Talk:Year zero

Archive 1 12 June 2004 – 11 February 2006
Archive 2 15 November 2005 – 11 August 2008

Chronologists

+I wonder if Cassini, La Hire and "several chronologists" ever considered the confusion their abandoning the n, n-1 sequence in favor of an n only representation of years. They equate the first year AD with Year l AD thus shoving Year 0 AD back to the first year BC. But what is sauce for the goose is sauce for the gander. The first year BC must be, according to their fiat, Year 1 BC, thus shoving Year 0 BC ahead one year. Now we have four years competing for two slots: Year 1 BC, Year 0 AD, Year 0 BC and Year 1 AD. Interesting. Wouldn't it have been better for Cassini to have stopped with the statement that " Year 0 is that in which one supposes that Jesus Christ was born"? Samhastings24.242.41.33 03:14, 1 December 2007 (UTC)

This "confusion" is only a product of ill-will. I can see no difficulty in equating 0 BC = 0 AD, nor in -0 AD = 0 AD. But without any doubt the best system would be ... -2 AD, -1 AD, 0 AD, 1 AD, 2 AD ... because this is in accordance with mathematics and there is no need to switch from "AD" to "BC" once you use negative numbers: entia non sunt multiplicanda praeter necessitatem. Of course this was in the mind of great Cassini, but out of courtesy he still kept the old denomination. This Cassini system is generally called "astronomical", because astronomers generally use it. It has nothing to do with astronomy though, but only with mathematics and computistics on the one hand and with the Alexandrene moon table on the other. By the way: I am not speaking about the same Cassini as you did. I refer to Cassini I, and you to his son Cassini II.

Wouldn't it have been better for Cassini to have stopped with the statement that " Year 0 is that in which one supposes that Jesus Christ was born"? - Certainly not, as Cassini was not a child, and knew very well to separate the question of the historical birthday of Jesus Christ from the construction of sound chronology.

Ulrich Voigt 84.143.107.232 08:55, 3 December 2007 (UTC)

+Ulrich: Is the notation Year 1 BC, Year 0, Year AD 1 not confusing to you? It is to me. There is a first year BC but not a Year 1 BC. So he abandons Year 1 BC, changes it to the first year BC and designates Year 0 as Year 0 AD. The arguments given in the Astronomers' section about the "interval" between the Years is faulty. We have three Years spanning one Year apiece so the sum is 3 not 2. I hope you don't find me exhibiting "ill-will". I just believe that the whole Astronomers' section fails to prove their point that the first year AD is Year 1 AD (n,n).

I'm still using my peculiar system of identifying cardinal Years with the capital letter. With that in mind I am assuming that your "best system" is - Year 2 AD, -Year 1 AD, Year 0 AD, Year 1 AD, Year 2 AD... This of course gives us 5 Years and the interval problem still exists. Also, I need to know your views on where to put Year 0 AD. Obviously I would want it to be equal (equivalent? or complementary  ?) to the first year AD(as in n,n-1). Thus we have a leap Year (like 2008), but it is inconvenient to have it as a Year as that causes it to interfere in the counting of years process. We need the ordinal numbers for that purpose. It seems to me that Year 0 AD presents a very serious problem that has yet to be solved. Samhastings24.242.42.17 (talk) 18:55, 29 February 2008 (UTC)

+Samhastings The best thing I could advise you to do is to forget about the distinction between Ordinal numbers and Cardinal numbers and restrict yourself to just "numbers", that is to say to Integers. "Integer" is a mathematical object whereas "Ordinal & Cardinal number" belong into the realm of application or fantasy.

Now, what old Cassini at bottom proposed to do is to use Integers to count years, which means to establish a one-one-relation between Integers and years. Once you look at it that way, you will perceive that there is no alternative to the so called astronomical counting (which, alas, has nothing to do with astronomy, but very much with mathematics). After this it will not matter if you call these years "AD" or "Christi" or "CE" or what not.

No, there is no problem in computing distances between Calendar dates. Between January 1 of year n and January 1 of year m, the distance is always n - m years.

Yes it is quite important that the year 0 was not introduced by Jacques Cassini or LeHire, but by great Giandomenico Cassini himself. The reason is this: It proves that "year zero" is not just a technical devise (as it turned out to be in the hands of down-to-earth Jacques), but reveals a deep historical understanding of the Dionysian moon table.

Ulrich Voigt (talk) 15:06, 25 April 2008 (UTC)

+Ulrich Voigt When you say that "the best system would be -2AD,-1AD,0AD,+1AD,+2AD", I ask if this sequence converts identically to the common era system? And I assume that we are talking about years as such. Is it not possible now that Year 0CE is equivalent to the first year CE? Samhastings24.242.42.17 (talk) 22:22, 4 May 2008 (UTC)

+Samhastings

"if this sequence converts identically to the common era system? "

Yes for n > 0. Once you admit year 0, you can use CE = AD for any years or you can just use + / - without any further term. This is one important advantage of "year zero": You have only one sort of years for all history instead of two.

"is it not possible now that Year 0CE is equivalent to the first year CE?"

The question makes no sense, as (once you admit 0) there is no first (and no last) year. The years are just numbered according to the sequence in Integers. Ulrich Voigt (talk) 20:25, 18 May 2008 (UTC)

+When you ask me to admit zero in the sense that it is in this statement taken from the "Astronomers" article: "Both Cassini and La Hire used BC years before their year 0 and AD years thereafter (hence the sequence 1BC, 0, AD1). That is why Cassini stated that their sum yielded the interval. For example, 1 + 1 = 2" you leave me perplexed. They refer to year 0 but it has no quantity associated with it. Three years, 1 BC, 0 and AD 1 are called years so the sum must be 3. Obviously I have to admit to a mystical (mythical?) year zero. If I am forced to do that I much prefer the sequence Year 1 BC, Year 0 AD, Year AD 1. Now we have a Year 0 AD for the first leap year and we can do away with the controversial (and to my mind the nonsensical) notion that the third millennium started on the first of January 2001. 24.242.42.17 (talk) 21:25, 23 May 2008 (UTC)

Yes. Rather nonsensical. The sume should be an algebraic difference, i.e., 1-(-1)=2. The interval that measures 3 is from the beginning of 1 BC (i.e., Jan 1) to the end of AD 1 (i.e., Dec 31) (assuming a year 0 intercalated). But when you evaluate the interval between (mm/dd/BC 1) and (mm/dd/AD 1) you find it to be 2 years, not 3. You all people should, for some time, forget the Year Zero and play with intervals and sequence numb3rs, e.g., like mathematicians do, with the fence and posts setup. You have 11 posts for 10 fence panels. And, surprise, the interval between panels MUST be equl to the interval between posts. (Assuming a regular periodic fence.) After you have practiced enough with such a syustem play to number the panels with any numbering system you wish, and evaluate distances, intervals, etc. Happy Calendar afterwrds. And yes, one of the panels can be assigned the numeral zero. Jclerman (talk) 22:41, 23 May 2008 (UTC)

Jclerman: I have always insisted that Dionysius had planted a stop sign at the beginning of his new calendar. It represented zero in my mind as the beginning of the first year. Your analogy with the fence posts and panels has helped me to take a new view of my stop sign, It follows that the first fence post (zero) is the beginning of the first panel (year Zero). Does this in any significant way interfere with the astronomers need? 24.242.42.17 (talk) 19:38, 25 May 2008 (UTC)

The first panel can be called (i.e., numbered) with any number. The most used numbering systems are two:

• a) System with origin (or index) zero, in which the first panel is numbered 0.
• b) System with origin (or index) one, in which the first panel is numbered 1.

