Although it is no longer used for general computation, the sexagesimal system is still used to measure angles, geographic coordinates and time. In fact, both the circular face of a clock and the sphere of a globe owe their divisions to a 4,000-year-old numeric system of the Babylonians.
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.
Minutes and seconds, however, were not used for everyday timekeeping until many centuries after the Almagest. Clock displays divided the hour into halves, thirds, quarters and sometimes even 12 parts, but never by 60. In fact, the hour was not commonly understood to be the duration of 60 minutes. It was not practical for the general public to consider minutes until the first mechanical clocks that displayed minutes appeared near the end of the 16th century. Even today, many clocks and wristwatches have a resolution of only one minute and do not display seconds.
Thanks to the ancient civilizations that defined and preserved the divisions of time, modern society still conceives of a day of 24 hours, an hour of 60 minutes and a minute of 60 seconds. Advances in the science of timekeeping, however, have changed how these units are defined. Seconds were once derived by dividing astronomical events into smaller parts, with the International System of Units (SI) at one time defining the second as a fraction of the mean solar day and later relating it to the tropical year. This changed in 1967, when the second was redefined as the duration of 9,192,631,770 energy transitions of the cesium atom. This recharacterization ushered in the era of atomic timekeeping and Coordinated Universal Time (UTC).
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.
References
- Time's Pendulum. Jo Ellen Barnett. Plenum Press, 1998.
- A History of Mathematics. Florian Cajori. MacMillan and Co., 1894.
- History of the Hour. Gerhard Dohrn-van Rossum. University of Chicago Press, 1996.
See what we're tweeting about
25 Comments
Add Commenthi;
Reply | Report Abuse | Link to thisThe life is decimal. But the lojic sisytem is binary. it is error. the computer sytems necacacery ise decimal. it is very good systems. we have decimal CPU systems. what do say decimal systems about.
Necmettin Türkoglu.
http://www.betoser.com
THE NEW COMPUTER SYSTEM
As it is widely known, the arithmetical logic units (ALU) of computer systems operate on binary basis. While people, all nations and languages and basic science disciplines such as physics, chemistry, electronics based on mathematics work on basis of tens (decimal); the devices of artificial intelligence named computer (computer, mobile phones , databank ,satellite receivers ,digital programmable devices) operate on binary basis.
Human brain thinks decimally due to its nature and can make decimal comparisons. This causes the recent computers obtain data as image, music, color, number on decimal basis and convert into a binary based number at ALU and then process. ALU converts the decimal values it obtains into binary and makes them binary and then for people to understand them, converts them into decimal. This causes conversion havoc in processors.
--
Edited by sistem19 at 12/07/2007 5:13 PM
nice write up relevant 2 all thinking individuals
Reply | Report Abuse | Link to this..it is unknown why the base 60 was chosen? Nobody of our so skilled professors tryed to forget the base 10 and use all our fingers (organized in four groups) to count ...
Reply | Report Abuse | Link to thisIf you are counting your 12 finger joints with your thumb on one hand (base 12) then when you have used up all of them, where do you record it? On the 5 fingers of your other hand. Thus you get 5 times 12 = 60 and you have a base 60 system.
Reply | Report Abuse | Link to thisI read somewhere that the minute was divided into sixty seconds because an average person's heart beat sixty times per minute. I know the "standard" is now considered to be 72. Is there any truth to the heartbeat foundation for the sixty second minute story?
Reply | Report Abuse | Link to thisgalileo
Reply | Report Abuse | Link to thisIf I remember well , when looking at the oscilation of the pendulum used his hearth beat to measure time , he then discovered that the oscilation period of a pendulum was constant , and started the drive to find a mechanical meassurement of time, doctors used pendulums to measure your hearth beat,
3*2-36 is equal to...12
Reply | Report Abuse | Link to thisb coz when it is difficult to view..but .when viwing becames possible... so do our time table......does it mean that?......18*2....36 of the time table r allowed...which means b coz of the viwing our world has missed...all the approximate...archological and what year estimation..proportionally...like (4milion yrs*36-24.0)/36=33.33prcnt of what the guss suld b.
The 24/7 aspects of time: Formula: [d x SQRTvLE = A1 = A2]. Sample Quadratic Equation:
Reply | Report Abuse | Link to thisAbstracts: [d = 0=5280 x SQRTvLE= Area1 a line 43560 = Area2 a square 1/640: and: 5280 x SQRT8.25 = 43560 x 4.27 = 186001.2 the speed of light at the elastic limit: and: Area2 = 640 x �3.125 = 2000 ÷ the square 4 = 500 ÷ 60 = 8.33&2 = 69.44& the vector cone x 360° = 25000 miles for the circumference of the earth: and: 500 x 186001.2 = 93,000,600 miles = one astronomical unit (1AU): and: light speed 186001.2 ÷ A1 a measuring line 43560 = operator 4.27]. Light energy must have a complex whole number unity: for instance: {22 ÷ T7 = Pi x [24 x 7 = 168(0) = 5280 = 1.0 = unity]
To explain the 24/7 aspects of time can be a major project. Yet, there is a formula that has evolved over the course of written history. And, of course the zones of the GUT universe are 1 thru 10. And a single formula does exist for all evolution and creation, from a single beginning. Sorry, complete analysis takes more spaca
Why time is measured using 60 seconds in a minute (not 50 or 100)?
