This sextilingual website (called millennium) consists of two chapters, called millennium question and millennium mistake, which both are not only about the millennium question. The first is written in six languages (Dutch, English, German, French, Italian and Spanish), the second solely in Dutch (millenniumvergissing) and in English (millennium mistake), but a German language version of the second chapter is still under construction. These two chapters contain the same subjects, but in the second these subjects are treated much more extensively than in the first. These subjects are our era (this subject is treated in Sections 1 and 2), the millennium question (idem in Sections 3 and 4), the Julian calendar (idem in Section 5), Alexandrian Paschal full moons (idem in Section 6), the date of Jesus’ crusifixion (idem in Section 7) and Metonic structure (idem in Section 8).
When someone asserts that the year 2000 was the last year of the previous millennium then people often react with a denial, such as: “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 time interval existing of exactly one thousand years. But what is meant by “the year zero”? To be able to answer this question, in order to solve the tricky millennium question, 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 this purpose we will enter the field of chronology, which, as the science of locating historical events in time, is part of the discipline of history. Chronology is the backbone of history. In practice locating an event in time boils down to placing the moment of the event in question in the framework of our era, i.e. the Christian era.
After we have taken note of the history of the coming into existence of our era (in Section 1), we will establish that there is simply no year zero in our era and explore why our era contains no year zero (in Section 2). After we have thus established which is the connection between the moment zero (i.e. the beginning moment) of our era and the millennium question the solution to this question (see Section 3), as well as the justification of the term ‘millennium mistake’ (see Section 4), is there for the taking. Not surprisingly it is just the sections mentioned in this paragraph which together represent the original core of each of the former websites “Millenniumvergissing” and “Millennium Mistake” (in different languages but with the same content) of the same author. 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 pieces of text or were included among the deductions of Section 3 or incorporated into the objections of Section 4.
Besides the millennium question still some other interesting subjects of chronology (but not being of vital importance for the solution of the millennium question) are treated in this essay, e.g. in Section 5 calendars, in Section 6 Paschal full moons, in Section 7 Anni Domini (i.e. the years of the life of Jesus), and in Section 8 the connection between three historically important 19-year periodic sequences of dates of Paschal full moon. This essay is ended with a brief delineation of the author, in Section 9.
Our era is the complete Christian era. This era, since the year 1582 in combination with the Gregorian calendar by far the most widespread chronological system on earth, was originally (until the year 1582) coupled to the Julian calendar, which had been introduced by Julius Caesar as early as before the beginning of our era, but was replaced in the year 1582 with the Gregorian calendar by decree of pope Gregorius XIII. The Julian calendar was a drastically improved version of the primeval Roman calendar. The Alexandrian calendar was an improved version of the primeval Egyptian calendar.
The founder of our era is the monk and scholar Dionysius Exiguus, who, originating from a region in or near the Danube delta area, settled in Rome around the year 500. In or shortly before the year 526 he presented his Paschal table (see Table 1) at the request of a few officials of the papal chancery. Unfortunately neither this excellent Easter table nor his new era included in this table was accepted then immediately by the church of Rome. This happened not earlier than in the seventh and tenth century respectively.
Dionysius Exiguus’ Paschal table is a continuation of the Paschal table which has been attributed (probably wrongly) to bishop Cyrillus of Alexandria (Egypt). The Paschal table attributed to Cyrillus was composed around het jaar 440; probably it was the first Alexandrian Paschal table which contained Julian instead of Alexandrian calendar dates. The Julian calendar dates in this Paschal table are numbered according to the era of the emperor Diocletianus, whereas the ones in Dionysius Exiguus’ Paschal table are numbered according to Dionysius Exiguus’ 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. So it is not so surprising that Dionysius Exiguus was not able to do 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. Then he listed the successive Roman years from this Roman year and numbered them 1, 2, 3, ……. With the duration of a year as unit of time, the incomplete Christian era thus obtained, better known as Anno Domini (literaly ‘in the Year of the Lord’) era, boils down to our first timeline (Figure 1):
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 (so this Julian calendar year began at moment * and ended at moment 1) and e.g. year 10 = the year 10 (of our era) = the Roman year 763 (so this Julian calendar year began at moment 9 and ended at moment 10). The first day of our era is not the day of the birth of Jesus, but simply 1-1-1.
In Roman antiquity Roman 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).
Neither about any moment zero nor about any year zero Dionysius Exiguus, who used no other numerals than Roman ones in his Paschal table and in his calculations, ever worried. Though he understood very well that the division (in his case boiling down to repeated subtraction of the divisor, for in his time in Europe division algorithms were not available yet) of a positive integer by e.g. 19 sometimes does not leave a remainder, the number zero, a seemingly insignificant but exceptionally important mathematical concept, was not known to him. This 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 unique number o with the property that x + o = 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 precursors of the number zero were used (e.g. in Egypt and in Mesopotamia), i.e. words or symbols which represented literally ‘nothing’ or an empty spot in a positional system and were not considered to be (abstract) numbers by their users.
Why must the digit 0 be considered (historically seen) to be 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 (e.g. the digits 1, 2, 3, 4, 5, 6, 7, 8, 9) for the first nine positive integers and next a tenth symbol (e.g. the digit 0) for the number zero (with an eye to the extension of the set consisting of the first nine positive integers downwards), which however also must be used to be put together with the symbol (e.g. the digit 1) destined for the first positive integer in order to form a symbol (e.g. the compound 10) destined for the tenth positive integer (with an eye to the extension of the set consisting of the first nine positive integers upwards). 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 our decimal positional system, but he had no knowledge of the real significance of the digit 0. It is thanks to the digit 0 that one was able to construct our decimal positional system starting from the first nine positive integers. Just as inventing the number zero did not precede the discovery of the positive integers, inventing the digit 0 did not precede the coming into existence of our symbols for the first nine positive integers.
The presence of the Latin word
“nulla” in the third column of his Paschal table creates strongly the
impression that Dionysius Exiguus must have been familiar with the number zero.
However, that Latin word means ‘nothing’, which is logically equivalent to ‘no
days’. There where we say that in the first year the epact is no more than
0 days (see Table 1),
he must have said something like “annus primus non habet epactas”, which means
“the first year has no epacts”. There where computists like Dionysius Exiguus
calculate not with epacts (e.g. 18 + 12 = 0 modulo 30) but
with numbers of epacts (e.g. 18 days + 12 days ≡ no days
modulo 30 days), the way infants do with numbers of apples (e.g.
12 apples – 12 apples = no apples), we cannot speak yet of ‘being
familiar with the number zero’. There where Dionysius Exiguus sees simply a
(structured indeed) column of numbers of days (such as ‘12 days’ and ‘no
days’), it is our modernized mind which thinks to see a purely mathematical
structure, a sequence of (abstract) integers.In his calculations Dionysius
Exiguus used no other than Roman numerals, and he never made use of any symbol
for any zero. His number system contains only positive numbers, “nulla” in the
third column of his Paschal table means
simply ‘no days’, not 0. 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. We establish that Dionysius Exiguus is no exception to
the generally accepted rule that in early medieval Europe nobody knew the
number zero. It is only around the twelfth century that medieval Europe was
able to integrate this extremely important number, accompanied by the decimal
positional system, in its culture (see
also Section 2).
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, which took place in sixth century India, 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.
The first year of our eera is not any year zero but the year 1. And 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 (unlike for the measuring of the length of whatever) we do not need the number zero at all. Consequently the counting of years is not different from the counting of any other kind of things, and therefore someone born on 1-1-1 (under the supposition that the day on which he was born was not considered as his first birthday) will have celebrated his first birthday probably (as usual) on the day he completed the first year of his life, on 1-1-2, and consequently his tenth birthday probably on the day he completed the tenth year of his life, on 1-1-11 (not.on 1-1-10).
