Thought of this in the shower this morning, if anyone has an answer I’d be very interested!
The use of base-60 for time and base-10 for most other things originates from different historical and mathematical practices. Base-60, or the sexagesimal system, is thought to have originated from the ancient Sumerians and Babylonians who used it for their astronomical calculations. This system has 12 divisors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, allowing it to be easily divided into halves, thirds, quarters, fifths, sixths, tenths, twelfths, and more, without resulting in fractions. This versatility has made it useful for timekeeping and angle measurement, both of which continue to be used to this day.
Conversely, the base-10 system, or decimal system, likely derives from the fact that humans have 10 fingers, making counting in this system intuitive and easy to learn. The base-10 system has fewer divisors: 1, 2, 5, 10, meaning it can only be cleanly divided by 2 and 5. While this system is less flexible for representing certain fractions, it’s more straightforward for counting and calculation, leading to its wide use in daily life, mathematics, and scientific calculations.
The integration of base-60 and base-10 systems hasn’t been widely adopted due to the significant societal change required. During the French Revolution, a decimal timekeeping system was attempted, with a day consisting of 10 hours, each hour containing 100 minutes, and each minute made up of 100 seconds. However, this system lacked popularity and was soon discarded.
Despite this, decimal watches exist today. These watches follow the concept of decimal time, dividing a 24-hour day differently, with an “hour” on a decimal watch being longer than a traditional hour, a “minute” being longer than a traditional minute, and a “second” being slightly shorter than a traditional second. They are typically seen as novelty or specialty items, appreciated by those who prefer the mathematical simplicity of a base-10 system. But due to the wide prevalence and deep entrenchment of the base-60 system in societal, technological, and legal systems, traditional timekeeping remains dominant.
(Source: I saw it on QI once - a British pub quiz style tv show)
I really want a decimal watch, just as a talking piece.
But I’m sure it would be a nightmare for actually keeping track of time.
People are probably thinking “fuck it, let’s go with the upheaval! Let’s get rid of the silly base 60 system!”. Ok then. First, we could divide the length of a year into 100 days. Wait, no, that has to be 365 because otherwise the seasons would get out of whack.
Ok, but we could definitely have 10 months right? They did that before. Perfection. So every month should have exactly … Uh 36.5 days… fuck
Well, how about having 10 day weeks? Shit. Same type of problem.
Fine, let’s ignore months and weeks. What about the 24 hour day? Instead, we could break the day into 100 units. Each unit would be 14.4 “old minutes” long. That seems fine. You could subdivide that into 100 subunits, each of which would be about 8.6 “old seconds”. To keep things reasonable the final divisor would be 10, so our new short “human counting” units would be about 0.86s. Groovy. Pity that years, months and weeks don’t work out.
So why are there “really” 360s in an hour? Probably for the same reason that there are 360⁰ in a circle. Early astromomers and mathematicians probably thought that the universe was a perfectly created system. They likely modelled dates and geometry on earth’s annual journey through the sky, but we’re a little bit “off”. Like how the months are supposedly lunar. We only discarded the idea of perfect celestial spheres relatively recently.
You hurt my brain …… 🤕 Exactly why base 60.
(Yeh. Geometry is also base 60)
Fun fact: base 60 was adopted by the Babylonians for two major reasons:
- It splits evenly in common fractions, such as halves, thirds, quarters, fifths, sixths…
- The Babylonians used a finger-counting method where the left thumb scrolled across each phalanx of the finger (giving a core base 12) and each of the other left fingers was used to keep track of how many rounds of twelve had been counted (hence 12 times 5 = 60)
Don’t let americans see that watch!
Haha. Why?
Probably due to americans using different units compared to “most” of the world, like miles, feet, inches, fahrenheit and others. Just a meme I guess.
So why didn’t we stupid humans have evolved the 6th finger yet??? We had thousands of years! We could have everything in base 12 but no, we are a lazy species…
Interesting to note, when babies are born, we tend to remove any 6th finger or toe.
