Considerations & the Asymmetrical Universe

When we begin studying astrology, we tend to think of it as this perfect and harmonious thing in front of us, but we forget that things may seem perfect, but deep down there is always an asymmetry that is not instantaneously recognized. We tend to think planet Earth as a perfect rounded planet. The year has 365 days, while the Zodiac wheel actually has only 360° degrees. Then comes the Humans trying to fix and fit into our reality – Each 6 years, as we “invented”, occurs the ‘leap year’, in order to adjust/correct the ‘asymmetry’ of our solar calendar. Things and people are not perfect, but they indeed can be similar to the idea of what is, always attempting/adjusting themselves to approach perfection in a general sense. The Zodiac on paper is/was designed for practical reading or visual approach and dynamical yet limited to a 2D attempt, where it happend that many astrologers forget that we are actually seeing an interface of a 3D mapping, full of astronomical imaginary circles and constellations, and for predictive work, a natal chart alone is nothing but the beginning of a true enigma.

 

The Imaginary Symmetry of the Zodiac

Charles Robert Darwin [Saturn in Sagittarius], an English naturalist whose scientific theory of evolution by natural selection became the foundation of modern evolutionary studies, at first shocked religious Victorian society by suggesting that animals and humans shared a common ancestry. Darwin was studying the “entire Zodiac” if you look closer enough, the circle of the little animals! We compare our lives to the figure of animals from above [constellations], and we instinctually know we indeed share behaviors alike in many ways. Darwin’s other grandfather, Erasmus Darwin, a freethinking physician and poet fashionable before the French Revolution, was author of Zoonomia; or the Laws of Organic Life (1794–96). Carl Jung also had his discussion published [Man and his Symbols] on humans and their “animal spirit”, pointing out the cultures of the past and their religious rituals imitating animals from Earth. 

The Zodiac [zōdĭăcus] has such name because of the prevalence of the animals on the ecliptic, it seemed obvious I guess. The Zodiac belt also has humane figures [Gemini, Virgo, Aquarius and first half of Sagittarius] and inanimate objects such as the sign of Libra [scales], or, if you dig deep enough, there are less popular representation like the 2 identical Towers, or Pillars of Society that is known as Gemini the twins [1st humane and air sign], the Aquarius’ barrel, Sagittarius’ arch, Aries’ fountain of life, Saturn’s scythe, Neptune’s trident etc. – indicating the need of Human intervention, our conception of the world and power of observation, not to mention humans’ need to control/manipulate over or own the animal kingdom. A Radix [root] is a sort of a blueprint of the universe at the time you [or an event] were [is] born – with you or the event at the center of the univere.

Like a fingerprint pattern in all humans, your chart [radix] is unique. The attempted symmetry and natural patterns we can find in astrology are “imaginary” and for a good purpose, yet they are both based on astronomical observations and philosophical/alchemical. The Zodiac wheel has been well adjusted throughout generations of astrologers to fit our reality the most perfect as possible, yet what is perfect for me may not be perfect for you, thus many discussion on House Systems – but it will never be that perfect and you know why? Otherwise, the “game” would be a total spoiler, and what’s the fun in that? The next breath will never be the same like the last, suppose the matrix changes its “code” each time – the quality of everything changes each second. As the day progresses and the diurnal Arc of the Sun in sequence completes full journey around the ecliptic [daily revolution], it means it is done in real time [with your chart as well] and ready to move on to another day – what was yesterday will never exist like it again, perhaps quality alike, but never the same day. That makes astrology so satisfying to study, to predict events, read people, etc. exactly even more when our predictions worked some way or another.

Why imaginary? First, we simple imagine there is a Zodiac belt in the skies, the same with the meridian and horizon circles, and for the sake of simplicity, we put ourselves at the center of a circle in order to visualize and grasp the concept faster and easier while turning the skies into a 2D figure and make the circles simple straight lines, we learn this in school, not a mystery – not to mention we imagine the Sun is moving [in order to vizualize the Ecliptic] when is actually planet Earth. Now, of course there is this attempt to “perfection” in nature, like the instinctual food chain found on animals to keep the world moving on organically, the Sun “giving” us food and the Moon keeping the water down to us, the seasons where we witness the death of nature followed by its powerful rebirth; the animals that resemble our behavior while many were well designed and adapted to this world more than humans are, like their higher and acute senses, physicality to fly or to breath under water, and not to mention durable length of life; Weren’t we also some kind of higher intelligence intervention in some period of Human’s history? Where do our intelligence and intentions come from? Supposed the Aquarius sign is actually an extra-terrestrial being pouring us down over Earth, or some kind of intercession? The Fibonacci forever sequence of the so-called golden ratio of 1.618 [often called as The Most Beautiful Number In The Universe] – nature patterns include the trees, spirals [cauliflower; Pineapples and Bananas; also Galaxies] and continuous or discontinuous curvature, meanders, waves, foams, tessellations, cracks and stripes – As if nature is secretly telling is that there is an order behind the scenes, and that seeds of a team’s design [?] had been poured down to this planet Earth intentionally and let them evolve from there and see what happens.

