the Week and the Fortnight

29 August 2012

Symbols of time, space, and theAbysmal Calendar.

I’ve been ruminating on the relationship between the ancient planets (Sun, Moon, Mercury, Venus, Mars, Jupiter, Saturn) as well as the constellations of the sidereal zodiac (Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Ophiuchus, Sagittarius, Capricorn, Aquarius, Pisces). These were used as an integral part of the calendar by the time of the Babylonians (minus the constellation Ophiuchus). We’ve come to use the astrological zodiac, which is more akin to the Persian calendar than it is to the Gregorian calendar or astronomy.

So, with the re-introduction of Ophiuchus in 1930 by the International Astronomical Union, I’ve been playing with the 13 signs, and have discovered some interesting symmetries. Nevertheless, I wanted to label certain measures of the week using the signs of the zodiac in addition to the planets (as we currently do with weekdays). Here’s the mess I’ve come up with. It is by no means final, or conclusive. Just a riff, more or less. Some aspects of this are stronger than others. Don’t let me influence your decision – decide for yourself.

Integers of the Year

The math of the Year for theAbysmal works out as follows:

2 x 2 x 7 x 13 = 364
+1 (New Year Day) = 1
+ 1/4 – 1/128 (Leap Year Day) = 0.2421875

The 364 Days of the Year have been divided into 7~Day Weeks and 13~Day Fortnights. There are 7 ancient planets associated with the Weekdays, so the extension of associating the 13 signs of the zodiac with the Fortnight seems reasonable. I’ve followed the steps by which the weekdays have been determined. Follow along. It may be fun.

Here is the circle of the Year divided into 7~Day Weeks, 4~Week Months, and 13~Week Quarters:

And here is the Year divided into 13~Day Fortnights, 4~Fortnight Houses, and 7~Fortnight Quarters:

Planetary Hours and Days

First, let’s take a look once again at the star from which the 24 Hours of the Day and 7 Days of the Week are derived.

There are two orders in which the symbols for the planets can be read, both beginning with Saturn at the bottom to the left. Following the circle clockwise, we get the order of the planets from their longest orbital period to the shortest: Saturn, Jupiter, Mars, Sun (365 days for Earth to orbit the Sun), Venus, Mercury, and the Moon (29.53 days to orbit the Earth). Tracing the star within the circle, again starting from Saturn upwards, we get Saturn, Sun, Moon, Mars, Mercury, Jupiter, Venus. This is the sequence of the weekdays, using traditional planetary associations: Saturday, Sunday, Monday, Tuesday, Wednesday, Thursday, and Friday.

I begin with Saturn, because he was the Roman equivalent of Cronus, the Greek Deity who divided the Earth (Gaia) from the Sky (Ouranous) and began time. Cronus is the root for words such as chronological, chronometer, and so on. He is the deity of time.

The 24 Hours of the Day begin at midnight. So the Hour between midnight and 1 a.m. is the first Hour of each Day. Beginning with Saturn, and following the sequence around the circle, we assign a planet to every Hour of every Day. You will note that the first hour of each corresponds to the weekday it represents, i.e. Saturn is the first Hour of Saturday, the Sun is the first Hour of Sunday, the Moon is the first Hour of Monday and so on. Here’s the table:

Constellation Hours and Days

Here’s the same process applied to the Constellations of the sidereal Zodiac. The circular order is already established. Here’s the key (note the symbol for Ophiuchus has gone from the question mark to a U with a tail wrapped around it. You’ll see):

For the traditional order of the zodiac, begin with Aries at the bottom left, and proceed clockwise through Taurus, Gemini, Cancer and so on. If we follow the lines of the star as we did with the planetary symbols, we would get a new sequence: Aries, Libra, Pisces, Virgo, etc… which doesn’t tell us much. I tried applying the Constellations to each Hour of the Day, and the end result wasn’t particularly satisfying (call me an aesthete, or a stickler. Go ahead, I double dog dare you).

