Talk:Year zero/Archive 2

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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 09:22, 14 November 2005

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 08:37, 15 November 2005

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 21:37, 15 September 2006

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.

-- 84.143.94.80 Ulrich Voigt, www.likanas.de 05:55, 30 March 2007

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 {{User:FredrickS|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. 24.5.41.120 FredrickS 01:40, 6 February 2006 24.5.41.120

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 ${\begin{matrix}year=\left\lfloor {\frac {daynumber}{365.2425}}\right\rfloor \end{matrix}}$, an asymetric function. The logical year → millennium function, according to short thinking contemporaries and myself, ${\begin{matrix}millennium=\left\lfloor {\frac {year}{1000}}\right\rfloor \end{matrix}}$ ]

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. FredrickS 14:27, 2 March 2006

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)

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).

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)

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)

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)

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

+It is stated in the section "Third Millennium" of the article "Year Zero" that "The 3rd millennium of tahe Gregorian calendar began on 1 January 2001 (rather than the popularly celebrated 1 Jan 2000). This a direct consequence of the absence of a year zero in the Common Era. Had there a year zero, which might be considered part of the first millennium, then 1 January 2000 would indeed mart 2000 years since the year numbering datum and be the start of the third millennium. I have never seen any proof that there was a "missing year zero". Throughout the article one is cautioned to be careful in considering whether one is referring to a year 0 or the first year. No one believes in a zeroth year. Therefore much of the material in the article has to be taken with a grain or two of salt. For example (in the Astronomers section) it is stated that "Both Cassini and La Hire used BC years before their year zero and AD years thereafter (hence the sequence 1BC,0,AD1)". Zero is not a numeral in this system (as was finally realized over the years). Also, it is obvious that they did not look on it as being a zeroth year or the sum would be three not two. They are mixing apples and oranges. It is correct that 1BC is bang up against AD1. The only zero involved is the zero associated with the beginning of the time period (the first year AD). Under "Historians" this same error is encountered as follows:{In common usage Anno Domini 1 is preceded by the year 1BC, without an intervening year zero. Thus the year "2006" actually signifies "the 2006th".} Whaat does an intervening year zero mean? I'm sure that we agree that it is not a zeroth year. As mentioned above it is simply the numeral zero delineating the beginning of the first year AD. It is stated in "Historians" that the year zero was absent in the Common Era. It follows that 1AD must represent the first year CE. In the section "Numerical Explanation" it is pointed out that "first" is an ordinal number (first, second, third, etc.). Thus 1BC represents the first year before Dionysius' AD calendar was established. Confusion arises at this point. What does 1BC mean exactly mean other than that it directly preceded AD1. It means that if other calendars were replaced with Dionysius' calendar 1BC would represent the first year in that calendar before the change. For example, the first year BC (or BCE) would be the3760th year in the Hebrew calendar according to my calculations. Any year zero possibly associated with the Hebrew calendar would have been 5767 years ago. Now I would like to restate my claim that there was no missing year zero. The first year AD was itself the so-called missing year zero. This is because the first year AD or CE started at zero and continued at zero until its completion. Zero is a cardinal number as described under "Numerical Explanation". The notion that the ancients did not understand the concept of zero is just no so. One needs only to look at the sundial to realize that XII (their zero) represents the end of a period of time measurement and the beginning of a subsequent period of twelve hours. Halfway through the first hour is represented by 1/2 an hour or 0.5 hours or zero plus 1/2 hour. Surely one must acknowledge that the "first" hour, day, week, month, year, decade, century and millennium all began at the same instant, namely zero. The concept of cardinal numbers arose with the "invention" of the numeral zero and the decimal system. Truly, the third millennium started on January 1, 2000. Samhastings 24.242.43.82 21:17, 20 July 2007 (UTC)

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 ...

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

To Samhastings from 24.242.43.82

You seem to know the basic facts about this dispute; but your logic is hard to follow and you arrive at the wrong conclusion (namely “Truly, the third millennium started on January 1, 2000.”).

So either your logic is flawed, or you’re missing something.

Let me first use a related case: counting time in a person’s life. Afterwards, I will go to the calendar.

You say: The only zero involved is the zero associated with the beginning of the time period. Let's call the instant time counting began birth in the first example, and the epoch when talking about calendars.

Consider somebody, preferably not born on February 29. Let's forget his mother’s pain and labour and consider his birth instantaneous. Well, at that instant, his first day of life begins. At the same time, his first week of life begins, and his first year of life begins. A week later, his second week of life begins. A year after his birth, his second year of life begins, he than has the age of 1 year. During his nth year of life, he has the age of n–1 year.

No, to the calendars. It does not matter if we're discussing Julian calendar or proleptic Gregorian calendar. It does matter, however, that we consider a calendar without a year called year 0 (which is the historian's way of reckoning). To keep things simple, assume that the year has always started on the same day (January 1) and the day has always started during the night at midnight. (Both assumptions are incorrect, but that doesn't change the logic.)

So there is a moment we switch from BC to AD, or BCE to CE if you want to be less Christianity-centric. That moment is the epoch of the calendar: it's the midnight at the beginning of 1 January AD 1. At that instant, the first day begins, the first week begins, the first year begins, the first decennium begins, the first century begins and the first millennium begins.

One year after the epoch (midnight starting January 1 AD 2), the second year begins. n–1 years after the epoch (midnight starting January 1 AD n), the nth year begins. Now here is the catch: when abandoning ordinal numbers, and counting in cardinal numbers, historians do not do the “–1” operation: the nth year is simply AD n, not AD n–1.

The second century starts 100 years after the epoch, that is midnight starting January 1 AD 101. The 20th century starts 1900 years after the epoch, that is midnight starting January 1 AD 1901. The third millennium starts 2000 years after the epoch, that is midnight starting January 1 AD 2001.

Now, consider a calender which does have a year zero between year –1 and year 1: the astronomer's way of counting, or ISO 8601:2004. Here, it makes sense to put the epoch at the switch between negative and nonnegative year numbers (which should never be regarded as ordinal numbers). The epoch becomes midnight staring January 1 of year 0000, which is a year earlier than the epoch of the historian's calendar. The first year in such reconing is actually year 0000, or the year prior to the first year of historian's reckoning. Second century starts in year 0100, 20th century starts in year 1900, third millenium starts at midnight starting January 1 year 2000. Every period referring to the epoch now starts a year earlier (and ends a year earlier) than the historian's way of counting simply because the epoch is a year earlier.

– Adhemar 11:39, 22 July 2007 (UTC)

+I agree with you completely about counting time in a person's age. I am 88 years old and am in my 89th year. Subtract 88 from both these numbers and one finds that I was zero years old in my first year. This is such a beautiful illustration of the need to be careful about defining whether you are referring to a counting number (putting things in order) or to a measure of the passage o time.

You state that "the moment we switch from BC to AD is the epoch of the calendar: it's the midnight at the beginning of 1 January AD 1. At that instant, the first day begins, etc. & the first millennium begins." All of this is true if you admit that 1 January AD1 represents the first year of the Lord.

+I don't know about your understanding of the word epoch but Wikipedia defines it as a period of time such as a distinctive historical era. It also characterizes it as the defining moment when such an era begins. Thus the Christion Era began with the birth of Christ (the first year AD) and the moment that year began was zero and continued as year zero until the year was over as explained in my original edit above. So the first year AD is itself the so-called missing year zero.

Sam Hastings 24.242.43.82 21:40, 22 July 2007 (UTC)

Sam, I don't have to "admit" that "AD 1 represents the first year of the Lord." (Actually, I am an atheist.) AD 1, or in full: "Anno Domini 1" means "(in) the first year of the Lord". "Anno" is Latin for "in the year" (ablative for annus); "Domini" is Latin for "of the Lord" (genitive of Dominus); 1 was originally an ordinal number as explained above.

Whether Jesus was born 7 BC, 4 BC, AD 1 or any other year is irrelevant. (Whether he even existed, is irrelevant.) At one time, Bede thought Christ might very well have been born in a given year he called "AD 1" and defined the Christian or Common Era thus. By establishing the calendar, he defined the epoch to be "January 1 AD 1", whether that is (close to) the exact birth date of Jesus or not.

I use the word epoch correctly in the second definition: the defining instant of an era. An epoch just needs to define an era, it does not need to coincide with the special event that was thought to be happening around that instant.

The first year AD (which is numbered AD 1, not 0, by historians and astronomers alike) is not itself the so-called missing year zero. One does not equal zero, and year one does not equal year zero.

– Adhemar 18:30, 24 July 2007 (UTC)

+You state:The first year AD (which is numbered AD 1, not 0, by historians and astronomers alike is "not" itself the so-called missing year zero. At this point you seem to agree that 1 Jan AD 1 represents the first year of the Lord (or the first year CE). You also state that 1 was originally an ordinal number. Of course it was and still is (first, second, etc.). Why do you say originally? You are referring back to what you said earlier: "Now here is the catch: when abandoning ordinal numbers and counting in cardinal numbers, historians do not do the "-1" operation: the nth year is simply ADn, not ADn-1". You don't use cardinal numbers for placing things in order. The system is reserved for measuring the passage of time. It starts with zero and there is no nth number in that system. You are mixing apples and oranges and unfortunately, have created what is probably a "catch 22" problem. The first year is ordinal and year zero is cardinal and as such refer to the same year. We arrived at the end of the 2000th year on Dec.31,1999. The 2001st year was year 2000. Can this be why under "3rd Millennium" the 21st century is shown to consist of the 2000s? Sam Hastings 24.242.43.82 02:10, 26 July 2007 (UTC)

Sam,

I’m curious: When you say I’m mixing apples and oranges, do you mean that I’m mixing “cardinal numbers” and “ordinal numbers”? Or that I’m mixing “instants” with “periods” of time? Or that I’m mixing the “grammatical” definition of “cardinals” and “ordinals” (where “2” is a cardinal, and “2nd” is an ordinal) with the “semantic” definition (where a cardinal defines a quantity and an ordinal is used to number the items on a list in order) and/or with the “mathematical” definition (Cantor)? To answer the last question: I’m using those terms in the grammatical definition all this time.

