Year zero

There is no year zero in the widely used Gregorian calendar, nor in its predecessor, the Julian calendar. Under those systems, 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 (where it coincides with the Gregorian year 1 BC) as well as in all Buddhist and Hindu calendars.

Numerical background

There are two different ways of reckoning time:

The first way of reckoning is the traditional one in historiography and in common usage to label years, centuries, and millennia via a counting method. The second is used, for example, with a person's age which reckons time according to a measuring system.

Counting

One way is to use cardinal numbers (e.g. one, two, three, ...) or ordinal numbers (e.g. first, second, third, ...) This corresponds to treating time as a discrete variable, and the labels as "counts". Under this point of view, the first year counted after the starting point will come immediately after the first year counted before the starting point.

Measuring

In some contexts, however, such as astronomy, it can be more convenient to regard time as a continuous variable, and label time periods as "intervals" on a continuous scale, that is, as measurements of the total time elapsed since the start of the era. According to this interpretation, elapsed time year 1 begins exactly one full year "after" the starting point, and the first year is year 0 (meaning that zero full years have elapsed since the starting point).

Third millennium

According to the normal historians' usage, the third millennium of the Gregorian calendar began on 1 January 2001, rather than the popularly-celebrated 1 January 2000. This is a direct consequence of the absence of a year zero in the "anno Domini" era. Had there been a year zero, which might be considered part of the first millennium, then 1 January 2000 would indeed mark 2000 years since the year numbering datum and be the start of the third millennium.

Note that this also applies to centuries. Thus, the 20th century actually began on 1 January 1901.

Historical, astronomical and ISO year numbering system

Historians

Dionysius Exiguus (c.470–c.544) introduced the "anno Domini" era, which he used to identify the several Easters in his Easter table, but did not use it to date any historical event. When he devised his table, Julian calendar years were identified by naming the consuls who held office that year — he himself stated that the "present year" was "the consulship of Probus Junior [Flavius Probus] ", which he also stated was 525 years "since the incarnation of our Lord Jesus Christ". [http://hbar.phys.msu.su/gorm/chrono/paschata.htm Nineteen year cycle of Dionysius] ] How he arrived at that number is unknown. He invented a new system of numbering years to replace the Diocletian years that had been used in an old Easter table because he did not wish to continue the memory of a tyrant who persecuted Christians.

Bede (c.672–735) was the first historian to use a BC year, and hence the first one to choose 1 as the origin of the BC era, thus 1 BC, in his "Historia ecclesiastica gentis Anglorum" ("Ecclesiastical history of the English people", 731). Bede did not sequentially number days of the month, weeks of the year, or months of the year, but 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 week), used by Africanus, or "anno Abrahami" ("in the year of Abraham") beginning 3,412 years after Creation according to the Septuagint, used by Eusebius, 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". [ [http://www.fordham.edu/halsall/basis/bede-book1.html Ecclesiastical History of the English Nation] ] 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 (albeit with a correct year).

It is often stated that Bede did not use a year zero because he did not know about the number zero. Although the Arabic numeral for zero (0) did not enter Europe until the eleventh century, and Roman numerals had no symbol for zero, Bede and Dionysius Exiguus did use a Latin "word", "nulla" meaning "nothing", alongside Roman numerals or Latin number words wherever a modern zero would have been used. [Faith Wallis, trans. "Bede: The Reckoning of Time" (725), Liverpool: Liverpool Univ. Pr., 2004. ISBN 0-85323-693-3.] ["Byrhtferth's Enchiridion" (1016). Edited by Peter S. Baker and Michael Lapidge. Early English Text Society 1995. ISBN 9780197224168.]

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"). [Werner Rolevinck, " [http://www.cervantesvirtual.com/servlet/SirveObras/80248064097793506388868/index.htm Fasciculus temporum] ".] The "anno Domini" nomenclature was not widely used in Western Europe until the 9th century, and the 1 January to 31 December historical year was not uniform throughout Western Europe until 1752. 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.