Reply | Report Abuse | Link to this1 radian = 55.6 degrees approximately 60 degrees (say)= 10 minutes
Reply | Report Abuse | Link to this1 hour = 360 degrees or say 6 radians or 60 minutes.
So 1 minute = 360/60 =6 degrees.
So it takes the minute hand to make one revelution around the axis to make one minute which is 360 degrees.
ie; 360 degrees/6= 60 which is termed second.
This movement of the minute hand for 60 minutes is equivalent to movement of minute hand for 60 seconds. One can also consider one minute movement as movement of a smaller circle which again makes 360 degrees.
Also that the Earth rotates at a speed of around 56 miles/hour which is considered as the distance between two longitudes. So one hour is the time taken by the Earth to rotate a distance between two longitudes. Since this is close to 60 it can be that the time taken for measuring the time taken to move earht 1 mile is taken as 1 minute approximately.
Reply | Report Abuse | Link to thisThe Earth rotates on it's axis at a speed of 56 miles per hour. So it takes close to a minute to travel 1 mile. So 60 minutes or 1 mile in 1 minute is the rounded figure the time taken by Earth to cover a distance between 2 longitudes.
Reply | Report Abuse | Link to thisThis is also the time taken by a Ship traveling at 5 knots(1knot=12 miles/hour) to cover a distance beteween 2 longitudes that is 12 x5 = 60
Every 60 years, the planetary combinations relative to earth are repeated. That's why the day is divided into 60 parts (Naazhigais in the tamil calendar), each naazhigai into 60 naadi, and each naadi into 60 vinaadis; 60 days to a season, 6 seasons to a year, and a 60 year cycle...
Reply | Report Abuse | Link to thisA normal person's heart beat 72 times per minute
Reply | Report Abuse | Link to thisGreetings,
Reply | Report Abuse | Link to thisThank you for a very interesting description as to why we use 12, 24, 60, 360 as basis for various measurements, but I would like to make a comment if I may.
It would seem that one of the reasons for picking 12 as a base is because of it's large number of even divisors, 5 in all (namely 1, 2, 3, 4, and 6), as compared to only 3 for a base of 10. This would apply to all the other numbers mentioned as they are all multiples of 12.
In summary then, my theory would only hold up if the ancient people could not deal with fractional parts of a whole and I do not know the answer to this.
Thanks.
good calculation pally,but are you not taking the approx. wrong?
Reply | Report Abuse | Link to this55.6~60
you are diverting 4.4degree/10 minutes so for total 60 minutes the value becomes 26.4 degrees,
is't it is a very large value.
so if the Egyptians observed a group of 36 stars that divided the circle of heavens into equal parts, could this also be related to 360 degrees in a circle? Just a thought...
Reply | Report Abuse | Link to thisThe concept of fixed-length hours, however, did not originate until the Hellenistic period, when Greek astronomers began using such a system for their theoretical calculations. Hipparchus, whose work primarily took place between 147 and 127 B.C., proposed dividing the day into 24 equinoctial hours, based on the 12 hours of daylight and 12 hours of darkness observed on equinox days. Despite this suggestion, laypeople continued to use seasonally varying hours for many centuries. (Hours of fixed length became commonplace only after mechanical clocks first appeared in Europe during the 14th century.)
Reply | Report Abuse | Link to thisI am sorry it is totally a baseless darkage european invention.
check Persian nowrouz from 600BC
The concept of fixed-length hours, however, did not originate until the Hellenistic period, when Greek astronomers began using such a system for their theoretical calculations. Hipparchus, whose work primarily took place between 147 and 127 B.C., proposed dividing the day into 24 equinoctial hours, based on the 12 hours of daylight and 12 hours of darkness observed on equinox days. Despite this suggestion, laypeople continued to use seasonally varying hours for many centuries. (Hours of fixed length became commonplace only after mechanical clocks first appeared in Europe during the 14th century.)
Reply | Report Abuse | Link to thisI am sorry to say that these statements and alike are made up mostly during darkages of europe
Chinese Indians and persians 800 to 550 BC had already a very developed time division based calander specially the Koshanian and Hakhmaneshiyans.