I would have loved it, if, in the commonly used historian’s way of thinking, the first year after the epoch really was year 0. It would have made the 2001st year = year 2000. It would have meant that the 3rd millennium started on 1 January 2000. We could simply call it millennium number 2. In short: I would have loved it if you were right. Such a system I would have found more logical and pleasing.

Likewise, it would have been logical if the first day of this month was July 0 instead of July 1. As computer scientists know, there's good reason to start counting at 0, the convention favoured in C-like and other programming languages. (See also Dijkstra’s EWD 831.)

Hélas, the commonly used historian’s calendar just doesn’t work that way. As repeated numerous times: the astronomer’s way and ISO 8601:2000/2004 do work this way (for year numbering, not for days of the month), and introduced a year 0 prior to A.D. 1, effectively replacing the C.E. epoch with another epoch 1 year earlier.

I go back to the normal, historian’s practice. In Latin, the date “IV Oct A.D. MCMLXX” is said and written in full as “die quarto mensis Octobris, anno Domini millesimo nongentesimo septuagesimo” which translates litterally as “(on) the fourth day of the October month in the thousand-nine-hundred-seventieth year of the Lord” (example from Paulus PP. VI, Mirabilis in Ecclesia Deus). Some languages say “4 October”, others say “the 4th of October”. If I’m mixing (grammatical) cardinals with ordinals in the “wrong” way, it’s because common practice does it the wrong way.

– Adhemar 19:30, 26 July 2007 (UTC)

+It has finally dawned on me that your unshakeable belief that the first year and year zero cannot be compatible is based upon the notion that 1 always equates with 1. Thus you invoke the untenable position that you can willy-nilly substitute cardinal numbers for ordinal numbers. You have the first year equal to year one and leave the required year zero (the first cardinal numeral) shoved back a year and now called year zero or the first year BC. This is not possible. The first year BC (as explained earlier) is simply the last year in any calendar system that has been replaced with Dionysius's calendar (AD). You do not place years in order (ordinal) with the cardinal numbering system. See "Numerical explanation" in the main "Year zero" article. Samhastings 24.242.43.82 16:38, 27 July 2007 (UTC)

Sam,

I do not disbelief that the first year and year zero could be compatible; I just argue that common practice is different. If we all would be using the astronomer’s way, you would be completely correct (in stating, amongst other things, that 3rd millennium started on 1 January 2000). This year, 2007, would be the 2008th year.

I regret the “willy-nilly” practice of substituting (grammatical) ordinal numbers (like 1970th) with cardinal numbers (like 1970). But our mutual dislike of this substitution does not prevent it from happening, no matter how much you deny it.

In many books, “Chapter 1” is the first chapter. (There are a few authors who start with “Chapter 0”, but they do not form the majority.)

Wikipedia is an encyclopedia. It describes how people number years, it does not prescribes should have been numbering them more sensibly.

The “Numerical explanation” section is right: Historians use ordinal numbers (in the semantic sense). In some languages, such as Latin, these numbers are spoken as grammatical ordinal numbers. However, by now, in English and most other languages we use a grammatical cardinal to denote a year which is semantically an ordinal. Just like most authors do with chapter numbering.

The “Numerical explanation” section is apparently also right that but then ambiguity can result if one uses the numeral 1 to stand for the first in a sequence, and "2" for the second (as historians do with years and days of the month). Otherwise we wouldn’t be having this discussion.

You claim it to be impossible to define year 0000 as the first year BC. Astronomers and the ISO 8601 authors don’t agree; and did so anyway.

It’s all very well described in the article, especially in section “Historians” and “Third millennium”.

– Adhemar 17:54, 27 July 2007 (UTC)

+You seem to have not read, misunderstood or rejected my comments concerning the real explanation of why the first year BC does not equal zero (whether one considers it year zero or a zeroth year). Sam Hastings 24.242.43.82 18:31, 30 July 2007 (UTC)

I have read your original comment many times now. I admitted from the beginning that your logic is hard to follow. I tried my best to explain all the subtle points you possibly might be missing, to show that the article, as it is, explains the issue rather well. It is, however, not unimaginable that I misunderstood you. In any case: for an illustration of the sequence of days in several used conventions, I prepared calendar snippets. Maybe this clarifies things. A warning: the snippets take into account a number of other calendrical issues as well; I hope it doesn’t confuse you further. – Adhemar 20:25, 30 July 2007 (UTC)

+I like the proleptic part of the first snippet since it gives the starting date of the first yeat CE as 0000-01-01, This is what I have been arguing all along. One does equate with zero. I believe the n, n-1 stuff is sophistry since it must be based upon the incorrect notion that 1BCE is equal to zero. As I have illustrated above, the first year BCE must be compared with the last year in any other calendar in existence at the instant that the first year CE begins. I have discussed this idea with a local rabbi and he confirms that in the Hebrew calendar the first year before 0000-01-01 CE the 3760th year began on Jan. 12. Samhastings 24.242.43.82 20:52, 2 August 2007 (UTC)

+Oops. An inadvertant error. The 3760th year in the Hebrew calendar began on Sept. 12, not Jan. 12th. Sorry for the carlessness. Sam

Exactly: you like (ISO 8601). Its mathematical elegance (with the first year after the epoch numbered 0000) appeals to your aesthetic senses. I like 8601 too. But that's no reason to assume that everybody uses a calendar with the same properties

For your information, according to the algorithms I found on the Hebrew calendar:

• 1 Tishri of the 3761st year of the modern Hebrew calendar

(Note that the epoch of the Hebrew calendar is 1 Tishri Anno Mundi 1, not Anno Mundi 0, so the 3761st year is 3761!) equals:

• Julian day 1 721 319 at noon
• 16 before Kalends of October, 753 AUC (consulship of Lentulus and Piso) in the Roman calendar
• Saturday, 18 September 1 BCE in the Julian calendar
• Saturday, 16 September 1 BCE in the proleptic Gregorian calendar
• 0000-09-16 in ISO 8601

– Adhemar 19:10, 3 August 2007 (UTC)

+As far as I am concerned it is apparent that the first year BCE is not (emphasize NOT) year zero. What does this do to the n,n-1 concept? Samhastings 24.242.43.82 21:38, 3 August 2007 (UTC)

Sam, I’ll answer one more time. If I fail to enlighten you, so be it. Unless you clarify where you stand and exactly what makes you think 1 BCE isn’t year 0 (because you still haven’t made your argument cohesively) I’ll give up.

Please consider the historian’s convention (which is the commonly used one) and the astronomer’s way as two separate calendars – or, to be more precise: two variants of the same calendar (usually the Julian calendar for any date before 1582).

As explained in the article: the sequence of years in the historian’s variant is …, 3 BCE, 2 BCE, 1 BCE, 1 CE, 2 CE, … or …, 3 BC, 2 BC, 1 BC, AD 1, AD 2, …. In the astromoner’s way it is …, -2, -1, 0, 1, 2, …

The historian’s notion of 1 CE or AD 1 is the same as the astronomer’s notion of year 1: it is the period between 16 Teveth AM 3761 and 27 Teveth AM 3762, inclusive (according to modern Hebrew calendar).

For the historians, year 1 BCE is the year (366 days long) immediately prior to 1 CE, thus it is the period between 6 Shevat AM 3760 and 15 Teveth AM 3761, inclusive. For the astronomers, year 0 is the year (366 days long) immediately prior to year 1, thus it is the period between 6 Shevat AM 3760 and 15 Teveth AM 3761, inclusive.

Therefor, for all purposes, the statement that year 0 (a concept from the astronomer's variant of the calendar) equals the year 1 BCE (a concept from the historian's variant of the calendar) is true. – Adhemar 20:30, 5 August 2007 (UTC)

+Adhemar: I believe it is reasonable for me to assume that when you refer to "years 1 BCE and 1 CE" you mean the "first" years. Is this not so? And we both believe that zero (unmentioned) represents the instant the first year BCE ends and the first year CE begins. Now the astronomers require a year zero because they need an initial leap year. So they devise a variant from the historians' calendar by deciding to count the years CE by equating the first year to year one. This unreasonable maneuver shoves year zero back one year to the first year BCE. However, they shoudn't have done this, not only because it violates commen sense, but because they didn't need to. By using the cardinal numbering system they really should have realized that there would have to have been two (emphasize TWO) years zero.

               --,year 1 BCE, year zero BCE:year zero CE, year 1 CE,----

These are all numerals in the cardinal numbering system. The colon represents zero as in the historians' variant of the calendar; it is simply the beginning point.

I don't believe I need to argue that 1 BCE does not equal year zero anymore because it is moot. I have definitely established that the first year CE was year zero. Thus the third millenium really began on the first day of January, 2000. Sam Hastings 24.242.43.82 23:42, 7 August 2007 (UTC)

I knew I said I would stop arguing, but you continue to bring up new confusions (2 years zero? Where do you get that idea?).