The posts can also be numbered either with index 0 or index 1. Notice that the first element (post or panel) is always the first, independently of the names or numbers given to the posts (and/or panels). The little guy (Dionysius) defined his system as with "panels" and named/numbered the fist year as AD 1. This is consistent with all Gregorian calendrical entities (day, month, year, century, millennium, billennium) being based on index 1. The rest is, as they should say, history. Jclerman (talk) 23:03, 25 May 2008 (UTC)

+Jclerman: Present day commentators tell me that I should forget about cardinal and ordinal numbers. You, at least, give me an alternative. I prefer your system (a) origin or index 0. Dionysius did not have the numeral 0 available but there is no doubt that he "mulled" about "nulla" and other concepts of the absence of anything. Calendarians tend to ignore the initial part of any day, the hour. Dionysius had the opportunity every day to observe a sundial. He could see and appreciate the fact that (unknown to him as 0) the meridian (12 o'clock) was the start of the first hour. That was his 0. And it follows that the first hour was hour 0. When 30 minutes have passed it is 12:30 or 0 + 1/2. I have no doubt that the first hour was the initial point of all the calendrical entities you have mentioned. It seems to me that the sequence ...-2,-1, 0, 1, 2.... could satisfy the astronomers' needs.24.242.42.17 (talk) 17:36, 30 May 2008 (UTC)

What the brief monk saw, thought, or dreamed is absolutely irrelevant to the construction of his calendar. He chose index 1 as it already was in use for the other calendrical entities mentioned. BTW, the beginning is not Hour Zero, but Minute Zero. OOPS, shouldn't it be Second Zero? NO, NO, it should be Decisecond Zero, but no! it should be ...... Nanosecond Zero, or... I hope you get the gist. Where you wish to stop the granularity is your choice. Take each year as a panel of the analog model described above, i.e. granularity = 1yr. Within each panel you can measure or count time as you like, e.g., index 0 seems approprioate to measure intervals as with a stop watch. PLease don't assign mythical, mystical, or obscure higher standing to zero. Once adopted and their domains defined, all systems can coexist. Epson printer software tells me "printing page 0 of 1". That's because electrical engineers usually prefer index 0 (e.g. also to number the hardware components, and also the bits, etc in drives and other hardware; instead, programmers use index 1 to number the bits, bytes, etc of logical memory arrays, stacks, etc). Both systems can coexist and high-school math allows to convert between them. Sure it can appear conflicting when a memory's physical page and its corresponding logical page differ by 1, or more if binary and decimal systems coexist. In fact, programs have to be initialized before running, i.e. have to "know" which indexes and systems are used and where.

The litttttle monk would believe we are all crazy if he would be able to come back and read these threads. He was really very, very short. I can't remember the name of the artist that depicted him in a painting that I saw in the Phoenix art museum (Arizona, USA). I became familiar with his indexing in the period 1970-1990 when researching dating methods. The posts/fence model helped me as well as reaserching the origin of the arabic numbers.

Kind regards, Jclerman (talk) 23:24, 11 June 2008 (UTC)

+Well, I think you are teasing me just a little bit. I chose an hour to illustrate my point because I know Denny the Runt had a sundial available to him. It has a XII marking the meridian, the highest point of the sun in its travel across the sky. This marked the beginning of the first hour (or the thirteenth, if we are getting picky). Nowadays millions watch, either in person, or on TV, the falling of the ball in New York's Times Square and scream with delight when the ball hits bottom and indicates the end of one year and the beginning of another. The big question is "what year is it". Instantly the last moment of one hour disappears and the beginning of another appears. The beginning of your calendrical entries surely begin with the first hour and you don't have a I instead of the XII on your clocks or watches. I have railed against the weird explanations given in this article but I notice that the author admits that there is a first year BC and a first year AD. But he decided to assign year 0 to AD instead of BC thus putting him in agreement with you that the first year AD is also year 1 AD. I have a difficult time accepting that. 24.242.42.17 (talk) 23:54, 19 June 2008 (UTC)

No teasing at all, just exercising our minds in order to push the spectrum of Alsheimer's away. The usually quoted Apple keeps the M.D. doctor away. The PC keeps my brain active. Warning, spoiler follows. Physical duality and modular arithmetic take away the magic of the ticking celestial spheres that fall in Times Square. BANG! and two points in time are juxtaposed in a physical duality to be spoiled by the modular 'rithmeticist that is watching the scene on the Rabbit's pocket watch. The Rev (aka Lewis Carroll) who taught 'Rithmetik and other 'Rs would fully agree with the modulicist sitting in Times Square who squarily believes that these two instants are really one and the same: 2004-12-31 24:00 and 2005-01-01 00:00. Based on the same modular rules, 2010-01-10 is identical to 2009-13-10. [Homework: how does it work when there are interveaning leap years and/or seconds?]. Cheers, on today May 51. Jclerman (talk) 01:43, 21 June 2008 (UTC)

+Now, at last, I have to shoot the last arrow in my quiver. The hour is just as much a calendrical entity as the day, the week, the month, the year, the decade, the century and the millennium. Dionysius needed as much as any of us to be on time for his various daily obligations such as evensong. He probably could take care of the problem mentally - he wouldn't waste papyrus unnecessarily. Today we have monthly appointment books in which we can indicate our needs to carry out certain obligations. The midnight shift worker, for example, would pencil in this important deadline. He (or she) would indicate the time agreed upon to have breakfast with the spouse somewhere. Thus the hour is an important calendrical entity. A calendar day is defined as the period from one midnight to the next midnight. Thus the day starts at midnight (zero). So do each and every calendrical entity. The astronomers seem to need a very special numerical sequence to achieve their goals. I say let them do exactly as they need to but it makes no sense to me for the rest of us to see Wikipedia aver that the third millennium began on January 1,2001 when the arguments in favor of that conclusion are varying and inconsistent. 24.242.42.17 (talk) 03:06, 21 June 2008 (UTC)

You are absolutely correct. Within your system of definitions, linguistic and metrologic. But they do not agree with those established by the relevant authorities. None of the time units is a calendrical entity. By definition. You do not need to prove anything. Writing appointments in a book titled calendar does not make time units calendrical. I write mine on a roll (a paper towel) and it does not make them rollical, unless I follow your convention. Which is OK unlesss we want to communicate with others and they do not find such meaning codified in the catalog of definitions. Then, the short guy defined the AD era of the Gregorian Calendar with index origin one. Thus the BC era was also defined with index origin one. Other cultures have different calendars and each one has its particular index origin. The astronomers adopted a sequence that matches the sequences mathematicians use every day. All this by definition and no lengthy justifications are needed. Those are definitions and can not be tampered with. Then, since the Gregorian Calendar begins on AD 1, January 1, it follows that if a millenium contains 1000 years, the fist millennium begun on 1001, January 1. Any other date would be inconsistent with the Gregorian Calendar. The counting exercise goes like this: First year in the Gregorian Calendar, by definition, is AD 1. The first decade, by definition of decade, has to contain ten years which are these: AD 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. End of the first decade. Then the second decade contains the years: AD 11, 12, ....20. Go on counting like this and you will find when the 3rd millennium really begun. Cheers in the eigth year of the third millennium. or the year 1008 of the second millennium, or the year -992 of the fourth millennium. Jclerman (talk) 06:11, 21 June 2008 (UTC)

+At the dropping of the ball in Times Square, instantly the first hour of the New Year began as did the first year. If you have that year start at 1 then you must start your clock at 1, not 12. This is not possible. Did he truly have knowledge of the indices you cite? I believe he would have chosen Index 0 (which, of course, was not possible at the time). It looks to me that index 0 starts the cardinal numbering system and Index 1 starts the ordinal numbering system. The astronomers apparently cannot use either system but must invent their own. All attempts to force their system to work with well-established numbering systems seem doomed to failure.24.242.42.17 (talk) 23:47, 23 June 2008 (UTC)

