create a complete decimal positional system we need nine symbols for the first nine positive integers (e.g. the digits 1, 2, 3, 4, 5, 6, 7, 8, 9) and next a tenth symbol (e.g. the digit 0) to make it possible to compose a symbol (e.g. the symbol 10) for the tenth positive integer. And thus it has gone. Gerbert, the French mathematician who became pope Sylvester II in the year 999, knew of the first nine digits belonging to the decimal positional system, but it is certain that he did not know the real significance of the digit 0. It is the digit 0 which has enabled us to construct our decimal positional system. As inventing the number zero did not precede the discovery of the positive integers, inventing the digit 0 did not precede the formation of symbols for the first nine positive integers.
The number zero is a relatively modern concept, which could jell only after one had got sufficient experience with the use of its precursors. The last phase of that development was the phase in which one became definitely familiar with carrying out abstract calculations with all ten digits (including the digit zero) in the decimal positional system (this explains that the invention of the number zero happened so long after the discovery of the positive integers). However, in early medieval Europe one used no other numerals than Roman ones and one had to make do, just like in ancient Rome, with abacuslike aids and simple calculations in which neither a numeral zero nor the number zero was used. In that Europe nobody was acquainted with a numeral zero or the number zero. Neverless, the presence of the Latin word “nulla” (meaning ‘none’) in the third column of his Easter table (see table 1) creates the impression that Dionysius Exiguus did know that important number. However, by analyzing the text accompanying his Easter table, we can convince ourselves of the fact that that impression is false (see also section 4).
Of course ‘the year 1’ means simply ‘the first calendar year of our era’, as ‘the king William I’ means nothing else than ‘the first king named William’. Numbering of tickets begins at 1, for the counting of any kind of things we do not need the number zero at all. So the counting of years is not different from the counting of any other kind of things (even though sometimes for a moment one could think that the counting of months actually ought to start from the number 0 instead of the number 1, for javascript planners thought to do science a service by assigning in their system the number 0 instead of the number 1 to the first month of the year). Someone born on 1-1-1 will have celebrated his tenth birthday probably (as usual) on the day he completed the tenth year of his life, so on 1-1-11.
Not relevant to the solution of the millennium question but illustrative for the fact that it is absolutely not obvious indeed that in case of the introduction of a new era one begins with a year zero, is the example of the French revolutionary era. When on 22-9-1792 French revolutionaries proclaimed the first French republic they also resolved to begin a new era on this special day; this day was regarded as the first day of the first month of the year 1 of their new era. They also had no need for a year zero, although in France as early as in the course of the eighteenth century the number zero had been generally accepted (see also section 5). Apart from that it is interesting to remark that the introduction of the era of the French revolution, unlike the introduction of the Anno Domini era, was accompanied by a drastic reform of the calendar. Any calendar year of the French revolutionary era began close by the September equinox and consisted of twelve months of thirty days each and five or six single days. The French revolutionary era was in use only until 1-1-1806.
In Roman antiquity calendar years were frequently counted from any supposed year of foundation of the city of Rome. However, in reality the Anno Urbis Conditae era, like the Anno Domini era, did not exist yet in antiquity, for it was used systematically for the first time not before the beginning of the fifth century, namely, though in a rather careless way, by the Iberian historian Orosius. Though probably Dionysius Exiguus was acquainted with (but never used) the Anno Urbis Conditae era, pope Boniface IV (around the year 600) seems to have been the first who recognized the connection between those two important eras (i.e. AD 1 = AUC 754). However, the complete Christian era (see also section 5) came actively into use as a coherent system for dating historical and current events only in the eighth century. Only in the tenth century our era was used for the first time for the dating of a papal document (namely in the year 967), and only about the year 1060 the church of Rome put this era definitely into use. Never any authority or government or the United Nations did definitely away with our era or replaced this (nowadays generally used) era definitely with another.
The next section being of importance for the solution of the millennium question is section 5.
3 calendars
Besides the millennium question still some other subjects related to our era are treated in this article, e.g. in this section calendars, in section 4 easter tables, in section 11 Anni Domini, in section 12 the initial connection between dates of Alexandrian Paschal full moon and dates of the fourteenth day of Nisan (however, for the solution of the millennium question these subjects are not essential). The next section being of importance for the solution of the millennium question is section 5.
Relatively shortly before he was assassinated, Julius Caesar had modernized the then gradually hopeless outworn Roman calendar, at which he had decreed not only that henceforth every new calendar year should begin on 1 January and once every four years there should be a leap year but moreover that this regulation was considered to apply (retrospectively) to the calendar years gone by. However, in the first half century of its existence the leap year regulation according to the Julian calendar did not function well (see also section 7). For that reason the emperor Augustus made (around the beginning of our era) a regulation according to which henceforth every fourth calendar year after the Roman year 757 should be a leap year; this regulation boiled down to the rule that henceforth any calendar year of the Anno Domini era after the year 4 should be a leap year if and only if its number is divisible by 4 (see also section 11). Only in the sixteenth century the Roman calendar was adjusted once again, namely by pope Gregory XIII in the year 1582, which resulted in the (nowadays mondially used) Gregorian calendar provided with the current leap year regulation (see also section 7). Although the Julian calendar was no ideal calendar, it functioned precisely and unbrokenly from 1-3-4 up to and including 4-10-1582 (see also section 7). Not surprsingly the dates given in Dionysius Exiguus’ Easter table are Julian calendar dates.
In the first four centuries of our era besides the Julian calendar still another solar calendar was in general use in the Roman empire, namely the Alexandrian calendar, which just like the Julian calendar was equipped with a leap year proportion of one to four (each Alexandrian calendar year consisted of twelve months of thirty days each and five or six single days). Though those two calendars were mutually convertible, the conversion of dates from one calendar to the other was no sinecure. Contrary to those two calendars, the Egyptian calendar (the calendar without leap year regulation of which the Alexandrian calendar was an improved version) was only used for agricultural and practical astromical purposes. It is a matter of course that with respect to historical events after the year 1582 we normally make use of Gregorian calendar dates and with respect to historical events before the year 1582 we normally make use of Julian calendar dates (which sometimes are Alexandrian calendar dates converted to the Julian calendar).
Unlike the Julian and the Alexandrian calendar, the Jewish calender is a lunar calendar, in which each new month begins shortly after a (actual) Newmoon (i.e. point in time of conjunction of sun and moon). But since its coming into being, far before the beginning of our era, until the moment (about the year 360) at which the Jewish calendar was fixed, the beginning of the new Jewish calendar month and of the new Jewish calendar year depended not only on astronomical but indirectly also on local meteorological circumstances (namely the ones under which in Palestine the first appearance of the moon crescent after Newmoon was searched for). As a consequence, with regard to the time before the moment at which it was fixed, the Jewish calendar is not exactly verifiable. Every Jewish calender year consisted then (and still consists now) either of twelve (mostly) or of thirteen calendar months of 29 or 30 days each. In that time Nisan was the first, Iyyar the second and Adar the twelfth month of the Jewish calendar year and Pesach, i.e. Passover, i.e. the Jewish Paschal feast (which lasted eight days), was always prepared in the morning and afternoon of the fourteenth day of Nisan. In that time Pesach began always with the sunset of the fourteenth day of Nisan and the meal in which the Paschal lambs slaughtered in the afternoon of this day were eaten usually with the rise of the full moon roughly an hour after this sunset (see also section 12).
From its coming into being until the moment at which the Jewish calendar was fixed, by tradition the beginning of every new month of the Jewish calendar was determined at a very special moment, namely at sunset in Palestine at the beginning of the thirtieth night after the sunset by which the expiring Jewish calender month had begun. At the time, once a month, always at such a special moment, roughly 24 hours after Newmoon, a decision had to be taken concerning the beginning of the new Jewish calendar month. If at such a special moment the first appearance of the moon crescent after Newmoon was confirmed by the Jewish authorities in Palestine (this happened roughly once every two months) then at that moment the first day of the new Jewish calender month began; otherwise the first day of the new Jewish calender month began at the moment of the then next sunset (hence each of the Jewish calender months thus defined, consisted of 29 or 30 days). As it rarely happens that a waxing moon is visible at sunset with the naked eye earlier than 24 hours after Newmoon, at the time the first day of a new Jewish calender month usually began with the second sunset in Jerusalem after Newmoon and at the time the (actual) Fullmoon (i.e. point in time of opposition of sun and moon) of a Jewish calender month fell on average roughly near the midnight point in time between the thirteenth and the fourteenth day of this Jewish calendar month.
From the coming into being of the Jewish calendar until the moment at which this whimsical calendar was fixed, in Palestine at set times not only a decision had to be taken with respect to the beginning of the new month of the Jewish calendar (once a month) but also a one concerning the beginning of the new year of the Jewish calendar (once a year). In that time the Jewish authorities in Palestine possessed the competence to interfere once a year, at the end of Adar, with the current Jewish calendar year (they did this about once every three years) by extending this Jewish calendar year by an extra month consisting of thirty days. In that time the Jewish authorities in Palestine could (by applying that competence carefully) not only prevent that the Jewish calendar year would become on average too short or too long but also that Pesach would be celebrated too early (i.e. entirely or partially still in winter) or too late. As a matter of fact, at the time the principle that Pesach should be celebrated as early as possible in spring was the only not opportunistic criterion they used as part of the exercise of that competence. At the time they must have been familiar with the growing of the days in winter and the phenomenon of the March equinox, which marks the beginning of spring on the northern hemisphere of the earth, although they then (being familiar neither with the Julian nor with the Alexandrian calendar) were not yet acquainted with any date of the March equinox.
After the destruction of Jerusalem in the year 135, too, there were always Jewish communities in Palestine. In the course of the first millennium their number fluctuated greatly, around the third turn of the century their total size numbered probably no more than ten percent of their total size in the first half of the first century. At a particular moment (about the year 360) the jewish calendar was fixed (namely explicitly related to the Alexandrian calendar and in consequence implicitly also to the Julian one). Thus as from that moment in particular all dates of the fourteenth day of Nisan were fixed. But in the second and the third century and in the fourth century until that moment the beginning of the new month and the beginning of the new year of the Jewish calendar were determined officially still in Palestine and in principle still in the same way as in the first century.
Unlike the Jewish communities in Palestine, the Jewish community in third century Alexandria (Egypt) felt compelled (because it wanted to celebrate its festivities as much as possible at the same time as the Jewish communities in Palestine) to make use of a lunar calendar scheme adjusted to the Alexandrian calendar by means of which the Alexandrian calendar dates of forthcoming Jewish festivities could be determined independently of the Jewish authorities in Palestine (usually accurate to a day). That (unfortunately unknown) lunar calendar scheme, constructed by Alexandrian Jewish calculators in the beginning of and perfected in the course of the third century, of course with the help of tables of lunar phases calculated by Alexandrian astronomers, was a system according to which successive time intervals each with a total duration of 19 Alexandrian calendar years were subdivided always as much as possible in the same way into 235 Alexandrian lunations (each consisting of 29 or 30 days) as precisely as possible consonant with Jewish calendar months. The possibility thereto rests on the fact as early as in the fifth century before Christ known in Mesopotamia but rediscovered by the Greek astronomer Meton that time intervals consisting of 19 solar calendar years contain on average nearly as many days as a time interval consisting of 235 synodic months (namely about 6940 days), which is a result of the astronomical fact that the synodic period of the moon is on average approximately 29.53059 days (this implies that the moon is taking about 6939.689 days to pass through all of its phases 235 times). Although the Julian calendar was no ideal calendar, it functioned precisely and unbrokenly from 4 to 1582. All that time every century lasted 36525 days; so a time interval of 19 calendar years lasted an average of 6939.75 days then.
Though neither the dates of the fourteenth day of Nisan of third century Palestine nor the dates of the fourteenth day of the Alexandrian lunation of Nisan (this lunation did not always precisely coincide with Nisan) are exactly calculable, any of these dates separately can be estimated, usually accurate to a day, with the help of tables of lunar phases and obvious rules of thumb, such as the (rather rough) rule that at the time the first day of Nisan began usually with the second sunset in Jerusalem after the Newmoon of Nisan and the (also rather rough) rule that at the time the date of the Fullmoon of Nisan usually coincided with the date of the thirteenth or of the fourteenth day of Nisan. Not surprisingly, it is in a similar way that the Alexandrian lunations being part of the lunar calendar scheme which was used by the Jewish community in third century Alexandria were obtained. By the way, that lunar calendar scheme can certainly have been a source of inspiration for the Alexandrian computists who around the middle of the third century, on behalf of their Paschal tables (see also section 4), began to experiment with sequences of dates with a period of 19 years. Those (Christian) computists as well as the (Jewish) producers of that lunar calendar scheme must then have been, probably independently of each other, on the lookout for a suitable and preferably as regular as possible sequence of dates of Paschal full moon with a period of 19 years standing in for a not exactly calculable sequence of dates of the fourteenth day of Nisan. In any of both cases (in order to be able to succeed in that endeavour) one must have been aware of the phenomenon of the March equinox (because Pesach should in principle be celebrated as early as possible in spring) and that endeavour must have led around the year 260 to the construction of a sequence of dates of Paschal full moon with a metonical structure. A metonically structured sequence of dates is by definition a sequence of dates with a period of 19 years such that every following date of the sequence can be obtained by subtracting from the last preceding date either 11 days modulo 30 days (normally) or 12 days modulo 30 days (only in the case of a “saltus lunae” occurring once every nineteen times); this definition rests on the congruence 18 · 11 + 1 · 12 ≡ 0 modulo 30. It is not so difficult to check that the sequence of Julian calendar dates of column F of table 1 has a metonical structure with 21 March as earliest possible date and a saltus lunae at the transition from 550 to 551.
Around the year 10 the (real) March equinox fell sometimes on 23 sometimes on 22 March, around the year 70 on 22 March, around the year 200 on 21 March, around the year 270 sometimes on 21 sometimes on 20 March, around the year 330 on 20 March. However, all that time the date 25 March was considered by the Roman civil authorities to be the date of the March equinox. The Jewish authorities in Palestine must have been then, because of the decision they had to make then once a year with regard to the beginning of the new year of the Jewish calendar, intuitively more familiar with the phenomenon of the March equinox than the Roman civil authorities. According to the Alexandrian astronomer of Greek descent Ptolemy the March equinox in his time (around the year 140) fell on 22 March. From around the year 250 to around the year 320 that date was considered by the church of Alexandria to be the date of the March equinox. Around the year 270 the Alexandrian scholar Anatolius, who was bishop of Laodicea from around the year 270 until his death around the year 290, made an attempt to reconcile the discrepant viewpoints of the churches of Rome and Alexandria with respect to the date of the March equinox by conceiving the moment of the March equinox not as a point in time or as a date but as a time interval consisting of four consecutive dates (22 up to and including 25 March). But around the third turn of century, possibly under the influence of Eusebius, the historian who became bishop of Caesarea shortly after the year 313, the (not objective) Alexandrian date of the March equinox was reconfirmed on 22 March. However, relatively soon after that the church of Alexandria definitely decided to consider the date 21 March so familiar to us (in that time and nowadays once again in reality usually the first day after the real March equinox) as the date of the March equinox. That happened around the year 320; the church of Rome took that step not much later.
The (unfortunately unknown) lunar calendar scheme the Jewish community in third century Alexandria used, must have been as early as before the middle of the third century of such a quality that its sequence of dates of the fourteenth day of the Alexandrian lunation of Nisan must have had something of a metonical structure. The discovery, by Jewish calculators or by Christian computists, connecting with the construction of that lunar calendar scheme or evolving from that lunar calendar scheme that it is possible (thanks to the astronomical fact that time intervals consisting of 19 solar calendar years contain on average nearly as many days as a time interval consisting of 235 synodic months) to approximate sequences of successive dates of the fourteenth day of Nisan by means of metonically structured sequences of substituting dates was the key to the solution of the great problem of the calculation of the date of Easter Sunday,
We will show here by means of a table in which way Alexandrian Jewish calculators, making use of dates of lunisolar conjunction and of lunisolar opposition (calculated by Alexandrian astronomers), could have obtained their metonically structured sequence of dates of the fourteenth day of the Alexandrian lunation of Nisan. That (unfortunately unknown) metonically structured sequence of dates of (which I call for convenience) Jewish Paschal full moon must have been constructed by Alexandrian Jewish calculators around the year 260 on the basis of dates of lunisolar conjunction and of lunisolar opposition situated around the year 240. As a matter of fact an adequate reconstruction of the sequence of dates of Jewish Paschal full moon will yield only a sequence of most probable dates of Jewish Paschal full moon. Hence in table 2 (with dates according to the Julian calendar) we see for each indicated calendar year (in the primary column A) mentioned in column B the best possible estimated point in time for Alexandria of the (actual) Newmoon of Nisan, in column C the most probable date of the first day of Nisan estimated on the basis of column B (using the fact that at the time the first day of Nisan usually began with the second sunset in Jerusalem after the Newmoon of Nisan), in column D the best possible estimated point in time for Alexandria of the (actual) Fullmoon of Nisan, in column E the most probable date of the fourteenth day of Nisan estimated on the basis of column C, in column F the most probable date of Jewish Paschal full moon estimated on the basis of columns D and E (the dates of column F have been chosen such that the sequence made up by these dates satisfies the requirement of metonical structuredness). In column B always the best possible estimated point in time for Alexandria of the first Newmoon after 5 March 18:00 is mentioned; the choice for this utmost point in time is closely connected with the principle that Pesach should be celebrated as early as possible in spring (in column E as well as in column F the earliest date is 21 March).
