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Why is a minute divided into 60 seconds, an hour into 60 minutes? (scientificamerican.com)
170 points by smalu 1199 days ago | hide | past | web | 148 comments | favorite

As an American with a physics background, a while ago I casually reviewed how bad our non-metric system is -- http://joshuaspodek.com/metric-system-isnt -- and found it not nearly as bad as people treat it. Among other things, when I build things it's useful to divide in half a few times, which is easier with inches and feet. And I've found no benefit to Celsius's 0 and 100 coinciding with water's state changing.

I bring that up here because I've never heard even the staunchest metric proponents use kiloseconds or megaseconds or hesitate to use hours, minutes, days, and so on. I know people experimented with decimal times, especially around the French Revolution, but it didn't stick. It's funny when someone talks about the value of using base ten and then switches to base 60, base 12, and base 24 in the next sentence.

I should say that in physics experiments people used seconds only (which is where I learned that to within about a percent a year is pi times ten to the seventh).

As a European living in America I disagree. The one value of metric vs imperial is that you (for the most part) don't have to do any math when converting between units.

If I have 1.73 miles, I have to do the math to figure out how many feet that is, 1.73*5280~=9134, which is not something that's easy for me to do in my head.

However, 1.73 km is 1730 meters, which is way easier (at least for me, but that might be my bias).

No, you're absolutely right. Thing is, most of the time, when dealing with miles, I don't care how many feet it is. Any distance measured in miles is sufficiently large that its equivalent in feet is largely irrelevant. I suppose it's nice to know that 1.73 km is 1730 meters, but either way, it's a medium-long walk. If I needed to convert all the time ( I suspect this it's really only when using compound units like pound-feet ), that is where I find metric more useful.

Also, I haven't read GP's post, but I find Fahrenheit degrees easier to work with primarily because they're smaller; differences in temperature are easier to express in whole numbers.

Gallons, cups, tablespoons, quarts can go DIAF; I have to convert between these all the time, and it drives me batty!

I live in a country with metric system. We use different units of measurement interchangeably because it's easy to do so and we have gotten used to it. I am 1.74m or 174cm tall. The bus stop is 500m or half a kilometer away from my home, etc. While nobody converts 250km to meters, when the value is closer to one, both units of measurement are equally useful and equally used.

Also all physics and engineering formula are designed to get and return metric values. When I see K = 0.5mv^2, I know v is supposed to be m/s and m is in kilograms and the result would be in Joules. If it's E = m*c^2, the same thing could be inferred about it.

I'm curios with all different units of measurement, how do you know when to use which. Is there a convention to always e.g. use ft/s or is it different in each formula?

Something I never thought about is that there are differences between metric countries too in usage.

E.g. in italy you refer to a glass of 200ml, 100 grams of pasta and two hectograms of parmigiano, while in hungary they routinely use deciliters and decagrams, which I'd never seen outside of school.

And the beauty is that you are still able to easily convert it to the type you are used to. I, as a Belgian, might blink once when you use hectogram, but it is trivial to convert it to what I am more used to (say kg or g).

And as ward has pointed out, it is so easy to convert between them.

On the other hand I don't understand for examples why in the US they still use measures like "cup", "oz" "pint" in cooking. Should I buy a specifically sized "cup" to cook a us recipe? :)

By watching UK television it seems that even they are using kilograms, liters and also Celsius for oven temperature, and some weeks ago there was a UK famous baker talking with some US guest and saying almost the same thing.

disclaimer: I'm Italian

This is exactly why metric is so powerful: I also have no inherent concept of a deciliter or decagram, but I can convert to my understood liter and kilogram in moments.

Even more crazy when dealing with it as an angular unit as Minute of Arc.

Historically: 1 Minute of Great Arc = 1 Nautical Mile

Great Arc = Earth circumference

1 Minute of Great Arc = Great Arc / (360 * 60)

Fun Fact:

Earth Circumference = 4 times great circle distance Pole to Equator historically defined as 10000km or 10 Million Meters (They were that serious about being decimal)

That also explains why the earth radius can still approximately be expressed as 10000km/(π/2) = 6366.2km (just 4.8km off the current mean radius defintion of 6371 km)


A funny rant on imperial units you might find amusing.


Cups are nice because it promotes a "feel" for cooking rather than treating it as a science where the recipe must be followed exactly.

But it's much easier and quicker to simply weigh your ingredients on a digital scale. Step into a professional kitchen and you'll never see anyone using measuring spoons or cups...

Not to mention, having everything in metric and by weight allows you to easily figure out ratios of ingredients, making scaling recipes much easier and quicker.

The usefulness of cups comes from the fact that you create your own home unit depending what you need eith out needing to weight anything. It's just giving proportions, you can use a small cup for one portion size, or a big kettle for a battalion.

In a professional kitchen, scales are mainly used for baking.

On "the line" where food is cooked, measurements are mainly by hand and by eye.

I know how it's done, I used to be a chef, at higher end restaurants than most people will ever eat at.

Yes, during service you're not busting out scales, and a lot of things aren't precisely measured. But anything where precision is necessary, you weigh it. Where it isn't, you don't.

Good luck ever finding a cup measure, or a measuring teaspoon in a professional kitchen though...

