Epoch (reference date)
In the fields of chronology and periodization, an epoch is an instant in time chosen as the origin of a particular era. The "epoch" then serves as a reference point from which time is measured. Time measurement units are counted from the epoch so that the date and time of events can be specified unambiguously.
Events taking place before the epoch can be dated by counting negatively from the epoch, though in pragmatic periodization practice, epochs are defined for the past, and another epoch is used to start the next era, therefore serving as the ending of the older preceding era. The whole purpose and criteria of such definitions is to clarify and co-ordinate scholarship about a period, at times, across disciplines.
Epochs are generally chosen to be convenient or significant by a consensus of the time scale's initial users, or by authoritarian fiat. The epoch moment or date is usually defined by a specific clear event, condition, or criteria— the epoch event or epoch criteria —from which the period or era or age is usually characterized or described.
- by events:
- by criteria:
- The spurt in exploration, mercantilism, and colonization in the Age of Discovery
- Particular ratios of animal fossils in a rock strata —various Geology epochs
Each calendar era starts from an arbitrary epoch, which is often chosen to commemorate an important historical or mythological event. For example, the epoch of the anno Domini calendar era (the civil calendar era used internationally and in many countries) is the Incarnation of Jesus. Many other current and historical calendar eras exist, each with its own epoch.
Asian national eras 
- The official Japanese system numbers years from the accession of the current emperor, regarding the calendar year during which the accession occurred as the first year.
- A similar system existed in China before 1912, being based on the accession year of the emperor (1911 was thus the fourth year of the Xuantong period). With the establishment of the Republic of China in 1912, the republican era was introduced. It is still very common in Taiwan to date events via the republican era. The People's Republic of China adopted the common era calendar in 1949 (the 38th year of the Chinese Republic).
- In India, the Indian national calendar follows the Saka era.
- North Korea uses a system that starts in 1912 (= Juche 1), the year of the birth of their founder Kim Il-Sung. The year 2011 is "Juche 100". Juche means "autarky, self-reliance".
- In Thailand in 1888 King Chulalongkorn decreed a National Thai Era dating from the founding of Bangkok on April 6, 1782. In 1912, New Year's Day was shifted to April 1. In 1941, Prime Minister Phibunsongkhram decided to count the years since 543 BC. This is the Thai solar calendar using the Thai Buddhist Era. Except for this era, it is the Gregorian calendar.
Religious eras 
- In Israel, the traditional Hebrew calendar, using an era dating from Creation, is the official calendar. However, the Gregorian calendar is the de facto calendar and is commonly used. Government documents usually display a dual date. The beginning of year 1 of the Hebrew calendar occurred in the autumn of 3761 BC. Therefore, "Rosh Hashanah, the Jewish New Year, in September 2003 marked the transition from 5763 to 5764".
- In the Islamic world, traditional Islamic dating according to the Anno Hegiræ (in the year of the hijra) or AH era remains in use to a varying extent, especially for religious purposes. The official Iranian calendar (used in Afghanistan as well as Iran) also dates from the hijra, but as it is a solar calendar its year numbering does not coincide with the religious calendar.
- In Hinduism, all festival are according to the Hindu calendar, based on the Vikram Samvat, which also functions as the national calendar of Nepal and Bangladesh.
- The Buddhist calendar is used on mainland Southeast Asia in the countries of Thailand, Cambodia, Laos, Burma (officially known as Myanmar) and Sri Lanka in several related forms.
- In the French Republican Calendar, a calendar used by the French government for about twelve years from late 1793, the epoch was the beginning of the "Republican Era", September 22, 1792 (the day the French First Republic was proclaimed, one day after the Convention abolished the monarchy).
- In the scientific Before Present system of numbering years for purposes of radiocarbon dating, the reference date is January 1, 1950 (though the use of January 1 is quite irrelevant, as radiocarbon dating has limited precision).
- Different branches of Freemasonry have selected different years to date their documents according to a Masonic era, such as the Anno Lucis (A.L.).
In astronomy, an epoch is a specific moment in time for which celestial coordinates or orbital elements are specified, and from which other orbital parametrics are thereafter calculated in order to predict future position. The applied tools of the mathematics disciplines of Celestial mechanics or its subfield Orbital mechanics (both predict orbital paths and positions) about a center of gravity are used to generate an ephemeris (plural: ephemerides; from the Greek word ephemeros = daily) which is a table of values that gives the positions of astronomical objects in the sky at a given time or times, or a formula to calculate such given the proper time offset from the epoch. Such calculations generally result in an elliptical path on a plane defined by some point on the orbit, and the two foci of the ellipse. Viewing from another orbiting body, following its own trace and orbit, creates shifts in three dimensions in the spherical trigonometry used to calculate relative positions. Interestingly, these dynamics in three dimensions are also elliptical, which means the ephemeris need only specify one set of equations to be a useful predictive tool to predict future location of the object of interest.
