From Seconds to Precessions

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.

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