Comparing the sequences of dates of columns D, E, F of table 2 with each other, we can verify that the sequence of dates of column F is a reasonable metonically structured approximation of the sequence of dates of column D as well as of the one of colum E (a saltus lunae occurs at the transition from 224 to 225 and a one at the transition from 243 to 244) and as such indeed would have been an ideal sequence of dates of Jewish Paschal full moon. Jewish calculators in third century Alexandria had every reason to obtain such a sequence of dates, with 21 March as most probable earliest possible date (occurring in years 235 modulo 19) and 18 April as most probable latest possible date (occurring in years 227 modulo 19). In what extent the dates of column F indeed belong to the historically real (metonically structured) sequence of dates of Jewish Paschal full moon, remains a moot question.
4 easter tables
Besides the millennium question still some other subjects related to our era (but not being of vital importance for the solution of the millennium question) are treated in this essay, e.g. in section 3 calendars, in this section Easter tables, in section 11 Anni Domini, in section 12 the original connection between dates of Alexandrian Paschal full moon and dates of the fourteenth day of Nisan. The next section being of importance for the solution of the millennium question is section 5.
At the end of the first century the Christian Paschal feast was mostly celebrated on the fourteenth day of Nisan (see section 3), at the end of the second century on the first Sunday after the fourteenth day of Nisan. But because around thr second turn of century the beginning of Nisan was still not exactly computable, in the beginning of the third century computists of some churches, among which the church of Rome and the one of Alexandria (Egypt), began to calculate their own dates of Paschal full moon, in order to be able to determine their own dates of Easter Sunday. One of their primary original purposes was to produce a periodic sequence of dates adjusted to one of the two (mutually convertible) solar calendars prevailing then in the Roman empire (see section 3) which had to be not only independent but also as few as possible different from the (not exactly calculable) sequence of (successive) dates of the fourteenth day of Nisan. Initially computists of the church of Rome as well as of the church of Alexandria experimented with sequences of Julian respectively Alexandrian calendar dates with a period of 8 years, but these experiments were not particularly successful. Contrary to the church of Rome the church of Alexandria would succeed within two centuries in finding a satisfactory solution (Annianos’ Easter cycle) of the great problem of the calculation of the date of Easter Sunday, which is due to two circumstances; the first is that there was a flourishing Jewish community in third century Alexandria, the second that this Alexandria was a center of science in a much larger extent than third century Rome. Around the middle of the third century computists of the church of Alexandria began experimenting with sequences of calendar dates with a period of 19 years, computists of the church of Rome with sequences of calendar dates with a period of 84 years.
At the first council of Nicaea, convened in the year 325 by the emperor Constantine I, was decided that henceforth Easter Sunday should be celebrated every year early in spring by all Christians in principle on the very same Sunday after the day on which the last preparations were made for the celebration of Pesach (see section 3). At that important council one came also to the conclusion that anyhow it was necessary to be always amply in advance well informed about dates being eligible for the celebration of Easter Sunday, and that therefore, because of the then incalculability of the Jewish calendar (see section 3), accurate Easter tables adapted to the Julian calendar (see section 3) or to the Alexandrian calendar (see section 3) were required. The bishops who were together in the year 325 in Nicaea, were agreed about that Easter Sunday always ought to be preceded by “the Paschal full moon” as well as by the March equinox (see section 3). However, they could not reach agreement with regard to the way in which the date of Easter Sunday had to be calculated, owing to the fact that they remained in disagreement about the date of the March equinox and about the way in which “the full moon” of Nisan should be calculated.
In the time of the first council of Nicaea some considerable time Paschal tables were in use. At that time for the calculation of Easter Sunday by the different churches, e.g. the church of Alexandria and the church of Rome, (sometimes different) periodic sequences of dates of Paschal full moon were used, which dates were intended to be substitutes for the (not exactly calculable) dates of the fourteenth day of Nisan, in the morning and afternoon of which Pesach was prepared. Of course in no case (periodic) sequences of (successive) dates of Paschal full moon and (not exactly calculable) sequences of (successive) dates of the fourteenth day of Nisan, although initially as few different as possible, tallied entirely with each other. But from the third to the eighth century the sequences of dates of Paschal full moon plied by the different churches could also mutually show (sometimes even very great) differences, which was the main cause of the fact that the Paschal tables propagated by the different churches could be mutually strongly different and by no means always led to the same dates being eligible for the celebration of Easter Sunday.
The (unfortunately unknown) lunar calendar scheme which was used by the Jewish community in third century Alexandria (see section 3), must have been a source of inspiration for the Alexandrian computists who about the middle of the third century began to experiment with sequences of dates with a period of 19 years. Anyway, it is around the year 250 that they took over, on behalf of the construction of their Paschal tables, the system of the Alexandrian lunations being part of that lunar calendar scheme and the accompanying system of (Alexandrian) lunar phase numeration, in which lunar phase numbers varied from 1 to 29 or 30 (where sometimes lunar phase number 30 was replaced with a precursor of the number zero) and e.g. lunar phase number 14 indicated the “age” of the moon (i.e. the lunar phase) in days on the fourteenth day of every lunation (as a matter of fact roughly fifteen days after Newmoon). It is obvious that it is the fourteenth day of the Alexandrian lunation of Nisan, i.e. the day on which in the third century Pesach was prepared by the Jewish community in Alexandria, with which they then tried to identify the day of their Paschal full moon. That lunation did not always precisely coincide with Nisan. Although the Alexandrian “age” of the moon on any date of her Paschal full moon was (and remained) always 14, the adaptation of Nisan to the Alexandrian calendar brought about by the church of Alexandria would ultimately result in substantial changes of position of this date with respect to Nisan which would land this date in almost all Julian calendar years around the year 320 on or near the twelfth (instead of the fourteenth) day of Nisan (see also section 12).
Around the middle of the third century the church of Alexandria started using the date 22 March, which date it then considered as the date of the March equinox, as a lower limit of its dates of Paschal full moon. The first by name known Alexandrian computist who applied that principle to sequences of dates with a period of 19 years was Anatolius (see section 3). Supposedly he was one of the Alexandrian computists who around the year 260, so still before his episcopal consecration, constructed their very first sequence of dates of Paschal full moon provided with a metonical structure (see section 3); it is plausible that a decade later Anatolius started virtually from this (unfortunately unknown) metonically structured sequence of dates of (which I call for convenience) preanatolian Paschal full moon to construct his famous Paschal cycle with a period of 19 years. It is around the year 270 that Anatolius’ Paschal cycle (see also section 14), which can be considered as a brave attempt to overcome almost irreconcilable differences of opinion between different churches, was constructed. However, the dates of Anatolius’ Paschal cycle were rather Anatolian than Julian calendar dates and did not all fall on a real Sunday. Anatolius’ Paschal cycle was a rather impractical Easter table, which must have gone out of use already before the third turn of century.
As a matter of fact an adequate reconstruction of the sequence of dates of preanatolian Paschal full moon (constructed around the year 260 and not to be confused with the (definitive, “classical”) sequence of dates of Alexandrian Paschal full moon constructed about sixty years later) will yield only a sequence of most probable dates of preanatolian Paschal full moon. It is plausible that the sequence of dates of preanatolian Paschal full moon was obtained in the same way as the sequence of dates of Jewish Paschal full moon (see section 3), namely on the basis of Alexandrian tables of lunar phases concerning the time around the year 240. However, in order to get in that way a metonically structured sequence of dates which ideally could be identical with the sequence of dates of preanatolian Paschel full moon we must take into account the fact that around the year 260 the church of Alexandria considered 22 March as the date of the March equinox, which implies that the earliest possible date of preanatolian Paschal full moon should not be 21 March but had to be 22 or 23 March. Hence the table thus obtained, i.e. table 3, differs only in two horizontal rows, namely one concerning the year 235 and one concerning the year 254, from table 2. We note that for the years 235 and 254 the most probable date of Jewish Paschal full moon is 21 March but the one of preanatolian Paschal full moon 20 April. Anyway, it is not impossible that the sequence of dates of preanatolian Paschal full moon was simply obtained by adding thirty days to the earliest possible day of the sequence of dates of Jewish Paschal full moon.
For the sake of completeness we still give a description of the structure of table 3; in this table (with dates according to the Julian calendar) we see for each indicated calendar year (in the primary column A) mentioned in column B the best possible estimated point in time for Alexandria of the (actual) Newmoon of the month Nisan^ as assessed by Alexandrian Christian computists, in column C the most probable date of the first day of Nisan^ estimated on the basis of column B (in just the same way as in section 3), in column D the best possible estimated point in time for Alexandria of the (actual) Fullmoon of Nisan^, in column E the most probable date of the fourteenth day of Nisan^ estimated on the basis of column C, in column F the most probable date of preanatolian Paschal full moon estimated on the basis of columns D and E (the dates of column F have been chosen such that the sequence made up by these dates satisfies the requirement of metonical structuredness). In column B always the best possible estimated point in time for Alexandria of the first Newmoon after 6 March 18:00 is mentioned; the choice for this utmost point in time is closely connected with the principle that Pesach should be celebrated as early as possible in spring and with the fact that around the year 260 the church of Alexandria still considered 22 March as the date of the March equinox (in column E as well as in column F the earliest date is 23 March).
Comparing the sequences of dates of columns D, E, F of table 3 with each other, we can verfy that the sequence of dates of column F is a reasonable metonically structured approximation of the sequence of dates of column D as well as of the one of colum E (a saltus lunae occurs at the transition from 224 to 225 and a one at the transition from 243 to 244) and as such indeed would have been a relatively ideal sequence of dates of preanatolian Paschal full moon, with 23 March as most probable earliest possible date (occurring in years 224 modulo 19) and 20 April as most probable latest possible date (occurring in years 235 modulo 19). In what extent the dates of column F indeed belong to the real (metonically structured) sequence of dates of preanatolian Paschal full moon, remains a moot question.
Around the year 320 the church of Alexandria decided to consider henceforth 21 March as the date of the March equinox and to choose definitely for the metonically structured sequence of dates of Alexandrian Paschal full moon (being a final result of calculations made around the third turn of century of course directly or indirectly on the basis of tables of lunar phases) which had 21 March as earliest possible date and for more then twelve centuries, thanks to the Alexandrian monk and computist Annianus (around the year 410) and Dionysius Exiguus (see section 2) and his followers, would be crucial for the celebration of Easter by all churches simultaneously with all other churches. Fortunately that sequence of dates is fully known (see e.g. column F of table 1). It is not quite clear in which way the dates of Alexandrian Paschal full moon came about. But it is plausible that the classical (definitive) sequence of dates of Alexandrian Paschal full moon ultimately evolved, in any way, whether via Anatolius’ Easter cycle or not, from the sequence of dates of preanatolian Paschal full moon (see also section 14). Be that as it may, it is a matter of fact that the sequence of dates of Alexandrian Paschal full moon forms the backbone of all Easter tables composed in Alexandria around the year 320 as well as of all Easter tables which evolved from such an Easter table (by means of extrapolation). The metonical core of each of the Alexandrian Easter tables composed around the year 320 covers the special time interval consisting of the years 304 up to and including 322 (the first saltus lunae occurs at the transition from 322 to 323), and it is the repetitions of this metonical core which are so characteristic for all classical Alexandrian Easter tables. A famous example of a classical Alexandrian Easter table is Dionysius Exiguus’ Easter table (see section 2); the metonical core of this Easter table (see table 1) covers the special time interval consisting of the years 532 up to and including 550 (the first saltus lunae occurs at the transition from 550 to 551), which time interval not surprisingly is congruent modulo 19 years with the metonical core of the Alexandrian Easter tables composed around the year 320.
Already since the beginning of the third century the church of Alexandria respected the principle “Easter Sunday is the first Sunday after the Paschal full moon” for the determination of the date of Easter Sunday. According to that principle the date of preanatolian Easter Sunday is the date of the first Sunday after the date of preanatolian Paschal full moon. Julian calendar dates of Alexandrian Easter Sunday determined according to that principle we can find in column G of table 1. The earliest possible date of Alexandrian Easter Sunday is 22 March.
In the fourth century in the western half of the Roman empire Roman Easter tables were in use which had one and the same special periodic sequence of dates of Roman Paschal full moon with a period of 84 years in common. In that time dates of Roman Easter Sunday were determined according to the principle “Easter Sunday is the first Sunday after the first day after the Paschal full moon” as far as this yielded a date between (exclusively) 21 March and 22 April; this restriction sometimes led to problems (e.g. in the years 303 and 360). In the fourth century the earliest possible date of Roman Paschal full moon was 16 March (in the year 352) and the earliest possible date of Roman Easter Sunday 22 March (in the years 330, 341, 352), in spite of the fact that still in the first half of the fourth century the Roman civil authorities considered 25 March to be the date of the March equinox.
By the publication around the year 320 of the first generation of classical Alexandrian Easter tables the church of Alexandria was the first church who opted definitely for 21 March as the earliest (and for 18 April as the latest) possible date of (Alexandrian) Paschal full moon. That made the church of Alexandria at the same time the first church who opted definitely for 22 March as the earliest (and for 25 April as the latest) possible date of Easter Sunday (because of the Alexandrian formula for the date of Easter Sunday, going for all classical Alexandrian Easter tables). In the fourth century at the curches in the western half of the Roman empire chiefly Roman Easter tables were in use, at the curches in the eastern half chiefly Alexandrian ones. It is plausible that, under the influence of Eusebius, at the curches in fourth century Palestine (among which the churches of Jerusalem and Caesarea) no other Easter tables than Alexandrian ones were in use.
The Easter table of bishop Theophilus of Alexandria, which was composed in the year 385, was the first classical Alexandrian Easter table which contained Julian instead of Alexandrian calendar dates (of Alexandrian Paschal full moon and of Alexandrian Easter Sunday). In the beginning of the fifth century Annianus composed a classical Alexandrian Easter cycle, in which not only the sequence of dates of (Alexandrian) Paschal full moon is periodic (with a period of 19 years) but also the sequence of dates of (Alexandrian) Easter Sunday (with a period of 532 years). Annianus’ Easter cycle just like Theophilus’ Easter table was obtained as a result of extrapolation from a classical Alexandrian Easter table composed around the year 320. The Easter table attributed to Cyril (see section 2), which was obtained as a result of extrapolation from Theophilus’ Easter table and was intended for use in the western half of the Roman empire, was just like Theophilus’ Easter table provided with Julian instead of Alexandrian calendar dates. Dionysius Exiguus obtained his Easter table, which is also provided with Julian calendar dates, by extrapolation from the Easter table attributed to Cyril. The Easter table attributed to Cyril concerns the years 437 up to and including 531, Dionysius Exiguus’ Easter table the years 532 up to and including 626. Because the Alexandrian formula for Easter Sunday holds for all classical Alexandrian Easter tables, in all these Easter tables the Alexandrian lunar phase number of the date of Easter Sunday is always an integer between 14 and 22.
