The Astronomical Square

Let us explore the square. We will tie in astronomical and numerical considerations as we go along.

A square is a two dimensional representation of embodiment. It is the four directions that an incarnated human being is embedded in or bound to (front, back, right, left). When projected into three dimensions as a cube, the directions of above and below complete the picture. The square can then be said to signify all of the manifested cosmos, all that is bound by form. This includes galaxies, stars, planets or any other body. The square is a symbol of form. Matter. And matter is subject to time.

the cosmic square

If we wish to signify the earth we must insert a smaller square. Thus:

The earth as our focus in the cosmos (Not proportional 🙂 )

We have said that matter or form is subject to time. Time becomes visible to us through the cycle of day and night, which is marked by the presence or absence of the sun in the sky. Let us add a vertical line to our diagram to illustrate this. Since we are ‘facing’ the square the top represents sunrise or the east. The bottom, our ‘back’ represents sunset or west.

Division by day and night

If we are perceptive we will note that at one point in the day the sun is at its highest and the midpoint of the day is reached. After sunset we may count the time and halfway through it is midnight. This is the complementary point to mid-day. We represent this with an additional, horizontal, line. So we now have the four divisions of the day; sunrise, mid-day, sunset and mid-night (I, II, III and IV respectively).

The cycle of day and night

 If we count accurately and for a longer period of time we notice that day and night are never equal except for two times during the year. These are the equinoxes. We also will observe that after one of the equinoxes the days become longer and the nights shorter, the sun’s path across the sky is longer during the day. At one point the longest day is reached this is the summer solstice. After the solstice the days begin to shorten until an equinox is reached. After this equinox the days continue to decrease until at one point they are at their shortest and night is at its longest. This is the winter solstice. Again the days lengthen until the next equinox is reached. This cycle of light, which can be likened to breathing, marks the four seasons and also one solar year. It is not surprising then that the sun is described as square in Indian astrology. Not because he appears square in the sky but because his path is ‘square’! The inner square represents  one revolution of the earth around its axis and the outer square one revolution of the earth around the sun.

The solstices and the equinoxes are the turning points of the year. They are the ‘turning points’ or in Greek the τρόπος (tropos or ‘turn’). This is where the english word ‘tropical’ comes from. The corner points of the inner square mark the hinges. Corner 1 marks the spring equinox, corner 2 the summer solstice, corner 3 the autumn equinox and corner 4 the winter solstice. We can give these corner points names. Traditionally these points are also called the beginning of Aries (1), Cancer (2), Libra (3) and Capricorn (4).

The corner points or equinoxes and solstices

 Just as we divided the inner square into four parts, we can also divide each of the four larger divisions into four parts, leaving 12 equal divisions surrounding the four inner divisions. (We have an interesting progression of 1², 2², 4², 4² −2² ) We can represent this division thus:

The 12 divisions of the solar path and space around the earth

 Each of these 12 boxes divides the cosmos around the earth into, let us call them 12 quadrants. These quadrants are empty. They represent the sky without stars. No cosmic body has yet been mapped into them. Remember this. These 12 quadrants are also known as the tropical zodiac and each traditionally has a name. So a is Aries, b is Taurus and so on. With this diagram we have arrived at the South Indian chart which surprisingly is an ideal representation of the tropical zodiac! Unfortunately these names are also used to describe collections of stars or constellations and much confusion arises. The Sanskrit word ‘rasi’ is actually better because it simply describes what the boxes contain: a heap, mass, quantity, number, collection. So in each box there is a collection of galaxies, stars, planets, asteroids, or cosmic dust if you wish. There are two contending viewpoints as to how the position of planets and sensitive points should be mapped into the rasis. I leave you dear reader to draw your own conclusions as it is possible to use both methods, the so-called tropical and so-called sidereal zodiac, to map the positions into this chart.