In or shortly before the year 526 Dionysius Exiguus received a request to give an explanation on his Paschal table. This request was coming from official representatives of pope John I. Unfortunately the information afforded by Dionysius Exiguus as a result of this request did not lead to that the church of Rome directly accerpted his Paschal table. Only in the seventh century the church of Rome decided to take in use a continuation of this Paschal table. In the tenth century she began to use the Anno Domini era included in this table also outside the framework of this table. However, the first who did this, was not the church of Rome but Beda Venerabilis, the first English historian. As early as about the year 730 the Christian era was actively put into use by this great scholar as a coherent system for dating historical and current events. Only in the tenth century the Christian 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. Though quite drastically adapted to the seasons by pope Gregory XIII in the year 1582, our era was never definitively replaced with another.
In order to create the possibility of localizing on our timeline 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 Julian calendar years 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, ……, in which 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. It is since and thanks to Beda Venerabilis (see Section 1) that the calendar years of our era are subdivided into calendar years after Christ and calendar years before Christ, which division essentially 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):
in which (modern) picture year -1 = the year 1 = the year 1 before Christ (consequently this Julian calendar year began at moment -1 and ended at moment 0) and e.g. year -10 = the year 10 = the year 10 before Christ (consequently this Julian 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 simply summarized in our observation that year -x = the year -x (of our era) = the year x = the year x before Christ, in which, however, we must realize that until in the thirteenth century negative numbers were entirely unknown in Europe.
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 of those calendar years are not always precisely equally long. Usually the difference between the lengths of two of those calendar years is either nil or one day. 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 3) 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 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 midnight 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 like it marks the direct transition (turn of century) from the first century before Christ to the first century (after Christ). Just like 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 had not 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. In early medieval Europe division algorithms did not exist yet and division boiled down to repeated subtraction. There where Beda Venerabilis in his 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”, which literally means “there remain three” (not “there remains 3”). But he refrains from naming the number zero in order 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 logically equivalent “non remanet aliquid”, which cannot mean anything else than “there remains nothing”. 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 for any cipher zero. There is nothing from which we could infer that Dionysius Exiguus was acquainted with any cipher zero or with the number zero; apparently 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 also Section 6), with our modern digits and with epacts (see also Section 6) being 0 once every nineteen years, and even mentioning the year ‑1. But all Latin manuscripts written before the thirteenth century contain no non positive numbers at all, and not surprisingly in such a manuscript you will find there where the number zero would have been in its place only the Latin word “nihil” (meaning nothing but ‘nothing’) or a Latin word like “nulla” (which means ‘none’). 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 makes calculations 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’; 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 the skill to perform calculations with positive integers.
Like Dionysius Exiguu, Beda Venerabilis 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 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. The idea 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 (see also Section 6), but no mathematicians (and also no astronomers). One does not need to be a mathematician to be able, starting from the sequence of Julian calendar dates of the (classical) Alexandrian Paschal full moon (see also Section 6) and making use of the leap year regulation according to the Julian calendar (see also Section 5) and the Alexandrian formula for the date of Easter Sunday (see also Section 6), to determine really all Julian calendar dates of the (classical) Alexandrian Paschal Sunday. And if you want to do that with the help of Dionysius Exiguus’ Paschal 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 Metonic structure (see also Section 6) as an approximation for a sequence of dates (of consecutive years of the Alexandrian calendar) which were consideered as adequate substitutes for dates of the fourteenth day of Nisan (see also Section 5) was an impressive arithmetical finding, which can be attributed to Anatolius (see also Section 5).
The great Alexandrian astronomer Ptolemaios 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 (“The Grounde 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 Paschal table), and Beda Venerabilis too could manage very well without these “unusual” numbers. Although the (incomplete) Anno Domini era was used by the church of Rome only in the tenth century for the first time, the complete Christian era was brought into use as a coherent system for dating historical events by Beda Venerabilis as early as around the year 720. However, the modern concept of the bilateral linear time scale, necessary to be able to understand our second timeline (see Figure 2), only could make its entry after people in Europe had got to hand the number zero (around the year 1200) and 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 temperature 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.
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 November of 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; this military action, which took place in the year -55, was dated by Beda Venerabilis in the year 60 before Christ.
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 [1-1-1; 0:00]. That symmetry is rather obvious, we think, as we take it for granted that every century consists of one hundred years (as every kilometre contains thousand metres), and that every (positively or negatively numbered) calendar year of our era belongs to exactly one (positively or negatively) numbered century of our era (e.g. the year -100 does not belong to both the first and the second century before Christ). Consequently, in our era there simply cannot be a year zero (provided that we want to preserve symmetry). For such a year zero would have to belong to the first century before or to the one after Christ, but then also (due to the symmetry) both to the first century before and to the one after Christ; but this is incompatible with the principle that every calendar year of our era belongs to exactly one numbered century of our era.
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 an obvious practical reason 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 chronologer Joseph Scaliger, was taken in use in its present form (including a year zero and negatively numbered calendar years) by Jacques Cassini 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):
in which (modern) picture year 0 does not exactly coincide with the year -1 (of the Christian era), which began two days later but ended one day later, which was a consequence of the initially (during almost half a century) inadequate functioning of the Julian calendar (see also Section 5).
The Christian era has a bilaterally symmetrical structure, and 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 unconsciously or consciously, prefers symmetry. Astronomers never proposed seriously to replace our bilaterally symmetrical era with their astronomical era. We owe our era to Dionysius Exiguus, its bilateral symmetry, and with this its consistency, 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.
In order to keep the March equinox, which marks the beginning of spring on the northern hemisphere of the earth, in its place (since the year 1582 on or close to 20 March) it is for the time being sufficient to drop, around the year 4915 for the first time, a leap day per four centuries once every 3333 years. That way it will last as late as Millennium 325, i.e. the millennium of which 1-1-324001 is the first day, before all our leap days are used up. We do not know whether there still will be human beings then. The present century is the first century of Millennium 3. Therefore, there is not the slightest reason to in the short term replace our era with an other one.
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 era of the French revolution. 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. 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. Each calendar year of the era of the French revolution began close by the September equinox, which marks the beginning of autumn on the northern hemisphere of the earth, and consisted of twelve months of thirty days and five or six single days; this era was in use only until 1-1-1806.
In Section 2 we ascertained that our era, i.e. the complete Christian era, is quite all right but contains no year zero. That 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. That implies that the first turn of decade took place at [31-12-10; 24:00] = moment 10 = [1-1-11; 0:00].
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.
As as matter of fact, 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. That implies that the Roman year 1 was the fourth Roman year of the sixth Olympiad, and so also that the Roman year 753 was the fourth Roman year of the 194th Olympiad. Apparently the year -1 was the fourth Roman year of the 194th Olympiad, the year 1 the first Roman jaar of the 195th Olympiad.
On 1-1-1801 the Italian astronomer Giuseppe Piazzi discovered the planetoid Ceres. At the time that day was generally considered by scientists to be the first day of the first year of the nineteenth century.
Now that we have given account of the fact that our era is quite all right and that 1-1-1 is the first day of our era (see Section 1), 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; 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 exactly 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 did not take place at the “magic” moment 1999 at which all four of the digits of the momentaneous calendar year number changed simultaneously, i.e. the point in time [31-12-1999; 24:00] = [1-1-2000; 0:00], but exactly one year later, namely at the “dull” moment 2000 at which only the last digit of the momentaneous calendar year number changed, i.e. the point in time [31-12-2000; 24:00] = [1-1-2001; 0:00].
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 decade, 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 2) 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 2). 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].
According to the Roman historian Titus Livius, who lived around the beginning of our era, Rome was founded in the Roman year 1, the first year of the Anno Urbis Conditae era (see Section 1). 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. By the way, according to modern historians Rome was not founded in the eighth but in the seventh century before Christ.
“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 at first sight 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 1-1-2000!”. Indeed that is true, but the last decade of the twentieth century had begun only on 1-1-1991, and so it had passed only on 1-1-2001. Likewise the book with the pretentious title “The complete History of the twentieth Century”, rashly (just before 1-1-2000) printed in a very big edition, which finishes off with the treatment of the nineties of the twentieth century, is no complete history of the twentieth century, because what happened in the last year of the twentieth century is not in there.
