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Year zero does not exist in the Anno Domini/Common Era system usually used to number years in the Gregorian calendar and in its predecessor, the Julian calendar. In this system, the year 1 BC is followed by AD 1. However, there is a year zero in astronomical year numbering (where it coincides with the Julian year 1 BC) and in ISO 8601:2004 (where it coincides with the Gregorian year 1 BC) as well as in all Buddhist and Hindu calendars.
The Anno Domini era was introduced in 525 by Dionysius Exiguus (c. 470–c. 544), who used it to identify the years on his Easter table. He introduced the new era to avoid using the Diocletian era, based on the accession of Emperor Diocletian, as he did not wish to continue the memory of a persecutor of Christians. In the preface to his Easter table, Dionysius stated that the "present year" was "the consulship of Probus Junior [Flavius Anicius Probus Iunior]" which was also 525 years "since the incarnation of our Lord Jesus Christ".^{[1]} How he arrived at that number is unknown.
Dionysius did not use AD years to date any historical event. This began with the English cleric Bede (c. 672–735), who used AD years in his Historia ecclesiastica gentis Anglorum (731), popularizing the era. Bede also used a term similar to the English before Christ once, but that practice did not catch on until very much later. Bede did not sequentially number days of the month, weeks of the year, or months of the year, however, he did number many of the days of the week using a counting origin of one in Ecclesiastical Latin. Previous Christian histories used anno mundi ("in the year of the world") beginning on the first day of creation, or anno Adami ("in the year of Adam") beginning at the creation of Adam five days later (the sixth day of creation according to the Genesis creation narrative), used by Africanus, or anno Abrahami ("in the year of Abraham") beginning 3,412 years after Creation according to the Septuagint, used by Eusebius of Caesarea, all of which assigned "one" to the year beginning at Creation, or the creation of Adam, or the birth of Abraham, respectively. Bede continued this earlier tradition relative to the AD era.
In chapter II of book I of Ecclesiastical history, Bede stated that Julius Caesar invaded Britain "in the year 693 after the building of Rome, but the sixtieth year before the incarnation of our Lord", while stating in chapter III, "in the year of Rome 798, Claudius" also invaded Britain and "within a very few days … concluded the war in … the fortysixth [year] from the incarnation of our Lord".^{[2]} Although both dates are wrong, they are sufficient to conclude that Bede did not include a year zero between BC and AD: 798 − 693 + 1 (because the years are inclusive) = 106, but 60 + 46 = 106, which leaves no room for a year zero. The modern English term "before Christ" (BC) is only a rough equivalent, not a direct translation, of Bede's Latin phrase ante incarnationis dominicae tempus ("before the time of the lord's incarnation"), which was itself never abbreviated. Bede's singular use of 'BC' continued to be used sporadically throughout the Middle Ages.
Bede did not use a year zero because he did not know about the number zero. The Arabic numeral for zero (0) did not enter Europe until the eleventh century, and Roman numerals had no symbol for zero. Wherever a modern zero would have been used, Bede and Dionysius Exiguus did use Latin number words, or the word nulla (meaning "nothing") alongside Roman numerals.^{[1]}^{[3]}^{[4]} The Babylonian system of the BC era had also used the idea of "nothingness" without considering it a number.
The anno Domini nomenclature was not widely used in Western Europe until the 9th century, and the January 1 to December 31 historical year was not uniform throughout Western Europe until 1752. The first extensive use (hundreds of times) of 'BC' occurred in Fasciculus Temporum by Werner Rolevinck in 1474, alongside years of the world (anno mundi).^{[5]} The terms anno Domini, Dionysian era, Christian era, vulgar era, and common era were used interchangeably between the Renaissance and the 19th century, at least in Latin. But vulgar era was suppressed in English at the beginning of the 20th century after vulgar acquired the meaning of "offensively coarse", replacing its original meaning of "common" or "ordinary". Consequently, historians regard all these eras as equal.
Historians have never included a year zero. This means that between, for example, January 1, 500 BC and January 1, AD 500, there are 999 years: 500 years BC, and 499 years AD preceding 500. In common usage anno Domini 1 is preceded by the year 1 BC, without an intervening year zero.^{[6]} Thus the year 2006 actually signifies "the 2006th year". Neither the choice of calendar system (whether Julian or Gregorian) nor the era (Anno Domini or Common Era) determines whether a year zero will be used. If writers do not use the convention of their group (historians or astronomers), they must explicitly state whether they include a year 0 in their count of years, otherwise their historical dates will be misunderstood.^{[7]}
To simplify calculations, astronomers have used a defined leap year zero equal to 1 BC of the traditional Christian era since the 17th century. Modern astronomers do not use years for intervals because years do not distinguish between common years and leap years, causing the resulting interval to be inaccurate.
In astronomy, the numbering of all years labeled Anno Domini remain unchanged. However, the numerical value of years labeled Before Christ are reduced by one by the insertion of a year 0 before 1 AD. Thus, astronomical BC years and historical BC years are not equivalent. To avoid this confusion, modern astronomers label years as positive or negative, instead of BC or AD.
The current method was created by Jacques Cassini, who explained:
The year 0 is that in which one supposes that Jesus Christ was born, which several chronologists mark 1 before the birth of Jesus Christ and which 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.