+Really, JC, I most emphatically thank you for introducing the fence-line analogy. But you and I and everybody else have been chasing the wrong rabbit. The years (rails) are really not the answer to the dilemma, the posts are. If you had chosen index 0 instead of index 1 you would have identified the first post as 0. It follows that the second post (at the end of the zero year) is 1. and the post present at the beginning of the first year BC is -1. Thus, with the posts we have the sequence -1,0,+1. Is this not exactly what chronologists and astronomers require? Further, this applies equally to the first hour as indicated on Dionysius' sundial or our clocks. We know that 12 represents 0. The first hour ends at 1 o'clock and the last hour (11 o'clock) ends at 12 (0). So we have an interval of 2 hours with an absolute zero in-between. The third millennium started at midnight between Dec. 31, 1999 and Jan. 1, 2000. 24.242.42.17 (talk) 15:36, 10 July 2008 (UTC)

+Back to your last edit you state "The first decade. by definition of decade, has to contain ten years which are these: AD 1, 2, 3, 4, 5, 6, 7, 8, 9, 10." Does not the first decade have to start with the first year? Surely it must. Why do you say that by definition it is AD1? Are you referring to the proleptic Gregorian Calendar? A decade can also go from the first year to the tenth. Sam Hastings24.242.42.17 (talk) 04:07, 12 July 2008 (UTC)

Sam:

LThe decade AD 1, AD 2, .... AD 10 is the first decade of the AD era of the Gregorian Calendar, as follows from the relevant definitions, conventions, and conclusions:

• A decade means ten consecutive years.
• The Gregorian Calendar's counting origin index is 1 (one).
• The first year AD is AD 1.
• The first years of the first decade, century, millennium AD are: ad 1, AD 1, AD 1.
• The last years of the first decade, century, millennium AD are: AD 10, AD 100, AD 1000.

Go on counting from there.

For the BC era, change in the above the acronym AD for BC.

Most building floors in the USA are similarly numbered:

• GOING UP: up-floor 1, up-floor 2, up=floor 3, ....etc.

• GOING DOWn: down-floor 1, down-floor 2, down-floor 3, etc.

Jclerman (talk) 15:59, 12 July 2008 (UTC)

JC: I find it difficult to believe that you don't believe in the significance of your own concept of the fence line of posts and rails. You continue to pursue the rabbit of years (rails). In so doing you must represent the first post as 1 (one). I find no problem with my claim that the first hour is as much a measure of the passage of time as is the first year and as such must be indexed with 0. I, too, can come up with other examples, as you have, to support my particular position. Interstate Highway 35 starts at Laredo, TX. There are mile markers along the way. Each exit gives the total number of miles traveled to that point {having started at zero (post zero)}. At the border between Texas and Oklahoma the mile counting starts over again at 0. At each border, Kansas, Missouri, Iowa and Minnesota, we get a new zero. This is a succession of posts and rails. The beauty of your concept is that it contains only one zero. No need to try and assign it to BC or AD. Sam 24.242.42.17 (talk) 02:29, 13 July 2008 (UTC)

I apologize for a big blunder. The analogy of the Gregorian Calendar is not the fence. It induces readers to mix two different sets but the Gregorian years are a homogenous set. Consider each year to be a marble on a sequence. The AD era in one string with the AD sequence, and the BC era with the BC sequence. Both in line, model the Gregorian Calendar. By definition and usage.

Miles, on the contrary, are not such a set of discrete elements. To measure road distances and sizes of marbles we use a ruler with a zero. To count years in the Gregorian style we count marbles beginning with 1. A different calendar can label the same years with a different sequence. In fact, I could envisage a calendar in which each year and each month and each day as well as centuries, etc. could be named by the elements of a Fibonacci sequence. It would make the arithmetic more difficult but not impossible and more fun.

Jclerman (talk) 20:15, 13 July 2008 (UTC)

JC: You refer to a big blunder. I need to know for sure that to which you refer as a big blunder. I think I know but let me be certain. Sam24.242.42.17 (talk) 16:52, 15 July 2008 (UTC)

I thought I said it but I'll expand it: I apologize for a big blunder: The analogy of the Gregorian Calendar is not a fence because it induces readers to mix two different sets, namely posts and rails, while each Gregorian era consists of a homogenous set, like a sequence of marbles.

Jclerman (talk) 18:44, 15 July 2008 (UT

+JC: As far as I am concerned your fence line analogy if perfect for the purpose I have in mind which is to find out if there is an appropriate numerical system available to fill the chronologists' and astronomers' need. If you index your system with the first post as zero one finds that the second post is +1 and the first post before the zero post is -1. This satisfies the need mentioned above. Supporting evidence for this numerical system is easily provided if one looks at a simple rectilinear graph. The point where the x-axis and the y-axis cross is zero. The end of the first box (year, for example) is +1 and the end of the first box before the zero post is -1. This is a never-ending system and can be broken into at any time, the first post at the break-in being zero. Our problem all along has been the fruitless search for a year zero. We should have been concentrating on point zero and not year zero. I need to emphasize that nearly everyone (including us) has been chasing the wrong rabbit. The moment the ball hits bottom in Times Square is the moment between the end of one year and the beginning of the next. The big question is which years. Chlodius was on the right track in the very first item in the Talk: Year Zero article when he defined the infinitesimal point between year -1 and year +1 as zero but he took his eye off the "ball." He stayed with "undefined" years when he should have identified them as first!!!! Now Catholics can start their calendar on Dec. 25, the conceptionists can start of Mar. 25 and all of us (who are so inclined) can start our individual calendars on our birthdates. Perhaps that is what Joe Kress had in mind when he chose the date of April 21st to illustrate his problem in counting. I will continue to claim that Wikipedia is in error when it states that the 3rd millennium started on Jan. 1, 2001. Especially, as far as I have been able to determine, that conclusion is based on the intellectually and mathematically discussion in the section on "Astronomers." It has been reported that 80% of the world's population voted with their celebration dollars the night of Dec. 31, 1999 as the last day in the 2nd millennium, not only in Times Square but all over the world in places such as Birmingham, England (see The Birmingham Post of Jan. 1, 2000). 24.242.42.17 (talk) 22:07, 25 July 2008 (UTC) Sam Hastings

Dear Sam:

Here is a simpler and clearer model of the AD and BC eras of the Gregorian Calendar, both by counting and time measuring, on the same objects. I hope it is clearer than marble counting and than my erroneous fence model:

I wanted to buy bananas. I visited two different stores. I wanted a bunch of ten bananas.

• Grocer A counted them: one, two, .... ten. [This is analog to, e.g., counting years in a decade. This is the calendar approach, based on counting.]

• Grocer B weighed them on a balance with a scale starting at zero. The pointer indicated 1.2 kg. [This is analog to, e.g., measuring time in hours. This is the clock type of approach, based on measurements. It appears, Sam, that you are trying to construct a calendar based on measurements, like Grocer B, rather than on counting as true calendars are constructed, like Grocer A counting bananas.

I hope this clarifies the difference between counting and measuring.

JC

PS: Naturally, you are free to construct the calendar you find fit to your thinking, even if ten bananas (a decade) are, in fact, nine bananas. And if following your approach we are going to validate mathematical and scientific knowledge by polls conducted by the media, we better first close all schools. Otherwise we would risk serious cognitive conflicts.

Jclerman (talk) 02:12, 26 July 2008 (UTC)

From the news:

Famed science-fiction author Arthur C. Clarke is fed up with people thinking 1999 is the last year of the second millennium.

He says the fascination with the year 2000 is psychological, not scientific.

"Because the Western calendar starts with Year 1, and not with Year 0, the 21st Century and the Third Millennium do not begin until January 1, 2001," Clarke said in a statement.

Clarke, author of 2001: A Space Odyssey, issued a statement on Thursday from his home in Sri Lanka. He offered "a very simple analogy" to make his case.

"If the scale on your grocer's weighing machine began at 1 instead of 0, would you be happy when he claimed he'd sold you 10 kilograms of tea? And it's exactly the same with time. We'll have had only 99 years of this century by January 1, 2000: we'll have to wait until December 31 for the full hundred."

