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Pick a any notion of year and any type of day measurement. Outside of history and the common cycle of day an night, why are these viewed as integrally or even fractionally commensurate?

Why all the stunts with leap days and leap seconds, etc... when we now have atomic clocks? Why not decouple the two?

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    $\begingroup$ Sometimes we don't do things as accurately as we might otherwise, simply because we're human. It's easy to think of how long a period is in days, but if we want to say "Neptune's period is X Mercury periods", then it's a lot less intuitive. It's similar to how we use 24 hours in a day and 360 degrees in a circle. They're numbers we're familiar with and have an intuitive grasp of. $\endgroup$ – Phiteros May 3 '17 at 5:33
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    $\begingroup$ How do you know what a year is without a calendar? - see Sidereal Time and Sidereal Year. You might also find this Vsauce video informative (which, in a way, augments the comment above and the answers below - mankind taking control of how we want to define what a day / year is). $\endgroup$ – Dhruv Saxena May 4 '17 at 14:06
  • $\begingroup$ Because it JustWorks(TM AppleCorp). $\endgroup$ – Carl Witthoft May 5 '17 at 11:33
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    $\begingroup$ This question really should just be denied (in the Zen sense). It makes no sense and has no foundation. $\endgroup$ – Carl Witthoft May 5 '17 at 11:34
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The year is not defined as a multiple of days.

The year is the time for the Earth to orbit the sun once. This is not a constant amount of time. So it is not defined in seconds or days or any other length of time. However it only varies a little.

The (synodic) day is the amount of time for the Earth to rotate once relative to the Sun. This is also not a fixed amount of time. But like the year only varies a little.

Time is measured in seconds. one second is 9,192,631,770 cycles of the radiation produced by the transition between two levels of the caesium 133 atom. This is among the most stable clocks we know. The second can be redefined if a more stable clock exists.

Now for the practical aspect of calendar forming it is convenient to have a simple rule that anyone can apply and can decide, without the need to make careful observations, which day is in which year. To this end the Gregorian Calendar gives a fairly simple but accurate approximation to the true astronomical year.

The disadvantages of using astronomical observations to decide the first day of the year are significant. Politically, who makes the observations? Russia? China? Japan? Botswana? In theory it would mean that I could not know which day a year was in, until after that day had been reached, and the observations done. In practice there would be no difference from the Gregorian calandar for many centuries; so why bother.

To summarise: The astronomical year is approximated by the Gregorian year. This is simple to use. It is accurate for most calendar applications. It allows for the calendar to be extended into the future. The Gregorian calendar has wide acceptance among many countries. If precise timekeeping is needed then one doesn't use "years" instead one uses the SI unit of time, the second.

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  • $\begingroup$ The modern caesium fountain clock is more accurate & more stable than the caesium beam clocks that were state-of-the-art in 1968 when the Cs-133 hyperfine transition was adopted as the basis of the second, and Cs-133 is still the international standard today. However, we now have clocks with better accuracy and long term stability. See Wikipedia for details. $\endgroup$ – PM 2Ring May 10 at 3:41
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Why all the stunts with leap days and leap seconds, etc... when we now have atomic clocks?

Science exists to serve mankind, not to rule it. Calendars were one of the first concepts developed by humankind, arguably predating writing. Timekeeping is even more important to modern society than it was to the ancients. You're not going to get rid of calendars.

One key purpose of the Gregorian calendar is to keep the calendar in sync with the seasons. Every solar calendar requires some intercalation mechanism. The Gregorian calendar uses leap days. The Gregorian scheme (years divisible by 4 have an extra day, except for years that are multiples of 100 that aren't divisible by 400) will fall out of sync with the seasons at at the very slow rate of one day per 3030 years.

Leap seconds are a rather different beast. They are inserted, unpredictably, to keep the clock in sync with the day/night cycle. Without leap seconds, counting 86400 atomic clock seconds = one day would already have the clock out of sync by about half a minute. Leap seconds are problematic for business. There is an ongoing effort to remove leap seconds and just live with a day of 86400 seconds going out of sync with the day, at least until it truly becomes noticeable.

Why not decouple the two and say that day X belongs to year Y if at 12:00 noon of that day is "in" year Y?

What's this "year Y" thing you're writing about? How do you know what year it is without a calendar?

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I think that sometimes we do things for convenience, not just scientific rigor.

For instance, it may be much more computationally efficient for humans to choose a new number system based on 12 numeric symbols, because 12 has factors 2,3,4,6 rather than a decimal number system which has factors only 2,5.

But we stick to the decimal system because its simpler to count on our 10 fingers.

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