Talk:Year zero

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Older topics in Archive I:

1.	Calendar making	5.	Year link	9.	Gregorian before 1582 ?	13.	1 BC/BCE and 1 AD/CE
2.	Organizing this article.	6.	Millenium-end Confusion	10.	Bede changes	14.	Countries that use year zero
3.	Interwikis	7.	Happy birthday Jesus!	11.	Millenium-end Confusion 2	15.	'Mathematically skilled'
4.	Move page?	8.	German Wiki	12.	Zero and First	16.	English of the intro

Contents 1 Year zero and ordinal numbers 2 Christian Era started on December 25 3 Ian Cairns edits 4 Third millenium 5 An interesting question 6 Bad grammar? 7 Third Milennium once more 8 Giandomenico Cassini, Dionysius Exiguus, and the year zero 9 Year Zero and Julian / Gregorian Calendar 10 Intention of the article 11 Beda Venerabilis 12 Dionysius Exiguus 13 Roger Bacon / Christopher Clavius 14 Dionysius Petavius 15 Common sense? Historical fact! 16 On Counting

[edit] Year zero and ordinal numbers

In a series of cardinal numbers used for numbering objects (counting) the number zero is reserved for an object that is not there.
A series of years consists of countable objects (years), with an object always present in any place of the series. We cannot make a series of years with an empty place for one year that has not been there. Example:
...year minus two, year minus one, year one, year two ... (correct)
...year minus two, year minus one, year zero (no year!) year one, year two ... (incorrect)

That is why the number zero is meaningless when used in the time scale. The point zero, however is the infinitesimal period of time between year minus one and year one, and is therefore a correct term.

Likewise, if you measure a height of a house, you start from the ground (zero meters, no length at all) and then you count the first meter, second meter, and so on, not zero meter as first above ground, first meter as the second..

Another analogy: I give you four coins: the zeroth (none), first, second and third. Are you satisfied?

Chlodius

Special:Contibutions/Frederick A COMMENT BY A MEMBER

Hello, the gentlemen claiming that there could not have been a year 0 is perfectly right.

There is a problem with many people who use English and the Romance languages, because they fail to understand that the calendar is a system using ordinal numbers (year 1 AD means the 1st year, 9/11/2001 means the eleventh day of the ninth month of the 2001st year).

There is no "zeroth" day, month, year, century or millennium, and whoever does not recognize this has a serious intellectual problem. Will there ever be a 0/0 attack by Al Qaeda? Did anything happen in the "year zero" of the World War II? Was there a World War Zero?

Now, why the astronomers use the number zero to indicate the year 1 BC: either to make it easier for themselves to calculate the leap years pre-AD, or there is something wrong with them intellectually speaking.

Try to work this one out: how many years does the period between the year 5 BC and the year 5 AD comprise? Please count the whole years from the beginning of the 5 BC through the end of the 5 AD.

The answer is 10, and even my niece (aged 7) worked it out just fine.

Your last chance is to count the segments between the cardinal numbers from the point -5 to the point 5. There are 10 such segments, each one representing one full year. The point -5 represents the beginning of the year 5 BC, and the point 5 the end of the year 5 AD, i. e. the point in time when the five full years of the Common Era were completed.

If you do not understand this, than the Gods of algebra will be very angry with you.

Frederick

Even though your argument is sound, a year zero is included in the sequence of years by astronomers, so they don't think it is meaningless. — Joe Kress 18:50, 14 November 2005 (UTC)

It would be interesting to get here an astronomer's explanation why they use this convention. Maybe they have good reasons, but it is not consistent with the normal use of ordinal numbers. Chlodius

The argument is only as sound as its premise: "In a series of cardinal numbers used for numbering objects (counting) the number zero is reserved for an object that is not there." Chlodius has yet to justify this. It makes perfect sense to use the number zero as any other number. As Joe Kress points out, astronomers don't reserve zero for an object that is not there. Why should they? The analogies to numbers of coins and metres of height are misleading. In these cases zero signifies nothing (not that it doesn't signify something but that that which it signifies is nothing). However years appear in a continuum (at least for this purpose) their numbers are labels given to them. The label zero is just as valid as any other. Why use this convention? It makes so much mathematical sense. Jimp 05:50, 3 March 2006 (UTC)

The point is: Astronomers don't use ordinal numbers for counting years, but well cardinal numbers. They do so because the years – in the opposite to the cyclical months and its days – must be counted in a continuous manner. If not, it's not a chronology, but a chronicle.

"Zeroth" or "nilth" don't exist in ordinal numbering. Even if, as a "quoted sophistry", the use of these terms is not always completly senseless.

Ordinal numbering of years would only be consistent if we retain a "very first" year – e.g. since Big Bang or since the "beginning of History" – in condition that both, we are able to determinate it and we never consider any year "before". This is neither realistic nor requested.

In conclusion:
Any consistent chronology counts years with cardinal numbers, of course with a year zero, just like astronomers do. (However, historians can't recognise 1 BC = 0 CE.)

Paul Martin 09:54, 3 March 2006 (UTC)

As was pointed out above, the usual BC/AD historicaI timeline consists of two sets of counting numbers, one going forward and one backward. You point out that the demarcation between the two is an infinitesimal point in time. However, you label the years going backward as negative years rather than BC years. But negative 'counting' years can be used to illustrate the problem that astronomers have with the historical timeline. Astronomers must be able to calculate the amount of time that has elapsed between any two events, even if they occur on opposite sides of the epoch. The usual way to determine the length of such a period is to subtract the earlier year from the later year. Thus 2000 - 1999 = 1 year between identical dates/times in the two years. But the consecutive years on either side of an infinitesimal epoch would mathematically yield 1 - (-1) = 2, which is definitely wrong. Astronomers solved this problem by adding a year zero between the two counts of years. 1 - (-1) still yields 2, but it is now correct. 1 - 0 = 1 would also be correct.

For the annual identical dates/times astronomers typically use the instant at the beginning of the year, which was noon 1 January before 1925 when the astronomical day began at noon. If there were no year zero or it was an infinitesimal point in time, then the absurd difference of 1 - 0 = 0 results. Note that time always flows from the past to the future, thus for all years before the epoch, whether thay are identified as negative years or as BC years, the beginning of the year is 1 January. Of course, the year assigned to any event before the epoch in this astronomical timeline will differ from that assigned to it in the historical timeline by one. This prevents any historian from adopting it—if he did so, his dates would disagree with those of all other historians.

Thus the astronomical timeline is the classic number line, with positive and negative numbers on either side of zero. Subtraction can be correctly performed across the epoch on such a number line only if zero is present. However, the first astronomers to use a year zero continued to 'count' the years on either side of their zero year with BC and AD years, not negative and positive years. So they added the years containing the two events (ignoring their era labels) if they were on opposite sides of the epoch (subtracted if on the same side). Again, this will produce the wrong timespan if the timeline does not include a year zero. This was one of the reasons given by Jacques Cassini, a famous French astronomer, for including a year zero in the timeline which formed the backbone of the astronomical tables he published in 1740, whose purpose was to enable the calculation of the positions of the Sun, Moon, and planets on the celestial sphere for over two thousand years (beginning 300 BC). His other reason was that with a year zero, all years, whether before or after the epoch, that were evenly divisable by 4 would be a leap year.

— Joe Kress 05:48, 18 November 2005 (UTC)

The confusion between ordinal and cardinal numbers occurs in other areas as well, such as floor numberings and exit numbers on highways. I have inserted a brief mathematical explanation into the article, avoiding all use of mathematical symbols. I hope it makes everything clear. — Aetheling 21:54, 27 August 2006 (UTC)

There seems to be confusion of the premise- the idea of year zero is that, by common usage, saying it is January of year one would mean that a year has passed- in a similar fashion, the day starts at 12:00 AM (or 0:00 in 24-hour time), not 1:00. The year zero would cover the time from the zero point (on the basis of the Gregorian calendar, the birth of Christ) and exactly one year after that; the date would be read as "Zero years and two months", for example. It was the use of ordinal years that made people deviate from the typical mathematical standard. 76.211.3.86 01:47, 12 November 2006 (UTC)

The hour starting at 0:00 is the first hour. So, if you were to number the hours of the day, you would undoubtedly number them 1 to 12. Not 0 to 11.

As for the numbering of years, you could of course argue that it would make sense to speak of fifteenth January of the year zero. But then, on the other hand, January not yet being complete, you would have to write 15-00-00. Which, I take, you do not.

Or you can look at it this way: Take a basket of apples and number them. Will you start with 0? Or look at the street you live. Is the first house number 0? It is not, as having it called house 0 would mean that there was no house. No house, no apple, no year.Unoffensive text or character 15:10, 3 January 2007 (UTC)

I should like to continue the argument of User:76.211.3.86.

I am now 66 years old (cardinal number 66), which means that I am in my 67th year (ordinal number 67). When I was 1 year old, I was in my 2nd year, and before that I was 0 years old in my first year. If you ask: "How old is that baby?" The answer will be something like "three months", but the meaning of this answer is "0 years + 3 months = 0,25 years". The same with time on my watch: "What time do we have?" "Well, 3 : 30 a.m.", which means 3 h 30m (= 3,5 h). But, starting your count with 00:00 midnight this is the 4th hour (ordinal number).

The Romans, when talking about their age, expressed themselves the same way as we do. Here is Cicero (Cato maior de senectute § 14): annos septuaginta natos tot enim vixit Ennius. which means that Ennius reached the age of 70 years, that is to say he died in his 71st year. So the Romans only counted "full years", just like we do, and though we are not used to talk about the age of 0 years, we still presuppose it. And this usage has nothing to do with the knowledge of a mathematical system to handle the number zero by a decimal system.

In short: thinking about the years of Our Lord in analogy to the years of our life or the hours on the watch, there is simply no way to avoid "year zero".

The consequence is this: That it makes very much sense to maintain that Dionysius Exiguus (from whom through Beda Venerabilis we inherited "our" years), presupposed a year zero before his year 1. In fact it is just this what he did when treating mathematically about the matter (in his argumentum XII). Venance Grumel (La chronologie, Paris 1958) has shown that Early Christian moon tables invariably presuppose knowledge of the year before the year no. 1 of the table, and that the tables rarely are intelligible if you do not take this into account.