Jclerman (talk) 11:53, 26 July 2008 (UTC)

+JC: Of course he is correct about the weighing machine which he uses as an analogy to the passage of time. But he is as incorrect as everybody else who obsess with years. I'd ask him to look at a clock and consider XII as the meridian (zero). What does he find to be the number of hours between 11 PM and 1 AM. The first year started at 0 and remained year 0 until the arrival of year 1. 24.242.42.17 (talk) 03:35, 27 July 2008 (UTC) Sam

Sam, you (a) are misinterpreting the meaning of his analogy, and (b) you keep mixing the measuring approach with the counting approach (i.e., clock vs calendar). That's why I gave you the bananas example. Clarke's opinion was not written as an analog of anything else than if the first year was AD 1, the first decade, century, millennium, begun on years AD 11, 101, 1001. He meant his scale to point to 1 when there was no tea in the scale and that you'd feel cheated if given 9 pounds of tea when the scale pointed to 10 because there would be only 9 pounds of tea. Please, re-read the bananas analogy.

The same day seen in each approach:

• Calendar (counting) approach: First day of AD era: AD 1, year AD 1.
• Clock (measuring) approach: First day of AD era: Started at clock reading AD 1 HR:MIN 00:00 ended at clock reading AD 1 HR:MIN 24:00.

If you insist in concluding that we are all wrong and a decade of bananas consists of 9 bananas, close all schools because they are perpetuating the wrong arithmetic.+

JC: Let me unravel the confusing clock face for you. We have 1 AM occupying the same space as 1 PM. An easy way to straighten out this confusion is to detach each of the two counting systems at XII and lay them out on the x-axis with the XII attached. What you get is the following:

                                           AM                  -1, 0, +1             PM         

XII,-11,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,XII,+1,+2,+3,+4,+5,+6,+7,+8,+9,+10,+11,XII

The initial XII of the AM system and the final XII of the PM system obviously are reattached to the initial XII on the clock face. Thus the numbering system proposed for counting years is identical to the numbering system necessary for the chronologists and astronomers. 24.242.42.17 (talk) 15:50, 29 July 2008 (UTC) Sam

   XII-11,-10,--9-8-7-6-5-4-3-2-1-XII+1,+2,+3,+4,+5,+6,+7,+8,+9,+10,+11,XII

In clocks, one of the 12s represents 00:00 (i.e. midnight), so that you get 11pm, then an hour later Midnight, then an hour later you get 1am. But with BC/AD in calendars it is different. There is no year 0 (the equivalent of there being no midnight). The year after 1BC was 1AD, not Year 0. The beginning of 1AD started as soon as 1BC had finished. Deamon138 (talk) 21:11, 29 July 2008 (UTC)

+ Deamon: I'm sorry but you are missing the "point". Point zero is the instantaneous moment between the "first" positive year and the "first" negative year. It is not representing Year Zero. JC's fence line analogy is so great for representing this invaluable numbering system. 24.242.42.17 (talk) 15:54, 30 July 2008 (UTC) Sam

Okay fine, so the point zero you're talking about is representing an instantaneous point between 1BC and 1AD. Fair enough, I can handle that, but just one question: why all the talk of clocks that you did above my last comment? With clocks, the "Midnight hour" is not an instantaneous point in time, but an hour the same as all the rest. What does the hours on a clock have to do with the BC/AD system? Deamon138 (talk) 18:55, 30 July 2008 (UT

+I'm not referring to a midnight "hour". Midnight is a point in time, the point between the end of the last hour before midnight and the first hour after midnight. On a clock midnight (XII) occurs at the same point as noon (XII). Noon is the meridian (the point between the last hour AM and the first hour PM. These hours are shown on the clock as 11AM and 1 PM, but the interval between them is 2 hours. Thus the sequence -1,0,+1 gives the proper measure of elapsed time. This applies equally well to years. The point in time at which the first year started is zero. And it remains zero (the so-called missing year zero) until that first year is over and the second year starts. If one accepts Lerman's fenceline analogy with index 0 then the first post is zero and the first rail is also zero. Now we have eliminated the need for the awkward mating of Year 0 AD with Year 1 BC. We have no need to use the AD and BC designations. Nowadays CE and BCE work fine. Furthermore, with this numbering system we have ordinal and cardinal numbering systems in full and accurate play. 24.242.42.17 (talk) 02:03, 31 July 2008 (UTC) Sam

"I'm not referring to a midnight "hour"" Well I think you are/were, as the Midnight hour is the hour from 12PM/0AM to 1AM, so in the statement, "Thus the sequence -1,0,+1 gives the proper measure of elapsed time" 0 to +1 represents the midnight hour so you were talking about that.

Anyway, onto the rest of your comment. You say, "Now we have eliminated the need for the awkward mating of Year 0 AD with Year 1 BC. We have no need to use the AD and BC designations. Nowadays CE and BCE work fine." I'm sorry but you couldn't be more wrong. the AD/BC system and the CE/BCE system are exactly the same. So 1363AD is the same as 1363CE, and 756BC is the same as 756BCE. Both systems are the same. The only reason we have two names is because "Before Christ" and "Anno Domini" are inherently Christian, so some see it as a way to not offend non-Christians (note: I'm non-Christian and I'm not particularly bothered either way, but others might be, so meh). Also, THERE IS NO YEAR ZERO! Since both systems are the same, if there's no 0AD, then there's no 0CE either. 0AD is represented by 1BC and 0CE by 1BCE. End of. You can't eliminate the "awkward mating of Year 0 AD with Year 1 BC" since if you invented a new calendar system (or just used astronomical year numbering) with a year zero, but with all the AD years in our current system being represented by the same positive number (e.g. 6AD is year 6 in the new system), then this means that you get:

• 3AD=Year 3 (in your new system)
• 2AD=Year 2
• 1AD=Year 1
• 0AD= N/A (Remember: there is no year zero!)
• 1BC=Year 0 (in your new system)
• 2BC=Year -1
• 3BC=Year -2

Notice that 1AD and 1BC are still next to each other (inventing a new system doesn't change the old system) and with the introduction of a zero into the new system, all the BC values are moved by one in the new system. Deamon138 (talk) 00:52, 1 August 2008 (UTC)

+Let me reiterate - I referred only to "midnight" which I find from my encyclopedia is defined at the point in time when the last hour of one day ends and the first hour of the next one begins. This point in time is often marked by the tolling of bells. At midnight in New York City it is enjoyed by thousands at the falling of the ball denoting the end of one year and the beginning of another. The main question seems to be what years. Actually, Lerman's suggestion of the fence-line analogy when used with his index zero instead of the index one he proposed was a very good example of the chronologists' and astronomers' need for a single zero so that the years after the start of the current calendar can relate quantitatively with the prior years. This is NOT a new or invented numbering system. It is adequately supported by the appearance of an ordinary graph paper filled with square blocks of equal size. Running horizontally and vertically in the center of the graph are the well-known x-axis and y-axis. The point where they intersect is zero. Let's look at the x-axis. One can count from 0 to +1 to + 2 etc. indefinitely. And one can count from 0 to-1 to -2 etc. indefinitely. And it does give the necessary -1,0,+1 sequence. Keep in mind that these are "points" or "posts" in Lerman's analogy. They are not hours or years but indicators like the I on a sundial or clock that shows that the first hour has been completed or the I that should be acknowledged as the end of the first year. Actually, as I have shown previously, if you stretch out the AM and PM versions of the clock you get a sequence that fits on the graph. 24.242.42.17 (talk) 02:45, 1 August 2008 (UTC)Sam

+I offer Wikipedia itself to prove that the sequence -1.0,+1 is not an "invention". In the article on "Time" you will find references to the Prime Meridian and the International Date Line. I let them speak for themselves. 24.242.42.17 (talk) 16:08, 7 August 2008 (UTC) Sam