Perhaps if we were perfect as humans, we probably would look like shinning but indestructible porcelain dolls, unable to evacuate or pee because there would be no need once food and water wouldn’t be necessary, we would never get diseases while living in a continuous state of orgasmic ecstasy, and we wouldn’t get old too soon or even die. Life would be a real “PlayStation”. But no dear, life is hard, we go through surgeries and get nasty sicknesses, painful development process, we bleed and it hurts, we get very old in such a short span and we die, not to mention the sheet we signed up for. In between the time on Earth/Gaia, humans will try to look out for things they lack which bring them closer to symmetry or excellence/mortality, panting here and there as they/we find it fit. We can only do, but to rely on creativity, technology and evolution of the human body to also fulfill our instinctual need/desire to perfect. Reminding the reader that Astrology is also some kind of ancient technology.

To picture a clear image, it is imagined a 360° degrees circle, and yet many didn’t or don’t see the design of the wheel/circle as a circle, but of a square. My thought is that some cultures they indeed used the square chart because the symmetry of astrology is found on the degrees of the Zodiac – in a whole house system for example [House by Counting], the meridian and horizon will always square exact, the grand cardinal crux/cross, that is, they viewed life as serious and hard [square], I guess they couldn’t imagine the chart being a circle once it suggests exactness [no corners, no beginning or end], a loop or a revolution, but rather then something to be fixed, questioned and cross-examined. On the side note, I still use the circle because I am used to and I think is more practical than reading a chart through a square.

 

The Aspectual Polygons

Now, it is not just your normal kind of circle, it is a diagram that can easily turn into graphics and calculations. The thing is that you can’t actually predict from a circle, again, it has no beginning and no end. In order then to grasp they needed interposition based on polygons [math mediation]. Ancient astrologers knew well the difference between the Degrees of the Zodiac wheel and what Aspect meant. In the course of time, The Zodiac is/was pictured with points [sides and eventually degrees] within the signs of the “invented” precious wheel of life. We can imagine the Zodiac being anchored by/of Polygons, and polygons can’t have curvature neither can be opened, as if chains were in there securing the segments’ endpoints, or, they are the points themselves. Polygon comes from Greek where “Poly” means “many” and “ Gon” means “angle” = many angles. Astrology dwells with angles [or, the four corners] of Earth. A convex polygon has no angles pointing inwards, or, no internal angle can be more than 180° degrees [opposition aspect of the degrees in the “circle”], otherwise it would be concave polygon, which indeed can happen when the complex irregular star polygon [5 points connected – the pentagram] is formed in the chart. Since the belt of the Zodiac is imagined as a circle englobing around us at the “center”, it suggests that points and regions in that huge polygon shape in the skies will be looking at others’ points/regions eventually, making connections in a symmetrical format. 

Aspect is sign based, followed by the imaginary segments adjoined from the vertices of a Polygon in relation to others regions, while the degree to degree is based on the connection of the planet(s) along the ecliptic. Thus, the Moon does not aspect Saturn [alone], but the Moon at 10° degrees Aries will square Saturn at 10° degrees in Capricorn. They will only really square in the Zodiac if they share a connection of 4 signs apart from each. Then, the Moon in 29° degrees in Aries will not exactly square Saturn at 00° degree Aquarius, once by sign they are already considered a sextile by then. But that won’t mean it will not have signification altered, but perhaps reduced in power once the planets [sometimes for the better] are not sharing 4 signs apart anymore but 3. The house is huge and from one room to another, a body may take a while [or, its own time]. Note that althougth Sextile are beneficial and helpful Aspect, it is considered the “weakest” of all the classical Aspects, yet decidedly significant. Now, as for Conjunctions in different signs [out-of-sign], they can’t really form a joint anymore, they are now sharing a sign where they are in Aversion to. Again, that won’t mean it will not have signification altered, but perhaps reduced in power, or less powerful than a real conjunction of planets sharing the same Zodiac sign would – the planets had already being separated by an enpoint and a new house was presented to the planet, a new segment/sector, or a new theme and decoration which already begins from the entrance door.

An Aspect actually means to look at something else besides the sign itself. Thus a Conjunction is not an aspect, there is nothing to look out for next, and it’s more a conjoined thing, a team, or union of bodies, a specific point/region of meeting of planets. The Oppositions on the other hand are the signs, points that share the same Axis and competing the half of a circle itself, thus looking at each other right face to face [2 points formed in an ultimate interval of 180°]. Conjunctions and Oppositions are considered the major astrological configuration among planets and the degrees of the Zodiac wheel. Such can be considered either detrimental/harmful or of great advantage.

