Decimal time

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French decimal clock from the time of the French Revolution
French decimal clock from the time of the French Revolution

Decimal time is the representation of the time of day using units which are decimally related. This term is often used to refer specifically to French Revolutionary Time, which divides the day into 10 decimal hours, each decimal hour into 100 decimal minutes and each decimal minute into 100 decimal seconds, as opposed to the more familiar standard time, which divides the day into 24 hours, each hour into 60 minutes and each minute into 60 seconds.

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[edit] History

[edit] China

Main article: Ke (unit)

For its entire recorded history of two to three millennia, decimal time had been used in China alongside duodecimal time. The day was divided into both 100 parts called ke (Hanzi: 刻; Pinyin: kè) and into twelve double hours called shi (Traditional Chinese: 時辰; Simplified Chinese: 时辰; Pinyin: shíchen). To make ke compatible with shi, each ke was subdivided into 60 fen. Jesuits introduced Western time into China during the 17th century, at which time the day was redefined as having 96 ke (as well as 12 shi). Additionally, each month was divided into three periods of 10 days called xun (Hanzi: 旬; Pinyin: xún). xun are still used in formal documents.

[edit] France

In more modern times, decimal time was introduced during the French Revolution in the decree of 5 October 1793:

XI. Le jour, de minuit à minuit, est divisé en dix parties, chaque partie en dix autres, ainsi de suite jusqu’à la plus petite portion commensurable de la durée.
XI. The day, from midnight to midnight, is divided into ten parts, each part into ten others, so on until the smallest measurable portion of duration.

These parts were named on 24 November 1793 (4 Frimaire of the Year II). The primary divisions were called hours, and they added:

La centième partie de l'heure est appelée minute décimale; la centième partie de la minute est appelée seconde décimale. (emphasis in original)
The hundredth part of the hour is called decimal minute; the hundredth part of the minute is called decimal second.

Thus, midnight was reckoned as 10 o'clock, noon as 5 o'clock, etc. Although clocks and watches were produced with faces showing both standard time with numbers 1-24 and decimal time with numbers 1-10, decimal time never caught on; it was not officially used until the beginning of the Republican year III, September 22, 1794, and was officially suspended April 7, 1795 (18 Germinal of the Year III), in the same law which introduced the original metric system. Thus, the metric system at first had no time unit, and later versions of the metric system used the second, equal to 1/86400 day, as the metric time unit.

Decimal time was introduced as part of the French Republican Calendar, which, in addition to decimally dividing the day, divided the month into three décades of 10 days each, and was abolished at the end of 1805. The start of each year was determined according to which day the autumnal equinox occurred, in relation to true or apparent solar time at the Paris Observatory. Decimal time would also have been reckoned according to apparent solar time, depending on the location it was observed, as was already the practice generally for the setting of clocks.

The French made another attempt at the decimalization of time in 1897, when the Commission de décimalisation du temps was created by the Bureau des Longitudes, with the mathematician Henri Poincaré as secretary. The commission proposed a compromise of retaining the 24-hour day, but dividing each hour into 100 decimal minutes, and each minute into 100 seconds. The plan did not gain acceptance and was abandoned in 1900.

[edit] Conversions

There are exactly 86,400 standard seconds (see SI for the current definition of the standard second) in a standard day, but in the French decimal time system there are 100,000 decimal seconds in the day, so the decimal second is shorter than its counterpart.

Decimal to Standard

  • One decimal second is 86,400/100,000 = 0.864 standard seconds.
  • One decimal minute is 1,440/1,000 = 1.44 standard minutes, or 1 standard minute and 26.4 standard seconds.
  • One decimal hour is 24/10 = 2.4 standard hours.

One hundredth of a day is 14 standard minutes 24 standard seconds, or approximately 15 minutes.

Standard to Decimal

  • One standard second = 1.15740 decimal seconds
  • One standard minute = 69.44 decimal seconds (or .69 decimal minutes)
  • One standard hour = 4,166.67 decimal seconds (or 41 decimal minutes and 67 decimal seconds)

[edit] Fractional days

The most common use of decimal time of day is as fractional days used by scientists and computer programmers. Standard 24-hour time is converted into a fractional day simply by dividing the number of hours elapsed since midnight by 24 to make a decimal fraction. Thus, midnight is 0.0 day, noon is 0.5 d, etc., which can be added to any type of date, including:

As many decimal places may be used as required for precision, so 0.5 d = 0.500000 d. Fractional days are often reckoned in UTC or TT, although Julian Dates use Astronomical Time (TT+12h) and Microsoft Excel uses the local time zone of the computer. Using fractional days reduces the number of units in time calculations from four (days, hours, minutes, seconds) to just one (days). Fractional days are often used by astronomers to record observations, and were described in relation to the time of day by the 19th century astronomer John Herschel in his book, Outlines of Astronomy, as in these examples:

Between Greenwich noon of the 22d and 23d of March, 1829, the 1828th equinoctial year terminates, and the 1829th commences. This happens at 0d·286003, or at 6h 51m 50s·66 Greenwich Mean Time...For example, at 12h 0m 0s Greenwich Mean Time, or 0d·500000...

[edit] Swatch Internet Time

Main article: Swatch Internet Time

On October 23, 1998, the Swiss watchmaking company, Swatch, introduced a decimal time called Swatch Internet Time, which divides the day into 1000 .beats (each 86.4 s) counted from 000-999, with @000 being midnight and @500 being noon CET (UTC +1), as opposed to UTC. The company sells watches which display Internet Time. Internet Time has been criticized for using an origin different from Universal Time, misrepresenting CET as "Biel Mean Time", and for not providing for more precise units, although third-party applications have proposed "centibeats" (864 ms) and "millibeats" (86.4 ms).

[edit] Decimal times in fiction

Some science fiction authors use decimal time to reinforce the sense of "otherworldliness", notably Infocom's Planetfall and Stationfall games, which use "1 chronon = 1/10000 day" such that 0000 = midnight and 5000 = noon.

Isaac Asimov also uses and describes the use of Decimal time by the humans from the planet Solaria in his novel "The Naked Sun," in which he describes the Solarian hour as been divided into ten decads, each of which is divided into a hundred centads.

[edit] Other decimal times

Numerous individuals have proposed variations of decimal time, dividing the day into different numbers of units and subunits with different names. Most are based upon fractional days, so that one decimal time format may be easily converted into another, such that all the following are equivalent:

  • 0.500 fractional day
  • 5h 0m French decimal time
  • @500 Swatch Internet Time
  • 50.0 centidays
  • 500 millidays
  • 50.0% Percent Time
  • 12:00 Standard Time

Some decimal time proposals are based upon alternate units of metric time. The difference between metric time and decimal time is that metric time defines units for measuring time interval, as measured with a stopwatch, and decimal time defines the time of day, as measured by a clock. Just as standard time uses the metric time unit of the second as its basis, proposed decimal time scales may use alternative metric units.

[edit] See also

[edit] External links

[edit] References

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