The point with Beda Venerabilis is that he aimed at something totally new, namely at numbering the years ante Christum in the same system as he was used to number the years post Christum. Not knowing a mathematical device to denote the number zero, nor Negative numbers, he switched to 1 B.C., 2 B.C. etc. and thus established a very strong tradition, which, alas, is mathematically stupid. For Dionysius Exiguus on the other hand, the year zero was something like the absolute starting year of (Christian) time, and the years were without exception counted in one direction only.

--Ulrich Voigt, www.likanas.de

[edit] Christian Era started on December 25

[This topic, originally named "question" by DJ Clayworth is a missed talk with FredrickS who didn't find this chapter. I shifted here his older statements from David's talk page.]
-- Paul Martin 08:57, 4 February 2006 (UTC)

Will whoever is adding screeds of stuff with doubtful history, such as asserting that Jesus was born on December 25th 1BC, please explain where you references are from? Without them all your edits will simply be reverted. DJ Clayworth 03:13, 30 January 2006 (UTC)

Hi David,

I noticed you are erasing the facts about the second version on which date the beginning of the third Millennium starts. The facts that I am using for a different possibility is from a highly respected source: the Roman Catholic Church. For them, the Christian era started with the birth of Christ (which is why it is called the Christian Era) on December 25. I don't think they care about what name that year is known by. The Church opened the Holy Millennium Year on December 25, 1999 and closed it on the beginning of the 2001st year on December 25, 2000.

As you can see there are very good reasons to include this second view in the Wikipedia page Year_Zero, heading Third Millennium, and the source is, well, immaculate. A year containing the actual event is a better representation for the beginning than the following year that does not contain the event; even when that is just seven days later. For me, the third Millennium started in 2000, but I want Wikipedia to include all sides because otherwise it becomes a political platform and ceases to be an encyclopedia. Please accept contributions that are factual, though possibly not in concordance with other views.

I do have to extent an apology here to you as well. I edited the page one more time, and I used a copy/paste method from an email I sent myself, and that changed your 1 -> 2 segment under that same heading. I am looking into fixing it, but may not find it before you notice it.

Greetings

FredrickS 19:58, 1 February 2006

Let's talk about this at Talk:Year zero. DJ Clayworth 20:04, 1 February 2006 (UTC)

Hi. Thanks for your explanation of the 'December 25th' additions. However for them to be valid contributions to this article you need to make some changes. Firstly, and most importantly, we need some verification. That means providing some sources - academic papers, books, or reputable web sites, that confirm your statements.

Secondly once you have provided verification then you also need to adjust the article to show that it is only the RC church that counts like this. The impression we give at the moment is that all dates are taken from Dec25th (which is clearly wrong). Please ask if you don't understand what I mean here. DJ Clayworth 20:02, 1 February 2006 (UTC)

Ah, I see a few confusions here. Just because the Catholic church declared a special year which lasted from December 25th 1999 to December 25th 2000 does not mean that they count years in general from that date. It's much the same as there may be a 'school year' which runs from September to June, or a financial year for a company. It doesn't bear on actual year numbering. For one thing pretty much nobody in the Roman Catholic church believes that Dec 25th was actually Jesus' birth date. However come back with some references and let's see what happens. DJ Clayworth 20:10, 1 February 2006 (UTC)

I looked you up here, but did not see anything. FredrickS  21:52, 2 February 2006 (UTC)

Hi David,

I made some changes to Year_Zero, so a source is now included. I try to write as neutral as possible, and as a non-religious person, I find it kind of funny to use a Catholic source to show a differing view. I cannot state that the Catholic Church is the only one with a different point of view on when the Millennium started, so I state that their view differs from that of historians, that they have their own clockwork so to speak. Not to aggravate you, because I have no problem with my views being different from what is generally accepted and want to respect that view, but for me the Millennium did start January 1, 2000, since it contains the 2000th culmination of the event the Christian Era is named after, so the following day at the end of that year (December 25, 2000) is the first day of the 2001st year.

Greetings

FredrickS  21:52, 2 February 2006 (UTC)

To the anonymous person who keeps adding stuff about a 'catholic year'. I read the reference you added - I could find nothing in there to back up your assertions. If you continue to add this meterial without providing references it will be treated as vandalism. DJ Clayworth 23:10, 3 February 2006 (UTC)

The link that I submitted shows that the Catholic Church opened the Holy year on December 24, 1999; a year and eight days before historians have the third Millennium start. I am not arguing about a year zero, hence I did (later) not write information in that segment, but I disagree that no other view on the third Millennium is available (though not from historians' point of view). I claim to have a valid link, and found more. All I ask is for the differing view to be mentioned under the heading 'Third Millennium' and for the deletion of the statement that only one vision on this otherwise peculiar phenomenon is possible. The Holy Christian year started with the opening of the door on December 24, 1999. Other links with the same information is [1], while on the website [2] the pope "officially announced the celebration of the Jubilee for the year 2000 with his apostolic letter "Tertio Millenio adveniente" for that day in 1999 so it would be a fact exactly one year later. The commencement date starts with "the Holy Doors at St. Peter's [...] opened during midnight mass on December 24, 1999." And: "I therefore decree that the Great Jubilee of the Year 2000 will begin on Christmas Eve 1999, with the opening of the holy door in Saint Peter's Basilica in the Vatican,...." A peculiar fact is that these doors closed after New Years on Epiphany - January 6, 2001 showing the peculiar timing for the Christian church. The Roman Catholic Church is known for its inclusion, and several rites of opening doors took place, such as "the holy door in St. John Lateran [which] was opened by the pope the following day [December 25], and that of St. Mary Major on January 1, 2000" as found on [3] which also mentions: "The fourth holy door, that of St. Paul outside the Walls, was not opened until January 18, 2000, to launch the week of prayer for Christian Unity." I suspect that all this opening and closing of doors is the result of the broohaha about the change of the Century in 1900 when a similar brawl of confusion took place. Last link: a report by CNN [4] appears to indicate that the pope rang in the new Millennium in 1999, which is something I do not agree with: he rang in the last year of the old Millennium on December 25, 1999.

Let me state it clear again here: I have no dispute with the Millennium seen as starting on Jan 1, 2001, yet I find information that show differing views. It is like whether the American pledge should include "Under one god" or not, but while that phrase is currently standard part of it, it is notable and of interest to describe how this was a later addition (I believe this happened in 1954), it was not part of the original, thus showing the existence of different points of view in this matter. There are two (actually more) versions - one is the original and the other is the adjusted version. It is convention that won over originality. It is also very similar to how Wikipedia itself functions: even when only the latest version is visible, all pages, all additions (and all reversals) remain stored. To mention Wikipedia correctly without this phenomenon of stored previous versions does injustice to Wikipedia, and should be considered as incomplete. And that is how I view the page on the Year_Zero, in particular under the heading Third Millennium - as incomplete. Convention makes all of us accept or reject the one standard in use, but that does not mean there are no other versions worth mentioning in this wonderful tool called Wikipedia. Some time ago, the Common Era and the Christian Era were not the same, but are now regarded as one (or at least no more fuss is made about it). CE is therefore an accepted convention now indicating both Christian Era and Common Era. Yet as far as I know, BC and BCE are still not the same.

Also, I have no interest in questioning the date of Jesus' birth — I don't care what day that was in this respect — but had he been born on January 10, I have not a single doubt that the new year would have started nine days prior; this in stark contrast to the seven days later as is now the case. The fact that a sixth century abbot calculating the birth of Christ did not use the year zero, does not change the outcome, only the point on how to view the matter. Later, historians started to use this calculation, in the process of using it creating a convention that that abbot did not have in mind. Admittingly, I am second guessing here, but according to what I have learned about abbots in those days, everything before Christ's birth was 'unimportant because it was before Christ and therefore it was before there was the light." I truly don't think that the abbot said at any point in his life: "Oh, now I can see that Plato lived from 427 BC to 347 BC." Historians did that, and they created the convention, and with it a lot of trouble to straighten it out over the centuries because not the block of a year is the essence, but the day (except for historians).

The calendar is not a seamless affair, the Christian Era starts with that birthday; the day is therefore the counting measure at least for the Catholic Church and directly/indirectly (depending on your point of view) the origin for our CE calendar. Thinking that the point I am making is not a personal point of view, I consider the history and differing views a remark worth mentioning in Wikipedia: about how people view the systems they use, and change their argumentation to what seems a good fit - in the process creating and changing convention. We are left with something not perfect, so lets talk about that in Third Millennium.

I do personally consider the arguments for 2000 as more valid since that is how we view time normally (so my choice is also based on convention, but a different one than historians use for the Millennium). An example already mentioned is the decades of my life and when they start. My birthday is in Nov 1960, and the decades would start normally on my birthday, but if I had to appoint the years of my decades they would be 1970, 1980, 1990, etc. not 1971, 1981, 1991 etc. since my year of birth is 1960, and I truly cannot appoint any other year. It is not the context of the framework that rules, but the actual length of the contents, which is ten full years to the date. The starting year for our calendar is then 1 BCE, and while this seems incorrect, it is only incorrect because not the year, but only the date is exactly correct: December 25, 1 BCE. For the Christian Era it is day One.

Even when you not agree with me, I consider the arm-wrestling itself on this topic, as found throughout history since the day of conception of the Christian calendar, worth mentioning in Wikipedia, giving more clarity on what we humans argue about, and how we are often ourselves (or others like us) the reason why we argue.

With Regards,

FredrickS 21:54, 4 February 2006 (UTC)

This is way too complicated. You are answering questions that I have not asked. Let me try to put this very simply. Your edits stated that the Catholic church numbered years from December 25th to December 25th - i.e. that the year increased in number on December 25th. I simply find no actual evidence that this is true..

