Why was decimal time unsuccessful?

Just an addition (or an extended comment) to other answers.

I wouldn't say that people being conservative could not change time units quickly. They use time measurements everyday, it is more often than eg. measuring distances, however, people use money everyday also very often. Most money reforms (the largest are converting to euro in EU countries) takes at most two-five years. So it is not a big endeavor. And the time switch would also not be (if related to brains only, the financial effort would be large), but it should allow to use two units of time in parallel (eg. "old hours" and "new hours", or maybe "hour" and "dour" - "decimal hour"). The calendar switches were performed and nothing bad happened.

What is most important here, is that in fact no-one can force anybody to abandon the old unit. A government can make you use new money by removing the old ones from the market. Of course, it can punish for using "hours" instead of "dours", but it wouldn't be accepted by people in democracies.

The time reform would also be difficult, as it should be performed worldwide, probably in the very same moment. This is difficult and requires lots of effort. There are many things that are time-dependent, in today's era software, which 1. has to be modified, 2. has to be verified and tested, 3. has to be introduced at once, 4. should understand older time, 5. should be rapairable (support for all devices would require lots of people, and this is sure that software would have bugs). Also, there are devices that use time not to count your worktime, but which guard and control power plants, trains, planes, nuclear weapon etc. Do you remember the "Year 2K problem"? Even if all the measurements taken were not necessary, you can remember the effort that was taken.

The option why people are conservative is in fact the life experience "if it works relatively good, why should I change it?". Everyone knows that any small modification of a system is a risk of big collapse. The only problem with 24 hours a day (not 10 or 100) is when you need to calculate some time difference - how long did something last? But it's quite easy to convert parts of an hour to minutes, as someone mentioned, 60 is very good number for division, it has many dividers (2, 3, 4, 5, 6, 10, 12, 15, 20, 30), having 2, 5, 10, 20 - all the necessary that one use most often (take a look to your wallet and see, what bills / bank notes you have). Would it be easy to divide an hour on three parts if it had 100 minutes?

The main problem with time is then only when calculating time differences - how often do you perform it daily? How many times have you a problem to calculate "it started 4:45, ended 7:08, how long did it last?" Damn, that's easy: there are eight minutes between 7:00 and 7:08, fifteen minutes between 4:45 and 5:00, so together 8+15=23, there are three hours between 4 and 7, so 3 hours minus 60-37=23 minutes is 2 hours and 37 minutes. Is this really harder than subtracting from 100? How often do you need to solve "how much time are 157 minutes?" And - how often you need to know exact difference? Most people would say "about two and half hours".

This revolution could have been made before, for example 200 years ago, or even in Renaissance - not now. Would it be possible for the United Kingdom to switch from the left-side-driving? There are so many cars to be changed, so many traffic signs... (IIRC Sweden did it in the beginning of 1960s. as the last country). But is it necessary for the UK to do this swap? Who would benefit? How would this change pay back? When?

So the reason is that it in fact is not necessary. People do not have problems with this. Only those who count time, and software engineers who code software for them. I suppose this is a minority in each population.

Because you can express a quarter or a third of an hour in integer number of minutes (15, 20 respectively).

The same with the day: a quarter of a day is 6 hours, a third of a day is 8 hours.

For the same reasons, it is much more convenient to measure angle by dividing circle into 360 degrees: you can express angles like 1/2, 1/4, 1/8, 1/3, 1/6, 1/12, 1/9, 1/5, 1/10, 1/20, 1/30, 1/40 of a circle in integer amount of degrees.

Why did decimal time fail?

Rhetorical question: Why did the International Standards Organization's (ISO) Open Systems Interconnection (OSI) fail? The answer is that there wasn't a mess that desperately needed to be cleaned up. ISO was a bit late. An ad hoc standard was already maturing and taking over. You wrote your question, and I wrote this answer thanks to the people who developed TCP/IP as opposed to the members of the ISO OSI committee.

At the time of the French Revolution, a person traveling from town to town was forced deal with different units of length, area, volume, and mass in each town. On the other hand, that same person could look at a sundial anywhere in western Europe and know what time it was. Time was already standardized across western Europe.

Standards organizations are at their best when there's an absolute mess that desperately needs to be cleaned up. Standards organizations are at their worst when things are already nice and tidy, but perhaps in an ad hoc way. Time was already nice and tidy (but perhaps in an ad hoc way) at the time of the French Revolution.

At the time of the French Revolution, time had already been standardized in an ad hoc way for a long, long time. The concept of dividing a day and a night into twelve hours dates back to ancient Egypt. The concept of dividing an hour into sixty minutes and a minute into sixty seconds is based on how we measure angle, which dates back to ancient Babylonia. The concept of a day divided into twenty four hours, which in turn were divided into sixty minutes, which in turn was divided into sixty seconds, was quite entrenched and quite standard.

TL;DR: "If it ain't broke, don't fix it."

Because:

a) time change was more complex than the change of other measures, and

b) in contrast with the other changes, it actually did not impove anything.