>Good luck ever finding a cup measure, or a measuring teaspoon in a professional kitchen though...

In which case, it matters little if you use metric or not...

> In which case, it matters little if you use metric or not...

Well, you still will measure things, most cooks will do a stint in the pastry kitchen, plus in the higher end restaurants a lot of pastry techniques transfer over to the savoury side (ie. a lot of what we think of as "molecular gastronomy").

While metric vs imperial doesn't matter for accuracy (whereas weight is more accurate than volume if you're measuring anything that's not liquid, and even with liquids it's easier to measure volume incorrectly), metric is just easier.

Baking is actually science-like and needs to be done with precision while cooking is much more about having a feel for the ingredients and tastes.

It's really just the 3 teaspoons in a tablespoon that is annoying to remember. All of the others are just 2 or 4 of the one below it. A week and a restaurant and they start becoming quite natural.

And now that I think of it, Aussie tablespoons are 4 teaspoons (20ml), where US tablespoons are 3 (15ml)

Peter piper picked a peck of pickled peppers.

Thank goodness no one seems to use Pecks / Bushels / Dry Gallons (the dry volume versions of Pints / Quarts / Wet Gallons). The only time I ever hear of "Pecks" is in the Tongue Twister.

For some reason, I get confused between 8 ounces in a cup and 16 in a pound. But a scale will measure in grams just fine, do I tend to prefer that.

>If I have 1.73 miles, I have to do the math to figure out how many feet that is, 1.73*5280~=9134, which is not something that's easy for me to do in my head.

How often do you need to do this in reality? Most people in their day-to-day have no need to these conversions.

you should also consider the extensibility of the metric system as well. Any unit when has a kilo prefix is understood to be x1000 even if you are not familiar with the original quantity. kJ is kilo joules, km is kilo meters. I have no idea how this is handled in your non-metric system is but this property of the SI system definitely makes it much more extensible. you immediately get a sense of the ratio of different metrics. for example consider the ratios of miles/feet ??? feet/inch ??? (I have no idea) compared to kilometers/meters meters/millimeters... this makes it possible to define a metric for a quantity ( meters for distance for example ) and represent all the related quantities easily without having to define a new name for a constant multiple of that quantity.

of course perception of a metric also plays a tremendous role here. I don't have a 'feel' for how long it is 12-feet for example but I can eye-ball a distance and tell how many meters it is pretty accurately. I guess this perception is the main issue that prevents imperial system to be abandoned in favor of SI - people are too much used to it.

I also hate the left driving lane of UK btw. It screws up with my head every time I rent a car in London...

stupid metric-ism ;)

Whereas quite often you'll need to know how long it’s going to take to drive to a city 90 miles away, and it's quite convenient to use the "1 mile ~= 1 minute" approximation to estimate that it'll take 90 minutes.

And this is where metric really shines: at Autobahn speed (130 kph), 90 miles is only some 66 minutes -- 24 minutes saved over imperial. :)

Finally, a convincing argument for the metric system! It will shorten our commutes!

The worst aspect is the real cost of interacting with both metric and imperial systems in America. Those costs manifest themselves in things like the crash of the Mars Climate Orbiter, or closer to home, the fact that I have to have both metric and standard wrench sets at home sitting in my garage to work on a range of projects.

Wait... you're comparing feet to meters. When you should be comparing meters to yards. 1.73 miles * 1760 yards.

Sorry, I wasn't trying to compare units, and the whole example is a bit contrived tbh. The point was simply that in the metric system, when converting between units, all you need to do is move the decimal point, no math required.

This doesn't mean metric is more accurate over imperial, it just means that on a day-to-day, conversion is easier. Also, you can work out the relationship of units simply by their name.

deci = tenth, so decimeters means there is ten of them in one meter. deciliters means ten in one liter. so on and so forth. centi = hundred... milli = thousand...


Isn't the fact that the rest of the world uses those definitions an advantage in and of itself? What is there to be gained by being inconsistent?

Relevant picture I found on twitter: https://pbs.twimg.com/media/Bdp2YLFCIAAM1Dy.png

What's that a map of, countries that have placed a man on the moon?

I think it's a map of countries that lost a 125 million dollars Mars probe after failing to properly convert between imperial and metric units.

Exactly! This is why it's dangerous and irresponsible to allow the metric system into your space program.

Which is precisely the reason why the US military has adopted the metric system.

Metric mils? Ha!

Imperial system is bad, even for you who grown up with it, it should be obvious how inconvenient it is. As for temperature, while F is not telling me anything useful, C is always telling me if it will rain or snow, actually when it snows it is always closer to 0 (or 32).

As article mentioned, we got time from Babylonians, who got it from Summerians. Time and calendar are one of the weirder things we deal with. I used internet time for a while, you know the Swatch thing. It looks weird in the beggining, but very quickly you get it and it works well and it is convenient that it is not time-zone dependant. And that was just a marketing gimmick from Swatch.

I think the whole idea that we somehow manage to create bridges and build buildings despite weird measures we use, is more testament to our ability to overcome difficult obstacles.

Similarly, people will claim it makes no sense that American M/D/Y dates are neither monotonically increasing nor decreasing, but then they'll find it totally natural to use "D/M/Y H:M:S" or "H:M:S D/M/Y" and not even notice that they share that same alleged flaw.