So I decided instead to do as the Chinese, which is to apply a 2~Hour period to each sign (which works out well with their 12~symbol system of earthly branches, the rat, ox, tiger, rabbit, and so on). This was a much more satisfying result, as the Days of the Fortnight are in reverse order to the sequence of the circle above. This follows the order in which the Sun enters each sign of the Zodiac on any given Day as it progresses through the 25,772 year long Precession of the Equinoxes. However, in order for this to retain its symmetry, the first Hour begins with Pisces, and we get the following table:

Naming the Months and Houses

Currently, the Months and Houses are assigned numbers from 0~12 and 0~6 respectively, however, we can still name them after constellations and planets, as the numerology of the calendar allows. Here are the 13 Months:

I’ve already published this idea before, and it turns out it wasn’t even original. A 13~month calendar with the New Year at the Winter Solstice and the Months named after the Constellations was proposed previously (although I can’t for the life of me find the references to it). Nevertheless, the names of the Houses are new, so here they are:

This would give us the House of Saturn, House of Jupiter, House of Mars, House of the Sun, House of Venus, House of Mercury, and House of the Moon. This has nothing to do with traditional Western astrological houses. It was suggested to me by a commenter on the site, and it sounded better than anything I’d come up with.

This same system of labelling can be applied elsewhere. There are 13 Weeks per Quarter, and 7 Fortnights per Quarter. There are also 28 Days per Month, and 28 Fortnights per Year, as well as 52 Days per House, and 52 Weeks per Year.

Just don’t get me started on the Market Weeks.

114 Days to Dec 21st 2012


I Ching and the Year

23 June 2012

twos by two

the I Ching is a Chinese oracular system that has developed over the centuries into a rather elaborate system. It began as two options – yes or no, represented as a solid line, and a broken line, respectively. After serving its purpose in addressing yes/no questions, the lines were stacked vertically, such that there were now four options (lines are read from the bottom up): two solid lines, a broken line under a solid line, a solid line under a broken line, two broken lines. The next step created the eight trigrams of three lines. Finally, the trigrams were placed one over the other, which created the 64 hexagrams of the I Ching.

When using the I Ching as an oracle, the lines of the hexagram are determined using yarrow stalks or coins (or any of a number of online applications). However, in determining the six lines of the hexagram, one also determines how many of them, if any, change. So after determining the initial hexagram, the changing lines are switched to their opposite creating a second hexagram. The point of the oracle is to consider the change from one hexagram (or state) to another. It is quite an amazing system.

Nevertheless, despite the popularity of theAbysmal I Ching page, my interest in exploring it has always been primarily related to timekeeping (same with astrology, for what its worth). Some posters have asked that I attribute the hexagrams to theAbysmal Calendar. This is mathematically tricky, as the 64 hexagrams don’t fit evenly into 365, 364 or 360 days. I must admit that I enjoy this type of challenge.

Although I’ll be looking a bit at some of the symbolic associations with the trigrams and hexagrams, I won’t go too far down the rabbit hole of symbolism, as undoubtedly it will take me to places I’m not equipped to deal with in this context. The more I can deal with this at its most fundamental, the better the result.

and I apologize ahead of time for any missteps.

Trigrams

The cardinal directions play an important role in traditional timekeeping. The Winter is associated with the North (pardon the Northern Hemisphere bias). theAbysmal wheel of the Year already has particular dates set aside for these points of the Year. So we end up with

  • Kun – North – Winter Solstice (Dec 20-22)
  • Chen – NE – Feb 5
  • Li – East – Vernal Equinox (Mar 22-23)
  • Tui – SE – May 7
  • Chien – South – Summer Solstice (Jun 21-22)
  • Sun – SW – Aug 6
  • K’an (theAbysmal!) – West – Autumnal Equinox (Sep 20-21)
  • Ken – NW – Nov 5

The advantage to choosing these dates, although they may not fall precisely on the Solstices or Equinox, is that they are precisely 45 days apart.