Yes but how is that relevant to the BC/AD system? Deamon138 (talk) 16:11, 7 August 2008 (UTC)

+It is relevant because what the chronologists and astronomers need is the sequence -1,0,+1. These are all POINTS, not hours or years but instantaneous separations between adjacent hours and years. As i keep pointing out, the interval between 11 AM and 1 PM is obviously 2 hours. With that sequence the difference between -1 BC and +1 AD is 2 years. Trying to effect the correct number of years with a YEAR 0 does NOT work. The International Date Line is POINT 0 and is the point between the last hour of one day and the start the first hour of another. We might as well do without the BC/AD designation. BCE and CE suffice. When the longitudes and latitudes of the earth are rendered parallel we have a grid similar to the graph I have described earlier. The intersection of the International Date Line and the equator is ZERO. 24.242.42.17 (talk) 18:15, 7 August 2008 (UTC)Sam

The BCE/CE system is EXACTLY the same as the BC/AD system. The only reason BCE/CE exists is to be politically correct. Also, the International Date Line isn't a straight line like latitudes and longitudes are, though I get the analogy. Deamon138 (talk) 21:15, 7 August 2008 (UTC)

+I'm glad you get the analogy. Our sequence is -1,0,+1 (where the numerals indicate posts or points in time). For the Christian era the post 0 represents the beginning of the first year AD and the post +1 represents its conclusion. The post -1 marks the beginning of the first year before the 0 post. The interval is two years, correct mathematically. To continue the analogy, since the first rail in the fence line is also zero and the adjacent post is +1 we have established a mathematically correct cardinal numbering system for the era. This system does not apply to the years BC. It follows that the third millennium started on Jan. 1, 2000. Sam —Preceding unsigned comment added by 24.242.42.17 (talk) 02:28, 8 August 2008 (UTC)

Why doesn't apply to BC? Deamon138 (talk) 15:56, 8 August 2008 (UTC)

+Because Dionysius merely interrupted a fence line that already existed. It's kind of like I35 crossing from Texas to Oklahoma. The fence started whenever any already existing calendars started. In the case of the Hebrew calendar the fence line started with Genesis: Chapter 1 verse 1. Perhaps the absolute zero occurred with the big bang. 24.242.42.17 (talk) 03:08, 9 August 2008 (UTC)Sam

The following post is moved from the article because it is a comment and does not cite a verifiable source (Lerman has not been published in a reliable source). — Joe Kress (talk) 21:16, 18 August 2008 (UTC)

In spite of the astronomical amount of discussion in the search for "an astronomical year 0" it turns out that the search should have centered on the search for a "point" 0. Lerman has proposed using a fence line analogy for setting up the desired -1,0,+1 sequence. Thus the first "post" (point) between the first year BC and the first year AD is simply the numeral 0. This was obvious to Dionysius as he contemplated the sun dial. The numeral I represented the end of the first hour and the beginning of the second. The first rail (hour or year or etc.) is also 0. All of the posts simply represent the end of some interval and the beginning of the next. The sequence is dimensionless in that it can be applied to many situations. Examples are given in the section "Chronologists". It follows that the third millennium started on Jan. 1, 2000. 24.242.42.17 (talk) 15:48, 18 August 2008 (UTC) Sam Hastings

+Joe: Thanks for moving my comments from the "Astronomers" section. I didn't realize that it was inviolate. I tried to place the comments there because that section needs to be revised, The reasoning there is simply erroneous as I have pointed out many times. It shows Year 1 BC, Year 0 and Year 1 AD in sequence. Three Years as such and yet the interval is calculated as 2 not 3. And Year 0 must exactly be meant to be a Year because it is eventually assigned to the first year BC. You, yourself contested this with your problem with the interval between two April 21st using such a system, two years instead of one. 24.242.42.17 (talk) 21:24, 19 August 2008 (UTC)Sam

No section of any Wikipedia article is inviolate. You are welcome to make any changes you like (do not add your name or any signature line). But all edits are subject to removal or modification by other editors if they do not meet Wikipedia's guidelines, especially Wikipedia's verifiability policy, which you must read. Especially note its very first sentence: "The threshold for inclusion in Wikipedia is verifiability, not truth—that is, whether readers are able to check that material added to Wikipedia has already been published by a reliable source, not whether we think it is true." So what you or Lerman think is correct does not matter—if any edit is questioned, the editor must provide a verifiable (published) source to support their opinion. Sources for astronomers' use of a full year 0 (not an instant), even between 1 BC and AD 1, is provided. It does not matter whether their use is wrong or right, only that it has been published. Even if you can find published support, it may still be removed according to Wikipedia's consensus policy if a majority of editors agrees that it does not belong in the article. — Joe Kress (talk) 00:26, 20 August 2008 (UTC)

Well, Joe, guess where I find published material which I certainly believe puts an end to the indefensible concept of Year 0 AD being equal to the first year BC. In Wikipedia itself. Please see the article " Astronomical year numbering" which refers to the necessary NUMBER 0 being used on occasion. It also says that astronomers did not exclusively use the -/0/- system until the mid twentieth century. 24.242.42.17 (talk) 22:03, 28 September 2008 (UTC)Sam Hastings

I wrote that section, but I obviously didn't write it well enough do avoid your misunderstanding. "Years" within the phrase "the years were designated 2 BC, 1 BC, 0, 1 AD, 2 AD" applies to all five years listed, where 0 is the number they applied to an entire year between the whole years that they designated (in Latin and French) as 1 BC and 1 AD. When I said that –/0/+ was not exclusively used until the mid 20th century, I meant that some astronomers were still applying the term "1 BC" to the year two years before 1 AD, skipping the year immediately before 1 AD, which they labeled "0", not 0 AD. Presently, all astronomers apply the term "–1" to the whole year two years before "+1" (AD 1) and apply the term "0" to the whole year immediately before "+1", which is the usage to which you object. — Joe Kress (talk) 01:18, 29 September 2008 (UTC)

+I've been on vacation and also having some health issues (probably related to my obsession with the year zero discussion). However, I would like to continue our discussion. It is true that I need some clarification on the contents of the "Astronomical year numbering" article which you also edit. As I understand the article it relegates the use of "0AD equal 1BC " to situations "critical when calculating astronomical events like eclipses or planetary conjunctions to determine when historical events which mention them occurred". This is certainly a different situation exclusively of interest to astronomers. Earlier the article states that "For normal calculation a number zero is often needed, here most notably in a period that spans the epoch; the end years need only be subtracted from each other". This sets up the relationship -n,0,n where 0 is the instantaneous point where one year ends and another begins. It is a generalized numbering system applicable to many situations (e.g., hours, days etc.). Does this not demonstrate conclusively that the first year CE is also Year zero CE? 24.242.42.17 (talk) 01:52, 7 November 2008 (UTC)

The basic problem is to determine the number of years between anniversaries, specific dates within any year. Let's arbitrarily chose July 1. For astronomers, the number of years between July 1, −1 and July 1, +1 is two years, consisting of the last half of year −1, a full year labeled 0, and the first half of year +1. This agrees with subtracting the year numbers (+1 − (−1)) = 2, because astronomers place a year 0 between −1 and +1. For historians, the number of years between July 1, 1 BC and July 1, 1 AD is only one year, consisting of the last half of year 1 BC and the first half of year 1 AD, because historians do not use a year zero. However, because historians do not apply arithmetic signs to their years, the magnitude of any BC year must be added to any AD year. Here, 1+1=2, which disagrees with the actual duration between anniversaries. Thus historians must remember to subtract 1 from their total duration, otherwise they get the wrong answer. Astronomers avoid this problem be using a year zero. French astronomers near the beginning of the 18th century did not use signed years, but inserted a year 0 (without any era lable) between the years 1 BC and 1 AD, effectively renumbering all BC years to accomodate the year 0. For them, the number of years between July 1, 1 BC and July 1, 1 AD was 2 years, consisting the last half of 1 BC, an entire year labled 0, and the first half of 1 AD, which agrees with adding the magnitudes of the BC and AD years, 1+1=2. (I replaced three long paragraphs with this single paragraph.)