You wrote: “I believe it is reasonable for me to assume that when you refer to "years 1 BCE and 1 CE" you mean the "first" years. Is this not so?” – Yes, it is so in the historians way. “1 BCE” and “1 CE” are respectively the first year before and after the epoch. Historians use ordinal numbers (semantically) but in most languages (such as English, but not Latin) usually expressed as cardinal numbers (grammatically).

Astronomers use grammatical cardinal numbers as semantical cardinal (even integer) numbers. Their year 0 is not supposed to be a first year (even though it is), it is supposed to be the year between year -1 and year 1; and year -1 is supposed to be the year between year -2 and year 0. They do not want symmetry around their epoch (1 year before the historian’s epoch); they want their astronomical formulas to be accurate. Having two years 0 creates a discontinuity which is just as unhelpful as having year 1 BCE followed by year 1 CE.

You wrote: “And we both believe that zero (unmentioned) represents the instant the first year BCE ends and the first year CE begins.” – I have no problem with calling the epoch “instant zero” (which is a point in time) but that does not mean there can’t be a “year zero” (which is a period) in a calendar that wishes to start counting at 0.

You wrote: “year zero BCE:year zero CE”. – Please do not use era-designations (BCE / CE or BC / AD) when using astronomer’s years. The astronomical year numbers are integers. Use minus sign. – Adhemar 09:59, 8 August 2007 (UTC)

+You are correct - there is no point in our continuing this discussion. Your belief in a calendar that "wishes to start to start counting at 0" is not one to which I am willing to subscribe. One does not "count" with cardinal numbers - they are used to measure the passage of time (as in year zero). Samhastings 24.242.43.82 17:20, 8 August 2007 (UTC)

+Somehow our last two sessions got transposed but no problem. As to where I got the notion of two years zero I thought it was original with me. However, in checking back I guess I somehow internalized it unconsciously from the section Astronomers in the main year zero article ("Several "expanded" fornats are possible: -0000 and +0000 ......" So it is not original but it appears that it is considered a possibility. In this same section the third paragraph shows the sequence 1 BC, 0, AD 1, referring to all of these as years but in calculating the sum and difference year 0 has no value. One can't argue that they represent ordinal years or we have knighted a zeroth year. This reminds me of the rediculous comment by Chlodius at the start of the year zero article that he had four coins - zeroth, first second and third. This foolishness is akin to the claims about floor zero or chapter zero. I have four coins - a quarter, a penny, a nickel and a dime. I want to line them up in order of size - dime, penny, nickel and quarter - no zeroth coin. These ideas are just not germane to the main question. It seems to me that the sequence is first year BC. year zero, first year AD. Are we not mixing apples and oranges? Samhastings 24.242.43.82 19:53, 9 August 2007 (UTC)

+Well, I'm back. Maybe I have my problems with the section titled "Astronomers" in the article "Year Zero" better defined and more clearly defended. A basic problem is that the Cassini quotes and the discussion that follows do not adequately differentiate between ordinal and cardinal numbers. My comments will denote cardinal Years with a capital Y. The cardinal numbering system denotes the passage of time and includes the concept and symbol for zero as a starting point. The ordinal numbering system is used for placing things in order as the first, second etc. There is no "zeroth" year. Cassini is quoted "The year 0 is that in which one supposes that Christ was born..." I can suppose that, but I can also suppose that he was born at the beginning of his first year which was obviously Year 0 AD as confirmed by the definitions above. Cassini is also quoted "...which several chronologists mark 1 BC and we marked 0 so that the sum of the years before and after Jesus Christ gives the interval which is between these years and where numbers divisible by 4 mark the leap Years as so many before or after Jesus Christ". From these quotes we realize that he is searching for a leap Year 0 and that he expects to have two series of Years, one running forward (AD) and one running backward (BC). The notion of BC Years will be addressed later. In the discussion following these Cassini quotes a sequence is proposed as reflecting the ideas proposed by Cassini (and La Hire?):1 BC, 0, AD 1. At this point one must examine what these terms stand for. I conclude that they all should stand for Years: Year 1 BC, Year 0, Year AD 1. Cassini obviously realized the first year BC could not logically be equivalent to Year 0 BC so he labeled it Year 0 AD. This confirms Year 0 as an actual Year, a measure of the passage of time, and a member of a cardinal series of numbers and gives lie to the notion that the sum of the Years before and after Christ gives the interval between the Years. The sum given for 1 BC, 0 , AD 1 is 2 (ignoring Year 0). The correct answer is 3. By setting Year 0 AD equivalent to the first year BC another complication arises. We now find that Year AD 1 is equivalent to the first year AD (which is what Wikipedia espouses). This requires the replacement of the usual n,n-1 equivalency of ordinal and cardinal numbers with an n,n equivalency. For consistency we must conclude that the first year BC is equivalent to Year 1 BC (a non-existent Year) and Year 0 BC (another non-existent Year) is moved forward to apparent equivalency with the first year AD. Now we have four Years competing for only two spots: Year 1 BC, Year 0 AD, Year 0 BC and Year AD 1. With Years 0 BC and 1 BC non-existent we are left with only Year 0 AD and Year AD 1 as viable candidates for the two spots. Surely abandoning the usual n,n-1 relationship for an n,n relationship in an effort to create a Year 0 for leap Year has led to many difficulties mathematically and intellectually. As Cassini undoubtedly knew, the only Years 0 and 1 in the Years before Christ belong exclusively to those calendars extant at the time Dionysius established his calendar. Cassini would have been much better off arbitrarily defining Year 0 BC as equivalent to the first year BC. Now we have a defined cardinal series extending backward indefinitely (even though it is a fiction). This gives the astronomers two leap Years, one forward and one backward. If the astronomers find two leap Years acceptable, well and good. And I think they should because it is now not necessary to invoke a mythical Year 0 between the BC and AD Years which is later abandoned (as actually being between the Years) and is arbitrarily defined as Year 0 AD and set as equivalent to the first year BC. With the two leap Years 0 in the equation the sum of the Years AD and BC now does equal the interval between the Years:Year 1 BC + Year 0 BC +Year 0 AD +Year AD 1 equals 4. Is Year 0 BC the so-called "missing year"? It is still an artifact created solely for the purpose of giving astronomers a way to refer to the Years BC. Can we now accept that January 1st, Year 2000 (the 2001st year) was the first day of the third millennium as it was of the 21st century? Samhastings 24.242.42.17 03:38, 19 February 2008

Regarding your statement "The sum given for 1 BC, 0 , AD 1 is 2 (ignoring Year 0). The correct answer is 3.": The correct sum is indeed 2 when it is realized that Cassini wanted the number of elapsed years between corresponding instants within each year. The instant that astronomers typically use for any year (unless otherwise specified) is the beginning of the year, specifically noon January 1. Thus only the years 1 BC and year 0 are between the implied instants (year AD 1 is outside the interval). Another view is to consider anniversaries within each year, such as the Parilia or Founder's Day (of the city of Rome) on April 21. The number of years between April 21, 1 BC and April 21, AD 1 is two years, not three, when a year 0 is included (astronomical years), thus matching 1+0+1=2. April 21, year 0 is the first anniversary and April 21, AD 1 is the second anniversary. If a year 0 is not included (historical years), where 0 is only a point in time, then adding 1+1=2 would give the wrong answer because then there is only one year between April 21, 1 BC and April 21, AD 1 (April 21, AD 1 is the first anniversary). — Joe Kress (talk) 04:00, 2 March 2008 (UTC)

+Joe: Recently in the section "Chronologists" Lerman proposed a fence line analogy to represent a numbering system useful in counting years. He also proposed the possibility of using an index 1 or index 0. Unfortunately he chose index 1 and then decided the whole idea was wrong. I emphatically proposed that with an index 0 all things fall into place. We must keep in mind that index 0 means that the FIRST POST stands for ZERO, the instantaneous POINT between two rails. All of the preceding and subsequent points are also simply instantaneous points -1 etc and +1 etc. The rails can be anything we choose that will apply. This sequence -1.0,+1 lets us show that the interval between your dates April 21, 1BC and April 21, 1AD is exactly 1 year. Sam Hastings 24.242.42.17 17:18, 15 August 2008 (UTC)

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 84.143.127.180 13:45, 29 March 2007

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 84.143.61.207 19:28, 29 March 2007

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 84.143.94.80

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 84.143.117.86 07:30, 31 March 2007

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? +Dionysius probably did think about the first year before the institution of his calendar, just as Bede did. The first year BC was simply the last year of any existing calendars such as the Hebrew calendar. The first year before AD1 was the 3760th year in the Hebrew calendar and started Jan1, 3759. Any year zero possibly associated with the Hebrew calendar would have been 5767 years ago. Sam Hastings24.242.43.82 18:00, 30 July 2007 (UTC) 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 84.143.117.86

WP:OR Vincent Valentine 18:11, 21 May 2008 (UTC)

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 84.143.117.158 12:50, 1 April 2007

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)

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)

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)

On Symmetry

There is a Dutch webside www.millenniummistake.net by Jan Zuidhoek which argues as follows:

"in our era there simply cannot be a year zero (provided that we want to preserve symmetry)."

It is true that in the Bede system there is symmetry, as 1 A.D. corresponds to 1 B.C., 2 A.D. corresponds to 2 B.C., etc., and this symmetry is lost once you admit of a year zero. But symmetry is not a condition of sound chronology, and I do not think that symmetry was ever mentioned by any computist or chronologer as an important (or even unimportant) condition to be observed in chronology. In other words: symmetry is only an easy argument to win the day, an argument without any value whatever.