Hexagrams

there are traditional arrangements and associations of the hexagrams as well, however, their role in terms of timekeeping are multifaceted. First, the radial arrangement:

the Chinese lunar calendar also associates a hexagram with each of the 12 months as follows (note that I’ve changed the solid lines to white, the broken lines to black):

Image Hexagram Lunation Gregorian Equivalent
http://theabysmal.files.wordpress.com/2006/10/11-peace.jpg?w=450 11 – Tui – Peace

1st

Feb – Mar
34-the-power-of-great 34 – Ta Chuang – Power of the Great

2nd

Mar – Apr
43-break-through-(resoluteness) 43 – Kuai – Breakthrough

3rd

Apr – May
01-the-creative 1 – Chien – the Creative

4th

May – Jun
44-coming-to-meet 44 – Kou – Coming to Meet

5th

Jun – Jul
33-retreat 33 – Tun – Retreat

6th

Jul – Aug
12-standstill-(stagnation) 12 – P’i – Standstill

7th

Aug – Sep
20-contemplation-(view) 20 – Kuan – Contemplation

8th

Sep – Oct
23-splitting-apart 23 – Po – Splitting Apart

9th

Oct – Nov
02-the-receptive 2 – K’un – the Receptive

10th

Nov – Dec
24-return-(the-turning-point) 24 – Fu – Return

11th

Dec – Jan
19-approach 19 – Lin – Approach

12th

Jan – Feb

I honestly don’t remember what my source material was for these associations. It was 6 years ago that I had come across it. I only remember that it wasn’t explained in any detail. Make of it what you will. I will note that theAbysmal Lunations begin with Lunation 0 which contains the Solstice, which coincides with the Chinese 11th lunar month. Although the hexagram for K’un (the Receptive) is more appropriate for the Winter Solstice. I hope I haven’t mistaken this association.

Dale Bruder further extrapolates this (and it doesn’t look like I was mistaken after all – phew), such that the above hexagrams represent the first six days of the lunar month. So there are 60 hexagrams associated with the days of the 12 lunar months (nothing about the 13th month when it occurs), and the remaining four hexagrams represent the seasons.

Sergey Leonidovich Panphilov has an elaborate web page that covers the calendar of 28 days and the moon in the context of the I Ching, and the lunar calendar. There’s too much information to summarize here. Explore it and enjoy.

theAbysmal Calendar and the I Ching

I think that in the end, the 64 hexagrams fit best with the year as 60 hexagrams, each of which covers 6 days, and the remaining 4 hexagrams are associated with the cardinal points – i.e. the Equinoxes and Solstices, or alternatively, with the days midway between the cardinal points (i.e. Feb 5, May 7, Aug 6, Nov 5). I think I prefer this latter association with the annual year.

What to do about the lunar calendar? 12 Lunations work out to 354 days, which falls 11 days shy of the annual year. And there is some variety in this, such that the 12 Lunations may be 353 or 355 Days. There may be another way of looking at this. 13 Lunations work out to 384 days (+/- 1 Day). 384 = 6 x 64. There are 64 hexagrams, each made of 6 lines, such that there are the same number of lines in the 64 hexagrams as there are days in 13 lunations. The cycle of 13 Lunations wouldn’t line up with the annual Year, however, the cycles of the Moon are every capricious.

One last consideration: the Leap Year. The Leap Year Day is added every 4 Years, with an exception every 128 Years. 128 = 64 x 2. It would be possible to assign a hexagram to each Year of the Abysmal Calendar for two cycles. Or, it might be possible to use heptagrams, an image using seven lines, of which there would be 128. The extra line would take its place between the two trigrams. Considering theAbysmal Year is divisible by 7 (as a function of the 7-Day Week), this may be something to consider.

However, for the moment, it’s just a speculative exercise. I may develop an image to illustrate this in the next few days.

181 Days to Dec 21st 2012


Natural Timescales

19 June 2012

the development of time

Virolution was an eye-opener. It provided a view at new theories in various branches of biology, mostly dealing with viruses, genetics, and evolution, explained in such a way that I didn’t feel that an advanced degree in microbiology was necessary. Its focus is the role of viruses in genetics, heredity, and evolution. What I found most encouraging was my own paradigm shift: viruses aren’t evil parasites. Such a judgement results from experience with viral illnesses, and fearing pandemics. Although those are certainly a part of our relationship with viruses, it is a narrow view.

