# 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 š )

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 āfacingā the square the top represents sunrise or the east. The bottom, our ābackā 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

Ā 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 sunā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 āsquareā! The inner square representsĀ  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 āturning pointsā or in Greek the ĻĻĻĻĪæĻ (tropos or āturnā). This is where the english word ātropicalā 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

Ā 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 ā22 ) We can represent this division thus:

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

Ā 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 ārasiā 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,Ā  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 āturningā and is therefore the pivotal part of the season of Spring. It can also be called ācardinalā which means the same as āpivotal.ā In quadrant b Spring has established itself and is therefore āfixedā. 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 ādualā. 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.

# The Sun and those Retrogade Outer Planets

Sometimes the obvious is invisible, most likely because we are inclined to look at details and just simply overlook the greater picture. Although I have seen many charts and read many astrology books it never occurred to me nor has anyone recorded, in an astrology book that is, the simple observation that when an outer planet is in opposition to the Sun it is always retrograde. Always. And in the middle of the retrograde arc. I came across this in James Evans, ‘The History and Practice of Ancient Astronomy’ in the chapter on planetary theory (p. 296).

Let’s try to put this in an astrological context. To be retrograde is considered a major accidental debility, William Lilly gives it 5 points in a scale of 1 to 5. An opposition is an aspect of conflict; at best the opposing planet is in its domicile or exaltation, angular and maybe conjunct Spica; at worst it is in detriment or fall, cadent and conjunct Algol. Most likely it will be the dominant aspect in the chart forming a personal pole around which the rest of the chart ‘rotates’ (figuratively), the house axis pointing to a major life theme with which the native wrestles. An aspect of a lifetime as many years can pass until the planet goes direct by secondary progression!Ā  For example Jupiter may take 60 or more years before he goes direct by secondary progression!

# And the Winner isā¦

If you recall, 2009 is the year of astronomy. Some may wonder why astrologers should take any interest, considering how modern astronomers seem to avoid the topic of astrology and when pressed must ridicule it so as not to lose face with their colleagues. On the other hand many modern astrologers do not seem to have a very high opinion of astronomers. Both sciences however share a common history and for centuries were not to be separated from one another. With that said I would like to present the ultimate modern book on astronomy for the astrologer and for the astronomer interested in the history of his or her science: “The History and Practice of Ancient Astronomy” by James Evans. Note that ‘practice’ is italicized, and that for a purpose. The book makes good its promise and presents also the tools used by ancient astronomers (or astrologers!) and how to use them. I have seldom been so excited by an astronomy book. This is it. I only regret that it has recently come to my attention and not in 1998 when it was first published. In terms of presentation, content and clear precise and riveting language this book has top scores and is my personal winner of Astronomy Book for the Year of Astronomy.

The author in his preface already shows the character of the book:

In the sciences, it is common to encounter monographs in which the author interrupts the development from time to time by posing problems and exercises for the reader. This is the author’s way of saying, ‘You can’t be sure you understand this material unless you can use it.’ But the exercises and suggestions for observations that are interspersed throughout this book are unusual features for a historical work. These are meant to give the reader a chance to practice the art of the ancient astronomer. Any attempt at a grand historical synthesis or a philosophical analysis of the Greek view of nature that is not underpinned with a sound understanding of how Greek astronomy actually worked is headed for trouble. (p. ix)

I think that this should also be taken to heart when trying to understand ‘traditional’ astrology, whatever the source.

In the very first chapter, ‘The birth of Astronomy’, the gnomon is introduced. This is the most ancient instrument of all ā a stick set into the ground in a sunny place. The shadow is measured. And you will be surprised what wealth of insight such a simple device can deliver.

# International Year of Astronomy

Just a note on the side. Today the International Year of Astronomy begins. The opening ceremony takes place in Berlin, Germany.
Here is the link to the official site. Th.

# Algol and Pluto: Two Astrological Hobgoblins

In traditional astrology the fixed star Algol, head of the ghoul or demon, is considered the most baleful of stars. In modern astrological practice he is generally ignored, he has been replaced by Pluto. Astronomically both have something in common. Let us have a closer look.

Algol, is an eclipsing binary (actually there are three) star, Beta Persei Ī±, Ī² and Ī³. The brighter star, Beta Persei Ī± is regularly eclipsed by Beta Persei Ī² so that every few days its magnitude dips from a magnitude of 2.1 to 3.4. The following animation demonstrates this quite well.

Eclipse pattern of Algol, source Wikipedia

Now any form of eclipse with a diminution of light is considered a form of debilitation and so with a little imagination it is not hard to see this constant eclipse, it occurs roughly every 2 days, as the baleful winking of the ghoul’s eyes.

Now, most are aware of Pluto having been degraded to a ‘dwarf’ planet. You might understand why if you compare the size of Pluto to the Earth. Relative to the Earth, Pluto has a radius of 0.18 and a mass of 0.0022 (the Earth having the value 1). It is tiny!

Comparison of sizes between Earth/Moon/Pluto/Charon, source Wikepedia

Not as widely known is the discussion whether Pluto and Charon form a binary dwarf planet! Unique in our planetary system. This reasoning has some factual basis:

1. Pluto and Charon rotate around one another
2. The centre of mass is outside of both bodies, each can so to speak be viewed as being the others moon!
3. They are gravitationally locked so like the Moon with the Earth they always show the same ‘face ‘ to one another. This is because Charon is half the size of Pluto. Its gravitational field has an enormous influence on Pluto.

So like Algol, where Beta Persei Ī² constantly eclipses Beta Persei Ī±, we have ‘Pluton’ where Charon constantly eclipses Pluto roughly every 6 days. This at a magnitude of 13.65 (compared with Algol’s 2.1). Most of Pluto(n)’s bugbear qualities have been associated with his name (Lord of the Underworld) but seen from the above standpoint, this may in fact be grounded in Pluto’s continually eclipsing nature.

So both Algol and Pluton are binary systems that constantly eclipse. They are the hobgoblins or bugbears in astrology ready to grab you and pull you into the dark closet where they hide. The only difference is the quality of light that is eclipsed. Algol at its weakest magnitude is 4 times brighter than Pluton. Compared to Pluton it glows. Just to give you an idea of the quality of light:

• Sun ā magnitude ; -26.73
• Full Moon ā magnitude; -12.6
• Sirius, the brightest star in the sky ā magnitude; -1.4
• Saturn ā magnitude; 0.24
• Algol ā magnitude; 2.1 to 3.4
• faintest stars visible with the naked eye under optimal conditions ā magnitude; 6.5
• Neptune ā magnitude; 7.7
• Pluto ā magnitude; 13.65

This is where the traditional astrologer and the modern astrologer have their differences. The traditional astrologer considers light, only where there is light can there be an influence. The modern astrologer likes to speak of ‘energy’, but what exactly this ‘energy’ is is often unclear. It is certainly not in the form of light. Maybe in the form of ‘ecliption’ (for lack of a better word)?