"Without value"? This would be a nice compliment, indeed! Fact is, that symmetry, far from being of any advantage, causes a break in the flow of numbered years. Once you eliminate the year zero, the centuries "before" and "after" CHRIST behave differently. E.G., if you start the "christian" centuries in the Bede system with 01, you will be forced to start the "pre-christian" centuries with 00; if you start the "christian" centuries with 00, you will be forced to start the "pre-christian" centuries with 01. But in the Cassini system the centuries always start with 00.

So, in a way, the Venerable Bede, by applying the natural way of counting to the years of the world, brought about that "CHRIST" broke into pieces chronology, and Cassini tried to bring things back to their original level.

Ulrich Voigt 201.19.4.244 03:08, 11 April 2007 (UTC)

Jan: In the “Bede system” the first century AD corresponds perfectly to the first century BC, the second century AD corresponds perfectly to the second century BC, etc.. Tell me, Ulrich, what must be the first century BC in the “Cassini system”?

Cassini (1696) himself, by writing “44 ante Christum” in place of vulgo “45 ante Christum”, implied that 1st century before Christ = -100 CE – -1 CE. And this is, of course, the way mathematicians think: They end the negative numbers with -1. Zero is a non-negative number, and habitually mathematicians split the integers into the negatives and the non-negatives, so that zero in a way becomes part of the positive numbers, though not properly speaking. Just like this the Christian era Cassini-style starts with the year zero, the first Christian century being 0 – 99 CE. Every century then starts with zero.

Jan: but during ten centuries its consequence, i.e. the non existence of a year zero, has not been experienced, by historians, as an inadequacy of the Christian era, the opposite is true.

Well, habit is a strong force, so all of us got accustomed to the Bede system. And it is not common, to complain of instututions so well established. On the other hand the computists, i.e. the experts of the subject matter, without much ado changed the matter by feigning the existence of a year zero, as can be easily seen from the distribution of leap-days in the Gregorian calendar. By the way, historians, judging from our contemporaries, will not easily be bothered by mathematical inadequacies, as they do not have the habit to do much computation at all.

Ulrich Voigt 84.143.84.205 13:55, 21 July 2007 (UTC)

Knowledge of the number zero

As to knowledge of the number zero independent of "our" decimal system, Zuidhoek (www.millenniummistake.net ) will not admit its existence.

To argue his point, he writes: "Being acquainted with the number zero implies ‘knowing how to carry out abstract calculations with the number zero’."

He should have written: ’Knowing how to carry out calculations with the number zero implies being acquainted with the number zero. ’ Because then he might have noticed that it is absurd to deny knowledge of the number zero for Dionysius Exiguus and Beda Venerabilis in particular and the computists in general.

Here we see a very strong prejudice at work, which does definitely not represent scientific standard. What a pity that Wikipedia takes this as solid knowledge!

In order to win his day, Zuidhoek even writes: “Zero is a name of our tenth digit (mostly indicated with the symbol 0) … ”

And why not “the first digit”? To my opinion the digits are numbered by their very nature in the mathematical way: 0 < 1 < 2 < 3 < 4 < 5 < 6 < 7 < 8 < 9. To call 0 the tenth digit is just an attempt to get rid of a fact.

Ulrich Voigt 201.19.12.45 14:30, 11 April 2007 (UTC)

Jan: knowing how to calculate with any numeral zero is a necessary and sufficient condition for knowing the (abstract) number zero.

O.k., I could accept this statement. But what, after all is a numeral? To my opinion the word “nullus” or even the description “nihil remanet” can be taken as a numeral, if there is a calculation being made which uses the word or the description like a numeral. For example, if I say “the root of zero is zero”, or “the root of nothing is nothing” the words “zero” or “nothing” become intelligible substitutes of the numeral 0, and this I consider as true even if the numeral 0 would be unknown to the person that uses that statement about "the root of".

Jan: So it is not absurd to deny knowledge of the (abstract) number zero (with its ins and outs) for Dionysius Exiguus and Beda Venerabilis.

Look, you need an addition “(with its ins and outs)” to make your point. Of course in no way had Dionysius Exiguus or the Venerable Bede an understanding of the number zero equal with the one we have. How could they? But to deny them any knowledge at all, is insensible. The argumenta of Dionysius Exiguus show very clearly that he entered into situations which imply a number zero, and it is fascinating to watch him struggling with this difficulty. And it is very obvious as well that he was aware of the situation. Indeed, if Dionysius Exiguus did anything new in comparison with Alexandrene computistics, it has invariably to do with this number-zero-situation.

Jan: Creating a decimal positional system we need nine different symbols for the first nine positive integers (e.g. the digits 1, 2, 3, 4, 5, 6, 7, 8, 9) and thereupon (not earlier) a tenth symbol (e.g. the digit 0) to make it possible to compose a symbol (e.g. the symbol 10) for the tenth positive integer. And thus it has gone.

This may be true. But mathematically it is irrelevant. Mathematically the numbers are ordered by <, so that -1 < 0 < 1 etc. This is why in the mathematical way of counting, 0 precedes 1.

Ulrich Voigt 84.143.84.205 14:02, 21 July 2007 (UTC)

Century zero

Bede`s method to compute S = J mod 19 seems to have been the same as that used throughout the middle ages up to Christopher Clavius, viz. ( to put it in modern terms) making use of J = 100 x J div 100 + J mod 100 = 100 H + E, and S ( J ) = S (S ( 100 H ) + S ( E ) ).

I have already pointed to Roger Bacon`s neat way of representing this method.

This method was intended to calculate mentally S ( J ) by the following device.

To know S ( E ) you have to know the sequence 0, 19, 38, 57, 76, 95.

Here the number 0 can be neglected , as you must not be aware of its being there.

To know S (100 H ) there is a fine trick, viz. S (100 H ) = 5 x H mod 4 + H div 4.

E.g. to compute mentally S ( 1148 ) you have

S ( J ) = S (S ( 100 H ) + S ( E ) )

= S ( 5 x 11 mod 4 + 11 div 4 + S ( 48 ) )

= S ( 5 x 3 + 2 + ( 48 – 38 ) )

= S ( 15 + 2 + 10 )

= S ( 27 )

= 8

In fact, this computation was neatly split up into two independent parts by medieval computists, namely S ( 100 H ) and S ( E ), the difficult part being S ( 100 H ), of course.

Now, to accomplish this “difficult part” there is known a mnemonic device since the times of the Venerable Bede:

Look at the four principal fingers of your left hand, and number them 0, 1, 2, 3 // 4, 5, 6, 7 // 8, 9, 10, 11, etc., imagine these numbers on the finger joints, so that from bottom to top on your first finger ( = finger no. 0 ) you will find the numbers 0, 4, 8, 12, etc., on the finger joints of the second finger ( = finger no. 1 ) you will find the numbers 1, 5, 9, 13, etc..

These numbers are the “centuries” H.

Together with the sequence 0, 1, 2, 3, you should know the sequence 0 ( = 0 x 5 ), 5 ( = 1 x 5 ), 10 ( = 2 x 5 ), 15 ( =30 x 5 ), so what you actually will have to memorize is the sequence 0 => 0 , 1 => 5 , 2 => 10 , 3 => 15.

In the above example J = 1148 ( that is to say H = 11, E = 48 ), you compute 11 = 2 x 4 + 3.

From 11 mod 4 = 3 you know at once that the century to H = 11 will be found on your finger no. 3 ( = the fourth finger ). As 3 => 15, here you have the number to count from.

From 11 div 4 = 2 you know that you have to add 2 to 15, which can be accomplished by climbing up two joints of your third finger and count aloud: “15, 16, 17.”

Now let us try to understand this procedure with respect to the question if or if not knowledge of number zero must be admitted for Beda Venerabilis and the medieval computists.

Let us take for example the year 1200.

The very first step, 12 = 3 x 4 shows that there is no remainder left. But what to do with this “nothing here”? Which thought will lead you from this to your first finger if not the idea that there equally “is nothing”. So “nothing” constitutes the relation between the result of a veritable computation ( viz. 12 – 4 – 4 – 4 ) and the number of a finger.

And there is more: As the numbers on your finger joints represent the numbers H ( = J div 4 ), that is to say “centuries”, what does this “nothing here” on the bottom joint of your first finger mean if not “the century before the century H = 1 “? Do you have a better answer than simply H = 0? Of course, those medieval computists were at a loss to express this idea mathematically, as there is no Roman numeral for zero. But it is not possible to understand their construction without giving them credit of having formed a clear notion of a century zero, which can be “seen” at the bottom joint of your first finger.

Please note that the clever device to avoid the number zero by speaking of “remainder 4” instead of “reminder zero”, which even great Petavius resorted to, does not work with Bede`s finger joint machine. If in the example J = 1200 you switch from "zero" to ”4”, the matter will go wrong. As 1200 div 4 = 3, you should certainly count “0, 1, 2, 3”, and not “4, 5, 6, 7” to get the right result S ( 1200 ) = 3.

Ulrich Voigt 201.19.12.45 14:53, 11 April 2007 (UTC)

Philology? Mathematics!

We are talking about the history of a technical matter. So we have to enter into technical detail. This should be fairly common place, but funny enough, is not.

Jan Zuidhoek ( following George Desclerq ) argues that Dionysius Exiguus, though using “nulla” in a column which otherwise comprise only numbers, and in a place where we should expect 0 because of the underlying algorithm of that column, still did not know the number zero.

His argument is based on an analysis of the following text:

Dionysius Exiguus: Anno primo, quia non habet epactas lunares, … ( = In the first year, which does not have lunar epacts, ...).

