From Seconds to Precessions

10 June 2014

Numerology in Calendar Systems Makes Memorization Easier.

Well, recently having come across a series of posts on slashdot.org regarding the second as regards “universal” timekeeping. These are programmers who rely on the SI second (the official for our purposes) as the basis of calculation, whereas I’ve been focusing on the day, month, year, etc.

One of the points that came up in the discussion (well, the end of a long post refuting some of the claims):

Days, months and years aren’t SI units, and the one true SI unit of time has jack shit to do with any of them

So, this is in the context of exactitude. Days aren’t really precisely 86,400 seconds, any more than lunar months are 29 or 30 days long. It got me thinking back to the days when I started looking at all these different calendar systems. One in particular (a Babylonians and Early Egyptians shared a lot of the same features in their calendars).

The year was observed as 360 + 5 days (with no leap year. That meant that every 4 years, the calendar day would fall one day earlier relative to the Equinox, and it would take 1,460 days until a particular date fell at the same time of year again. Aside from that, they divided the 360 days of the year into 12 months of 30 days. Each day was divided as we do today, 24 hours x 60 minutes x 60 seconds = 86,400 seconds or 2 x 43,200 or 72 x 1,200.

Each hour was associated with one of the 7 ancient planets – Saturn, Jupiter, Mars, Sun (Earth orbit), Venus, Mercury, Moon (in order of their orbital period). The first hour of each day (i.e 0:00, beginning at midnight) is assigned a planet. At the time, the week began with Saturday, so Saturn was attributed to the first hour. the hour beginning at 1 am would be assigned Jupiter, 2 am began Mars, etc. Midnight of the next day is assigned the Sun, which makes it Sunday, etc.

It is merely a symbolic representation of the planets, however, at the time, as they were actually more easily visible, the associations between celestial observation and timekeeping was always associated.

So every hour and every day is assigned one of the seven planets. Consider the periodicity of the planets as (such as with the moon, looking at the duration approximated in terms of days of each synodic cycle – i.e. the length of time it takes for a planet to return to the same apparent location in the sky as seen from Earth.

Each hour was comprised of 3,600 seconds, or 60 x 60. Considering the Babylonians used a base 60 system (and you thought memorizing timetables was hard), each second, and each minute was assigned one of the symbols

Alright, so they have that all going on with the seconds to hours. Withe the 360 days of the year, they associated those with the 360 degrees of the circle. As well as not bothering with a leap year associating particular calendar dates with particular times of year, the Babylonians apparently took the Precession of the Equinox into account. Long story short; there’s a wobble in the rotation of the Earth’s axis, which causes the stars to shift position by about 1 degree (along the ecliptic) every 72 years.  This means that it would take 72 x 360 years for the full Precession to return the stars to their original starting point, or about 25,920 years.

the rate of precession varies, but it is estimated at about 25,772.
25,920 years/Precession = 60 x 60 x 72 = 60 x 60 x 24 x 3
360 days/year = 60 x 6
86,400 seconds/day = 60 x 60 x 24

I could see why programmers might prefer to use TAI, where leap seconds are not counted as it would be cleaner, even if the days eventually drifted relative to the Equinox. The UTC counts every second, either inserting it in June or December if one is required.

celestial_watch_face

The point was, if one is willing to count the odd second, the odd day (or five) outside of the perpetual calendar, as did the Babylonians and Early Egyptians (I just recalled). One could approximate the SI second to the day, the day as the base unit for longer periods of time (calendar time like weeks and months, or natural time, like lunar months, or years).

Define theAbysmal Calendar year as 364 + 1 + 1/4 -1/128 Days, where each Day = 86,400 SI seconds, with provisions for leap seconds as per the International Earth Rotation and Reference System Service (IERS).

Each day is defined then as 86,400 seconds
Each week is 604,800 seconds
Each month is 2,419,200 seconds
Each quarter is 7,862,400 seconds
Each year is 31,449,600 + 86,400 (annually) + 21,600 (observed every 4 years) – 675 (observed every 128 years) seconds per calendar year

and then the leap second here or there – there have not been any leap seconds since the inception of theAbysmal Calendar (which means that we can expect another one soon).  These will be counted along with leap year days and all that.

Let’s see how that works out, mmm’kay.


Second Guessing

1 June 2014

Seconds, how they leap, and universal time measures.

The Slashdot.org article about the Terran Calendar generated much discussion about the poor definitions in some cases, and the lack of a resolutions of time-keeping on the level of seconds. Often, comments referred to the SI second maintained by the International Bureau for Weights and Measures. This is their definition:

The unit of time, the second, was at one time considered to be the fraction

1/86 400 of the mean solar day. The exact definition of “mean solar day” was left to the astronomers. However measurements showed that irregularities in the rotation of the Earth made this an unsatisfactory definition. In order to define the unit of time more precisely, the 11th CGPM (1960, Resolution 9) adopted a definition given by the International Astronomical Union based on the tropical year 1900. Experimental work, however, had already shown that an atomic standard of time, based on a transition between two energy levels of an atom or a molecule, could be realized and reproduced much more accurately. Considering that a very precise definition of the unit of time is indispensable for science and technology, the 13th CGPM (1967/68, Resolution 1) replaced the definition of the second by the following:

 The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.