Over time, inexactitudes and other errors accumulate, creating more and greater errors of prediction, so ephemeris factors need to be recalculated from time to time, and that requires a new epoch to be defined. Different astronomers or groups of astronomers used to define epochs to suit themselves, but in these days of speedy communications, the epochs are generally defined in an international agreement, so astronomers world wide can collaborate more effectively. It was inefficient and error prone for data observed by one group to need translation (mathematic transformation) so other groups could compare information.
- The Julian date 2451545.0 TT (Terrestrial Time).
- January 1, 2000, 11:59:27.816 TAI (International Atomic Time). or
- January 1, 2000, 11:58:55.816 UTC (Coordinated Universal Time).
When dates or times are expressed as years with a decimal fraction from J2000, the years are of exactly 365.25 days, which is the average length of a year in the Julian calendar.
The time kept internally by a computer system is usually expressed as the number of time units that have elapsed since a specified epoch, which is nearly always specified as midnight Universal Time on some particular date.
Software timekeeping systems vary widely in the granularity of their time units; some systems may use time units as large as a day, while others may use nanoseconds. For example, for an epoch date of midnight UTC on January 1, 1900, and a time unit of a second, the time of the midnight between January 1 and 2, 1900 is represented by the number 86400, the number of seconds in one day. When times prior to the epoch need to be represented, it is common to use the same system, but with negative numbers.
These representations of time are mainly for internal use. If an end user interaction with dates and times is required, the software will nearly always convert this internal number into a date and time representation that is comprehensible to humans.
Notable epoch dates in computing 
||This section needs additional citations for verification. (September 2008)|
The following table lists epoch dates used by popular software and other computer-related systems. The time in these systems is stored as the quantity of a particular time unit (days, seconds, nanoseconds, etc.) that has elapsed since a stated time (usually midnight UTC at the beginning of the given date).
|Epoch date||Notable uses||Rationale for selection|
|January 1, 0||MATLAB, Symbian and Turbo DB|
|January 1, 1||Microsoft .NET, Go (programming language), REXX, Dershowitz and Reingold source code (where it is known as Rata Die)|
|January 1, 1601||NTFS, COBOL, Win32/Win64||1601 was the first year of the 400-year Gregorian calendar cycle at the time Windows NT was made.|
|January 1, 1753||Microsoft SQL Server||First full year after the adoption of the Gregorian calendar by Britain and her Colonies.|
|December 31, 1840||MUMPS programming language||1841 was a non-leap year several years before the birth year of the oldest living US citizen when the language was designed.|
|November 17, 1858||VMS, United States Naval Observatory, DVB SI 16-bit day stamps, other astronomy-related computations||November 17, 1858, 00:00:00 UT is the zero of the Modified Julian Day (MJD) equivalent to Julian Day 2400000.5|
|December 30, 1899||Microsoft COM DATE, Object Pascal||Technical internal value used by Microsoft Excel; to simplify calculations by falsely assuming 1900 to be a leap year.|
|January 0, 1900||Microsoft Excel, Lotus 1-2-3||While logically January 0, 1900 is equivalent to December 31, 1899, these systems do not allow users to specify the latter date.|
|January 1, 1900||Network Time Protocol, IBM CICS, Mathematica, RISC OS, Common Lisp, Michigan Terminal System|
|January 1, 1904||LabVIEW, Apple Inc.'s Mac OS through version 9, Palm OS, MP4, Microsoft Excel (optionally), IGOR Pro||1904 is the first leap year of the twentieth century.|
|January 1, 1950||SEGA Dreamcast|
|January 1, 1960||S-Plus, SAS|
|December 31, 1967||Pick OS and variants (jBASE, Universe, Unidata, Revelation, Reality)||Chosen so that (date mod 7) would produce 0=Sunday, 1=Monday, 2=Tuesday, 3=Wednesday, 4=Thursday, 5=Friday, and 6=Saturday.|
|January 1, 1978||AmigaOS|
|January 1, 1980||DOS, OS/2, FAT16 and FAT32 filesystems, VOS|
|January 6, 1980||Qualcomm BREW, GPS, ATSC 32-bit time stamps||GPS counts weeks (a week is defined to start on Sunday) and January 6 is the first Sunday of 1980.|
|January 1, 1981||Acorn NetFS|
|January 1, 1984||CiA® (CAN in Automation) CANopen® TIME_STAMP|
|22 August 1999||Galileo satellite navigation system time|
|January 1, 2000||AppleSingle, AppleDouble, PostgreSQL|
|? ?, 2000||FATX filesystem|
|January 1, 2001||Apple's Cocoa framework||2001 is the year of the release of Mac OS X 10.0.|
Problems with epoch-based computer time representation 
Computers do not generally store arbitrarily large numbers. Instead, each number stored by a computer is allotted a fixed amount of space. Therefore, when the number of time units that have elapsed since a system's epoch exceeds the largest number that can fit in the space allotted to the time representation, the time representation overflows, and problems can occur. While a system's behavior after overflow occurs is not necessarily predictable, in most systems the number representing the time will reset to zero, and the computer system will think that the current time is the epoch time again.