Time has to be logic, simple and easy to learn. The 24 hour system is not logic, simple and easy to learn. So I developed a new time system that I called "Logic Time" (LT). It corrects most of the "build in errors" of our conventional 24 hours system. The space that is available on this page isn't enough to explain in detail how LT works so if you are interested in knowing more about it take a look at an online example of a LT clock (with detailed explanation). http://dhost.info/jose/Logic_Time_v3.00_DTD_html_4.01.html
Reply | Report Abuse | Link to thisWe cannot completely explain anything considering time measuring. That's could be clear on paper but in real life its not. How many <a style="color: black; text-decoration: none;" rel="dofollow" href="http://www.uk-dissertation.com">dissertations</a> and projects have been written on this theme, and have they really revealed relative nature of time? No. Because the matter of "time" is purely subjective for every person, regardless of its measuring.
Reply | Report Abuse | Link to thisThis is pure speculation but just suppose, way back when, the average heart beat was around once per second. No one would have known this but somebody got a wild hair about the heartbeat, probably a profound personal and spiritual part of ife, and a tribal member was chosen.
Reply | Report Abuse | Link to thisHere’s my alternative:
Consider one pair of hands – use them to count seconds. Two hands count 10 beats (the second hands). A second pair of hands is added. The third hand counts multiples of 10 heartbeats up to 50. On the 60th count, the first three hands revert to no counts and the fourth becomes the ‘minute hand’. A third set of hands is added. Each time the previous four hands accumulate a maximum number of counts, the fifth and sixth hand accumulate a six minute block. A fourth set of hands is added. The seventh hand becomes the ‘hour hand’. The eighth hand accumulates blocks of 6 hours. This starts at sunrise or sunset and concludes at the same point of the next day. It is repeated over the seasons from solstice to solstice for years/decades until an accepted total count per day is established and the method refined for repeatability. Over generations, the concepts are proven and easily passed on by the use of finger counts without the difficulty of mechanically manipulating finger joints and the difficulty of perceiving the movement of those joints.
As with most of my ideas, I am probably full of crap but I hope my idea can generate a discussion or two. If nothing else, maybe someone can, gently, show me the error of my ways.
I'm unpleasantly surprised to note that most of the comments here contain a vast amount of spelling errors. Here I was thinking that SciAm readers were literate. Anyway, very interesting article. However there is a mistake. It is mentioned above that Egyptians were the first civilization to break the day into smaller parts. What about the Sumerians? They were around long before Egypt, and from what I read they were very advanced for their time. Surely they would have used complex measurements of time and split their days into segments, but I am guessing now. The other correction I am not guessing the answer: Egyptians liked to put their deeds on the walls of their buildings in great artistic detail. In the Great Pyramid at Giza there is a wall painting that depicts either Anubis or Horus holding up what looks like an elongated light bulb. It even shows the little copper coils inside and a wire coming out of the end of the bulb. Inside this room there are no carbon marks on the walls or ceiling from torches, and the room itself is so isolated in the pyramid that even with their best mirrors, reflected sunlight would not be sufficient. Related to this, has anyone heard of the Baghdad Battery? Archaeologists a few years back discovered a clay jar that contained layers of alkaline metals and acids, penetrated by two copper wires which protruded from the lid of the jar. When applied to a voltmeter, this object gave off 4.something volts of electricity. They dated the jar to be about 4,000 (or was it 14,000?) years old. Google this, I'm not bullshitting you. If people 4,000 years ago could make a battery, I'm sure the 'almighty' Egyptians could figure out how to make artificial light.
Reply | Report Abuse | Link to thisPerhaps the measurement of time, and the degrees of a circle, both of which lend themselves to navigation were taught to us by a civilization that had 12 fingers, hence a base 12 compared to our base 10 which I assume is because of our 10 digits. I am on this site because I was wondering why a circle is measured by 360 degrees and not 100. I've read the remarks about planets and they could have easily chosen 10 planets to denote the passage of the night rather than 12. Planets lining up every 60 years makes some sense but it seems a stretch as a reason for 360 degrees in a circle.It's not like I'm saying 12 fingers isn't a stretch, but there you go.
Reply | Report Abuse | Link to thisActually, as early as 1500 B.C., the Egyptians had developed a more advanced sundial. A T-shaped bar placed in the ground, this instrument was calibrated to divide the interval between sunrise and sunset into 14 parts.
Reply | Report Abuse | Link to thisHowever, Theodontus the Weird, proposed that rather than 14 parts it should be 12. He was givent the appellation, "the Weird", due his a strange genetic abnormality which he had inherited from his mother, namely he had an extra digit on each hand.
He was also a peerless warrior, this ability also being attributed to his extra digits. He swore vengeance of the 14 parters and left a terrible legacy of slaughter in his wake. In twelve days all would divide the sunset into 12 parts.