Set Your Clocks to Decimal Time

Many stop lights at street intersections display a countdown of the remaining seconds before the light changes. If you’re like me, you count this time in your head and then check how in sync you are. But did you know that if the French had their way back in the 1890s when they tried to introduce decimal time, you’d be counting to a different beat? Did you know the Chinese have used decimal time for millennia? And did you know that you may have unknowingly used it already if you’ve programmed in Linux? Read on to see what decimal time is along with the answers to these questions.

How We Got Where We Are

Babylonian numerals
Babylonian numerals, By Jose117 [CC BY-SA 4.0], via Wikimedia Commons

First off, just why do we have 60 seconds, 60 minutes and 24 hours in a day? The 24 hour day started with the Egyptians breaking the number of daylight hours into 12. One possible reason for using 12 is that it’s the number of segments we have separated by knuckles on the four fingers of each hand. Notice how easily you can count them using your thumbs, something you should be comfortable with in these days of thumb-manipulated mobile phones.

The use of 60 minutes in an hour and 60 seconds in a minute didn’t come into everyday use until the invention of mechanical clocks in the 16th century. Prior to that their use just wasn’t practical. The selection of 60 for the divisions stems ultimately from the Sumerians with their sexagesimal (base 60) number system, though it’s difficult to find just when they were chosen for the units of time. The words minute and second come from the latin pars minuta prima, which means “first small part”, and pars minuta secunda, or “second small part”.

The second was for a long time defined to be 1/86400 of a mean solar day (60*60*24 = 86400). It was recently defined more precisely as “the duration of 9,192,631,770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium 133 atom”.

But as you can see above, though necessary and useful, all our units were derived from fairly arbitrary sources and are of arbitrarily selected lengths.

Metric Time Vs Decimal Time

Before getting into decimal time, we should clear up what we mean by metric time, since the two are often used incorrectly. Metric time is for measurement of time intervals. We’re all familiar with these and use them frequently: milliseconds, microseconds, nanoseconds, and so on. While the base unit, the second, has its origin in the Sumerian base 60 number system, it is a metric unit.

Decimal time refers to the time of day. This is the division of time using base 10 instead of dividing the day into 60, 60 and 24.

French Decimal Time

French decimal time clock
French decimal time clock, By Cormullion, Own work [CC BY-SA 3.0], via Wikimedia Commons

There were a few attempts in France to switch to decimal time. The first began use in 1794 during the French Revolution (1789-1799). They divided the day into 10 hours, each hour being 100 minutes long, and each minute containing 100 seconds.

This allowed for time to be written as we would, 2:34 for 2 hours and 34 minutes, but also as the decimal numbers 2.34 or even 234. For timestamping purposes we’d write 2016-12-08.234. We could also write it as the fraction 0.234 of the day or written as a percentage, 23.4% of the day. The seconds can simply be added on as an additional 2 digits.

That’s certainly simpler than what we currently have to do with our standard system. To convert 2:34 AM to a single number representing the duration of the day in minutes we have to do:

(2 hours*60 min/hour)+34 min=154 minutes

As a fraction of the day it’s:

154 min/(60 min/hour * 24 hours)=0.1069

And finally, 0.1069 as a percentage is 10.69%. Summarizing, that’s the time 2:34 AM represented as 154 minutes, 0.1069, and 10.69%. You can hardly blame the French for trying. Vive la revolution!

Decimal time went into official use in France on September 22, 1794 but mandatory use ended April 7, 1795, giving it a very short life. Further attempts were made in the late 1800s but all failed.

Swatch Beat watch
Swatch Beat watch

If you do the math, each hour in the French decimal system was 144 conventional minutes long, each minute was 86.4 conventional seconds and each second was 0.864 conventional seconds. If you can get used to an hour that’s twice as long, probably not too difficult a feat, the minutes and seconds are reasonably close to what we’re used to. However, science uses the second as the base of time and that’s a huge amount of momentum to overcome.

Incidentally, in 1998, as part of a marketing campaign, the Swatch corporation, a Swiss maker of watches, borrowed from the French decimal time by breaking the day into 1000 ‘.beats’. Each .beat is of course 86.4 seconds long. For many years they manufactured watches that displayed both standard time and .beat time, which they also called Internet Time.

Chinese Decimal Time

China has as long and varied a history as that of the West, and for over 2000 years, China used decimal time for at least one unit of its time system. They had a system where the day was divided into 12 double hours, but also a system dividing it into 100 ke. Each ke was further divided into either 60 or 100 fen at different times in its history.

Fractional Days

But decimal time is in use today. The fractional day is also a form of decimal time and is used in science and in computers. The time of day is expressed as the conventional 24 hour time but converted to a fraction of the day. For example, if time 0 is 12:00 midnight, 2:30 AM is:

((2*3600 sec/hour) + 30*60 sec/min) / 86400 sec/day = 0.10417

As many decimal places as needed can be used.

One example where fractional days are used is by astronomers for Julian days. Julian days are solar days in decimal form with 0 being noon Universal time (UT) at the beginning of the Julian calender, November 24, 4717 BC. For example, 00:30:00 UT January 1, 2013 as a Julian date is 2,456,293.520833.

Microsoft Excel also uses fractional days within dates similar to Julian dates but called serial dates. The time of day is stored as a decimal fraction of the 24 hours clock starting from midnight.

Unix/Linux Time

We may be repulsed by the idea of switching to an unfamiliar decimal time in our daily lives but many of us have used it when calling the time() function in Unix variations such as Linux. This function returns the current time in seconds since the beginning of some epoch. The Unix epoch began on 0:00:00 UTC January 1, 1970, a Thursday. But at least those seconds are of the length we’re used to — no need to resynchronize our internal counter there.

Vive La Revolution!

But while the French revolution is in the past, rebels do exist here at Hackaday. [Knivd] is one such who has devised a decimal time called C10 that’s slightly different from the French’s. And he already has at least one fellow conspirator, [Danjovic], who’s already made a decimal clock called DC-10. How long before we’re all counting to the beat of a different drum, and crossing those intersections before the light has changed?

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