Indeed, this does not sound like e = 0, but like “no epacts there”. Zuidhoek writes: “But as long as one is calculating with numbers of epacts as infants calculate with numbers of apples we cannot speak of ‘knowing the number zero’.” Which seems to mean that Dionysius did not only ignore the number zero, but the other numbers as well. In fact, Zuidhoek writes: “There where we say that the epact is 12, he [Dionysius Exiguus] says “duodecim sunt epactae”, which literally means “twelve are the epacts”, which boils down to “12 epacts”. And: “There where Dionysius Exiguus sees purely and simply a column of mutually related separate “numbers” of epacts (such as “12 epacts” and “no epacts”), it is our modernized brain which thinks to see a mathematical structure (a finite or an infinite sequence) of pure nonnegative integers. “

Oh sancta simplicitas philologiae! I wonder how that argument would run in face of the argumenta paschalia of Dionysius Exiguus, which do contain a detailed description of that very mathematical structure.

Sometimes the historian, trying to avoid the common mistake of anachronistically assuming the past to be identical with our present times, falls into the opposite trap in denying undeniable identity, and constructing a bewildering “past” which, alas, is nothing but his own fancy.

Ulrich Voigt 201.9.232.160 23:29, 11 April 2007 (UTC)

Jan: He did not consider his ‘nulla’ as an integer with which abstract calculations could be carried out actively.

This seems to be the point which made you follow the judgement of those ill-guided philologists. But you are completely wrong, as can be seen from argumentum 3 and 12 Dionysii.

Jan: By the way, DE and BV were skilled computists, but no mathematicians.

As to DE it is obvious that he did not just take over ready made mathematics from Alexandria but shaped it in a new way to make it suit the Roman calendar with january 1st as the first day of the year. And if it only was for the argumentum 12 (day of the week of january 1st ), he would deserve the title of a mathematician. This can be argued by comparison with modern attempts to find a formula for the day of the week. In Butkewich and Selikson, Ewige Kalender, Moskau 1970, you can read a series of different mathematical attempts being made since the 19th century. And the finest formula of them all is the Drosdow formula, invented in 1954. But the Drosdow formula is identical with the formula implicit in the argumentum 12 of DE. Of course neither Drosdow, nor Butkewitch and Selikson did dream of that. "Of course" because of either prejudice or ignorance.

The imagination of child-like DE just counting, as it were, his fingers, is very difficult to upheld in view of the fact that DE was mathematically more versed than so many modern mathematicians in handling the day-of-the-week problem. By the way, the number zero, which enters his device as consequence of "reducing the number of the year by one" is just the trick to ensure a formula independent of the distinction between leap-year and common year, a clever device, which was Drosdow`s trick. And his device of argumentum 3 to compute the epacte (again depending on the number zero) was just the device used by the Dutch mental calculator Wim Klein, again, of course, without knowledge of the historical origin of e = (11 J mod 19 ) mod 30. By the way, these matters are published in Ulrich Voigt, Das Jahr im Kopf. Kalender und Mnemotechnik, Hamburg 2003, S. 41 f.,151 ff. May be for our philologist-historian, the imagination that a simple computist of old is mathematically superior to himself, is somewhat hard to bear. Much more easy to imagine that with our modernised mind we overestimate the mathamatical capability of men like DE!

Ulrich Voigt 84.143.84.205 15:41, 21 July 2007 (UTC)

The dionysian epact

"Facilius namque ac brevius omnia argumenta pascalia calculabis", writes Dionysius Exiguus to explain the reason behind his mathematical commentary on his Easter table. This I take to mean that he used to calculate the relevant entities mentally. And, no doubt, his instructions are good enough to achieve this very aim.

The dionysian method to calculate the epacte e of a dionysian year j ( with S = j mod 19 ) boils down to e = ( 11 x S ) mod 30. Interesting enough it is just this formula which was proposed by the 20th century Dutch mental calculator Wim Klein to establish mental calculation of the Easter date.

And why did Dionysius Exiguus not avoid the epact and calculate directly the ecclesiastical full moon (he luna XIV)? Because g = ( 19 x S + 15 ) mod 30 would be more difficult for mental calculation. Certainly this is the reason why Wim Klein did not use g ( though Gauss, who did not care for the needs of mental calculation, did use g, avoiding e ), but only e.

The relation between g and e is given by the equation g = ( 15 - e ) mod 30, by the way, which, implying negative numbers, was not accessible for Dionysius Exiguus. Still he was able to infer luna XIV on april 5 (that is to say: g = 15 ) from e = nullus. After all the epacte is only a means to calculate luna XIV.

On the marble Easter table in Ravenna, which is parallel to Dionysius Exiguus, there are no epactes, but only lunae XIV. It is not known, if those Ravennatic computists did use epactes at all.

And what do our modern philologists have to comment on this fine mathematical device of our Donysius Exiguus to calculate the epacte? "[He is] calculating with numbers of epacts as infants calculate with numbers of apples", and: "it is our modernized brain which thinks to see a mathematical structure". Oh boy! It is your modernized mind which makes you unable to understand or even perceive a mathematical endeavour which is not in line with our modernized terminological equipment!

Strange to say: To-day the authority of the philologist-historian, who does not understand mathematics, and does not even wish to understand it, nay, does every effort to avoid looking at mathematical structures (as represented in Germany by illustrious names like Grotefend, Krusch and Borst), is so overwhelming that even the mathematician-historian bends to it and refrains of opening his eyes and judge himself. This holds true notably for Germany, the Netherlands, and England, but (happily) much less so for France. Wikipedia, following what is generally believed to be sound knowledge, is only the victim of a (momentary) retrograde scientific development.

Ulrich Voigt 12:33, 17 April 2007 (UTC)

Reply to Ulrich Voigt’s criticism on www.millenniummistake.net

1 Ulrich Voigt says in his “On symmetry”: “But symmetry is not a condition of sound chronology”. Of course symmetry is not a necessary condition of chronology, but why should the christian era (without year zero) be unsound? The bilateral symmetry in question is only a consequence of the choice Bede made. Of course bilateral symmetry was never “mentioned by any computist or chronologer as an important (or even unimportant) condition to be observed in chronology”, but during ten centuries its consequence, i.e. the non existence of a year zero, has not been experienced, by historians, as an inadequacy of the Christian era, the opposite is true. It is remarkable that the objection argued by Ulrich against the “Bede system” (which has no century zero at all) is just an objection against the “Cassini system”. In the “Bede system” the first century AD corresponds perfectly to the first century BC, the second century AD corresponds perfectly to the second century BC, etc.. Tell me, Ulrich, what must be the first century BC in the “Cassini system”?

2 (“Knowledge of the number zero”) “Being acquainted with the number zero implies ‘knowing how to carry out abstract calculations with the number zero’” is in general an inadequate formulation indeed, in which the second “the number zero” has to be replaced with “any numeral zero”. The reverse implication is true as well, for it is a matter of abstract calculations. The general formulation thus obtained is a reference to the fact that knowing how to calculate with any numeral zero is a necessary and sufficient condition for knowing the (abstract) number zero.

3 (“Knowledge of the number zero”) There where Dionysius Exiguus calculates with (abstract) positive integers, as soon as the (abstract) number zero comes into sight (i.e. enters our field of vision) he lapses into a less abstract terminology (no epacts or nothing instead of zero), and so does Beda Venerabilis. So it is not absurd to deny knowledge of the (abstract) number zero (with its ins and outs) for Dionysius Exiguus and Beda Venerabilis. So “Here we see a very strong prejudice at work, ……” is no more than a premature conclusion by Ulrich which I can not take seriously.

4 ("Knowledge of the number zero”) Why it should be wrong to consider 0 as our tenth digit? Counting precedes calculating, personally as well as historically. Initially one counted (and children count) by means of the cardinals one, two, three, four, …… (in words). Thus without zero, for if we have nothing, then we have nothing to count. Creating a decimal positional system we need nine different symbols for the first nine positive integers (e.g. the digits 1, 2, 3, 4, 5, 6, 7, 8, 9) and thereupon (not earlier) a tenth symbol (e.g. the digit 0) to make it possible to compose a symbol (e.g. the symbol 10) for the tenth positive integer. And thus it has gone. For instance, Gerbert, the French mathematician who became pope Sylvester II in the year 999, knew of the first nine digits (and their real significance), but at any rate he did not know the real significance of the digit 0. It is the digit 0 which has enabled us to construct our decimal positional system. Like inventing the number zero, inventing the digit zero did not take place “in the mathematical way”.

5 (“Philology? Mathematics!”) DE was familiar with the positive integers (e.g. 7 - 5 = 2) but not with the (abstract) number zero (e.g. 7 epacts – 7 epacts = no epacts). He did not consider his ‘nulla’ as an integer with which abstract calculations could be carried out actively. By the way, DE and BV were skilled computists, but no mathematicians.