In Dionysius Exiguus’ Easter table (see table 1) we see for each indicated calendar year (in the primary column A) mentioned in column C the epact (i.e. the lunar phase number of 22 March according to the Alexandrian numeration of lunar phases), in column D the concurrent (i.e. the weekday number of 24 March), in column F the Julian calendar date of Alexandrian Paschal full moon, in column G the Julian calendar date of Alexandrian Easter Sunday, in column H the Alexandrian “age” of the moon on the Alexandrian Easter Sunday (i.e. the Alexandrian lunar phase number of the date of Alexandrian Easter Sunday). The epacts of column C served for simplifying the determination of the dates of column F: for each calendar year in column A the date in column F can be obtained by interpreting the epact in column C as a number of days (here “nulla” must be taken as “0 days”) and subtracting this number of days modulo 30 days from the date 5 april. For each calendar year in column A the date in column G can easily be obtained from the number in column D and the date in column F (by means of the principle “Easter Sunday = the first Sunday after the Paschsal full moon”), and the number in column H from the date in column F and the date in coloumn G (because of the fact that the Alexandrian lunar phase number of the date of Alexandrian Paschal full moon is 14) as well as from the epact in column C and the date in column G (because of the fact that the Alexandrian lunar phase number of 22 March is the epact). Columns B and E are not relevant.
In all classical Alexandrian Easter tables the successive dates of (Alexandrian) Paschal full moon form a lunar cycle, i.e. a sequence of dates with a metonical structure. But in each of those Easter tables not only the successive dates of Paschal full moon form a lunar cycle but mutatis mutandis also the successive epacts, because when these epacts are interpreted as numbers of days like in the previous paragraph each following epact of the sequence can be obtained by adding either 11 modulo 30 days (normally) or 12 modulo 30 days (only in the case of the “saltus lunae”, once every nineteen times) to the last preceding epact. The fact that in Dionysius Exiguus’ Easter table the epacts (see column C) as well as the dates of Paschal full moon (see column F) forms a lunar cycle is the reason of the subdivision of the columns of this table into (five) groups of nineteen calendar years.
Dionysius Exiguus was not familiar with Annianus’ Easter cycle, and he had no proper understanding of the possibility to extend his Easter table to an Easter cycle, as little as of the fact that the concurrents in the fourth column of his Easter table (see table 1) form a solar cycle; a solar cycle is a sequence of numbers with period 28 such that every following number of the sequence can be obtained by adding either 1 modulo 7 (normally) or 2 modulo 7 (once every four times) to the last preceding number (this definition rests on the congruence 21 · 1 + 7 · 2 ≡ 0 modulo 7). The periodicity of the solar cycle rests on the leap year proportion of the Julian calendar (one to four) and the fact that a week holds seven days. Theophilus’ Easter table was not only the first classical Alexandrian Easter table which contained Julian instead of Alexandrian calendar dates (of Alexandrian Paschal full moon and of Alexandrian Easter Sunday) but also the first one which was provided with a special column containing the concurrents of the calendar years in question. In the Roman Easter tables used in the fourth century not only the dates of Paschal full moon had a period of 84 years but also the dates of Easter Sunday. So those Easter tables are real Easter cycles (with a period of 84 years). However, they fell out of step with the rhythm of the moon phases much earlier than the specific metonical Easter tables.
In the year 616 an anonymous extended Dionysius Exiguus’ Easter table to an Easter table concerning the years 532 up to and including 721, and it is this Easter table which around the year 640 was accepted by the church of Rome, which from the third century up till then had given preference to go on using her own, relatively inadequate, Easter tables. In the year 725 the great English scholar Beda Venerabilis published a new extension of Dionysius Exiguus’ Easter table to an Easter cycle which is essentially a reinvention of Annianus’ Easter cycle. Beda Venerabilis’ Easter cycle and Annianus’ Easter cycle contain essentially just the same dates of Paschal full moon and of Easter Sunday. Like in Annianus’ Easter cycle in Beda Venerabilis’ Easter cycle the concurrents form a solar cycle (with period 28) and the dates of Paschal full moon a lunar cycle (with a period of 19 years), and consequently the dates of Easter Sunday a sequence of dates with a period of 532 years. In the Byzantine empire thanks to Annianus’ Easter cycle at all times the churches were acquainted with the “only correct” date of the next Easter Sunday. It is Beda Venerabilis’ Easter cycle by means of which also the churches in the part of Europe outside the Byzantine empire got that possibility.
It is the classical Alexandrian Easter tables composed in Alexandria around the year 320 from which (a century later) Annianus’ Easter cycle, (two centuries later) Dionysius Exiguus’ Easter table and (four centuries later) Beda Venerabilis’ Easter cycle would evolve. At the moment the western half of the Roman empire went down (in the year 476), in the eastern half classical Alexandrian Easter tables were in use abundantly. Also in the Byzantine empire no other Easter tables than classical Alexandrian Easter tables were used. However, in the part of Europe outside the Byzantine empire it lasted as late as the eighth century, when Beda Venerabilis’ Easter cycle was accepted by the churches in Britain and Ireland and in the Frankish kingdom, before all Easter tables being in use were substituted for classical Alexandrian Easter tables. The thus realized general use of classical Alexandrian Easter tables (by means of which at last the churches could realize their old ideal of celebrating Easter Sunday simultaneously) was continued for centuries, in the Byzantine empire until the fall of this empire in the year 1453, in the greater part of Europe until the year 1582, when Beda Venerabilis’ Easter cycle was replaced with Easter tables adjusted to the Gregorian calendar (see section 3).
The presence of the Latin word ‘nulla’ in the third column of his Easter table creates the impression that Dionysius Exiguus did know the number zero. But it is not difficult for us to convince ourselves (by analyzing his text accompanying his Easter table) that he was no exception to the generally accepted rule that in early medieval Europe nobody knew the number zero (see section 2). There where we say that the epact is 12, he says “duodecim sunt epactae”, which means “there are twelve epacts”; this clearly implies that “12” in the third column of his Easter table means “12 epacts”. An interesting question is what he means there where he indicates the epact in his Easter table with the Latin word “nulla”, where we would say that the epact is 0. In that case he says “Anno primo, quia non habet epactas lunares, ……”, which means “In the first year, which does not have lunar epacts, ……”. That clearly implies that the meaning of “nulla” in the third column of his Easter table is “no epacts” (which indeed boils down to ‘nothing’). Furthermore he tells us what is the connection between his “nulla” of the calendar year in question and his “18 epacts” of the previous calendar year, namely by means of the addition 18 + 12 = 30 followed by something like our calculating modulo 30, where however “30 epacts” is congruent to “no epacts” modulo “30 epacts” (instead of 30 ≡ 0 modulo 30), since for the calendar year in question he establishes “nihil remanet de epactis”, which means “nothing remains from the epacts”. But where people calculate with numbers of epacts the way infants do with numbers of apples we cannot speak yet of ‘being acquainted with the number zero’. There where Dionysius Exiguus sees purely and simply a column of mutually related separate “numbers” of epacts (such as “12 epacts” and “no epacts”), it is our modernized brain which thinks to see a mathematical structure, a sequence of (abstract) nonnegative integers. Dionysius Exiguus had no symbol for ‘zero’ at his disposal which was actively used by him in his calculations. Dionysius Exiguus’ “nulla” in his columns of epacts stands for “no epacts”, not for the number zero. As a consequence, his set of numbers contains no other numbers than positive ones. But to call an erudite person like Dionysius Exiguus stupid because he did not know the number zero (which some people do) that is really stupid.
There is nothing from which we can deduce that Dionysius Exiguus was acquainted with the number zero. In medieval Europe one had to wait until as late as around the twelfth century before one got dispose of that important number (see also section 5).
5 complete era
Dionysius Exiguus (see section 2) presented his Easter table, with his Anno Domini era (see section 2) included in it, to official representatives of pope John I in or shortly after the year 525. However, eventually it would last still a bit more than two centuries before one got round to put that era into use actively as a coherent system for dating historical events. That happened only in the year 731 through Dionysius Exiguus’ great follower Beda Venerabilis (see section 4).
In order to create the possibility of localizing on the new time scale historical events that happened before the beginning of our era as well, of course the (incomplete) Anno Domini era had to be extended to a complete era. For that purpose first the calendar years (according to the Julian calendar) preceding the year 1 were numbered further and further back into the past 1, 2, 3, ……, which sequence of calendar years then was joined together with the sequence of calendar years 1, 2, 3, …… to the complete sequence of calendar years ……, 3, 2, 1, 1, 2, 3, ……, where the year 1 = the year 1 before Christ = the Roman year 753, and e.g. the year 10 = the year 10 before Christ = the Roman year 744. Thanks to Beda Venerabilis the calendar years of our era were divided into calendar years after Christ and calendar years before Christ, which division ultimately boils down to a division into positively numbered and negatively numbered calendar years without the number 0 being allocated to any calendar year. With the duration of a year as unit of time, the complete Christian era thus obtained, boils down to our second timeline (figure 2):
…… -3 year -3 -2 year -2 -1 year -1 0 year 1 1 year 2 2 year 3 3 …… time (in years)
in which (modern) picture year -1 = the year 1 = the year 1 before Christ and e.g. year -10 = the year 10 = the year 10 before Christ (this calendar year began at moment -10 and ended at moment -9). The running of things at extending the (incomplete) Anno Domini era to the complete Christian era can be roughly summarized in our observation that year -x = the year -x (of our era) = the year x = the year x before Christ, where, however, we have to realize that negative numbers became available only in the course of the second millennium.
We observe that our second timeline (see figure 2) looks like a complete linear time scale (with the duration of a year as unit of time) supplemented with the positions of the positive numbered and of the negative numbered calendar years of our era. However, on closer inspection that timeline cannot represent a pure linear time scale, because two calendar years are not always precisely equally long. Usually the difference between the lengths of two calendar years is either nil or one day (see also section 7). For instance, the difference between moment 11 and moment 12 (this difference is 366 days) is not the same as the one between moment 10 and moment 11 (this difference is 365 days). Nevertheless we may interpret our second timeline (provided that the year -x is taken as the year x before Christ) as a simple and as such consistent mathematical model of the complete Christian era. Likewise our first timeline (see figure 1) is to be interpreted as a simple and as such consistent mathematical model of the (incomplete) Anno Domini era.
What strikes us most (perhaps even is bugging us) in our second timeline is of course that in here there is no room for a year zero. We will still see (in section 6) why our era from the outset to this very day had to do without a year zero, even though the number zero is common property now for a long time. Modern historians who know their job (and of course we take these people serious) really let the year 1 come immediately after the year -1. It is moment 0, the unique point in time from which the calendar years of our era are counted and which is identical with the point in time [1-1-1 0:00] (in modern notation), which marks the direct transition (turn of year) from the year -1 to the year 1, just as it marks the direct transition (turn of century) from the first century before Christ to the first century (after Christ). Just as there is no zeroth century (and no zeroth millennium), there is also no year zero, thanks to Beda Venerabilis.
Beda Venerabilis calculated (just like Dionysius Exiguus) only with positive integers represented by means of Roman numerals (these are the letters i, v, x, l, c, d and m of the Latin alphabet). He did not feel the slightest need for a numeral zero; e.g. the sum of cc = 200 and i = 1 was noted in Roman numerals simply as cci. Division algorithms were not available yet in early medieval Europe; in this Europe division boiled down to repeated subtraction. There where Beda Venerabilis in his important book “De Temporum Ratione” about “reckoning of time” explains dividing 725 by 19 he says first that 19 times 30 makes 570 and that 19 times 8 makes 152 and then “remanent iii”, meaning that the remainder is 3. But he refrains from naming the number zero to tell us which remainder one obtains when dividing 910 by 7, for answering this question he says, after having noted that 7 times 100 makes 700 and that 7 times 30 makes 210, simply “nihil remanet” or the equivalent “non remanet aliquid”, meaning “there is nothing left over”. Calculating, he never uses any symbol or word for ‘zero’. And there where he enumerates Greek numerals, he does not observe that there is among them no symbol or word for some numeral zero. There is nothing from which we can deduce that Dionysius Exiguus was acquainted with a numeral zero or with the number zero (see section 4); the same holds for Beda Venerabilis.
In the standard work about “De Temporum Ratione” written by the Canadian historian Faith Wallis we find a modern version of Beda Venerabilis’ Easter cycle (see section 4), with our modern digits and with epacts (see section 4) being 0 once every nineteen years, and even mentioning the year -1. But in original manuscripts written by Beda Venerabilis himself you will find no nonpositive numbers at all and you will see only the Latin word ‘nihil’ (meaning nothing but ‘nothing’) or a Latin word like ‘nulla’ or ‘nullae’ (which means ‘none’) on the places where we would expect to meet the number 0. For our modern brain it is difficult to interprete “de octaua decima in nullam facere saltum” else than as “to make a jump from 18 to 0”. But even modern people use phrases such as “jump into nothingness”. It is our modernized brain which tries to hoax us into believing to see the number zero there where by early medieval scholars simply ‘nothing’ or ‘none’ was meant. There where Beda Venerabilis calculates with (abstract) positive integers, as soon as the number zero comes into sight (i.e. enters our field of vision) he lapses, just like Dionysius Exiguus, into a less abstract terminology. Dionysius Exiguus’ “nulla” and Beda Venerabilis’ “nulla” or “nullae” in their columns of epacts are typical examples of precursors of the number zero, they stand for “no epacts”, which boils down to ‘nothing’ indeed; but the term ‘nothing’ is, in contrast to the number zero, no mathematical concept. For Dionysius Exiguus and Beda Venerabilis as well as for us ‘adding nothing’ boils down to ‘doing nothing’. But to be able to conceive refraining from any action (‘adding nothing’) as a special case of adding something (‘adding zero’) it takes more than skill in carrying out calculations with positive integers.
Beda Venerabilis like Dionysius Exiguus knew no other numbers than positive ones, just like everyone in first millennium Europe. Even Boetius (around the year 500), the only somewhat important mathematician in early medieval Europe, and Gerbert (see section 2) were anything but familiar with the number zero. Nowhere in European literature come down to us from the first millennium the number zero itself can be found. So there is no reason at all to abandon the current opinion that the number zero was unknown in early medieval Europe. So the opinion that Dionysius Exiguus en Beda Venerabilis should be acquainted with the number zero remains really without any rational basis. They were great scholars and skilled computists, but not mathematicians (and also not astronomers). One does not need to be a mathematician to be able, starting from the periodic sequence of Julian calendar dates of Alexandrian Paschal full moon (see section 4) and making use of the leap year regulation according to the Julian calendar (see section 3) and the Alexandrian formula for the date of Easter Sunday (see section 4), to determine really all Julian calendar dates of Alexandrian Easter Sunday. And if you want to do that with the help of Dionysius Exiguus’ Easter table then you can restrict yourself to the use of columns A, D, F of table 1. By the way, that does not alter the fact that the very first construction (around the year 260) of a sequence of dates provided with a metonical structure (see section 3) as an approximation for a sequence of dates of the fourteenth day of Nisan (see section 3) was an impressive arithmetical finding, which we probably owe to Anatolius (see section 3).
Ptolemy (see section 3) handled the symbol o for a numeral zero in the (originally Babylonian) sexagesimal positional system. But that symbol was not actively used by him as a numeral zero in combination with the Greek numerals (these are the 24 letters of the Greek alphabet supplemented with the obsolete Greek letters digamma, koppa and sampi) he used in his calculations; e.g. the sum of s = 200 and a = 1 was noted in Greek numerals simply as sa. In the sixth century the decimal positional system being then already a few centuries in use in India, which was already provided with symbols for the digits 1 up to and including 9, was increased with the symbol 0 for the digit zero, due to which it became possible to carry out abstract calculations in an efficient manner (by means of convenient algorithms). The clarification of the concept of number ensuing from the introduction of the symbol 0 for the digit zero inspirered the great Indian mathematician Brahmagupta about the year 630 to the invention of the number zero; he was the first who made explicit the most important properties of the number 0 (for any number x we have x + 0 = x and x · 0 = 0). The dissemination of the number 0 across Asia took centuries, as did the dissemination of this number across Europe, which began to get into its stride only around the twelfth turn of century (in Italy, after a hesitant beginning around the eleventh turn of century in Spain). Fibonacci (whose important book “Liber Abaci” was finished in the year 1202) was the first Italian, Robert Recorde (“Ground of Artes” in the year 1543) the first Briton, Simon Stevin (“De Thiende” in the year 1585) the first Dutchman who was familiar with that utmost important number. Without the number zero there would be no modern mathematics, and without modern mathematics our technology would have been completely impossible.