As I mentioned in Talk:Astronomical year numbering, a '+' at the beginning of your comment means nothing to Wikipedia. Wikipedia indents your comment by the number of colons ':' that you place before it. Editors indent (or not) to differentiate their comment from another editor's comment. Becuase you did not use a colon, I placed one colon at the beginning of each paragraph of my comment to indent it. — Joe Kress (talk) 09:30, 7 November 2008 (UTC)

Sorry, I just didn't know about the change. The head of a local astronomical group told me categorically that there was no year zero. I take that to mean that the series -n0n includes a POINT ZERO, not a year zero. I believe this is in agreement with your statement in Astronomical year numbering that astronomers determine the interval between BCE and CE by simply using the difference between the end years. To my mind the -n0n series is independent of AD/BC other than that the point 0 represents the beginning of Dionysius' calendar. He also stated that they go to the Julian day number in event-type situations. Here the concept of year zero is included. —Preceding unsigned comment added by 24.242.42.17 (talk) 20:12, 8 November 2008 (UTC)

An astronomer does not have to use astronomical year numbering if he does not want to. But if so, he must identify years before our era with an English term like BC or BCE, or an equivalent term in another language. He must not use negative years, which imply the use of a year zero, otherwise he will confuse his readers. I have repeatedly stated that a whole year exists between the years −1 and +1, not a point. I have already explained that the extra year disappears when you consider anniversaries within the end years. Although your source is correct in stating that the Julian day number is used for events, it only counts days—it does not use years of any kind, neither −/+ years nor BC/AD years, let alone a year zero. When converting a date into a Julian day number, software can be designed to accept either historical year numbering or astronomical year numbering.

Let us consider a real world example. A historian would state that Julius Caesar was assasinated on March 15, 44 BC, but an astronomer (using astronomical year numbering) would say that he was assasinated March 15, −43. Both dates identify the same day. The shift of one for the year number accommodates a year 0 between −1 and +1. — Joe Kress (talk) 23:25, 8 November 2008 (UTC)

In your article you state "For normal calculations a NUMBER ZERO is often needed, here most notably when calculating the number of years in a period that spans the epoch; the end years need only be subtracted from each other". Do you abandon YEAR ZERO at this point? You say it disappears - how is that?24.242.42.17 (talk) 23:33, 9 November 2008 (UTC)

Joe - if you have not done so already, I would like to suggest that you bring up "geocities.com/calendopaedia/counting". I find the sections "Was Jesus born in the year 0?" and "Does the lack of a year zero cause a problem?" seem to support my position.

Sam Hastings24.242.42.17 (talk) 21:22, 21 November 2008 (UTC)

Joe - Not hearing from you gives me pause. Do you not accept Michael Astbury's PUBLICATION as suitable?

Let's take another look at the sequence used as a starting point in the "Chronologist" article: Year 1 BC, Year 0, Year 1 AD. These are all definitely considered as actual "full" years. The immediate conclusion is that Year 1 BC must be somewhere in antiquity right behind Year 0 BC, the starting point of any calendar in existence at the moment Dionysius established his calendar. Now I suggest that we rewrite the sequence as Year 1 BC, (Year 0 BC or Year 0 AD), Year 1 AD. Cassini and others chose Year 0 AD. Thus the sequence is now Year 1 BC, Year 0 AD, Year 1 AD. But Year 1 BC must follow Year 0 BC back to the beginning of any of the previous calendars. Now all we have left is Year 0 AD and Year 1 AD. You may argue that Year 0 AD can still be equal to the first year BC but i have always argued that the first year BC can only be equal to the last year of earlier calendars. This brings the beginning of the first year of the third millennium to January 1st, 2000. 24.242.42.17 (talk) 16:01, 7 December 2008 (UTC). Added to on December 11, 2008.24.242.42.17 (talk) 15:57, 11 December 2008 (UTC)

Joe - You do not respond but I am not giving up. I would like to go back to your comments of 7 Nov. 2008. Your arguments with reference to the astronomers' calculations is in opposition to the fact that an astronomer told me that they do not use a "year zero". They do use a "point zero". You point that out yourself in the article "Astronomical year numbering". The sum of the ending half year of the first year BC and the beginning of the second half of the first year AD is thus one year. Your arguments for historians uses the same erroneous Year 1 BC which exists only after the Year 0 BC of any calendar in existence when Dionysius instituted his calendar. It does not occur in the sequence used. With regard to Julian day numbers Wikipedia acknowledges Scalinger's starting year 4713 (although you state that such a year is not needed). However, another reference to Julian day number (www.friesian.com/numbers.htm) used the concept of Year 0 AD = the first year BC. This resulted in the need to use Year 4712 to represent his Year 4713 because of the extra year added to BC (Year 0 AD). This is just another example of the confusion introduced by this unsupportable concept.24.242.42.17 (talk) 03:43, 28 December 2008 (UTC)

Joe - Two months have passed and a new year is here; you have abandoned the discussion (as far as I am aware). It appears that we have reached an impasse so I recommend that we submit a "Request for mediation" to Wikipedia. 24.242.42.17 (talk) 17:33, 9 January 2009 (UTC) Sam Hastings

Joe - I have consulted Wikipedia's rules and find that if we have a dispute we must first attempt to engage in mediation on our own before we can have Wikipedia appoint a mediator. At this point we each have an unshakeable position and I desire to try to find a Wikipedian willing to do this job for us. Sam24.242.42.17 (talk) 19:19, 19 January 2009 (UTC)

Joe - Since you seem uninterested in our going to mediation at this point I suggest that we state our positions on the issues one at a time. Because so much misunderstanding occurs about a person's intent when referring to years I am continuing my effort to differentiate between ordinal (first) years and cardinal (passage of time) Years. As you know I refute the validity of the arguments in the Year Zero article entitled "Astronomers". I contend that the sequence Year 1 BC, Year 0, Year 1 AD is flawed and in no way brings us to the conclusion that the interval between the Years is 2 Years not 3. The basic error is that Year 1 BC exists only in antiquity right after Year 0 BC. I also contend that the first year BC can only be the last year (Year X) of any calendar in existence at the time Dionysius established his calendar. This gives us the sequence Year X, Year 0 AD, Year 1 AD. Year 0 AD being the first year AD we have the proper interval of 2 Years between the beginning of the first year BC (Year X) and the end of the first year AD (Year 0 AD). 24.242.42.17 (talk) 23:18, 27 January 2009 (UTC)

Joe. I continue to find you unresponsive. I have offered to submit to an effort to mediate our differences and have laid out my bases for finding that the "Astronomers" article is flawed and needs to be rewritten. I presume that if you refuse to enter into a mutual agreement to submit our dispute to a mediator that the Mediation Committee will perhaps rule that something needs to be done to keep us from this stalemate. 24.242.42.17 (talk) 19:05, 9 February 2009 (UTC)

Samuel Butcher (1877) speaking

Samuel Butcher, The Ecclesiastical Calendar: Its Theory and Construction, Dublin/London 1877, is one of the more important works ever written on the subject matter.

p. 187: "Hitherto we have considered this Expanded Table [of the Epacts] only in relation to centuries after the reformation of the Calendar [in 1582]. Clavius applies it to the old Calendar also in the following manner:

Butcher then goes on to put forth how Clavius tried to anchor the new system in the remote past. "Here [at the year 550 A.D.] he [Clavius] places what he calls the radix or origin of the Lunar-Equation."

and in his summary (p.229): "The Gregorian reformation of the old Church Calendar consisted, as we have seen, of two very distinct parts, which may be called the retrospective and the prospective."