In some instances, the relationship is mutualistic-symbiosis.Who’da thought?

In and among the interviews and revelations, the Virolution got me thinking about our individual, cultural, and evolutionary bodies, and how we have perceived time over the long haul. The essential elements are: the period of the Year, Lunar orbit, and Earth’s rotation; the development of light-sensing organs; our reproduction and gestation periods, and; our cultural perception of time.

The Earth’s rotation around its axis has been slowing down since its creation 4.5 billion years or so ago. Shortly after its creation, the Earth rotated once every 6 hours, four times faster than now.

  • 4.5 billion years ago – it slowed to once every 10 hours
  • 4.0 billion years ago – once every 13.5 hours
  • 900 million years ago – once every 18.17 hours
  • 400 million years ago – once every 22 hours
  • 245 million years ago – once every 22.75 hours
  • 100 million years ago – once every 23.5 hours
  • today – once every 24 hours
  • 225 million years hence – 25 hours

1 second is added to our year every 62,500 Years or so.

source: Introducing Biological Rhythms

  • 3.8 billion years ago – simple cells
  • 3.4 billion years ago – photosynthesis
  • 1 billion years ago – multicellular life
  • 600 million years ago – animals
  • 500 million years ago – fish
  • 475 million years ago – terrestrial plants
  • 300 million years ago – reptiles
  • 200 million years ago – mammals
  • 150 million years ago – birds

The genus Homo developed some 2.4 million years ago, and Homo sapiens about 200,000 years ago. As early as 3.4 billion years ago, with the development of photosynthesis, life on Earth entered into an intimate relationship with the Sun’s light (its heat is a given), one that remains fundamentally important to all living things.

The life cycles of the oceans are tied in part to the phases of the Moon (29.53 Days), in part due to tidal action (12.4 hours). The sexual cycles of a variety of marine species are tied to the Full Moon, such as the palolo worm (on which the Trobriand Islanders base their lunar calendar). On a particular Full Moon, the worms teem at the ocean’s surface in a frenzy of reproduction.

There’s little doubt that our behaviour is still tied to the cycles of the Moon, despite how much we have removed ourselves from its influence.

Human Reproduction

Pregnancy and birth are likewise tied to the Moon. Granted there is a great deal of variability from one individual to another, however, menstruation is linked to the New Moon, ovulation to the Full Moon. Regardless, we gauged pregnancy by estimating 9 lunar months (266 days), although modern estimates put it at 40 weeks (280 days), and scheduling C-sections is a step further away from this link.

Nevertheless, natural birth often takes place at the New or Full Moon.

Our mother’s tie to the timing of the Day, the Year, and the Moon is the medium in which we gestate in the watery darkness of the womb. Our first perception of time as individuals comes from our mothers, our gestation, and our emergence into the world at birth.

Cultural Time

After our birth, our emergence into the world and first breath comes our education and acculturation. At some stage, we learn about the seasons, and the calendar or calendars in use. This is the final stage in our perception of time, beyond our evolution, beyond our gestation, or observation. We are tied to a particular notion of time, whether it be cyclical, such as the Chinese calendar, fractal, such as the Maya, or linear like the Gregorian.

There is also little doubt as too the fundamental role a calendar plays in one’s life. If you remain skeptical about this last point, suggest to someone they change their calendar, and see what reaction you get. Often, at least in my experience, it is equivalent to asking someone to change their language, their religion, or their hockey team. However, as it has become second nature, very seldom does anyone have a cogent argument. It is not an easy point of view to defend with logic, because it is so ingrained it would be like asking someone to change their internal organs.

Nevertheless, the fundamental timepieces in the longer view, the Earth’s rotation, the apparent motion of the Moon, the Sun, the Planets, and Stars are what we have in common. The particular ways in which we have chosen to organize these phenomena are key to our various traditions of cultural expression, and will continue for the foreseeable future.

theAbysmal Calendar is simply one more.