Now these quadrants are very interesting. Quadrants a and b face the East,  d and e the South, g and h the west and j and k the North, if you remember our earlier exposition. They also have a correspondence with sunrise/Spring, mid-day/summer, sunset/autumn and mid-night/winter. Quadrant a is after the ‘turning’ and is therefore the pivotal part of the season of Spring. It can also be called ‘cardinal’ which means the same as ‘pivotal.’ In quadrant b Spring has established itself and is therefore ‘fixed’. In the corner quadrant c Spring begins to change direction, it is the period leading up to Summer the next turning point Quadrant c, being in a corner has two directions, East and South. It is ‘dual’. Quadrants a, d, g and j may be called cardinal. Quadrants b, e, h and k may be called fixed. Quadrants c, f, i and l may be called dual.

Ignore the Mayan Apocalypse: the Sensation and the Task

Way back in May 2010 I posted an article called,

2012: Time of Change, but in which Direction?

Because of all of the hype in the media and because some find themselves worried (albeit without cause) I would like to balance out some of the nonsense. Here is the core sentence:

2012 is the year that Regulus, the heart of the Lion, one of the royal stars, moves into Virgo after a 2149 year sojourn in Leo. That is an end of a cycle. More profoundly so, as it will join the other royal stars, Aldebaran, Antares and Fomalhaut who have been in mutable signs for a while now.

I would recommend reading the whole article because there the task of a “Virgoan” Heart of the Lion is explained.

Mayan time-keeping was extremely cyclic. There were tiny cycles within larger cycles within yet larger cycles, not unlike the time cycles we find in the Vedic tradition where even larger cycles then those of the Mayans are described. (see Manvantara at wikipedia).

The fourmilab Calendar Converter site has this to say:

The Mayans believed at at the conclusion of each pictun cycle of about 7,885 years the universe is destroyed and re-created. Those with apocalyptic inclinations will be relieved to observe that the present cycle will not end until Columbus Day, October 12, 4772 in the Gregorian calendar. Speaking of apocalyptic events, it’s amusing to observe that the longest of the cycles in the Mayan calendar, alautun, about 63 million years, is comparable to the 65 million years since the impact which brought down the curtain on the dinosaurs—an impact which occurred near the Yucatan peninsula where, almost an alautun later, the Mayan civilisation flourished. If the universe is going to be destroyed and the end of the currentpictun, there’s no point in writing dates using the longer cycles, so we dispense with them here.

For more useful information about the Mayan calendar please visit their site.

Dear reader, I wish you a good solstice and after that a happy Christmas season and when our calendar ends on December thirty-first and the next official yearly cycle begins a happy New Year, preferably with family and friends…

2012 Mayan Apocalypse? Don’t Count on It!

There is a rumour that in the year 2012, the Mayan calender ends, and with it the world. This is the type of sensation that inspires film-makers. Apocalyptic themes promise a good box office. I have another reason for discussing this theme, and that is to present a nifty tool that can be found at fourmilab.ch. This tool can also be downloaded and used off line. What does the calendar converter do? It simply converts any date of choice into different calender systems, including the Mayan system. I use it primarily to quickly find dates for time periods larger than a month, for example searching for the conception date when using the trutine of Hermes. An example:

Take say the 15th of February 2009. What was the date 289 days before this day?

1. Enter the 15th of February 2009, 12:00 in the Gregorian calendar. Press calculate.
2. note the Julian day: 2454878
3. subtract 289 = 2454589
4. enter 2454589 in the Julian day field. Press calculate
5. Look up the day in the Gregorian calendar, May 2, 2008

And what day was May 2, 2008 in the Mayan Long Count calendar?

12 baktun 19 katun 15 tun 5 uinal 7 kin or 12.19.15.05.07.

The day that is getting so much media coverage is the 19th of December 2012 or 12.19.19.17.19. This is the end of the 12th baktun cycle that is 144.000 days long. But this isn’t the end of a pictun cycle. It takes 20 baktun to make up a pictun cycle. It is only at the end of a pictun cycle that the Mayan’s believed the universe was destroyed and remade. There are still 8 baktun cycles to go! So if you are waiting for the Mayan apocalypse you have a long wait. That will be on October 12, 4772.

