
Why is a minute divided into 60 seconds, an hour into 60 minutes? - smalu
http://www.scientificamerican.com/article.cfm?id=experts-time-division-days-hours-minutes
======
spodek
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](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).

~~~
edvinbesic
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).

~~~
eric_the_read
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!

~~~
jonesetc
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.

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

------
brudgers
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.

Exercises:

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?

[http://en.m.wikipedia.org/wiki/Babylonian_number_system](http://en.m.wikipedia.org/wiki/Babylonian_number_system)

------
treenyc
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."

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

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

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

~~~
toki5
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.

------
nmc
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.

~~~
jbert
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).

~~~
redial
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.

~~~
wtbob
> 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.

------
justwrote
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

~~~
nmc
Interestingly enough, in French you find the hexadecimal system:

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

~~~
jhanschoo
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.

~~~
nmc
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".

------
dirktheman
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.

[http://en.wikipedia.org/wiki/French_Republican_Calendar](http://en.wikipedia.org/wiki/French_Republican_Calendar)

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

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

~~~
gourlaysama
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](http://www.gefrance.com/calrep/decrets.htm)
(in french)

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

~~~
Aardwolf
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.

~~~
gourlaysama
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...

------
abgv
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.

~~~
fjcaetano
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.

~~~
dribnet
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.

------
VLM
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.

------
mVChr
> 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...

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

------
sdfjkl
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.

~~~
mdisraeli
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.

------
petercooper
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.

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

------
headbiznatch
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/](http://www.kenalder.com/measure/) (science
history goodness)

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

------
yardie
I read this book about the history of numbers.

[http://www.amazon.co.uk/gp/product/0747597162/ref=oh_details...](http://www.amazon.co.uk/gp/product/0747597162/ref=oh_details_o00_s00_i02?ie=UTF8&psc=1)

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

~~~
jakub_g
Another interesting read I can recommend is this one:

[http://www.amazon.com/Universal-History-Numbers-Georges-
Ifra...](http://www.amazon.com/Universal-History-Numbers-Georges-
Ifrah/dp/186046324X/)

~~~
b0rsuk
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.

------
auvrw
"The trains are not only running on time, they're running on _metric_ time."

------
chiph
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.

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

------
jokoon
a sexagesimal base has some advantages.

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

------
netcan
legacy systems

------
squirejons
why is the sky blue, Daddy?

~~~
nmc
because of Rayleigh scattering [1], son

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

~~~
MereInterest
Why isn't the sky purple, daddy?

~~~
mVChr
Because you have inaccurate cones[1], son

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

------
fjcaetano
>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.

~~~
zb
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...](https://en.wikipedia.org/wiki/Christopher_Columbus#Geographical_considerations)

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.

~~~
dragonwriter
> 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.