If only because of the fact that in the early middle ages the number zero and the negative integers still were completely unknown in Europe, Dionysius Exiguus and Beda Venerabilis could not possibly have understood our second timeline. Dionysius Exiguus did not worry about that, because he did not at all need those nonpositive numbers for the setting up of his incomplete era (which actually was used by him only for the benefit of his easter table), and Beda Venerabilis too could manage very well without these “unusual” numbers. The complete Christian era was brought into use as a coherent system for dating historical events by Beda Venerabilis in the year 731, and was used by the church of Rome only in the tenth century for the first time (see section 2). But the modern concept of the bilateral linear time scale, necessary to be able to understand our second timeline, only could make its entry after people in Europe had got dispose of the number zero (around the year 1200) and of the negative numbers (around the year 1500). The nonpositive integers began to be common property only in the first half of the eighteenth century by the invention of the thermometer (which sometimes indicates degrees below zero). Restrictions with regard to the lowest or the highest possible temperature excepted the scale of Anders Celsius is a bilaterally symmetrical linear calibration; it is the bilateral symmetry which we besides in this calibration also see in figure 2 (of which e.g. the second decade before Christ corresponds to the temperature interval consisting of the temperatures between -20ºC and -10ºC). The French astronomer Jacques Cassini was the first who explicitly availed himself of negatively numbered calendar years (see also section 6).
In times of scarcity of reliable historical factual material the dating of historical events was no simple matter. So by Beda Venerabilis the coming into power of the emperor Diocletianus (which took place in the year 284 but still had been dated by Orosius in the Roman year 1041) was dated in the year 286, the capture of Rome by Visigothic troops (which took place in the year 410) was dated in the year 409, and the death of pope Gregory I (who starved in the year 604) was dated in the year 605. Beda Venerabilis was the first medieval historian who, making use of the complete Christian era, ventured to date the first landing of Julius Caesar in Britain. That military action, which took place in the year -55, was dated by Beda Venerabilis in the year 60 before Christ.
6 argumentation
If we have a
look to our second timeline (see figure 2) just a
bit longer and abstract from the fact that two calendar years are not always
precisely equally long then we observe that our era, i.e. the complete
christian era (taken as a linear system of numbered calendar years), is in
principle (namely restrictions with regard to the beginning or the end of times
excepted) bilaterally symmetrical with respect to moment 0, the unique point in time which is identical
with
Our era is a bilaterally symmetrical era without a year zero. Both an alternative era with the year 1 as a year zero and a one with the year -1 as a year zero (in fact there are no other possibilities to be taken into consideration seriously) are necessarily not symmetrical with respect to moment 0. It is for that reason that none of those two alternative eras became common property, though sometimes a variant of the latter one is used sometimes for practical purposes by scientists (mainly astronomers and chronologists). That (nonsymmetrical) variant is the astronomical era; this era, defined on the basis of the Julian dating system (not to be confused with the Julian calendar), which in the year 1583, shortly after the introduction of the Gregorian calendar, had been proposed by the great chronologist Joseph Scaliger, was taken in use in its present form (including a year zero and negatively numbered calendar years) by Jacques Cassini (see section 5) in the year 1740. With the duration of a year as unit of time the astronomical era boils down to our third timeline (figure 3):
…… -3 year -2 -2 year -1 -1 year 0 0 year 1 1 year 2 2 year 3 3 …… time (in years)
in which (modern) picture year 0 does not exactly coincide with the year -1 (of the Christian era), which began two days later and ended one day later, both of them owing to the initially (during almost half a century) inadequate functioning of the Julian calendar (see also section 7).
It is just as well that the followers of Dionysius Exiguus did not saddle his and our (certainly for historians ideal) era with any year zero. When push comes to shove, everybody, either unconscious or conscious, prefers symmetry. Astronomers never proposed seriously to replace our bilaterally symmetrical era with their astronomical era (which had been brought into use only for practical reasons). We owe our era to Dionysius Exiguus, its bilateral symmetry to Beda Venerabilis. The absence of a year zero in our era is not in the least a mistake of Dionysius Exiguus or of Beda Venerabilis; it is purely and simply a condition our era has to satisfy in order to preserve its bilateral symmetry. We can but we do not have to be sad about the absence of a year zero in our era; it is such a thing as the absence of “the king William zero” in a company of kings named William.
The next section being of importance for the solution of the millennium question is section 8.
7 deductions
The fact that in the complete Christian era no year zero exists, has farreaching consequences, e.g. that the first decade (after Christ) can be nothing but the time interval consisting of the years 1 up to and including 10 and the first decade before Christ nothing but the time interval consisting of the years -10 up to and including -1; these two decades are separated not by means of a year zero but by means of a point in time, namely moment 0 (see section 5).
Any person born in the year 1 must have been conceived in the year -1 or at moment 0 or in the year 1. And someone born in the year -1 will have celebrated his tenth birthday preferably on the day it was ten years ago that he was born, so in the year 10, and this seems to be (but is not) inconsistent with the mathematical fact that -1 + 10 = 9.
From (inclusive) the year -776 up to and including the year 389 the officially recognized ancient Olympic games were held at Olympia every four years. It is easy to check that the year -4 was the first calendar year of the 194th Olympiad, the year 1 the first calendar year of the 195th Olympiad.
The Julian calendar (see section 3) was introduced in the year -46, which was accompanied by a single lengthening of the calendar year (Roman calendar) of eighty days, which lenghening (by means of which was effected that the March equinox was in fact put to 23 March), however, was neutralized immediately by the provision that the rule that a calendar year consists of 365 or 366 days was considered to hold not only for future calendar years but for all calendar years, including the calendar year in which the Julian calendar was introduced and (retrospectively) all calendar years gone by.
Unfortunately, in the first half century after Julius Caesar had died (in the year -44) the leap year regulation according to the Julian calendar did not function well. The fact is, after the leap year -45 there was until the year -8 by mistake a leap year every three years (instead of every four years). That implies that between the leap years -45 and -9 there were three leap years too much, namely eleven instead of eight. The regulation made for that reason by the emperor Augustus (see section 3), according to which every fourth calendar year after which boils down to the Roman year 757 should be a leap year, effected in addition that none (instead of three) of the fifteen calendar years between the leap years -9 and 8 was a leap year. That implies in particular that the year 4 was no leap year.
In the year 325 the Julian calendar was adopted as official calendar of the church (see section 4). However, the leap year regulation according to the Julian calendar was not accurate enough to be suitable to be used just like that indefinitely (for instance around the year 1500 the March equinox fell in reality on 11 March). That is the reason why in the year 1582 the Julian calendar was replaced with the Gregorian calendar, on the understanding that the Julian calendar, implicitly inclusive of the regulation made by the emperor Augustius mentioned in the previous paragraph, remained holdong for all calendar years before the year 1582. In that year pope Gregory XIII ordered ten days to be dropped from the tenth month (in fact in that year Thursday 4 October was the last day of the Julian calendar, and Friday 15 October the first day of the Gregorian calendar) and decreed that any calendar year of our era after that year should be a leap year if and only if its calendar year number is divisible by 4 but not by 100 unless by 400. We establish that the year 1582 comprised only 355 days, and so is the only exception on the rule that a calendar year of the Christian era consists of 365 or 366 days, and that [4-10-1582 24:00] = [15-10-1582 0:00].
The leap year regulation according to the Gregorian calendar was brought into force for an indefinite (future) time, and for the time being it will not be necessary to adjust it (once every approximately 3300 years an adaptation the size of one day will be needed). Thus all leap years (and so all calendar years) of the complete Christian era (with its proleptic leap year regulation according to the Julian calendar for all its calendar years before the year 1582 and its nonproleptic leap year regulation according to the Gregorian calendar for all its calendar years after the year 1582) from the far past until the far future (about the year 5000) have been fixed. With regard to that far future we note that in the time from 1582 to the beginning of the fifth millennium the March equinox falls sometimes on 19 March indeed but beyond this always on 20 or 21 March; however, with regard to that far past we have to realize that in the time after the last past glacial period only since the twelfth century before Christ the March equinox falls in March.
It is in combination with the Gregorian calendar (valid for all its calendar years after the year 1582) that the complete Christian era has been the most widespread dating system on earth. That era was never abolished or replaced with the astronomical era (see section 6), which is a variant of an alternative era with the year -1 as a year zero, as in our third time line (see figure 3). The astronomical era was complemented not with a proleptic leap year regulation according to the Gregorian calendar holding for all its calendar years, but with the (proleptic) leap year regulation according to the Julian calendar holding without reservation for its calendar years before the year 1582 and the (nonproleptic) leap year regulation according to the Gregorian calendar holding for its calendar years after the year 1582. Because, moreover, by definition the year 1582 of the astronomical era and the year 1582 (of our era) are identical, the astronomical era and the Christian one coincide exactly where it concerns the calendar years after the year 4, which implies that the moments 2000 of these eras are exactly equal. For that reason a choice for the astronomical era instead of for the complete Christian era would not have led to an other point in time of the second turn of millennium than [1-1-2001 0:00] (see also section 8). The fact that the year -1 (of our era) ended one day later than the year 0 of the astronomical era does not detract from that conclusion.
The year -1 (of our era) began two days later and
ended one day later than the year 0 of the astronomical era. The
reason for that is that the years 0 and 4 of the
astronomical era are leap years but the years -1
and 4 (of our era) were not. The
fact that the year -4 of the astronomical era is a leap year but
the year -5 (of our era) was
not, implies that the leap
According to the Roman historian Titus Livius, who lived around the beginning of our era, Rome was founded in the Roman year 1. That calendar year is the first year of the Anno Urbis Conditae era (see section 2). Should Rome indeed be founded in that calendar year then this important historical event will be three thousand years ago not in the year 2247 but in the year 2248 (I am just saying it meanwhile), because the Roman year 1 = the year -753 (of our era). Anyway, the 800th anniversary of the foundation of Rome was celebrated exuberantly in the year 47, the 1000th one in the year 248. However, according to modern historians, Rome was founded not earlier than in the seventh century before Christ.
8 conclusion
As soon as we have given account of the fact that our era, i.e. the complete Christian era (see section 6), is quite all right and that 1-1-1 is the first day of our era (see section 2), the millennium question can be settled rapidly and definitely.
Someone born on 1-1-1 will have celebrated his tenth birthday preferably on 1-1-11 (see section 2); and likewise he would, if all was well, have celebrated his 1000th birthday preferably on 1-1-1001, and his 2000th birthday preferably on 1-1-2001. By analogy with that we recognize that, because every millennium consists by definition of one thousand years, the second millennium began on 1-1-1000, and the third millennium on 1-1-2001.
Millennium mistake 1 was made by medieval people who thought that the world would perish on 1-1-1000; what these people did not realise was that on that very day only 999 years of the first millennium had passed. However, the first turn of millennium took place one year later, namely at [31-12-1000 24:00] = moment 1000 = [1-1-1001 0:00].
Millennium
mistake 2 was made by modern people who had been fooled by commerce
and media and authorities that also did not know any better (and by many a
historian who had completely forgotten for a while that our era has no year
zero) into believing that, rather than the “dull” date 1-1-2001, the “magic” date 1-1-2000 (with its millennium problem and its
millennium madness) had to be the first day of the new millennium. However, the
second turn of millennium took place one year later, namely at
Because moment 0 is identical with [1-1-1 0:00] the year 1 is the starting year of our era, and so it is the opening year of the first century and of the first millennium. It is not difficult to check that the year 2000 is the last year of the last decade of the last century of the second millennium and that the year 2001 is the first year of the first decade of the first century of the third millennium. The “magic” year 2000 is the closing year of the previous millennium and of the previous century, the “dull” year 2001 is the opening year of the new millennium and of the new century. And of course the year 3000 is the closing year of the third millennium (just as the year 300 is the closing year of the third century and the year 30 the closing year of the third decade).
The reason why a choice for the astronomical era (see section 6) instead of for the complete Christian era would not have led to a point in time of the second turn of millennium different from [1-1-2001 0:00] is that the moments 2000 of these two eras are exactly equal (see section 7). A choice for an alternative era with the year 1 (of our era) instead of with the year -1 (of our era) as a year zero indeed would have yielded a moment 2000 coinciding with the turn of year with which the year 2000 of this alternative era began; but evidently also this turn of year would have been identical with [1-1-2001 0:00].
9 objections
“All well and good” someone still objects, “but after all the twentieth century does consist exactly of those calendar years of our era whose numbers start from 19? This implies that the year 1999 is the last year of the twentieth century!”. The calendar years of our era whose numbers end in 00 throw a spanner into the works. There is no year zero in our era (see section 5); it follows that the year 100 is the last (closing) year of the first century, that the year 200 is the last (closing) year of the second century, that the year 300 is the last (closing) year of the third century, and so on. So the year 1600 is the last (closing) year of the sixteenth century. On closer inspection the apparantly interesting standpoint of Maarten Prak (university of Utrecht) that the battle of Nieuwpoort (which took place in the year 1600) is one of the rare real battles the army of the Dutch republic fought out in the seventeenth century, turns out to be something like the remark that New Year’s Eve is one of the rare really cosy days of the month of January.
“All well and
good” someone still objects, “but who is really mistaken? After all, the nineties
of the twentieth century had passed on
“All well and good” someone still objects, “but what about my odometer? After I have driven exactly 1000 kilometers, it clearly shows three zeros!”. That is right, but what we state here is not a similarity, but it is just a difference between era and odometer, because of the fact that during its first kilometer the odometer indicates 0000, not 0001. It is true, there is a similarity between odometer and age (so during its twentieth kilometer the odometer indicates 0019, and during the twentieth year of your life you are nineteen years of age), but this is beside the point.
“All well and good” someone still objects, “but when numbering the floors of a building surely it is logical and common practice to name the first floor floor 1, the ground floor floor 0, and the successive basements floor -1, floor -2, floor -3, ……? When numbering the calendar years of our era we cannot do without the number 0 either!”. We are able to do without a year zero very well (see section 6). Because when numbering the floors of a building sometimes floors are taken not as spaces but as horizontal dividing planes between spaces sometimes the numbering of floors does not correspond to the numbering of the calendar years but it corresponds to the one of the turns of year of our era, as in our second timeline (see figure 2).
“All well and good” someone still objects, “but what does it matter? After all, the beginning of our era was only chosen at a venture!”. The beginning of our era is moment 0, the unique point in time from which the calendar years of our era are counted and which is identical with [1-1-1 0:00]. In the year 1582 for an indefinite time the number of days of any calendar year of our era was fixed (see section 7). That makes all turns of year, turns of decade, turns of century and turns of millennium of our era fixed for an indefinite time.
“All well and good” someone still objects, “but what does it matter? After all, it is completely unknown when Jesus was born!”. It is not the (indeed unknown) date of Jesus’ birth that matters for the solution of the millennium question, but it is the first day of the Anno Domini era, i.e. 1-1-1, that is essential here (see section 8). Strictly speaking “the first century before Christ” is not “the last century before the birth of Jesus”, but “the last century preceding 1-1-1”.
“All well and good” someone still objects, “but surely the millennium question can be solved much more simply? Because there exists no year zero the supposition of a turn of millennium at [1-1-2000 0:00] leads to the absurd conclusion that the first decade consisted of nine years (so the tenth birthday of someone born on 1-1-1 coincided officially with his ninth birthday)!”. That reasoning is correct and leads to the observation that the supposition of a turn of millennium at [1-1-2000 0:00] cannot be part of a consistent system. So that supposition is (scientifically) untenable. But the solution of the millennium question still requires a proof of the fact that our era is quite all right (see section 6).
“All well and good” someone still objects, “but the fact that in the year 67 games were held at Olympia does not agree with the assertion that the officially recognized ancient Olympic games were held at Olympia every four years (see section 7)!”. The games held in the year 67 were no Olympic games but games which were organised at Olympia, Delphi, Nemea and Isthmia specially on behalf of the emperor Nero.
“All well and good” someone still objects, “but what on earth was against the celebration of the second turn of millennium on 1-1-2000?”. Of course nothing is against it to celebrate any memorable event whatever at any moment whatever (e.g. a turn of year on 30 December or your twentieth birthday on your nineteenth birthday). But the question is here that we have to distinguish between the direct transition from the year 1999 to the year 2000 (the “magic” moment at which all four digits of the number of the calendar year at present changed at the same time) and the accompanying turn of millennium, i.e. the direct transition from the second to the third millennium, exactly one year later, and that at the supreme moment relatively few people realized this.
“But nevertheless the people have the last word!” someone still objects. That means in my opinion that the people have right to self-determination, not that the people are always perfectly right. Something does not automatically become true if many people believe that it’s true. The earth does not become less round if many people believe that the earth is flat. Nor does something automatically become true by deciding it just like that, not even when this happens in a democratic way. It was possible to decide to go celebrate the second turn of millennium at [31-12-1999 24:00] = moment 1999 = [1-1-2000 0:00]; but it was impossible to finish the second millennium as early as at this “magic” point in time (see section 8).
