Decimal time

French decimal clock from the turn of the 19th century

Decimal time is the representation of the time of day using units which are decimally related. This term often is 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.

History

Egypt

Decimal time was said to have been introduced in Ancient Egypt by Thoth. The day was divided into 10 parts, each part into 100 subdivisions, each further divided by 100, making 100,000 divisions in a day. Additionally, each Egyptian month was divided into three periods of 10 days called decans, and each of the 36 decans of the year was represented by a different constellation.

China

For its entire recorded history of two or three millennia decimal time had been used in China alongside duodecimal time. The day was divided into both 100 parts called ke and into twelve double hours called shi. 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).

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 an 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. The French Republican Calendar, which was introduced at the same time and divided the month into three décades of 10 days each, eventually also fell out of use, and was abolished at the end of 1805. The original metric system, also adopted during the Revolution, beginning in 1790, had no unit of time; later versions of the metric system used the second equal to 1/86400 day as the metric time unit.

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.

Conversions

There are exactly 86400 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.

One decimal second is 86400/100000 = 0.864 standard seconds.
One decimal minute is 1440/1000 = 1.44 standard minutes, i.e. 1 minute 26.4 seconds.
One decimal hour is 24/10 = 2.4 standard hours.
The average adult human heart rate is close to 1 beat per decimal second, or 100 beats per decimal minute.

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

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:

Gregorian dates: 2000 January 1.5
ordinal dates: 00001.5
Julian dates: 2451545.0
Excel serial dates: 36526.5

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 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 0^d·286003, or at 6^h 51^m 50^s·66 Greenwich Mean Time...For example, at 12^h 0^m 0^s Greenwich Mean Time, or 0^d·500000...

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 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, and for not providing for more precise units, although third-party applications have proposed "centibeats" and "millibeats".

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
5:00 French decimal time
@500 Swatch Internet Time
500 millidays
50.0% Percent 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.

Decimal time and speed

In most countries around the world, speed is measured in kilometres per hour (km/h). In the United States, it is measured in miles per hour (mph or sometimes mi/h). Speed is also measured in metres per second (m/s). When decimalizing the day by 10s, the only units there are for time and distance measurements are the metre and the day.

Decimal time speeds are measured in metres/day. 100 km/h (about 62 mph) is equivalent is to 100,000 metres per hour, that is similar to 2,400,000 metres per day.

This is equivalent to:

2400 Mm/kd (megametres/kiloday)
240 Mm/hd (megametres/hectoday)
24 Mm/dad (megametres/dekaday)
2.4 Mm/d (megametres/day)
2400 km/d (kilometres/day)
240 km/dd (kilometres/deciday)
24 km/cd (kilometres/centiday)
2.4 km/md (kilometres/milliday)
2400 hm/dd (hectometres/deciday)
240 hm/cd (hectometres/centiday)
24 hm/md (hectometres/milliday)
2400 dam/cd (dekametres/centiday)
240 dam/md (dekametres/milliday)
2400 m/md (metres/milliday)
2.4 m/μd (metres/microday)
24 dm/μd (decimetres/microday)
240 cm/μd (centimetres/microday)
2400 mm/μd (millimetres/microday)

24 and 240 are more practical values than 2400 and 2.4. Megametres, hectometres, and dekametres are rarely used. Barring them, the likely possibilities for, for eample, car speed, measuring in decimal time is km/dd and km/cd, depending upon how much granularity is necessary. The speed of light would be approximately 26 megametres per microday, the rate the Himalayas are growing by about 1.5 millimetres per centiday.

External links

References

National Convention of the French Republic (1793) LE CALENDRIER RÉPUBLICAIN Textes officiels Décrets Relatifs à l'établissement de l'Ère Républicaine published by Philippe Chapelin 2002
Sizes, Inc. (2000) decimal time units Last revised February 27 2004
Herschel, John (1849) Outlines of Astronomy published by Gallica 1995