I'm just glad that nobody in Europe seems to use YYYY/DD/MM. This means that the format "YYYY-MM-DD" is unambiguous and the lexical ordering of dates is the same as their natural ordering[1], which is useful for sorting files in folders.

[1] Except for years BCE which the scheme doesn't treat.

Indeed. And even better, Y-M-D H:M:S is monotonically decreasing.

Except at DST switch.

DST and timezones in general are an abomination anyways.

"They" really don't. Either way you described is still either sorted in ascending or descending order: H:M:S D/M/Y (321 123) or D/M/Y H:M:S (123 321), as opposed to using MDY, which is neither ascending nor descending, but 213.

Additionally, the point of doing it the other way round is that the most important thing is on the left, where we start reading, followed by less important things. If I need to know the time of day, the hour is the most important thing, once I know whether it's 4 or 6, I can look at the minutes and first then do I perhaps (and does one really ever?) care about the seconds. As a matter of fact, my old wristwatch only had hour and minute hands... The opposite is true for the date. It starts, again, with the most significant thing on the left: the day. This assumes that people will probably have it easier to remember the month or year they live in.

And a final example: I have an appointment on the 24/01/2014 at 10:15:00. The most important questions are: What day do we have? And if it happens to be the 24th, what hour of the day is it? Is it 5? Good, 5h left. Is it 10? Oh boy, better look at the minutes...

> 321 123

I think you mean 321 456. It's not monotonically anything.

> most important thing is on the left

See, I feel that the month is the most important part of the date. "My birthday’s in June" or "My birthday is on the eight of some month"? "The harvest is in October" or "The harvest is on the 30th of something?"

When you are asked what date it is, do you think hardest about the month or the day? For most people it's the day, so it makes sense for it to come first.

When I ask what time it is, do you think harder about the minute or the hour?

The hour. Minutes are usually unimportant for day to day life, as long as I am in the right hour. This is not true of month-day though. I imagine most people would be caring more about day than month. The day is both more important and harder to remember, so it makes sense for it to come first.


The hour. Is this supposed to be a trick question? 90% of the time, if I give the hour to quarter-hour resolution then I've done a good enough job of saying what time it is. I don't even think about minutes.

  > when I build things it's useful to divide in half a few times
Fahrenheit adjusted his earlier scale, changing from 30° to 32° for freezing, and 90° to 96° for body temperature, in order to simplify constructing thermometers by bisecting between the calibration points.

Here's another example: One of this past weekend’s NFL games had a final score of 23 to 10. A nice, natural measurement that's easy to grasp.

But under the metric system, the score would have been 14.38 to -6. Completely awkward and out of touch with the human scale.

It is extremely inconvenient that time is base-24 and base-60 while everything else in the metric system is base-10; it leads, for example, to a difficult conversion between the "meters per second" of the physics class and the "km/hr" of the highway. One surprisingly frustrating thing is that if you view a day as a million "instants" then an instant is actually a very human number, about the human reaction time or so; and a kiloinstant is a very human timescale too; 86.4 seconds or just shy of a minute and a half. We already know that when someone says "be there in five minutes" they mean 7-8; if they said "be there in five ki" they would be more accurate.

Fun things:

1. I wrote an HTML5 base-10 clock here with some togglable layers. Try out base-10 time: http://drostie.org/time/ . It's actually much easier than reading a normal clock because it's a digital readout, "8, 5, 6" rather than "two past a quarter after 8, that's 8:17." (It might not seem that way at first -- but that's because we spent long hours learning to tell time.)

2. For the exactly opposite view, that the number system should be base-12, see http://www.dozenal.org/ . It's actually a good way to work with numbers, and I've used the "counting on the joints/pads of your proper fingers" trick a number of times; sometimes you only have one hand free and want to count to something that's less than 48 (you can encode 2 extra bits with "hand facing up, hand facing down, hand facing up again, hand facing down again"; I've found it gets confusing after 4 or 5 of these though.)

3. I am very sympathetic to Feynman's "we don't need more units!" claim, but the reason we use various units is because we have different interests -- masses in eV/c^2 for example reflect someone who is interested in the atomic interaction energies (eV) of relativistic particles (c^2); energies in Kelvin reflect someone who is interested in how much they need to cool their experimental apparatus to see certain effects; energies in inverse centimeters reflect people who have spectrometers. Following this, I've tried to think whether the base-10 clock could be used to construct a set of "rational units" which would try to get the "human scale things" right while making all of these other units amount to a power-of-10 difference. I've not condensed these speculations to a final form yet but the speculations are themselves at: https://github.com/drostie/essay-seeds/blob/master/misc/rati... .

"we don't need more units!"

Yes, some units are useful for particular interests. Create them as they're needed and useful. Base-10 time would make more sense. Celsius at least coordinates notable values with common materials.

Some units are just stupid. The lead article gives an unsatisfactory explanation of base-12/60 time (admitting near the end the reason for base-60 is unknown); trying to explain clocks to toddlers is proving annoying (I can't explain it if it doesn't make sense, and it doesn't make sense). Fahrenheit is just an arbitrary marking on a scale and seeing how reality happened to line up.


