# Why is the second the SI base unit for time?

Specifically, during the moves towards Le Système international d'unités in the 18th and 19th centuries, why didn't anyone attempt to move us away from the definition of there being 24 hours in a day?

Wikipedia informed me that the name second comes from the second division of an hour. It also claims that the concept of having 24 hours in a day dates back at least 6000 years to the earliest Egyptian civilization. It also says the word second (as a measurement of time) didn't make it into English until the 1500's and couldn't be measured with any accuracy for 100 years. So by one way of looking at things, the base unit of time (or perhaps the grand-pappy unit of time) is the hour.

Is there some convenient property of 24 hours = 1 day that caused it to hold on while other units were phased out? I understand the significance of a degree being 1/360th of a circle (360 = 60 * 6 = 23 * 32 * 5), and 24 shares all of its factors (23 * 3), but that seems a flimsy reason. The math for converting earth's rotation to elapsed time doesn't even work out very conveniently (IMO) with these units.

I expected to find a reason in time being one of the basic properties of the universe, being immutable (in 18th century eyes) and therefore used as a pivot point for other unit definitions. But the dependency graph of SI units mostly dispelled me of that: both temperature and mass were found to be as independent as time, and both units were redefined during this period (to Kelvins and kilograms, respectively).

During the same period, other units were attempted to be re-measured from new standards:

• The measure of Length was changed to be the meter, at one ten-millionth from the North Pole to the Equator in 1793
• The measure of Mass was changed to the gram, at the cube of the hundredth part of the meter filled with water (at STP) in 1795
• The measure of Temperature was changed to be degrees Celsius, one hundredth of the separation between boiling and freezing of water (and eventually Kelvins).

And yet, efforts to define the second seem to center on more perfect measures of the existing definition of 1/86,400th of the Earth's rotation. Given the predilection for base 10 (and the gradual move away from units depending on our earthly frame of reference), why was the second left at such a cumbersome, ancient interval? Why didn't we redefine a new measure of time to be (say) 1/100,000th of a day, put 10 hours in a day, etc. etc.?

Did no one think to challenge the convention of 24 hours in a day? Why not?

That came out a little more jumbled than it was in my head, so let me sum up: I'm mainly interested in answers addressing attempts to redefine units of time and why they didn't achieve wide adoption in the scientific community.

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Seconds are the right time scale for bench-top mechanics experiments and for human movements or motion over laboratory scale distances. – dmckee Jul 2 '14 at 22:19
The meter: there is some discussion over the fact that $g$ is so close to $\pi^2$ in SI units. Some speculate that the French fudged the surveyors results a bit to match commonly used length standard of the length of the "seconds pendulum" (half-period = 1 second). – garyp Jul 3 '14 at 0:44
I have studied this a bit. The key is that the SI metric was developed by and for a small class of "eggheads" who knew Greek and Latin and were involved in the sciences. Their communications had almost no effect on the average person. Changing the units of time would be everybody's business. I have not seen any documents about Church opposition, but I can imagine the difficulty of finding new ways to determine when to ring the bells. – C. Towne Springer Jul 3 '14 at 3:58
@C.TowneSpringer: I don't think that's right. The metric system was developed in the wake of the French Revolution largely in response to populist anger over France's mess of differing and unstandardised units, as these were seen as being used by merchants to rip-off their customers. Rather the opposite of being used by elite scientists, the whole point was that they replaced the mish-mash of units used in everyday life by a single, rational, system. – simplicio Jul 3 '14 at 23:33
@simplicio I can understand a demand for a sane system, but I have a hard time with every shop customer knowing their Latin and Greek prefixes so they could differentiate between amounts bigger or smaller than 1. I have not seen any demands like that. Also, the syllable rich SI metric flies in the face of any practical use. Other systems use single syllable words for units that are very difficult to mistake when shouted across a work place. SI units sound very similar. I'll stand by the egghead source. – C. Towne Springer Jul 4 '14 at 1:15

A long time ago, the Chinese had a decimal time system, dividing the day into 100 ke (just under a quarter of an hour each). See for example item (2) in the following excerpt from "Heavenly Clockwork: The Great Astronomical Clocks of Medieval China" By Joseph Needham, Ling Wang, Derek John de Solla Price (image source)

The French revolutionaries tried it too - they kept 12 months, but they were 30 days each and divided into 3 weeks of 10 days; the day was divided into 10 hours of 100 minutes of 100 seconds. They made clocks that showed both times side by side - presumably to help in the transition. Like so much in the Revolution, it didn't last...

