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

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 :-) )

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

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

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

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

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.

Round or Square?

Most standard texts on astrology, from the more ancient to the recent, western or Indian begin with a description of the signs, planets and houses. Indian texts often add a description of the nakshatra or lunar mansions. Quickly an example is introduced in which the combination of the three for a particular time is presented. This may be called a figure, a diagram, a chart, a horoscope, a chakra, a wheel or in a specialised form, cosmogram. Some texts provide a description of the, let us call it chart. Other texts don’t. Usually the student adopts what is presented, and later, what seems more convenient. Generally no further thought is given to the matter. So the answer to the question whether the choice of round or square is through convention or tradition can be answered that it is generally through convention. The form first encountered or a software default seems to decide the issue. Yet, the chart is a potent astrological image. And in my opinion greater care should be given in its choice. In fact, depending on the focus, the appropriate form should be used! Do you know what the twelve divisions in your favourite chart form represent? Are they signs? Constellations? Houses?

There is also the other side of the question. Is there such a thing as a traditional chart? Modern western astrology has adopted a round chart form. But is this the traditional form? O. Neugebauer and H. B. van Housen in their book on Greek Horoscopes include a drawing after the Oxyrhynchus 235 papyrus which shows a lopsided, wobbly, hand drawn circle divided by a horizontal and intersecting vertical line that represent the axis of the horizon and the zenith. It is a chart for a person born between 15 and 37 AD. They also say that such diagrams are very rare and that only later in Byzantine codices do diagrams appear with greater frequency. There, however, various forms of the square chart are used. It seems that up to the 19th century the square chart was the dominant form in the West. It is still the dominant form in India.

The chart is a map of the heavens for a certain moment of time at a particular location. It can be for a person, an event or even for the moment of a question. Just how the heavens are depicted remains to be explored. The planets can be mapped against the constellations or using the tropical zodiac. This is also where we have to be absolutely sure what is meant by ‘sign’ or in Indian astrology ‘rasi.’  We’ll explore this later in more detail.

For the moment location is of interest to us. It can be described as the intersection of two imaginary great circles known as the longitude and latitude or as being situated in an area between two longitudinal and latitudinal sections which we can call a quadrant. In fact one of the few situations where circles may form a square is in mapping in two dimensions. Keep this in mind when we explore the construction of square and round charts in the next articles.

Tradition, Convention and Dogma

Tradition is difficult to define. It can be described as a body of knowledge that is considered so valuable that it must be bequeathed from one generation to the next. Quite often it has a divine source or is based on supra-sensible perception or lacking that is based on superior knowledge and experience. Traditions generally have a set of seminal ideas that are their essence. Out of this they enfold. Around these seminal ideas a whole body of knowledge and practice grows from generation to generation. But traditions, if access to their core is lost, can become encrusted with what can be called convention and dogma. Both convention and dogma can become the greatest enemies of a tradition and in the end undermine it. Convention endangers tradition because it accepts without question subtle changes in interpretation or practice that may occur over time due to changes in consciousness or understanding and at worst may be fueled by those who would use such subtle changes to their own advantage. Convention is acceptance without understanding. Convention encourages sluggish thinking. It is the comfortable approach as it accepts without question and answers uncomfortable questions with, ‘it has always been done so’ or ‘my teacher has said it is so’ or ‘it is written thus.’

Dogma is more insidious. It takes a conventional interpretation of a traditions core ideas and turns them into canon, declaring ‘it can only be so.’ Sluggishness is replaced with militancy and questioning outside of the canon is declared heresy which is usually punished in one fashion or other. Other traditions are rejected on principal.

A tradition is not a monolith that stands in a field unchanged and unchanging, to  be protected from the elements and erosion. It is the field itself in which the seed of the tradition, its essence, is sown, nurtured and cultivated; grows, flowers, is pollinated, comes to fruit and then regenerates. The monolith, which embodies the verbal and written aspects of tradition, merely marks where the tradition can be found. It is the minds and hearts of those who cultivate the tradition that plant the seeds of their understanding in the soil of the field. That understanding which is in accord with the tradition thrives and prospers and keeps the field fertile. Convention leaches the fertility out of the field around the marking monolith. There is still growth but it is meagre by comparison. Dogma roots out all that grows in the field so that only the monolith remains and the field is barren.

The next articles are devoted to a simple question: is use of a square or circular chart based on convention or tradition and what does it show? Some of my conclusions may not be acceptable to everyone. That does not mean that anyone who does not agree with me is conventional or dogmatic. What it does mean is that I and you, dear reader, will try to tap into the core of the tradition or traditions presented and to the best of our abilities try to plant a few viable seeds and bring them to growth.