Fahrenheit was supposed to be 0 degrees for freezing, and 100 for body temperature.

It turns out that Fahrenheit's reference thermometer was a bit... off... however.

Interestingly, Fahrenheit has 180 (212-32) degrees between freezing and boiling. Zero is set to a brine solution -- a reproducible metric about as cold as you could make. So it's not an insane system.

0 was the coldest temperature he could reliably reproduce - which is salt water just above the freezing point.

How did it manage to be off by 32 (!) for freezing, but fairly close for body temperature? I would expect a constant (or at least same ballpark) error.

I imagine it had something to do with the medium used for the thermometer?

He was trying to find a salt mixture that went through a phase change at 0 degrees:


That wasn't so reliable, and neither was using 100 for human body temperature, so when he discovered that water boiled at 212 he began calibrating with that.

> We already know that when someone says "be there in five minutes" they mean 7-8; if they said "be there in five ki" they would be more accurate.

But then they would actually show up in 7-8 ki, meaning 10-12 minutes!

On the other hand, maybe this is just the cure for high-intensity fast-paced society that we need. ;)

What about scaling instants up to a year? A kiloday would be 2.74 years. Which doesn't seem to mean anything in human terms.

All of the english system measurements were built on "human" terms.

A furlong is the distance a horse can plow in one day. This also gives a relationship between horsepower and furlongs. A chain is the distance you keep crops apart, and one chain by one furlong is an acre.

If you had 20 acres of land, you knew a horse could plow the land in 20 days.

The aging English system of Feet, Yards, Furlongs, Miles, Rods, Chains, Acres, Horsepower... they don't mean anything to non-farmers. So, we can replace these with a different system: the Metric system.

However, everyone uses the Point / Pica (1/72th an inch, and 1/6th an inch respectively) system for font measurement. As we are computer literate people today, font-size measured in "points" is quite important.

12-Point font (aka, font one pica in size) is a standard font size. No one cares that 12-points is really 4.233 mm. Hell, saying 4.233mm font means nothing to me.

But the day, night, moon, and sun cycles (approximated by day, month and year) is obvious to everyone. As such, an arbitrary 10-base system like Metric Time ignores the "reality" for most people... that the day, moon, and sun are related.

Nitpick: horsepower is not an old English unit; James Watt invented it in the late 18th century (http://en.wikipedia.org/wiki/Horsepower)

I doubt most people understand or think of "Point" as a measure of length. It is just some completely arbitrary scalar that exists only due to poor UI design and so that teachers can mark off points for it not being set to "12". In many other cases, such as modern web browsers, it is being replaced with the concept of "zoom" which just uses natural numbers with "100" being arbitrarily defined as some loose concept of "default".

They would certainly never dream of using it for anything other than choosing how large they wanted their font, or possibly line.

The basic answer is that (1 year) / (1 day) = 365.242199... is a pure number with no units associated to it, so there exists no set of units which can eliminate it.

The question then is, should we synchronize on the year, or on the day? The advantage of using the year is that it's a more stable unit of time; the length of a day is actually incredibly noisy and days are slowly getting longer every century as the Sun's and Moon's tidal forces deform the Earth, turning rotational energy into heat.

Unfortunately, there are a bunch of disadvantages. There are a lot of calendars in effect today, and they don't always settle on the same definition of "year" -- for that matter, there are a lot of astronomical definitions of "year" -- since the Earth's axis doesn't point at the same stars eternally, do you mean orbiting the Sun once relative to the distant stars (ignoring the axis) or do you mean coming back to the same tilt relative to the Sun so we can start the seasons over again (including the axis)? Or do you just mean a full cycle of phases of the moon, as lunar calendars do it?

The best way that I can see is to settle approximately on a day with an atomic clock; and push the question of actually trying to keep dawn at the same time each day (correcting for the slowdown of the Earth) to the time zones, which already sometimes try that in the sense of Daylight Saving Time.

As someone who bakes, I loathe imperial measurements. For one, measuring by weight instead of volume is just much easier and more precise. (I'm looking at you "cups of flour.") For two, it's a lot simpler to scale recipes given in metric amounts.

It is the non-metric units for volume that really turn into a shitfest.

I grew up in America, went to public schools, learned to cook from American cookbooks, and still can't keep all of them straight.

Pints in a gallon? Quarts in a gallon? Quarts in a pint? Teaspoons in a cup? Cups in a pint? Who fucking knows? The best I can do is a pint is roughly how much beer you get at a bar (but that changes from region to region!) and milk comes in a gallon while other beverages do not.

I think the main problem isn't the quality of the system of measurement used by the US, but more that it is one of only three countries still not using the metric system.

The world would be an easier place without that headache.

>And I've found no benefit to Celsius's 0 and 100 coinciding with water's state changing.

I agree, I like how Fahrenheit degrees are smaller and therefore degrees in Fahrenheit are more exact.

Can you feel a difference of 1 degree Fahrenheit? Does it change your behavior? Do you need an extra sweater because it is 57 degrees inside instead of 58? As someone who has grown up with it, I would argue that the Fahrenheit system is too granular.

