For thousands of years, we've divided days into 24 hours, hours into 60 minutes, and minutes into 60 seconds. But why do we *have* to do that? Here's the story of the one gloriously failed attempt to decimalize time.

*Top image: **Steve Wilde/Flickr.*

#### Dividing Time

It's easy to forget just how arbitrary the way we measure time — or measure *anything*, for that matter — really is. Yes, the Earth's rotation means it makes sense to look at one spin around the planet's axis as a unit, so that gives us the day. And the time it takes the Earth to revolve once around the Sun makes sense as another unit, so that's the year. The month is not *quite* as intuitive as those first two, though its etymology from the word "moon" is a rather gigantic clue. It is indeed derived from the lunar cycle, and there's evidence that humans have marked the monthly changes of the Moon as part of timekeeping since the Paleolithic.

But weeks, hours, minutes, and seconds? There's no compelling reason why we *must* divide them the way that we do, other than the fact that that's how we've apparently always done it. Weeks have been anywhere from three to ten days long. In a rather pleasing inversion of what we're used to, the Sinhalese people in ancient Sri Lanka divided the day into 60 *Peya*, which we might consider their version of the hour, and then in turn divided these into 24 *Vinadi*. This means a *Vinadi* is exactly as long as a minute — just arrived at in the opposite way.

In general, it does seem that most ancient cultures settled on dividing the day into twelve parts, or first splitting this into day and night halves and *then* dividing by twelve. The exact reason why so many civilizations settled on multiples of 12 or 24 to divide the day is lost to history. The fact that there are about twelve lunar cycles in a year might have something to do with it, or it might also have been because it's really easy to work with the number twelve. Our current system of 24 hours divided into 60 minutes, which in turn is split into 60 seconds each, comes from the Babylonians, who themselves used a base-60 system. Speaking of which...

#### The Base Problem

The fact that we build our number system around ten is an evolutionary fluke. Certainly, it's a very *ancient* evolutionary fluke — five-fingered hands go right back to some of the very first organisms to emerge from the ocean. The two hands are our most convenient counting aids, and it's only natural that our species would be drawn to organizing our numbers in terms of this fact of our anatomy. We let computers have base-2 in their binary codes, but otherwise base-10 is so omnipresent that it's difficult for us to even contemplate alternatives.

That's a shame, because honestly, base-10 is really pretty crap, mathematically speaking. Because the divisors of ten are just 2 and 5, fractions involving multiples of 3 and 4 are necessarily clunky. People who like to argue about the best possible base for our number system, quite apart from the fact that they're clearly the life of any party, tend to point to base-12 as the clearly preferable option. There's certainly something to this - instead of .333..., 1/3 would be .4 in base-12, and 1/4 gets shortened from .25 to .3. 1/5 has to become the repeating decimal .24972497..., and 1/7 is still a mess, but it's arguably still a worthwhile trade-off to get simpler decimals - or **duo**decimals, I should say - for the thirds and fourths.

While humanity has settled on base-10 for counting, the usefulness of base-12 endures in our measurements. Beyond the fact that we divide the day into two sets of 12 hours apiece, "dozen" and "gross" still persist as special terms for 12 and 12^{2}. There's twelve inches in a foot, and the same used to be true of the relationship between ounces and pounds before the old Troy system was replaced by Avoirdupois, which uses a 16-ounce pound.

#### Time to Decimalize

Throughout history, not all have been comfortable with the fact that we split time between base-10 and base-12, and so various pushes have been made for us to abandon one in favor of the other. While there's a theoretical argument that it would be better to go completely duodecimal, the pervasiveness of base-10 meant that was never really an option. The only way forward was redefine all our units of measurements in units of ten.

This, of course, is the motivation behind the metric system. The idea was first proposed back in 1586 by a Flemish mathematician and engineer named Simon Stevin, who argued for the widespread adoption of decimal notation, with the use of decimal fractions presaging the inevitable introduction of decimal weights and measures. Robert Hooke's mentor (and my non-ancestor) John Wilkins advocated for what would be the metric system when he proposed the idea to the Royal Society in 1668, and the ensuing decade saw a great deal of writing on the virtues of decimalization.

It wasn't just that decimal units would bring measurements into line with how humans counted - it also provided a chance for the great powers of Europe to actually start using the *same* measurements. Each nation had its own units of measurement, which made trading between countries a headache for everyone except those who profited off of these discrepancies, which in turn meant they had the fortune necessary to ensure no reforms were made. If reform was to happen, something cataclysmic would be needed to force the issue.