How many miles away was Samuel Butcher from the present-day "discussion"!

Needless to add that Butcher was in favour of "year zero":

p.21: "But historians and chronologers have not adopted this (correct) mode of reckoning [to call 1 B.C. the year which is now called 2 B.C. etc. as proposed by M. Cassini.]"

Ulrich Voigt (talk) 22:35, 24 October 2008 (UTC)

Third opinion

A third opinion was requested. Please state what changes to the article are being suggested and their rational. NJGW (talk) 20:07, 16 February 2009 (UTC)

I have been asked to clarify my request for a third opinion. The article Year Zero has a section entitled Astronomers in which a Cassini equates Year 0 to the first year BC. The arguments presented in support of this equating utilize a sequence Year 1 BC, Year 0, Year 1 AD. This sequence is flawed. Year 1 BC follows Year 0 BC as the first two years of any calendar extant at the time Dionysius instituted his calendar. The sequence is now Year X, Year 0 AD, Year 1 AD where Year X is the last year of any of the earlier calendars. For the Hebrew Year X was about Year 3758. Thus we have Hebrew Year 3758, Year 0 AD, Year 1 AD. Thus we have an interval of three years and no need for the Year 0 to "disappear" as Joe maintains. The sequence also becomes the last year of the Hebrew calendar BC, the first year of Dionysius's calendar (Year 0 AD), and the second year AD. —Preceding unsigned comment added by 24.242.42.17 (talk • contribs) 00:57, 20 February 2009 (UTC). Comment originally left on the WP:3O page

Please list here exactly the text you propose to remove, followed by the new text you are proposing. Joe, please give your brief opinion on why you oppose. NJGW (talk) 05:12, 20 February 2009 (UTC)

The article "Year Zero" contains a section entitled "Astronomers Year Numbering". I propose that the entire article be deleted. The sequence Year 1 BC, Year 0, Year 1 AD contains an error. Year 1 BC does not belong before any AD Years. The only Years 1 BC belong after the Years 0 BC in the actual calendars extant at the time Dionysius established his calendar. 24.242.42.17 (talk) 19:20, 23 February 2009 (UTC)

First I'm going to assume that you mean Year zero#Astronomers, as there is no section titled "Astronomers Year Numbering." Second I'll assume that you mean that the section should be removed, not the entire article. Second, could you provide the source you are using for the claim "The only Years 1 BC belong after the Years 0 BC in the actual calendars extant at the time Dionysius established his calendar"? This will allow me to evaluate your position. Thank you. NJGW (talk) 20:12, 23 February 2009 (UTC)

Ulrich Voigt, Adhemar, Jclerman, and I have tried to explain the astronomical year zero to Sam Hastings but he refuses to accept it. The discussion labeled Chronolgists above is only half of the total discussion on this point, the rest is in Archive 2 beginning at "An interesting question" about two years ago.

The three years which historians (see Year zero#Historians) label 2 BC, 1 BC, 1 AD are labeled −1, 0, +1 by modern astronomers, but were labeled 1 BC, 0, 1 AD by French astronomers near the beginning of the 18th century (they used the equivalent French terms avant Jesus-Christ/après Jesus-Christ or the Latin terms ante Christum/post Christum). All three years lasted from 1 January to 31 December—none was a single point in time, certainly not year zero. Jacques Cassini stated "the sum of the years before and after Jesus Christ [year 0] gives the interval which is between these years". A critical point which Cassini does not mention in this quote is that the calculated interval is between specific instants within the end years, noon 1 January. Thus the interval between 1 BC and 1 AD (using the early French designations) is 1+1=2 years, which are the years that they labeled 1 BC and 0 between noon 1 January 1 BC and noon 1 January 1 AD. The entire year 1 AD is outside the interval. Modern astronomers call these three years −1, 0, +1, so would state that only the first two years −1, 0 are within the interval.

I stated this back on 2 March 2008 in Archive 2 at Third : once more. I recently said the year outside the interval "disappears", which was a poor choice of words. These crucial instants (epochs) of noon 1 January should be in the "Astonomers" section of the article. It should be emphasized that the French astronomer usage of 1 BC differs by one year from the historical and modern year 1 BC. Sam is correct that adding/subtracting years is no longer used by astronomers to determine the interval between two instants—they now use Julian days which were invented by the astronomer John Herschel in 1849, well after French astronomers began using year 0 near 1700. — Joe Kress (talk) 20:15, 23 February 2009 (UTC)

3PO Thank you both for providing your sides so clearly. It seems that there is no reason to remove the section, but it should be clarified so that lay readers can understand more easily. In particular, the concept of "the interval between 1 BC and 1 AD... is 1+1=2" is confusing in the article, but much more clear here in Joe's description. The section should also contain a short explanation of why the adding/subtracting of years has been depreciated for the usage of Julian days. NJGW (talk) 20:28, 23 February 2009 (UTC)

I apologize for mislabeling Astronomical year numbering. But I now contest the validity of Joe's statement "The entire Year 1 AD is outside the interval." Do we not all agree that there is an instantaneous point zero between the end of one Year and the beginning of the next? Although I do not accept the validity of Year 1 BC it turns out that it is not a problem at all. One ends up with a numerical sequence that is essentially independent of labels. There is a POINT -1 between Year 2 BC and Year 1 BC. There is a POINT 0 between Year 1 BC and Year 0 AD, a POINT +1 between Year 0 AD and Year 1 AD and a POINT between Year 1 AD and Year 2 AD. Thus we have the sequence -1, 0, +1. As I have pointed out earlier this numbering system applies to hours on a clock or sundial and is universally used in rectilinear graph paper.16:59, 24 February 2009 (UTC) —Preceding unsigned comment added by 24.242.42.17 (talk)

24.242... we all agree that for historians there is no year zero. For astronomers there appears to be a year zero. These are two different ways of numbering the years. Please allow Joe to clarify the section. As for "The entire Year 1 AD is outside the interval," think of January 1, 2008 to January 1, 2009: The entire year 2009 falls outside the interval, so it is only one year (365 days) vs. 2 years (2008 and 2009). NJGW (talk) 17:11, 24 February 2009 (UTC)

Section rewrite

I have rewritten the Year zero#Astronomers section taking into consideration all of the discussion above. Included is a substantial portion which explains the relationship between calendar years and the instants at the beginning of those years as used by astronomers, which is the main concern of Sam Hastings (24.242.42.17). Astronomical practice is identical to Sam's most recent statement around year 0. If we identify instants by placing them in parentheses and identify years without them, then the sequence around year 0 is: −2 (−1.0) −1 (0.0) 0 (1.0) 1 (2.0) 2. — Joe Kress (talk) 06:22, 25 February 2009 (UTC)

It looks better. I made some changes to help out the lay people in the room. Sam, if you could read through this and tell us if there are any sections which are still unclear to you, that would be very helpful. It's not always easy to know the wording most appropriate for explaining a technical subject. NJGW (talk) 07:10, 25 February 2009 (UTC)

I would suggest adding to the 1st paragraph under the "Astronomers" rewrite the following: Thus we may consider that when astronomers use the notation -1, 0, +1 they mean instantaneous points in time, not years (or words to that effect).24.242.42.17 (talk) 03:06, 26 February 2009 (UTC)

When modern astronomers use the notation −1, 0, +1 they always mean calendar years. A decimal zero must be added to indicate instants at the beginning of those years, −1.0, 0.0, +1.0. However, this is a modern convention—it was not used before the 20th century. Also note that the modern mathematical astronomer Jean Meeus used the words "arithmetical purpose" when referring to negative calendar leap years, which do not involve intervals. — Joe Kress (talk) 04:20, 26 February 2009 (UTC)

Joe, can you write something into that paragraph which briefly explains the use of intervals and instants in Astronomy? NJGW (talk) 04:59, 26 February 2009 (UTC)