In general, if I ask someone what the temperature is, it will be estimated as "low 70s" or "high 50s". Never have I met anyone who would feel the temperature and then declare that it is 72 degrees, as opposed to 71 or 73. This suggests that the granularity is greater than what people feel, and is unnecessary for day-to-day use.

I can hardly think of a situation where a centigrade is not granular enough. The example GP gives with the air conditioner is IMHO a huge stretch - a 1 deg Celsius difference is pretty negligible. Disclaimer: Fahrenheit is the most annoying and nonsensical of imperial measurement scales to me, so I am biased against it.

W.r.t the Celsius scale, a comment from Celsius' country of origin in response to:

> Nobody lives their life around freezing and boiling temperatures. I live my life around 50 to 90 degrees and if you live yours around 10 to 40, I don’t see the advantage.

The natural response is of course we live close to freezing! 0 °C is the temperature that differentiates frozen lakes from open lakes, snow from rain, slippery dangerous roads from regular.

We just use decimal degrees, e.g. 23.5ºC.

That said, and as an European, if had to stop using one unit of measure it would certain be the Celsius scale.

IMO the reason why Americans prefer Farenheit to Celsius is that the 0 and 100 points correspond to roughly the limits of common outdoor temperatures, rather than water's state changes.

Pretty much the same argument for miles per hour vs kilometers per hour - 100 mph is all anyone's ever going to go during a normal day.

That's an interesting point about being able to divide by half more than once for feet/inches, though - I hadn't thought of that before.

(From another American with a physics background)

Let's face it -- people have a strong preference for whatever system they are used to. There's extremely strong inertia, and efforts to try and justify one system over the other are not especially effective.

In theory I'd prefer a timekeeping system that had its base unit in terms of the smallest discrete unit of time (basically planck time) and let everything else arise naturally from that. Sure, days may not be a perfectly XX kilo-mega-ultra-plank times (I'm unsure of the Metric nomenclature going from a power of -44 to a power of around +4) but I am always peeved we have designed our timekeeping, temperature, pressure, etc measurements bound to arbitrary properties of things on the surface of our planet than on the fundamental properties of the universe.

It is going to make space travel a much bigger hassle, to say the least.

Does it also peeve you that the decimal system is based on the number of fingers we have? I can only assume you're being facetious -- I can't see any practical reason for wanting a system of measurements that isn't designed around the world we all live in.

You seem to have missed the convenience of secondary definitions using SI.

Using SI, 1 J = 1 N * 1 m = 1 W * 1 s.

You can't do the same with calories, miles, horsepower, and other Imperial units.

"Among other things, when I build things it's useful to divide in half a few times, which is easier with inches and feet."...

If you find it easier to work with base 12 than base 10, you are not like most of the people.

"And I've found no benefit to Celsius's 0 and 100 coinciding with water's state changing."

So the fact that pure water freezes at 0 and boils at 100 is of no benefit to you?

I don't buy it.

On the topic of metric vs. otherwise, you may enjoy Matt Parker's "Guide to the Imperial Measurement System." [0] Matt Parker is an eminent stand-up mathematician, often featured on James May's excellent Number Hub series

0: http://www.youtube.com/watch?v=r7x-RGfd0Yk

"to within about a percent a year is pi times ten to the seventh"

The way to remember that is "pi seconds in a nanocentury"

12, 24, 60 are all used because they are cipherable using one's fingers.

To cipher on 12, pick a hand and assign the values 1 to 12 to each finger joint so that the tip of the index finger is one, the middle joint of the index finger is 2 ... the base joint of the little finger is twelve. Use the thumb as pointer to a number. Add and subtract by moving your thumb as you count.

Cipher on 24 by using each joint on both hands.

Cipher on 60 by using one hand to cipher on 12. The other to cipher on 5 in the traditional way but value each finger as 12. Example: Base joint of pinky on right hand and ring finger of left hand is 48.

To get the full Babylonian number system allow the exponent to float based on context. It's really just an extension of the move from ciphering on 12 to ciphering on 60.


1. [M05] Where are the indexes after adding 13 and 8?

2. [10] Change the system to use natural numbers.

3. [50] Is abandoning sexigisimal ciphering for decimal ciphering the oldest case of changing a computational system so as to make it easier for beginners at the expense of vastly reduced expressive power?


Short version. They don't really know.

"Although it is unknown why 60 was chosen, it is notably convenient for expressing fractions, since 60 is the smallest number divisible by the first six counting numbers as well as by 10, 12, 15, 20 and 30."

Yet another headline phrased as a question without a clear answer in the article body...

A slight rephrasing of the headline allows us to apply Betteridge's law[1]: "Have we solved the mystery of why a minute is divided into 60 seconds...?"

[1] http://en.wikipedia.org/wiki/Betteridge%27s_law_of_headlines

There is so much interesting information in the article that people really forget what they came for, the answer to the proposed title question.

Personally, I wasn't upset at all. I really liked the article although it had a deceiving title.

How else would you have an article referring to an open question phrased?

"We wasted our time writing this. Now you can waste your time reading it."

That's not fair at all. I enjoyed reading about ancient timekeeping and the theories that powered them. I had no idea how they tracked time at night, for example; now I do.

"The mystery of why is a minute divided into 60 seconds, an hour into 60 minutes?"