“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 second floor floor 2, 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!”. Because floors must not be taken as spaces but as horizontal dividing planes between spaces (e.g. the ground floor) numbering the floors of a building does not correspond to numbering the calendar years but to numbering 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, 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 1). 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 what does it matter? After all, the beginning of our era was chosen haphazardly!”. That more or less haphazardly but “once and for all” chosen moment is 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]; it is just this unique point in time from which the calendar years of our era are counted. In the year 1582 for an indefinite time the number of days of any calendar year of our era was fixed (see Section 5). 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 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 confirms our conclusion that [1-1-2001; 0:00] must be the second turn of millennium (see Paragraph 3)..
“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 3)!”. The games held in the year 67 were no Olympic games but games which in that year 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 current calendar year 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 these two striking moments 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 is 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. One can decide to go over to summer time but not that henceforth the sun will rise one hour later. It was possible to decide to celebrate the second turn of millennium at moment 1999, so just one year too early (see Section 3). It was even possible to decide to do as if that was not one year too early, but not to decide that that was not one year too early.
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). However, in order to determine whether something is true, sometimes logical (watertight) reasoning is necessary and sufficient. So the logical reasoning of Section 2 inevitably leads to the conclusion that an adequate era, being a linear system of numbered calendar years, is bilaterally symmetrical if and only if it has no year zero.
Thanks to Dionysius Exiguus (see Section 1) and Beda Venerabilis (see Section 2) we have at our disposal a bilateral symmetrical era without any year zero (see Section 2). The year 1 comes immediately after the year ‑1, just like the first century (after Christ) comes immediately after the first century before Christ; there is in our era no year zero, just like there is no century zero. This is the official standpoint of our modern historians, and with good reason (as we saw in Section 2). 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 3) and justifies the use of the term ‘millennium mistake’ for 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 second millennium.
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 (inclusively Homo sapiens), that all life is only temporary, that God is a product of human imagination and exists only as such (man proposes, God does not exist), that it is a mistake to think that atheists think they can prove that God does not exist (as a matter of 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 in fact 1-1-2000 could not be the first day of the third millennium.
By the way, what is the sense of education? By no means only to emancipate people. Stimulating clear thinking and careful formulating by way of joint attention to essentials is an at least equally important education objective. Pupils ought to be able to calculate the sum of -753 and 3000 by heart. 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 3), three thousand years will exist is not the year 2247 but the year 2248. It is not all that difficult.
The Gregorian calendar was introduced in the year 1582 by pope Gregorius XIII in substitution for the Julian calendar, which had been introduced sixteen centuries earlier by Julius Caesar. The Julian calendar was introduced in the year ‑46 by means of a drastic adaptation of the then by no means adequate Roman calendar. That adaptation boils down to the measure according to which the then present Roman calendar year was shifted eighty days in the direction of the future (owing to which the March equinox, which marks the beginning of spring on the northern hemisphere of the earth, was moved abruptly from 11 June of the previous Roman calendar to 23 March of the new one) and the provision that henceforth Roman calendar years (in past, present and future) would be supposed to begin or to have begun on 1 January and to consist of 366 instead of of 365 days once every four years, to begin with in the then next Roman calendar year (boiling down to the year -45).
Unfortunately, in the first half century after the death of Julius Caesar (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 as a matter of fact three leap years too much, namely eleven instead of eight. This problem was solved around the beginning of our era by the emperor Augustus by replacing all leap years between the leap years -9 and 8 with ordinary Roman calendar years consisting of 365 days. That implies in particular that the year 4 was no leap year. Julian calendar years betwecn 4 and 1582 are leap years only if their year numbers are divisible by 4. Although the Julian calendar was no ideal calendar, it functioned perfectly from 4 to 1582, more precisely from 1-3-4 up to and including 4-10-1582. Not surprsingly the dates given in Dionysius Exiguus’ Easter table are Julian calendar dates.
It is under the influence of the emperor Constantine I that the Julian calendar was accepted as official calendar by the churches who were represented at the first council of Nicaea in the year 325. 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 (nowadays worldwide used) Gregorian calendar, on the understanding that the Julian calendar, 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 (as a matter of 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 with regard to the calendar years of our era after the year 1582 that such a calendar year should be a leap year 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]. Thus all calendar years of our era from the far past until the far future have been fixed. However, with regard to that far past we must realize that from the fiftieth to the twelfth century before Christ the March equinox fell in April (and from the ninetieth to the fiftieth century before Christ in May).
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. In order to keep the March equinox in its place (on or close to 20 March) it is for the time being sufficient to drop, around the year 4915 for the first time, a leap day per four centuries once every 3333 years. That way it will last as late as Millennium 325, i.e. the millennium of which 1-1-324001 is the first day, before all leap days of the Gregorian calendar are used up. But it is not certain whether there are still human beings then. Our century is the first century of Millennium 3.
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 2), 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 a proleptic leap year regulation according to the Julian calendar holding for its calendar years before the year 1582 and the 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]. 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. That is caused by the fact that the years 0 and 4 of the astronomical era are leap years but the years -1 and 4 (of our era) 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 year -9 (of our era) began three days later than the leap year -8 of the astronomical era. It is not difficult to check that the leap year -21 (of our era) began two days later than the leap year -20 of the astronomical era and that the leap year -33 (of our era) began one day later than the leap year -32 of the astronomical era, and that the leap year -45 (of our era) = (exactly) the leap year -44 of the astronomical era. That implies that Julius Caesar, who was murdered at 15-3--44, died on 15 March of the year -43 of the astronomical era as well as of the year -44 (of the Christian era). By the way, every year x (of our era) after the year 4 (of our era) is exactly equal to the year x of the astronomical era, but every year -x (of our era) before the year -42 (of our era) is exactly equal to the year (-x+1) of the astronomical era. It is also true that the year -40 (of our era) = (exactly) the year -39 of the astronomical era.
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.
Unlike the Julian and the Alexandrian calendar, the Jewish calender is a lunar calendar, in which each new month begins more or less simultaneously with an (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 a beginning was made with its definitive fixation the beginning of the new Jewish calendar month depended not only on astronomical but indirectly also on local circumstances (in particular meteorological circumstances under which in Palestine the first appearance of the moon crescent after Newmoon was searched for). Every Jewish calender year consisted then (and still consists now) either of twelve (mostly) or of thirteen calendar months each consisting of 29 or 30 days. 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 in principle lasted seven 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 ideally roughly an hour after this sunset.
Since the coming into being of the Jewish calendar until the moment at which it had been completely fixed, the beginning of each new Jewish calendar month was in principle determined in Palestine at a special moment (about half an hour after sunset) at the beginning of the thirtieth night after the sunset with by which the first day of the expiring Jewish calender month had begun. 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 this meant that the first day of the new Jewish calender month had just begun with the sunset having taken place in Jerusalem about half an hour ago; if not, then the first day of the new Jewish calender month began at the moment of the next sunset taking place in Jerusalem (hence all Jewish calender months thus defined consisted of 29 or 30 days). Because usually a waxing moon is visible with the naked eye not earlier than 24 hours after Newmoon, at the time the first day of a new Jewish calender month usually began with the second sunset taking place in Jerusalem after Newmoon. For the same reason 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 of the fourteenth day of this Jewish calendar month.
Since the coming into being of the Jewish calendar until the moment at which it had been completely fixed, in Palestine at set times not only a decision had to be taken with respect to the point in time at which a new month of the Jewish calendar had to begin (once a month) but also a one concerning the beginning of a new year of this 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 were not only able (by applying that competence carefully) to 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 of which they were able to make use within the scope of that competence. At the time they must have been familiar with the growing of the days in winter and spring and the phenomenon of the March equinox, although they then (being familiar neither with the Julian nor with the Alexandrian calendar) were not yet acquainted with any, either alleged or correct, date of the March equinox. However, in actual practice the rule of the equinox in question was ignored more often tnan not, and in consequence Pesach celebrated one month too early many a time. As a matter of fact, the Jewish calendar can only be related to the Julian calendar insofar as the former is in accordance with the current fixed Jewish calendar, the completion of which took place in the second quarter of the ninth century.