Back in the day, sure - nowadays they’re removed only if they have no mobility or otherwise cause discomfort to the wielder.
Decimal time was introduced in Revolutionary France, just like the metric system and a decimal calendar. They made it non-mandatory after 17 months, partly because of the enormous costs to replace all clocks. The decimal calendar survived longer and was abolished by Napoleon as part of his reconciliation strategy with the Catholic church.
Decimal time is still used by the way. Astronomers use fractional days because it’s easier to do calculations with. And that very same ease of use is why Microsoft Excel uses fractional dates to calculate dates, as it requires less calculations.
Love the modified Julian date. You’ll also find some satellite-based astronomers measuring their observations in kiloseconds (I think Hubble does it in orbits but most of the X-ray satellites use kiloseconds).
Pilots keep their logbook in decimal hours, and the tach meter (engine hours at a certain speed) and Hobbs meter (aircraft operated hours) are decimal too.
Each decimal hour (0.1) is equal to 6 minutes. So if I ‘fly’ for 1 hour and 13 minutes I log 1.2 hours. I don’t do the mental math though, I just record what the Hobbs says.
IIRC, people have tried to create, and enforce, metric time in the past but it always fails. Basically it seems like that ever since the Mesopotamians invented base 60 mathematics for keeping track of time, some geometry, and related concepts it is stuck for that purpose because it really does seem to be the best number set for the job. It did not stick around for anything else though because it’s basically garbage for those tasks. Base 10 works pretty good; it’s easy to move around zeroes and decimal places, and since most people have 10 fingers it’s pretty intuitive.
Agreed, most people have ten fingers.
The short answer to why we use it is that we inherited it - base 12 of hours/months from the Egyptians and base 60 of second and minutes from Mesopotamians (who got it from the Sumerians).
Egyptians used base 12 a lot for a similar reason that we use base 10 a lot. We use 10 because we have ten fingers, and they used 12 because one hand has 12 knuckles (they’d count on one hand). But it was handy because there are 12 lunar cycles, so it helped keep things more consistent.
Base 60 is also handy because 60 is first number divisible by the first six counting numbers and by 10, 12, 15, 20 and 30. If you use 60, you have options! Note that we also use 60 for angles and dividing up the globe.
Yep. Your four fingers have three knuckles each. You count along them with your thumb. Then each count of 12 is counted with an extended finger on your other hand. Extend all five fingers and you have 60.
I was confused and counting the knuckles on my thumb and getting 14. I thought there was something wrong with me at first.
I accidentally came upon this same system messing around during long periods of boredom, and now I do all my counting this way. I also include the base joint of each finger so I can count 4 per digit
1 2 3 4 | 5 6 7 8 | 9 10 11 12 | 13 14 15 16
Yes, 60 is pretty much a goldilocks number that is small enough to be easily graspable for most humans, but still a highly composite number (11 factors!) so it is neatly divisible into many smaller units.
Knuckles turning out to be useful for base 12 doesn’t make them the source / reason for establishing base 12.
I find it far more likely that Egyptian academics decided on base 12 because of its useful calculus properties rather than their knuckles.
I think it’s because there are important, naturally occuring units of time that simply don’t divide well - that is, the day and the year. Having it standardized to metric would still leave us with 1:365.24 conversion. Using metric time would require us to stop being metric beyond the day, or just have a cumbersome conversion number to talk about years.
On the other hand, things like weight, length, and temperature are completely arbitrary and there’s no natural standard unit, so changing those to another completely arbitrary unit is easy.
What if you redefined the length of a second?
Could you not divide a day into, say 10000, and just call that length of time 1 second? 100 seconds in an hour and 100 hours in a day? At least for the day to day clock.
No idea how you would deal with weeks and months.
If you redefine the length of a second, all sorts of bad things would happen because of the transition. And that’s even before you remove the standard for what a second means because the length of a day will change over time. As for weeks and months, check out https://en.m.wikipedia.org/wiki/International_Fixed_Calendar for one such idea.