—Jacques Cassini, Tables astronomiques, 5, translated from French
In this quote, Cassini used "year" as both a calendar year and as an instant before a year. He identified the calendar year 0 as the year during which Jesus Christ was born (on the traditional date of December 25), and as calendar leap years divisible by 4 (having an extra day in February). But "the sum of years before and after Jesus Christ" referred to the years between a number of instants at the beginning of those years, including the beginning of year 0, identified by Cassini as "Jesus Christ", virtually identical to Kepler's "Christi". Consider the three instants ('years') labeled 1 avant JesusChrist, 0, 1 après JesusChrist by Cassini, which modern astronomers would label −1.0, 0.0, +1.0. Cassini specified that his end years must be added, so the interval between the instants (noon 1 January) 1 avant JesusChrist and 1 après JesusChrist is 1 + 1 = 2, but modern astronomers would subtract their 'years', +1.0 − (−1.0) = 2.0, which agrees with Cassini. The calendar years between these two instants would be 2 BC and 1 BC, leaving the calendar year 1 AD beginning at +1.0 outside the interval.
Astronomers use year numbers not only to identify a calendar year (when placed alongside a month and a day number) but also to identify a certain instant (known in astronomy as an epoch). To identify an instant, astronomers add a number of fractional decimal digits to the year number, as required for the desired precision: thus J2000.0 designates noon 2000 January 1 (Gregorian), and 1992.5 is exactly 7.5 years of 365.25 days each earlier, which is the instant 1992 July 2.125 (03:00) (Gregorian). Similarly, J1996.25 is 3.75 Julian years before J2000.0, which is the instant 1996 April 1.8125 (19:30), onequarter of a year after the instant J1996.0 = 1996 January 1.5. In this notation, J0000.0 is noon of −1 December 19 (Julian), and J0001.0 is 18:00 on 0 December 18 (Julian). This astronomical notation is called Julian epoch and was introduced in 1984; before that time, astronomical year numbers with decimal fractions referred to Besselian years and were written without a letter prefix.^{[citation needed]}
During the 19th century astronomers began to change from named eras to numerical signs, with some astronomers using BC/0/AD years while others used −/0/+ years. By the mid 20th century all astronomers were using −/0/+ years. Numerical signs effectively form a new era, reducing the confusion inherent in any date which uses an astronomical year with an era named Before Christ.
In 1849 the English astronomer John Herschel invented Julian dates, which are a sequence of numbered days and fractions thereof since noon 1 January −4712 (4713 BC), which was Julian date 0.0. Julian dates count the days between two instants, automatically accounting for years with different lengths, while allowing for any arbitrary precision by including as many fractional decimal digits as necessary. The modern mathematical astronomer Jean Meeus no longer mentions determining intervals via years, stating:^{[8]}
The astronomical counting of the negative years is the only one suitable for arithmetical purpose. For example, in the historical practice of counting, the rule of divisibility by 4 revealing the Julian leapyears no longer exists; these years are, indeed, 1, 5, 9, 13, ... B.C. In the astronomical sequence, however, these leapyears are called 0, −4, −8, −12 ..., and the rule of divisibility by 4 subsists.
—Jean Meeus, Astronomical algorithms
In 1627 the German astronomer Johannes Kepler first used an astronomical year which was to become year zero in his Rudolphine Tables. He labeled the year Christi and inserted it between years labeled Ante Christum (BC) and Post Christum (AD) on the mean motion pages of the Sun, Moon, and planets.^{[9]} Then in 1702 the French astronomer Philippe de la Hire used a year he labeled Christum 0 at the end of years labeled ante Christum (BC), immediately before years labeled post Christum (AD) on the mean motion pages in his Tabulæ Astronomicæ, thus adding the designation 0 to Kepler's Christi.^{[10]} Finally, in 1740 the French astronomer Jacques Cassini (Cassini II), who is traditionally credited with the invention of year zero,^{[11]} completed the transition in his Tables astronomiques, simply labeling this year 0, which he placed at the end of years labeled avant JesusChrist (BC), immediately before years labeled après JesusChrist (AD).^{[12]}
ISO 8601:2004 (and previously ISO 8601:2000, but not ISO 8601:1988) explicitly uses astronomical year numbering in its date reference systems. Because it also specifies the use of the proleptic Gregorian calendar for all years before 1582, some readers incorrectly assume that a year zero is also included in that proleptic calendar, but it is not used with the BC/AD era. The "basic" format for year 0 is the fourdigit form 0000, which equals the historical year 1 BC. Several "expanded" formats are possible: 0000 and +0000, as well as five and sixdigit versions. Earlier years are also negative four, five or sixdigit years, which have an absolute value one less than the equivalent BC year, hence 0001 = 2 BC. Because only ISO 646 (7bit ASCII) characters are allowed by ISO 8601, the minus sign is represented by a hyphenminus.
All eras used with Hindu and Buddhist calendars, such as the Saka era or the Kali Yuga, begin with the year 0. All these calendars use elapsed, expired, or complete years, in contrast with most other calendars which use current years. A complete year had not yet elapsed for any date in the initial year of the epoch, thus the number 1 cannot be used. Instead, during the first year the indication of 0 years (elapsed) is given in order to show that the epoch is less than 1 year old. This is similar to the Western method of stating a person's age – people do not reach age one until one year has elapsed since birth (but their age during the year beginning at birth is specified in months or fractional years, not as age zero). However if ages were specified in years and months, such a person would be said to be, for example, 0 years and 6 months or 0.5 years old. This is analogous to the way time is shown on a 24hour clock: during the first hour of a day, the time elapsed is 0 hours, minutes.
Many Maya historians, but not all, assume (or used to assume) that a year 0 exists in the modern calendar and thus specify that the epoch of the Mesoamerican Long Count calendar occurred in 3113 BC rather than 3114 BC. This would require the sequence 1 BC, 0, AD 1 as in early astronomical years.^{[13]}