The reference you cite does not back up what you say. The Catholic church did indeed declare a 'special year' from Dec 25th 1999 to Dec 25th 2000. That was just a period of twelve months, whose beginning and end did not coincide with the beginning and end of a regular year. It does not mean (and the reference does not say) that they consider the new millenium started at either the beginning or the end of that period of time. It actually says that during this period 'the old millenium will end, and a new one being' - so they consider the change of millenium to happen sometime during that period. A 'special year' does not have to coincide with a numbered year. Once upon a time the start of the year was on different days, but right now the Catholic church numbers years the same as everyone else. DJ Clayworth 15:03, 6 February 2006 (UTC)

Let's make it simple then: the information about opening the door to the third Millennium on December 25, 1999 by the pope is a peculair fact that is worth mentioning under the heading of Third Millennium in the light of historians' view that 1/1/2001 was the Millennium mark. No matter how you twist it, that is more than the usual 365 days in a year. We don't have to talk about the whole complicated history, just showing that counting is NOT a black and white issue would already improve the wiki page. I don't want to pick your words apart, but your words do confirm what I like to have included on the wiki page heading third Millennium. I quote you: "The Catholic church did indeed declare a 'special year' from Dec 25th 1999 to Dec 25th 2000." and "they consider the change of millenium to happen sometime during that period." DJ Clayworth 15:03, 6 February 2006 (UTC)

I am considering asking outside help since I am afraid I will start to escalate. FredrickS

Please do ask for outside assistance. I have no intention of escalating anything. It is possible that you are completely right, but without any independent evidence it is impossible to say that. If you can supply evidence to back up what you say then I will be entirely happy. DJ Clayworth 19:31, 7 February 2006 (UTC)

• In Roman Church, since 1450, Jubilees Years or Holy Years are celebrated every twenty-five years. (Sometimes there are additional Holy years the two last one 1933 and 1983.)
• For the "Great Jubilee" A.D. MM, "the Holy Doors at St. Peter's were opened during midnight mass on December 24, 1999 and the Jubilee ended on January 6, 2001." [cf. ref. 4]
• John-Paul II wrote in his spiritual testament (additions dated on 12-18. III 2000):
  "As the Jubilee Year progressed, day by day the 20th century closes behind us and the 21st century opens.
  According to the plans of Divine Providence I was allowed to live in the difficult century that is retreating into the past..."
  (The departed Bishop of Rome verbalised as philosopher, nowhere he gives a clear definition when exactly the New Millennium begins.
  That was his right. As a spiritual leader, he wasn't obliged to give a clear scientific definition.)

Not any source given by Fredrick allows to assert neither that "the clergy too would have the new Millennium start on January 1, 2000" nor that in Roman Church the third Millennium began on 2000, December 25. This latter date seems "logical" if – like it is usual – the date of "birth" of Jesus Christ is retained for the era. However the Incarnation date is on III–XXV. (Dionysius Exiguus gave only a year, not a date.) Like David rightly noted above "the Catholic church numbers years the same as everyone else" i.e. with J. Caesar's New Year's Day.

-- Paul Martin 05:31, 8 February 2006 (UTC)

PS. It stands free to you, Fredrick, to make new researches trying to find an ignored document stating explicitly and doubtless that – like you allege it – Roman Church retains another date in the calendar for the beginning of the third millennium than year two thousand one, first month, first day. Without this hypothetical document Rome is supposed to support right this date. Furthermore: If a suchlike document would really exist, it is highly probable that it would be well-known and famous. Finally: It is not to expect that Rome in future will ever publish a suchlike document – stating for example that definitively the third millennium began on 2000, Jan. 1 – because the case of Galilei was surely instructiv enough, to not tread in a gratuitous contradiction with sciences.

Thank for delivering a free passage to get outside help. I have asked for help; at the same time, I do not feel the need to find more evidence, since there is plenty here already. While your points are correct, the existence of that birthdate — not on Jan 1, but Dec 25 — stands, and while CE is commonly regarded as standing both for Common Era and Christian Era (and normally not disputed as being the same), December 25 is the beginning of the Christian Era since December 27, 1 BCE (the year one Before Common Era) is not BC (Before Christ). There is a discrepancy, and it is note-worthy enough to be mentioned in this Wikipedia page under the heading Millennium. The Catholic church indeed has burned itself badly on Galileo, and it is therefore no surprise that it does not want to lose its face in any major way. It will therefore not let trivial issues like when the third Millennium started be all-consuming, but found a middle of the road to by-pass the issue. To counter your arguments at the basis: lack of information does not prove something doesn't exist. So if you don't want this information included I want evidence from you that the Catholic Church states unequivocally that the Millennium starts on January first. I charge that you cannot provide that information. The Catholic Church says what I like to get added onto this page (opening Millennium celebrations on December 24, 1999 — a date of December 25 would be fine with me too). The catholic Church does not black-and-white deny the Millennium is not on Dec 25, 2000, therefore creating a hole in the story on that side. Again, the Wikipedia threshold is not about the fact that one fact is true and another is not true in that same light; Wikipedia's threshold is whether something is note-worthy under a certain heading, and can be sustained by outside sources. I provide that information. To counter your arguments therefore at a higher level: that what the Catholic Church ís delivering speaks loud and clear. Their focus is on December 25 (or Dec 24), and that ís what they celebrate. I think they view the Millennium issue correctly, but that is my opinion; I do have by my side the argument that Millennia can be counted both in years and in exact dates; which in this case delivers two different outcomes. Again, I have no problems with other versions, conventional or not as long as there is an interesting angle delivered by official organizations, like in this case, the Catholic Church.

The disappointment I am experiencing is that the gate-keepers of this page are not willing to turn this issue on Wikipedia into the colored issue it really is, but desire a black and white single answer that fits convention. What I am looking for is inclusion of information, not dispute, and if we need to mince words to make it fit so we are both happy? No problem.

FredrickS 01:36, 11 February 2006 (UTC)

Frederick, you have misunderstood something very important here. If you make the statement that the Catholic church considers the millenium to begin on December 25th it is up to you to find evidence to back it up. Otherwise someone might come and say that they millenium began on July 19th, or May 9th, or any other day. It would be very hard for anyone, including you, to come up with evidence to prove that it was not the case.

Now I read very carefully the document you made reference to, and I found nothing in it to say that the Roman Catholics believe that the millenium changover occurred on December 25th. In fact when I read it I found it said that "during the year [from Dec 25th 1999 to Dec 25th 2000] the old millenium will come to an end and the new one will start." That can only be true if the actual new millenium happens sometime during that year - i.e. not at its beginning and not at its end. Now it is possible that I missed something, so if I did please point it out to me. Remember I am not saying you are wrong necessarily, just that I have found no evidence to support what you say.DJ Clayworth 00:11, 13 February 2006 (UTC)

In one point I don't agree with you David: "during the year [from Dec 25th 1999 to Jan 6th 2001]..." because the ecclesiastical Holy Years traditionally doen't last exactly twelve months but almost 54 weeks. (The two main reasons for this should be both to give more opportunities to the pilgrims and the great importance of the Feast of Epiphany.) Otherwise just like you "I found nothing in it to say that the Roman Catholics believe that the millenium changover occurred on December 25th."

Yes, Frederick, in science, not seldom it's "black" or "white", one "single answer", true or false. The date of 2000, January 1st for the beginning of the New Millennium was always false, is presently false and will be false forevermore; just like the geocentric model of the universe. Or do you think we should tolerate at Wikipedia an assertion like "there are also good reasons to defend Ptolemy's ideas". Just for having an encyclopaedia less "black and white", more "colorated"!

For the Dec 25th date I'm less categorical. However there are several problems. Question: Is it entirely assured that "the traditionally-reckoned date of the birth of Jesus of Nazareth is indeed the date I-XII-XXV BC? I remember me to have read more than one time in different publications also the date AD I-XII-XXV. In your CNN source [6] above – dated on 1999, December 24 – I read: "Meanwhile, thousands of people turned out to celebrate 2000 years of Christianity -- the millennium Christmas -- at midnight Mass in Bethlehem." 2000 years before AD MCM.XCIX-XII-XXIV was II-XII-XXIV BC!  The date I-XII-XXV BC should be surely the most logical and there are many indices for presuming that's the retained date. However even there I know no mandatory, explicit statement. Liber de Paschate doesn't help for clarification. On the contrary Dionysius counts from Incarnation: Perhaps from I-III-XXV BC?

In addition: With many "if" and "perhaps", I'm not categorically opposed to see a short two or three line statement in the paragraph "Third millennium" saying for example s.th. like: "If the birth of Jesus is retained for the era, a third millennium would have begun on 2000, Dec 25, etc." In no case – with your present sources – you can assert that "the the Roman Church officially states that the New Millennium began on MM-XII-XXV." On the contrary, since "the Catholic church numbers years the same as everyone else" the third Millennium in the Gregorian Era, also for the Catholic church, should have begun one week later on Jan 1st.

If you want to apprehend this suggestion, I propose you to formulate here a discussion version of these lines, to insert – perhaps afterwards – below the astronomical numbering.

However, because personally I don't see the necessity to do so, please Frederick don't be mad at me, I'm not willing to defend your concern if David or others stay to be opposed.

-- Paul Martin 10:47, 13 February 2006 (UTC)

Thanks, Paul, I will try to make the wording as acceptable as possible. However, I feel there is one note left I think we too disagree on. Let me try to explain it using your reference to the geocentric model as a starting point. This geocentric model did not survive scrutiny since it was based on human ideas of just their surroundings, not on the actual physics of the solar system. You will find in me a great supporter of physics, and when in conflict with a man-made idea, I know which one to choose. But we are not talking physics vs. human construct when we discuss the Millennium, we are talking human construct vs. human idea here. If we had to look for anything physical in this conflict than one aspect only exists: the birth of jesus. There is no other physical information, other than man-made constructs of counting (actually two forms of counting: one back in time to — well not zero — the beginning of the calendar, and the other back in time continuously gaining numbers in the negative, and as such they got stitched together, no gap allowed).

I believe that the evidence for what this Wikipedia can and cannot contain should not be based on the requirements as they exist in physics — since physics is not involved — but as in encyclopedias; is it note-worthy about who we are. I think so. Where physics can root out the incorrect human ideas, one human idea placed on top of another human idea is not enough to say that top exists and bottom does not. Just the opening of the Millennium year on December 24, 1999 by the Catholic Church is note-worthy all by itself, since it delivers a view on the conflict the calendar poses because it is based on convention (as in this argument wins over that argument). I will look if I can find some information on the struggles surrounding this point of view as took place around 1900, which supposedly was a more difficult conflict, and that was won by the historians. I am wondering if the catholic Church is still licking its wounds. FredrickS 20:19, 17 February 2006 (UTC)

I'm afraid I still believe that none of this stuff has a place in this article. Not only do I think Frederick is misunderstanding what the Catholic Church says, but it is also irrelevant in an article about Year zero. The date of start of any millenium, even if it could be shown to be significant, would have no impact on the question of whether there was a year zero. DJ Clayworth 22:22, 17 February 2006 (UTC)

When you talk about the year zero only, I partially agree with what you say, but the second you say anything about Third Millennium, you talk about the consequences that creating a man-made calendar like this one has. So, once you mention Third Millennium, you open up a can of worms. If you remove Third Millennium from this article, my demands would most likely lose their grounds. FredrickS 20:59, 19 February 2006 (UTC)

• The Third Millennium section is necessary because some short thinking contemporaries argue: "With a year zero, the New year's day 2000 is the beginning of the third millennium." Far wrong!
• I agree with DJ Clayworth that you are largely "misunderstanding what the Catholic Church says" and you continue to confound Holy Year, Millennium Year and New Millennium.
• You talk about "man-made calendar" and "physics vs. human construct" etc. without understanding that the logic is just as well weightily than in other context the physical realities.
  -- Paul Martin 21:51, 19 February 2006 (UTC)

PS. I wish you, you can find outside assistance, with new, never heard arguments. However I doubt on.