6 (“Philology? Mathematics!”) Long before the invention of the number zero (in India in the sixth century) only precursors of the number zero were used (e.g. in Egypt and in Mesopotamia), i.e. symbols representing an empty spot in a positional system or words representing literally ‘nothing’, which however were not considered by their users as (abstract) numbers with which abstract calculations could be carried out actively. In the same way DE and BV did not consider their ‘nulla’ or ‘nullae’ (meaning ‘no epacts’ or ‘nothing’) as an (abstract) number. For DE and BV as well as for us ‘adding nothing’ boils down to ‘doing nothing’. But to be able to conceive refraining from any action (‘adding nothing’) as a special case of adding something (‘adding zero’) it takes more than arithmetical skill. Of course it is not DE or BV but Ulrich who makes use of our modern mathematical notation system (including mod and div, and digit and number zero) to reproduce their arithmetical lines of thought. Anyway, BV obtained his computational skill from DE in a roundabout way, and DE did so from Alexandrian computists of around the fourth century. As a matter of fact, DE and BV had only to extrapolate from Alexandrian easter tables. So the arithmetical content of DE’ and BV’ easter tables (impressive though it is) is essentially no more than the arithmetical content of their predecessors’ easter tables. But the number zero (with its ins and outs) in fourth century Alexandria is an anachronism. Thus, the opinion that DE en BV should be acquainted with the number zero remains without any rational basis. Of course this does not exclude that they, mentally calculating, had a zerolike idea in mind, for which they had no special symbol, but only a latin word meaning ‘nothing’. This so-called Latin zero has its origin in the so-called Alexandrian zero, for which the Alexandrian computists had not a special symbol either, but only a word (‘albo) meaning ‘nothing’, which was not considered by them as a number. It was the great Indian mathematician Brahmagupta who (about the year 630) was the first who not only used the digit zero in his calculations but also made explicit the most important properties of the number zero. Jan Zu 21:55, 10 July 2007 (UTC)

Jan! I answered your points above under the corresponding numbers.

Ulrich 84.143.84.205 19:45, 21 July 2007 (UTC)

Start of an era

Hi there,

I'm getting crazy of all the discussions about the start of an era.

As far as I know:

When you follow the Common Era (used in the Gregorian Calender) you count the era that is currently running. In other words. The 1st century(first 100 years), is the century that start at 001 and ends when 100 years are over.

Same with millenniums. The second millennium(second era of 1000 years) start at the start of that 1000 years(01 Jan Year1001) and ends after those 1000 years(31 Dec Year 2000).

So, why is it not the same with years ?

The 4th century start at 301 and ends at 400.

The 1st century start at 1 and ends at 100.

The first year ends when 1 year is over and is called Year 1.

So.... There is no Year 0. Same as there is no Century 0, millennium 0 and week 0.

I just don't get the problem with this, it is just that easy, and when not, please tell me in a short story why not.

User:TijhofGraphics 13:07, 30 September 2007 (UTC)

Fact remains that the distribution of leap years in the Gregorian Calendar implies that the (Gregorian) centuries start with 00 (and not with 01).

Ulrich Voigt 84.143.86.6 19:56, 7 October 2007 (UTC)

"There is no Year 0" - what, exactly, does this statement mean to say? Nothing!

Ulrich Voigt 84.143.112.57 10:31, 29 October 2007 (UTC)

It means that both eras, AD and BC, are defined with counting index (i.e., the first cardinal number assigned to them) "1" rather than "0". The index can be any number. Most frequently used are "1" and "0". The "year 0" is introduced by some when they join both eras in a sequence. Some thought that there should be a "0", for misunderstood arithmetic needs.

This article, in fact, could be condensed in a few statemnts:

• Of application to the Gregorian Calendar, as defined.
  • The AD and BC eras are counted with index "1".
  • The AD era increases to the future.
  • The BC era inceases to the past.
• Corolary: there is no "year 0" intercalated between both eras.

Suggested TODO:

Recast the sentences with the appropriate wikilese, insert the few relevant references, and for deference to the zero and zeroth confusion explain that both scales don't need to be in sync, e.g., the 1st term can be 0, or -395, or any number. This applies also to deconvolute elaborate discussions concerning an inexisting 13th floor. The 13th floor exists always, but sometimes it is assigned the number 14.

Jclerman 21:06, 29 October 2007 (UTC)

The 13th floor exists always, but sometimes it is assigned the number 14.

The year 0 exists always, but sometimes it is assigned the number 1.

The AD and BC eras are counted with index "1".

This implies that these two "eras" have two different epoch years.

The AD and BC eras are counted with index "0".

This implies that these two "eras" have the same epoch year.

The zero and zeroth confusion only exists in the heads of those who try to defend the common practice (of indexing by "1") by rational argument.

Ulrich Voigt 84.143.68.224 16:15, 9 November 2007 (UTC)

edit and spawn

Like they say, the rest should go to history. After the numerics are clearly based on the meaning and use of counting index, all the references to Bede and the Romans should go to an article on the Gregorian Calendar and/or its history. The Year 0 article should be to clarify that such a datum has not been defined. The other topics belong, obliquely, to calendar history and to counting indices. Spawn them and the waters will be clearer. Jclerman 02:21, 30 October 2007 (UTC)

Jclerman: The Year 0 article should be to clarify that such a datum has not been defined.

How can this be the case? After all the Year 0 clearly is defined, and even well established since the times of Cassini I.

Jclerman: Spawn them and the waters will be clearer.

I hope that Wikipedia is not the instrument to enforce confused thought by force.

Ulrich Voigt 84.143.68.224 16:26, 9 November 2007 (UTC)

Jclerman: Like they say, the rest should go to history.

The rest comprises "Bede and the Romans" and "the Gregorian Calendar". So, let me ask: What is left once you discard the rest?

Ulrich Voigt 84.143.67.237 11:59, 11 November 2007 (UTC)

counting index - what's that?

It might be simpler to replace "index" by "counting origin" since the concept is not clearly defined elsewhere in the Wikipedia. Jclerman 11:13, 30 October 2007 (UTC)

comments by samhastings

+This article is a case in point in favor of being very explicit when referring to years. My comments will show cardinal years with a capital Y. Let us consider the sequence of years as set up by Cassini and LaHire: 1BC,0,AD1. Does the numeral 1 represent the first year or Year 1? If we say it represents the first year then 0 ought to represent a zeroth year (which does not exist). So we have Year 1 BC, Year 0, Year AD 1. One presumes that Year 0 represents the "interval" which Cassini later abandons in favor of equating it with Year 1 BC. The sequence shown above looks like two sequences of cardinal numbers with a missing Year 0: Year 1 BC, Year 0 BC, Year AD 0, Year AD 1. Now let's look at the concept of a Year 0 BC and a Year 1 BC immediately preceding a Year 0 AD. An important argument against invoking Years 0 and 1 (both BC) is that both would have had to begin with January first. The years BC are not a mirror image of the years AD in a "cardinal" sense. In effect Dionysius planted a "STOP" sign ("Zero") with AD years following. The only Year 0 and Year 1 associated with any calendar extant at the onset of Dionysius' calendar would have had to be at the onset of the referenced calendar. For example, the first year BC would have been the 3760th in the Hebrew calendar. Any Year 0 associated with the Hebrew calendar would have been 5767 years ago (give or take several years). Thus we have eliminated Year 0 BC and Year 1 BC from the sequence set up by Cassini and LaHire (as modified above). What we have left is simply Year AD 0 and Year AD 1. Obviously Year AD 0 is the first year AD and Year AD 1 is the second year. Now I think it is clear that the first day of the third millenium was January first, 2000. January first, Year 0 AD is quite obviously the start of a leap year. Samhastings 66.93.220.197 (talk) 21:06, 18 November 2007 (UTC)

Samhastings: "Let us consider the sequence of years as set up by Cassini and LaHire: 1BC,0,AD1."

It is of importance to know that LaHire and Jaques Cassini (= Cassini II) were not the first to use this sequence, but Giandomenico Cassini (= Cassini I). Cassini I had a much deeper understanding of the niceties of the Dionysian system than his son Cassini II.

Samhastings: "Does the numeral 1 represent the first year or Year 1?"

Once you use the Cassini system this question looses all its sense: the number of years correspond to the integers (once you introduce 0, you can safely idetify 1 BC = -1 AD etc.) which, alas!, have neither beginning nor ending.

Samhastings: "In effect Dionysius planted a "STOP" sign ("Zero") with AD years following."

I do not understand this statement. Could you, please, explain yourself more clearly?

Samhastings: "Any Year 0 associated with the Hebrew calendar would have been 5767 years ago (give or take several years)."

Why this imprecision? Actually the Hebrew calendar can only be understood if you take into account the year before Tishri 1 year 1. Gauss, in his attempt to tranform Hebrew calendar into mathematics, started expressly from 1 Nisan Year 0.

Ulrich Voigt 84.143.73.74 (talk) 22:50, 25 November 2007 (UTC)

Ulrich: I was responding to the Cassini quoted in the Article: Third:Once More. Does it make any difference which one was quoted? If so, please explain.

I refer to the numeral 1 used in the section I was concerned with. It certainly does make a difference. There is no zero in the ordinal system and I needed to establish that his setting up the sequence Year l BC, Year 0, Year AD 1 was an imcomplete set of two cardinal systems and did not satisfy his conclusion that the sum of the three Years was 2. The sum is 3.

Dionysius Exiguus set up a new calendar system. It started at zero, an infintesmal point of time. That Year was Year 0 AD (or CE). That infinitesmal point was the STOP sign I was referring to. All the years before that time belonged to whatever calendars were extant at the time.

The Year 5767 was given to me by a local rabbi. Is the exact Year important. We all know that Dionysius miscalculated by a few years.

Samhastings 24.242.42.17 (talk) 04:16, 28 February 2008 (UTC)

No astronomer uses the proleptic Gregorian calendar

No historian – excepting some Maya-historians – uses the proleptic Gregorian calendar.
Just like all astronomers use Julian Calendar for all dates before AD 1582, Oct. 15. (Cf. for examples: the Meeus tables)

1. Gregorian centuries are unequal. Therefore the astronomers prefer the all-equal Julian centuries.
2. It doen't be unusual that historians refer to astronomical data, thus astronomers must deliver their dates in the same format, excepting well-known -1 year in BC.
3. Mere very incompetent, falsely "hypermodernist" astronomical algorithms implement the proleptic Gregorian Calendar. Denied by all serious astronomers.

