
Why is a minute divided into 60 seconds? (2007) - ggonweb
http://www.scientificamerican.com/article/experts-time-division-days-hours-minutes/
======
jacobsimon
I'm surprised there's no mention of the relationship between time and the
origin of the metric system in this article. Interestingly enough, it takes a
1-meter pendulum 1 second to swing from side to side, no matter how high you
raise it. Mechanical clocks relied on pendulum motion to keep time, and so the
meter was created (at least partly) to standardize the size of the pendulum
needed to create an accurate clock! Now that's an interesting story.

~~~
taejo
> it takes a 1-meter pendulum 1 second to swing from side to side, no matter
> how high you raise it

If I remember correctly, this is true if sin _x_ = _x_ ; IOW, "how high you
raise it" is exactly what takes you away from this approximation being true.

Also, the meter was also originally defined as 1/10 000 000 of the distance
from the north pole to the equator. It just so happens that these two come
pretty close (it turns out that they had a big error in their measurement; a
quarter-circumference of the earth is closer to 12 000 km than 10 000).

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malkia
10 vs 12 - A coworker nicely put it to me when I asked him why US is still
using 12, as 12 inches is one foot, and he told me that during the great US
expansion it was much easier to deal in units of 12 - you can divide 12 by 2,
3, 4 and 6, while 10 was divisible only by 2 and 5. Now whether that was
really the case I don't know, but sounds like cool theory.

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droidist2
> 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.

So the second should be a tiny bit longer? Like 1.00000015 times longer?

~~~
brute
Leap seconds can be positive or negative (never happened) and are irregularly
announced up to two times a year.

The wikipedia article on leap seconds[1] is worth reading and has this[2]
great figure showing the variations of day length over the years due to
various astronomical factors. It also shows how these small deviations slowly
desync UT1 and UTC (red line), and that this issue cannot be solved by a
linear scaling.

[1]
[https://en.wikipedia.org/wiki/Leap_second](https://en.wikipedia.org/wiki/Leap_second)

[2]
[https://upload.wikimedia.org/wikipedia/commons/thumb/5/5b/De...](https://upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Deviation_of_day_length_from_SI_day.svg/512px-
Deviation_of_day_length_from_SI_day.svg.png)

------
diminish
60=2x3x2(4)x5 makes sharing farming products easier among 2,3,4,5,6,10,12
people.

77=7x11 is cool too, but families/partners with 7 or 11 people are less common

~~~
tomsthumb
It feels like this reasoning is related to 13 being an "unlucky" number. You
really can't split anything nicely between 13 people, or put them in even
groups.

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walshemj
The babylonians where into base 60 doesn't everyone know that?

~~~
tjradcliffe
The Sumerians, not the Babylonians.

The Babylonians were an Assyrian people who conquered the Sumerians and
adopted much of their culture, much the way the Romans took over the Greeks.

The answer to why the Sumerians used base 60 is: nobody knows, although as the
article points out, 60 is a very convenient number with lots of useful
factors, including 12, which was the number of divisions of the night.

~~~
atemerev
5 fingers, 4x3=12 phalanxes to point with thumb. 5x12=60.

~~~
tjradcliffe
5 fingers, 2x5 = 10

4 fingers, 2x4 = 8. Same for feet => 16

7 major joints on each side of the body, 2x7 = 14

"Explanations" of this kind "explain" what was chosen, but offer no
information about why it was chosen over all the other possibilities, and can
always be easily adapted to "explain" the alternatives equally well, so in
fact they tell us almost nothing.

Whereas we know that heliacal rising stars were used to divide the night into
six "double hours" (danna) by Sumerians which gave twelve divisions of the
sky. This was based on lunar months, which are a unique--albeit approximate--
source of the number 12, as opposed to anatomical speculations, which clearly
are capable of generating just about any number you care to name.