It looks like we have ended this conversation, especially since you confirm my suspicion that you consider two man-made time-frames stitched together as amounting to something that needs to fulfill the requirements of physics. I apologize for stepping on toes, and I regret that my wording is (unintentionally) not always conventional, but we clearly disagree on what Wikipedia should deliver on this subject (subject being Year Zero including the Third Millennium). FredrickS 01:34, 20 February 2006 (UTC)

Paul Martin wrote:

The Third Millennium section is necessary because some short thinking contemporaries argue: "With a year zero, the New year's day 2000 is the beginning of the third millennium." Far wrong!

The article says:

Use of Astronomical year numbering cannot be used to support year 2000 as the first year of the 3rd millennium because the year zero (which corresponds to 1 BC) is still not considered part of the first millennium AD. Instead it is considered either part of the first millennium BC or not as part of any millennium. Thus the celebrations of the beginning of the New Millennium on 1 January 2000 are a celebration of the beginning of the millennium of "the 2000's", rather than the beginning of the third millennium of the Gregorian calendar.

Including year 0 in the first positive millennium (0 to 999) while excluding it from the first negative millennium (−1000 to −1) would be inconsistent. But consistency produces unusual results: either year 0 separates the first positive millennium (1 to 1000) from the first negative millennium (−1000 to −1) or it is included in both (−999 to 0 to 999). The consistent solution is that any year zero must be defined "out of centuries". A Year Zero is a Year Zero. It does not belong to any millennia. With regards to the decades like "the 1990s", the year zero, if recognised, is both the first year of the years plus zeros and the first year of the years minus 0s. However, the 200th decade ends, like the 20th century and the 2nd millennium: 2000, December 31 at midnight.

Can anybody give a source for that?

I know and understand that, because there is no year 0 in the normal (historians') way of counting, the third millennium starts on 1 Jan 2001. But I would tend to agree with these short thinking contemporaries that in calendars with a year 0, such as the astronomers' way or even ISO 8601, it would make a lot of sense to define 1 Jan. 0 the first day of the first millennium, and therefor 1 Jan. 2000 the first day of the third.

The consistency (symmetry) argument is not very convincing. If you go beyond the numerals of year numbering, the calendar is not symmetric itself. If you define 1 Jan 0 as day 0 (which is logical), you'll see that day -1 (31 Dec -1) belongs to year -1, but day 1 (2 Jan 0) not to year 1. [ The daynumber → year function would be , an asymetric function. The logical year → millennium function, according to short thinking contemporaries and myself, ]

So, I would like to see some evidence that any authority that consistently uses a year 0 (astronomers' or ISO 8601 or other), consistencly does not use the first day of year 0 as the first day of the first century/millennium (or century/millennium 0).

— Adhemar 18:17, 26 September 2006 (UTC)

If no-one answers this question convincingly in the coming days (perhaps weeks), I eventually will delete the paragraphs in question in the Third millennium section. — Adhemar 15:28, 29 September 2006 (UTC)

Avia reverted this deletion, and described it as "vandalism" in the history log. I reverted the revert: the paragraphs in question are deleted again. I do not mind putting the paragraphs back in if someboday can answers my question convincingly, preferably in the form of an authorative source. — Adhemar 09:57, 9 October 2006 (UTC)

---

Okay, guys, here it is. I created a Mock Page. You may notice that I took out most of the school teacher speak, making the text appear more neutral, without deleting any essential information. I added a line about the Christian Era consisting of two time frames, and I inserted text about the peculiar behavior of the Roman Catholic Church under the headrer Third Millennium. I feel I found a good compromise between stating what I felt was necessary, and leaving the text intact. FredrickS 03:28, 21 February 2006 (UTC)

The 'mock page' seems to be nearly identical to the current version with a couple of exceptions. The third paragraph of the 'Third Millenium' section is irrelevant to the subject of year zero and really should be somewhere else, just as it was when you added the same information to the current article. If it were not removed it would need to be cleaned up because it implies that the Catholic church somehow counts years differently from other organisations, which it doesn't. It should also be made clear that 25th December is a 'traditonal' birthdate of Jesus, i.e. nobody takes it as being factually accurate.

It looks as if this mock page is simply the current version with the things you want to add (which we have already talked about) added. Maybe you could point aout any other differences? DJ Clayworth 14:28, 21 February 2006 (UTC)

Thanks David for your dry comment to that so-called "mock page". -- Paul Martin 21:19, 21 February 2006 (UTC) (amused)

I maintain that it seems me possible to keep a very short mention respective to the 2000 years between I BC-XII-XXV and AD MM-XII-XXV, but surely not as the official beginnig of third millennium in Roman Church.
I give you reason that even then this "section is irrelevant to the subject of year zero and really should be somewhere else." Nor the other changes by Fredrick are actually helpful and surely will not survive alltoo long.

The deletion of the thorny issue of Third Millennium was made undone. I guess the issue is back on then. What I have done this time is corrected the 999 years example. In the text the dates were July 1, 500 BC and July 1, 500 AD. Per our conversation, the date should be January 1, and I weigh my respect for you based on whether you acknowledge that that is indeed the date from which we must deliver the Wikipedia reader information on the year zero, and that this information remains part and parcel of this wikipedia page (at least not erased by one of you). The example has been changed to start at January 1 in both cases, and show-cases where exactly the year zero is missing (the AD segment of the calendar), since the BC is the part that counts backwards and therefore does not have a zero year. | Mathematical information suggest that zero exists when stating one, two, three, four, five.

As far as I can see the July 1 example is just as valid, as the same example using January 1. What it states is just as true, in the same way that there is one year from July 1 2004 to July 1 2005. Also there is no need to say 'where' the year zero is missing. The two form a single system for year numbering. DJ Clayworth 18:30, 2 March 2006 (UTC)

Then I have lost my respect for you. The dates were chosen to cover up the idiosyncrasy of the calendar; it does not help that way to deliver clear understanding of what goes on. I do not mention anything about missing on the page itself; the example is loud and clear enough: it is a men-made calendar. FredrickS 18:38, 2 March 2006 (UTC)

Please explain why you think this. I see that the statement (999 years between these dates) is as true for 1 July as for 1 January. DJ Clayworth 18:40, 2 March 2006 (UTC)

OK, if I understand correctly you are concerned about saying "500 years BC and 499 years AD", while using July 1st as an example means you are not being exact about that. OK, I can buy that. The January 1 example is no less useful. DJ Clayworth 18:46, 2 March 2006 (UTC)

Fortunately, this is the best way to show what is happening in this calendar, and therefore it is serving the readers of this Wikipedia page best by using that example of the 999 years that pass between - what seems to be 1000 years - from 500 BC to 500 AD. The example must be started on January first, and not on any other day, to make the example truly become a tool of understanding. From January 1, 500 BC to January 1 of the year 1 AD, we will all count 500 years. From January 1, 500 AD counting backwards to that same date of January 1 of the year 1 AD, we will all count only 499 years. Where December 31 completes the year in our era, January first in the BC segment of the calendar is the day that completes the full year. As such there is no need for a year zero on that side of the calendar because there we count backwards, and the peculiarity of filling a year is therefore done on January first in the BC segment. In the AD segment of this calendar the filling of the year is completed only on December 31, showing the human hand in the design of this calendar for it leaves off the normal year zero that is otherwise counted to get to the completion of the first year on December 31. This latter conclusion does not need to be mentioned itself on this Wikipedia page, since that would amount to another war of words between me and others. My goal is to have readers of Wikipedia understand how the missing year zero came about, and where exactly this is occurring. We can all live with a men-made calendar, so there is no reason to argue about using January 1 (since this has been used as an argument against my previous edits). FredrickS 18:47, 2 March 2006 (UTC)

[edit] Ian Cairns edits

Hi Ian,
I'm not happy with your changes in the year zero article:

1. Self-evidence that in Gregorian calendar there is no year zero since it doesn’t exist before AD 1582, October 15.
   So, the first phrase in its current version is senseless.
2. Quotation of the Anno Domini article:
   This Christian era is currently dominant all around the world in both commercial and scientific use.
   Presently, it is the common, international standard, recognised by international institutions such as the United Nations and the Universal Postal Union.
   If this is the case, your objection "by using "our" you are making assumptions about the reader's own calendar" is not consistent, since we are all living in "one world". Almost everyone lives in a state member of UNO. Everyone is obliged to manipulate daily the international dates, cf. dates of history at Wikipedia! So "our current – internationally recognised – calculation of times, like it is universally used by the historians" is obviously and without doubt the Christian Era. [However, like you know, a proposal for changing this well exists.] Next to this official, international calendar everyone has – of course – the right to use a secondary calendar for the notice of, for example, Buddhist or Jew feasts.
3. Concerning ISO 8601: Perhaps a little polemical, accorded, but not a "rant". Tell me: Who uses the proleptic Gregorian calendar with a year zero? Originally a bungling of some incapable and uncultivated computer programmers, this botch has curiously acquired an official status by ISO 8601. However, luckily ignored by everyone: astronomers, historians and Christians. Tell me Ian, who uses ISO 8601 in this part?? If nobody uses it, this must be clearly said also in our encyclopaedia. (The truth formulated sometimes a little polemical is "the salt in the soup", even in a good encyclopaedia. At least in a Note! This prevents from stuffiness. However I respect if other users like it less "flavoursome" and moderate it by respecting the content. Then regularly I don't insist.)
4. Now a problem of good understanding: You changed into (like before you Frederick):  Astronomers [...] "have used for" several centuries a defined leap year zero. Instead of the former: ... "since" several centuries use...  Doesn't this assume "they use no longer"?
5. Last point. You wrote: "The first documented use of zero in the Hindu-Arabic numeral system occurred towards the end of the 9th century and so postdates Dionysius Exiguus." You took this information from the concerned Wikipedia article, so I have nothing to reproach you. However know, that the Indian lokavibhaga of AD 458 already describes the positional system with zero. When I'll have the time, I'll rework first the "Hindu-Arabic numeral system" article. However, it's true, the first Arabic sources dates from the beginning of the 9th century (of "our" calendar, of course;-)

You can reply me here. I'll shift it to the year zero talk page later on.

