8 ms·

Why is a minute divided into 60 seconds, an hour into 60 minutes?

170 points by smalu 13y ago

nmc 13y ago
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.
- maaarghk 13y ago
  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!
  - te-x 13y ago
    You're probabbly talking about numberphile's video : https://www.youtube.com/watch?v=U6xJfP7-HCc https://www.youtube.com/watch?v=U6xJfP7-HCc
    - maaarghk 13y ago
      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
- phaemon 13y ago
  > 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.
  - nmc 13y ago
    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.
    - pygy_ 13y ago
      While we're picking nits, You could have replaced "exacerbated" with "magnified" in the original sentence. "it intensifies" sounds a bit weird too.
- jbert 13y ago
  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 13y ago
    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 13y ago
      > 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.
netcan 13y ago
legacy systems
deleted 13y ago
[deleted]
dirktheman 13y ago
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 13y ago
  It has nothing to do with how one day is divided, it's the calendar.
  - Two9A 13y ago
    "Decimal date and time" is probably the more proper phraseology. But that'd just be pedantry, of course.
  - gourlaysama 13y ago
    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 13y ago
      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 13y ago
yardie 13y ago
I read this book about the history of numbers. http://www.amazon.co.uk/gp/product/0747597162/ref=oh_details_o00_s00_i02?ie=UTF8&psc=1 http://www.amazon.co.uk/gp/product/0747597162/ref=oh_details... The book author declares the Babylonians had a base 60 system. some native cultures have none at all. (well 1 and many)
- jakub_g 13y ago
  Another interesting read I can recommend is this one: http://www.amazon.com/Universal-History-Numbers-Georges-Ifrah/dp/186046324X/ http://www.amazon.com/Universal-History-Numbers-Georges-Ifra...
  - b0rsuk 13y ago
    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.
VLM 13y ago
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.
squirejons 13y ago
why is the sky blue, Daddy?
- nmc 13y ago
  because of Rayleigh scattering [1], son [1] http://en.wikipedia.org/wiki/Rayleigh_scattering http://en.wikipedia.org/wiki/Rayleigh_scattering
  - MereInterest 13y ago
    Why isn't the sky purple, daddy?
    - mVChr 13y ago
      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?
justwrote 13y ago
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 13y ago
  Interestingly enough, in French you find the hexadecimal system: dix, onze, douze, treize, quatorze, quinze, seize | dix-sept, dix-huit, dix-neuf
  - jakub_g 13y ago
    In Spain on contrary, pentadecimal: diez, once, doce, trece, catorce, quince | dieciséis, diecisiete, dieciocho, diecinueve
  - oleganza 13y ago
    In Russian, decimal: восемь (8), девять (9), десять (10) | одиннадцать, двенадцать, тринадцать, четырнадцать, пятнадцать, шестнадцать, семнадцать, восемнадцать, девятнадцать.
  - srl 13y ago
    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.
  - jhanschoo 13y ago
    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.
treenyc 13y ago
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 13y ago
  Yet another headline phrased as a question without a clear answer in the article body...
  - hugofirth 13y ago
    How else would you have an article referring to an open question phrased?
    - DougWebb 13y ago
      "We wasted our time writing this. Now you can waste your time reading it."
      - toki5 13y ago
        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.
    - robmcm 13y ago
      "The mystery of why is a minute divided into 60 seconds, an hour into 60 minutes?"
  - coldpie 13y ago
    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 http://en.wikipedia.org/wiki/Betteridge%27s_law_of_headlines
  - 13y ago
spodek 13y ago
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).
- manish_gill 13y ago
  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 https://pbs.twimg.com/media/Bdp2YLFCIAAM1Dy.png
  - edvinbesic 13y ago
    Which is precisely the reason why the US military has adopted the metric system.
    - adolph 13y ago
      Metric mils? Ha!
  - raldi 13y ago
    What's that a map of, countries that have placed a man on the moon?
    - 13y ago
chiph 13y ago
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.
abgv 13y ago
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 13y ago
  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 13y ago
    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.
auvrw 13y ago
"The trains are not only running on time, they're running on metric time."
sdfjkl 13y ago
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 13y ago
  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.
fjcaetano 13y ago
>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.
- vmind 13y ago
  It was theorised/known the Earth was round a lot earlier than Galileo: http://en.wikipedia.org/wiki/Spherical_Earth http://en.wikipedia.org/wiki/Spherical_Earth
- minikites 13y ago
  Uh, what? They knew the earth was a sphere: https://en.wikipedia.org/wiki/Eratosthenes#Measurement_of_the_Earth.27s_circumference https://en.wikipedia.org/wiki/Eratosthenes#Measurement_of_th...
- njharman 13y ago
  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 http://en.wikipedia.org/wiki/Spherical_Earth http://scienceblogs.com/startswithabang/2011/09/21/who-discovered-the-earth-is-ro/ http://scienceblogs.com/startswithabang/2011/09/21/who-disco...
- 13y ago
petercooper 13y ago
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 13y ago
  Not here in Portugal, we only teach up to 10x10.
brudgers 13y ago
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
carsonreinke 13y ago
Thought it was very interesting of thinking the minute/second as base 60
jokoon 13y ago
a sexagesimal base has some advantages. you can divide it by 10, 5, 4, 3, 2, etc.
mVChr 13y 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. And thus, the programmer's nightmare begins...
- dsego 13y ago
  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
headbiznatch 13y ago
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)

