### Non-Orthogonal Coordinate Systems, Non-Decimal Systems

I'm sorry that I have to start with such an intimidating-looking topic. It's not, really. There are two facts that make it almost impossible for most people to understand Anieth astronomy. First is that none of the locals of Anieth had paper. They did not think of a world as being like a map, or of the sky as being laid out on a map. For most of us, a map is square or rectangular and has a coordinate system that is called "orthogonal" meaning that it's filled with perpendicular lines to make more squares in the bigger square. We see at times, maps of the globe that look like peeled oranges, but most of our maps are orthogonal. The other fact of the modern world is that we count in tens, using a decimal system of numbers. Deci is just another word for ten. This seems logical to people because they have ten fingers.

The people of Anieth (and those of Ancient Europe) used several different number systems, but their main counting system was not base ten, or like a clock, base twelve, but bases nineteen and twenty. This was because they counted on one hand using the other index finger to count the joints of the right hand with the left finger or vice versa. They also counted the tips of the fingers. Because the thumb base joint is on the wrist, it seemed more logical to them to count in base nineteen. We could argue about this, reasoning all kinds of different "logical" "human" systems until we are blue. We count in base ten, the natives of Anieth, both the Nine Nations and the Clans used base nineteen, many Europeans still use base twenty. For those of Anieth, a generation was nineteen years, plus or minus one. Over and over, we see a pattern emerge: base plus one or minus one. A fian (king's company) was twelve warriors plus one--the king. A year was thirteen months and a day. A day was nineteen hours plus one and a generation was sometimes nineteen years plus one. A people were four castes plus one: worker, trader, scholar, warrior and king (who was supposed to be all four and more.) The directions were four plus one or east, west, north, south and center. There were many things that were different, but this pattern emerges as one of the sacred patterns, or patterns dealing with cycles.

Numerically, the four into five became four fives or nineteen into twenty. This pattern of fives emerges as the one significant in astronomical mapping. The astronomers looked up and did not see an orthogonal system, but a spiral. I will now show you how they turn this spiral into a coordinate system.

#### Visual Mnemonics in Anieth

I'm going to show you familiar things from Terran astronomy, because the skies are identical, or were, four thousand years ago.

When we look up at the sky in modern times, we do not see what the ancients saw. There are many differences. The most remarkable difference between our skies and theirs is the visibility. I think that one of the reasons Stonehenge is perceived primarily as a lunar and solar monument is because the stars have faded into insignificance--literally. But go to any desert, away from the lights, or up into the mountains and the stars become the dominant factor of the sky. In particular, the Milky Way becomes prevalent in a way that none of us have ever thought about. I laughed when I read books and books about stellar monuments and no one had ever thought of the Milky Way as being part of stellar mythology.

When astronomers talk about precession, they speak of two things. Everyone has heard of the "Age of Aquarius" because of the song popular in the sixties. Equatorial precession is what causes headaches for astrologers because the signs around the zodiac, a belt around the equator of the earth, "slip" so that the vernal equinox once began in 1 degree Aries, but in these days is more like 5 degrees Pisces. We "lose" about a degree every 72 years. As far as I can trace, Aries was occluded about the same time as our modern version of astrology was created, sometime in the 3rd Century B.C. in Greece. The equinox will begin in Aquarius in another four hundred years, so we're not in the "Age of Aquarius" yet! In the time of the pyramids, the sun occluded Taurus at the vernal equinox. There are many myths that put the vernal equinox as far back as Cancer. But for my purposes, Taurus ruled the vernal equinox. This shift in stellar and solar position, made most stellar calendars obsolete by the time of the Greeks.

The other kind of precession is called precession of the poles. This is more like a wobble. It is speculation that the pole wobbles, but we have confirmed from many of the astronomy oriented mythology and monuments like the Pyramids, that the pole star was not always Polaris. It will not stay Polaris. But this shift is very slow and is not something that any of us have to worry about, unless, like me, you travel to an Earth-like world four-thousand years in the past.

