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

by smalu on 1/15/14, 10:58 AM with 148 comments

• by spodek on 1/15/14, 1:43 PM

  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 -- 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).

• by brudgers on 1/15/14, 3:07 PM

  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

• by treenyc on 1/15/14, 1:16 PM

  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."

• by nmc on 1/15/14, 11:19 AM

  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.

• by justwrote on 1/15/14, 1:15 PM

  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

• by dirktheman on 1/15/14, 11:56 AM

  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

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

• by abgv on 1/15/14, 2:04 PM

  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.

• by VLM on 1/15/14, 12:46 PM

  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.

• by mVChr on 1/15/14, 5:51 PM

  > 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...

• by sdfjkl on 1/15/14, 2:14 PM

  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.

• by petercooper on 1/15/14, 2:24 PM

  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.

• by headbiznatch on 1/15/14, 9:14 PM

  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/ (science history goodness)

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

• by yardie on 1/15/14, 12:36 PM

  I read this book about the history of numbers.

  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)

• by auvrw on 1/15/14, 2:07 PM

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

• by chiph on 1/15/14, 1:53 PM

  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.

• by carsonreinke on 1/15/14, 5:14 PM

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

• by jokoon on 1/15/14, 5:40 PM

  a sexagesimal base has some advantages.

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

• by netcan on 1/15/14, 11:29 AM

  legacy systems

• by squirejons on 1/15/14, 1:02 PM

  why is the sky blue, Daddy?

• by fjcaetano on 1/15/14, 2:20 PM

  >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.