Whether something is true, is prescribed neither simply by the people nor simply by some authority. Not even by the queen of the Netherlands (even though sometimes one for a moment could think she does, for the fact that there exists a statistical connection between smoking and lung cancer seems to be determined by Royal Decree). In order to determine whether something is true, sometimes logical (watertight) reasoning is necessary and sufficient. So the logical reasoning of section 6 and section 8 inevitably leads to the conclusion of section 8.
10 justification
Thanks to Dionysius Exiguus (see section 2) and Beda Venerabilis (see section 4) we have disposal of a bilateral symmetrical era without any year zero (see section 5 and section 6). The year 1 comes immediately after the year -1, as the first century (after Christ) comes immediately after the first century before Christ; there is in our era no year zero, as there is no century zero. This is the official standpoint of our modern historians, and with good reason (as we saw in section 6). Because our era has no year zero, we have to count our decades (and likewise our centuries and millennia) from [1-1-1 0:00]. That implies that the third millennium began not before 1-1-2001 (see section 8). Therefore we are rather allowed to indicate the phenomenon that around the year 2000 commerce, media and authorities were amply under the delusion that the year 1999 was the last year of the twentieth century and of the second millennium with the term ‘millennium mistake’.
People believe
all sorts of things. And usually what once is believed, is not given up easily.
Insights that are at right angles to what once is believed often hardly get a
chance to be tested to reason. Hence that people resisted so long against the
insight that our earth is not flat but round, that the sun is a star and the
earth is a planet revolving round the sun instead of the sun revolving round
the earth, that under special circumstances primitive life (extremely
gradually) comes into being, that all higher developed biological species
(including Homo sapiens) are evolved out of other biological species, that all
life is only temporary, that God is a product of human imagination and exists
only as such (man proposes but God does not exist), that it is a mistake to
think that atheists think they can prove that God does not exist (in fact
atheists believe that there exists no God outside of human imagination). But to
make it possible to continue our mental growth it is sometimes necessary to
recognize that we were wrong (this concerns each of us personnally as well as
mankind as a whole). So I got round to it, inspired to this by critical pupils
who wanted to know all the ins and outs, to find out why
By the way, what is the sense of education? By no means only to emancipate people. Stimulating clear thinking and carefully formulating by way of joint attention to essentials is an at least equally important education objective. Pupils ought to be able to calculate without calculator what is the sum of -753 and 3000. But also they have to know, I think, what structure our era has, in order to be able to understand that the answer to the question in which year Rome, assuming that this eternal city was founded in the year -753 (see section 7), three thousand years will exist is not the year 2247 but is the year 2248. It is not all that difficult.
11 anni domini
Now that we solved the millennium question completely (see section 8) and justified the term ‘millennium mistake’ (see section 10), the still unanswered question concerning the precise connection between the Anno Domini era (see section 2) and Anni Domini (literaly ‘the Years of the Lord’), in particular Jesus’ birth and death, goes on intriguing us. Likewise closely connected with the millennium question (and neither essential for the solution of it) is the interesting question concerning the connection between the starting year of the Anno Domini era chosen by Dionysius Exiguus (see section 2), i.e. the year 1 (of our era) = the Roman year 754 (see section 2), and Annus Dominicae Incarnationis, i.e. the calendar year of Jesus’ incarnation in the view of Dionysius Exiguus; also on the answer to this question historians do not entirely agree yet. In the writings of Dionysius Exiguus himself no clarification can be found about this, and in the writings of Beda Venerabilis (see section 4) we meet diverse arguments leading to contradictory deductions. But the majority of modern historians think that Dionysius Exiguus believed Jesus was born in or shortly before the year 1.
Peter Rietbergen (university of Nijmegen) is of the opinion that Dionysius Exiguus believed Jesus was born one week before the year 1, so in the year -1 (of the complete Christian era) = the Roman year 753. The opinion of Robert Fruin (around the year 1900) that Annus Dominicae Incarnationis = the year 1 is confirmed by Peter Verbist (university of Leuven) and by Georges Declercq (university of Brussels). It seems to me personally that the latter opinion is more plausible than the other one if only because of the analogy probably obvious for Dionysius Exiguus between the beginning of his Anno Domini era and the beginning of the Anno Urbis Conditae era (see section 2): “just as Rome was founded (on 21 April?) in the course of the Roman year 1, Jesus was conceived (on 25 March?) and born (on 25 December?) in the course of the year 1 (of the Anno Domini era)” Dionysius Exiguus may have thought.
One of the most influential figures of the first council of Nicaea (see section 4) was Eusebius (see section 3). He thought Jesus was born in the third calendar year of the 194th Olympiad (see section 7), in accordance with the opinion of Orosius (see section 2), a century after, that Jesus was born in the Roman year 752. Nevertheless Dionysius Exiguus chose (indirectly) the Roman year 754 as the starting year of his new era (see section 2). It may be that he did so only with a view to effect that in his new era (just like in the era of the emperor Diocletianus) the rule should hold that leap year numbers are divisible by 4.
Probably Dionysius Exiguus considered the question in which calendar year Jesus was born as unanswerable. But we too do not know the answer to that question. Nobody believes that moment 0 (i.e. the moment zero of our era), the unique point in time which is asterisked (*) so suggestively in our first timeline (see figure 1) and is identical with [1-1-1 0:00], could be the moment of Jesus’ birth. According to modern historians Jesus was born sometime between the years -9 and -1, so some time before the beginning of the Christian era, a remarkable paradox. On the year (let alone on the date) of Jesus’ birth authorities do not yet agree. We conclude that in all probability Jesus was born about the year -5. Somewhere in the nineties of the previous century the day on which it had been two thousand years since Jesus was born, slipped by.
Related to the question when Jesus was born is the question when Jesus died. Neither the year in which nor the date on which Jesus died is known for certain. It is common knowledge that Jesus died about the year 30 in Jerusalem, on a Friday in the afternoon, namely on (according to the fourth canonical gospel) or on or one day after (according to the three synoptic gospels) a day on which Pesach (see section 3) was prepared, so on a fourteenth or on a fifteenth day of Nisan (see section 3). It is certain too that Jesus died during the reign of the emperor Tiberius (who reigned from 13 to 14 jointly with the emperor Augustus and from 14 to 37 alone) and during the government of Pontius Pilatus, who was procurator of Judea (from 26 to 36).
Beda Venerabilis tried to find Jesus’ dying day with the help of his Easter cycle (see section 4), taking his departure from the Christian tradition which says that “Paschal full moon = 14 Nisan”. He hoped to arrive at 25-3-34, evidently partly due to the tradition dating back to the third century according to which Jesus would have died on a Friday 25 March (of an as yet unknown calendar year). Beda Venerabilis took it for granted that the validity area of his Easter cycle extended without fail to the beginning of the Christian era. However, making use of the columns of his Easter cycle corresponding with columns F and G of Dionysius Exiguus’ Easter table (see table 1) he had to establish to his disappoinment that in the year 34 (like in the year 566, for 34 ≡ 566 modulo 532) the date of the Alexandrian Paschal full moon (see section 4) was Sunday 21 March and not the Thursday 24 March expected by him. Evidently his presuppositions were inconsistent.
The persuasion that Jesus died on 25 March is without any rational foundation. For quite a while one cherished the conviction, resting on the oldest known Roman Easter table, namely the Easter table of Hippolytus Romanus (around the year 220), afterwards proved to be unreliable, according to which Jesus should have died on 25-3-29. But the more one got dispose of Easter tables which kept better step with astronomical reality (see section 4), the more the perception grew that that thesis was untenable. Nevertheless in the course of the fourth century the idea that Jesus both was conceived on 25 March and died on 25 March came into being. Not only we may have doubts about the correctness of that vision (to which after all still two calendar year numbers are lacking) but also about the perfectness of Beda Venerabilis’ Easter cycle, which, accurate as it may be, could ultimately prove to be imperfect, still besides the fact that the dates of Alexandrian Paschal full moon included in this Easter cycle anyhow not all correspond exactly with the dates of the fourteenth day of Nisan whose substitutes they were (see section 4). Nevertheless it remains an interesting question whether it is possible or impossible for us to trace Jesus’ dying day in the manner of Beda Venerabilis.
Because Julian calendar dates of Alexandrian Paschal full moon are defined meaningfully only insofar the Julian calendar (see section 3) after intervention of the emperor Augustus functioned properly, the (definitive, “classical”) sequence of Julian calendar dates of Alexandrian Paschal full moon, which forms the backbone of Beda Venerabilis’ Easter cycle, reaches in fact from 4 to 1582 (see section 3). Because that sequence of dates is periodic with a period of 19 years, we may take that sequence of dates as a strictly regularly running (of course imaginary) clock with a dial of which the hour hand has been replaced with a year hand which takes without surcease 19 years (instead of 12 hours) to go round one time. Around the year 300 that clock, which can be supposed to have run precisely and unbrokenly from 4 to 1582, nearly kept time with astronomical reality (with regard to the real phase of the moon on the date of Alexandrian Paschal full moon), because the “classical” sequence of dates of Alexandrian Paschal full moon (defined around the year 320) was a final result of calculations made (on the basis of tables of lunar phases) around the third turn of century. But thereafter that clock more and more went to lose time, as a result of the fact that a time interval consisting of 235 synodic months and a time interval consisting of 19 years contain not precisely the same number of days (see section 3).
There is no need to let the fact that (which I call for convenience) Beda Venerablis’ great clock, i.e. the sequence of Julian calendar dates of Alexandrien Paschal full moon indicated by Beda Venerabilis’ Easter cycle taken by us as a clock, only during a time interval around the year 300 nearly kept time with astronomical reality get us down. Namely, we can, in contrast to Beda Venerabilis, calculate how much time after the moment of exactly keeping time that clock lost a whole day, and even which was the astronomical reality at the moment of exactly keeping time (see also section 12).
Although the
Julian calendar was no ideal calendar, it functioned precisely and unbrokenly
from 4 to 1582. All that time a time interval of
19 calendar years lasted an average of 6939.75 days but the moon was
taking about 6939.689 days to pass through all of its phases
235 times (see section 3). From that it follows
that Beda Venerabilis’ great clock with the elapsing of time after the moment
of exactly keeping time lost time more and more, namely after every new time
interval consistong of 19 years approximately
Jesus died in the time of the government of Pontius Pilatus, so certainly between the years 25 and 37. Beda Venerabilis’ great clock did not keep time then with astronomical reality, but it gained roughly a day. In order to make an attempt to determine Jesus’ dying day we therefore correct the Julian calendar dates of Alexandrian Paschal full moon according to Beda Venerabilis’ Easter cycle holding for the years 26 up to and including 36 (these dates are the same as those of the years 558 up to and including 568 in column F of table 1 and have been stated also in column B of table 4) by adding one day to each of them and determine then (with the help of column D of table 1 or normally with the help of the Julian calendar) for each of the dates thus obtained on which day of the week this date fell; the corrected dates of Alexandrian Paschal full moon thus obtained, are stated in column C of table 4 (in which all dates are Julian calendar dates).
Actually, in order to determine Jesus’ dying day we would want to have at our disposal dates of the fourteenth day of Nisan (which are unfortunately not exactly calculable). However, we would make a serious mistake now if we took it for granted that only to a negligible extent there would be a difference between the sequence of corrected dates of Alexandrian Paschal full moon obtained in the last paragraph and the sequence of dates of the fourteenth day of Nisan represented by them. Therefore the corrected dates of Alexandrian Paschal full moon stated in column C of table 4 may tentatively be regarded at most as very roughly estimated dates of the fourteenth day of Nisan. We establish that the method of Beda Venerabilis to determine Jesus’ dying day is certainly inadequate as long as we have no idea of the connection between the sequence of dates of the fourteenth day of Nisan and the sequence of dates of Alexandrian Paschal full moon representing them (see also section 12).
Fortunately we can obtain estimated dates of the fourteenth day of Nisan along a different route as well, roughly in the same way as was originally done by Jewish calculators, for the obtaining of their dates of Jewish Paschal full moon (see section 3), and by Christian computists, for the obtaining of their dates of preanatolian Paschal full moon (see section 4) in third century Alexandria (Egypt). They operated with the help of tables of lunar phases (with dates according to the Alexandrian calendar) of around the year 240; in the same way we can obtain estimated dates of the fourteenth day of Nisan directly with the help of modern tables of dates (of course according to the Julian calendar) of Newmoon. We will show that by means of table 4 (with dates according to the Julian calendar); in this table we see for each indicated calendar year (in the primary column A) mentioned in column B the (uncorrected) date of Alexandrian Paschal full moon, in column C the corrected date of Alexandrian Paschal full moon, in column D the best possible estimated point in time for Jerusalem of the (actual) Newmoon of Nisan, in column E the most probable date of the first day of Nisan estimated on the basis of column D (in just the same way as in section 3), in column F the most probable date of the fourteenth day of Nisan estimated on the basis of column E. In column D always the best possible estimated point in time for Jerusalem of the first Newmoon after 7 March 18:00 is mentioned; the choice for this utmost point in time is closely connected with the principle that Pesach should be celebrated as early as possible in spring (in column F the earliest date is 23 March). We see to our amazement a rather large difference between columns C and F, which difference does need a further investigation (see also section 12).
Jesus died on a Friday, on a fourteenth or on a fifteenth day of Nisan. It is possible that in the year Jesus died Pesach was (by mistake or for an opportunistic reason) celebrated a month consisting of thirty days “too early” or “too late” (see section 3). It is therefore possible that Jesus died on 23-4-34 (e.g.). But because determining Jesus’ dying day can not be more than a question of cancelling much less probable against much more probable possibilities we may neglect the probability of such an exceptional eventuality. It is therefore very probable that Jesus died either on or one day after one of the dates stated in columns C and F of table 4, namely either on 19-4-26 or on 11-4-27 or on 7-4-30 or on 3-4-33 or on 30-3-36 (see column G), because Jesus died on a Friday. On further consideration we may still reject the first two and the fifth of those five in principle possible dying dates of Jesus, the first two because Jesus was baptized not earlier than in the year 27 (this can be deduced from the third canonical gospel) and manifested himself thereafter during at least two years (this can be deduced from the fourth canonical gospel), the fifth by reason of the fact that it is virtually certain that not later than in the year 35 the apostle Paul became a follower of Jesus (after the death of Jesus). Therefore the most probable two possible dates of Jesus’ dying day are 7-4-30 and 3-4-33; in each of both cases either the day itself or the day before must have been a day on which Pesach was prepared.
Our temporary
conclusion with regard to Anni Domini is that it is very probable that Jesus
was born about the year -5 and
died either on 7-4-30 or on 3-4-33. There are, apart from that, various
arguments on the basis of which 3-4-33
could be considered as the most probable possible date of Jesus’ dying day. As
early as in the year 1910 that date
was presented as such by Friedrich Westberg (who was Oberlehrer at a German
language public secondary school in Riga). He thought, rightly or mistakenly,
that 6-4-30 was a day on which Pesach
was prepared and 7-4-30 a day on
which one did not administer justice in Jerusalem. Apart from that, the fact
that the Roman procurator Pontius Pilatus only from the year 31, in which year his patron Lucius Sejanus
fell in disgrace with the emperor Tiberius, had no need to defy the Jewish
authorities in Jerusalem, is a strong argument in favour of the opinion that
Jesus died on
12 full moons
Relatively shortly before the first council of Nicaea (see section 4) the church of Alexandria (Egypt) decided to consider henceforth 21 March as the date of the March equinox (see section 3) and to determine definitely the dates of Alexandrian Paschal full moon (see section 4), so important to the history of Christianity. Because the sequence of dates of Alexandrian Paschal full moon was a final result of calculations made around the third turn of century (of course on the basis of tables of lunar phases) we could expect (as much as Dionysius Exiguus and Beda Venerabilis did) that within a substantial time interval around the year 300 the dates of the day on which Pesach (see section 3) was prepared, which day always coincided with the fourteenth day of Nisan (see section 3), anyhow usually would differ no more than a day from their Alexandrian substitutes. If, however, we relate within such a time interval the dates of Alexandrian Paschal full moon as well as the most probable dates of the fourteenth day of Nisan (which can be obtained in the same way as in section 3) to dates of (the actual) Newmoon and of (the actual) Fullmoon then it turns out, and this is relatively new (January 2005), that within the time interval in question the date of Alexandrian Paschal full moon was mostly at least two days earlier than the date of the fourteenth day of Nisan. We will show that by means of table 5 (with dates according to the Julian calendar).