Thus the Cassini Year Zero refers well to the Julian Year 1 BC.

-- Gluck 123 11:28, 1 December 2007 (UTC)

This is certainly true. But it still implies the equation "0 AD = 1 BC" for the Gregorian Calendar.

Ulrich Voigt 84.143.107.232 14:20, 3 December 2007 (UTC)

No. An equation implies that all terms have been defined, i.e. that are within the valdity domain of the set. Since 0 AD [sic] has not been defined, that is not a valid equation. Jclerman (talk) 04:22, 5 December 2007 (UTC)

+Nor has 1 BC. Does it stand for the first year BC? It seems to me that the only cardinal Years BC belong exclusively to any calendars extant at the moment Dionysius established his calendar. Samhastings 24.242.42.17 (talk) 17:50, 1 March 2008 (UTC)

I really want to insert the following sence into the article, but I'm sure you won't like the grammar...

I will be glad if someone will rewrite it and add it to the "Numerical Explenation".

thanks a lot --217.132.56.202 (talk) 15:36, 8 January 2008 (UTC)

Jean Meeus (born 1928) speaking

The Belgian Jean Meeus is author of the famous book Astronomical Algorithms, a man of international renown.

Here I cite from Chapter 7 The Julian Day (p. 60 of the edition 1998):

"There is a disagreement between astronomers and historians about how to count the years preceding the year 1. In this book, the "B.C." years are counted astronomically. Thus, the year before the year +1 is the year zero, and the year preceding the latter is the year -1. The year which the historians call 585 B.C. is actually the year -584. (Do not use the mention "B.C." when using negative years! "-584 B.C.", for instance, is incorrect.)

The astronomical counting of the negative years is the only one suitable for arithmetical purposes. For example, in the historical practice of counting, the rule of divisibility by 4 revealing the Julian leap years no longer exists; these years are, indeed, 1, 5, 9, 13, ... B.C. In the astronomical sequence, however, these leap years are called 0, -4, -8, -12 ..., and the rule of divisibility subsists."

End of quotation.

It is all too obvious that "astronomical" counting (including 0) is good enough for the purpose of history, but that "historical" counting (excluding 0) ist not good enough to serve the purpose of astronomy or computistics.

Ulrich Voigt 84.143.85.197 19:07, 11 January 2008 (UTC)

This is the exact text appeare in answers.com

http://www.answers.com/year%20zero —Preceding unsigned comment added by 217.132.56.202 (talk) 18:36, 12 January 2008 (UTC)

Yes, see what they say at the bottom of the page: FilipeS (talk) 20:16, 12 January 2008 (UTC)

'This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Year zero".'

current changes

I did some preliminary reorganizing of the outline of the article. I will later draft some paragraphs about granularity and index as related to calendars. Hopefully it will contribute to coalesce the text into something useful to stop the endless loop of the current fruitless recursive discussion about the BC/AD transition. Jclerman (talk) 22:26, 1 August 2008 (UTC)

Gregorian system numbering

Problems:

• No sources in the section.
• It appears to be back-derived from the 3rd millennium section now contained in it (which also didn't have sources)
• There's no consensus as to where decades start; the Wikipedia consensus is that 1910s go from 1910 to 1919, not 1911 to 1920.

Not IMHO, the Wikipedia article decade says:

A decade may also be a well-defined historical period of ten years in a dating system. In that sense, the first decade of the 20th century indicates a period from January 1, 1901 until December 31, 1910.

Jclerman (talk) 20:36, 6 August 2008 (UTC)

There is consensus in and out of Wikipedia for days-in-month, months-in-year, centuries (not years-in-centuries), millennia, and the AD/CE and BC/BCE eras. (If that's what you mean be era, you need to say it. It's not standard.)

• Did I say there were no sources for the section?
• — Arthur Rubin (talk) 19:24, 6 August 2008 (UTC)

I have removed the statements that years within decades, centuries, and millennia begin with one as original research. However, they may be added provided that a non-Wikipedia source can be provided, AND, because it is contentious, that the other view that years within each are counted from zero is included according to Wikipedia's neutral point of view policy, which is non-negotiable. Sequentially counting the days of a month is a modern invention—the 1582 papal bull announcing the Gregorian calendar, Inter gravissimas, written in Latin, uses the Roman method of counting backwards inclusively. — Joe Kress (talk) 22:04, 6 August 2008 (UTC)

"AND, because it is contentious, that the other view that years within each are counted from zero" Erm, there's such a thing as having a neutral point of view, but if we accept the opinion that centuries and millenia start with say 2000 and not 2001, then you would have to say that "year zero" exists, which is contrary to this article, and established facts: i.e that year zero does not exist. Deamon138 (talk) 22:37, 6 August 2008 (UTC)

OR, one of the decades/centuries/millenia has only 9/99/999 years...

See the meaning of Corollary and a reference to the western calendar now included in the article. Jclerman (talk) 22:47, 6 August 2008 (UTC)

By the way, can people stop removing Jclerman's edits please, as has just happened again. This is becoming an edit war. This isn't a BPL, so there's no need for people to be so harsh against what is perceived as unsourced material. Please leave in and discuss. If CONSENSUS finds that we need sources, then they will be found or else the info is removed. But we don't need to remove it straight away since this is not a BPL, and the info is hardly POV pushing. There is lots in this article that isn't sourced but you're not removing that. Please seek consensus that sources are needed before removing. Thank you. Deamon138 (talk) 23:07, 6 August 2008 (UTC)

Nonsense. As always, it's the responsiblity of the editor adding material to justify it. As for specifics:

• The attempt to justify consensus (not Wikipedia consensus) as to the start of decades/centuries/millennia with arithmetic is meaningless.
• The use of the word corollary is just wrong.
• Mathworld is wrong as to terminology more often than not; if there is any contrary source, even Wikipedia, Mathworld should be ignored. (Note; I've added Mathworld as a source to some articles, but primarily to contradict other Mathworld sources in that article.
• It's still apparently Jclerman's WP:OR, particularly the assertion that the decade/century/millennium issue is a matter of indexing.
• Unless some uninvolved admin protects the article, or if some argument for the new version is provided, I'm going to revert to the stable (and accurate, although not presently sourced) #3rd millennium form within a few days. — Arthur Rubin (talk) 08:10, 7 August 2008 (UTC)

"The use of the word corollary is just wrong." If you think it is used wrong, correct it with a better word, don't delete it. Bad grammar or formatting is not a reason to delete a whole section.

"Mathworld is wrong as to terminology more often than not; if there is any contrary source, even Wikipedia, Mathworld should be ignored." No-one cares if you think a source is wrong: that is original research.

"I've added Mathworld as a source to some articles, but primarily to contradict other Mathworld sources in that article." If you think Mathsworld is so wrong, and yet you add it in other places, clearly it is a reliable source. Unless you were trying to make a point?

"As always, it's the responsiblity of the editor adding material to justify it." Yes when challenged. WP:BURDEN does say, "The burden of evidence lies with the editor who adds or restores material", but it also goes on to say, "Any material lacking a reliable source may be removed, but editors may object if you remove material without giving them sufficient time to provide references." That is the thing really: time. There is big message across the top of this page saying, "This article is actively undergoing a major edit for a short while" which was added by Jclerman. This tag also says,"This message is intended to help reduce edit conflicts" and clearly there will be a lot of edit conflicts if people keep deleting whole sections. Maybe you didn't see that message?

Now let's take a look at the totally disputed tag you added to this page. It says, "The neutrality and factual accuracy of this section are disputed." Firstly, what in particular isn't neutral about this section? It follows on basically from the concept of the calendar not having a Year zero. Is there some verifiable source that you can provide that says that there is a year zero? If not, then there is no neutrality dispute.

Let's also look at this section's factual accuracy. At WP:AD, it says, "The accuracy of an article may be a cause for concern if":

• "it contains a lot of unlikely information, without providing references." Please show in what way this information is unlikely.
• "it contains information which is particularly difficult to verify." You haven't tried to verify this information, so this doesn't apply.
• "in, for example, a long list, some errors have been found, suggesting that the list as a whole may need further checking." This isn't a list so that doesn't apply.
• "it has been written (or edited) by a user who is known to write inaccurately on the topic." Are you accusing Jclerman of this? Please state other areas in this subject area that he has written inaccurately in if this is the case.

"The attempt to justify consensus (not Wikipedia consensus) as to the start of decades/centuries/millennia with arithmetic is meaningless." Please provide the reasoning for the "alternative" view: i.e. that even with a year zero, the 3rd millenium started in 2000 and not 2001.

"It's still apparently Jclerman's WP:OR, particularly the assertion that the decade/century/millennium issue is a matter of indexing." Again, how is not? You are just making statements like "It isn't based on arithmetic though" but not showing why not. If the first AD year was Year 1, then the tenth would be Year 10. Since a decade is defined as "a group of ten years" more or less, then how can Year 11 not be the start of the second decade? The same can be said of Centuries and Millennia.

"Unless some uninvolved admin protects the article, or if some argument for the new version is provided, I'm going to revert to the stable (and accurate, although not presently sourced) #3rd millennium form within a few days." If you believe that section is accurate, why delete it? You should be looking for sources if you think it needs them.