#### The Revolutionary System

As it happened, what was arguably the biggest cataclysm in European history, certainly dwarfing anything before the 20th century, erupted in 1789. The French Revolution hadn't just executed King Louis XVI - the Revolution had destroyed the entire *ancien regime* that he had stood for. Suddenly, every aspect of everyday life was being called into question as a symbol of repression, of the bad old ways.

While the political leaders of the Revolution dealt with this upheaval by guillotining everyone who wandered into their field of vision, the philosophers and scientists turned their attention to measurements. After some initial failed attempts to enlist the British and the Americans in devising a new system, the French devised their own system. On April 7, 1795 — or, as their new revolutionary calendar had it, 18 Germinal of Year III — they unveiled what would eventually become the modern metric system.

The initial five units of this system dealt with length, area, volume of a solid (firewood specifically), volume of a liquid, and mass. While the system's inventors ultimately had to just pick some arbitrary values for these measurements, they at least put some thought into their choices. The meter was defined as a ten millionth the length of the distance between the North Pole and the Equator along the line of longitude passing through Paris. The litre was a cubic decimeter worth of liquid. The gram was the mass of a cubic centimeter of water. These have since changed multiple times, but there was a basic logic to it all that helped make the metric system something worth keeping around.

#### A Matter of Decimal Time

If only the same could be said of the first great scientific reform of the French Revolution. A year and a half before the introduction of the initial metric system, a decree was put out on October 5, 1793 that France was switching to decimal time. With the sole exception of an ancient Chinese unit of measurement for 1/100 of a day that was used alongside the preferred duodecimal system, this failed reform remains the only known attempt to institute decimal time.

The day was now ten hours long, which in our reckoning means each hour was 144 minutes long. The decimal hour was then divided into 100 minutes, each 86.4 seconds long. The decimal minute was in turn split into 100 decimal seconds, which you can probably work out means that these were the equivalent of .864 of our seconds. This was complemented by the Revolutionary Calendar, which introduced ten day weeks, or *décades*, which combined to form the twelve 30-day months of the year.

There's nothing logically wrong with this, I suppose, but there was a whole hell of a lot practically wrong with it. Just imagine if such a system was introduced today. We think of time passing in terms of our familiar hours and minutes - now think of how interminable things would seem if every hour lasted more than twice as long as it does now. And no, I don't think the reduction in number of hours would make this any more palatable for clock-watchers. The ten-day week is, if anything worse - imagine that everyone was expected to work eight or nine days in a row before getting any time off. Perhaps if you were used to it this wouldn't seem so bad, but coming from the old seven-day week, this would just be brutal.

Indeed, that's the point. Part of the metric system's success with the other units is that, while length and mass and volume are all crucial, they aren't fundamental to our existence in the same way time is. How often do you actually need to know the *precise* measure of how wide something is or how much something weights? Sure, these crop up on a regular basis, but now compare that to how often you need to know what time it is, how long an event lasts, or when a future event will be. Every single time you look at a clock, you're reinforcing the traditional way of timekeeping.

No decree could overcome that, and even the leaders of the Revolution were forced to admit this. Decimal time was abandoned in the very same decree that established the rest of the metric system in 1795. The revolutionary calendar, with its ten-day weeks and uniform months, lasted a bit longer, perhaps because weeks and months still aren't *quite* as important to us as our minutes and hours. But when Napoleon brought back the old calendar in 1806, nobody complained, and so the last great gasp of decimal time was heard.

In its way, decimal time might actually be seen as the flip side of the duodecimal system. Both are perfectly logical ways of approaching the world, and there are decent arguments to be made that they might be preferable to our current way to doing things. But that simply isn't how history worked out, and sometimes it's best to admit that we passed the point of no return a long, long time ago. A gross of kiloyears ago, even.

#### Image Credits

Image of decimal clock by Cormullion on Wikimedia.

Image of clock dial by Rama on Wikimedia.

## DISCUSSION

You can divide 12 into 2, 3, 4 or 6 parts.

You can divide 24 into 2, 3, 4, 6, 8 or 12 parts.

You can divide 60 into 2, 3, 4, 5, 6, 10, 15, 20 or 30 parts

You can only divide 10 into 2 or 5 parts.

A 12-based system is much more convenient. The only reason we use base 10 is that through an evolutionary accident we happen to have ten digits that we don't walk on.