Around the third turn of century, and hereafter still until the moment at which the Jewish calendar was fixed (about the year 360), the beginning of the new month and of the new year of the (not exactly calculable) Jewish calendar (see section 3) was determined officially still in Palestine and still as in the first century of our era (see section 3). Hence in table 5 we see for each indicated calendar year (in the primary column A) mentioned in column B the best possible estimated point in time for Jerusalem of the Newmoon of Nisan, in column C the most probable date of the first day of Nisan estimated on the basis of column B (in just the same way as in section 3), in column D the date of Alexandrian Paschal full moon, in column E the best possible estimated point in time for Jerusalem of the Fullmoon of Nisan, in column F the most probable date of the fourteenth day of Nisan estimated on the basis of column C. In column B always the best possible estimated point in time for Jerusalem of the first Newmoon after 5 March 18:00 is mentioned; the choice for this utmost point in time is closely connected with the principle that Pesach should be celebrated as early as possible in spring (in column F, just like in column D, the earliest date is 21 March indeed). One could still object that the most probable dates of the fourteenth day of Nisan mentioned in column F could possibly insufficiently fit with historical reality; however, it will turn out that it is not these dates which deviate for the major part at least one day from the dates of (the actual) Fullmoon mentioned in column E but the dates of Alexandrian Paschal full moon mentioned in column D.
We must realize that there are different phases of the moon which with the naked eye look like full moons indistinguishable from each other. A midnight pure full moon (i.e. nearly Fullmoon) is always preceded by a (still waxing) seemingly full moon one night earlier and followed by an (already waning) seemingly full moon one night later (see figure 4). For example as shown in table 5 in the year 308 at Jeruzalem insofar as the meteorological circumstances were favourable one could see during the night beginning with the sunset of the date of Alexandrian Paschal full moon (22 March) a (which I call for convenience) waxing full moon (i.e. roughly one day “younger” than Fullmoon) and during the night beginning with the sunset of the most probable date of the fourteenth day of Nisan (24 March) a (which I call for convenience) waning full moon (i.e. roughly one day “older” than Fullmoon), and during the night in between a pure full moon.
Looking at columns D, E, F of table 5 and comparing them with columns D, E, F of table 2 and of table 3 we establish first of all that the (definitive, “classical”) sequence of dates of Alexandrian Paschal full moon must have been obtained in another way than the sequence of dates of Jewish Paschal full moon (see section 3) or the sequence of dates of preanatolian Paschal full moon (see section 4). If the sequence of dates of Alexandrian Paschal full moon would have been defined really exclusively on the basis of tables of lunar phases concerning the time around the third turn of century then this sequence of dates would have looked more or less the same as the sequence of dates of Jewish Paschal full moon (see table 2), because in each of these two cases either explicitly or implicitly a March equinox falling on 21 March was supposed. Though in column B of table 2 as well as in column D of table 5 the earliest possible date is 21 March and the latest possible date 18 April those sequences of dates differ essentially; in the first case most dates belong to the “waning full moon category”, in the second case to the “waxing full moon category”. Because it does not belong to the “waning full moon category”, the sequence of dates of Alexandrian Paschal full moon can certainly not be a metonically structured approximation of a sequence of successive dates of the fourteenth day of Nisan.
The second remarkable observation for which table 5 gives cause, is that in each of the years 292 and 311 the date of Alexandrian Paschal full moon in all probability fell outside Nisan, namely roughly 28 days after the fourteenth day of Nisan, so roughly two days before the fourteenth day of Iyyar (see section 3). That leads, with reference to Beda Vernerabilis’ great clock (see section 11), to the conclusion that in the years 330 modulo 19 between the years 280 and 360 the date of Alexandrian Paschal full moon (unlike the date of Roman Paschal full moon) mostly must have fallen outside Nisan, namely roughly on the twelfth day of Iyyar instead of on the fourteenth day of Nisan.
Consideration of columns D and E of table 5 leads to the observation that within the time interval in question the date of Alexandrian Paschal full moon insofar as not falling outside Nisan fell on average about 1.5 days (so usually either one day or two days) before the date of the Fullmoon of Nisan. At the time one usually saw in Palestine in the night beginning with the sunset of the date of Alexandrian Paschal full moon a waxing full moon (roughly one day “younger” than Fullmoon) which had been risen roughly an hour and a half before sunset, and so this is the astronomical reality with whitch Beda Venerabilis’ great clock nearly kept time around the third turn of century.
The fact that the average difference between columns E and F of table 5 is about 0.4 days, is simply a consequence of the fact that around the third turn of century the Fullmoon of Nisan fell on average roughly near the midnight point in time of the night of the thirteenth to the fourteenth day of Nisan (see section 3). In the first three centuries of our era and in the fourth century until the moment (about the year 360) at which the Jewish calendar was fixed the fourteenth day of Nisan coincided usually either with the date of the Fullmoon of Nisan or with the first day after the date of the Fullmoon of Nisan. At the time one usually saw in Palestine in the night of the fourteenth to the fifteenth day of Nisan a waning full moon (roughly one day “older” than Fullmoon) which had been risen with great splendour roughly an hour after sunset; it is this astronomical reality to which the Jewish tradition of the celebration of Pesach in Palestine was closely joined for centuries. We can quite well imagine that at the time the emergence of an impressive full moon roughly an hour after sunset must have been experienced as an ideal beginning moment for the most important meal of Pesach, which must have urged the Jewish authorities to take care to keep the Jewish calendar under control and particularly to be time and again careful with regard to the determination of the beginning of Nisan.
Consideration of columns D and F of table 5 leads to the observation that within the time interval in question the date of Alexandrian Paschal full moon insofar as not falling outside Nisan fell on average about 1.9 days (usually two days) before the date of the fourteenth day of Nisan and (with reference to Beda Vernerabilis’ great clock) to the conclusion that between the years 280 and 360 the date of Alexandrian Paschal full moon mostly coincided with the date of the twelfth instead of with the date of the fourteenth day of Nisan. That confirms the obvious conjecture arising from the remarkable difference between columns C and F of table 4 (see section 11). That conjecture was of course that the Alexandrian computists who around the year 320 were composing the first classical Alexandrian Easter tables towards obtaining their dates of Alexandrian Paschal full moon chose for dates which were almost all roughly two days “too early” (which implies that in an extremely important case the of course not completely right formula “Paschal full moon = 14 Nisan”, which nevertheless was assumed to be approximately correct, is not right at all and therefore simply wrong). The question presents itself why they did that. In order to get an answer to that question, we will have a try (in section 14) to create, of course at first roughly and more or less by guess, an explanatory scenario (meant as a working hypothesis) through which can be understood how the transition from the (metonically structured) sequence of dates of preanatolian Paschal full moon, which more or less must have looked like the sequence of dates in column F of table 3, to the (later and also metonically structured) sequence of dates of Alexandrian Paschal full moon could come about. That transition took up about sixty years and perchance passed off via Anatolius’ Paschal cycle (see section 4).
13 supplementary result
The fact of the rather substantial changes of position with respect to Nisan demonstrated in section 12 by which the definitive replacement of dates of the fourteenth day of Nisan with dates of Alexandrian Paschal full moon (see section 4) implemented around the year 320 by the church of Alexandria (Egypt) was attended upon, implies that Jesus very probably died on a fourteenth day of Nisan, which may be shown by the reasoning following now.
We establish that the replacement of dates of the fourteenth day of Nisan with dates of Alexandrian Paschal full moon involved for each of the years 330 modulo 19 years of the time interval between the year 280 and the moment (about the year 360) on which the Jewish calendar (see section 3) was fixed in all probability a shift of roughly 28 days to roughly the twelfth day of Iyyar and for each of the other Julian calendar years of this time interval in all probability a shift of roughly two days to roughly the twelfth day of Nisan (see section 12). Around the year 30 Beda Venerabilis’ great clock gained roughly a day (see section 11). Therefore the (uncorrected) date of Alexandrian Paschal full moon fell in the year 26 in all probability roughly 27 days after the fourteenth day of Nisan but in each of the years 27 up to and including 36 in all probability roughly three days before the fourteenth day of Nisan. That enables us to make an improved version of table 4, by replacing column C of this table by the column of corrected dates of Alexandrian Paschal full moon which is obtained by subtracting 27 days from the first date of column B and adding three days to each of the remaining dates of column B and adjusting column G (which stems from columns C and F) accordingly. In the table thus obtained, i.e. table 6 (with dates according to the Julian calendar), columns C and F show no significant difference (we had not expected anything else). That table confirms not only our temporary standpoint that Jesus very probably died either on 7-4-30 or on 3-4-33 (see section 11) but in addition it is in a greater extent than table 4 an argument in support of the religious persuasion that Jesus died a few hours before celebration of Pesach (see section 3) began.
14 explanatory scenario
It is chiefly a particular sequence of dates provided with a metonical structure (see section 3) which we will need to explain why the rule “Paschal full moon = 14 Nisan”, at least in the singularly important case that we have to do with dates of Alexandrian Paschal full moon (see section 4) in the time of their coming into existence, is wrong. That sequence of dates is the sequence of dates of preanatolian Paschal full moon (see section 4). As a matter of fact, there is no obvious reason why the classical (definitive, metonically structured) sequence of dates of Alexandrian Paschal full moon and the sequence of dates of preanatolian Paschal full moon constructed about six decades earlier should differ as much as they in fact do. That does not alter the fact that it is the difference between the sequence of dates of preanatolian Paschal full moon and the sequence of dates of Alexandrian Paschal full moon which underlies the conclusion formulated in section 12 that between the years 280 and 360 the date of Alexandrian Paschal full moon mostly coincided with the date of the twelfth day of Nisan (see section 3). We still remark that it is the difference between the sequence of dates of Jewish Paschal full moon (see section 3) and the sequence of dates of preanatolian Paschal full moon which underlies the conclusion formulated in section 12 that in the years 330 modulo 19 between the years 280 and 360 the date of Alexandrian Paschal full moon (unlike the date of Roman Paschal full moon) mostly fell roughly on the twelfth day of Iyyar (see section 3); this difference is exclusively a result of the stand taken by the church of Alexandria (Egypt) from around the year 250 until around the year 320 with regard to the date of the March equinox (see section 3).
Towards obtaining their dates of Alexandrian Paschal full moon required for the calculation of their dates of Alexandrian Easter Sunday (see section 4) the Alexandrian computists who around the year 320 were composing the first classical Alexandrian Easter tables (see section 4) chose for dates which were almost all roughly two days “too early” (see section 12). We can establish (see section 12) that the classical sequence of dates of Alexandrian Paschal full moon must have been obtained by them in quite another way than the sequence of dates of preanatolian Paschal full moon by their predecessors, and therefore must have been defined not so much directly with the help of tables of lunar phases but rather on the basis of concrete results of these predecessors. The most important of those concrete results were the (metonically structured) sequence of dates of preanatolian Paschal full moon and Anatolius’ Paschal cycle (see section 4), and we can wonder how out of these important results the dates of Alexandrian Paschal full moon could have been evolved.
It is plausible that the church of Alexandria around the year 260, still before Anatolius (see section 3) constructed his ingenious Paschal cycle and still before his episcopal consecration, could dispose of the sequence of dates of preanatolian Paschal full moon with the matching sequence of dates of preanatolian Easter Sunday (see section 4). That implies that in all probability Anatolius for the construction of his Paschal cycle virtually started from the sequence of dates of preanatolian Paschal full moon and that ultimately the sequence of Alexandrian Paschal full moon in any way, whether via Anatolius’ Paschal cycle or not, must have been evolved from the sequence of dates of preanatolian Paschal full moon. Contrary to the sequence of dates of Alexandrian Paschal full moon the sequence of dates of preanatolian Paschal full moon is not exactly known, but fortunately we can dispose of the (metonically structured) sequence of most probable dates of preanatolian Paschal full moon (see table 3), and in addition, thanks to the Alexandrian formula for the date of Easter Sunday (see section 4), of the sequence of most probable dates of preanatolian Easter Sunday.
It is thanks to the work of Daniel McCarthy (university of Dublin) and Aidan Breen (idem) that we can dispose of Anatolius’ Paschal cycle; this Paschal table constructed around the year 270 has a period of 19 years and contains among other things a metonically structured sequence of epacts (see section 4), within the framework of his Paschal cycle explicitly used by Anatolius to construct his sequence of dates of Anatolian Paschal Sunday with matching Anatolian lunar phase numbers. At first sight those dates of Anatolian Paschal Sunday seem to be Julian calendar dates, but in fact they are calendar dates belonging to a variant of the Julian calendar ingeniously invented by Anatolius. However, during a relatively short (about seven years lasting) time interval the dates of Anatolian Paschal Sunday must have been Anatolian as well as Julian calendar dates (and so also real Sundays). For that reason it can be worth (e.g. in order to work out to what extent it is possible to relate the sequence of dates of Anatolian Paschal Sunday to the sequence of preanatolian Easter Sunday or to the sequence of Alexandrian Easter Sunday) making an inquiry into the sequence of dates of (which I call for convenience) Anatolian Paschal day which we get by taking the given dates of Anatolian Paschal Sunday simply as if they were Julian calendar dates; we can take this sequence of Julian calendar dates not all falling on a real Sunday as a first approximation of the sequence of Anatolian Paschal Sunday in the Julian calendar. Because each date of Anatolian Paschal Sunday has an Anatolian lunar phase number which is an integer between 13 and 21, we get, by reckoning back from dates of Anatolian Paschal day to dates with Anatolian lunar phase number 14, a sequence of dates of (which I call for convenience) Anatolian Paschal full moon, which (just like the sequence of dates of Anatolian Paschal day) has a period of 19 years but (likewise just like this sequence of dates) no metonical structure.
Please note not only the differences between the definitions of the dates of preanatolian, Anatolian and Alexandrian Paschal full moon, but also the ones between the definitions of the dates of Anatolian Paschal Sunday, Anatolian Paschal day and Anatolian Paschal full moon. The sequence of dates of Anatolian Paschal full moon must have been implicitly used by Anatolius to construct his sequence of dates of Anatolian Paschal Sunday. The fact that 23 March (and not 22 or 21 March) is the earliest possible date of Anatolian Paschal full moon, is a decisive reason why the sequence of dates of Anatolian Paschal Sunday must go back to the second half of the third century and so in all probability must originate from Anatolius himself indeed.
Until recently (June 2009) there was a difficulty with regard to the anchorage of Anatolius’ Paschal cycle in the Christian era (see section 5), but with the help of our sequence of most probable dates of preanatolian Paschal full moon and the sequence of dates of Anatolian Paschal full moon it is not difficult to solve this problem. If in case the date 16 April of Anatolius’ Paschal cycle was intended for the Anatolian Paschal Sunday of any year 260 modulo 19, which case according to Daniel McCarthy and Aidan Breen is the very first possible case eligible for closer examination, we relate the sequence of dates of Anatolian Paschal full moon to our sequence of most probable dates of preanatolian Paschal full moon then more than once, even 7 times out of 19, the date of Anatolian Paschal full moon proves to differ more than one day from the corresponding most probable date of preanatolian Paschal full moon. In an analogous manner in case the date 16 April of Anatolius’ Paschal cycle was intended for the Anatolian Paschal Sunday of any year 263 modulo 19 we establish that 14 times out of 19 the date of Anatolian Paschal full moon differs more than one day from the corresponding most probable date of preanatolian Paschal full moon, but in case the date 16 April of Anatolius’ Paschal cycle was intended for the Anatolian Paschal Sunday of any year 271 modulo 19 that this is the case none times out of 19 (such as in table 7). In all other in principle possible cases always all 19 times out of 19 the date of Anatolian Pasachal full moon differs more than one day from the corresponding most probable date of preanatolian Paschal full moon. That implies, and this is new (June 2009), that the date 16 April of Anatolius’ Paschal cycle must have been intended for the Anatolian Paschal Sunday of the year 271 (this is not so surprising, after all, because it is around the year 270 that Anatolius constructed his Paschal cycle).
We can use the result of the previous paragraph (this result was never before published) to make a table which on a substantial time interval around the year 280 gives an impression of the relation between dates of preanatolian Paschal full moon, of Anatolian Paschal full moon, of Anatolian Paschal day and of Alexandrian Paschal full moon. Hence in table 7 (with dates according to the Julian calendar) we see for each indicated calendar year (in the primary column A) mentioned in column B the most probable date of preanatolian Paschal full moon, in column C the date of Anatolian Paschal full moon with matching Anatolian lunar phase number, in column D the date of Anatolian Paschal day with matching Anatolian lunar phase number, in column E the date of Alexandrian Paschal full moon.
