Year zero

There is no year zero in the traditional Christian calendar used by historians , but there is in the astronomical year counting .

In the traditional system, the years are counted with ordinal numbers before and after the birth of Christ : The year 1 before the birth of Christ ends on December 31st ( 1 BC ), the next day, January 1st, the year 1 AD begins Birth ( 1 AD ).

The astronomical counting of the year, however, uses the natural numbers extended by zero and negative numbers , the so-called whole numbers . The 0 contained in this series of numbers corresponds to the year 1 BC. BC, the number −1 the year 2 BC Assigned.

Comparison of traditional and astronomical year counting

In the traditional system, the years from the “birth of Christ” are counted, beginning with 1, once in the past and once in the future. The system consists of two independent chronologies based on natural numbers.

The system of astronomers is a continuous chronology based on integers, which for natural numbers is the same as the traditional system.

In contrast to the historical counting of the year, the astronomical counting has a uniform calendar mathematics. All formulas and relations that can be produced uniformly on the basis of the astronomical year count for all years of the world break down into two heterogeneous parts in the historical year count.

The years 2 BC BC, 1 BC Chr., 1 AD (or 2 AC, 1 AC, 1 AD) of the historical counting of the year are called −1, 0, 1 in astronomical counting.

More recent astronomy manuals explain the differences as follows:

“When a new year is started, one has to clarify how the previous years are to be designated. Beda Venerabilis , the English historian of the eighth century, established a practice of counting the years before the year A.D. 1. […] In this, the year A. D. 1 goes to the year 1 BC. Without a year 0 in between. Because of its numerical discontinuity, this 'historical' system is cumbersome to differentiate between ancient and modern dates. Astronomers today use +1 for A.D. 1. And the year A.D. 1 is preceded by the year 0, this year by the year −1. As the use of the zero developed slowly in Europe, this 'astronomical' system was delayed. It was introduced by Jacques Cassini in the 18th century . "

- PK Seidelmann

“There is a disagreement between astronomers and historians about how to count the years before year 1. In this book, the years 'before Christ' are counted in an astronomical way. So the year before year 1 is year zero, and the year before this year is year −1. The year historians refer to as 585 BC is actually the year −584. (For negative years, 'BC' is not used! For example, '-584 BC' is incorrect.)
The astronomical way of counting the negative years is the only one that is suitable for arithmetic purposes. For example, the rule of divisibility by 4 for determining the Julian leap years in historical counting no longer applies ; these years are actually 1, 5, 9, 13, ... before Christ. In the astronomical series, however, these leap years are referred to as 0, −4, −8, −12, [...] and the rule of divisibility by 4 remains. "

- J. Meeus

History of the astronomical counting of the year

The method of counting preferred by astronomers is optionally known as astronomical or scientific year counting. At its core, the thing has nothing to do with astronomy, but with calendar mathematics .

It is very likely that the idea of replacing the traditional year counting with a counting method that is also suitable for arithmetic, in which the year before the year 1 is denoted by the number 0, came from the Italian astrologer Luca Gaurico (1476–1558). He justified his setting arithmetically. As an astrologer he was interested in reflections in chronology, he needed the year zero as a center of symmetry. In the 17th century, the astronomical year counting was common at the Academy of Sciences in Paris, as is evident from the lecture given by the astronomer Giovanni Domenico Cassini in 1696. The new counting method was then made public mainly by his son Jacques Cassini , who used it in astronomical tables. Today Jacques Cassini is often thought to be the father of the astronomical year counting.

Comparison between modern and Roman chronology

The traditional historical time calculation corresponds to the Roman calendar of Christian time calculation, but uses the Arabic number system despite the missing year zero . The astronomical calendar has zero this year. The year 1 BC According to legend , the year 753 corresponds to the founding of Rome .

Comparison of modern dates and Latin dates
Modern date	Historic year	Astronomical year		Roman year	Latin date
December 31	1 v. Chr.	0	=	DCC.LIII a. u. c.	pridie Kal. Ian.
January 1st	1 (ad)	1	=	DCC.LIV a. u. c.	Kalendis Ianuariis

Notes on the table

↑ The table shows the theoretical, correctly applied Julian calendar . Julius Caesar introduced his new calendar on January 1st DCCIX a. u. c. (709 = 45 BC) a. This year was a leap year. The previous year is called the Confused Year (because it had 445 days). After Caesar's death, however, a wrong, misunderstood switching mode was used for 36 years. The year 709 a. u. c. was immediately understood to be the first year again and a leap year was inserted again in the “fourth” year 712, ie after three years. So were the Roman years 715, 718, 721 etc. up to and including 745 a. u. c. (9 BC) all actually leap years. 36/3 = 12, but 36/4 = 9. The year 745 would have been a Roman leap year even if the switching rules were correctly applied. The actual leap years 749 a. u. c. (5 BC), 753 a. u. c. (1 BC) and 757 a. u. c. (4 AD) were canceled - so they were common years - to correct the calendar.

↑ In the Latin context: Ante Christum natum (AC) - Latin: "before the birth of Christ"; Anno Domini (AD) - Latin: "in the year of the Lord", ie after the birth of Christ.

↑ Ab urbe condita (a. U. C.) - Latin: "since the foundation of the city (Rome)".