Due to the precession of the pole, at the time of the building of the great pyramids, the "north star" was not Polaris, but the third star in the constellation of Draco, named Thuban. The constellation of Draco appeared to be revolving around his tale, giving rise to the myths of the world tree surrounded by the snake, serpent, or dragon, or ouroboros, over and over and image of a sea snake or serpent who encircles the earth. But also because of precession of the pole, the ancient people of the northern hemisphere had a period of time where the Milky Way appeared as a girdle, or serpent around the sky, giving rise to the many tales of the world being encircled. This idea of a girdle translated to the Northern peoples in the idea of Arianrhod, or the silver wheel, and is tied to many ideas of a wheel being the universe. As the year progress, this girdle would open up and become a bridge across the sky, moving from east to west to south east-north west. This is often spoken of by the ancients as the bridge across the river upon which the souls tread to go to the other world.

Because of polar precession, the peoples of the north can no longer see some stars visible 4,000 years ago: namely Hadar, Rigel Kentarus, and Acrux. Formalhaut was also visible at an earlier date. Some stars that now set, were in the sky year 'round. Two important things to note were that Arturus just hit the northern horizon at its lowest and Sirius and Antares were visible at the same time in the sky for a short period of time. Understanding polar precession helps us make sense of many ancient myths.

It has been established by archeo-astronomers that the first observatories were stellar as well as solar and lunar. Some of the best work has been done by John North. It is also well established that the Egyptians began their stellar year with the heliacal viewing of Sirius. It also seems evident by the number of sites dug up in the British Isles that not all stellar observatories were aimed at the same stars. In Anieth, different Clans and Nations began their years at different times and used different stars to orient their observatories and ritual sites.

Work done by archeo-astronomers use stars that are bright enough to be marker stars, stars that rise and set in seasonal patters (not circumpolar stars), and make observatories oriented or focused on a very few stars. In Anieth, twenty stars were of major importance, fifteen of them predominant as calendar stars. These stars are marked on the chart above. (Castor and Pollux is treated as one star) The bright star on the lower right is Canopus which could not be seen as far north as we are in this chart.

The fifteen calendar stars and five polar stars were memorized both in myth and using visual mnemonics. In Anieth two visual mnemonics were used. These diagrams were usually place in the stonework on the observatory floor. (See Observatories) It is important to remember that although the above chart shows all the stars, the mnemonic was for risings and settings and is adjusted accordingly. In this chart, Sirius, Rigel, Betelgeuse, Aldebaran, the Pleiades, and Algol have set and Altair has not yet risen. The circumpolar stars are Thuban and Arcturus, Capella, Vega and Deneb. But the mnemonic is for a certain time of year, when the girdle can be seen. So the mnemonic is adjusted for setting and rising and the stars overhead will be Thuban, Arcturus, Spica, Regulus and Polux. It is very important in describing stellar mnemonics to understand that the mnemonic is just that, a way to memorize the stars, not to chart their positions. The observatory itself was for marking positions. The mnemonic was used by the Hazel to chart the differences in the Clans and Nations and to design their observatories.

In Anieth, there are two great cycles. The first is the heroic cycle which is anti-clockwise. This is because of the ancient pattern that in the heavens the magical world is reversed from that on earth. If your feet are on this map, your are upside-down, in the magical world. It is very important in all dealings with magic to realize this important rule: things happen reversed in the magical world or the heavenly world. It was thought by the ancients that when a star was occluded that it was on earth, thus its first appearance in the skies at night after occlusion was a sign of its ascendancy into the magical world, but it lost power over the earth. Thus a star such a Sirius would have earthly form while occluded by the sun, but then "die" and go to heaven when the sun passed into the next constellation. So, here is the spiral, anti-clockwise, of the heroic or left hand way. Put your left fist up and curl it. See the original spiral? Remember, the left hand is the hand of right in the magical world. Note also that the spiral begins with Regulus, a late summer constellation. Another mnemonic in that Regulus is the star of a heroic animal, associated both with Isis and Hercules. But note that the ruler of this magical world is not the hero, but the dark king. His queen is the Bride. This cycle is known as the Heroic Cycle, but the spiral is known as the Bridal Spiral.

Here is the right-handed spiral, called the Witch Spiral or Priestess Spiral. This spiral maps the Trickster Cycle and begins with the serpent, or the dragon. Note that it ends with Antares, which was also known as the wolf. The ruler of the world was known to many as Hel or Tiamat before she was cast down by the hero, another myth to indicate the rise of the spring stars and the setting of the winter stars. In Anieth, these two cycles with mis-matched spouses are essential for the balance of power. Not only do rulers trade off metonic cycles, but the queens and kings are forbidden certain kinds of spouses. Thus a heroic king can only rule once every 38 years in a particular cycle. (Two metonic cycles of 19 years each.) Both these kinds of spirals are used. The spiral maze at An Doras is a right-handed spiral because it is on the ground, and thus is a Bridal Spiral. This is because it is used by the Oak to elect heroic kings who are paired with Holly tanists (dark champions).