From table 7 we can deduce that in each of the eight years 264 up to and including 271 the Anatolian Paschal day was a (real) Sunday of which the date coincided with the most probable date of preanatolian Easter Sunday (and in addition seven times out of eight with the date of Alexandrian Easter Sunday). That confirms the relevance of the sequence of dates of preanatolian Paschal full moon as well as the rightness of our conclusion with regard to the anchorage of Anatolius’ Paschal cycle in the Christian era. Besides the concentration of Anatolian Paschal days falling on Sunday around or relatively shortly before the moment at which Anatolius’ Paschal cycle was constructed, the relatively great resemblance between columns B and C is remarkable (the sequence of most probable dates of preanatolian Paschal full moon and the sequence of dates of Anatolian Paschal full moon even have the same earliest possible date 23 March in the same years 262 and 281). The sequence of dates of Anatolian Paschal full moon turns out to be the result of manipulating the (real) sequence of dates of preanatolian Paschal full moon, which seems to have been a metonically structured sequence of dates with a saltus lunae (see section 3) occurring at the transition from 264 to 265; it is here that we to some extent catch sight of the until recently (July 2009) missing link in the series “14 Nisan” ® “preanatolian Paschal full moon” ® “Anatolian Paschal full moon” ® “Anatolian Paschal day”. The historical context of that series is formed by the churches of Alexandria and Laodicea around the sixties of the third century.
Though in the second half of the third century the church of Alexandria considered 22 March as the date of the March equinox, the earliest possible date of the sequence of most probable dates of preanatolian as well as of the sequence of dates of Anatolian Paschal full moon is 23 March. It is possibly under the influence of Eusebius (see section 3) and probably partly due to discord with the view of Anatolius with regard to the moment of the March equinox crystallized out in Anatolius’ Easter cycle (see section 3) that the church of Alexandria got round to pointedly reconfirming its (of course subjective) date of March equinox on 22 March, while not being objective about Anatolius’ Paschal cycle. That must be happened around the year 300, not long after the death of Anatolius. It is plausible that that led to modifications in or a revision of or perhaps even substitution for the Paschal table then used by the church of Alexandria (it is not known whether this Paschal table was Anatolius’ Paschal cycle). It is the definitive confirmation by the church of Alexandria of its date of March equinox on 21 March (this happened around the year 320) which was the immediate cause of the (ultimate) definition of the sequence of dates of Alexandrian Paschal full moon (with 21 March as earliest possible date).
We establish that there were two moments at which the church of Alexandria received a strong impulse to adjust “some” dates of preanatolian Paschal full moon for the first or for the second time; the first of these two moments is the moment (around the year 300) of the reconfirmation by the church of Alexandria of her (subjective) date of the March equinox on 22 March, the second the moment (around the year 320) of the definitive confirmation by this church of her date of the March equinox on 21 March. But by heeding the differences between the corresponding dates of columns B and E of table 7 (mostly two days) we must subsequently conclude that the transition from the sequence of preanatolian Paschal full moon to the sequence of Alexandrian Paschal full moon must have been happened roughly in two rather sturdy steps (the first around the year 300, the second around the year 320) at each of which not only some but all or almost all dates of the sequence of dates in question must have been advanced by a day. Further on we will see why at each of those two steps the choice made was by no means also the best one.
If we relate column E of table 7 to columns B, C, D of this table then the only striking thing we descry is a surprisingly simple connection between columns B and E. That makes it plausible that the ultimate definition of the sequence of dates of Alexandrian Paschal full moon must have been evolved not via Anatolius’ Paschal cycle but along another way from the sequence of preanatolian Paschal full moon. That implies that the reconfirmation by the church of Alexandria of its date of March equinox on 22 March did not lead to a balanced revision of Anatolius’ Paschal table but to modifications in or a revision of the dates of preanatolian Paschal full moon being at its disposal yet. It is on the basis of the conclusion of the last sentence but one of the preceding paragraph that we can establish the plausibility of the supposition that around the year 310 an (unfortunately unknown) metonically structured sequence of dates of (what I call for convenience) postanatolian Paschal full moon with 22 March as earliest possible date must have been used by the church of Alexandria which stood roughly midway between the sequence of preanatolian Paschal full moon and the classical sequence of Alexandrian Paschal full moon. Besides the sequence of dates of Anatolian Paschal full moon (defined in the fourth paragraph of this section) and the sequence of postanatolian Paschal full moon there are still two more sequences of dates which possibly played a part in the development from preanatolian to Alexandrian Paschal full moon, namely the sequence of “Anatolian dates” of Paschal full moon suggested by the German historian Eduard Schwarz (around the year 1900) and the one suggested by the American historian Alden Mosshammer (around the year 2000).
In order to gain insight into the way in which the sequence of dates of Alexandrian Paschal full moon (with 21 March as earliest possible date) in the course of a time interval from around 260 to around 320 could have evolved out of the sequence of dates of preanatolian Paschal full moon (with 23 March as most probable earliest possible date), we would want to bring together the restrictions of all sequences of dates which could have played a part in this development (these sequences of dates are all periodic with a period of 19 years) to (e.g.) the time interval consisting of the Julian calendar years between the years 270 and 290 in one table. Hence since recently (August 2009) we can see in table 8 (with dates according to the Julian calendar) for each indicated calendar year (in the primary column A) mentioned in column B the most probable date of preanatolian Paschal full moon (according to table 3), in kolom C the date of Anatolian Paschal full moon (according to table 7), in column D the most probable date of postanatolian Paschal full moon, in column E the “Anatolian date” of Paschal full moon suggested by Eduard Schwartz, in column F the “Anatolian date” of Paschal full moon suggested by Alden Mosshammer, in column G the date of Alexandrian Paschal full moon.
We call attention that each of the six sequences of dates presented in table 8 belongs to one of three clearly different astronomical categories, namely the “waning full moon category”, “pure full moon category”, and “waxing full moon category” defined in section 12. Most dates of preanatolian Paschal full moon as well as most dates of Anatolian Paschal full moon defined in the fourth paragraph of this section were, just like most dates of the fourteenth day of Nisan and most dates of Jewish Paschal full moon, marked by a sunset accompanied by a night waning full moon (first category). The dates of postanatolian Paschal full moon (and also the “Anatolian dates” of Paschal full moon suggested by Eduard Schwarz) were for the most part marked by a sunset accompanied by a night pure full moon (second category). The dates of Alexandrian Paschal full moon (and also the “Anatolian dates” of Paschal full moon suggested by Alden Mosshammer) were for the most part marked by a sunset accompanied by a waxing full moon (third category). We note that the dates of Anatolian Paschal full moon belong for the most part to the first of the three astronomical categories defined in section 12, which is in perfect accordance with the fact that they were defined amply before the third turn of century. Because on the face of it both a waning full moon and a waxing full moon look like a pure full moon (see figure 4), the church of Alexandria, which almost two centuries after the elimination of the Jewish community of Jerusalem possibly no longer wanted to have to do with the whims of the (then still not exactly calculable) Jewish calendar (see section 3), which then still was determined in Palestine and used nearly exclusively in Palestine, found itself around the year 320 in a position to choose its metonically structured sequence of dates of Alexandrian Paschal full moon with no heed for distinction between the aforesaid three astronomical categories.
By relating columns C, E, F of table 8 to column B of this table we can establish that the sequence of “Anatolian dates” of Paschal full moon suggested by Eduard Schwartz and the one suggested by Alden Mosshammer, contrary to the sequence of dates of Anatolian Paschal full moon (defined in the fourth paragraph of this section), differ to such an extent from the sequence of dates of preanatolian Paschal full moon that they cannot possibly have underlain Anatolius’ Paschal cycle. By the way, the date 21 March in the sequence of “Anatolian dates” of Paschal full moon suggested by Alden Mosshammer can be considered as an anachronism, because Anatolius was not acquainted with the real date of the March equinox, which is evident from the fact that the earliest possible date of Anatolian Paschal full moon is not 21 or 22 but 23 March.
By relating columns C, D, E, F of table 8 to columns B and G of this table we can establish that the sequence of dates of postanatolian Paschal full moon (particularly by its earliest possible date 22 March occurrung in the year 281) can be considered as a real bridging of the gap between the sequence of most probable dates of preanatolian and the sequence of dates of Alexandrian Paschal full moon, and that the sequence of “Anatolian dates” of Paschal full moon suggested by Eduard Schwarz, although to some extent kindred with the sequence of dates of postanatolian Paschal full moon, serves this purpose to an insufficient degree.
We establish, and this is new (August 2009), that we can represent the history of development of the dates of Alexandrian Paschal full moon schematically by the series “14 Nisan” ® “preanatolian Paschal full moon” ® “postanatolian Paschal full moon” ® “Alexandrian Paschal full moon” in which “Anatolian Paschal full moon” does not occur. The historical context of this series is the history of the church of Alexandria between the middle of the third century and the first council of Nicaea (see section 4). Probably the saltus lunae of the sequence of dates of postanatolian Paschal full moon occurred either at the transition from 300 to 301, in accordance with the position of the saltus lunae in the sequence of most probable dates of preanatolian Paschal full moon, or at the transition from 303 to 304, in accordance with the position of the saltus lunae in the sequence of dates of Alexandrian Paschal full moon. We still remark that neither the position of the saltus lunae in the sequence of “Anatolian dates” of Paschal full moon suggested by Eduard Schwartz nor the one in the sequence of “Anatolian dates” of Paschal full moon suggested by Alden Mosshammer agrees with the one in the sequence of dates of Alexandrian Paschal full moon.
Looking at column B of table 8 we can imagine how Alexandrian computists could have acted in order to replace a metonically structured sequence of dates with 23 March as earliest possible date (like the one of column B) with a metonically structured sequence of dates with 22 March as earliest possible date. However, instead of advancing an as little as possible number of dates of preanatolian Paschal full moon by a day (in the case of the metonically structured sequence of dates of column B it even would have been sufficient to do this only with the date 23 March) the church of Alexandria chose for advancing all or almost all dates of preanatolian Paschal full moon by a day. Thus the church of Alexandria obtained indeed a metonically structured sequence of dates with 22 March as earliest possible date (namely the sequence of dates of postanatolian Paschal full moon) but this sequence of dates was unfortunately not of the first but of the second of the aforesaid three astronomical categories.
Around the year 310 the sequence of dates of postanatolian Paschal full moon (with 22 March as earliest possible date), now for us an unknown link, was a reality for Alexandrian computists. Around the year 320 the date which according to the church of Alexandria had to be considered as the date of March equinox was put definitely at 21 March. That was the immediate cause of the replacement of the sequence of dates of postanatolian Paschal full moon with a metonically structured sequence of dates with 21 March as earliest possible date. But instead of simply reverting to a metonically structurered sequence of dates of the first of the aforesaid three astronomical categories with 21 March as earliest possible date, such as the sequence of dates of Jewish Paschal full moon (in the case of table 2 a really ideal metonically structured approximation of the incalculable sequence of dates of the fourteenth day of Nisan), or contenting itself with a metonically structured sequence of dates of the second of these three astronomcal categories with 21 March as earliest possible date by simply advancing the earliest possible date 22 March of the sequence of dates of postanatolian Paschal full moon and eventually still a relatively little number of dates of postanatolian Paschal full moon by a day, the church of Alexandria chose again for advancing a relatively large number of dates of Paschal full moon (in this case dates of postanatolian Paschal full moon) by a day, which resulted in the sequence of dates of Alexandrian Paschal full moon. Just as she replaced around the year 300 her sequence of dates of preanatolian Paschal full moon with the sequence of dates of postanatolian Paschal full moon, she replaced around the year 320 her sequence of dates of postanatolian Paschal full moon with the classical sequence of Alexandrian Paschal full moon, in each of these two cases by advancing all or almost all dates of the sequence in question by a day (probably in one of these two cases not without a shift of the salti lunae). But by doing that she went, though she obtained in that way indeed a metonically structured sequence of dates with 21 March as earliest possible date (namely the sequence of Alexandrian Paschal full moon), from bad to worse, for this sequence of dates was a one of the third of the aforesaid three astronomical categories. It is not primarily through the fact that sometimes Pesach (see section 3) was celebrated too early or too late but by the combination of the modifications made to the sequence of dates of preanatolian Paschal full moon sketched in the previous paragraph with the missed chance sketched in this paragraph (in both cases the change was needlesly drastic) that in the first half of the fourth century sometimes the church of Alexandria was confronted with a coincidence of her Easter Sunday with a day on which Pesach was prepared (see also section 16).
It is a matter of course that the fact that the explanatory scenario sketched in this section (it may have happened this way) is not falsifiable (due to the scarcity of reliable historical factual material as to this) by no manner of means implies that this scenario accords in all possible details with historical reality; in fact this scenario is no more than an as realistic as possible working hypothesis, schematically represented by the series “14 Nisan” ® preanatolian Paschal full moon ® postanatolian Paschal full moon ® Alexandrian Paschal full moon, and consisting of four plausible suppositions, namely that in Alexandria around the year 260 the (metonically structured) sequence of dates of Jewish Paschal full moon with 21 March as most probable earliest possible date was drawn up by Jewish calculators (see section 3), also around the year 260 the (metonically structured) sequence of dates of preanatolian Paschal full moon with 23 March as most probable earliest possible date was drawn up by Christian computists (see section 4), around the year 310 a (metonically structured) sequence of dates of postanatolian Paschal full moon with 22 March as earliest possible date was used, and around the year 320 the classical (definitive, metonically structured) sequence of dates of Alexandrian Paschal full moon with 21 March as earliest possible date was drawn up (see section 4). We realize that, irrespective of the degree to which the details of that scenario correspond to the (real) historical running of things, we can establish that the adaptation of Nisan to the Alexandrian calendar (see section 3) effected by the church of Alexandria must have happened in three phases, namely a phase which boils down to the replacement of the earliest possible date of the fourteenth day of the Alexandrian lunation of Nisan (probably 21 March) with the latest possible date of preanatolian Paschal full moon (probably 20 April) followed by two successive drastic changes; the first of these two drastic changes was the advancing of all or almost all dates of preanatolian Paschal full moon by a day for the obtaining of the dates of postanatolian Paschal full moon, the second the advancing of all or almost all dates of postanatolian Paschal full moon by a day for the obtaining of the dates of Alexandrian Paschal full moon.
After all, the sequence of dates of Jewish Paschal full moon defined in section 3, just like the sequence of dates of Alexandrian Paschal full moon a sequence of dates with 21 March as earliest possible date and 18 April as latest possible date but unlike this sequence of dates a real metonically structured approximation of “the” sequence of dates of the fourteenth day of Nisan, really would have been an ideal sequence of dates of Paschal full moon to generate dates of Easter Sunday which between the years 310 and 1582 would as good as never have coincided with any date of the fourteenth day of Nisan (see also section 16).
15 corroboration
Unlike the date of the day on which in Palestine traditionally early in spring Pesach (see section 3) was prepared, wich day always coincided with the fourteenth day of Nisan (see section 3), the date of Alexandrian Paschal full moon (see section 4) in the time it was defined (around the year 320) coincided mostly with the date of the twelfth day of Nisan. We justified that statement in section 12 and not surprisingly no facts are known which are inconsistent with it (and as for the vague formula “Paschal full moon = 14 Nisan”, it is just the question to what extent this is a fact which is under discussion here). That does not exclude that it might be worth pointing that the difference of mostly two days between date of Alexandrian Paschal full moon and date of the fourteenth day of Nisan is perfectly in line with the difference of on average exactly two days between the dates of Alexandrian and the dates of Anatolian Paschal full moon (see section 14), which can be easily deduced from table 8 (compare column C with column G). In addition there are two interesting remarks of Beda Venerabilis (see section 4), both made around the year 720, which lead to conclusions confirming the correctness of the statement in question. The first of those two remarks arised from his (wrong) assessment of the date of the total solar eclipse which was observed in Britain and Ireland in the year 664, the second amounted to the (correct) observation that in his time sometimes the (Alexandrian) Paschal full moon seemed “older” than normal.
