Year zero is not used 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 ISO 8601:2004 (where it coincides with the Gregorian year 1 BC) as well as in all Buddhist and Hindu calendars.

[edit] 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.

[edit] 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.

[edit] 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).

[edit] 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.

This also applies to centuries. Thus, the 20th century began on 1 January 1901; and the 21st century began on 1 January 2001.

[edit] Historical, astronomical and ISO year numbering system

[edit] 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 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".^[1] 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, 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 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".^[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 (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.^[1][3][4]

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 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.^[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. 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.^[7]

[edit] Astronomers

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 25 December), 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 Jesus-Christ, 0, 1 après Jesus-Christ 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 Jesus-Christ and 1 après Jesus-Christ 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.

[edit] Astronomical notation

Astronomical years can be used to identify a calendar year (when placed alongside a month and a day) or to identify a certain instant (known in astronomy as an epoch). Modern astronomers identify an instant with a small number of fractional decimal digits after the year, unless higher precision is necessary: 2000.0 is understood as noon 1 January 2000, 1992.5 is 1 July 1992, and 1996.25 is an instant one-quarter of a year after the beginning of 1996. Near year 0, −1.0 is noon 1 January −1 (2 BC), 0.0 is noon 1 January 0 (1 BC), 1.0 is noon 1 January 1 (1 AD), and 2.0 = noon 1 January 2 (2 AD).

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.

Before 1925, all astronomical years began at noon 1 January at the meridian of some observatory—Kepler used the meridian of Uraniborg (Tycho Brahe's observatory), La Hire and Cassini used the meridian of the Paris Observatory, whereas modern astronomers use the meridian of the Royal Observatory, Greenwich.

[edit] History of astronomical usage

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 leap-years no longer exists; these years are, indeed, 1, 5, 9, 13, ... B.C. In the astronomical sequence, however, these leap-years are called 0, −4, −8, −12 ..., and the rule of divisibility 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 Jesus-Christ (BC), immediately before years labeled après Jesus-Christ (AD).^[12]

[edit] ISO 8601

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, 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.

[edit] Other traditions

[edit] 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, n minutes.

[edit] 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.^[13]

[edit] Year zero in popular culture

Computer Games

• 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."
• Wildfire Games' 0 A.D. is set in the fictional time period that is 0 A.D., justifying the appearance of all the civilizations at the height of their power

Film

• In the film 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 film The Beach, Leonardo DiCaprio's character is, during his mental instability, crazed about the term Year 0.
• 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 in the film Star Wars Episode IV: A New Hope is used to calculate year 0. Since the Battle of Yavin takes place in the third month of the calendar year, the years 0 BBY and ABY make up three and nine months of the same calendar year, respectively.

Theater

• Year Zero is a theatrical play that ran from September 11 to October 18, 2009 at the Victory Gardens Theater in Chicago, Illinois. The play was written by Michael Golamco, directed by Andrea J. Dymond, and featured a cast of four actors: Allan Aquino as Glen, Tim Chiou as Han, Joyee Lin as Vuthy Vichea, and Jennifer Shin as Ra Vichea. Year Zero, set in Long Beach, California, highlights the everyday struggles of a Cambodian-American family that immigrated to the United States after the rise of the Khmer Rouge regime in Cambodia.^[14][15]

Music

• Nine Inch Nails front man Trent Reznor used a fictional year 0 as the main theme in the concept album Year Zero.

Theology

• The fictitious theologian Franz Bibfeldt's most famous work relates to the year 0: a 1927 dissertation submission to the University of Worms entitled "The Problem of the Year 0".

[edit] References

v • d • e Chronology Major subjects Time · Astronomy · Geology · Paleontology · Archaeology · History Chronology Portal Eras and Epochs Calendar Eras: Ab urbe condita · Anno Domini / Common Era · Anno Mundi · Byzantine Era · Spanish era · Before Present · Hijri  · Egyptian · Sothic cycle · Hindu units of measurement · Hindu Yugas Regnal year: Canon of Kings · King lists · Limmu · Seleucid era Era name: Chinese · Japanese · Korean Calendars Pre-Julian Roman · Original Julian · Proleptic Julian · Revised Julian Gregorian · Proleptic Gregorian · Old Style and New Style Lunisolar · Solar · Lunar · Islamic · Chinese sexagenary cycle Astronomical year numbering · ISO week date Astronomic time and techniques Astronomical chronology · Cosmic Calendar · Ephemeris · Galactic year · Metonic cycle · Milankovitch cycles Geologic time scale and techniques Deep time · Geological history · Geological time units: Eons · Eras · Periods • Epoch • Age Dating Standards: GSSA • GSSP Chronostratigraphy · Geochronology · Isotope geochemistry · Law of superposition · Optical dating · Samarium-neodymium dating Archaeological techniques Dating methodology Absolute dating · Incremental dating · Archaeomagnetic dating · Dendrochronology · Glottochronology · Ice core · Lichenometry · Paleomagnetism · Radiocarbon dating · Radiometric dating · Tephrochronology · Thermoluminescence dating · Uranium-lead dating Relative dating · Seriation · Stratification Genetic techniques Amino acid dating · Molecular clock Related topics Chronicle · New Chronology · Periodization · Synchronoptic view · Timeline · Year zero · Circa · Floruit