The Geometrical Principle of Formation of Aspects

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THE GEOMETRICAL PRINCIPLE OF FORMATION OF ASPECTS

Dane Rudhyar

When on April 12, 1962, the first man to orbit the Earth - the Russian astronaut Gagarin saw our globe from a distance he was able to perceive the planet as a whole. He saw it as a spherical object. He, and through him mankind, had gained an objectively conscious, direct and visual experience of the wholeness of the Earth and, as a result, of mankind as a whole. One can never gain a truly objective awareness of that within which one is still enfolded. One needs to be distant from it, even if only for a moment, in order to gain a true perspective on its existence - and gradually to understand and evaluate it dispassionately in clear consciousness. One can then return to it with a new and realistically concrete image of what it really is.

Consciousness - as we understand the term in the Western world - begins in separation. It may be fulfilled in eventual identification, but only at the end of a process made possible by the gaining of a sufficient perspective. The development of consciousness begins with the realizaton of duality. The whole to which a man belonged by birth and which enfolded him like a womb must be sundered. The circle of unconscious prenatal wholeness must be divided into two halves; and this division must be directly perceived, felt, experienced: I and the other, I and the world.

This experience may be long in coming, even if it may be foreshadowed by intellectual realization and temporary emotional feelings of loneliness. Its meaning is never fully realized until the instinctual-emotional drives of the physiological and social natures of man have reached either some kind of fulfillment, or have led to a total breakdown of one's relationship with the society and culture which had enwombed the first part of one's life. These two alternatives are characteristic of the astrological aspect which we call an "opposition," and the Full Moon is the archetypal symbol of such an aspect. The opposition aspect at the same time ends a period of growth and starts a new process of objective conscious realization. It is essentially a mental process - indeed a process of rebirth at a new level. The physical organism (or any kind of relationship) may begin then to disintegrate; but in counterpoint to this disintegration, consciousness develops and slowly matures at the ideological level.

The beginning of the Sixth Century B. C. particularly in the person of Pythagoras marks "the end of the archaic ages." The Greek civilization brought to this present mankind - there may have been other mankinds very long ago a capacity for objective and rational consciousness. It also developed a worship of the human form as a symbol of the wholeness of Earth-existence. Pythagoras and other Greek philosophers of his time stressed the symbolic and indeed sacred meaning of geometry, inasmuch as geometry is the science of form-in-space. The perfect cosmic form being thought to be the circle, other basic forms were seen to be derived from it. They were derived through a process of division and differentiation.

The fecundated ovum, origin of human existence, likewise divides itself into many cells, through a process of self-multiplication. The whole becomes the parts, which nevertheless in their togetherness remain the same whole in a multitude of differentiated aspects.

This is the process which today is usually considered to be the basis for the generation of astrological aspects; yet such a process does not account for the quincunx (150 degree) aspect, which only belongs to the "involutionary" series of aspects, as we saw in the preceding chapter. Dividing the circle into two accounts for the opposition. Dividing it by three produces the trine - by four, the square - by five, the quintile (72 degrees) - by six, the sextile - by seven, the septile (51 degrees, plus an endless series of decimals) - by eight, the semi-square (45 degrees) - by nine, the novile (40 degrees) - by ten, the semi-quintile.

Actually if we consider the characteristic meaning of this process of dividing a whole circle into refers to a process of exteriorization and concretization. Is this process "bad"? It is so only from the point of view of the single entity, or (in Christian terminology) of the Soul that loses its "purity" and in a sense its wholeness when it "falls into matter"; which means, when it becomes involved in relationship.

The OPPOSITION aspect refers to the conscious facing of existence, and therefore of relationship; for there is no existence without relationship. Most individuals rush into a variety of relationships without consciously facing them; they are drawn into them by biological and psychological needs and wants, by "Karma," by complexes and illusory dreams. It is only after many things affecting a relationship have occurred that finally the individual faces up to it and discovers its real meaning and value. This confrontation in full awareness may result either in fulfillment or in an eventual breaking-up. In other words, the opposition exteriorizes and makes actual a capacity for consciousness which was only latent or unclearly expressed in the participants in an existential relationship. The relationship acts upon its participants; it may transfigure their lives, or separate them. It may produce illumination in consciousness, or frustration and bitterness.

