by Gregorian Bivolaru
The revealed secrets of the Golden Ratio explain the Mysterious Intelligence of Nature and in the same time they allow us to discover the fascinating mysteries of the Divine Proportions.
Without a doubt all of us have wondered about the secret of beauty, harmony and diversity of the wonderful forms that appear in nature. Aren’t they governed by the mysterious Sphere of force of the Great Cosmic Power Tripura Sundari that only the initiates have access to?
Man has always asked himself these questions and through certain revelations offered to him in elevated states of consciousness, he thus obtained many stirring answers. In reality, all the amazingly beautiful creations of nature are manifestations of a divine harmony which makes us perceive intuitively that behind any form there is a constant necessity. From the Golden Ratio to the mystery of the beauty of the forms of nature, to natural selection, passing through genetics, fractal geometry and art, we offer you through this book new answers to this search, which is as old as human kind.
Many geniuses, visionaries with the eyes wide open and with effervescent minds, as well as many scientists aimed to decode the secret of beauty and harmony of forms in the natural world. Fascinated by the diversity of beauty and the harmony of all structures created continuously by nature – the shells’ spiral, the shape of fish or of the human body, etc. – the initiates, geniuses, artists, philosophers, mathematicians, naturalists, physicists or informaticians have always aspired to remove the veil of appearances. They were and are still convinced that eventually they will discover, beyond any manifestation, a mysterious general and generating principle, the universal law of natural morphology, the essential “formula” that creates the beautiful form: The Golden Ratio. This mythical number – The Golden Ratio– is in fact the expression of existence and manifestation of the secret Sphere of force of the Great Cosmic Power TRIPURA SUNDARI.
A divine revelation regarding the Golden Ratio
The Golden Ratio is the Mysterious number after which all species of life that have appeared in water, earth and air, were made. It is the same fundamental Number (?) that man was based upon and it is the same as the Number of Grace and Love and as the Number of Salvation and final Resurrection into Spirit.
Listen carefully and try to understand as well as possible that which no one until you has understood: this Golden Ratio is the mysterious essence of eternal Love. At the same time, it is the expression of Universal Order and of the Divine Law of Love, Order and Law which exists now and will always exist, forever expressing God’s beauty, greatness and endless power.
And then Love took ground, which was like the cream on the milk and, with the mysterious power of Her hands, kneaded it properly and made the first human out of it, according to the Golden Ratio of Her Order. Then, She blew upon him the Breath of Life. And Her Breath became Soul in the man, which spread immediately in man’s entire being, forever sealing his connection with the Golden Ratio of Order, after which man was created. But know that not only man was created after this Ratio, but all the spirits and all the worlds that exist in the Infinite Space (Macrocosm), including both the Earth, with everything on it, as well as the Moon and the Stars.
The words full of wisdom of Jesus Christ, dictated to the famous prophet Jacob Lorber.
“Everything is a sign. Moving from sign to the signified thing means entering the mysterious depths of the World, which reveals God.” Andre Malraux
In the western world, arithmological and geometrical symbolism is almost inevitably associated to Pythagoras’s name and to his followers, the Pythagoreans and the Platonists. Long after the age of the original Pythagorean schools, the so-called “mysticism of numbers” was highly cultivated in the circles of the cabalists and Christian mystics. It is a less-known fact that the Fathers of the Church such as Saint Augustine, Maxim the Confessor (see the Philokalia), or Christians such as Jan van Ruusbroec (1293 – 1381) believed that Numbers are symbols and paradigms of the Divine Principles.
For the Greeks, arithmology has a long history. It was studied and applied practically together with “the scientific number”, far from the market trade of the “vulgar number”, being respected as the pure science of the universal laws of the Cosmos.