Let's go with "a". For dealing with weights, lengths and volumes, sellers would usually have some simple measuring tools, using reference units;

• for measuring lengths of cloth they would have a stick of the appropiate length, and use it to measure the point where to cut.
• for volumes (usually liquids like milk), they would have some jars with the more common units, and fill them to provide the desired quantity (if the customer asked 1 pint and a quarter, you would just have to fill the 1 pint jar and the quarter jar).
• for weights, the most common (and easiest to maintain) tool were the balance scales1 with a similar set of measured weights.

Replacing those measures just mean switching those reference units to the new ones (and, I expect, changing the prices proportionally). I remember reading a reference to a French public announcement, telling merchants that they could go to the city hall to change their old yards and half-yards for meters and half meters.

Now, changing time is quite a different thing. Usually, time measuring devices are quite complex; at the time of the French Revolution making chronometers precise enough for determining the ship position was still "advanced science"; building clocks was expensive enough ¹ (even without the need of redesigning the mechanism to match the new "second" definition) that it is easy to find why it was a more difficult change.

Now, for the relevance of the change, think that the beginning of the XIXth, almost every country (and, in big country, almost every region) had its own sets of measures, usually with similar names but variable values. This had a deep impact in commerce; some merchant buying clothes in Antwerp and selling them in Paris had to buy X (belgian) yards of cloth to find that he could sell Y (Parisian) yards of cloth. If there were customs, he would have to know also which measure were used for taxation. As trade increased, standardization was more important².

Now, the same (lack of standards) was true for time keeping, but there was a big difference: before the spread of artificial lighting, timekeeping was inherently a local issue because daily activity depended on sunlight. [Hours] 3 were set depending of dawn or dusk time; the "timezone" of each town was dictated by the clock (if there was one) or the bells of the church. There was no need for keeping a local timezone, because there was no process that could benefit from it (remember than the "maximum absolute speed" was that of a man on horseback). It was not until the expansion of railways and telegraph that it even began to make sense thinking of synchronization of the different towns.

¹from the link: The new technology was initially so expensive that not all ships carried chronometers, as illustrated by the fateful last journey of the East Indiaman Arniston.[14] However by 1825, the Royal Navy had begun routinely supplying its vessels with chronometers.

²Of course, standardization could have been happened with any set of measures, but the metric system had two advantages:

• It was designed as an universal system. Instead of some local sizes (the foot of the local King, for example), it was defined in base to natural properties (the size of Earth, the density of water).

• It was a decimal system, which make switching between units way more convenient (80 centimeters where 0.8 meters, instead of 7 inches being 7/12 feet).

They also introduced decimal angle measures (100 degrees in the right angle, each degree is 100 minutes. This explain why the kilometer was originally defined as it was: it is one decimal minute of the Earth's meridian, like the nautical mile is one ordinary minute of the same).

I can name three reasons why the decimal system for time did not survive. First, people are very conservative in their habits and it is hard to implement such a dramatic change. More people use time measurement and more frequently than any other measures. And the revolutionary regime was not long enough to force French people switch. Decimal time was abandoned at the time of Napoleon or shortly before that. How conservative people are one can see from the example of America where the decimal system was never accepted.

A second reason may be that the common time and angle units are based on a very good sexagesimal (Babylonian) system which is actually more convenient for mental computations than the decimal one. (Because the numbers like 60, 24 and 12 have many divisors unlike 10.) So in some respects it is more rational than the decimal one.

Finally the third reason is that our system of time measurement was universal, accepted almost everywhere in the world (unlike the systems of other measures which varied from country to country at the time when the metric system was introduced). The main gain from the metric system was unification of the units. In the case of time the system was already so unified that nobody felt the need for replacement.

Remark: By the way, the decimal system is not universally accepted. I already mentioned America. Let me also mention the airline industry. Even in an Air France liner made by the Airbus company, the altitude is measured in feet and speed in knots.

Remark 2. In general, decimal system has only one advantage: convenience of counting using fingers. Systems with bases 8 and 12 are more convenient in most other respects.

Remark 3 (8.26.21) It turns out that the use of 12 in time measurement is not related to the number of divisors. 12 comes from the fact of nature that a year consists of approximately 12 months. So ancient Babylonians divided the Sun's yearly path (ecliptic) into 12 parts (Zodiac signs). Since rising of the parts of ecliptic was used to measure time during night, this led to division of a night in 6 parts (double hours). Then it was very natural to divide into the same number of parts another circle, the equator. Which led to the division of day+night into 12 "hours" which were later called "double hours". Why and when they decided to divide these "hours" into two halves, is not clear. Moreover, since a month is divided into 30 days, the same division was applied to the Zodiac signs which led to division of the circle into 12x30=360 degrees.

Thus there is a (well-documented) evidence that 360 was not chosen by "mathematical convenience" but was forced on us by the nature: the approximate number of months in a year times the number of days in a month.

Ref. B. L. van der Waerden, Science Awakening II, Springer 1974.