The SQUARE aspect is produced by dividing-by-two the two halves of a whole circle. It refers thus to a further stage of exteriorization and actualization; it carries the process begun by 2 to an even more evident and concrete phase of operation: What this may mean is that, if number 2 (the opposition aspect) represents a confrontation, number 4 (the square aspect), symbolizes a condition of existence in which the results of this confrontation have become either set into a definite form or have led to a clear-cut crisis impelling or compelling action of a definite type.

We can think of an opposition as an international conference in which the diplomats of two nations face each other trying to resolve a basic conflict in policies. If the conference leads to an agreement - caused by a realization of the interdependence of all groups of men - a treaty is signed which sets down, or crystallizes, the good will having been generated, and embodying it into some plan for action. If, on the other hand, the conference breaks up and the conflict of interests or ideologies cannot be resolved, the next move may be mobilization for war.

If we are considering an entire cycle of relationship, from one conjunction to the next, and if we compare the "waxing" square of the first hemicycle to the "waning" square of the second hemicycle, we should realize that while these two squares refer to moments of crisis, the meanings of the two types of crises are basically different. The waxing square represents essentially a crisis in spontaneous, self-exteriorizing, impulsive, bodybuilding action, while the waning square refers rather to a crisis in the building of a form of consciousness which would be the foundation on which a new cycle of activity can start. The waxing square deals with the process of establishing oneself and one's basis for action in the community within which one was born; the waning square refers to the process of giving - as the result of a confrontation in relationship - a more or less permanent form to an experience of meaning.

Let us consider the Jupiter-Saturn cycle which began in 1940-41 as the United States under President Roosevelt was preparing for a nearly inevitable participation in World War II. When the waxing square of these two planets occurred in 1945-46 our nation was triumphant and trying to establish its new leadership in the international community on a definite military and financial economic basis. This of course polarized a similar attempt by Soviet Russia, and the "cold war" was the result. The waning square occurred in 1955-56 and it referred to a far different social and international situation. The McCarthy era was closing. The U .S. Supreme Court had ruled school-segregation unconstitutional and that event - an ideological decision - led to a series of physical actional developments which were to be characteristic of the next Jupiter-Saturn conjunction beginning in 1960. A new type of consciousness was, as it were, triggered into being by a revulsion against McCarthyism and the old failure to assimilate the Negro people as firstclass citizens. A comparison between Soviet Russia in 1945-46 under a victorious Stalin, and the same country under Khrushchev' s process of deStalinization would also be significant - also between the defeated and bitter France and Germany of 1945 and these two countries beginning to cooperate in terms of the idea of European unity.

The SEMI-SQUARE is the result of a further process of dividing-by-two. If there had been "mobilizaton," then comes "action." If one considers an electro- magnetic field it appears that the 45-degree angle refers to points of maximum dynamic intensity. We are dealing here with an eight-fold pattern, and the number 8 has been in many mythological and Gnostic systems related to the Sun. The semi-square should not be considered as a' "weaker square"; it exteriorizes within definite limits the dynamic quality of the square. At the waning semi-square of Jupiter and Saturn, Fidel Castro was on his way to establish a new government in Cuba - an event which deeply affected the future Kennedy Administration. The old cycle of social-political and economic developments was breaking up, and revolutionary forces were released in preparation for a new cycle.

The number 3 symbolizes all modes of expression and activity which have polarity as a basis, but in which polarity is transcended through understanding and often through some kind of "vision." No conflict can be resolved harmoniously unless a "third factor" is present which, because it can encompass the two poles of the struggle from another "dimension," is able to see the meaning and the value of the confrontation. This is why when a man and a woman unite in matrimony according to a truly religious ideal they are expected to realize that a third factor is present in their union. In a transcendent sense this invisible "third" is God, or in more mundane sense society or the human race as a whole. It is also the potential child which will in due time bring the conjugal relationship to the level of a family relationship; and at that level, social and cultural forms are basic. The coming of the child involves the two participants in the conjugal confrontation and interaction in the wellbeing and the future of their culture and society - and, in some cases, even if there is no child, the third factor may be a social, cultural or spiritual work undertaken in a community of understanding, efforts and goal.

Real consciousness is always awareness (the opposition aspect) plus understanding and the sense of value; the TRINE is an aspect of growth in understanding. What has been "seen" in the opposition phase, is now understood because it is related to a larger frame of reference. The vision or intuition becomes related to the collective mind and to the values of the culture; it can then be expressed and formulated by appropriate symbols and words.