It follows that the hyperfine splitting in the ground state of the caesium 133 atom is exactly 9 192 631 770 hertz, nu(hfs Cs) = 9 192 631 770 Hz.

At its 1997 meeting the CIPM affirmed that:

    This definition refers to a caesium atom at rest at a temperature of 0 K.

This note was intended to make it clear that the definition of the SI second is based on a caesium atom unperturbed by black body radiation, that is, in an environment whose thermodynamic temperature is 0 K. The frequencies of all primary frequency standards should therefore be corrected for the shift due to ambient radiation, as stated at the meeting of the Consultative Committee for Time and Frequency in 1999.

The standards for counting seconds include Coordinated Universal Time:

Coordinated Universal Time (UTC), maintained by the BIPM, is the time scale that forms the basis for the coordinated dissemination of standard frequencies and time signals. The UTC scale is adjusted by the insertion of leap seconds to ensure approximate agreement with the time derived from the rotation of the Earth. These leap seconds are inserted on the advice of the International Earth Rotation and Reference Systems Service (IERS).

Compare to the International Atomic Time (TAI):

A practical scale of time for world-wide use has two essential elements: a realization of the unit of time and a continuous temporal reference. The reference used is International Atomic Time (TAI), a time scale calculated at the BIPM using data from some two hundred atomic clocks in over fifty national laboratories.

The long-term stability of TAI is assured by a judicious way of weighting the participating clocks. The scale unit of TAI is kept as close as possible to the SI second by using data from those national laboratories which maintain the best primary caesium standards.

TAI is a uniform and stable scale which does not, therefore, keep in step with the slightly irregular rotation of the Earth. For public and practical purposes it is necessary to have a scale that, in the long term, does. Such a scale is Coordinated Universal Time (UTC), which is identical with TAI except that from time to time a leap second is added to ensure that, when averaged over a year, the Sun crosses the Greenwich meridian at noon UTC to within 0.9 s. The dates of application of the leap second are decided by the International Earth Rotation Service (IERS).

Now, the IERS has this to say about leap seconds:

The Coordinated Universal Time (UTC, replacing GMT) is the reference time scale derived from The Temps Atomique International (TAI) calculated by the Bureau International des Poids et Mesures (BIPM) using a worldwide network of atomic clocks. UTC differs from TAI by an integer number of seconds; it is the basis of all activities in the world. UT1 is the time scale based on the observation of the Earth’s rotation. It is now derived from Very Long Baseline Interferometry (VLBI). The various irregular fluctuations progressively detected in the rotation rate of the Earth lead in 1972 to the replacement of UT1 as the reference time scale . However, it was desired by the scientific community to maintain the difference UT1-UTC smaller than 0.9 second to ensure agreement between the physical and astronomical time scales.

Since the adoption of this system in 1972, firstly due to the initial choice of the value of the second (1/86400 mean solar day of the year 1820) and secondly to the general slowing down of the Earth’s rotation, it has been necessary to add 25 s to UTC. The last additional second has been introduced on 1 July 2012, at 0hUTC.

The decision to introduce a leap second in UTC is the responsibility of the Earth Orientation Center of the International Earth Rotation and reference System Service (IERS). This center is located at paris observatory. According to international agreements, first preference is given to the opportunities at the end of December and June, and second preference to those at the end of March and September. Since the system was introduced in 1972, only dates in June and December have been used.

and in an earlier Bulletin:

                          INFORMATION ON UTC - TAI

 NO leap second will be introduced at the end of June 2014.
 The difference between Coordinated Universal Time UTC and the 
 International Atomic Time TAI is :		
		
     from 2012 July 1, 0h UTC, until further notice : UTC-TAI = -35 s

 Leap seconds can be introduced in UTC at the end of the months of December 
 or June,  depending on the evolution of UT1-TAI. Bulletin C is mailed every  
 six months, either to announce a time step in UTC, or to confirm that there 
 will be no time step at the next possible date.

As far as Universal Time (UT1), I found little online that was overly trustworthy, but his definition is at least cited to an actual book.

UT1 is the principal form of Universal Time. While conceptually it is mean solar time at 0° longitude, precise measurements of the Sun are difficult. Hence, it is computed from observations of distant quasars using long baseline interferometry, laser ranging of the Moon and artificial satellites, as well as the determination of GPS satellite orbits. UT1 is the same everywhere on Earth, and is proportional to the rotation angle of the Earth with respect to distant quasars, specifically, the International Celestial Reference Frame (ICRF), neglecting some small adjustments. The observations allow the determination of a measure of the Earth’s angle with respect to the ICRF, called the Earth Rotation Angle (ERA, which serves as a modern replacement for Greenwich Mean Sidereal Time). UT1 is required to follow the relationship

ERA = 2π(0.7790572732640 + 1.00273781191135448Tu) radians
where Tu = (Julian UT1 date – 2451545.0)

Okay, that’s enough of that, because it does overwhelm.