Priming up for Primary Directions

In the epoch of the whizz-machine one only needs to click a few buttons in a computer programme to generate a chart. This is tremendously convenient. It also has one side-effect. It is easy to forget the mathematics that underlie the chart.

A chart generally is a projection that simplifies navigation. In the case of an astrological chart it is a projection of a number of factors combined to give the best possible overview. It can in a sense be described as a planetary seal whose very 2-dimensionality provides a window to grasping both a complex astronomical as well as metaphysical reality. It is a navigation tool.

What is it a projection of? Here we need to look closer at the three-dimensional reality and must resort to spherical geometry. Have no fear! I am not going to present the theoretical geometry. Instead I will try to help you envision the geometry.

Place before your minds eye a transparent sphere. This sphere will represent the earth. Next imagine that this sphere is divided into two equal halves by a circular section. The section is the equator and the halves are the north and south hemisphere.

Next imagine another circular section that is perpendicular to the first. This section divides the sphere into an eastern and western hemisphere going thorough its north and south poles. Let us say that this particular section bisects a point that has been established, by convention, to be the starting point of 360 sections that equally bisect our imagined equator. This is the meridian that passes through Greenwich, England. All 360 equal sections are also called degrees of longitude. You still awake? Yes? See, it’s easy!

But what if we want to exactly pinpoint the position of Greenwich, which is a little more than halfway the distance from the equator to the North Pole? Here we have to imagine 90 increasingly smaller sections that are parallel to the equator. These are degrees of latitude. And so we can exactly define the position of any place on earth, not only Greenwich, (51N28 latitude, 0E00 longitude), with two coordinates. I won’t go into detail here, but the parallel of latitude also helps define the horizon.

But we are not finished yet. Let us take another position east of Greenwich, say Berlin which is roughly 13 degrees east of Greenwich and 52 degrees north of the equator. But why do we used the term degrees? Well, the distance from Berlin, let us call it point B, along the same meridian, to a point on the equator, let us call it E, is the arm of an angle that runs from B to the centre point of the earth and from there to point E. (Point E can be said to be a projection of point B onto the equator) This is a 52 degree angle. The 13 degrees of latitude longitude are also an angle between the projection of B on the equator and the projection of Greenwich to the equator. You can see here that our reference is always to the equator. This is important because this same principle is used elsewhere. We’ll get to that later.

Now these 360 degrees are special because they can also be converted to time. How’s that possible? Well if we imagine that our imaginary sphere rotates around its axis in one day then we can divide the 24 hours for one revolution into equal divisions of time. There is just one tiny catch, when applied to the earth the revolution is 4 minutes shorter than clock time. We speak of a sidereal time to make just that distinction. If you are calculating a chart the old-fashioned way, this will be one of the first conversions you will make. From clock time to sidereal time. This revolution of the earth around its axis in one day is also called primary movement and it is reflected in our chart by the houses, whose movement is also clockwise. Primary movement is also what underlies what is known as primary directions. (I’ll discuss these in a followup article). Up to here, with the aid of a Table of Houses we have the first set of calculations needed for our chart. We have an empty chart with the house divisions.

Now there are two other spheres that we consider in our calculations. These are the celestial sphere and also a sphere whose “equator” is formed by the path of the Sun in its yearly revolution around the earth. This is the ecliptic. The ecliptic is not divided into 24 hours but into 12 Celestial Signs of 30 degrees each. The beginning point for both the ecliptic and the celestial sphere is where the ecliptic crosses the celestial equator at 0 degrees Aries.

The celestial sphere shares the same equator as the terrestrial sphere. But instead of describing the position of a planet on the celestial sphere in terms of longitude and latitude we speak of right ascension and declination. The angle of projection of a planetary body to the celestial equator is the Declination. The angle on the celestial equator formed by this projected point to 0 degrees Aries is known as Right Ascension.

