Let’s Get to Making Holydays for the holidays

14 December 2014

because holidays!

What good is a calendar if we don’t schedule holydays to celebrate, which requires not shopping (as if), but getting together, dressing up, sharing music, food, a little something-something intoxicating, and like that. However, as our holydays have been polluted by wealth-addicts, it is time to abandon the malls, the tinned music, the forced merriment and to make it new.

So let’s start with the Leap Year.

And check out HolydayMaker, a site just begun, which has as its purpose, the collective, creative endeavour to celebrate every day as holy.

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.


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.

Leap Year Day 0

20 December 2012


the Leap Year Day falls today (technically because 2012 is a leap year on the Gregorian Calendar). It occurs every 4 years with an exception every 128 years, when we don’t bother with a leap year day. This most closely aligns the annual year with the tropical year (or the calendar year with the observed year).

In four years’ time, we will observe Leap Year 1, the day before the New Year Day between Years 3 and 4.

Another advantage to having the Leap Year at the end of the year (as opposed to the ridiculously disruptive end of the second month as the Gregorian calendar currently does), is that the calendar remains perpetual. Also, as the day lengthens over time, leap seconds can be added to the leap year day.

Chromatic: Year 0 Lunation 0 Day —
Lunar: Year 0 Lunation 0 Day 7
Annual: Year 0 Month — Day LYD

What’s so Great about Zero?

8 June 2012

Absolutely nothing – zero is the antithesis of great and big.

As sometimes happens I was noodling around, thinking while waiting for work to start, and I got to thinking on the whole counting from 0 aspect of theAbysmal Calendar. It’s a different way of counting that what we’re doing with the Gregorian, with it’s 1st, 2nd, 3rd of each month. It’s also a different way of thinking about time. With the ordinal numbers, and years, we are counting the day and the year before it is finished. In a sense, this is putting our thinking into the future, when the day is done, instead of the present, which continues to progress.

In another sense, it lends itself to aligning days, months, and years with the way we tell time. This may provide a notion of how best to create notation for theAbysal Calendar. From the largest measure of time to the smallest, from left to right. This is also the way the Mesoamericans have arranged the Long Count Calendar: is toay’s date – 12 baktun, 19 katun, 19 tun, 8 vinal, 4 kin (where kin = days and each is an order higher in magnitude by factors of 20 – where vinal is an exception of 18).

At any rate, theAbysmal would look something like this:

Year 8 Month 7 Day 6 05:43:21

We can easily figure out the number of days or even seconds, by multiplying each number (seeing as the number represents the number of completed time periods elapsed)

Year 8 x 365 + Month 7 x 28 + 6 days (for the leap year + Year 8/4  – 8/128 = 2)

So if the Year number = Y, the Month = M, the Day = D then the formula to figure out the total elapsed days since the calendar began is

365 x Y + 28 x M + D + (Y/8 – Y/128) = total days elapsed.

it’s pretty unwieldy with the Gregorian. For example Choose December 4th 1923

  1. first the Calendar began in 1582, not year 1. (before that it was the Julian Calendar, and it had begun according to the Roman Year 753 BC). 1923 – 1582 = 341 years
  2. second, the leap year is 1923-1582/4 = 85 days – no leap years in 1700, 1800, 1900 = 82 leap year days
  3. third 31+28+31+30+31+30+31+31+30+31+30 = 334
  4. finally December 4th = 3 days (the 4th isn’t complete)
  5. 341 x 365 + 82 + 334 + 3

Pretty messy. And this is the system we’re currently using to correlate dates between lunar calendars, solar calendars, solilunar calendars. It’s really an impractical little machine as far as that goes.

I’m going to borrow the “z” from “zero” and catch some “zzzzzzz”s.

196 Days to Dec 21st 2012

Leap Year Day

29 February 2012

February 29th: the most disruptive weekday of all time.

The leap year, or leap day, is the most disruptive aspect of the Gregorian Calendar. Not the leap year day itself, which keeps the calendar year aligned with the seasons, but making a leap year day a weekday throws what would otherwise be a reasonable calendar system out of whack.

If leap day were not a weekday, then it would be easier to follow the Gregorian Calendar. If we only look at the 365 days of the year, then the weekdays would progress regularly. Jan 1st 2012 fell on a Monday. Without a leap day, Jan 1st 2013 would be Tuesday, 2014 a Wednesday, 2015 a Thursday, 2015 a Friday, 2016 a Saturday, 2017 Sunday and so on. An even schedule of progressive weekdays. This would be the same situation for birthdays, holidays and observations based on dates (Groundhog’s Day, Halloween, Christmas and so on). However, because February 29th is a weekday, every four years (with omissions 3 days out of every 400 years) this progression is thrown off.

Also, observing the leap day two months into the year is more disruptive than if it were added at the end of the year (March used to be the first month of the Roman Calendar. The switch to January 1st didn’t include a change in the leap year observation. As a result, instead of the cycle of months and weekdays repeating itself every 7 years, they repeat themselves every 400 years, with lesser cycles every 28, but these are thrown off every century.