One thought occurred to me (prior to reading through all this material, some supplementary stuff, giving it all a good shake, and see what ferments): theAbysmal Calendar would be able to use TAI for the perpetual calendar, and UT1 would be able to apply to the lunar calendar, as it counts every second, every day, every lunar month, every year, as most accurately described within our current means.

The other convenience as regards leap seconds (or minutes, or whatever all else might befall us) is that they can be inserted between any two days. It simply wouldn’t count towards the 364 x 24 x 60 x 60 + 24 x 60 x 60 seconds of the year. It will fall outside of them in June, or as part of the New Year day, or Leap Year day should the leap second be inserted in December.

I may be oversimplifying the case (may, ha!), however, I’ll leave the more complicated task of figuring out how to define the second, the day, the year as accurately as is possible, that I might benefit from those findings to base my system of time-reckoning.

Still a work in progress.


A Refutation of All Proposed Calendars

30 May 2014

Funny, because, alas, so much of it is true.

This is not my material – for the original article, click on the title.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

You advocate a ________ approach to calendar reform

You advocate a

( ) lunisolar ( ) atomic ( ) metric ( ) Luddite ( ) overly simplistic

approach to calendar reform. Your idea will not work. Here is why:

( ) solar years are real and the calendar year needs to sync with them
( ) solar days are real and the calendar day needs to sync with them
( ) the solar year cannot be evenly divided into solar days
( ) the solar day cannot be evenly divided into SI seconds
( ) the length of the solar day is not constant

( ) the lunar month cannot be evenly divided into solar days
( ) the solar year cannot be evenly divided into lunar months
( ) having months of different lengths is irritating
( ) having months which vary in length from year to year is maddening
( ) having one or two days per year which are part of no month is stupid
( ) your name for the thirteenth month is questionable

( ) the lunar month cannot be evenly divided into seven-day weeks
( ) the solar year cannot be evenly divided into seven-day weeks
( ) every civilisation in the world is settled on a seven-day week
( ) having one or two days per year with no day of the week is asinine

( ) requiring people to manually adjust their clocks is idiotic
( ) local time should not be discontinuous
( ) local time should not go backwards
( ) people like to go to work/school at the same time every day all year round
( ) no amount of clock-moving can increase the amount of solar energy received by Earth
( ) "daylight saving" doesn't

( ) UTC already solves that problem
( ) zoneinfo already solves that problem
( ) rearranging time zones yet again would make the zoneinfo database larger,
    not smaller
( ) the day of the week shouldn't change in the middle of the solar day
( ) local "midnight" should be the middle of the local night
( ) I shouldn't need to adjust my wristwatch every few miles

( ) there needs to be a year 0 and negative year numbers
( ) no, we don't know what year the Big Bang happened
( ) years which count down instead of up are not very funny
( ) planetary-scale engineering is impractical
( ) not every part of the world has four recognisable seasons
( ) "sunrise" and "sunset" are meaningless terms at the poles
( ) Greenwich is not unambiguously inferior to any other possible prime meridian
( ) the Earth is not, in fact, a cube
( ) high-tech applications need far more accuracy than your scheme allows
( ) leap seconds have been a fact of life for more than forty years
( ) leap seconds are more frequent than leap years
( ) TAI already solves that problem
( ) most of history can't be renumbered with atomic accuracy
( ) everybody in the world is already used to sexagesimal time divisions
( ) date formats need to be unambiguous
( ) abbreviated date formats should be possible and still unambiguous
( ) a leading zero on the year number solves nothing
( ) date arithmetic needs to be as easy as possible
( ) 13-digit numbers are difficult for humans to compare, even qualitatively

Specifically, your plan fails to account for:

( ) humans
( ) clocks
( ) computers
( ) the Moon
( ) the inconsistent rotational and orbital characteristics of Earth
( ) rational hatred for arbitrary change
( ) unpopularity of weird new month and day names
( ) total incompatibility with the SI second
( ) general relativity

and the following philosophical objections may also apply:

( ) BC and AD aren't
( ) technically, our calendar is already atomic
( ) they tried that in France once and it didn't take
( ) nobody is about to renumber every event in history
( ) good luck trying to move the Fourth of July
( ) nobody cares what year you were born
( ) the history of calendar reform is horrifically complicated and no amount of
    further calendar reform can make it simpler

Furthermore, this is what I think about you:

( ) sorry, but I don't think it would work
( ) this is a stupid idea, and you're a stupid person for suggesting it
( ) please just shut up and fix your broken date/time code