And now to the ecliptic. This can be considered as the equator of a sphere that is tilted roughly 23 degrees away from the terrestrial and celestial spheres. Now a planet’s position can also be defined in terms of the ecliptic. Here again we speak of a planet’s longitude and latitude. This is the second set of calculations needed to cast a chart. This is done with the aid of an ephemeris. This second set of calculations are for the secondary movement of the planets which is counter clockwise. Secondary Progressions are based on this movement of the planets. That is in fact the origin of the names for Primary Directions and Secondary Progressions.

There is just one last point to be made. When we calculate our planetary positions and place them in the chart, we reduce their three dimensional position to two dimensions. When I say a planet or a fixed star is at 29 degrees Leo I have projected its real position to the ecliptic. For example we read in our ephemeris that Mars and Jupiter are conjunct at 27 Gemini. If the sky is clear, and both planets do not have the same degree of latitude we will see that one is above the other. Astrologically we say that the planet with the higher latitude is stronger. What we are saying is that when we project their position in the celestial sphere to the ecliptic they both share the same ecliptic point.

Dear reader. If you could follow all of this then you should have no difficulty in understanding primary directions in particular and I haven’t mentioned such creatures as sin., cos., tan., cot., semi- diurnal or nocturnal arcs until now”! 🙂 You have been primed! You see the general confusion about directions is such that even most programmer’s of astrological software get them wrong and should the rare programmer get them right they are presented in an unusable form!*

*If you are a purveyor of astrological software please do not solicit your software here. You may of course send me a message in the “Reply” section provided at the bottom of the home page. If you are convinced that you have the primary directions programme then you may certainly send me a usuable demo version! 🙂 or :-(?

Time for Time

If you remember we mentioned the idea of the mundus imaginalis in Henry Corbin’s work awhile back and how it is worthwhile looking at it in an astrological context. There are other texts that we can consult which also have relevance to this theme. One such text is Friedrich Schiller’s, “On the Aesthetic Education of Man”. At the risk of being academic I would like in the next few articles to draw your attention to a few passages from this work.

The first passage is from his twelfth letter:

“Since everything that exists in time exists as a succession, the very fact of something existing at all means that everything else is excluded. When we strike a note on an instrument, only this single note, of all those it is capable of emitting, is actually realized; when man is sensible of the present, the whole infinitude of his possible determinations is confined to this single mode of being. Wherever, therefore, this drive functions exclusively, we inevitably find the highest degree of limitation. Man in this state is nothing but a unit of quantity, an occupied moment of time – or rather, he is not at all, for his Personality is suspended as long as he is ruled by sensation, and swept along by the flux of time.” [from the German/English parallel translation of E. Wilkinson and L. Willoughby, Clarendon Press, 1982 (p.79)]

This is part of his description of three different drives that may be found in human nature; the sensuous drive, the form drive and the balancing drive of play. (Stofftrieb, Formtrieb, Spieltrieb). Here the drive toward matter or sensation.

We have a very perceptive description of how man is embedded in time. A theme also central to astrology. Looked at closely we find that the perceptual reality, the actual looking at the heavens is so exclusive and so limited that it is not accessible to interpretation, partly because we are physiologically only able to focus on one star or planet at a given moment! The chart we may look at; whether horary, natal or mundane, is merely a quantitative description of sensible experience transposed to glyphs and numbers, nothing more. It is one moment of time conserved on paper, much like a concert conserved in a folio and as such utterly meaningless. Some other human activity is required to give it meaning! We’ll explore this soon.

There is another aspect to this and that is what truly is the astrologer’s sensible reality? What “substance” does he manipulate or seemingly manipulate? We could say that this is time. Time is movement and if the astrologer forgets this he has closed one of the major portals of understanding. This is perhaps why in the astrological tradition the application and separation of planets to one another is so important and why transits, a modern preoccupation, are generally neglected. Why? A transit, although the name implies movement, is a quantification and not the movement itself. It really isn’t important whether Saturn is transiting your natal Sun. You are not going to die and you might not experience any unpleasantness at all! (and don’t bother about hearsay or statistics, a Venus transit or any other planet might statistically give the same result or lack of result). What you might want to do instead is consider whether that Saturn applying square to the Sun in your natal chart is far more significant.