There are a number of strategies to deal with aligning one’s calendar to the year.

Lunar and lunisolar calendars (Chinese, Hebrew, Hindu, Muslim) avoid this by inserting embolismic lunar months periodically, so they are excluded from this comparison. They follow the moon and don’t have the same problems as do purely solar calendars.

The Egyptian Calendar had 12 months of 30 days, and an extra five days left over. They didn’t insert a leap year day (at least not initially, they were later brought into alignment with the Roman Calendar). This isn’t necessarily a big deal. The Mesoamerican calendar does the same dance. The Winter Solstice would fall one day later every four years. At that rate, it would take 1460 years for the calendar to drift with respect to the seasons to come around to its starting point again.

The way we measure the year varies a great deal. We generally accept the mean tropical year of  365.2421897 or 365 days, 5 hours, 48 minutes, 45.19 seconds (as of Jan 1st 2000). The leap year is meant to account for that fraction of 0.2421897 or 5 hours, 48 minutes, 45.19 seconds. There are a number of schemes to account for it, some of which are more accurate than others.

Here’s a comparison of some of different leap year schedules:

Mean Tropical Year

0.242 189 7


Leap Year Schedule




1 day per 4 years

0.25 + 0.007 810 3


1 day per 4 years

– 3 days every 400 years

0.242 5 + 0.000 310 3

Persian Calendar

8 days every 33 years

0.242 198 52 *see below


1 day per 4 years

– 1 day every 128 years

0.242 18 75 –  0.000 002 2

*the Persian Calendar system is much more complex than indicated above, as it uses astronomical observations to determine its leap year schedule. As a result, it is the most accurate of the periods measured above, as it doesn’t measure itself against the mean tropical year, and takes variance into account.

The advantage to theAbysmal Calendar is the simplicity compared to the Persian. Also, the Leap Year day can be added or removed to ensure seasonal accuracy without disrupting the year of 52-weeks. This is one of the biggest advantages to observing the leap year day at the end of the year, and excluding it from the cycle of weekdays. One can add or remove leap seconds, minutes, hours or days, while keeping the rest of the year perpetual.

What do you think?

296 Days to Dec 21st 2012

the question of non-weekdays

19 October 2009

weekdays vs new year’s day and the leap year day?

A common argument against proposed calendars focuses on the use of non-weekdays. In the case of theAbysmal Calendar, there are two such days. The New Year’s Day which falls on the equivalent of December 21st, between the last Friday of one year, and the first Saturday of the next, and; the Leap Year Day which falls on the day before the New Year’s Day every 4 years (with an exception every 128 years, when it is not observed).

Setting the Leap Year Day aside for the moment…

The New Year’s Day is a non-weekday in order that the structure of the remaining 52 weeks remain perpetual from year to year. Thus, every week begins on a Saturday, and ends on a Friday, as does every month (of 4 weeks), every quarter (of 13 weeks) and every year (of 52 weeks).

If the New Year’s Day were to be counted as a weekday, yet remained outside of the 52 weeks of the year, this would create a 7-year cycle of years, that would still remain structurally sound. The first day of each year would begin one weekday later than the previous one.

For example, Year 0 13-XIX, begins on Saturday and ends on Friday. The New Year’s Day falls on Saturday. The first day of Year 1 1-IV would fall on Sunday and end on Saturday. Year 2 2-IX would begin on Monday and end on Sunday, etc… See below for an illustration of the months for each year.

The Leap Year Day, however, should remain a non-weekday, as it would disrupt this otherwise logical progression of weekdays every four years, and again every 128 years. Currently, the observation of February 29th as a weekday causes the Gregorian Calendar to repeat its cycle of weekdays, months and days of the month every 400 years. Not exactly user-friendly.

An argument can be made to either observe the New Year’s day as a weekday or not, however, the Leap Year day should not be observed as a weekday. This simply makes a muddle of an otherwise logical arrangment of the days of the year.

Register your opinion on the Poll at the bottom:


Make every second count

9 December 2008

The Year in Secondary Moments

CBC.ca reported:
Extra second to make 2008 even longer

theAbysmal Calendar will likewise have to account for Leap Years (as 2008 is) and Leap Seconds (which have been added occasionally to ensure that the Gregorian CE Calendar and the atomic clock all work together in harmony).


A typical Year
365 Days x 86400 seconds/Day = 31,536,000 s/Year

A Leap Year
366 Days x 86400 s/Day = 31,622,400 s/Year

+ 1 Leap Second = 31,622,401 seconds for 2008

Any such adjustments, such as Leap Weeks, Leap Days, Leap seconds can be added at the end of any given Year, between the last Friday of one Year and the first Saturday of the next. This allows theAbysmal Calendar to remain one of the most accurate (in terms of its alignment with the Earth’s orbit and the Seasons), yet retaining a perpetual annual structure of Weeks, Months and Quarters.

theAbysmal is the Calendar that Japanese swordmakers would have made: it combines the qualities of strength (i.e. the perpetual structure of 52~Weeks) and flexibility (allows for Leap Year Days and seconds and so on without disrupting the perpetual 52~Week structure).