I cannot briefly explain the use of intervals and instants and maintain your reorganization of the Astronomers section. I must first describe astronomical notation before I can use it, hence I am in a quandary. I would prefer to merge the usage and notation sections, although a substantial amount of both can be moved to the history section without loss of understanding. It will take some time to rewrite it. — Joe Kress (talk) 07:11, 26 February 2009 (UTC)+

I object strenuously to the statemet "When modern astronometrs use the notation -1, 0, +1 they always mean calenday years. Were it true they could ot merely subtract the endpoints.24.242.42.17 (talk) 19:12, 26 February 2009 (UTC)

Sam, do you have a reason for your objection? Have you encountered astronomers who told you this, or read it somewhere? NJGW (talk) 06:04, 27 February 2009 (UTC)+

Indeed I have. Unfortunately I didn't copy an email I received from the head of the Heart of Texas astronomers group but he assured me that astronomers do not use a Year 0 but simply subtract the end years. This is in accord with the sequence -1,0.+1 where the numbers represent instantaneous points in time. This numbering system was put forward by Voigt in his response to my comments in the first article above. Joe requested a published article for verification and I asked him to access (about November 9 of last year) "geocities.com/calendopaedis/counting." He did not continue any contact with me after that time until we arrived at my request for a third opinion.24.242.42.17 (talk) 21:10, 27 February 2009 (UTC)

Sam's own source, Calendopaedia - Counting Years, confirms that astronomers do use a year zero, after stating "There is no year 0 [for historians]." To wit: "Does the lack of year zero cause a problem? Yes it does to astronomers who frequently use another way of numbering the years BC. Instead of 1 BC they use 0, instead of 2 BC they use -1, instead of 3 BC they use -2, etc." No private communication can satisfy Wikipedia's verifiability requirement. It becomes extremely tiresome arguing with someone who won't take no for an answer, hence Adhemar, Jclerman, and I quite the 'discussion'. — Joe Kress (talk) 01:11, 28 February 2009 (UTC)+

Joe- Why do you add [for historians] to the title of the first paragraph? That paragraph obviously sets up the sequence -1,0,+1 (as in the fence line proposal (with index 0)) as I have maintained. The second paragraph (year zero a problem?) seems to me to be addressed to A GROUP of astronomers who insist that Year 0 AD equals the first year BC. You yourself have written that some astronomers simply subtract the endpoints. The fence line proposal with index 0 applies equally to the passage of time as measured by a sundial or a modern-day clock. The beginning of 11 AM is post -1, the meridian (0) is post 0 and the end of 1 PM is post +1. And the interval in both cases is 2. Voigt has pointed out this numbering system is completely independent of BC/AD.24.242.42.17 (talk) 20:37, 28 February 2009 (UTC)

You and your source are correct that there is no year zero for historians, but there is a year zero for astronomers as your source and numerous other sources state, including two direct quotes now in the article. I never said astronomers subtract endpoints—that is your word, not mine. I said that some astronomers (like Cassini) subtract instants at the beginning of calendar years. An instant at the beginning of the last year of an interval is not an endpoint, which could be misunderstood to mean the end of that year, as you insist on doing. The fence line analogy applies both to historical years (without a year zero) and to astronomical years (with a year zero). One of the panels between posts can represent an astronomer's calendar year zero between posts representing the instant at the beginning of that year (0.0) and the post representing the instant at the end of that year (+1.0), which is also the beginning of year +1. Whole years cannot be used to calculate intervals as you insist on doing. Intervals can only be calculated between specified instants within those years. If the instants are at the beginning of all years (per Cassini), then the interval between the beginning of year 0 (1 BC) and the beginning of year 1 (1 AD) is only one year, the astronomical year 0 or the historical year 1 BC. Year 1 AD is outside the interval, so the interval in this case is NOT 1+1=2. — Joe Kress (talk) 02:47, 1 March 2009 (UTC)+

1-Editorializing at the end of a partial quotation is not good practice.

2-I really thought I remembered your saying that at one point. This has gone on so long I would have to go back to the archives to find it. I apologize.

3. My source specifically said that there was no Year 0. He further stated "Therefore AD 1 follows immediately after 1 BC with no intervening Year 0". He should, of course, have said the first year AD and first year BC. No one disputes that these two years are contiguous (and they also provide the acceptable sequence -1,0,+1).

4. You say whole years cannot be used to calculate intervals. But you apply it to the sequence Year 1 BC, Year 0, Year 1AD. And I have pointed out many times that that sequence is faulty.

5. The interval question brings us back to the fence line analogy. Focus on the rails (Years) has diverted our attention from the posts. Index 1 (a la Lerman) makes the first post 1 and the first rail Year 1 (a la Cassini). I have proposed index 0 for the first post and rail. We now have -1,0+1. This gets us away from intervals. As far as I am concerned the instant the clock struck midnight on Dec.31, 1999 the first hour AND the first year of 2000 started simultaneously. So 11 PM is -1, midnight is 0, and 1 AM is +1.24.242.42.17 (talk) 03:37, 2 March 2009 (UTC)

According to NASA your source is incorrect. I think it is time to start questioning your source instead of Joe. NJGW (talk) 03:56, 2 March 2009 (UTC)

3OP - I accidentally erased part of your comments. But I certainly will consult NASA and my reference. 24.242.42.17 (talk) 17:14, 2 March 2009 (UTC)

3OP- NASA states "In this catalog (Catalog of Transits of Venus) dates are counted using the astronomical numbering system which recognizes the year 0". The statement is open to the question of whether there is another "astronomical numbering system". My source lays out a good case for the consideration of the idea of a first year BC with a point 0 between it and the first year AD. I have no doubt that everyone accepts that sequence to be -1, 0,+1. I am not claiming that the system with year 0 is incorrect just that it not the only system. It obviously has its uses to astronomers who are interested in events that fall within years. Hence Joe's references to intervals (which I find too technical for me).

Joe states (1 March 2009) "I said that some astronomers (like Cassini) subtract instants at the beginning of calendar years". Here we are talking about whole years whereas the NASA quote refers to "dates" (within years?). Thus we have two astronomical numbering systems that are valid. Trying to meld them by insisting on a year 0 AD equal to the first year BC cannot be proved. Back in Archive I of Talk: Year zero Voigt states (84.143.68.224,16:15 9 November 2007)"The year 0 exists always: but sometimes it is assigned the number 1". But with "sometimes" we can certainly assign the first year AD to the Year 0 AD. He also states{"The AD and BC years are counted with index "1". This implies that these two "eras" have different epoch years."} It can also imply that different numbering systems are involved. Voigt states "The AD and BC eras are counted with index 0. This implies that these two "eras" have the same epoch year". They do, of course, and it is the first year AD.

The first year BC can only be the last year of any calendar extant at the time Dionysius established his calendar. The BC era then consists of the ordinal numbering system extending backwards indefinitely (.......-2,-1). I know I have been warned to avoid the use of the ordinal and cardinal numbering systems but they do fill the bill. Since the first year of the AD era is Year 0 AD it is obvious that we are dealing with a cardinal numbering system. The net result is -2,-1, 0,+1, +2. This numbering system {(introduced with the fence line analogy (index 0)} applies with equal effectiveness to the passage of time as measured on a sundial or clock.24.242.42.17 (talk) 02:45, 10 March 2009 (UTC)

• "... counted using the astronomical numbering system which recognizes the year 0" Looks to me like they left out a comma before "which". The ANS uses year Zero.
• "My source lays out a good case..." Is your source usable within the context of Wikipedia? If not, that statement doesn't matter.

- NJGW (talk) 16:04, 10 March 2009 (UTC)

3OP - That's your opinion, OK. To me it certainly is a qualifying expression. My source is available on the internet. It is up to Wikipedia to rule whether it is usable.24.242.42.17 (talk) 16:11, 10 March 2009 (UTC)