To form a Real Regular Polygon you need at least 3 points and so forth. It all begins with the number 3, the equilateral triangle [Trigon] of 60° interior angle , astrologically known as the Grand Trine [60° + 60° = 120°]. 3 signs having the greatest time [resembling as observed from our point of view the 3 “closest” bodies: the Sun, Earth and the Moon]. Then the polygon moves on the 4 sides, the quadrilateral [Tetragon], astrologically known as the Square Aspect, the Grand cross [or, 2 Axis crossing each others’ path supported by 2 oppositions] where exact 4 signs are 90° degrees apart having hard and difficult time.  Now, if you keep “opening” the regular polygon with exactness as astrologers look foward or is expected to, the next would be the 6 sided Hexagon of 120° interior angle, the shape of the astrological aspect Sextile [120° – 60° = 60°] – These polygons can also be found in nature, for example the honeycombs, snowflakes, Saturn’s top are a sextile, or, a 6 sided Hexagon polygon. 6 signs [or, half of the Zodiac Signs] having a blast in the Zodiac wheel. Inside this shape, we find not only signs socializying greatly, but supported from signs in trine to each other – Sextile Aspect is considered some sort of a kiss from heaven.

 

Sextile – 60° + 60° + 60° +60° + 60° + 60° = 360°
or 6° x 60° = 360°
Square – 90° + 90° + 90° + 90° = 360°
or 4° x 90° = 360°
Trine – 120° + 120° + 120° = 360°
or 3° x 120° = 360°
Opposition – 180° + 180° = 360°
or 2° x 120° = 360°

 

Thus far, #2 corresponds to a Zodiac sign each Axis’ extremity, #3 is related to the 3 modalities [triplicities] of the Zodiac signs [cardinal, fixed and mutable], #4 to the basic 4 elements [quadruplicities] fire, earth, air and water – informing their direct experience/relationship with each other at the most essential level as possible. There are #6 pairs of signs where its totally is known as the Zodiac. What happen when 2 planets share the same Axis [opposition]? What happen when a planet at a certain degree looks at another planet in the same modality [square]? What happen when you have 3 planets in different signs but same element [or 120° apart – Trine] or planets in 3 to 3 signs [sextile]? 

 

Quadruplicities – The 3 Modalities & 4 Signs

Cardinal [Movable] Signs – Aries, Cancer, Libra and Capricorn

Fixed [Static] Signs – Taurus, Leo, Scorpio and Aquarius

Mutable [Common] Signs – Gemini, Virgo, Sagittarius and Pisces

Triplicities – The 4 Elements & 3 Signs

Fire signs – Aries, Leo and Sagittarius

Earth signs – Taurus, Virgo and Capricorn

Air signs – Gemini, Libra and Aquarius

Water signs – Cancer, Scorpio, and Pisces

 

Supposedly then, the signs in Aversion to each are those which have no affinity at all, they simple don’t care or don’t see each others’ existence on/in the wheel/life – they neither add or subtract [?]. Note that in the case of the following sign, the Zodiac Sign in question will be ready to move on and no look back, like we do in life – As if the switching of the houses is distinctive enough to think “there is nothing there left or that interests me anymore – I’m done with it”.  In the case of Aries to Taurus for example, Taurus simple don’t support Aries’ rushy life, it will slow down everything Aries did or is doing and vice-versa. In the sequence of Scorpio to Sagittarius we can picture that a true Sagittarius would be so open about life like a book, whereas Scorpio would keep everything secret. 

Then comes the Pentagon, which can’t be an exactly what is known as an aspect in astrology once each sign is separated in intervals of 108° degrees forming 5 sides and is not exactly convertiable to the examples thus far, and although it is considered a regular polygon, the number bears no relation to the natural Zodiac neither does 108° degrees because these relationships and connections rely on exactness [60°, 90°, 120°, 180°] – With a “harmonic” quintile which interior angle is of 72° degrees, which is the division of 360° of the wheel to the proposed 5 points. I suppose it would really counts such if there are exactly at least 5 bodies close enough to these points, but why bother so much with just 2 bodies? Such quintile falls in the same Zodiac signs of the Sextile classical Aspect, and many ancient astrologers would not see that as something primary and major [see why ahead]. However we do find the #5 in many things in life, the 5 senses, 5 fingers & toes each extremity; in nature we can see it clearly in the echinodematas such as sea urchins, starfish, and sea cucumbers are five-actinomorphic – flower Petunia which is almost a perfect pentagon. Many modern astrologers go further and put “Inconjunction Aspect” into their astrology. If you want harmony and actual “Aspect”, Cancer will not “look to” [or, Aspect it] Sagittarius, once multiples of 150° does not fit into the symmetry of a polygon, thus not corresponding to modernly known as “minor harmonics”. 