Regarding the 12 hours division, they do suggest it is from "the number of finger joints on each hand (three in each of the four fingers, excluding the thumb)".

Interesting history lesson about the Egyptian's use of the duodecimal system.

I believe the last argument is understated: one big advantage of base 12 over base 10 is division by 3. This offers many ways of dividing a time interval into several sub-intervals of identical duration.

For base 60, this intensifies: as mentioned in the post, 60 is the smallest number divisible by 2, 3, 4, 5, and 6. This gives tremendous flexibility for dividing a time interval.

Duodecimal counting still persists in some places in inches-per-foot and in the UK until 1971 in the "pounds, shillings and pence" old-money system. (12 pence to a shilling and 20 shillings to a pound).

It's interesting to me that both duodecimal and decimal counting are recommended as being easy to calculate with.

The benefits of decimal come from our using base-10 for other purposes. I guess the best of all possible worlds would be to use duodecimal for all units (including our normal number system).

Then we'd get the ease of use of modern base-10 units plus the better factorisation of duodecimal.

(But we'd still have an impedance mismatch with the binary powers. The KB/KiB split wouldn't go away).

I don't see the point of a duodecimal system of units when a base 10 system is much more elegant. You would never end up with a 1/64th of something in the metric system. Fractions are a hack.

As an aside, I wonder how technology affects the units or systems we use. They had to rely on decimal or duodecimal systems for their units because they were doing all of their calculations manually (so did we until about 20 or so years ago btw,) but now that everyone* carries a computer on his/her pocket, what better systems could we design?

I guess binary might be an example of that. 2 values is not something that applies to everything, at least not naturally in the way the human mind works, but it is much more efficient for machines to process information, that makes sense.

> I don't see the point of a duodecimal system of units when a base 10 system is much more elegant. You would never end up with a 1/64th of something in the metric system. Fractions are a hack.

How is base 10 more elegant than base 12?

1/64th might result from a binary, octal or hexadecimal system; duodecimal tens to favour things like 1/3, 1/4, 1/6, 1/9, 1/12 and so on. The elegant thing is that in duodecimal all of those are non-repeating fractions: .4, .3, .2, .14, .01 respectively. Interestingly, in duodecimal 1/5 and 1/10 are non-repeating (this is also true in binary...).

Base 12 is far more elegant than base 10, but the conversions cost make the conversion to French units look cheap--and then we'd need to convert all our units to some sort of French units mark II.

> I guess binary might be an example of that. 2 values is not something that applies to everything, at least not naturally in the way the human mind works, but it is much more efficient for machines to process information, that makes sense.

For day-to-day use, it makes sense to use a system where you can express your age (in years) in one or two digits rather than five to seven. Hence, a hexadecimal system might be preferable as a representation.

Fractions are a hack? 'Cos decimal is so intuitive!

1/3 vs 0.3' ? Much elegance!

1/3+1/3+1/3==1 vs 0.3'+0.3'+0.3'==0.9'==1 or something.

This is also a good argument for switching to base 12 for normal every-day counting.

One interesting thing I heard once - a journalist was discussing the merits of counting in base 12 with someone whose society already adopted this method. When the journalist asked how we would teach kids to count with their fingers, the answer was simple - use the divisions created by your knuckles!

It would mess with everyone but I think there's a pretty strong argument for base 12.

edit: okay, i finished reading and it kind of says that already. But it's still cool!

You're probabbly talking about numberphile's video : https://www.youtube.com/watch?v=U6xJfP7-HCc

I have seen a lot of numberphile's videos but not this one! Thanks for the link.

I'm pretty sure my flatmate told me the story and he watches numberphile too so you're almost certainly right either way :P

> For base 60, this is exacerbated

Sorry to nitpick, but "exacerbate" is to make worse. It's like "ex-acerbate". It doesn't mean "even more so" in a good way. Just thought you'd like to know.

Thank you! As you may have spotted, I am not a native English speaker, and I was confused by "false friends".

The verb "to exacerbate" comes from French verb "exacerber", which means "to make more intense or more acute".

My post has been edited to reflect your comment.

While we're picking nits, You could have replaced "exacerbated" with "magnified" in the original sentence. "it intensifies" sounds a bit weird too.

You can also find the duodecimal system in languages like English and German:

  ten, eleven, twelve | thirteen, fourteen, fifteen, sixteen
  zehn, elf, zwölf | dreizehn, vierzehn, fünfzehn, sechzehn

"Germanic languages have special words for 11 and 12, such as eleven and twelve in English, which are often misinterpreted as vestiges of a duodecimal system. However, they are considered to come from Proto-Germanic ainlif and twalif (respectively one left and two left), both of which were decimal."


Interestingly enough, in French you find the hexadecimal system:

  dix, onze, douze, treize, quatorze, quinze, seize | dix-sept, dix-huit, dix-neuf

In Spain on contrary, pentadecimal:

  diez, once, doce, trece, catorce, quince | dieciséis, diecisiete, dieciocho, diecinueve

In Latin seventeen is septendecim, and sixteen is sedecim (fifteen is quindecim). Language drift has shortened most French words from their Latin ancestors, and the same goes for the numbers for 10-20. I presume that the early French chose to use dix-sept when their words for septendecim and sedecim started to sound the same.