-- Paul Martin 15:59, 22 February 2006 (UTC)

Hello Paul - Thanks for the above.

1. Yes, the Gregorian calendar doesn't have a year zero, because the Julian calendar didn't have a year zero. So, if I say "AD 100", am I using the Julian calendar or the Proleptic Gregorian Calendar? Quoting from Gregorian calendar#Proleptic Gregorian calendar: "For ordinary purposes, the dates of events occurring prior to 15 October 1582 are generally shown as they appeared in the Julian calendar, and not converted into their Gregorian equivalents." It was in this general sense that I used the term Gregorian calendar.
2. Wikipedia has articles in 208 languages (I just checked). While the Gregorian calendar may be dominant, it is not unique. It would be culturally aggressive to insist that only one calendar may be used and all others must be excluded. "Our" is a difficult word to use in Wikipedia, unless you use it in the sense of "Our planet" or similar. Gregorian is 'a' common international standard. ISO 8601 is another international standard (based on Gregorian). I suspect that you will find in many countries the 'international' Gregorian calendar is tolerated / accepted on an equal standing with the local calendar. But acknowledged as superior? I think not. BTW, I don't know the answer to this: If Gregorian is an international standard, what is its ISO number? If it does not have one, then what international convention / conference agreed this? Is it simply the International Postal Union, rather than the ISO? If not, then are we still using today Pope Gregory as the international basis for the definition of this calendar, with no subsequent international endorsement? (UTC was defined by the ITU and is monitored under the BIPM - however, we are getting close to those astronomers and their astronomical year numbering...)
3. In 30 years in the computer industry, I have had to deal with one main computer date format system (ISO 8601 and its precursors - 'ISO Date and time format' was available in the 1970s) and convert it to the local date format, be it Gregorian European, Gregorian American or Arabic. ISO 8601 is not a bungle and its inventors were trying to simplify date formats, not calendars - it is likely the only choice for international agreement / unification between the US and European date formats, e.g. YYYY/MM/DD could one day replace DD/MM/YYYY and MM/DD/YYYY. Obviously, it doesn't cover other calendars - but I readily acknowledge this fact. I looked at my PC firewall just now. This was written in the USA and uses ISO 8601 date formats to log events - why didn't they use MM/DD/YYYY? I think ISO 8601 is widely used inside computers - specifically because it is easier to sort. I know several genealogists who use this date format by preference.
4. The French construct 'Depuis <time period>...' and the German construct 'Seit <time period>...' usually translate into English as 'for <time period>'. The construct 'Depuis <date>...' and 'Seit <date>...' can be translated as Since <date>; otherwise Since means Because. e.g. I have been a Wikipedian for two years; or I have been a Wikipedian since 2004. (I still am a Wikipedian and I have not stopped being a Wikipedian). Since I enjoy working with computers and encyclopaedias, I joined Wikipedia (=I joined Wikipedia because I enjoy working with computers and encyclopaedias). This is not a strict rule, but is good colloquial English. The other combination 'Since two years, I have been....' sounds at best awkward.
5. I've sorted several paragraphs into some semblance of chronological order. It's possible that the resulting paragraphs may need adjusting for sense. However, it should lead to a single pass down the history, instead of the several passes in the previous version.

Regards, Ian Cairns 18:02, 22 February 2006 (UTC)

Hallo Ian, thanks for your reply.

Let's begin with ISO 8601, because you partially misunderstood.
You wrote: "YYYY/MM/DD could one day replace DD/MM/YYYY and MM/DD/YYYY."  Hopefully!  YYYY/MM/DD, wrt. sorting, is surely even better than DD/MM/YYYY. To propose an international standard for the date format is the role of ISO. In this respect ISO 8601 is reasonable. Nothing to reproach. (You overlooked "in this part" in my text above.)

Now, by postulating a proleptic Gregorian calendar, they proposed a new calendar system for the past. Did they consult the concerned professionals, astronomers and historians? Obviously they didn't. With a knowledgeable advice, never, never they could decree a botch like that!  —  Because it's still the Christian Era, let's start with Christians:

• Roman Church:  In Roman church the commemoration days of Saints are generally the anniversary of their death. (Considered as their day of birth in heaven.) I never heard, that according to ISO the commemoration day of, for example, Saint Francis of Assisi (died in the night before 1226, October 4) has been displaced to October 11. If I'm well informed, this commemoration day is always October 4. Thus the Gregorian calendar is explicitly not-proleptic and starts on 1582, October 15. Not a day before.
• Astronomers:  Astronomers universally don't manage the Gregorian calendar. They can't calculate inside Gregorian centuries because Gregorian centuries are unequal. One century of 36525 days is regularly followed by three centuries of 36524 days. This doesn’t allow calculations. Therefore, till our days astronomers continue to make all calculations by using Julian centuries. Then at the end of all calculations, they convert finally to the Gregorian dates.
  Astronomers also need the logical year zero: Since 1740, this is the so-called Cassini's Leap Year Zero equal the Julian year BC 1. Never, they want to switch to this improbable ISO's Leap Year Zero, pretended to have lasted from BC 1, January 3 to AD 1, January 2. The astronomers are certainly sapient enough, for never recognise this ISO botch.
• Historians:  Nor the historians will ever do so!  Never, we'll read in any history manual: "Julius Caesar was killed on 43 BC, March 13" instead of 44 BC, March 15. That's obvious.

The truth is: If you keep the Era, the millésime, any reformed calendar can't be proleptic. A great and hopeless confusion would be the only result of a suchlike proceeding. It's not necessary to be Einstein himself to understand this. On the contrary if one changes the era, it's not only possible, but – to be consistent – it's the duty to establish a proleptic calendar (cf. the Christian Julian calendar). If not, it's only a temporary Era like Tenno eras in Japan or the Roman Emperor eras, regularly abolished by the next "Caesar Augustus".

In France, so did Napoleon in 1806. Because the violent revolutionary Bourgeoisie didn't dare to pretend that all the living citizens were born in "negative dates" of their new, high-handed era. This is one of the multiples main reasons why the French Revolutionary Calendar – contrary to the decimal SI for example – never acquired universality.

In résumé: Because this part of ISO 8601, is neither accepted by historians, astronomers and Christians nor it is to expect that they ever will apply this part of ISO 8601, one can not have words hard enough concerning this monster of a proleptic Gregorian calendar. A "paper-tiger" of incompetent wanna-be reformers!

Let's be practical. I hope we are in agreement in this declarative statement:

• The Gregorian calendar with its Julian prolongation before 1582, October 15 is used by everyone except astronomers. The Christian Julian calendar has no year zero.
• The astronomers use the same Gregorian calendar, with its Julian prolongation before 1582, October 15, however with a defined leap year zero equal to BC 1 exactly one.

In the intro of the article this should be said without ambiguity. This is my concern. We can also mention the year zero in some Asiatic lunar calendars.
I propose to not mention the completely unused ISO 8601 leap year zero in the intro. I'll try to rework the concerned paragraph below (by also trying to moderate my aggressiveness;-).

Briefly:

• You asked, which calendar you use when you say "AD 100". Because you use the Christian Era you use the Christian Julian calendar, at AD 100 Gregorian calendar didn't exist.
• You asked, what is the ISO number of the Gregorian calendar?  Eh bien, its ISO number should be 8601. At least, if they didn't persist to cook their own unswallowable soup.
• As a user of Wikipedia everyone is obliged to recognise the Christian era as "our current world-wide" international era since our versions are stored in history exactly within this Era. Nowadays, in our modern times, this can be rightly considered to be an impertinence wrt. all not-Christians. However that's another question. Yet, that's a fact that every Wikipedia user, worldwide, edit in the Christian Era! Perhaps we can "dissimulate" this fact by avoiding the word "our". Why not. But what helps? The Christian era is currently "our common" Wikipedia Era.

Thanks a lot for your explanations in point four. For your point five: Until now I didn't study in-depth your changes in the chronological order. I rely that you improved. I'm sure.

-- Paul Martin 06:33, 24 February 2006 (UTC)

Paul Martin, I respectfully disagree when you state that

one can not have words hard enough concerning this monster of a proleptic Gregorian calendar. A "paper-tiger" of incompetent wanna-be reformers!

This part of ISO 8601 makes perfect sense.

The idea is that ISO 8601 defines a universal, but relative simple way of defining dates. The three main concerns: (a) Identical to common practice for all dates after the adoption of ISO 8601 (i.e. Gregorian calendar); (b) simple logic; (c) no cultural bias.

You don't want ISO 8601-enables handheld devices to spend half their logic on exceptions and historic calendar rules, because historic dates are going to be only rarely used on it. On the other hand, you do want them not to have some way of stocking historic dates, just in case somebody does need them. (More powerful computers can then be used to transform the ISO 8601 date into the correct date used back then, in that culture, based on geographical location, and a lot of look-up tables.)

Let's face it, historic calendar logic can be a pain in the ass.

First of all, not all countries switched Julian to Gregorian on the same date. Inter Gravissimas defined the switch on 15 October 1582, but only a few Catholic countries did so. UNIX calendar makes the switch on 14 September 1752, simply because that's when England and the US made the switch. Talk about cultural bias.

Second point: even if you find international agreement on a switch date for an international standard, there's an issue between 1 January 45 BCE and 1 March 1 CE. The Romans misinterpreted the Julian calendar, and they had leap years in the wrong years. (There's not even agreement which years exactly were leap years. I find Chris Bennett's research convincing, he argues the actual sequence leap years was: 44, 41, 38, 35, 32, 29, 26, 23, 20, 17, 14, 11, 8 BCE, 4 CE, 8, 12, ...).

Before the Julian reform, both the Julian and the Gregorian calendar were proleptic. The same argument against using Gregorian dates before 15 October 1582 can be made against using Julian calendar before 1 January 45 BCE.