I stared at this image for quite some time and still couldn't quite figure out what time it was. Pretty sure it was the 12th, and 80 minutes past midnight. What puzzles me is that the outer hand seems to indicate that it is about 10 past 2 (24 hour clock). Those two do not agree. Maybe the clock is broken. For sure five hands is too many.

As to "why they didn't achieve widespread adoption"? The French revolutionaries were a pretty toxic bunch - you might think they were your friends, but they another power grab put your friends behind bars and your own career in peril. Given that even Antoine Lavoisier, the chemist, lost his head during La Terreur, it is not surprising that mainstream scientists might be reluctant to associate themselves with the revolutionary movement. And presumably they already had all the measurement equipment calibrated in seconds; it would have taken some time (and instrument makers who kept their heads) for a transition even to begin to take place. Remember that changing the definition of the second would have required a whole family of calibrated, traceable instruments to be created. At the time, this was not a revolutionary priority.

A very complete treatment of the issues of digital time can be found at http://www-history.mcs.st-and.ac.uk/HistTopics/Decimal_time.html

Some of the key points worth reiterating:

• the French tried this twice
• Laplace actually wrote a couple of books using decimal time units ("Traité de Mécanique Céleste")
• decimal calendar started on the equinox:

thus the sun illuminated both poles simultaneously, and in succession the entire globe, on the same day that, for the first time, in all it's purity, the flame of liberty, which must one day illuminate all mankind, shone on the French nation (September 22 1792 was the day the Republic was founded... Year 1, day 1)

• Decimal time was scrapped very quickly; decimal calendar lasted a bit longer (until Jan 1, 1806)
• 10 months of 30 days left an inconvenient 5 or 6 days "unaccounted for"; these were holidays.
• a 10 day week was unpopular: a mid week holiday was inserted.
• Napoleon scrapped the decimal calendar "to get the church in his side" just before being crowned emperor
• the second attempt to go decimal (end of 19th century) met resistance everywhere since all tables, instruments, maps, and even units (base units of ampere and candela and 20 odd derived units) would end up needing to be redefined.
Two references quoted in the above article:

K. Alder, The measure of all things (Little Brown, London 2002)
P. Galison, Einstein's clocks, Poincaré's maps (W W Norton & Co, New York 2004)

One more recent attempt at "decimal time" was made by Swatch who created a "universal time" that had 1000 .beats (really - dot-beats!) in a day - equal to one French decimal minute. "Let's have coffee at @450" never really took off... It is used as the time reference in ICQ and some online games, and the php time functions have a b format specifier to convert conventional time to .beats time.

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This is interesting. Could you provide references for the rise and fall of decimal time in France? – Emilio Pisanty Jan 29 '15 at 11:05
@EmilioPisanty I have provided some additional reference material – Floris Jan 29 '15 at 13:33
Interesting thought from your St Andrews reference: "The metric system succeeded because it was the simplest and it put an end to a veritable incoherence in local measures; the decimalisation of time and circumference failed because the whole world employed the same measures and the proposals sinned precisely because of their lack of unity." – Emilio Pisanty Jan 29 '15 at 13:46
Maybe the fact tat we gravitate toward factorializable terms means we should be switching our counting system to base 12 instead of base 10. – ahnbizcad Feb 2 '15 at 20:00

It's my understanding that the invention of the metric system during the turbulence following the French Revolution also included a switch to decimal time, with ten hours per day, etc., but that it didn't take. There's a certain amount of cultural inertia that has to be overcome; as you're probably aware, those of us in the United States still have many miles to go before we can fully adopt the metric system.

As you say, you have to give anonymous inventors of the 24-hour day credit: while the metric approach of powers-of-ten relationships between units is dreadfully easy to handle when you're using base 10 arithmetic, it's quite difficult to divide ten things into three equal-size sets. Remember that base ten is essentially an arbitrary choice made because most people have ten fingers and spend their childhood grouping things into fives and tens to count them. Twenty-four has boatloads of divisors: you can separate into a dozen pairs, three groups of eight, or six quartets. Sixty would make a pretty nice base, since it's the first number divisible by two, three, four, and five; but sixty is too many things for most people to count in their heads.

The second is actually historically based not on the length of a year, not of a day: until the adoption of the cesium clock standard in 1960, the definition of the second was actually the appropriate fraction "of the tropical year 1900." It took roughly half a century for the standards committee to realize that we can't go back and re-run the year 1900 to see whether we're still producing correct seconds.