When the trine is reached during the involutionary first half of the cycle, what is being established in concrete substance reaches the point at which it can be felt or comprehended as a whole; the general purpose of the instinctive impulse born of need and desire begins to be realized; an appreciation of beautiful proportions is emerging. The technician or mason can become, to some extent at least, philosopher and artist. Interpreted in terms of the evolutionary second hemicycle, the trine refers perhaps to the formal systemization of an intuition, or to the final harvest of a truly fulfilled relationship.

It is because the trine refers to a process of growth, expansion and understanding that it is considered usually the most "favorable" of all aspects; yet an abundance of trines in a birth-chart often means an over-idealistic or dream-like nature or a type of mind which is too satisfied with pure abstractions or generalities and not enough focused upon practical applications. The 40-degree aspect, NOVILE, is the further expression of the dividing-by-three process. It should be considered to deal with a process of gestation by means of which the idea or the beautiful form is brought to a condition of organic viability. The 40 weeks of pregnancy, the 40 days in the desert, or 40 years in captivity refer actually or symbolically to such a process. However, if this aspect is used - and I believe it certainly should be in Humanistic Astrology - it has to be exact within one or at most two degrees.

The SEXTILE aspect, if considered in terms of the geometrical formation of aspects, has an ambiguous character; for it is a trine divided in two. In the sextile therefore two processes are combined: division-by-three and division-by-two. The latter refers to the exteriorization and practical application of the results of the former. The sextile has a character entirely its own. It is the most "constructive" or organizational of all aspects, and the most practical. In the zodiac Fire signs are in sex tile aspects to Air signs, Earth signs to Water signs; these two categories of signs are in a much more constructive relationship than those belonging to the same "elements," because the relationship is a productive one.

The SEMI-SEXTILE brings the process of dividing-by-two still a step further. A masculine sign is linking a semi-sextile relationship to a feminine sign, for instance Aries to Taurus. The principle of productivity is brought down to its most basic components, polarity and sexuality. We saw that the 30-degree aspect represents the fundamental step in the involutionary series. According to Greek philosophers the universal Whole was symbolized by a dodecahedron inscribed in a sphere. Here we find the basis for the concept of twelve-fold internal bio-psychic and universal or occult organization, in its most intimate manifestation.

With the QUINTILE aspect (72 degrees) we come to the process of "dividing by five." The number 5 stands for the creative mind which is the truly "human" principle in Man (in Sanskrit manas). The five-pointed star is traditionally the symbol of Man, who is able to transform his environment - for better or for worse! according to an "idea" or an impulse to action. A quintile aspect between two planets shows that the relationship between them can become a source of personal or social-cultural transformation.

As this power of creative - and negative or essentially destructive - transformation is not operative in the majority of human beings, content as they are to conform to what is around them or in them, quintile aspects in a birth-chart may refer only to latent, never really actualized, powers in the individual person. However, by the term, creative, I do not mean "artistic." A person is creative to the extent to which he can impress his essential individuality upon that with which he comes in contact. A statesman who successfully imparts his ideas or purpose upon a nation is far more creative than a second rate artist or novelist who only "produces" forms according to the standardized procedures of his society. The quintile may refer to "genius," but one can say that every man has potentially a genius of his own, or a certain type of creative imagination thus, a strictly individual way of meeting life situations and interpersonal relationships. But he may be afraid of using it, or too lazy to do so.

The SEMI-QUINTILE aspect (36-degrees) theoretically refers to the operations by means of which genius exteriorizes itself - thus, in a general sense, to "talent" - i.e., to the technical ability to give a concrete form to creative impulses.

With the SEPTILE we reach the first mode of division of a whole 360-degree circle which does not produce a "rational" number - i.e., 51.4285714 etc. Because of this it has been associated with irrational processes, compulsions of fate, sacrifice. If two planets in a birth-chart form an aspect of 50 to 53 degrees, the bio-psychological functions which these planets represent may serve as channels for the performance of actions which either are not acceptable according to the definite norm of social-cultural behavior in the person's environment or class, or else which can be interpreted in a super-personal sense as acts compelled by a collective need, an occult power, or fate; and these may lead to "sacrifice" and a symbolic life. For instance, President F. D. Roosevelt was born under a septile of Mars retrograde to Saturn, and one of the Moon to Neptune and Jupiter; Lenin, under a septile of Jupiter to Uranus (a fine symbol of revolutionary activity, upsetting the traditional Jupiterian social order); Edgar Allen Poe, who was the source in America of fantastic, drug-inspired literature, and of the murder story, has in his birth-chart a septile of Sun-Mercury to Neptune.