Before 45 BCE, the Pointiffs simply defined the calendar any way they felt like it. Reconstructing the calendar from back then is not easy. As far as I know, it hasn't been done convincingly correct.

And what about thousands of years BCE: what calendar should we use then?

To summarise: keeping it simple and just using the current Gregorian calendar proleptic makes perfect sence. By using a year 0000 (in astronomer's fashion), ISO 8601 simplifies the rules even further since the same modulo-rules can be used to determine whether a year is a leap year or not.

Best regards,

— Adhemar 12:59, 29 September 2006 (UTC)

Paul, Thanks for the above reply. A few comments:

I don't think that ISO 8601 postulates a Proleptic Gregorian Calendar as the only calendar. The Wiki article ISO 8601#Dates specifies:

"The standard uses the Gregorian calendar, already the de facto standard of international trade, with the year numbering following astronomical year numbering. The standard acknowledges that other calendars may be used, such as the Julian calendar. It suggests that senders and receivers should explicitly agree when another calendar is used with the standard's notation. Dates are otherwise assumed to be Gregorian. In principle, dates should usually be converted to the proleptic Gregorian calendar to avoid possible confusion."

I was interested in your idea that the Roman Church should consult a 'higher authority' (ISO) on the celebration of Saints' days. But I leave this to the Church and its members to decide - it is their affair not mine.

BTW, Julian calendar#Leap years error suggests that Julius Caesar was killed on 14 March 44 BC in the Julian calendar, but maybe this depends on which leap years you accept.

I agree your declarative statement, with the exception 'everyone' -> 'most people'. This is not universal. Similarly, I don't think that all countries will agree that they are using the Christian Era. As a matter of religious sensibility, many non-Christian and poly-religious countries would probably insist that they are using the Common Era / Common Era calendar (based on the Gregorian calendar) alongside any local calendar. The tone of this article should also reflect this, rather than insisting on universal Christian Era usage.

I would like to extend your declarative statement - if you agree:

• The Gregorian calendar is a de jure standard within the Roman church and a de facto standard outside it (many countries would have endorsed parallel laws in their own legislation). As a result, no-one or no one organisation today owns or maintains the entire Gregorian calendar standard. The common usage of the Gregorian calendar is to use Julian calendar for dates before its 1582 inception (varies from country to country).
• ISO 8601 is an international (therefore secular) de jure standard, which prescribes date formats, year zero and negative years, but which allows any of several calendars to be used, as agreed by a particular user community. ISO 8601 is widely used in the computing / internet areas, and is being taken up in other areas - see ISO 8601#Usage and external links from that article.

Thanks, Ian Cairns 12:49, 24 February 2006 (UTC)

Hi Icairns, I commenced a longer reply for you. Yet it's not finished. Thanks for your patience. — Have a good day, Paul Martin 09:07, 3 March 2006 (UTC).

[edit] Third millenium

I added that some consider there to be only nine years in the decades around the non-existant year zero, which brings it back in line with the decimal system, this idea was listed on the pages 0s and 0s BC 76.211.3.86 01:48, 12 November 2006 (UTC)

[edit] An interesting question

• Did anything happen on June 15, 0?

I though about that because 0 is an neutral number and I figured that since June 15 is the middle of the year and 12:00pm is the middle of the day. Something must have happened between the time points of B.C. and A.D. on June 15, 0 at 12:00pm on the dot. Kid Sonic +I really think that June 30th or July 1st would be considered the middle of the year. And, yes, something (I don't know what - perhaps Mary was feeding Jesus} did happen on that day which was in the first year A.D. The powers that be at Wikipedia state that it is "the free encyclopedia that anyone can edit", but they call my efforts "nonsense." They say I am wrong in my beliefs but they won't let the public chime in by leaving my comments where they belong (in Year zero-Numerical Explanation). You can find them buried in the ash-heap of "history" under Year Zero Sam HastingsSamhastings 21:19, 21 March 2007 (UTC)

The answer to the question is: No. Nothing at all happened on June 15, 0. Ask any historian. What's more, nothing at all happened between Jan 1, 0 and Dec 31, 0. Therefore, historians decided simply to ignore it. By the way: Whatever may have happend on March 0, 2007? Even though March 0 was not too long ago, I cannot remember. Honestly. Unoffensive text or character 09:54, 22 March 2007 (UTC)

There is no such day as March 0, 2007. February 28 precedes March 1. Georgia guy 14:48, 22 March 2007 (UTC)+Your "By the way" question isn't really germane. I have never heard or read of anyone sponsoring a day zero. It is a calendar item just as a month is. All of Wikipedia's entries give Jan. 1 as the beginning of any year. The question we are trying to solve is that of the "so-called" missing zero year. I am trying to demonstrate that the ancients definitely understood the concept of zero (although they didn 't have the symbol). What we are discussing here is the question of a year zero and the role played by the later identification of ordinal and cardinal numbering systems. You state that there is no way to avoid the ambiguity introduced by using the same numerals (such as 1) for placing things in order (ordinal) ( first, second etc.) or for the start of some period of time such as a year (1 or 0) I have shown that this is possible by means of a table making a direct comparison. Unfortunately, this table is garbled in the transmission to your rendition of it and is eventually discarded. So much for freedom of expression and an unbiased reception by Wikipedia. SamhastingsSamhastings 17:36, 23 March 2007 (UTC)

Logically, if there was a Year 0, there should also be a Day 0 in March of 2007. It's simply going along the same principle, and completely in line with the question. Nyttend 12:51, 28 March 2007 (UTC)

+You're correct, of course. If I am going to argue my point consistently I shouldn't pick and choose which units of time I want to consider and those which I want to disregard. Perhaps the main ones I did not include in my most recent table in "Year Zero:Numerical Explanation"(deleted immediately) would be months, weeks and days. Months are named and I don't think anyone is looking for a zero month. Weeks and days are parts of the months. Weeks is a no-brainer. Long-time usage considers the first day of the month just that, the first day. Wikipedia itself confirms this thought by consistantly referring to Jan. 1st of this or that year. SamhastingsSamhastings 01:36, 29 March 2007 (UTC)

[edit] Bad grammar?

Under "Media:"

"In the movie The Beach Leonardo DiCaprio is during his mental instability crazed about the term Year 0."

I've not seen the movie, but even still, this sentence is almost unreadable. Can someone who's seen the film fix it, please? Jinxmchue 06:16, 18 December 2006 (UTC)

[edit] Third Milennium once more

User Fireplace put a quotation tag to this claim: Historians[citation needed] consider that the 3rd millennium of the Gregorian calendar began on 1 January 2001 (rather than the popularly-celebrated 1 January 2000).

As the start date of the third milennium is an obvious fact anybody can verify by using their own brain, I think the phrase "historians consider that..." is superfluous. I have therefore deleted it (as well as the quotation tag). By the way, the beginning of the 20th century was universally celebrated on 1st January 1901 and most nations thought the Germans were making fools of themselves by celebrating one year earlier. But unfortunately I cannot source this claim. Unoffensive text or character 15:42, 12 February 2007 (UTC)

Unoffensive text or character writes: "3rd millennium of the Gregorian [resp. Julian!] calendar began on 1 January 2001 " and continues "As the start date of the third milennium is an obvious fact anybody can verify by using their own brain".

He writes this in order to make ( - unoffensively - ) clear that those poor people who do not consent with his statement, either have no brain or do not know how to use it.

But the statement itself ( - that 1 Jan 01 marks the beginning of the century - ) has very little to do with historical matter of fact, as it depends on the statement that the first century of the Christian era began on 1 January (Gregorian) resp. 1 january (Julian) 1 A.D., which is an invention of very modern times, now put forth as a universally acknowledged "truth". This is nothing but politics: A historical "truth" invented to decide a quarrell, backed by "common sense". The next step will be to make this statement part of the curriculum in primary schools and punish those poor pupils who do not understand it.

Unoffensive text or character continues: " ... the beginning of the 20th century was universally celebrated on 1st January 1901 and most nations thought the Germans were making fools of themselves by celebrating one year earlier. But unfortunately I cannot source this claim."

Of course you cannot find the source, as this statement is your personal fantasy. When the German Kaiser Wilhelm II ordered that the festivities for the new century should be held on 1st January 1900, he had one of his rare lucid moments. Or rather: he followed reasonable (and historically well founded) advice.

But of course, to-day it is fun to mock about the stupid Germans ...

Ulrich Voigt, Germany 84.143.74.217 09:15, 6 April 2007 (UTC)

[edit] Giandomenico Cassini, Dionysius Exiguus, and the year zero

On the Royal Academy of Science in Paris it was already customary to use a year 0 well before 1700, as in a lecture of Giandomenico Cassini held there in 1696 this usage is obviously presupposed: The text has "annus 44 ante Christum, qui vulgo habetur 45“. And in a script of Cassini from 1704 it is made quite clear why he judged this to be necessary. Only by using a year 0 you can count the place of a year in the dionysian moon table simultanuously with the year itself. I presume that Cassini himself was the first to introduce this usage, and there is no need to wonder about La Hire.

Besides I am of opinion that Cassini hit exactly the original thought of Dionysius Exiguus, as the argumentum XII of the Dionysian argumenta paschalia (the mathematical commentary on his Easter tables) presupposes a year 0 before the year 1 A.D. In Dionysian language: The first year of the first Easter cycle of 532 years, the year preceding the year 1 A.D., i.e. the year j = (1 - 1) A.D., has j mod 4 = 0 (for the leap year), j mod 19 = 0 (for the moon table), and e = 0 (for the epact). In short: Dionysius Exiguus used a smart chronological system based on the number zero.

In the Middle Ages this was not easily noticed because at that period there was great reluctance to use a number zero, so the Golden numbers were invented to avoid zero. But this was definitely not the problem of late Antiquity.

On the other hand, the notion of a year zero was also presupposed by late Medieval computists like Roger Bacon who started the centuries with 00, following the simple logic of our decimal system. But this is a different story, which has nothing to do with the origins of our Christian ("dionysian") years in late Antiquity.

But one thing should be clear from "Roger Bacon", and "Giandomenico Cassini": That the use of a year zero has nothing to do with astronomy, but only with mathematics.

--Ulrich Voigt, www.likanas.de

[edit] Year Zero and Julian / Gregorian Calendar

In the article it is stated that a year zero does not exist in the Gregorian calendar or in the Julian calendar.

Now I would like to challenge these statements.