Since Bede, historians have not counted with a year zero. This means that between, for example, January 1, 500 BC and January 1, AD 500, there are 999 years: 500 for BC years, and 499 for AD years preceding 500. In common usage "anno Domini" 1 is preceded by the year 1 BC, without an intervening year zero. [While it is increasingly common to place "AD" after a date by analogy to the use of "BC", formal English usage adheres to the traditional practice of placing the abbreviation before the year as in Latin (e.g., 100 BC, but AD 100).] 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. No historian includes a year 0 when numbering years in the current standard era. Historians even refuse to use a year 0 when using negative years before our positive era, hence their −1 immediately precedes 1. [V. Grumel, "La chronologie" (1958), page 30.]

Astronomers

Astronomers, for whom ease of mathematical calculation is more important, have used a defined leap year zero equal to 1 BC of the traditional Christian era since the 18th century. The first use of an astronomical year 0 is traditionally attributed to Jacques Cassini whose stated reasons for including a year zero were:

But Philippe de La Hire had used a year zero earlier in 1702 in his "Tabulæ Astronomicæ" ("Astronomical Tables") in the form "Christum o." ("Christ 0"), without explanation. Both Cassini and La Hire used BC years before their year 0 and AD years thereafter (hence the sequence 1 BC, 0, AD 1). That is why Cassini stated that their "sum" yielded the interval. For example, 1 + 1 = 2. Beginning in the 19th century, some astronomers began to use negative years before their year 0, while other astronomers continued to use BC years before their year 0. By the mid 20th century, all astronomers were using negative years before year 0 (hence the sequence −1, 0, 1). Thus modern astronomers would state that the years' "difference" yields the interval, just as it does if the years are both positive or both negative. For example, 1 − (−1) = 2, and 2000 − 1999 = 1. Although 'AD' is omitted from later years, leaving a bare number, a positive sign (+) is sometimes prefixed to the number. Because of possible confusion with the earlier use of an astronomical BC, only in the modern version can it be said that astronomical year 0 equals the historical year 1 BC.

ISO 8601

(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, whereas that is unusual. The "basic" format for year 0 is the four-digit form 0000, which equals the historical year 1 BC. Several "expanded" formats are possible: -0000 and +0000, as well as five- and six-digit versions. Earlier years are also negative four-, five- or six-digit years, which have an absolute value one less than the equivalent BC year, hence -0001 = 2 BC. Because only ISO 646 (7-bit ASCII) characters are allowed by ISO 8601, the minus sign is represented by a hyphen-minus.

Other traditions

South Asian calendars

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 24-hour clock: during the first hour of a day, the time elapsed is 0 hours, xx minutes.

Maya historiography

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.

Popular culture year numbering systems

*In the movie "Back to the Future", Dr. Emmett Brown, the inventor of a time machine, enters the input date of the "birth of Christ" on a keypad as "December 25, 0000", implying that he uses the astronomical year numbering. It should be noted that the DVD commentary clearly points out that the date was a joke.
*In the movie, "The Beach", Leonardo DiCaprio's character is, during his mental instability, crazed about the term Year 0.
*The fictitious theologian Franz Bibfeldt's most famous work relates to the year 0: a 1927 dissertation submission to the University of Worms entitled " [http://magazine.uchicago.edu/9502/Feb95Bibfeldt.html The Problem of the Year 0] ".
*The Zork timeline included with the comedy game Zork Grand Inquisitor features the year 0 GUE with the annotation: "As the year zero begins, people feel fairly confident that something big is about to happen."
*Panic in Year Zero! is a 1962 science fiction film directed by and starring Ray Milland. 1962 becomes the "year zero" when Los Angeles is destroyed by a hydrogen bomb as part of a worldwide nuclear war.
*In the Star Wars Expanded Universe, events take place in 0 BBY/ABY (Before the Battle of Yavin/After the Battle of Yavin). This is because the destruction of the Death Star is used to calculate year 0.

References

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