In concluding this all too brief and sketchy study of astrological aspects, I should stress again in a somewhat different way what I regard as a most important point. In Humanistic Astrology one should approach aspects in a birth-chart in a manner different from that required for the study of transits and progressions. The reason for this is, of course, that a birth-chart represents an "archetypal form" - a space factor - while transits and progressions (including solar and lunar returns) deal with time-sequences.

This basic distinction can be illustrated by comparing the portrait of a person made by an intuitive and talented painter, who has sought to evoke by his painting what he feels to be the individual character of the person, with a motionpicture taken of the same human being as he goes about the business of daily living. This illustration, for many reasons, is far from adequate but it may have some value in stressing a basic fact. A birth-chart is a static factor. It refers to whatever it is in an individual person which remains permanent from birth to death; we may call it man's "identity." Because it is a static archetypal factor it should be studied from the perspective of space. It is a geometrical pattern; but one which has a very specific meaning. I have spoken of it as a mandala - a hieroglyph basically constituted by a circle divided by a cross, and with planetary symbols scattered through the chart, or concentrated in some section of it in such a manner that a basic over-all design emerges from the whole figure.

When, however, we deal with planets and/or "angles" in motion, year by year, or day by day, we are studying something that belongs to a basically different level, i.e., to a constant process of change. This process is cyclic. Planets return by transits to their natal places; the progressed Moon returns to its natal zodiacal position in less than 28 years. Solar and lunar returns - and also the return of conjunctions of Jupiter and Saturn, of Mars and Venus, etc. - mark the beginnings of various cycles. But these beginnings merely outline patterns of wave-interferences, nodal points in the continuum of ever-dynamic, everchanging existence.

It should be obvious, at least from the point of view I am presenting in these essays, that we cannot think of interplanetary relationships in a birth-chart in the same way as we interpret them in terms of cyclic changes; and this is the basic reason why astrological aspects should be interpreted as parts of two series: one which represents a series of steps in the development of the lifeprocess from potentiality to actuality, the other which refers to a mental and objective picture of totality - which means to the "meaning" of the whole chart.

The opposition aspect represents, symbolically at least, the moment at which such an "objective structure of totality" is most likely to appear in terms of the relationship between two planets. It is particularly important in the case of the soli-lunar relationship, because the two Lights refer to the bi-polar life-force which sustains and feeds the whole organism, psyche as well as body. In a most general sense, and if we think of the entire life-span of a man, he who has experienced much of life and has enjoyed and suffered through a variety of endeavors and attempts at self-actualization should come at his life's mid-point (a symbolic Full Moon) to "see" vividly the picture of his own totality and identity - what I have called his "celestial Name." He should apprehend this entire celestial picture in an "esthetical" (i.e., holistic) act of perception, thus in terms of meaning and purpose.

Astrological interpretation is, in this sense, a process of "revelation." It certainly should not begin with the analysis of separate features, even less with the listing of data taken out of the ancient aphorisms or modern textbooks. The Buddhist monk meditates on mandalas in which are symbolized various processes of consciousnessunfoldment, various complex relationships between dynamic forces within organic wholes, be they human or cosmic. What one meditates upon is "Form." Meditation thus partakes of the nature of the truly esthetical experience. The Form "speaks" to him who faces it with an open and alert mind, a mind able to "see" even more than to cogitate.

It is difficult to teach this language of Form. One can only gradually develop the special ability to understand it by constant practice, and above all by maintaining a "holistic" attitude to any and all experiences. This implies the development of a new type of mind-perception and of a "resonance" of whole-being to whole-being. But resonance does not mean identification, anymore than empathy implies union! What is primarily involved is, I repeat, a sense of Form, and a capacity to respond to the totality of any lifesituation, rather than to study analytically and piecemeal various particular characteristics. Yet some of these characteristics may give essential clues to the whole situation, provided they are referred at once to this whole situation rather than perceived as things in themselves, i.e., as unrelated individual factors.

The essential study is a study of relationships, a study of the structural character of the interrelatedness of all the components of a whole whether it be a whole life-situation or an individual person. And this is why the study of astrological aspects is essential in a holistic interpretation of a chart. What is to be learned, however, is to apprehend at once the total pattern of interplanetary relationships, and to respond mentally and intuitively to its meaning in terms of the fourfold and twelvefold structure of astrological space defined by horizon and meridian.

I shall leave to the next essay in this series a more detailed discussion of "planetary patterns" and their general meaning in the interpretation of a birth-chart.

Person Centered Astrology