185 Days to Dec 21st 2012


Space News for the Now

3 May 2012

Because someone will prove something else, or disprove this, or dispute it, or claim intelligent happenstance.

A few random articles related to astronomy:

Did Exploding Stars help Life on Earth to Thrive?

Research by a Danish physicist suggests that the explosion of massive stars – supernovae – near the Solar System has strongly influenced the development of life. Prof. Henrik Svensmark of the Technical University of Denmark (DTU) sets out his novel work in a paper in the journal Monthly Notices of the Royal Astronomical Society.

When the most massive stars exhaust their available fuel and reach the end of their lives, they explode as supernovae, tremendously powerful explosions that are briefly brighter than an entire galaxy of normal stars. The remnants of these dramatic events also release vast numbers of high-energy charged particles known as galactic cosmic rays (GCR). If a supernova is close enough to the Solar System, the enhanced GCR levels can have a direct impact on the atmosphere of the Earth.

Was Earth a Migratory Planet?

By all accounts Earth should be a “snowball planet” like the frigid world Hoth in the 1980 Star Wars film “The Empire Strikes Back.”

Why? Because common theories of stellar evolution predict that the sun was only 70 percent of its current brightness when it first lit its fusion engine 4.5 billion years ago. The sun has been steadily growing brighter since then and will continue so into the future, eventually evaporating away Earth’s oceans.

Once Earth amassed an ocean 4.3 billion years ago, it should have quickly frozen over and reflected so much sunlight back into space that it squelched Earth’s ability to thaw out for billions of years.

The dilemma, called the “faint young sun paradox,” has been know about since the 1950s and was popularized by Carl Sagan. Geochemists and solar physicists have wrestled for answers all these years.

Lowering Earth’s reflectivity by reducing cloud cover doesn’t work. Models also show that a greenhouse effect from dense carbon dioxide and methane can’t warm the Earth enough either. In some simulations, methane and carbon dioxide combine to make a photochemical smog that would have chilled Earth even further.

Now, David Minton of Purdue University has come up with a novel solution that, by his own admission, straddles science fact and fiction. Minton proposes that Earth was closer to the sun when it formed and then migrated outward to its current orbit. To keep Earth tepid under a cooler sun, our planet would have needed to have been roughly 6 million miles (9.7 million kilometers) closer to the sun than it is today.

Findings Cast Doubt on Moon Origins

The moon, that giant lump of rock that has fascinated poets and scientists alike, may be about to get even more interesting. A new analysis of isotopes found in lunar minerals challenges the prevailing view of how Earth’s nearest neighbor formed.

Most scientists believe Earth collided with a hypothetical, Mars-sized planet called Theia early in its existence, and the resulting smash-up produced a disc of magma orbiting our planet that later coalesced to form the moon. This is called the giant impact hypothesis. Computer models indicate that, for the collision to remain consistent with the laws of physics, at least 40% of the magma would have had to come from Theia.

So, if the giant impact hypothesis doesn’t explain the moon, how did it get there? One possibility is that a glancing blow from a passing body left Earth spinning so rapidly that it threw some of itself off into space like a shot put, forming the disk that coalesced into the moon. This would explain why the moon seems to be made entirely of Earth material. But there are problems with this model, too, such as the difficulty of explaining where all the extra angular momentum went after the moon formed, and the researchers aren’t claiming to have refuted the giant impact hypothesis.

Weird Super-Earths found Orbiting Neighbor Star

Astronomers believe they have found a second distant planet around Fomalhaut, a bright young neighbor star, and that the far-out world — like its sister planet — is shepherding and shaping the star’s ring of dust.

If confirmed, theorists have some work to do explaining how the planet, believed to be a few times bigger than Mars, ended up 155 times as far away from its parent star as Earth is to the sun.

“We’re learning a lot about planets that are close to their stars, but that is not the full picture. We also want to know about systems where planets are very far out. By considering near-, far- and mid-range, we can get a complete picture of planet formation,” University of Florida astronomer Aaron Boley told Discovery News.