In the year 664 the date of Alexandrian Paschal full moon was 17 April and the date of the accompanying (actual) Fullmoon was 16 April; these dates were preceded by the unnoticed, after all invisible, (actual) Newmoon of 2-4-664 (in Britain early in the morning), and succeeded by the Newmoon of 1-5-664, which however did not go by unnoticed, for this Newmoon was accompanied by a total solar eclipse which was observed in Britain and Ireland in the afternoon. According to observers that solar eclipse occurred already fourteen days after the full moon of 17-4-664, which was understanded then by no one, as little as by Beda Venerabilis half a century later. Beda Venerabilis did understand that the last Newmoon preceding that solar eclipse must have taken place 29 days earlier (in Britain early in the morning) than that solar eclipse. But assuming that on 17-4-664 the “age” of the moon was 14 and that the Alexandrian lunar phase number of the day of the last Newmoon preceding that solar eclipse was 1, he thought to have to conclude that it was Newmoon on 4-4-664 and furthermore that that solar eclipse must have been happened on 3-5-664. He could impossibly accept that on 3-5-664 the moon could have been two days “older” in the heavens than in his tables.
The mistake Beda Venerabilis made with respect to the date of the solar eclipse observed in Britain and Ireland in the year 664 can be explained by remarking that he, though familiar with the fact that at the transition from 664 to 665 a saltus lunae (see section 3) of the sequence of dates of Alexandrian Paschal full moon occurs, but being ignorant of the fact that in the second half of the seventh century his (thought up by us) great clock (see section 11) lost already more than a whole day, neither he could know that in the year 664, due to astronomical causes connected with the mutual motions of sun, earth and moon which were unknown to him, the date of Alexandrian Paschal full moon could very well coincide with the date of the fifteenth (instead of the implicitly presupposed thirteenth) day after the last Newmoon preceding this solar eclipse. Besides we establish that Beda Venerabilis, on the other hand, had no trouble, perhaps even was familiar, with the idea (stemming from the first half of the fourth century) of an Alexandrian Paschal full moon on a date at the same time thirteen days after the date of the last Newmoon and sixteen days before the date of the next Newmoon, which corresponds to our idea of a date of Alexandrian Paschal full moon preceding the date of the Fullmoon of Nisan with a difference of on average roughly 1.5 days; we have to do here with a phenomenon which was around the year 320 a very usual thing indeed (in fact occurred even in about forty percent of the first forty calendar years of the fourth century), but around the year 720 (owing to the more and more getting behind of Beda Venerabilis’ great clock) no longer occurred at all. Of course the moment of Fullmoon itself is on average located midway between the two neighbouring moments of Newmoon; but it is only in the eighth century that the date of Alexandrian Paschal full moon was on average located in this position.
Beda Venerabilis’ great clock lost after the moment of exactly keeping time (around the third turn of century) with the elapsing of time more and more time, namely roughly a day per three centuries (see section 11). Around the year 290 the ecclesiastical full moon, in the meaning of the phase of the moon during the night which started in Jerusalem with the sunset of the date of Alexandrian Paschal full moon, was usually still a waxing full moon (see section 12), around the year 600 usually a pure full moon. Around the year 900 the ecclesiastical full moon was usually a waning full moon (see section 12), which implies that as late as in the course of the eighth century it must sometimes have looked more or less clearly like a waning moon, a fact which was reported indeed around the year 720 by Beda Venerabilis, who wondered “why the moon sometimes appears older than its computed age”. Around the year 1200 the ecclesiastical full moon looked usually like a waning moon and only rarely like a full moon, around the year 1500 as good as always like a waning moon.
Starting from the original (around the third turn of century) connection between the dates of Alexandrian Paschal full moon and the dates of Fullmoon (see section 12) it is easy to understand why it still had to last so long before it became possible to establish by means of direct observation of the moon that the ecclesiastical full moon clearly had become a waning moon. During the six centuries between the years 300 and 900 the ecclesiastical full moon was usually a full moon, i.e. with the naked eye indistinguishable from Fullmoon (see figure 4), and not surprisingly it is as late as from the eighth century onwards that the moon went to look more like a waning moon more and more frequently. That waning ecclesiastical full moon and a much too early date of the March equinox (see section 7) were only two out of many pressing problems with which the church of Rome was confronted in the sixteenth century; at least these two problems were solved in the year 1582 in a reasonable way by means of the replacement of the Julian calendar with the Gregorian calendar (see section 3) and (of course at the same time) the replacement of Beda Venerabilis’ Easter cycle (see section 4) with Easter tables adjusted to the new calendar.
16 coincidences
It is just the ultimate choice (around the year 320) of the church of Alexandria (Egypt) for her dates of Alexandrian Paschal full moon (see section 4) which was the cause of the well known fact that between the years 320 and 360 the date of Easter Sunday must have coincided more than once with the date of the fourteenth day of Nisan (see section 14). For example, in the year 323 the most probable date of the fourteenth day of Nisan was Sunday 7 April and the date of Alexandrian Paschal full moon Friday 5 April, which because of the principle “Easter Sunday is the first Sunday after the Paschal full moon” implies that two years before the first council of Nicaea (see section 4) the date of Alexandrian Easter Sunday (see section 4) probably coincided with the date of the day on which Pesach (see section 3) was prepared.
At the first council of Nicaea was stated emphatically that henceforth the date of Easter Sunday should never coincide with the date of the fourteenth day of Nisan, in the morning and afternoon of which in Palestine traditionally Pesach was prepared. One then thought to avert the “danger” of such a coincidence by equalizing any “Paschal full moon” whatever to the corresponding fourteenth day of Nisan. However, it is not by that (illusory) equalization, resulting in the Christian tradition which says that “Paschal full moon = 14 Nisan”, but by the fixation of the Jewish calendar (see section 3) almost forty years later, that the problem of the churches how to prevent that the date of Easter Sunday sometimes could coincide with the date of the fourteenth day of Nisan was solved, as a matter of course and for a long time, at last.
Between the year 325 (in which year the first council of Nicaea took place) and the year 360 (about which year the Jewish calendar was fixed) there was a real danger of coincidence of the date of the fourteenth day of Nisan with the date of Easter Sunday indeed. That emerges from table 9 (with dates according to the Julian calendar); in this table we see for each indicated calendar year (in the primary column A) mentioned in column B the best possible estimated point in time for Jerusalem of the (actual) Newmoon of Nisan, in column C the most probable date of the first day of Nisan estimated on the basis of column B (in just the same way as in section 3), in column D the date of Alexandrian Paschal full moon, in column E the most probable date of the fourteenth day of Nisan estimated on the basis of column C, in column F the date of Alexandrian Easter Sunday (on the basis of column D). In column B always the best possible estimated point in time for Jerusalem of the first Newmoon after 4 March 18:00 is mentioned; the choice for this utmost point in time is closely connected with the principle that Pesach should be celebrated as early as possible in spring (in column E the earliest date is 20 or 21 March).
According to table 9 between the years 325 and 360 the preparation of Pesach in Palestine could have taken place perchance still about three times on and about four times one day after Easter Sunday as well. In each of those cases the cause was rather a “too early” Paschal full moon than a “too late” Pesach (and anyway no “too early” Pesach). It is certain that in the year 346 the Christian Paschal feast was celebrated, with consent of Athanasius, at the time bishop of Alexandria, not on the date of Alexandrian Easter Sunday but a week later (on 30 March, the date of Roman Easter Sunday). By the way, table 9 confirms our conclusion (in section 12) that between the years 280 and 360 the date of Alexandrian Paschal full moon mostly coincided with the date of the twelfth day of Nisan (compare column D with column E); also our conclusion (in section 12) that in the years 330 modulo 19 between the years 280 and 360 the date of Alexandrian Paschal full moon mostly fell roughly on the twelfth day of Iyyar, is confirmed by this table.
In order to get insight into the consequences of the fixation of the Jewish calendar (about the year 360) for the date of the fourteenth day of Nisan related to the date of the (actual) Fullmoon of Nisan, which date formerly usually coincided with the date of the thirteenth or of the fourteenth day of Nisan (see section 3), as well as for the date of Alexandrian Easter Sunday related to the date of the fourteenth day of Nisan during the part of the fourth century from the moment at which the Jewish calendar was fixed, we look at table 10 (with dates according to the Julian calendar); in this table we see for each indicated calendar year (in the primary column A) mentioned in column B the date of Alexandrian Paschal full moon, in column C the date of the fourteenth day of Nisan according to the fixed Jewish calendar, in column D the best possible estimated point in time for Jerusalem of the Fullmoon of Nisan, in column E the date of Alexandrian Easter Sunday (on the basis of column B). We still note that the sequence of dates of column C has no metonical structure.
If we have a look at table 10 then we can see that the fixation of the Jewish calendar must have gone hand in hand with a threesome of notable changes, of which the first was a shift of the celebration of Pesach with respect to the Fullmoon of Nisan, the second a shift of Nisan with respect to the Julian calendar (as well as with respect to the Alexandrian calendar), and the third in all probability an intended effect of the first and the second. The first of those two shifts was a shift of the date of the fourteenth day of Nisan, which had been for centuries on average a little less than half a day later than the date of the Fullmoon of Nisan, to a new position on average roughly more than half a day earlier than the date of the Fullmoon of Nisan (compare column C with column D), the second entailed such a change of the average position of Nisan with respect to the Julian calendar that late dates (later than 16 April) of the fourteenth day of Nisan disappeared to make room for early dates (earlier than 21 March) of the day on which Pesach was prepared (compare column E of table 9 with column C of table 10). Those two shifts must have been intended to avert the danger of coincidence of the date of the fourteenth day of Nisan with the date of Easter Sunday. Indeed we can establish, by comparing in table 10 columns C and E with each other, that only with the fixation of the Jewish calendar (about the year 360) in Palestine as well as in Alexandria the annual celebration of Easter Sunday after the fourteenth day of Nisan was secured for a long time. Evidently for the Jewish authorities in Palestine in the time of the fixation of their calendar a good relationship with the churches in Palestine had a higher priority than their principle that Passover had to be celebrated not earlier than in spring. By the way, it is also due to those Jewish authorities that (owing to the first of the two shifts considered in this paragraph) inside the time interval consisting of the years 361 up to and including 400 instead of the date of the Fullmoon of Nisan the date of Alexandrian Paschal full moon usually coincided with the date of the thirteenth or of the fourteenth day of Nisan (compare column B with column C). We still observe that not only in the years 368 and 387 but also in the years 379 and 398 the date of Alexandrian Paschal full moon fell outside Nisan.
17 epilogue
It is moment 1999, i.e. [31-12-1999 24:00] = [1-1-2000 0:00], the “magic” moment at which all four digits of the number of the calendar year at present changed, which was at the same time the moment of the start of the countdown to what must pass for the next turn of millennium. So at present we are going with perfect precision straight to millennium mistake 3. It is to be hoped that towards the year 3000 people will know any better, for otherwise then once again we shall have to undergo, all over the world, how a crowd of singing and dancing people, made mad by commerce, media and authorities and one year too early, is waiting on the platform for the next millennium train, to get on then “all together” by mistake in the last year local preceding this millennium train. To be precise again: the last year train preceding the fourth millennium train will leave at [1-1-3000 0:00], the fourth millennium train itself will leave at [1-1-3001 0:00], for, do you remember (see section 5), the first millennium train left at the moment zero of our era, i.e. at [1-1-1 0:00], in order to reach its final destination at [31-12-1000 24:00].
Around the year 2000 certainly more than six hundred websites were made in which attention is given to the millennium question. In most of those websites one declares oneself, like in this website, in favour of the proposition that the year 2001 is the first year of the third millennium and relates this rightly to the fact that in our era we have no year zero. But, and this is the first (and original) reason for being of this website, only on this website (www.millenniummistake.net) and on its (Dutch language) alter ego (www.millenniumvergissing.net) one can find in addition the observation that the absence of a year zero is not in the least a mistake of Dionysius Exiguus (see section 2) or Beda Venerabilis (see section 4) but it is purely and simply a condition the Christian era (see section 5) must satisfy in order to preserve her bilateral symmetry (see section 6). Our era has no year zero because we want, either conscious or intuitive, to keep our era symmetrical with respect to its moment zero, as in our second time line (see figure 2).
A second reason for being of this website is the publication (since the year 2004) within the framework of this website of the result of my investigation into Anni Domini (see section 11). It is table 4 which played at that investigatioan an important part; this table provides us not only with the most probable two possible dates (of course according to the Julian calendar) of Jesus’ dying day, but also with a first indication that the ultimate substitution of “the” (not exactly calculable) sequence of successive dates of the fourteenth day of Nisan (see section 3) for the classical sequence of dates of Alexandrian Paschal full moon (see section 4), which substitution the church of Alexandria (Egypt) ultimately implemented on behalf of her classical Alexandrian Easter tables composed around the year 320, must have gone hand in hand with rather substantial changes of position with respect to Nisan which are not in agreement with the principle “Paschal full moon = 14 Nisan”. As a consequence of those changes of position the formula “Alexandrian Paschal full moon = 12 Nisan” had in that time a higher degree of truth than the more natural formula “Alexandrian Paschal full moon = 14 Nisan”. Hence a third reason for being of this website is the publication (since the year 2005) within the framework of this website of the result of my further investigation into those changes of position (see section 12), about which subject (to my knowledge) never was published before. Neither in the standard work about the important book “De Temporum Ratione” of Beda Venerabilis written by Faith Wallis (see section 5) nor in the essay “Anno Domini” about early Christian chronology and origin and spread of the Christian era written by Georges Declercq (see section 11), as little as in the extensive study recently written by Alden Mosshammer (see section 14) which is largely about the calculation of Easter in the time of early Christianity, such changes of position come up. Thus unintentionally the impression is given as if there would be no difference worth speaking of between “the Paschal full moon” and “14 Nisan”, a misconception going back to the first half of the fourth century (see section 16).
The replacement of (not exactly calculable) dates of the day on which Pesach (see section 3) was prepared with dates of Alexandrian Paschal full moon which the church of Alexandria ultimately, around the year 320, applied on behalf of the construction of the first generation of classical Alexandrian Easter tables, involved for the years 330 modulo 19 of the time interval between the year 280 and the moment (about the year 360) on which the Jewish calendar was fixed in general a shift of roughly 28 days to roughly the twelfth day of Iyyar and for the other Julian calendar years of this time interval an advancing by on average two days to roughly the twelfth day of Nisan (see section 12). It is that adaptation of Nisan to the Alexandrian calendar (see section 3) which gave the impetus to the origin of the classical Alexandrian Easter tables by means of which from the fourth to the eighth century the date of Alexandrian Easter Sunday and from the eighth to the sixteenth century for all churches the date of Easter Sunday was determined. But that adaptation of Nisan to the Alexandrian calendar must in the fourth century also have resulted in some celebrations of Easter Sunday on or one day before a fourteenth day of Nisan (see section 16); in each of these cases the cause was rather a “too early” Alexandrian Paschal full moon than a “too late” Pesach (and of course in no case a “too early” Pesach).
A fourth reason for being of this website is the publication (since the year 2006) within the framework of this website of an explanation from the perspective of the sequence of dates of preanatolian Paschal full moon (see section 4) for the rather drastic manner in which around the beginning of the fourth century the church of Alexandria definitively put things in order with regard to her dates of Paschal full moon (see section 14), a fifth the publication (since the year 2007) within the framework of this website of a consideration devoted to the possible coincidences of the date of Alexandrian Easter Sunday with the date of the thirteenth or of the fourteenth day of Nisan in the fourth century (see section 16), already touched on in the previous paragraph. Since the year 2009 section 14 contains still three more new first publications, namely one with regard to the anchorage of Anatolius’ Paschal cycle (see section 4) in the Christian era, one with regard to the relation between the sequence of preanatolian and the sequence of Anatolian Paschal full moon (see section 14) and one with regard to the plausibility of a sequence of dates of postanatolian Paschal full moon (see section 14) as a standing midway bridging of the gap between the sequence of dates of preanatolian Paschal full moon and the one of Alexandrian Paschal full moon.
18 author
Jan Zuidhoek (see figure 5), who was born in the year 1938, studied mathematics (with physics and astronomy) at the university of Utrecht from 1960 to 1969 and was a teacher of mathematics from 1970 to 2001 at the Gymnasium Celeanum in Zwolle. This website evolved from the article “Millenniumvergissing” that he, inspired to this by critical pupils who wanted to know all the ins and outs, wrote in the year 2000 about the millennium question for Euclides, the organ of the Dutch association of teachers of mathematics. His article “In the Wake of Beda Venerabilis” (see article 1) written in the year 2009 still awaits an editor. The purpose of that article and also of this website is to make a scientifically solid contribution to chronology. That applies also for the article being in preparation about the relevance of the sequence of Paschal dates which is part of the Paschal cycle “De Ratione Paschali” attributed to Anatolius (see section 3) and the one about the history of coming into being of the classical sequence of dates of Alexandrian Paschal full moon (the content of each of them is based on the results of section 14).