As for dix-huit and dix-neuf, the Romans counted down from twenty; duodeviginti (two-down-from-twenty) is eighteen and undeviginti (one-down-from-twenty).

So it probably made more sense to the early French to say dis-huit and dix-neuf instead.

But one interesting thing about French numbers that you have missed is that it possess a vestigial remnant of the vigesimal (base-20) number system of the Celtics, where 80 is quatre-vignts (four-twentys) to the French, and 90 is quatre-vignts-dix.

This actually goes for beyond that!

70 is sixty-ten (soixante-dix), then 71 is sixty-eleven... and so on, up to 99: four-twenty-nineteen. Indeed, 80 is 4 times 20, hence "four-twenty" (quatre-vingt, without the "s" at the end).

Interestingly enough, French-speaking Belgians use the regular forms: 70 is "septante", 80 is "octante", and 90 is "nonante".

Is that actually a vestige of a hexadec system, or just a strange quirk? Note that 2 sounds similar to 12, 3 to 13, and so on. That implies there's a relationship between those numbers, which only exists in decimal.

In Russian, decimal:

восемь (8), девять (9), десять (10) | одиннадцать, двенадцать, тринадцать, четырнадцать, пятнадцать, шестнадцать, семнадцать, восемнадцать, девятнадцать.

Dutch too: tien, elf, twaalf | dertien, veertien, vijftien, zestien

After the french revolution there was a short period (3 years) when the French had decimal time. It didn't catch on because that meant the workers had 10-day workweeks instead of 7.


As a result, decimal clocks from that era are very rare and highly sought after!

It has nothing to do with how one day is divided, it's the calendar.

There was a proposition for a day of 10 hours, each having 100 minutes, each having 1000 seconds.

And later, with the calendar came a simpler version with 100 minutes in an hour, 100 seconds in a minute, and so on (Article XI of the "Décret de la Convention Nationale concernant l'Ere des Français" [1]). It was only official (and mandatory) for a few months, however [2].

Edit: the one with 1M seconds a day was only an earlier draft version that never made it into law.

[1]: http://www.gefrance.com/calrep/decrets.htm (in french)

[2]: https://en.wikipedia.org/wiki/Decimal_time#France

I wonder if that's an error, 10 hours, 100 minutes each, with each minute 1000 seconds would mean 1 million seconds a day. Further on the article says there are 100k such seconds a day though.

You are completely right, I was confused by the first 1788 proposition. See edit.

Also, the weird thing was that, although they decided that an hour is divided in ten "parts", and each one of those in ten, and so one... they gave the name "minute" to the part of the part of the hour (so that 1 hour == 100 minutes), and the same for the second vs the minute.

I wonder how people managed to get a hang of this mess...

It has, the french went full on with the decimal system back then. And they didn't stop at the date and time, they also did away with all other measurements for size, weight and distance, but also things like the feudal system. Must have been confusing times!

"Decimal date and time" is probably the more proper phraseology. But that'd just be pedantry, of course.

From what I've read, the reason is simple:

Base 12: 12 is a number that can be divided by 2, 3, 4 and 6. This makes it a much better fit than base 10, which can only be divided by 2 and 5.

Base 60: As good as base 12 is, it misses division by 5. So what do you do to make it divisible? You multiply 12 x 5 = 60.

Now you can divide an hour in 2 parts of 30 minutes each, 3 parts of 20 minutes, 4 parts of 15 minutes, 5 parts of 12, or 6 parts of 10 minutes. This also means that if for example you want to divide a job in 3 shifts, every shift will be 8 hours, not 3,3333333 hours or similar, what you would get in a base10 system.

I mean, the stars and the gods and the tip or our fingers might be also a justification, but I think those were rationalized after the fact. I find it difficult that the guys that came with base12/60 didn't realize the particular properties of those numbers.

Base 60 has many advantages, but bare in mind that this is dated almost 4000 years ago. When people developed language and started counting, they would need something to keep track and help them go from one number to the other, so the finger tip theory is actually quite accurate.

I find the factor theory much more plausible for 4000 years ago than the finger tip theory. Why are there 24 beers in a case? Because 2 * 3 * 4 and the geometry of efficient packing. This would have been as true then as now.

Aside from previously discussed, the pendulum length is convenient, and water drop "clocks" are fairly reasonable at one drop per second.

Also people can count one digit per second pretty easily if the point is to cook or process something for 45 seconds or whatever. That would be tough if the second were 100 times smaller than it is.

Its a numerical base with two "digits" not just one digit. So its not just 60 sec/min its 60 min/hr and if you arbitrarily decided to use 2 for both, or 1000 for both, you don't get multiple levels that result in the second being useful. If you used 2 for both aka binary then each new-second would be 900 of our seconds long, thats useless. If you used 1000 for both then a new-second would be about 3 ms which might be handy for power EEs (not the RF guys...) but seems a bit inconvenient for the ancients.

One curiosity from the chem lab from decades ago was measuring to a milligram isn't all that challenging and a candle burned about a mg of wax per second (or was it a tenth?) anyway I'm well aware the gram is pretty recent, but the point is your stereotypical apothecary type in the ancient world should have been able to build a "mg capable" balance pan scale or at least approach it, so weighing a candle before and after would be a not too awful way to measure time and the least they could measure might have been around a second.