 


Happy New Years to South and Southest Asia

14 April 2012

Happy New Year in Assam, Bengal, Orissa, Manipur, Punjab, Tamil Nadu; Myanmar, Cambodia, Laos, Nepal and Thailand.

South Asia has presented me with more problems than any other region when it comes to trying to suss out what calendars are in use. It’s a similar situation to trying to figure out what languages they speak. A lot. Which often have similar roots but different interpretations (and if you believe in the proto-Indo-European language, then maybe European Calendars add to this variegated mullagatawny of time keeping).

There’s so much variation within any given system and between them, that in order to present a comprehensive view of these calendars might take me the better part of a month or two. The information I have found on it isn’t clear (at least not to me, and I have trouble keeping Sanskrit-derived names in my head). I’m going to give a general idea of the calendars, however, as they require a good deal of measuring of planetary bodies, it gets tricky. For the time being, I’ll avoid those details until I feel more confident that I understand them myself.

There’s a decent pdf here about the Vedic Calendar, and more information about Hindu Calendars.

 Vedic-Hindu Calendars

The Hindu Calendar is a solilunar calendar which relies on observations of the motion of the Sun and Moon across the heavens, in a way similar to astronomers tracking the Sun’s journey across the ecliptic, or astrologers tracking planets through the houses and signs of the zodiac.

The Day begins at sunrise, the Week begins on Sunday.

Nakshatras

The ecliptic is divided into 27 regions called nakshatras. The moon takes about one day to pass through a nakshatra. These are further subdivided into quarters (padas). The nakshatras are named after the prominent constellations or asterisms that occur within them and have mythological significance. Ashvini is the first of the nakshatras, equivalent to Aries (although the boundaries differ from those the IAU has designated for the constellation).

The starting point of Ashvini is defined as the point along the ecliptic opposite the star Spica (in the constellation Virgo). This starting point, at the beginning of the constellation Aries, is called the Meshaadi.

Yogas

No, not the stretchy pants and blue mats kind of yoga.

There are 27 of these measures. The one which is considered “active” at sunrise is applied to the day. This is done by calculating the angular distance along the ecliptic from our starting point (Meshaadi) to a particular object. Equivalent measures for the location of the sun and moon are then factored in. I don’t pretend I have the foggiest how these calculations are done.


Lunar & Solar Months & the New Year

There are twelve lunar months, determined by the New Moon prior to sunrise (which means sometimes it will coincide with theAbysmal lunar months, sometimes it will be off by a day). The first month, Chaitra takes place during the Vernal Equinox.

There are twelve solar months, which is how this New Year date is determined in the first place. The first of the solar months is Mesha, and is determined by the Sun passing before the constellation Aries. This is similar to the astrological “Sun in Aries”, with one notable exception: the Hindu system looks at the actual constellations, the astrological system uses artificial boundaries not related directly to the heavens.

There’s a series of calendars for 2012 for a variety of cities. Here is the pdf for Toronto.

New Year’s Celebration in Burma. I hope Aung San Suu Kyi election to head of the opposition signifies things to come.

South Asia
Assam New Year – Rongali Bihu
Bengali New Year – Pohela Boishakh
Oriya New Year – Vishuva Sankranti
Tamil New Year – Puthandu
Meiteis New Year - Sajibu Cheiraoba
Sinhalese New Year – Sinhala Aluth Avurudda
Malayali New Year – Vishu
Punjab New Year – Visakhi

Southeast Asia
Thai New Year – Songkran
Burmese New Year – Thingyan
Cambodian New Year – Chaul Chnam Thmey
Loa New Year – Pbeemai or Songkan

251 Days to Dec 21st 2012


Lunation 4 Year 12~IX

22 March 2012

Between the Equinox and the next Abysmal Quarter.


Evolution of the Moon

18 March 2012

or, Why I’m so Glad we’re spending a kajillion dollars on space stuff.

278 Days to Dec 21st 2012


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