Even today the idea according to which the laws that govern the Universe are “numerical” is very present, even if many claim to be more satisfied with “exact and scientific” formulas. Most of the time, the latter do not realize that the Numbers appear here also, though dissimilated. The difference is only in the language, because after all the Truth is only one. Thus, most of us remain fascinated by mysterious mathematical phenomena such as Fibonacci’s sequence of integers or Titius-Bode’s law of planetary distances (see fig 0.1). In ancient times, people tended to give special significance to Numbers, by analogy with the structure of the World, thus searching for a deeper meaning for all things and beings. Paradoxically, nowadays, when so many secrets of nature have been revealed and so many modern technologies have developed, yet we are flooded with spiritist and occult approaches, which popularize a pseudo-science of Numbers, full of superstitions such as “13 brings bad luck” and all sorts of mental patterns. In this mixture of contradictory information, many get the idea that the Pythagorean metaphysics of Numbers was just simple, ungrounded speculation, and the repeated warnings of Plato regarding an unwritten, oral, secret doctrine are hardly taken into consideration.
The natural logaritm of the planet's
period of rotation around the Sun
The order number of the planet
Fig 0.1 – In 1750, Titius and Bode discovered a simple law that made it possible to obtain a proportion between the measures of the planetary orbits. Thus, it starts from the numbers of the row: 0, 3, 6, 12, 24, 48, 96, 192 and 384 (we notice that starting from 3, the next term is obtained by doubling the previous one) and then number 4 is added. The resulting row: 4, 7, 10, 16, 28, 52, 100, 388 corresponds to the planetary orbits, except Neptune. The formula predicted a missing planet at 28 units between Mars and Jupiter. Later, on January 1st, 1801, Piazzi discovered the asteroid Ceres, the biggest one from the asteroid belt, which corresponds exactly to the missing planet.
History says very little about “the beginnings” of Arithmology; its method of study seems to aim rather to transmitting knowledge from one civilization to another, over time. But the spiritual approach is less concerned with the purely historical aspects, and more interested in the metaphysical principles and significance. Etymologically speaking, the word “beginning” comes from “in-caput” (which in Latin means: “in principle”, “in essence”). From this point of view, authentic spiritual traditions (and together with them the Pythagorean tradition, which Arithmology is part of) are asserted from the “in-caput” of the revelation offered by “gods” to a “founder”. The famous initiate Rene Guenon said that the Primordial Tradition is the divine, atemporal thesaurus of the Supreme knowledge, which nourishes all spiritual schools. Each spiritual school nuances it according to its specific time and place, but without altering its essence. This is where the confusion appears: according to certain thinking patterns, many would rather “somebody” “had invented” Arithmology (the Hindus, the Chaldeans, the Egyptians, the Greeks…), while all wise men say that it already existed in the mind of God, together with all the divine laws; “the founders” are those exceptional beings which (re)discovered it through the Grace of revelation. It is not by chance that we easily find the same laws of Numbers in the Chinese, Hindu, Egyptian, Greek, and Arabic traditions. In some situations the name is different, or the elements of the specifics, or at least the point of view. The correlations and analogies that can be made clearly reveal the common body of all doctrines: the Primordial Tradition.
The most convincing way to prove this is to aim at gaining some practical knowledge of Arithmology ourselves. Genuine individual search is the only way to experiment and understand, because we should not forget that “he who seeks, shall find” and “he who knocks, it shall be opened to him”.
In the following, we will outline some ideas and guidelines which, hopefully, will make us more pervious to the arithmological symbolism, at the same time revealing its intimate connection with the Divine Proportion.
The term “number” (defined through the word arythmos or rythmos in Greek) comes from the root rheo, which means “to flow”. In this way, it stands for the rhythm and vibration. Heraclites allegorical expression “everything flows” corresponds to the ancient Eastern saying “everything is vibration”. First of all, the Ratio signifies the steps of resonance or, in other words, of vibration of the Universe, which are manifested in the specific cycles of Multiplicity.
Within the Absolute or, in other words, within the Whole, the Number Decade is the archetypal cycle, the symbol of the non-separation between Being and Non-Being (associated to 1 and 0, respectively, in the arithmological symbolism) glyph of the perpetual return of things and beings to their Creative principle (One) and to the omnipresence of the Ultimate Essence (Zero), which sustains any emanation and resorption. Knowing this, we can correctly say that the Decade represents God the Father.
