Why is a minute divided into 60 seconds? (2007)

http://www.scientificamerican.com/article/experts-time-division-days-hours-minutes/

by ggonweb • 12 years ago

50 31 12 years ago

scientificamerican.com

walshemj• 12 years ago

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

tjradcliffe3• 12 years ago

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.

atemerev2• 12 years ago

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

Florin_Andrei2• 12 years ago

The Babylonians were an Assyrian people

I thought the Babylonians were some kind of Semitic people, and the Assyrians were their rivals? (and eventually their conquerors)

snoman• 12 years ago

If I remember my reading of A History of Mathematics well enough, they very much were into base 60 (sexagesimal) because of the numerous divisors (1/2/3/4/5/6/10/12/15/20/30/60).

kps2• 12 years ago

60 is a superior highly composite number¹. 12 (inches) and 360 (degrees) are also superior highly composite.

¹ http://en.wikipedia.org/wiki/Superior_highly_composite_numbe...

diminish• 12 years ago

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• 12 years ago

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.

whiddershins• 12 years ago

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• 12 years ago

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.

kps2• 12 years ago

  > However, the nice water/gravity correpondence is really nice in practice

One fluid once of water weighs (approximately) one ounce.

hackuser• 12 years ago

1 U.S. pint of water weighs 1 pound.

"A pint is a pound, all the world round."

That's the saying, at least, but in the UK a pint, what Yanks call an Imperial pint, is 20 oz and weighs 1.25 lbs: "A pint of pure water weighs a pound and a quarter".

Florin_Andrei2• 12 years ago

the nice water/gravity correpondence

Also:

1 atm (normal atmospheric pressure) is 1 kg / cm^2. Or the pressure of 10 meters of water (a column of water 10 meters tall, to be precise).

1kg of mass under normal gravity generates a gravitational force of ~10N.

It's super-easy to do everyday physics in your head, no calculator required, in the metric system.

echaozh• 12 years ago

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 ^.

phaemon• 12 years ago

and something as simple as dividing a piece of wood in to thirds is unnecessarily imprecise.

Nonsense. It's dead easy. If you have a 120cm piece of wood, one third of it is 40cm.

Now, let's try that in Imperial. 120cm is 3 foot, 11 2/10 inches. How on earth would you go about dividing 3' 11 2/10" into thirds?!

I'll leave you to think about it... ;)

dmckeon• 12 years ago

A carpenter in the US is unlikely to measure wood in 10ths of an inch. I make 120cm to be about 47.2441 inches - or almost 3 feet, 11 1/4 inches. Before we quibble over decimal precision, how wide is the saw blade?

Anyone in need of serious wood-butchering arithmetic should find the instructions that should come with an L-shaped carpenter's framing square, and learn what all the various scales can be used for - it's like a slide rule for wooden construction.

https://en.wikipedia.org/wiki/Steel_square

ninjaplease• 12 years ago

I was going to explain why you're a dick, but then I realized you already know you're a dick.

Nevertheless, it bears repeating: you're a dick.

brc• 12 years ago

Err, I do occasional woodwork, and working with imperial measurements is a nightmare.

Any serious carpenter will always work in mm, anyway.

grecy• 12 years ago

I've lived in a couple of different metric countries, and built many things in my life, worked on cars, etc. etc.

Nobody uses centimeters. Ever.

It's all millimeters, even when it's a round number, i.e. nobody says "Mark it at 10cm", they say "Mark it at 100 mil(limeters)".

It's not worth trying to cut many things to an accuracy greater than 1mm, so that's a fine enough "smallest" unit.

atemerev2• 12 years ago

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.

tjradcliffe3• 12 years ago

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.)

brute2• 12 years ago

This would mean that on one hand (literally) you count the phalanxes (12), while on the other hand you use a completly different system and count your fingers (5). Why would you ever use 2 different counting systems? It seems that your argument is more in favor of base 25(=5 * 5) or base 144(=12 * 12).

droidist2• 12 years ago

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?

digisign• 12 years ago

I believe it is the year that's off a bit in relation to the day.

HCIdivision17• 12 years ago

Surprisingly, I've found explanations that it's due to variation in the year and day. Remember, the year is based on the physical phenomena of goin'round the sun, and so we have the issue of theory meeting practice, where our ideal of a year fails to model the truly complex dynamics of the actual earth's orbit. There are errors being introduced due to the moon slowing our spin, other planets distorting our orbit, and other such subtle and difficult-to-account-for cumulative errors from ideal steady-state.

So even of the second was defined as slightly longer, we'd still have to issue corrective leap seconds.

I meant to look into this particular thing more closely last time I read about leap seconds here, so I'm glad for the reminder. If anyone has actual details and references about these effects, I'd be much obliged.

brute2• 12 years ago

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

[2] https://upload.wikimedia.org/wikipedia/commons/thumb/5/5b/De...

jacobsimon• 12 years ago

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• 12 years ago

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).

malkia• 12 years ago

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.

Why is a minute divided into 60 seconds? (2007)

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