Around the year 90 the (real) March equinox fell on 22 March, around the year 220 on 21 March, around the year 600 on 18 March, around the year 1500 on 11 March. Nevertheless, for centuries, until the year 381, the date 25 March was considered by the church of Rome to be the date of the March equinox. According to Ptolemaios (see section 2) the March equinox in his time (around the year 140) fell on 22 March. As a consequence, in the second half of the third century this 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 (Syria) around the seventies of the third century, 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 means of the construction of his famous 19 year periodic Paschal cycle, called by me Anatolian Paschal cycle, on the basis of the (mis)conception that the moment of the March equinox is not a question of a point in time or a date, e.g. 22 or 25 March, but of the time interval consisting of the four consecutive dates 22 up to and including 25 March. Shortly after the third turn of century the church of Alexandria definitely decided to consider the date 21 March so familiar to us (at the time and nowadays once again usually the date of the first day after the date of the March equinox) as the date of the March equinox. The church of Rome took that step only in the year 381.
At the end of the first century Easter (i.e. the Christian Paschal feast) was mostly celebrated on the fourteenth day of Nisan (see Section 5), at the end of the second century in principle on the first Sunday after the fourteenth day of Nisan. Around the second turn of century the moment of the beginning of Nisan was still not exactly computable. In order not to remain dependent on the not exactly predictable way in which in that time the beginning of Nisan was determined in Palestine, in the beginning of the third century calculators of some churches, among which the church of Rome and the one of Alexandria (Egypt), began to calculate their own so called dates of Paschal full moon adjusted to one of the two (mutually convertible) solar calendars prevailing then in the Roman empire (see Section 5). These dates of Paschal full moon served as substitutes for dates of the fourteenth day of Nisan which were not known in advance in the third century. Successive dates round dates of Paschal full moon were provided with successive lunar phase numbers (“age of the moon”). The dates of Paschal full moon themselves, as substitutes for dates of the fourteenth day of Nisan, got assigned the lunar phase number 14 (and so substitutes for dates of the first day of Nisan the lunar phase number 1). Generally dates of Easter were obtained from dates of Paschal full moon, and these ones, for their part, from dates of new moon.
In the first half of the third century the activities of the computists, i.e. practioners of the computus, i.e. the science developed since the beginning of the third century for the determination of their dates of Easter, led to the construction of Paschal (i.c. Easter) tables which mutually often differed in their dates of Paschal full moon and in their dates of Paschal (i.c. Easter) Sunday. Within the structure of such a Paschal (i.c. Easter) table, usually dates of Paschal Sunday must be obtained from dates of Paschal full moon which are arranged in periodic sequences of dates of consecutive years of either the Alexandrian calendar (see Section 5) or the Julian calendar (see Section 5). To be able to construct such Paschal tables, tables of lunar phases are indispensable.
Around the middle of the third century the church of Rome began to experiment with sequences of dates of Paschal full moon (of consecutive years of the Julian calendar) with a period of 84 years, the church of Alexandria with sequences of dates of Paschal full moon (of consecutive years of the Alexandrian calendar) with a period of 19 years. The sequence of dates of Paschal Sunday which was generated by the sequence of dates of the Roman Paschal full moon (of consecutive years of the Julian calendar) with a period of 84 years constructed by the church of Rome in the second half of the third century had also a period of 84 years. That the period of the sequence of dates of Paschal Sunday which was generated by the sequence of dates of Paschal full moon constructed by the church of Alexandria in the first quarter of the fourth century was no less than 532 years, was discovered around the fourth turn of century. Nevertheless it is the sequence of dates of the (classical) Alexandrian Paschal full moon (of consecutive years of the Alexandrian calendar) with a period of 19 years in question that would appear to be the key to an adequate solution of the great problem how to calculate the date of Easter (see also Section 8).
At the first council of Nicaea, convened in the year 325 by the emperor Constantine I, was decided that henceforth Easter should be celebrated every year early in spring by all Christians on the very same Sunday after the fourteenth day of Nisan, on which day traditionally the last preparations were made for the celebration of Pesach (see Section 5). 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 Paschal Sunday, and that therefore, because of the then incalculability of the Jewish calendar (see Section 5), accurate Paschal tables adapted to the Julian or to the Alexandrian calendar were required. The bishops who were together in the year 325 in Nicaea, were agreed about that Paschal Sunday always ought to be preceded by “the full moon of Nisan” as well as by the March equinox (see Section 5). However, they could not reach agreement with regard to the way in which the date of Paschal 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 Paschal full moon” and subsequently from this the date of Paschal Sunday had to be calculated.
The sole criterion for first new moon visibility with which third and fourth century Alexandrian computists were acquainted, is the primeval Babylonian rule that every new moon will be visible (to the unaided eye) for the first time, if weather permits, in the beginning of the evening, between 24 and 48 hours after Newmoon. That rule implies not only that the first day of Nisan usually began with the second sunset in Jerusalem after the new moon for Nisan, but also that the (actual) Fullmoon of Nisan fell on average around the midnight point in time of the fourteenth day of Nisan, because from the middle of the local Jerusalem ‘from sunset to sunset’ day of the Newmoon in question to the midnight point in time of the fourteenth day of Nisan it is just half a synodic period of the moon.
As early as around the middle of the third century the church of Alexandria had started using the date 22 March, which date she then considered as the date of the March equinox, as a lower limit of her dates of Paschal full moon. The first by name known Alexandrian computist who applied that principle to 19-year periodic sequences of dates of Paschal full moon was Anatolius (see Section 5). Supposedly around the year 260 (before his episcopal consecration) he took an actieve part in the construction of the sequence of dates of the proto Alexandrian Paschal full moon, the until recently unknown sequence of dates of Paschal full moon (of consecutive years of the Alexandrian calendar) with a period of 19 years from which some time later Anatolius must have started in order to be able to construct the Anatolian Paachal cycle (see Section 5). The Anatolian Paschal cycle, which was constructed aroud the year 270, has survived in the form of a sequence of nineteen consecutive Paschal dates in the Paschal table being part of the medieval Latin text “De ratione paschali”. However, this Paschal table was rather impractical, through the fact that it was not adapted to the Alexandrian or to the Julian calendar but to the Anatolian calendar, i.e. the variant of the Julian calendar ingeniously devised by Anatolius on behalf of this Paschal table, and must have gone out of use, if it was ever actually used, long before the end of the third century. That the 19-year cycle contained in “De ratione paschali” is really the thought lost Anatolian Paschal cycle, has been convincingly demonstrated by the Irish scientists Daniel McCarthy and Aidan Breen.
In the second half of the third century besides the sequence of dates of the proto Alexandrian Paschal full moon another important 19-year periodic sequence of dates of Paschal full moon was constructed (but probably never published), namely the sequence of dates of the Anatolian Paschal full moon (of consecutive years of the Julian calendar) of which the dates can be obtained one by one by taking each of the nineteen Paschal dates in the Paschal table being part of “De ratione paschali” as a Julian calender date and reducing it to the Julian calendar date with lunar phase number 14 with the benefit of the accompanying lunar phase number (mentioned in this Paschal table as well). On the other hand, the sequence of dates of the proto Alexandrian Paschal full moon cannot be deduced from any known historical source, but was reconstructed in the year 2009 by the author of this website. In addition, by comparing the sequences of dates of the proto Alexandrian and the Anatolian Paschal full moon he could establish that the initial year of “De ratione paschali” (i.e. the Julian calendar year for which the first Paschal date of “De ratione paschali”, 16 April, was intended) must have been the year 271. His pioneering article on his reconstruction of the sequence of dates of the proto Alexandrian Paschal full moon and the initial year of “De ratione paschali” will appear in print in July 2014.
In Section 8 we will relate the three 19-year periodic sequences of dates of Paschal full moon mentioned in this section to each other. The chronologically first and third of these three sequences of dates, namely the one of the proto Alexandrian Paschal full moon, also referred to as proto Alexandrian cycle, and the one of the (classical) Alexandrian Paschal full moon, also referred to as classical Alexandrian cycle, respectively, have both a so called Metonic structure (see Section 8) and are due to this, from an astronomical point of view, ideal sequences of dates of Paschal full moon. There exists a close relation between the chronologically first and second out of the three sequences of dates in question: the proto Alexandrian cycle is just the best Metonically structured approximation to the sequence of dates of the Anatolian Paschal full moon.