Most famously, older systems which counted time as the number of years elapsed since the epoch of January 1, 1900 and which only allotted enough space to store the numbers 0 through 99, experienced the Year 2000 problem. These systems (if not corrected beforehand) would interpret the date January 1, 2000 as January 1, 1900, leading to unpredictable errors at the beginning of the year 2000.
Even systems which allocate more storage to the time representation are not immune from this kind of error. Many Unix-like operating systems which keep time as seconds elapsed from the epoch date of January 1, 1970, and allot timekeeping enough storage to store numbers as large as 2 147 483 647 will experience an overflow problem on January 19, 2038 if not fixed beforehand. This is known as the Year 2038 problem. A correction involving doubling the storage allocated to timekeeping on these systems will allow them to represent dates more than 290 billion years into the future.
Other more subtle timekeeping problems exist in computing, such as accounting for leap seconds, which are not observed with any predictability or regularity. Additionally, applications which need to represent historical dates and times (for example, representing a date prior to the switch from the Julian calendar to the Gregorian calendar) must use specialized timekeeping libraries.
Finally, some software must maintain compatibility with older software that does not keep time in strict accordance with traditional timekeeping systems. For example, Microsoft Excel observes the fictional date of February 29, 1900 in order to maintain compatibility with older versions of Lotus 1-2-3. Lotus 1-2-3 observed the date due to an error; by the time the error was discovered, it was too late to fix it—"a change now would disrupt formulas which were written to accommodate this anomaly".
Epoch in Satellite-based Time Systems 
There are at least six Satellite navigation systems, all of which function by transmitting time signals. Of the only two satellite systems with global coverage, GPS calculates its time signal from an epoch, whereas GLONASS calculates time as an offset from UTC, with the UTC input adjusted for leap seconds. Of the only two other systems aiming for global coverage, Galileo calculates from an epoch and Beidou calculates from UTC without adjustment for leap seconds. GPS also transmits the offset between UTC time and GPS time, and must update this offset every time there is a leap second, requiring GPS receiving devices to handle the update correctly. In contrast, leap seconds are transparent to GLONASS users. The complexities of calculating UTC from an epoch are explained by the European Space Agency in Galileo documentation under "Equations to correct system timescale to reference timescale" 
See also 
- Annum, Anno Lucis, Anno Mundi
- Dating Creation
- Epoch (astronomy), Epoch (geology)
- Holocene calendar, Lunisolar calendar
- Metonic cycle, Saros (astronomy)
- Blackburn, B. & Holford-Strevens, L. (2003). The Oxford Companion to the Year: An exploration of calendar customs and time-reckoning. Oxford University Press. Glossary entry for "Incarnation era", p. 881.
- My Jewish Learning:Counting the Years
- Rosetta Calendar
- Higham, Thomas. "Radiocarbon dating - Age calculation". Retrieved 31 December 2009.
- Stuiver, Minze; Polach HA (1977). "Discussion; reporting of C-14 data.". Radiocarbon (University of Arizona) 19 (3): 355–363. Retrieved 31 December 2009.
- Seidelmann, P. K., Ed. (1992). Explanatory Supplement to the Astronomical Almanac. Sausalito, CA: University Science Books. p. 8.
- Seidelmann, P. K., Ed. (1992). Explanatory Supplement to the Astronomical Almanac. Sausalito, CA: University Science Books. Glossary, s.v. Terrestrial Dynamical Time.
- "Introduction to MATLAB" (PDF). p. 52. Retrieved April 21, 2009.
- Dershowitz, N. & Reingold, E. M. (2008). Calendrical calculations (3rd ed.). Cambridge University Press. p. 10 ISBN 978-0-521-70238-6.
- Why is the Win32 epoch January 1, 1601? The Old New Thing, MSDN Blogs, 6 March 2009
- "What happened in 1841?". M Technology and MUMPS Language FAQ. Retrieved March 8, 2009.
- vms-base-time-origin.txt archived from the original
- Spolsky, Joel. "Why are the Microsoft Office file formats so complicated? (And some workarounds)". Retrieved March 8, 2009.
- Timing on the Macintosh by Martin Minow
- Mark Pick, International Spectrum Conference April 2010
- Time and frequency distribution using satellites
- Time Systems and Dates - GPS Time
- "AppleSingle/AppleDouble Formats for Foreign Files Developer's Note". Retrieved October 23, 2007.
- Kay Wilkins, Customer Relations Representative , Lotus Development Corp. (1992) quoted in Dershowitz, N. & Reingold, E. M. (2008). Calendrical calculations (3rd ed.). Cambridge University Press. p. xxi, xxvi. ISBN 978-0-521-70238-6.
- European Space Agency: http://www.navipedia.net/index.php/Time_References_in_GNSS
- Section 5(d) "Equations to correct system timescale to reference timescale" of RDI: European GNSS (Galileo) Open Service Signal In Space Interface Control Document (OS SIS ICD), Issue 1.1, September 2010 http://www.integralgis.com/pdf/GALILEO.pdf
- Critical and Significant Dates (J. R. Stockton), an extensive list of dates that are problematic for various operating systems and computing devices
- Potential problem dates for computers (pdf) A list of potential problem dates for computers and software from 2001 to 2100 (IET).