 

Geometrical Astrology & Result of the Zodiac Signs as Aspects

By basing astrology on the ratio sequence, it means numbers, proportions and order matter; therefore the professional is expected to compare numbers by the same value, as #6 is part of #12, or 12 is counted 6 two times, or #3 is part of #9 once 3 is calculated 9 three times, etc. making it impossible for true harmonic aspects to happen after a sextile, had been practically “sealed” the signs and their kind of affinity to each. As we have learned there are 2 ways in order to judge affinities and direct approach of the Zodiac signs to each: part-to-part [degree-to-degree] or part-to-Whole [Aspect]. Like 7 days of the week, each Zodiac Sign looks to others signs in 7 [seven] orderly ways:

1 Opposition

2 trines

2 squares

2 sextiles

PLACE IN THE ZODIAC	OPPOSITION	TRINE	SQUARE	SEXTILE
1.       Aries [Asc]	Libra	Leo Sagittarius	Cancer Capricorn	Gemini Aquarius
2.       Taurus	Scorpio	Virgo Capricorn	Leo Aquarius	Cancer Pisces
3.       Gemini	Sagittarius	Libra Aquarius	Virgo Pisces	Aries Leo
4.       Cancer [Ic]	Capricorn	Scorpio Pisces	Aries Libra	Taurus Virgo
5.       Leo	Aquarius	Sagittarius Aries	Taurus Scorpio	Gemini Libra
6.       Virgo	Pisces	Capricorn Taurus	Gemini Sagittarius	Cancer Scorpio
7.       Libra [Dsc]	Aries	Aquarius Gemini	Cancer Capricorn	Leo Sagittarius
8.       Scorpio	Taurus	Pisces Cancer	Leo Aquarius	Virgo Capricorn
9.       Sagittarius	Gemini	Aries Leo	Virgo Pisces	Libra Aquarius
10.   Capricorn [Mc]	Cancer	Taurus Virgo	Aries Libra	Scorpio Pisces
11.   Aquarius	Leo	Gemini Libra	Taurus Scorpio	Aries Sagittarius
12.   Pisces	Virgo	Cancer Scorpio	Gemini Sagittarius	Taurus Capricorn

The mathematical intervention in astrology is somewhat “supreme”. When we speak of Aspects and degree-to-degree in astrology, we are talking about the geometrics of Astrology and the affinity of the signs of the Zodiacus. These classical Aspects values the harmonization of the signs looking at each and their relationship is considered only once [#1] and that’s it, which means a sign will look only once to another sign: for example, Cancer will look Virgo as Sextile and only that, and to continue, Cancer will look at Libra as a Square, to Scorpio as a Trine, Capricorn as Opposition and so forth with all the Zodiac signs. Simple put, signs looking from Trine and Sextile to others, ancients said to be loving each other, while signs looking from a square and opposition are said to be hateful and hostile to each. 

Ancient world would as well credit the planetary phenomenon concerning their idea of what an Aspect could mean. For example, the Opposition Aspect, you could simple imagine the Moon and its borrowed light from the Sun, which she will be only Full in light when she is Opposite it and never as a Conjunction when she is dark and likely invisiable. Or that she looks half-full when the Sun-Moon square forms in the skies etc. The ancient said the Square Aspect can be compare to proximities and change in motion – when planets reach a relative position in the skies that is their apogee, such planets will suffer alteration in motion by all intervals of 90° degrees from the distance of the apex. They also said that the Trine Aspect could be assumed by the position in the skies of the two superiors [Jupiter & Saturn] relative to the Sun, once technically when any of them distances 120° degrees from it, they switch motion’s status from direct to to retrograde and vice-versa.

Conclusion

The classical Aspects can’t be underestimated but better understood. The shapes may be elementary and rudimental, but if exactness you are searching, the symmetry begins here. The chain/points look at each other in a certain way which an irregular and concave polygon wouldn’t. Ancient astrologers then stopped there, no need to further/advance Aspects [signs looking with affinity at each], otherwise it would make the whole Zodiac solidly chaotic with no order, no signs in aversion [not looking at all] or looking badly to others, where everything is a party and everyone is drunk and happy while the circus is open. This sophisticated and beautiful sealed 360° imaginary wheel, the ancients divided the Zodiac signs where each sign or side of all regions of a shape to actually possess exact 30° degrees of longitude, making it possible to for an Aspect to occur within orbs of the planets moving on the wheel, or, to “look at”  from a certain region based on Zodiac signs, and to connect in exactness at beneficially or unfortunately level to another degree in a symmetrical way [orderly lines].

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References: 

Abù-Ma’shar – “The Great Introduction” translated by Benjamin N. Dykes, PhD [2020 – pages 30-35; 347; 425 and 443]

Saturn by Jenny Dusky

https://www.mathsisfun.com/geometry/polygons.html

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