Shortly after the third turn of century the church of Alexandria decided to consider henceforth 21 March as the date of the March equinox. This is one of the reasons why, around the year 310, the church of Alexandria replaced her sequence of dates of Paschal full moon then in use, probably the proto Alexandrian cycle, with the classical Alexandrian cycle. Hence the classical Alexandrian cycle has 21 March as its earliest possible date. Its latest possible date is 18 April.
As early as in the year 410 the great Alexandrian computist Annianus succeeded in using the classical Alexandrian cycle in order to construct the famous classical Alexandrian Paschal cycle (i.c. of consecutive years of the Alexandrian calendar), which contains a 532-year periodic sequence of dates of Paschal Sunday. In the year 525 the classical Alexandrian cycle was used by Dionysius Exiguus (see Section 1) in constructing his Paschal table so important from a chronological point of view. Beda Venerabilis’ Easter cycle is an extension of Dionysius Exiguus’ Paschal table as well as a reinvention of Annianus’ Paschal cycle. It is especially due to Annianus on the one hand (in the east) and by the agency of Dionysius Exiguus’ great follower Beda Venerabilis (see Section 1) on the other (in the west) that the classical Alexandrian cycle has been crucial for celebrating Easter simultaneously by all churches for a very long time (from the eighth to the sixteenth century).
Although the classical Alexandrian cycle is fully known (see e.g. column F of Table 1), it is only recently that we have some idea how it originated. It forms the backbone of all classical Alexandrian Paschal tables, i.e. the Paschal tables composed by the church of Alexandria around the year 310 and all Paschal tables which directly or indirectly evolved from these Paschal tables (by means of extrapolation), for example Annianus’ Paschal cycle, Dionysius Exiguus’ Paschal table and Beda Venerabilis’ Easter cycle.
Already since the beginning of the third century the church of Alexandria respected the principle “Paschal Sunday is the first Sunday after the Paschal full moon” for the determination of the date of Paschal Sunday. According to that principle the date of the proto Alexandrian Paschal Sunday is the date of the first Sunday after the date of the proto Alexandrian Paschal full moon. Julian calendar dates of the (classical) Alexandrian Paschal Sunday determined according to that principle we can find in column G of Table 1; we see that in this column the earliest possible date is 22 March, the latest possible 25 April.
In the fourth century in the western half of the Roman empire Roman Paschal tables were in use which were real Paschal cycles because not only their sequences of dates of Roman Paschal full moon but also their sequences of dates of Paschal Sunday, these dates called for convenience dates of the Roman Paschal Sunday, had a period of 84 years. In that time dates of the Roman Paschal Sunday were determined according to the principle “Paschal 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 the Roman Paschal full moon was 16 March (in the year 352) and the earliest possible date of the Roman Paschal Sunday 22 March (in the years 330, 341, 352), in spite of the fact that at the time until the year 381 the church of Rome considered the date 25 March to be the date of the March equinox. The Roman Paschal tables that were used in the fourth century, were of less quality than the Alexandrian ones in that their dates of Paschal full moon fell much earlier out of step with the rhythm of the real moon phases.
By the publication around the year 310 of the first generation of classical Alexandrian Paschal 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 her Paschal full moon. Thus she opted also definitely for 22 March as the earliest (and for 25 April as the latest) possible date of her Paschal Sunday, because of the Alexandrian formula for the date of Paschal Sunday, which applies for all classical Alexandrian Paschal tables. It is plausible that in the fourth century the curches in the eastern half of the Roman empire (among which the churches in Palestine) used for the most part classical Alexandrian Paschal tables, the curches in the western half for the most part Roman ones.
In the beginning of the fifth century Annianus composed his Paschal cycle, in which not only the sequence of dates of Paschal full moon is periodic (with a period of 19 years) but also the sequence of dates of Paschal Sunday (with a period of 532 years). Annianus’ Paschal cycle was obtained as a result of extrapolation from a foregoing generation of classical Alexandrian Paschal tables. The Paschal table attributed to Cyril (see Section 2), which was obtained in the same way and was intended for use in the western half of the Roman empire, was provided with Julian instead of Alexandrian calendar dates. Dionysius Exiguus obtained his Paschal table, which is also provided with Julian calendar dates, by extrapolation from the Paschal table attributed to Cyril. The Paschal table attributed to Cyril concerns the years 437 up to and including 531, Dionysius Exiguus’ Paschal table the years 532 up to and including 626. Because the Alexandrian formula for Paschal Sunday holds for all classical Alexandrian Paschal tables and in all these Paschal tables the age of the moon on the date of Paschal full moon is always 14 days, in all these Paschal tables the age of the moon on the date of Paschal Sunday is always an integral number of days between 14 and 22.
In Dionysius Exiguus’ Paschal table (see Table 1), in which all dates are Julian calendar dates, we see for each indicated calendar year (in the primary column A) mentioned in column C (what is called) the epact, this is (what is called) the “age” of the moon (this is a lunar phase number) on 22 March, in column D (what is called) the concurrent (i.e. the difference between 24 March and the date of the last Saturday before 24 March), in column F the date of the (classical) Alexandrian Paschal full moon, in column G the date of the (classical) Alexandrian Paschal Sunday, in column H the “age” of the moon on the date of the Alexandrian Paschal Sunday. The numbers in columns C, D, and H represent numbers of days; “nulla” in column C means ‘none’, which is logically equivalent to ‘no days’, and then also to ‘0 days’.
The structure of Dionysius Exiguus’ Paschal table (see Table 1) emerges from the coherence between columns C, D, F, G, H of this table, in concreto the manner in which successively column F from column C, column G from columns D and F, and column H from columns F and G can be obtained. Each date in column F can be obtained by subtracting the corresponding epact in column C from 5 April and reducing the outcome modulo 30 days to a date between 20 March and 19 April. Each date in column G can be obtained by subtracting the corresponding concurrent in column D from 25 March and reducing the outcome modulo 7 days to a date between the corresponding date in column F and the date obtained by adding 8 days to this date in column F. This calculation boils down to the same as applying the principle “Paschal Sunday is the first Sunday after the Paschal full moon” to each date in column F. For each number in column H it holds that the number of days in question can be obtained by adding 14 days to the number of days obtained by subtracting the corresponding date in column F from the corresponding date in coloumn G. Dionysius Exiguus’ Passah table is provided with two independent numerations of rows, namely one with a period of 15 years, represented in column B, and the other with a period of 19 years, represented in column E.
The sequence of epacts which all classical Alexandrian Paschal tables have in common, has a period of 19 years and the additional property that every 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 so called saltus occurring once every nineteen times) to the last preceding epact of the sequence (we remark that 18 × 11 + 1 × 12 ≡ 0 modulo 30). It is this particular structure of this sequence of epacts which is reflected in the so called Metonic structure of the classical Alexandrian cycle (see also Section 8).
Not only the sequence of epacts but also the sequence of concurrents occurring in Dionysius Exiguus’ Paschal table has a particular structure. The oldest classical Alexandrian Paschal table in which that sequence of concurrents occurs is the Paschal table of bishop Theophilus of Alexandria constructed in the year 385. That sequence of concurrents, which all classical Alexandrian Paschal tables constructed after the fourth century have in common with Theophilus’ Paschal table, has a period of 28 years and the additional property that every following concurrent of the sequence can be obtained by adding either 1 modulo 7 days (normally) or 2 modulo 7 days (once every four times) to the last preceding concurrent of the sequence (this definition rests on the congruence 21 × 1 + 7 × 2 ≡ 0 modulo 7). The particular structure of that sequence of concurrents rests on the leap year proportion one to four of both the Alexandrian and the Julian calendar and the fact that there are seven days in a week.