In this way, it resumes and synthesizes all the other Numbers (principles). Having this knowledge, the Pythagoreans experienced the living presence of the Decade in the world so intensely that they used to swear on Her Name. It is not by chance that Philo of Alexandria noted in “Quaestiones et Solutiones in Genesim”, 4.110, that “in the world as well as in the man, the Decade is everything”. With the same meaning, in the Pythagorean environment it was said that “the fundamental nature of the Number is the Decade”. The symbolic representation of the Decade through the ten points arranged in a triangular shape, called Tetraktys by the Greeks (see fig 0.2), is probably the most revealing manifestation that underlines the intimate connection between the Numbers of the decimal cycle. Paradoxically, its essential simplicity allows, among others, the understanding of the universal laws of resonance.
Fig. 0.2 - The Pythagorean Tetraktys
The point is the symbol of Unity, of the seminal principle of things. Therefore, the paradigm of the Tetraktys is that of the Decade of the first reflections of the emanating Power of God the Father. In this way it constitutes itself in an essential model, which reveals the intimate structure and the unity of all phenomena in the Universe to the one who knows the law of analogies and of subtle correspondences.
The Pythagoreans said that “the Decade is fulfilled by Four” (or, if we “develop” the metaphor, explaining it at length: the Decade is the fulfilment of a triangular growth in four steps), in this way outlining the fact that the fundamental cosmic cycles mutually sustain and generate themselves through the harmonious triplet of the process of expansion (emanation), balance (maintenance) and contraction (resorption); in such a vision, Four and Ten cannot be conceived separately. In fact, they are limit-thresholds of the unique Flow of the Divine number.
If we evoke some of the projections of this Archetypal Four in the world, we are amazed to find four seasons, four cardinal points, fours intermediary directions, the cross of the four elements, four ages of humanity, four fundamental states, etc. Thus, we intuit their mysterious and indestructible communion with the ten Great Cosmic Powers.
But, at the same time, we can see it differently: the Central point and the Cycle of its nine exterior points represents Transcendence and Immanence, Eternity and cyclic Time, which polarize each other and are always joined in the bosom of the Whole.
Seen from a different perspective, the tops of the big Triangle symbolize the Cycle of the three Worlds and the three bodies, the three phases of any phenomenon, while the six remaining points remind of the six days of the Creation and the six universal levels of polar vibration. The central point can be considered as the fixed FOCUS that governs the fundamental laws of Three and Seven.
We can continue the metaphysical and arithmological meditation indefinitely, because the correlations are many and all connect the Principle–Numbers into a Unique Flow, which converges at the Spring of Eternity. The simplicity of the symbol gives it force and magnetism which are worthy of Pythagoras’s name. At the same time, Tetraktys is the model of triangular “growth”, fruit of the transcendent Trinity, which thus contains, implicitly, the Secret and the Force of the Golden Proportion, which manifests as a perfect connection between any two things, as median or mediator term, as the core of all creatures.
Let us have a closer look at what it is that actually allows us to say that the Trinity and the Divine Proportion are so tightly united.
The term “proportion” comes from the Latin “proportio”, which has the same meaning as the Greek word “analogia”, which was essential in the metaphysic doctrine of the Pythagoreans. The etymologies of the two words are very helpful for understanding the original meaning of the concept of proportion. Thus, the term “analogia” comes from “ana” (which in Greek means “up”, “superior”, “corresponding to”, “which is reflected through”) and logos (meaning “raport”, but also “seed”, “germ”, “essence”, “word”). At the same time, the word “legein” is translated as “to connect”, “to unite”, “to gather”. In a metaphysical interpretation, we could say that what is up, in the world beyond, connects, gathers, brings back to the bed of the Primordial Spring – through the cause-effect relationship or even beyond the necessity – the fruit spread into the world of the Spirit. Thus, in a broader meaning, “analogia” signifies the similitude that connects and unites things and beings, the reflection of Ideas (infinite seeds) into the Manifestation, the law of the mysterious subtle correspondences between Whole and Part, between Earth and Sky, between Up and Down, between essential and substantial, between Macrocosm and Microcosm.