The Terms or Bounds and the D-30 Divisional Chart

In my article on the Terms and Bounds I went into detail about all of the three ‘systems’ available to the western astrologer. Ptolemy’s mystery manuscript somehow has captured my curiosity. Where did it come from? What did it contain other than the table of terms he listed? Where is the origin of the uneven number of degrees for the terms that all of the systems share? Of the three the Chaldean system has the most regular divisions (8 – 7 – 6 – 5 – 4 for all signs) while the Egyptian and the Ptolemaic are completely irregular, each sign having different divisions.

We know that in the ancient world there was some transfer of astrological knowledge. So I would like to postulate, and this is highly speculative, I have absolutely no proof, that the manuscript that Ptolemy saw might have been from a somewhat garbled treatise dealing with divisional charts, most particularly what is called the Trimishamsha Chakra, the 30th division of a chart. We find in Parasara’s treatise (I don’t think Ptolemy saw this) a passage on the 30th division:

Trimshamsa: In odd signs the lords of Trimshamsha are Mars, Saturn, Jupiter, Mercury and Venus each of them in order rules 5, 5, 8, 7 and 5 degrees. The same should be considered … in even signed, though in reverse order’ (BPHS, Sharma ed. p. 115)

Let’s compare:

Now of course the D-30 table would not be interpreted in the same way as the terms. It is not the planet that is looked at, it is the sign owned by the Lord of the Division that is important. Jupiter at 10 Pisces would in a western chart be in his own terms and so have additional dignity. With a position of 10 Pisces Jupiter would be placed in Virgo (Mercury’s even sign rulership) in the trimshamsha chart. There Jupiter would not be so well placed as he would be in the house of a planet that he considers an enemy. A significant difference. Now if Mercury were at 18 deg 12 Sagittarius he would be in his own terms and his detriment would be mollified to some extent. In the trimshamsha he would be placed in his own odd sign, Gemini and thus be strong and not cause much damage.

Now, you might think there is a catch, as in the first case we are dealing with the tropical position and in the second the sidereal. This would be no problem, you would say, if we were living in the 3rd century AD as then both the tropical and the sidereal positions would be coincident but in a modern chart we would have to compensate for the 23+ difference in degrees (ayanamsa). Saturn at a sidereal position of 20deg20 Capricorn would have a tropical position of about 13deg20+ Aquarius. He would remain in Capricorn in the trimshamsha and in the tropical chart be in the terms of Venus. But then that is something I wouldn’t recommend. Don’t try converting the western terms to a modern ayanyamsa just because Ptolemy lived a good 1900 years ago!

By the way the trimshamsha is used to focus on the potential for illness. In the western tradition terms are quite often used to describe the physical body. It might be worthwhile to look into the medical aspects, without getting crossed-eyed by trying to recalculate from the trimshamsha. Keep them separate! I am not at all suggesting mixing jyotish techniques with western techniques. What I am suggesting is that both make use of the 5 planets without the lights and both use systems of irregular division. It is the idea of dividing or using a 5-fold division to describe the physical body and the ills that can befall it that I want to draw your attention to. And then of course there is still the historical question if some sort of cross-over occurred when Ptolemy adopted his terms from the mysterious manuscript. Who knows, maybe some renegade Chaldean astrologer used a divisional system that he reinterpreted from a neighbor to his far east… 🙂


You may have wondered why in my last article I spent so much time discussing a chart layout. Well yes I did say that I wanted to get you, dear reader, comfortable with reading what might be an unusual chart format. But there is more.

In the day of the computer we make calculations, that would otherwise take us an hour or more (depending on the calculations) to do by hand, in seconds. We might even have a page or two of printout to immediately jump into. The novice is instantly overwhelmed. The more experienced know what to ignore or they might find themselves drawing out a chart by hand including only that information that seems to be relevant at the time. The instant chart, to be useful, requires that the astrologer recalls what it represents. It is a potent symbol that needs to be approached with a certain respect.

Now back to the south Indian chart. A blank chart is a window. When filled in it is a representation of an instant of time. You view it from a vantage point that verges on omnipotent. When you begin to concentrate on it you are in effect suffusing the chart with the light of your consciousness and in a certain respect merging with the cosmic picture that it represents. Each chart form is a gesture.  It reflects a different approach. A round chart as compared to a square one is a qualitatively different representation. And it is helpful to try to capture this difference as an image, maybe even linking to mythical imagery that makes the mind more receptive. to its message. The south Indian chart for example can be likened to the carapace of a tortoise and from there the connection with the mythical tortoise that supports the cosmos is instantly there. The relation is reciprocal as it becomes clear why the tortoise in the myth carries the cosmos. The carapace is domelike, much like the dome of the sky, and the ‘boxes’ like the boxes of the signs and houses that subdivide the heavens. To ground the whole in reality it wouldn’t hurt to visit a few real tortoises and observe their movement and character!