170 points by smalu 13y ago

nmc 13y ago

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.

maaarghk 13y ago
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!
- te-x 13y ago
  You're probabbly talking about numberphile's video : https://www.youtube.com/watch?v=U6xJfP7-HCc https://www.youtube.com/watch?v=U6xJfP7-HCc
  - maaarghk 13y ago
    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
phaemon 13y ago
> 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.
- nmc 13y ago
  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.
  - pygy_ 13y ago
    While we're picking nits, You could have replaced "exacerbated" with "magnified" in the original sentence. "it intensifies" sounds a bit weird too.
jbert 13y ago
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 13y ago
  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 13y ago
    > 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.

netcan 13y ago

legacy systems

deleted 13y ago

[deleted]

dirktheman 13y ago

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 13y ago
It has nothing to do with how one day is divided, it's the calendar.
- Two9A 13y ago
  "Decimal date and time" is probably the more proper phraseology. But that'd just be pedantry, of course.
- gourlaysama 13y ago
  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 13y ago
    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 13y ago

yardie 13y ago

I read this book about the history of numbers. http://www.amazon.co.uk/gp/product/0747597162/ref=oh_details_o00_s00_i02?ie=UTF8&psc=1 http://www.amazon.co.uk/gp/product/0747597162/ref=oh_details... The book author declares the Babylonians had a base 60 system. some native cultures have none at all. (well 1 and many)

jakub_g 13y ago
Another interesting read I can recommend is this one: http://www.amazon.com/Universal-History-Numbers-Georges-Ifrah/dp/186046324X/ http://www.amazon.com/Universal-History-Numbers-Georges-Ifra...
- b0rsuk 13y ago
  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.

VLM 13y ago

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.

squirejons 13y ago

why is the sky blue, Daddy?

nmc 13y ago
because of Rayleigh scattering [1], son [1] http://en.wikipedia.org/wiki/Rayleigh_scattering http://en.wikipedia.org/wiki/Rayleigh_scattering
- MereInterest 13y ago
  Why isn't the sky purple, daddy?
  - mVChr 13y ago
    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?

justwrote 13y ago

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 13y ago
Interestingly enough, in French you find the hexadecimal system: dix, onze, douze, treize, quatorze, quinze, seize | dix-sept, dix-huit, dix-neuf
- jakub_g 13y ago
  In Spain on contrary, pentadecimal: diez, once, doce, trece, catorce, quince | dieciséis, diecisiete, dieciocho, diecinueve
- oleganza 13y ago
  In Russian, decimal: восемь (8), девять (9), десять (10) | одиннадцать, двенадцать, тринадцать, четырнадцать, пятнадцать, шестнадцать, семнадцать, восемнадцать, девятнадцать.
- srl 13y ago
  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.
- jhanschoo 13y ago
  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.

treenyc 13y ago

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 13y ago
Yet another headline phrased as a question without a clear answer in the article body...
- hugofirth 13y ago
  How else would you have an article referring to an open question phrased?
  - DougWebb 13y ago
    "We wasted our time writing this. Now you can waste your time reading it."
    - toki5 13y ago
      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.
  - robmcm 13y ago
    "The mystery of why is a minute divided into 60 seconds, an hour into 60 minutes?"
- coldpie 13y ago
  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 http://en.wikipedia.org/wiki/Betteridge%27s_law_of_headlines
- 13y ago

spodek 13y ago

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).

manish_gill 13y ago
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 https://pbs.twimg.com/media/Bdp2YLFCIAAM1Dy.png
- edvinbesic 13y ago
  Which is precisely the reason why the US military has adopted the metric system.
  - adolph 13y ago
    Metric mils? Ha!
- raldi 13y ago
  What's that a map of, countries that have placed a man on the moon?
  - 13y ago

chiph 13y ago

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.

abgv 13y ago

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 13y ago
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 13y ago
  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.

auvrw 13y ago

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

sdfjkl 13y ago

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 13y ago
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.

fjcaetano 13y ago

>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.

vmind 13y ago
It was theorised/known the Earth was round a lot earlier than Galileo: http://en.wikipedia.org/wiki/Spherical_Earth http://en.wikipedia.org/wiki/Spherical_Earth
minikites 13y ago
Uh, what? They knew the earth was a sphere: https://en.wikipedia.org/wiki/Eratosthenes#Measurement_of_the_Earth.27s_circumference https://en.wikipedia.org/wiki/Eratosthenes#Measurement_of_th...
njharman 13y ago
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 http://en.wikipedia.org/wiki/Spherical_Earth http://scienceblogs.com/startswithabang/2011/09/21/who-discovered-the-earth-is-ro/ http://scienceblogs.com/startswithabang/2011/09/21/who-disco...
13y ago

petercooper 13y ago

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 13y ago
Not here in Portugal, we only teach up to 10x10.

brudgers 13y ago

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

carsonreinke 13y ago

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

jokoon 13y ago

a sexagesimal base has some advantages. you can divide it by 10, 5, 4, 3, 2, etc.

mVChr 13y 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. And thus, the programmer's nightmare begins...

dsego 13y ago
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

headbiznatch 13y ago

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)