(1) Julian Calendar

The Julian Calendar is independent of any particular way of numbering years, as the Romans used to call their years by names (of two consuls) rather than count them. This is why I consider the statement ("a year zero does not exist in the Julian calendar") as misleading. A year 1 does not exist in the Julian calendar either.

(2) The Gregorian calendar

Here the situation is different, as in the 16th century a universally acknowledged Christian numbering of years did already exist. But as to events "before Christ" there did not yet exist that consensus which we experience to-day, as it was still held more simple to use Byzantine anno mundi for the remote past. It was not before the beginning of the 17th century that the notation "B.C." with (1 - 1) A.D. = 1 B.C. became common usage.

On the other hand the Gregorian reform itself did imply the notation (1 - 1) A.D. = 0 A.D. for the following reason. The reform essentially consisted in dropping three leap days out of 400 years, and these were taken away in the "full centuries". 1700, 1800, 1900 are leap years in the Julian calendar, but common years in the Gregorian calendar. Consequently the effect of the change relative to the old calendar was to be felt from those years 00 onward until the year 99, which means that the Gregorian "century" begins with 00 and ends with 99. But if every century begins with 00, the first century cannot be an exception, and must be held to start with 00 too.

And this consequence is also visible in late Medieval computistics, which split the four-digit number of the year into two equal parts, like 1256 = 12 56 to fascilitate the computistic operations. But once you split the numbers that way, it is obvious that the centuries will run from 00 to 99, and not from 01 to 00.

Actually the general concern for "centuries" as a sort of natural period of time, so common to-day, seems to stem from the computist concern for easy arithmetic. This is very well argued in Arndt Brendecke, Die Jahrhundertwenden. Eine Geschichte ihrer Wahrnehmung und Wirkung , Frankfurt / New York 1999, one of the finest books on the "Millennium problem" brought forth in the 20th century.

This arguments leads me to maintain that in the Gregorian calendar the year 00 is an obvious presupposition, though, of course, contrary to the habits of the historians. But the Gregorian calendar is definitely not the work of historians, but rather the work of computists and astronomers.

I should add that the Gregorian calendar, being nothing but a reformation of the Julian calendar in respect of (1) the length of the solar year, (2) the length of the moon year, is a system based on the notion of a century which runs from 00 to 99.

Now, if you reckon with (1 - 1) A.D. = 1 B.C., your centuries run from 01 to 00. If, on the other hand, you reckon with (1 - 1) A.D. = 0 A.D., they will run fom 00 to 99. In other words: (1 - 1) A.D. = 0 A.D. is equivalent to a definition of centuries which run from 00 to 99. And this means that indeed the Gregorian reform of the Julian calendar would become unintelligible when you drop the year zero.

--Ulrich Voigt, www.likanas.de

[edit] Intention of the article

To my opinion the intention of the article cannot be to defend a position like "the third millennium started on ..." or "a year zero does not exist in our Christian chronology" or something like that, missionary style. The article should help the reader think about a complex of matters of fact and not try to draw him into a party.

To-day those who consider themselves more enlightened than the common people tend strongly to insist on the absense of a year 0. But the common people of to-day follow a usage which has been established by the more enlightened experts of times past, indeed they reflect the purely mathematical approach used by Christian computists since the emergence of the decimal system, and imbedded in the very structure of the Gregorian calendar.

Surely, the historians do follow Bede Venerabilis with his notation 1 B.C. = (1 - 1) A.D., and I have no difficulty in accepting this usage. But in doing so, I still know that this system is mathematically unsound, and historically new.

As to the original intention of those who invented the Christian era in Roman times, we enter into a very difficult subject matter. There is no use in maintaining dogmatically arbitrary positions about the intention of early Christian computists.

--Ulrich Voigt, www.likanas.de

[edit] Beda Venerabilis

That Bede took over the system which equates 532 A.D. with 248 Diocletian from Dionysius Exiguus is made clear in de temporum ratione. There is only one occasion which shows that Bede used the Dionysian system to denote years before the Christian era, as he dates the Roman landing in Britanny "ante Incarnationis Dominicae tempus anno sexagesimo", i.e. in the year 60 B.C. This is not part of de temporum ratione, Bedes systematic treatment of chronology, but only mentioned in the historia ecclesiastica. Bede did not device a system, but implied it. This Bede system consists in counting backward and forwards like this: ... 3, 2, 1, 1, 2, 3 ..., which means that there are to be used two different denominations, A.D. for the times of the Christian era, B.C. for the times before the Christian era.

Bede did not yet know Arabic numerals, and had to use Roman numerals, thus even if he had wanted to use a year zero, he would not have been able to do so. His solution of the problem How to describe years before Christ with the help of the Dionysian system, is about the only one. Besides it is in harmony with natural understanding, as can be seen in the present debate about the millennium problem. "Zero", if you want to bring it into the discussion, is reduced to an infinitesimal point between 1 B.C. and 1 A.D.

The Bede system is an original invention of the early Middle Ages and cannot be traced back to late Antiquity. Dionysius Exiguus did not think of applying his system on years before a Christian era. The Bede system become general usage of the historians, though not before 16th / 17th century, as Petavius Opus de doctrina temporum (1627) played a role in making it general.

This is about what is meant when in the present debate it is often maintained that a year zero has no place in "our" Christian chronology.

A different question is, if the Bede system should be replaced by the Cassini system which counts like this: ... 3, 2, 1, 0, 1, 2, 3, ... , taking advantage of mathematical progress. In modern terms the Cassini system is -3, -2, -1, 0, 1, 2, 3, ... of course, and thus has the additional advantage that you do not need do make a distinction between A.D. and B.C. Well, as long as the only thing you want to do with these numbers is to count years, you will not feel a necessity to change a well established practice. But if it comes to computistic questions, there is no argument against mathematics.

I would say that Bede, had he but known Arabic numerals, would have chosen the Cassini system, because it would have greatly facilitated his Easter computation. The great Easter cycle of Bede starts with 532 A.D., but 532 mod 19 = 0 shows a 1-year-discrepancy between the year and its place in the cycle. In fact Cassini (1704) argued just that way: If the Christian era started in the year 0 A.D. (= 1 B.C.), moon cyle and years A.D. would be in harmony.

--Ulrich Voigt

[edit] Dionysius Exiguus

The idea that Dionysius Exigus might have called the year before 1 A.D. "1 B.C.", as Bede did, is absurd for the following reason: Dionysius did not aim at applying his system on years before the Christian era, and never thought of something like "counting backwards". But who would invent a new denomination of years just to talk about a single year?

The assertion that Dionysius could not have even thought about a year zero preceding 1 A.D., because the Roman numerals do not contain an equivalent for Arabic 0, is false. "Nullus" and "nihil" are Latin words which can be used to describe the number.

Now, I would like to give a proof for my thesis, that Dionysius Exiguus indeed did use "year zero" for the year preceding 1 A.D., so that his construction can only be described by the equation 0 A.D. = (1 - 1) A.D.

Dionysius did not speak of the beginning of the Christian era. But in his argumenta paschalia you can read the following:

Si vis nosse diem calendarum Januarii, per singulos annos, quota sit feria, sume annos incarnationis Domini nostri Jesu Christi, ut puta, annos DCLXXV. Deduc assem, remanent DCLXXIV. Hos per quartam partem partiris, et quartam partem, quam partitus es, adjicies super DCLXXIV, fiunt simul DCCCXLII. Hos partiris per VII, remanent II. Secunda est dies calendarum Januarii. Si V, quinta feria; si asse, dominica; si nihil, sabbatum.

This is the famous argumentum XII, a very clear description of How to compute the day of the week of January 1st of any given year j A.D. in the Julian calendar.

Put into modern mathematical terms, the Dionysian solution runs like this (from Ulrich Voigt, Das Jahr im Kopf. Kalender und Mnemotechnik, Hamburg 2003, p. 41):

W ( year j A.D., january 1st ) = ( ( j - 1 ) div 4 + ( j - 1 ) ) mod 7

Here W = 1, 2, 3, 4, 5, 6, 0 denotes the day of the week, beginning with Sunday (= 1) as usual.

I write W = 0, as Dionysius writes "si nihil [remanet], sabbatum." This is a very remarable point. On the Easter table of Hippolytus in Rome you will find the number 7 for Saturday. But the approach of Dionysius is a mathematical one, and the remainder of the division e.g. 14 : 7 is not 7, but 0.

The term ( j - 1 ) div 4 is equally 0 if j < 5, a second proof of the fact that these computists of late Antiquity knew how to calculate with the number 0.

Of course, ( j - 1 ) = 0 for j = 1.

January 1st of the year j A.D. is the first day of the Roman year j A.D., the birthday so to speak of that year, the day following the completion of (j - 1) A.D., which is the preceding year. The calculation, put forth by argumentum XII, rests on the idea to take the number of completed years as basis.

Now apply this for the year j = 1 A.D., and judge yourself!

And note that the Dionysian solution is false for j < 1. The year zero, though part of the computation, being a year without a name, is not taken into consideration in respect of the day of the week. The Dionysian Jesus Christ is incarnated only on march 25 in 1 A.D. The year zero, on the other hand, has (as Venance Grumel knew) something to do with the notion of the origin of the world, but that is another subject matter.

--Ulrich Voigt, www.likanas.de

[edit] Roger Bacon / Christopher Clavius

In Roger Bacons book Computus, which dates from about 1265, you find a list of the full centuries, beginning with c (100), cc (200), ccc (300), ending with mcccc (1400). For every year j (= numerus annorum Domini) Bacon gives j div 19 (= cycli perfecti) and j mod 19 (= anni cycli imperfecti).

To understand the expression anni cycli imperfecti consider the year j = 400. Division by 19 renders 400 = 21 x 19 + 1, so there is 1 year of a 19year cycle which is not yet complete. This is the annus cycli imperfecti.

Of course, the practical motive was to compute the Golden number Z of a given year j, that is Z = j mod 19 + 1.

To understand the value of this technique for the computation of the Golden number Z, let us consider the example j = 1467. The list gives you 1400 mod 19 = 13. So all you have to do, is to compute 67 mod 19 = 10, and join the two results:

Z ( j = 1461 ) = ( 13 + 10 ) mod 19 + 1 = 23 mod 19 + 1 = 4 + 1 = 5.