12 and 60 divide nicely. A quarter of a 12-hour clock is 3 hours, but in decimal time it’d be 2.5 hours. A third is 4 hours in base 12, but some gross 3.33 repeating in decimal.
I just don’t like it.
That’s the same argument for (some) Imperial measurements, but people converted to metric anyways.
Metric isn’t better because it uses 10, it’s better because it uses the same base for everything. A measurement system (and number system) that uses 12 for everything would be better than both imperial and metric.
I think the benefit of having metric in base 10 rather than 12 is that it matches our numeric base system.
123mm is 12.3cm and 1.23dm and 0.123m.
Converting things in base 12 would be a bit more work, not sure it’d be worth it.
We’re not really going around converting time very often.
You can blame the babalonians for that. They have a 60 base number system and was used for time and dates.
Ancient Greece also liked highly factorable numbers. Plato called out 5040 being a handy population size for having many factors.
The French tried doing decimal time using base 10 during the French Revolution. People have thought about it in the past and tried
And Swatch for some weird reason. Absolute insanity.
We have 10 fingers and the ancient Babylonians liked the number 60.
While it would he handy to have everything integrated, it’s not always vital. We don’t need to convert kilograms to seconds very often. Artificially enforced systems have always had trouble replacing older anachronistic ones that are otherwise still useful. Ask people in the UK about their cars’ efficiency and you’ll often get an answer in miles per gallon.
There’s nothing magical about 10, either, other than the accidents of evolution that left us with ten fingers. Base 12 is also extremely convenient, and comes from Sumerians counting with their thumb against each of the three joints on 4 fingers. Go through that process once for each finger on the other hand, and you get 60. And of course, in any industry where things are packed into packages, like nearly everything we buy, dozens fit better than tens. 60 divides very neatly into many convenient and geometrically simple fractions, and a lot of what we do with circles benefits from this.
We probably would have been better standardizing on a base unit that’s a power of two, which has more mathematical weight than ten does.
Furthermore, there’s something to be said for units that are “the right size” as it were. It’s hard to measure the distance from your house to the store in parsecs for example, unless you own 1:1 scale copy of the millennium falcon.
A day cycle is a time unit that has been thrust upon us by physics and biology, and we have to then split it into useful segments, and base 10 honestly does a poor job of that. You end up having to describe most things as 0.5 decimal minutes or 2 decimal minutes depending upon how you want to round them, since very few things actual sit close to the amount of time described by 1 decimal minute.
Whether that’s because our culture thinks in “minutes” or not is debatable, but the point is that trying to move to such a system is nearly impossible, at least at the moment.
As you said there is really nothing special about 10 and you could easily redefine prefixes to whatever base you want.
In base 12 a day has 20 hours, an hour has 50 minutes and a week has 120 hours. The numbers are as arbitrary as before. Except the 0th index is always 0 in these cases.
While the origin has been explained well, a base change really doesn’t solve the underlying problem with time as we define it. I don’t think this has a good solution and probably doesn’t need one.
I was writing a reply but you said most of it, so I’ll add here. There has also been attempts and/or proposals for decimal time, but the base 12 system is quite rooted. For example during the French revolution: https://en.wikipedia.org/wiki/Decimal_time
Unix time is base 10 and I’d say it is pretty widely used. Not for wristwatches but by all kinds of software on the device you’re using to read this right now.
Unix time is just the number of seconds since January 1 1970, isn’t it? How is that base 10, or any other base? If anything, you might argue it’s base 2, since computers generally store integers in binary, but the definition is base-independent afaik.
Yeah, it’s definitely base independent. It’s just that representations of it are typically in base 10 because we as humans typically use base 10, so we show it as such to read it.
Base 10 is not how it is “widely used” though. It is widely used in encoded form. It’s not typically shown as a number when displayed for humans.
Dont forget we use base 2 and base 16 in computing ;)
Check out swatch beat time as well, another form of decimal time that was attempted
If we go below 1 second it seems we use base 10 when using milliseconds