We conclude that all classical Alexandrian Paschal tables constructed after the fourth century have one and the same sequence of epacts with a period of 19 years as well as one and the same sequence of concurrents with a period of 28 years in common. It is Annianus who around the fourth turn of century discovered that it must be possible to extend the classical Alexandrian Paschal tables until then constructed to a Paschal cycle with a period of 19 × 28 = 532 years. He completed his Paschal cycle already in the year 410. Dionysius Exiguus was not acquainted with Annianus’ Paschal cycle, and he had no proper understanding of the possibility to extend his Paschal table to an Paschal cycle.
In the year 616 an anonymous extended Dionysius Exiguus’ Paschal table to an Paschal table concerning the years 532 up to and including 721, and it is this Paschal table which as late as 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, Roman Paschal tables. In the year 725 Beda Venerabilis published a new extension of Dionysius Exiguus’ Paschal table to a Paschal cycle (i.c. of consecutive years of the Julian calendar) which is in fact a reinvention of Annianus’ Paschal cycle (i.c. of consecutive years of the Alexandrian calendar). Beda Venerabilis’ Easter cycle and Annianus’ Paschal cycle contain essentially just the same dates of Paschal full moon and of Paschal Sunday. Like in Annianus’ Paschal 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 Paschal Sunday a sequence of dates with a period of 532 years. In the Byzantine empire thanks to Annianus’ Paschal cycle at all times the churches were acquainted with the right date of the next Paschal Sunday. In the eighth century thanks to Beda Venerabilis’ Easter cycle also the churches in the part of Europe outside the Byzantine empire got that possibility.
It is the Alexandrian Paschal tables composed in Alexandria (Egypt) around the year 310 from which (a century later) Annianus’ Paschal cycle, (two centuries later) Dionysius Exiguus’ Paschal 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 Paschal tables were in use abundantly. In the Byzantine empire no other Paschal tables than classical Alexandrian Paschal 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 Paschal tables being in use were replaced with classical Alexandrian Paschal tables. The thus realized general use of classical Alexandrian Paschal tables (by means of which at last the churches could realize their old ideal of celebrating Easter 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 5).
Now that we solved the millennium question completely (see Section 1, Section 2, Section 3) and justified the term ‘millennium mistake’ (see Section 4), the still unanswered question concerning the precise connection between the Anno Domini era (see Section 1) 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, i.e. the year 1 (of our era) = the Roman year 754 (see Section 1), and Annus Dominicae Incarnationis, i.e. the Roman 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 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. That view agrees with the known historical fact that Charlemagne let himself crown emperor just on 25-12-800. The opinion of Robert Fruin (around the year 1900) that Annus Dominicae Incarnationis = the year 1 is supported by Peter Verbist (university of Leuven) and by Georges Declercq (university of Brussels); this opinion seems to be at least as plausible as the other one because of the analogy between the beginning of the Anno Domini era and the one of the Anno Urbis Conditae era: “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 could have thought.
One of the most influential figures of the first council of Nicaea was Eusebius, the historian who had become bishop of Caesarea shortly after the year 313. He was the first who hit upon the idea of an era with as its starting year the year of birth of Jesus according to the Julian calendar. However, he thought Jesus was born in the third Roman year of the 194th Olympiad (see Section 3), in accordance with the opinion of Orosius (see Section 1), a century later, 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 1). 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 did not know in which Roman year Jesus was born, and we do not know either. 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 scholars do not yet agree. We establish that in all probability Jesus was born about the year -5. Sometime in the nineties of the previous century the day on which it had been two thousand years since Jesus was born, slipped by.
At least as interesting as the question when precisely was the beginning of Anni Domini, is the question when precisely was its end. 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 one day after (according to the three synoptic gospels) a day on which Pesach (see Section 5) was prepared, so on a fourteenth or on a fifteenth day of Nisan (see Section 5). However, that Jesus would have been crucified on a fifteenth day of Nisan, may be doubted, because the fifteenth day of Nisan was a feast day on which one did not administer justice in Jerusalem. The religious persuasion that Jesus was crucified a few hours before celebration of Pesach began agrees, anyway, with the fact that at the end of the first century the Christian Paschal feast was mostly celebrated on the fourteenth day of Nisan. It is certain that Jesus died during the reign of the emperor Tiberius (who reigned from 14 to 37) and during the procuratorship of Pontius Pilatus, who was procurator of Judaea from 26 to 36.
Beda Venerabilis tried to find the date of Jesus’ dying day with the help of his Easter cycle (see Section 6), of course taking his departure from the principle “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’ Paschal 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 (classical) Alexandrian Paschal full moon (see Section 6) was Sunday 21 March and not the Thursday 24 March expected by him. Apparently he believed that Jesus had died on a fifteenth day of Nisan, and 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 Paschal tables which kept much better step with astronomical reality (see Section 6), the more the perception grew that this proposition 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 correctness of Beda Venerabilis’ evident presupposition that all dates of the (classical) Alexandrian Paschal full moon included in his Paschal cycle perfectly agree with the dates of the fourteenth day of Nisan whose substitutes they were (see Section 6). Nevertheless it is an interesting question whether it is possible to trace the date of Jesus’ dying day in the manner of Beda Venerabilis, i.e. by applying the principle “Paschal full moon = 14 Nisan” to the dates of the (classical) Alexandrian Paschal full moon between the years 26 and 36.
The dramatic confrontation between Jesus and the Roman procurator Pontius Pilatus must have taken place in Jerusalem elsewhere between the years 26 and 36. In order to be able to make a serious attempt to date Jesus’ crucifixion in the manner of Beda Venerabilis, we consider the Julian calendar dates of the Alexandrian Paschal full moon according to Beda Venerabilis’ Easter cycle holding for the years 27 up to and including 35 (these dates are the same as those of the years 559 up to and including 567 in column F of Table 1) closer by determining (with the help of column D of Table 1 or normally with the help of the Julian calendar) for each of these dates on which day of the week this date fell; the result can be seen in column B of Table 2 (in which all dates are Julian calendar dates). None of these dates appears to be a Thursday, which implies that none of these dates can be a date of Jesus’ crucifixion in accordance with the three synoptic gospels. The only one of these dates that could be a date of Jesus’ crucifixion in accordance with the fourth canonical gospel is 15‑4‑29 because this date is the only one of these dates that fell on a Friday. Beda Venerabilis did not pay attention to it.
Because Julian calendar dates of the (classical) Alexandrian Paschal full moon are defined meaningfully only insofar the Julian calendar after intervention of the emperor Augustus functioned properly (see Section 5), the sequence of Julian calendar dates of the (classical) Alexandrian Paschal full moon, which forms the backbone of Beda Venerabilis’ Paschal cycle, reaches in fact from 4 to 1582 (see Section 5). 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 clock (of course imaginary) 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. In the time that Alexandrian computists were constructing the original sequence of Alexandrian calendar dates of the (classical) Alexandrian Paschal full moon, around the third turn of century, by definition that imaginary clock, which can be supposed to have run precisely and unbrokenly from 4 to 1582, kept time with the then astronomical reality of an average lunar phase of about 1.4 days before Fullmoon. But thereafter our imaginary clock went more and more to lose time, as a result of the fact that a time interval consisting of 235 synodic months is a little shorter than a one consisting of 19 years (both about 6940 days).
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 19 × 365.25 = 6939.75 days but the moon was taking about 235 × 29.53059 ≈ 6939.689 days to pass through all of its phases 235 times. It follows that our imaginary clock with the elapsing of time after the moment of keeping time went to lose time more and more, namely after every new time interval consistong of 19 years approximately 6939.75 − 6939.689 = 0.061 days more, so after every new time interval consistong of 1 year approximately 0.0032 days more. That implies that after the moment of keeping time our imaginary clock was always taking about 310 years to get further behind a whole day. This implies that, compared to the astronomical reality of the third turn of century, around the year 600 our imaginary clock lost roughly a whole day, but in the time of the reign of the emperor Tiberius it gained almost a whole day. Not surprisingly, around the year 30 (classical) Alexandrian Paschal full moons were no nfull but waxing moons on average about 2.3 days younger than Fullmoon. This implies that there is little point in applying the principle “Paschal full moon = 14 Nisan” to the dates of the (classical) Alexandrian Paschal full moon between the years 26 and 36.