Furthermore, simply because knuckle-counting "just makes sense" to some modern
humans does not do more than incrementally raise the plausibility of the claim
that it was the source of the base-12 system in the ancient world.

If you accept that the fact that it "just makes sense" to you is somehow
compelling evidence for it, you have to accept that fact that it seems
completely ridiculous to me counts as compelling evidence against it. The
alternative--that I am an ignorant idiot and therefore my intuitions on this
matter don't count--is... empirically untenable.

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atemerev
> Although it is unknown why 60 was chosen

Oh come on. This is not rocket science.

There is an easy way to count to 12 with just one hand: place your thumb on
one of your phalanxes. There are three for each of the remaining fingers:
hence, 4*3=12 possibilities. Babylonians counted this way, hence the
duodecimal system.

You can use your second hand to count to five, as usual. 5x12 = 60. If you
show one of the fingers on your left hand, and one of the phalanxes of your
right hand, it really clearly communicates a number from 1 to 60.

This is why the base 60 was chosen.

~~~
tjradcliffe
To treat this as "obvious" rather than "interesting" is an epistemic error.

In particular, any ancient counting system could be given a similar anatomical
analysis. Base 30? Well, it's only the first two knuckles that are easy to
bend. Base 14? Clearly the major joints were being used for counting (because
counting, not communication was the issue: people had words for communication
and didn't need hand gestures). Base 8? Again, the first two knuckles,
multiply both hands to get 64... so maybe that would be base 64?

Simply because you can give an account of what people actually used is no
proof of explanation: you also have to given an account of why what was not
used was not used. Claiming it was because it was somehow less convenient than
the system you suggest is not an explanation, but a classic example of begging
the question (assuming the consequent.)

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whiddershins
This is why the metric system is stupid.

Now, last time I said this I was downvoted, but just because base 10 is
convenient academically doesn't mean it is a great idea in day to day life.

The metric system is great for doing science but totally annoying for doing
carpentry, for example. Centimeters are generally not a convenient size, and
something as simple as dividing a piece of wood in to thirds is unnecessarily
imprecise.

~~~
alricb
Well, they did think about making metric base-12, but in the hurry of the
revolution, they left that out. It WOULD be more useful with base 12.

However, the nice water/gravity correpondence is really nice in practice (1 kg
= ~ the mass of 1 L of water, 1 L = 1 dm cube). For instance you can easily
estimate the weigth of something given its metric dimensions and the density
of the material relative to water.

~~~
echaozh
If you make the units base-12, leaving the numerical system base-10, it will
be really inconvenient. How much is 12^4? 10^4 is obvious, even if this 10 is
a decimal 12.

Base 2 is successful partly due to the fact that 2^10 is very close to 1000,
which matches the kilo, mega scheme.

Edit: asterisks are for formatting, easier to use ^.

~~~
moron4hire
That's kind of the whole crux of the problem. It's all just culture. Some
mathematicians like to act like math is a universal language that transcends
culture, but ultimately it's impossible for a human to communicate anything
without the basis of culture, so that dirty, ol' not-hard-science has to creep
in somewhere. Or else what is the use of it, if you can't talk about it?

If we were more focused as a culture on a base-12 system, we'd be using a
base-12 numbering system as well, in which case 12^4 would be written as
"10000", leaving us to ask the crazy base-10 proponents just how easy they
expect it would be to represent 10^4 ("5954" in base 12).

Base-2's popularity has nothing to do with 2^10 ~= 10^3, except where it
serves hard drive manufacturers to sow uncertainty around the difference
between Mibi- and Mega- bytes. Otherwise, it's just happy circumstance. Base-2
works because binary computers were ready for work before trinary computers
were developed.

The numbers are only useful because we've decided as a culture that they
should be so. There is nothing sacrosanct about the number 10 (or 12 for that
matter). As all things, mathematics is only useful _insofar as it is useful_.
We get to choose the way we abstract reality. It's kind of one of the things
that makes us human.