The point is, that in this way, once you master Roger Bacons table, you can compute the Golden number easily in your head without writing down anything. From Christopher Clavius, novi calendarii romani apologia, Rome 1603, p. 328 it is clear how Roger Bacons list was "learned": There is a nice mnemonics of positions on the human hand, which reduces the calculation of j mod 19 for the full centuries to pure counting. In fact, the same technique ( substituting this sort of finger-counting for something more effective, but retaining finger-counting to remember the sequence 19 - 38 - 57 - 76 - 95 of multiples of 19 smaller than 100 ) is used in Ulrich Voigt, Das Jahr im Koipf. Kalender und Mnemotechnik, Hamburg 2003.

What does all this have to do with "the year zero problem"?

Using the full centuries ( Bacon has: "centenarii" ) in the way Roger Bacon does use them, the centuries start thence. In fact the years j are here being analyzed as j = 100 x j div 100 + j mod 100. And this means that the years of the centuries run from 00 to 99. If Roger Bacon had not started his table with c ( = 100 ), but one century before, he would have been forced to start with a year zero. He did not do so, but he used a system which admits of no alternative.

Note that with Bacon the matter has nothing to do with Arabic numerals. The years of the 11th century being m, mi, mii, ..., mic ( = 1000, 1001, 1002, ..., 1099 ).

This is what Arndt Brendecke, Die Jahrhundertwenden. Eine Geschichte ihrer Wahrnehmung und Wirkung, Frankfurt / New York 1999, called "Der technische Jahrhundertbegriff der Komputistik" (the technical notion of the century in computism).

And it was this notion of "century" starting with 00, ending with 99, which was used in devising the Gregorian calendar, as is clear from the fact that the three leap years ( out of 400 years ) were cancelled on the full centuries ( j mod 100 = 0 ). This is only technique, not history. But as technique it implies the year zero, so that from the point of view of this sort of calender technique the Christian era has to start with a year zero.

I have already shown that this technical approach is very much in line with the original draft of Dionysius Exiguus himself, not followed by the Venerable Bede.

And I should add that Clavius had an important hand in the Gregorian reform of the Julian calendar. So it is no wonder that the computistical notion of a century running from 00 to 99 is incorporated in the Gregorian calendar, which by the sheer distribution of the leap years implies the year 00 ( = zero), commonly called 1 B.C.

--Ulrich Voigt, www.likanas.de

[edit] Dionysius Petavius

In establishing Christian chronology a decisive role was played by the rationarium temporum of Dionysius Petavius ( = Denis Peteau, 1583 - 1652 ), a voluminous work, but itself only a popular abridgment of Petavius more profound, more extensive, and more difficult opus de doctrina temporum, which was written for the erudite, and first published in 1627. To-day the rationarium temporum can still be found in almost every library, and you can even buy it via internet, while the opus de doctrina temporum is a rare object.

Petavius was one of the most learned men of his time. With five years he already spoke Latin and Greek, with 12 years he composed Hebrew poems, and, needless to say, he got a solid astronomical education. Petavius was an outstanding Jesuit, and the pride of the French king, who did not allow him to go to Rome, though the Pope had wished Petavius to be custos of the Biblioteca Vaticana.

The task of Petavius was to check, and surpass great Scaliger. In fact, only after Petavius, Christian chronology could be called scientific, and could be incorporated without any questions into European curricula.

As to mathematics Petavius had a week point in his reluctance to accept the number 0. When he came to compute the remainder of, say, 38 : 19, he did not say "0", but "19". So he was very much disposed to welcome the Bede system ( ...3, 2, 1 B.C. / 1, 2, 3, ... A.D.), which suits so well to this disposition. In fact it was only after Petavius that the Bede system became canonical and general usage in Europe. The influence of his chronological work can hardly be overestimated.

Though Petavius propagated the Bede system, he was not of opinion that Bede had properly understood Dionysius Exiguus. He thought, that Bede had started to count just one year too late, so that the Bede system from the point of view of Dionysius Exiguus should be shifted one year backwards. In other words, Petavius maintained that 1 A.D. should be what is now 1 B.C.

This is why Petavius called "our" Christian era the "era communis", a pejorative name still used in the 19th century. Petavius thought wise to accept the general usage, but claimed to know better.

I call this way of numbering the years the Petavian system, and count it mathematically correct ( ... -2, -1, 0, 1, 2, ... ) with 1 P = 0 A.D.

No, I do not think Petavius interpretation of Dionysius Exiguus correct, I do not think that Dionysius Exiguus used the Petavian system. But I do not think that Petavius was just wrong, either. When great scholars like Petavius err, it is wise to assume that they still had something of extraordinary value in their mind: Though, perhaps, Dionysius Exiguus did not use the Petavian system, it still might be that he knew it, and considered it.

That the Petavian system indeed has a place in Early Christian chronology and computistics! This is not the place to prove this statement. But just imagine the statement to be true. Then the option to define Christian years by 533 P = 248 Diocletian, which has the advantage over the dionysian definition 532 A.D. = 248 Diocletian, that it holds the years in harmony with the moon table (533 mod 19 = 1 first year of the moon table, so that 1 P is the first year of the Christian era and the first year of the first great Easter cycle), was an option which Dionysius Exiguus had to consider. What he actually did, was to throw away the relation of the year to the anti-christian Diocletian together with the main computistical advantage of the Diocletian years (1 Diocletian is the first year in the Christian moon-table).

This means that in order to understand Dionysius Exiguus you will have to find out the advantage of 532 A.D. over 533 P.

-- Ulrich Voigt 84.143.63.76 09:14, 3 April 2007 (UTC)

[edit] Common sense? Historical fact!

In the so called millenium or year-zero debate practically all the argumentation brought forth is based on nothing but common sense.

Yet the problem on stake is not a common sense problem, but a historical one. And historical fact does not usually follow our common sense expectations. In fact it never does.

As a historical problem you may consider the matter on different levels. You may talk about Clavius and the Gregorian calendar, or about Cassini, or about medieval computists like Roger Bacon, or about chronological experts like Petavius. You may ponder about the Venerable Bede or about Dionyius Exiguus. You may even think about the very origins of Christian computism and chronology with Julius Africanus and Hippolytus of Rome. But whatever level you take, you cannot expect to succeed without taking into account the historical evidence which at no level whatever will match your expectations.

Ulrich Voigt 84.143.67.138 23:24, 4 April 2007 (UTC)

May be you do not like history. But even then our problem does not degenerate into a problem of sheer common sense, as in this case it will simply be reduced to a technical comparison of the Bede system and the Cassini system. And the answer is obvious, as only the Cassini system admits of a coherent mathematics. So ultimately you will be forced back to the historical position of Dionysius Exiguus, and allow a year zero (which in the terms of "modern" mathematics is the year 0, of course).

It is really very funny that to-day the so called experts all over the world argue in favour of the Bede system. And just compare their reasoning with the arguments brought forth by Petavius and Cassini in the 17th century: What a remarkable decline in chronological and computistical understanding!

The only technical argument brought forth to-day runs like this: "Counting starts with 1, and not with 0." There is no idea whatever about the niceties of our Christian ("dionysian") way of numbering years together with their places in the 19-year moon table and in the 532-year Easter table, just sheer ignorance. And there is no reasoning about the difference between counting a finite set of objects or an infinite set of objects.

--Ulrich Voigt 201.9.255.232 14:39, 9 April 2007 (UTC)

[edit] On Counting

The natural way of counting runs like this: "1, 2, 3, ...", and is originally intended to count small-sized finite sets of objects. The striking advantage of this way of counting is the fact that the number spoken always gives the number of objects counted. As when I count my fingers: "1, 2, 3, 4, 5, 6, 7, 8, 9, 10". Yes, indeed, I have exactly 10 fingers. Please note that there is no difference in interpreting the numbers as cardinal numbers or as ordinal numbers. I may count "finger no. 1, finger no. 2, etc." or "first finger, second finger, etc.", either way leads to the number 10 as the number total of my fingers.

This way of counting, though natural, has a subtle disadvantage: I count 10 objects by using nine 1-digit numbers (1,2,3,4,5,6,7,8,9) and one 2-digit number (10). This disadvantage is a mathematical one which, once I start counting with 1, will perpetuate itself: When I count 100 objects in the natural way, I will use ninety-nine 2-digit numbers ( interpreting the 1-digit numbers with 2-digit numbers by use of 1 = 01, 2 = 02 etc. ) and one 3-digit number, etc.

The mathematical way of counting runs like this: "0, 1, 2, ...", and is but rarely used even with mathematicians. It is a way of counting that stems from the very nature of the decimal number system itself. I would say that the numbers present themselves in a numbered way. Practically speaking: If applied to finite small sized sets of objects, the mathematical way of counting has a subtle advantage and a striking disadvantage. If I count my fingers like "0, 1, 2, 3, 4, 5, 6, 7, 8, 9" I may be content that I have a neat relation between ten 1-digit numbers and ten fingers, but the number 9 means that I have 10 fingers, which is strikingly awkward.

Now let us look at years numbered. I do not yet talk about the whole of human or world history, but only of the Christian era. Which system of counting is better suited here?

Of course it is very natural to apply the natural way of counting, which means that the Christian era begins with year 1. But where is that striking advantage now? What information is imbedded in the proposition that "the sum of all years since the beginning of the Christian era is 2007?" O.k., if Christ would have in fact been born in the year 1 A.C., I would admit that it would be nice to always know the number of years since HIS birth. But no-one ever seriously thought that the year 1 A.D. (or, as to that, the year before that year) was the true birth year of CHRIST. Not even did Dionysius Exiguus think so. Consequently the advantage of the natural way of counting simply does not exist when counting Christian years., and only the subtle disadvantage remains. But this disadvantage all of a sudden reveals itself as a very serious obstacle, as it forces us to make a distinction between history and mathematics, between naive (though "natural") finger counting of the "historian" and elegant J mod 100 of the computist. This distinction goes back into the Middle Ages, and is even older than the introduction of the decimal system into Christian chronology, as can be seen from Roger Bacon. The computists (like Clavius) were responsible for the Gregorian calendar, and imbedded the mathematical way of counting in "our" calendar, though only by implication. Cassini proposed to put the calendar and the counting of years on the same footing, which could only be done by way of the mathematical way of counting. And closer inspection of the Easter tables of Dionysius Exiguus reveals that long befor Beda Venerabilis and the Middle Ages the mathematical way of counting was already implied in his computistic commentary on his newly introduced "dionysian" way of numbering years. But this has already been said.

Ulrich Voigt 201.8.175.229 22:50, 9 April 2007 (UTC)