As a matter of fact, for dating Jesus’ crucifixion the dates of the proto-Alexandrian cycle (see Section 6) are far more suitable ingredients than the dates of the classical Alexandrian cycle (see Section 6), because around the year 30 proto-Alexandrian Paschal full moons were usually full moons on average about 0.1 days younger than Fullmoon. If Beda Venerabilis had been acquainted (but of course he was not) with the proto-Alexandrian instead of with the classical Alexandrian cycle then he could easily have come to the conclusion that solely 7-4-30, according to the three synoptic gospels, or 3-4-33, according to the fourth gospel, could have been the date of Jesus’ crucifixion (see columns C and D of Table 2).
It is the (nine) dates of the fourteenth day of Nisan between 26 and 36 which are essential for the determination of Jesus’ dying day. Unfortunately they are unknown. However, in order to obtain all possible dates of such a fourteenth day of Nisan, we may make use of the simple rule that the first day of Nisan usually began with the second sunset in Jerusalem after the new moon for Nisan. The rule that a new Jewish calender month usually began with the second sunset in Jerusalem after a lunisolar conjunction, is an obvious consequence of the primeval Babylonian rule that every new moon will be visible (to the unaided eye) for the first time, if weather permits, in the beginning of the evening (in practice during some time after a certain moment about 24 minutes after sunset), between 24 and 48 hours after this conjunction.
Applying the rule concerning the beginning of Nisan means that for each local Jerusalem point in time of lunisolar conjunction for Nisan an approximate date of (the daylight part of) the first day of Nisan can be estimated by simply adding 2 respectively 3 days to the (from midnight to midnight) date of lunisolar conjunction for Nisan depending on the point in time in question falls before respectively after 18:00. It is possible to locate the possible months Nisan in question in the Julian calendar by making use of the only not opportunistic Jewish principle in question, namely that Passover, in the meaning of the fourteenth day of Nisan, in fact had to be celebrated as early as possible in spring, i.e. on or as soon as possible after the March equinox, and in addition of the fact that in actual practice the Jewish authorities in Jerusalem ignored this rule and in consequence had begun their (i.c. the real) month Nisan and so also the celebration of their Pascha in fact a month too early (i.e. before the March equinox) many a time. Hence for each of the (nine) calendar years in question we will present two possible local Jerusalem points in time of lunisolar conjunction for Nisan, namely a one in column B of Table 3 and a one in column B of Table 4, of which the former will generate a possible date of the fourteenth day of Nisan after and the other a possible date of the fourteenth day of Nisan before the March equinox (see column D of Table 3 and column D of Table 4, respectively).
During the time interval consisting of the time between 20 and 40 the real date of the March equinox was sometimes 23 March sometimes 22 March (half of each). In order to be able to obtain (of course with the help of a suitable lunar phase table) for each of the (nine) calendar years in question the two most obvious possible local Jerusalem points in time of Newmoon for Nisan it is necessary and sufficient to establish a suitable lower and upper limit which in principle must differ about 59 days (being about twice the synodic period of the moon) between which limit dates possible local Jerusalem points in time of Newmoon for Nisan must occur in order to guarantee that the corresponding possible dates of the fourteenth day of Nisan will be not only not earlier than just 22 February (this date being just 29 or 30 days earlier than 23 March) but also not later than just 20 April (this date being just 29 days later than 22 March). It is not surprising that we will achieve our aim by taking our departure from a lower limit 6 February 18:00 and upper limit 5 April 18:00, because adding 3 + 13 days to 6 February gives 22 February and adding 2 + 13 days to 5 April gives 20 April. It is column B of Table 3 which contains for each of the calendar years mentioned in column A of this table the corresponding as good as possible estimated local Jerusalem point in time of the second Newmoon between those limits. It is column B of Table 4 which contains for each of these calendar years the as good as possible estimated local Jerusalem point in time of the first Newmoon between those limits. That is why column C of Table 3 contains for each of these calendar years a possible date of the first day of Nisan after 9 March (this date is just 13 days earlier than 22 March) and column C of Table 4 for each of these calendar years a possible date of the first day of Nisan before 9 March. That is why column D of Table 3 contains for each of these calendar years a possible date of the fourteenth day of Nisan after the March equinox and column D of Table 4 for each of these calendar years a possible date of the fourteenth day of Nisan before the March equinox.
Because the dates menmtioned in column C of Table 3 and the dates menmtioned in column C of Table 4 may be assumed to deviate no more than a day from what they represent, this applies also to the dates mentioned in columns D of these tables. Therefore it is only the Thursdays, Fridays and Saturdays in columns D of these tables which are of importance to us. We conclude that to begin with there are six dates which could be the date of Jesus’ dying day. Assumed Jesus was crusified on a fourteenth and not on a fifteenth day of Nisan, that is of course in the first place (because at first sight they are the most probable possible dates of Jesus’ dying day) the dates of the Fridays in columns D of Table 3 and Table 4, namely the Fridays 11-4-27, 7-4-30 and 3-4-33, and only in the second place (because at first sight they are less probable possible dates of Jesus’ dying day) the dates of the Fridays immediately following any Thursday in these columns or immediately preceding any Saturday in these columns, namely the Fridays 18-3-29, 14-3-32 and 6-3-33. The six Fridays in question are mentioned in columns E of Table 3 and Table 4.
The first of the three dates coming to the fore in the previous paragraph seems too early to be able to be the date of Jesus’ dying day since it may be considered as certain that Jesus was baptized not earlier than in January of the year 27 and manifested himself thereafter during more than a year. The third of those three dates seems to be a more probable possible date of Jesus’ dying day than the second, because the evident fact that at the decisive moment Pontius Pilatus thought that he could not permit himself to defy the Jewish authorities in Jerusalem seems to indicate his diminished self assurance due to the diminished support from Rome through the fact that his patron Lucius Sejanus had fallen into disgrace with the emperor Tiberius. Lucius Sejanus fell into disgrace with the emperor Tiberius in the year 31. That implies that 3-4-33 has the greatest chance to be the right date of Jesus’ dying day. It is the thirteenth century English monk and scholar Roger Bacon who was the first who substantiated that 3-4-33 is the most likely date for Jesus’ crucifixion.
We conclude this section with the remark that there exists a difference the size of average about two days between the dates in column C of Table 2 and the corresponding dates in column D of Table 3. That difference could be explained by assuming that the fourth century Alexandrian computists constructing the sequence of dates of the (classical) Alexandrian Paschal full moon chose the first day of their month Nisan just two days closer to the Newmoon of their month Nisan (as a matter of fact they defined it as the Alexandrian ‘from sunset to sunset day’ of the Newmoon in question) than their third century predecessors had done when they constructed the sequence of dates of the proto Alexandrian Paschal full moon (see also Section 8).
It is interesting to relate the three 19-year periodic sequences of dates of Paschal full moon mentioned in Section 6 to each other. Their dates fall between 20 March and 21 April, and each of their following dates can be obtained by advancing its immediate predecessor either 10 or 11 or 12 days modulo 30 days, in each of the three cases the total number of advanced days calculated on 19 successive advances always being 210 (e.g. 4 × 10 + 10 × 11 + 5 × 12 = 210 days). Among such 19-year periodic sequences of dates particularly the ones in which each following date can be obtained by advancing its immediate predecessor 11 or, once every 19 years, 12 days modulo 30 days (i.c. 18 × 11 + 1 × 12 = 210 days) are highly interesting, because they reflect in the most direct and realistic way the fact that time intervals of 19 years contain on average nearly as many days as time intervals of 235 synodic months (taking the years to consist of 365 ¼ days and synodic months of 29.53059 days, we get 19 × 365 ¼ and 235 × 29.53059 days respectively, in both cases just about 6940 days). The astronomical fact in question was known as early as in the fifth century before the beginning of our era in Mesopotamia and in Greece, among others to the Athenian astronomer Meton, hence such particular sequences of dates as well as their particular structure are called Metonic. Summarizing, it may be stated that a Metonic sequence is understood to be a sequence of dates between 20 March and 21 April of consecutive Julian calendar years which has a Metonic structure, i.e. a period of 19 years and the property that each of its following dates can be obtained by advancing its immediate predecessor 11 or, once every 19 years, 12 days modulo 30 days.