Most of this section follows from arithmetic as has been said, so very few sources are needed. You don't need a source to say the sun is blue or 2+2=4, so why here? The only problem with this section is maybe it could be written better and the links could be inline: but those aren't reasons to delete it, those are reasons to help Jclerman out and fix it. Deamon138 (talk) 17:09, 7 August 2008 (UTC)

The "alternative view", as you put it, that the presence of a year 0 has something to do with millennia starting with 1, is a WP:SYNTHESIS of alternative views, and should not be here.

The assertion that it's based on arithmetic is clearly (well, to me, anyway) wrong. No detailed assertions that arithmetic is involved have been made to be verified or falsified.

The current (Jclerman) section is just wrong. The #3rd millennium version is correct, but unsourced.

And I'm beginning to lose faith in the assumption that you are acting in good faith. — Arthur Rubin (talk) 16:48, 8 August 2008 (UTC)

Gregorian system numbering (copy)

Moving the section here, so it can possibly be improved. The work that needs to be done:

• Needed: support for it being an indexing question (and Mathworld is not an adequate source, even for the definition of "indexing"). This may be accurate, but it was better expressed in the #3rd millennium version.
• The granularity sentence actually looks good, but needs a reference (and Mathworld is, again, inadequate)
• Needed: support for it having something to do with arithmetic.
• The paragraph beginning "Corollary" is totally incomprehensible, but there's no concept of which this is a corollary. The Clarke and USNO statements, after rephrasing, probably can be used to support the #3rd millennium paragraph. The "era" version might be supportable. — Arthur Rubin (talk) 17:00, 8 August 2008 (UTC)

• {{totallydisputed-section}}
• {{OR|section}}

Further information: [[:Gregorian calendar, Anno Domini and Dionysius Exiguus]]

Two main schemes or systems are used for numbering the elements of a set. The systems are named according to the value of their first indexed[5] element. Hence they are known as:

• scheme based on counting index 0, and
• scheme based on counting index 1.

The Gregorian calendar (with its extensions as implemented in the current western calendar) consists of several levels of granularity, namely: month, year, decade[6], century, millennium, and era. Gregorian years within either the AD and BC eras have a counting index 1. Hence, the first year of the AD (or CE) era is AD 1 and the first year of the BC era is 1 BC.

Corollaries based on arithmetic, summary statement by Arthur C. Clarke[7] and counting practices described by the USNO[8]:

• the first/last years of the decades are 1/10, 11/20, 21/30, ... 1981/1990m, 1991/2000, ...
• the first/last years of the centuries are 1/100, 101/200, ... 1901/2000, 2001/2100, ...
• the first/last years of the millennia are 1/1000, 1001/2000, 2001/3000, ...

---

"The "alternative view", as you put it, that the presence of a year 0 has something to do with millennia starting with 1, is a WP:SYNTHESIS of alternative views, and should not be here." I assume you're referring to the sentence above, where I said, "Please provide the reasoning for the "alternative" view: i.e. that even with a year zero, the 3rd millenium started in 2000 and not 2001"? That should've been "without a year zero", sorry about that, that would be a typo on my part.

"And I'm beginning to lose faith in the assumption that you are acting in good faith." I'm sorry, but I am trying to act in good faith (though if I was acting in bad faith I would say that lol!). What in particular makes you think that I'm acting in bad faith?

"This may be accurate, but it was better expressed in the #3rd millennium version." Well personally, I believe these two sections should be merged together imo.

Now I'm going to look at the two tags that you have given:

Firstly, the "totally disputed" tag. This says that "The neutrality and factual accuracy of this section are disputed." Right, this means you dispute the neutrality and factuality of this section. What in particular is factually inaccurate, i.e. false, about that section by Jclerman? It looks truthful to me. Whether there is anything else wrong with it is besides the point right now, you dispute its factual accuracy, therefore there must be something untrue about it. What is it?

You also dispute it's neutrality. Okay, so what isn't neutral about it? For something to be non-NPOV, there has to be two or more points of view, and one of them has to be covered inadequately. At the moment the section contains the POV that the fact there is no year zero means that millenia or whatever start on a year ending in one. What is the alternative point of view that isn't making the neutrality balance? Perhaps you are referring to the belief of most laymen, that the third millenium started in the year 2000? But laymen, ordinary people, or whoever, are not reliable sources, and this would be violating WP:FRINGE surely? Anyway, if this is the other POV that you meant, then you have to show us that this belief is professed in reliable sources. If you can do that, that will be fine.

Now onto the other tag you added: the OR tag. This says, "This article or section may contain original research or unverified claims." So you are suggesting that the section isn't sourced adequately. One problem you have is "Needed: support for it being an indexing question (and Mathworld is not an adequate source, even for the definition of "indexing")." Personally, I've never used Mathworld really. Looking at the site, it looks okay. Why isn't Mathworld a reliable source? Seriously, I'm not being difficult, I don't know. If Mathworld is a reliable source, I think what it is doing is okay at the moment. However, I think the part, "Hence they are known as: scheme based on counting index 0, and scheme based on counting index 1" probably needs a source. Another problem you have is "The granularity sentence actually looks good, but needs a reference (and Mathworld is, again, inadequate)" I agree that Mathworld doesn't do a lot here, but personally, I don't see why "The Gregorian calendar (with its extensions as implemented in the current western calendar) consists of several levels of granularity, namely: month, year, decade[6], century, millennium, and era." needs a source. Personally, the fact that years, decades, centuries etc (though I don't get the "era" bit) make up the calendar seems like one of those self obvious things that Wikipedia says you don't need sources for. But if you think that it needs a source, that is fine. But really it shouldn't be too hard to find such a source, so maybe it would've made sense for you to look for one, instead of tagging the page with the OR tag. Imo, the amount that might need sourcing is small compared to the stature of the tag, surely one or two of those "cite" superscript things in the text would've been better?

The final OR problem you have is "Needed: support for it having something to do with arithmetic." I don't think this needs to be sourced personally (obviously a source wouldn't hurt, but isn't necessary imo). Of course, there is the Clarke and USNO sources there, but what other information needs to be sourced that either doesn't come from those, or the arithmetic that I am about to show you? If there is no year zero, then the first year of the AD era is 1 AD. The second is 2 AD, the third is 3 AD etc.... the eighty-first is 81 AD etc.... the ninety-eighth is 98 AD, the ninety-ninth is 99 AD, and the hundredth is 100 AD etc. Since a century is defined as a hundred years, then the start of the first century AD was 1 AD and the end was 100 AD. Thus it follows that the start of the second century AD is 101 AD, and so on. All that required was adding 1 onto the years repeatedly until the required number is reached i.e. Simple arithmetic. It doesn't need a source I feel.

So to summarize, what do I think needs to be done? The following:

1. "Hence they are known as: scheme based on counting index 0, and scheme based on counting index 1" needs a source or to be rephrased.
2. I don't understand the era bit, can someone explain it to me? I tried looking at the link, but I didn't know which bit was what I needed to know. What exactly is an era? I always thought it was this hypothetical period of time e.g. the Victorian era.
3. "The Gregorian calendar (with its extensions as implemented in the current western calendar) consists of several levels of granularity, namely: month, year, decade[6], century, millennium, and era." needs a source if you so wish (never mind the "era" bit I don't understand). If I'm not too busy, I'll help out if I can, and you still want such a source.
4. Sorry Jclerman and no offense, but I do think a bit of the style, formatting or phrasing could be worked on. But that's okay, it was done by one user, now we have a few of us here, and (this is one of the beauties of Wikipedia) working together we should be able to fix that.
5. Possibly the third millenium section could be merged into here?
6. If there are factual inaccuracies, I want you or someone to explain to me what they are. What is incorrect?
7. Finally, if there are POV problems, I want you or someone to explain (and source reliably) the other point of view that is needed to make it neutral, the one that I asked about above but made a big "boo-boo" with the typo, i.e. that even without a year zero, the 3rd millenium started in 2000 and not 2001. Unless of course there is a different point of view that I am overlooking. Whatever it is, can someone tell me?

Okay, I hope that lot above makes my views clearer. If not I'm sorry. But anyway, thanks if you can answer any questions above, and/or show me where my reasoning might have failed here. Deamon138 (talk) 20:06, 10 August 2008 (UTC)

In order corresponding to the original statement:

Using the computer science definition of "indexing" (which, oddly enough, doesn't appear elsewhere on Wikipedia or Wiktionary, as far as I can tell) to apply to the "year zero" question is probably correct, but requires a source of some sort. Mathworld provides a source for this definition of indexing, but not its applicability. This strikes me as an example of WP:OR.

For the granularity sentence, the apparent intent was for era to refer to AD or BC. That makes sense, although it needs to be stated, and it doesn't match the Wikipedia article. Perhaps day could be restored to the list of "granuals"(?). I think that also requires a source, but I really don't see any objection to it. Using the mathworld as a source for decade is just wrong. I think this one might be considered "common knowledge", even though we're generally not allowed to use that as a source.

Corollary is just wrong (requires it be a consequence of something like a theorem, which is not present), association of the problem with arithmetic is either incorrect or NPOV (depending on your definition of "arithmetic", and is clearly OR. Neither Clarke nor USNO used anything resembling "arithmetic".

The final year begin/end are logical consequences of what appears to be the intent of the rest of the section, except that the "decade" is wrong as to common usage and ambiguous as to technical usage.

Perhaps there really isn't any NPOV except as contained within the OR, there is some OR which is not necessarily incorrect.

— Arthur Rubin (talk) 02:51, 11 August 2008 (UTC)