> Interestingly, in order to keep atomic time in agreement with astronomical time, leap seconds occasionally must be added to UTC. Thus, not all minutes contain 60 seconds. A few rare minutes, occurring at a rate of about eight per decade, actually contain 61.

And thus, the programmer's nightmare begins...

The Problem with Time & Timezones - Computerphile http://www.youtube.com/watch?v=-5wpm-gesOY&feature=share

Interesting, although I stopped reading at the end of page 1. It seemed the article already explained most of it and while I would've scrolled down to skim the rest of the article, waiting for a page load seemed too much effort.

The most interesting part of page 2, in my opinion, was the below quote:

Each degree was divided into 60 parts, each of which was again subdivided into 60 smaller parts. The first division, partes minutae primae, or first minute, became known simply as the "minute." The second segmentation, partes minutae secundae, or "second minute," became known as the second.

And why are multiplication tables in school typically taught up to 12x12? Historically in the UK, there were 12 pence in a shilling, 240 pence in the pound, 12 inches in a foot, etc, but I'm not sure of the value nowadays.

Not here in Portugal, we only teach up to 10x10.

Fun topic which inspires me to mention two goodies that help fuel in-depth conversations about measurement and conversion:

1) The Measure of All Things - http://www.kenalder.com/measure/ (science history goodness)

2) Frink - http://futureboy.us/frinkdocs/ (one of my first discoveries on HN and still one of the most fun to return to)

I read this book about the history of numbers.


The book author declares the Babylonians had a base 60 system. some native cultures have none at all. (well 1 and many)

Another interesting read I can recommend is this one:


I strongly recommend this book, it's a really fun read. It explores different ways of measuring time and items used over centuries in various cultures. It clarifies why the invention of zero was such a big deal, and why latin numerals looked like letters (same reasons as runes! They were trivial to carve on measuring sticks). Heaps of trivia! This should be a mandatory book at schools, it explains how development of mathematics affected our life, with numerous examples.

More on topic, the book makes a good point how base 60 came to be. It appeared when two natural bases merged: base 12 and base 10. Base 12 is natural, because you can conveniently count to 12 using fingers of one hand. To do that, you use the thumb. Notice that each of your remaining fingers consists of 3 segments. 4 fingers left * 3 segments = 12.

Base 60 allows cultures using bases 12 and 10 to coexist. It's the least common multiple. Naturally, it ALSO made it easier to avoid fractions.

"The trains are not only running on time, they're running on metric time."

I asked this of a curator at the British Museum several years ago. And he replied that it was the Sumerians that first adopted the 24 hours in a day convention. But he didn't know who came up with 60 minutes in an hour.

Thought it was very interesting of thinking the minute/second as base 60

a sexagesimal base has some advantages.

you can divide it by 10, 5, 4, 3, 2, etc.

legacy systems

why is the sky blue, Daddy?

because of Rayleigh scattering [1], son

[1] http://en.wikipedia.org/wiki/Rayleigh_scattering

Why isn't the sky purple, daddy?

Because you have inaccurate cones[1], son

[1] http://physicsfaq.co.uk/General/BlueSky/blue_sky.html Section: Why not violet?

>The Greek astronomer Eratosthenes (who lived circa 276 to 194 B.C.) used a sexagesimal system to divide a circle into 60 parts in order to devise an early geographic system of latitude, with the horizontal lines running through well-known places on the earth at the time. A century later, Hipparchus normalized the lines of latitude, making them parallel and obedient to the earth's geometry. He also devised a system of longitude lines that encompassed 360 degrees and that ran north to south, from pole to pole. In his treatise Almagest (circa A.D. 150), Claudius Ptolemy explained and expanded on Hipparchus' work by subdividing each of the 360 degrees of latitude and longitude into smaller segments. Each degree was divided into 60 parts, each of which was again subdivided into 60 smaller parts. The first division, partes minutae primae, or first minute, became known simply as the "minute." The second segmentation, partes minutae secundae, or "second minute," became known as the second.

This makes no sense. For this to be true, it implies that the ancient Greek already had knowledge that the Earth is round, 1600 years before Galileo.

The ancient greeks, among others, had that knowledge.

What makes no sense is the perpetuation of the myth that spherical earth is "new" concept.

The concept of a spherical Earth dates back to ancient Greek philosophy from around the 6th century BC -- http://en.wikipedia.org/wiki/Spherical_Earth


Uh, what? They knew the earth was a sphere:


First of all, Columbus rediscovered America a good century before Galileo.

Secondly, the idea that people believed in a flat earth before Columbus is entirely a 19th Century conceit: https://en.wikipedia.org/wiki/Christopher_Columbus#Geographi...

In fact, the fact that the earth is (essentially) spherical was well-known to basically everybody since ancient times. For example, any sailor could have told you that when approaching land, the tops of mountains appear first over the horizon.

> First of all, Columbus rediscovered America a good century before Galileo.

Well, "encountered" would probably be more accurate. Discovery -- even rediscovery -- requires recognition, and Columbus insisted he had reached the East Indies.

It was theorised/known the Earth was round a lot earlier than Galileo: http://en.wikipedia.org/wiki/Spherical_Earth

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