It is the Metonic structure of the famous fourth century sequence of dates of the (classical) Alexandrian Paschal full moon that would turn out to be the key to the solution of the great problem of the calculation of the date of Easter Sunday. Contrary to the sequence of dates of the Anatolian Paschal full moon, the until recently unknown third century predecessor of the sequence of dates of the (classical) Alexandrian Paschal full moon, the sequence of dates of the proto Alexandrian Paschal full moon, must also have been a Metonic sequence.
Metonic sequences can be distinguished into two types: the ones of the first type, characterized by 11 ordinary advances of 11 days, 1 saltus advance of 12 days and 7 ordinary regressions of 19 days, and the ones of the second type, characterized by 12 ordinary advances of 11 days, 6 ordinary regressions of 19 days and 1 saltus regression of 18 days. For example, it is easy to verify that the 19-year periodic sequence of dates defined by column B of Table 5 as well as the one defined by column E of this table is a Metonic sequence of the first type. We note that in column B the immediate successor of 1 April is 20 April, in column E it is 21 March.
Thanks to the fact that the initial year of “De ratione paschali” is known (see Section 6), we can relate the sequence of dates of the Anatolian Paschal day and the one of the Anatolian Paschal full moon to the proto Alexandrian and the classical Alexandrian cycle. In Columns B, C, D and E of Table 5 (in which all years are Julian calendar years and all dates Julian calendar dates) we see not only the restrictions of all these four 19-year periodic sequences of dates to the time interval consisting of the time between the years 270 and 290, but also the four accompanying sequences of lunar phase numbers. Although the year 285, because it was the first year of consulship of the emperor Diocletian, was considered to be the initial year of the classical Alexandrian cycle, this sequence of dates was in fact not yet defined in the third century. It is easy to establish, by comparing column B with column C, that the proto Alexandrian cycle not only differs (one day) in no more than (its latest) 4 out of 19 dates with the sequence of dates of the Anatolian Paschal full moon but is also the best Metonically structured approximation to it. With this our reconstruction of the Metonic sequence of dates of the proto Alexandrian Paschal full moon has been completed. We conclude that the sequence of dates of the Anatolian Paschal full moon can be considered to be the link between the proto-Alexandrian cycle and the sequence of Paschal dates of “De ratione paschali”, which underlines the relevance of all these three 19-year periodic sequences of dates. There is every appearance that the Anatolian Paschal cycle was developed from the sequence of dates of the proto Alexandrian Paschal full moon via the sequence of dates of the Anatolian Paschal full moon.
Thanks to the fact that the initial year of “De ratione paschali” is known, we can establish (see columns B and E of Table 5) that there is a remarkably simple difference of 2 days (mostly) or 3 days between the proto-Alexandrian and the classical Alexandrian cycle. This can be qualitatively explained by realising that the replacement of the Metonic sequence of dates of Paschal full moon around the third turn of century in Alexandria in use with the classical Alexandrian cycle must have been not a question of in one way or another adapting the sequence of dates of the Anatolian Paschal full moon but of a completely new definition of her Metonic sequence of dates of Paschal full moon, actually by advancing her date of the March equinox by 1 day and defining the first day of her new month Nisan as the local Alexandria ‘from sunset to sunset’ day of its new moon instead of such a thing as the local Alexandria ‘from sunset to sunset’ day beginning with the moment of the second sunset in Alexandria after its new moon. This qualitative account of the simple difference in question can be supplemented with a quantitative one by performing a complete reconstruction of the classical Alexandrian cycle. Somewhere in the first quarter of the fourth century the church of Alexandria replaced her Metonic sequence of dates of Paschal full moon being in use around the third turn of century (possibly the proto Alexandrian cycle or else perhaps the Metonic sequence of dates of Paschal full moon of Anatolius’ lost Paschal table) with the classical Alexandrian cycle by redefining her dates of Paschal full moon, namely by advancing her date of the March equinox by 1 day and defining the first day of her month Nisan as the ‘from sunset to sunset’ dayof the lunisolar conjunction in question.
The fact that the year 271 is the initial year of “De ratione paschali”, has some more obvious consequences, among which that the Metonic sequence of dates of Paschal full moon which according to Eduard Schwartz as well as the one which according to Alden Mosshammer can be considered to be Anatolius’ Paschal cycle, contrary to our proto Alexandrian cycle, cannot possibly have underlain the Anatolian Paschal cycle (see Section 5).
Thanks to the fact that the initial year of “De ratione paschali” is known, we can also establish in which years the Anatolian Paschal day was a Sunday and which were the dates of the Anatolian Paschal Sunday between (e.g.) the years 260 and 290. This can be seen in Table 6 (in which all years are Julian calendar years and all dates Julian calendar dates). In this table Column B contains the sequence of dates of the proto Alexandrian Paschal full moon and Column C the one of the Anatolian Paschal day, and Column D shows dates of the Anatolian Paschal Sunday and Column E dates of the proto Alexandrian Paschal Sunday. We establish that only in the years 264 up to and including 271 the Anatolian Paschal day was a Sunday, and that just in the seventh decade of the third century it happened a lot that the date of the proto Alexandrian Paschal Sunday and the date of the Anatolian Paschal Sunday coincided.
Around the third turn of century (just like in the first three centuries of our era) the (actual) Fullmoon (see Section 5) of Nisan fell on average around the midnight point in time of the fourteenth day of Nisan (see Section 6), and in consequence the date of the fourteenth day of Nisan on average half a day after the date of its Fullmoon.
Somewhere in the beginning of the fourth century the church of Alexandria definitely opted for the classical Alexandrian cycle. In that time the date of the proto Alexandrian Paschal full moon fell on average about 0.8 days after the date of its Fullmoon, on the other hand the date of the (classical) Alexandrian Paschal full moon on average about 1.4 days before the date of its Fullmoon. The proto Alexandrian and the classical Alexandrian cycle have the same (Metonic) structure. The former sequence of dates functioned less than half a century, the other until the year 1582. The structure of the classical Alexandrian cycle was with regard to the rhythmicity of lunar phases so realistic that only after three centuries the average distance (i.e. the average absolute value of the difference) between its dates and the corresponding dates of Fullmoon had been decreased by a day. Only around the middle of the eighth century this average distance was minimal. Only against the end of the twelfth century it reached its initial value (1.4 days) once again; up to then the Alexandrian Paschal full moons had always more or less the appearance of a pure full moon (i.e. about Fullmoon). By nature a midnight pure full moon is always preceded by a waxing full moon (i.e. a still waxing seemingly full moon) one night earlier and followed by a waning full moon (i.e. an already waning seemingly full moon) one night later (see Figure 4).
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 is 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 3), 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 was given to the millennium question. In most of those websites one declared oneself, like in this website “Millennium”, in favour of the proposition that the year 2001 is the first year of the third millennium and related this rightly to the fact that in our era we have no year zero. But, and this is the original reason for being of this website, on this website one can find in addition the observation that that fact is not in the least a mistake of Dionysius Exiguus (see Section 2) or Beda Venerabilis (see Section 5) but purely and solely a condition the Christian era (see Section 5) must satisfy in order to preserve her bilateral symmetry (see Section 6). There is no year zero in our era simply because from the very outset it contained no year zero and also never any year zero was added to it because through the centuries preservation of its symmetry with respect to its moment zero, as in our second time line (see Figure 2), always had a higher priority. Between the first century before and the first century after the beginning of our era there is no place for a zeroth century, and, for the same reason, no place for a year zero.
Jan Zuidhoek (see Figure 5), the author of this sextilingual website “Millennium”, 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 (Dutch language) 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. The aim of this website is to make a scientifically solid contribution to chronology. That applies also for his contribution to the third international conference in Galway on the history of computus (see Section 6), in the year 2010, where he presented his treatise on the initial year of “De ratione paschali” (see Section 6). In this pioneering treatise, which will appear in print in July 2014, also both historically important Metonic sequences (see Section 8), the proto Alexandrian cycle (see Section 6) and the classical Alexandrian cycle (idem), are reconstructed.