There are several things that the SI system does that don't quite make as much sense as you might like. Why on earth does the base unit for mass, the kilogram, have a prefix? Why is the base unit for electricity the ampere, when we've known for a century that charge occurs naturally in standard-sized lumps? I put the SI endorsement of the historical relationship between the second, the minute, the hour, the day, and the year in the same category. It's a convenient unit with strong historical and popular support. I don't see a need to decimalize the day.

For historical timekeeping systems and the decimal time adventure of the French Revolution I happened across Carrigan, "Decimal Time", 1978, which cites

• For the division of the day in 24 hours by Egyptians, and the 60x60 subdivisions of the hour by Babylonians: O. Neugebauer, The Exact Sciences In Antiquity, Brown University Press, 1957.

• For a catalog by Hipparchus (ca 140 BC) of stars whose rising is separated by one-hour intervals, accurate to about one minute: the "time" article in the 11th edition of Encyclopedia Brittanica. The corresponding article in Brittanica online is quite lengthy, but hidden behind a paywall for me.

• For a medieval division of time into lit and dark "tides" (in English, "noontide" and "eventide"), each with twelve "hours" but only having equal length near the equinox: K. Welch, The History of Clocks and Watches, 1972.

• For a similar Oriental system not supplanted until Western commerce became important in the 1800s: J. Arthur, Time and its measurement, 1909.

Old papers have old references! Carrigan observes that while weights and measures are important enough for commerce that many local standards arose more or less at once, early precise timekeeping would be complicated by the vagaries of travel by ship or by land. The engineering skill to build a clock with a useful second hand "preceded to some extent the need for standards of communication at small time intervals[, which] may have led to the universality of the present time system."

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Upvote for "many miles to go before we can fully adopt the metric system". – Jordan Jul 2 '14 at 23:23
Isn't the Cesium definition of a second just a more precise way, just like how meter was? People were still using seconds, just in a less precise way before 1960... so I don't think this really addresses the historical roots of the second. – ahnbizcad Jan 27 '15 at 18:19
As for a 1959 person, a technical statement from that epoch reads, "In 1955 the [IAU] recommended that the second of Ephemeris Time be adopted as the fundamental unit of time, and in 1956 the [ICWM] redefined the second so as to make it identical with the second of Ephemeris Time (E.T.), .... The second of Universal Time is thus no longer the fundamental unit of time.... Ephemeris Time is defined by the orbital motion of the earth about the sun, but is obtained in practice from the orbital motion of the moon about the earth." – rob Jan 28 '15 at 4:34
As gwho points out, I'm mostly interested in references for the choice of the second as opposed to 'decimal time', and the failure of the latter in France. This is the "why" behind the choice of the second; everything after that is (very important but still) just details. – Emilio Pisanty Jan 29 '15 at 11:03
@EmilioPisanty Ah, I see. My metrological interest gives me a modern bias. – rob Jan 29 '15 at 21:00

The French Revolutionary Gov't did try to move towards a decimalized system of time measurement, with a second defined as one-one hundred thousandths of a day (along with decimal hours, minutes and a new calander), around the same time as it introduced the proto-metric system. But unlike the rest of the metric system, the new time keeping system and calender failed to catch on.

I suspect the reason is because while the rest of the metric system met a real need for standardized units in a France that had dozens of differing unit-systems for lengths, weights, volumes, etc., the sexigesmal system of time, along with the twelve month calendar, was already standardized enough by 1795 that the advantages to switching didn't outweigh the costs.

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I will search for some info on Decimal Time post revolution. Do you have a link for anything about it? – Patrick M Jul 3 '14 at 5:33
@Patrick: There's a wiki-page on "decimal time" which mentions several post-Revolution attempts to establish it in France. Not much detail there, but maybe you can follow the references there for more info if your interested. The same page mentions a Chinese decimal system that was apparently in-place for several millenia until the adoption of the European system. So not only does there not seem to be many places that have adopted a decimal system, at least one major civilization abandoned it. – simplicio Jul 3 '14 at 16:08
Do you know any good sources that will confirm this? There's some nice shiny rep for whoever does. – Emilio Pisanty Jan 25 '15 at 3:37
I seem to recall they (French revolutionaries) tried a ten-day week as well. Ironically, that experiment lasted ten years. As for the second - it's conveniently close to one-per-heartbeat. I have to believe that may have played a small part. – Floris Jan 28 '15 at 20:38