↑ Although Caesar clearly set the New Year as January 1st, dates such as "pridie Kal. Ian." Can be interpreted differently with the following year number, since the Romans counted backwards from December 14th (XIX ante Kal. Ian.). December 30th is the third [ sic ] day before the calendar , while December 31st is the previous day (pridie Kal. Ian.) Of the calendar of the coming New Year.

Criticism of the ISO 8601 standard

The International Organization for Standardization created a controversial definition with its ISO 8601 standard . A leap year is assigned to the Gregorian calendar and it is declared a proleptic calendar that also counts into the past.

The Gregorian calendar was introduced in 1582 and, in contrast to the Julian calendar, understood by the reformers as expressly not proleptic (not even before the time of the reform).

For astronomers , the Gregorian 400-year cycle, within which the centuries are of unequal lengths , is unfavorable . Astronomical calculations need a uniform passage of time, which is why astronomers today always calculate in Julian centuries first and only at the end of the calculations correct all data after October 4, 1582 in Gregorian dates. You will therefore hardly apply the ISO 8601 : 1988 = EN 28601: 1992 standard in the future either.

The historians have never used the year zero. For the past they use the well-known, proleptic, Julian calendar of the Christian era, i.e. without year zero . It is therefore not to be expected that historians will ever implement ISO standard 8601. A re-dating of all historical events, according to which Julius Caesar instead of March 15, 44 BC. BC was murdered on March 13th of the year −43 (in ISO notation: −0043-03-13) is not to be expected.

In the computer sector, date formats are always converted with reference to a more recent point in time. Today this is mostly January 1st, 1970, 00:00 UT (see Unix time ). Hence, computer science has no need for a proleptic Gregorian calendar with a year zero.

literature

Arnold Linke: When does the third millennium begin? In: Sternkieker. Journal of the Society for Folk Astronomy eV Hamburg , 37th volume, 2nd quarter 2000, No. 181, p. 88.

Web links

Eric W. Weisstein: Calendar . In: Eric Weisstein's World of Astronomy (English)
Peter Knöbber: Beginning of the third millennium after Christ. Why didn't the year zero exist? pirabel.de, archived from the original on October 3, 2017 .; accessed on April 6, 2018

Individual evidence

^ PK Seidelmann: Explanatory Supplement to the Astronomical Almanac . University Science Books, Mill Valley 1992, ISBN 0-935702-68-7 , p. 579.
^ J. Meeus: Astronomical Algorithms . Willmann-Bell, Richmond 1998, ISBN 0-943396-61-1 , chap. 7th
↑ Luca Gaurico, Calendarium ecclesiasticum novum , Venice 1552, C2v, C6v, -, De eclipsi solis miraculosa in Passione Domini observata , Paris 1553,12r, 40v-41r.
^ Reports of the meetings of the Academy of Sciences . Paris 1698, p. 390 and in Joh. Albertus Fabricius: S. Hippolyti Episcopi et Martyri Operum vol. etc. Hamburg 1716, p. 62!
^ Jacques Cassini: Éléments d'astronomie & Tables astronomiques . Imprimerie Royale, Paris 1740.

[6] The table shows the theoretical, correctly applied Julian calendar . Julius Caesar introduced his new calendar on January 1st DCCIX a. u. c. (709 = 45 BC) a. This year was a leap year. The previous year is called the Confused Year (because it had 445 days). After Caesar's death, however, a wrong, misunderstood switching mode was used for 36 years. The year 709 a. u. c. was immediately understood to be the first year again and a leap year was inserted again in the “fourth” year 712, ie after three years. So were the Roman years 715, 718, 721 etc. up to and including 745 a. u. c. (9 BC) all actually leap years. 36/3 = 12, but 36/4 = 9. The year 745 would have been a Roman leap year even if the switching rules were correctly applied. The actual leap years 749 a. u. c. (5 BC), 753 a. u. c. (1 BC) and 757 a. u. c. (4 AD) were canceled - so they were common years - to correct the calendar.

[7] In the Latin context: Ante Christum natum (AC) - Latin: "before the birth of Christ"; Anno Domini (AD) - Latin: "in the year of the Lord", ie after the birth of Christ.

[8] Ab urbe condita (a. U. C.) - Latin: "since the foundation of the city (Rome)".

[9] Although Caesar clearly set the New Year as January 1st, dates such as "pridie Kal. Ian." Can be interpreted differently with the following year number, since the Romans counted backwards from December 14th (XIX ante Kal. Ian.). December 30th is the third [ sic ] day before the calendar , while December 31st is the previous day (pridie Kal. Ian.) Of the calendar of the coming New Year.

[1] PK Seidelmann: Explanatory Supplement to the Astronomical Almanac . University Science Books, Mill Valley 1992, ISBN 0-935702-68-7 , p. 579.

[2] J. Meeus: Astronomical Algorithms . Willmann-Bell, Richmond 1998, ISBN 0-943396-61-1 , chap. 7th

[3] Luca Gaurico, Calendarium ecclesiasticum novum , Venice 1552, C2v, C6v, -, De eclipsi solis miraculosa in Passione Domini observata , Paris 1553,12r, 40v-41r.

[4] Reports of the meetings of the Academy of Sciences . Paris 1698, p. 390 and in Joh. Albertus Fabricius: S. Hippolyti Episcopi et Martyri Operum vol. etc. Hamburg 1716, p. 62!

[5] Jacques Cassini: Éléments d'astronomie & Tables astronomiques . Imprimerie Royale, Paris 1740.