Why is a minute divided into 60 seconds? (2007) | Hacker News Reader

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

scientificamerican.com

50 pointsggonweb31 comments

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.

> 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).

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.

> 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?

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

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.

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...

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

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.

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

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.

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

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.

> 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)

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).

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...

> 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.

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.)

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).

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.

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.

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

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

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".

> 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.

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 ^.

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.

> 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... ;)

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

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.

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

Any serious carpenter will always work in mm, anyway.

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.

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