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 are 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 criterion — the epoch event or epoch criterion — from which the period or era or age is usually characterized or described.

Calendar eras

Regnal 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 third 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).

Pre-modern eras

• Olympiads, the ancient Greek era of four-year periods beginning in 776 BC.
• Ab urbe condita (753 BC), used in the Roman imperial period.
• The Anno Domini or "Common Era" era, still in use with the Gregorian and Julian calendars today, marks the Incarnation of Jesus as calculated in the 6th century by Dionysius Exiguus.^[1]
• Anno Mundi (years since the creation of the world) as used in the Byzantine calendar (5509 BC).
• Anno Mundi (years since the creation of the world) as used in the Hebrew calendar (3761 BC).^[2][3]
• The Islamic calendar counts "lunar years" by Anno Hegiræ (in the year of the hijra) or AH era (AD 622). The year count shifts relative to the solar year as the calendar is purely lunar. 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.
• The term Hindu calendar may refer to a number of traditional Indian calendars. A notable example of a Hindu epoch is the Vikram Samvat (AD 56), also used in modern times as "national calendar" of Nepal and Bangladesh.
• Buddhist calendars tend to use the epoch of 544 BC (date of Buddha's parinirvana).

Modern eras

• The Baha'i calendar is dated from the vernal equinox of the year the Báb proclaimed his religion (AD 1844). Years are grouped in Váḥids of 19 years, and Kull-i-Shay’s of 361 (19 x 19) years.^[4]
• 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.
• 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).
• The Indian national calendar, introduced in 1957, follows the Saka era (AD 78).
• North Korea uses a system that starts in 1912 (= Juche 1), the year of the birth of their founder Kim Il-Sung.
• 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).^[5][6]
• Different branches of Freemasonry have selected different years to date their documents according to a Masonic era, such as the Anno Lucis (A.L.).

Astronomy

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 worldwide 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.

J2000.0

The current standard epoch is called "J2000.0" This is defined by international agreement to be equivalent to:

1. The Gregorian date January 1, 2000 at approximately 12:00 GMT (Greenwich Mean Time).
2. The Julian date 2451545.0 TT (Terrestrial Time).^[7]
3. January 1, 2000, 11:59:27.816 TAI (International Atomic Time).^[8]
4. January 1, 2000, 11:58:55.816 UTC (Coordinated Universal Time).^[9]

Computing

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 (00:00) on January 1, 1900, and a time unit of a second, the time of the midnight (24:00) 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

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).

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.^[24] 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".^[36]

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.^[37] 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" ^[38]

See also

• Annum, Anno Lucis, Anno Mundi
  • Common Era (CE) (Anno Domini (AD))
• Dating Creation
• Epoch (astronomy), Epoch (geology)
• Holocene calendar, Lunisolar calendar
• Timekeeping on Mars
• Metonic cycle, Saros (astronomy)
• Mya

Notes

External links

• 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).