The basic system of coordinates, takes into consideration the spirals and the rule of five and nineteen. For the natives of Anieth, the five-pointed star was sacred, not just as a symbol of Argeya who ruled the skies, but because it was a coordinate system. You can see the stars laid out on the next pictures, but this is just to show you the basic coordinate system laid out in every observatory in Anieth. It was marked out in some kind of stone on the floor of a wide circle, usually on a hilltop. My own observatory at Taranhai, looked like the mountain had been sliced off. You can see the pentagon in the center for the stars sacred to the goddess, wrapped around by the five points of the pentagram for the five main calendar stars. These stars tend to vary a little with each Nation and Clan. The outer two segments, on the outer pentagon are the stars lesser to the Nation or Clan, but still part of the system of twenty stars. This stellar system was nineteen calendar stars, plus "one" for the Nation's own mascot star that was mythologically tied to their patron Animal and Tree Clans.

For those of you who are scoffing because this system is not "logical," place it in Terran time, congruent with coeval cultures. The Babylonians came a bit after Anieth, but their own system is still carried in our mythology, of Gilgamesh and his journey. Many of these "stellar" myths are calendar myths of twelve, forced out of the sky into our version of the zodiac, the constellations of which do not cover their thirty degree segments around the equator in nice blocks, but overlap. Aries is a tiny constellation next to Pisces which takes up almost 70 degrees of the circle. The Chinese had twenty-four constellations for stations of the moon. This system predates Stonehenge by a thousand years. No system is perfect, even our "logical" one of 365.25 days for every year!

Here is an overlay of the star pattern upon the girdle chart. As you can see there is no neat fit of the stars into areas of the pentagram figure.

Here is the same star overlay is elongated a bit for you to see the stars beneath fit onto a map taken of the same sky an hour earlier. You can see that the stars rise and set at different areas on the horizon. In North's book, he plots the rise and set of different stars and gets an order. This order is mapped onto a circle that makes points from north to south that are mirrored on the other side. Arcturus, a circumpolar star makes a complete circle, just touching the north horizon. Acrux, the star farthest south had vanished fifty years later and barely cleared the southernmost tip of the map. The rest of the stars describe arcs across this map. The stellar mnemonic is a map of the order of these stars superimposed upon the relative positions when the girdle is visible on the horizon. The fact that it also coordinates loosely to the spirals is just gravy, as we say.

Here is a generic version of the map. Sirius, Rigel and Procyon are swapped. In many of the maps of the different Clans and Nations, stars are swapped from ancillary positions into one of the main points of the star. Sometimes the inner star is swapped with a point star. This is made clear on the Calendars pages, but for brevity, it is because the mnemonic is used in different ways depending on the rising of the star, the time of year, the star the observatory reflects, etc. This complicates the memorization, but makes it possible for the Hazel to modify the original format to fit each Nation and Clan that they track.

Here is the translation of the main stars into the language of the Tualárach. The stars have slightly different names in the Wood. There is a push from the animal constellations of the wood to the god constellations of the Zelosians, and the Horse People fall in between, just as they do religiously. I was able to observe, even in the constellations themselves, the transition from an animistic society to a theistic society. But for our purposes it is only important to know that the star names are different. The constellations are different. Instead of Canis Major and Sirius, the Horse People saw a bear with Sirius being its heart (Croí). Instead of Geminii or the Twins, the Horse People saw the Speakers, and the Wood Clans saw the Otters.

Here is the mnemonic with another, verbal, mnemonic imposed. The verbal will not agree because it is based on the constellations with some variation. Note also the swap in the vowel with the M consonant. This is a regular variation and is explained at length on the Calendars page. Those of you who have studied Ogham will start to see a pattern here. The star maps of Anieth are based on the same principals of Oghams, which were secret codes often corresponded to trees, animals, plants, colors, etc. It is part of the "llavar cudd" or the secret tongue spoken by the Celtic nobility that was wiped out with Cromwell. The Horse People lost their llavar cudd with the Zelosian invasion.