Fig.O.3 – The stages of the triangular growth of the Tetraktys
First Stage: a “little stone”
Second stage: we add a row with an extra “little stone”
Third stage: we add the third row and another “little stone”
Fourth Stage: the last one completes the decade (10 “little stones”)
In Latin, the term “proportion” (“pro” means “before”, “which offers grace and favours”, and “portio” means “part of the Whole”) refers to what is – ontologically speaking – before the part, meaning the Whole which sacrifices itself through partition and in this way it makes holy and divine the part it generated. If we look carefully, we notice that, indeed, the part is never separated from the Whole, like a wave that appears, for one moment, on the mirror surface of the Ocean, only to melt back in and to return to its Unique Plenitude. Analogically speaking, the proportion expresses both the uniqueness of individual manifestations (which can be seen as part) and the fundamental unity of the Creation (which can be seen as Whole).
The radical “logos” from the term “analogy” at the same time signifies the quantitative relationship between two measures, the actual rapport, so that the proportion is intimately connected to the equivalence of the relations. Here we make reference to the relation in the general understanding of the word, as being that which allows the perception of the secret connection between things, beings and ideas, in the vast space of the discriminating intellect.
For the Pythagoreans – philosophers, as well as mathematicians – the representation in numerical terms of the proportion was an enumeration such as:
1, 2, 4, 8, or, more generally, a, b, c, d,
which today would be written as the equality between two reports:
1/2=4/8 or, more generally, a/b=c/d.
In this way it is represented the fact that 1 is the same for 2 as 4 is for 8, and a is the same for b as c is for d, so that the rapport between 1 and 2 and the rapport between 4 and 8 is the same. At the same time, a and b are in the same rapport as c and d. Thus, the rapport between the consecutive terms of the proportion is the same and it underlines in a more realistic way the reflection, analogy, the “flow” of an identical secret vibration through the two rapport-relations, the one between 1 and 2 and the one between 4 and. Or, generally speaking, the relation between a and b and c and d. Of course, this flow is the effect of triggering a phenomenon of resonance, which tends to maintain the rapport between pairs of terms of the same kind. This rapport is the expression of a certain directive model, mirrored through a corresponding relation between the terms. Thus, proportion is intimately related to the phenomenon of resonance.
In Jesus’ parables we find a very good materialization of the archetypal model of proportion, which can help us understand it in a way, with an application in life. Jesus wisely pictured the law of karmic reward through the words “Do to people as you wish to be done unto you”, “He who lifts the sword, by sword shall he perish”, and “Give and it shall be given to you”, “It will be measured for you with the same measure you measure”, “Do not judge and you shall not be judged”, “Forgive and you shall be forgiven”, “He who sows wind, shall reap storm”. The old proverbs “Do good and you shall find good”, “You sleep as you make you bed” and especially “What you reap is what you sow”, also make reference to the same phenomenon. In any of these sayings, the maintenance of a certain relation is obvious, and of a certain proportion in the relationships between man and the world, but also between man and other people. Each one of them outlines the vivid way the principle of analogy functions. Thus, in the future, the others will behave towards us exactly in the way we behave now with the others and what we do to them, they will do to us. As we lift our sword against them, they will also lift the sword against us; as we give to them, they will give to us. In the same way, our attitude towards the others will be reflected in the other’s attitude towards us.
New Moon First Square Full Moon Last Square
Fig.0.4 – The quaternary division of the lunar cycle is one of the most known applications of the Tetraktys, seen as a 4 stage process. Each of the four stages of the Moon corresponds to the relative position of the Moon (seen from the Earth) in relation to the Sun. Thus, the New Moon stage corresponds to the conjunction (0º) Sun-Moon; the First and the Last square correspond to the two quadrants (90º) and the Full Moon corresponds to the opposition (180º).
In the sayings above, we have underlined the existence of a relation between “us” and “the others”, between “us” and “them”, exactly as before we had relations between 1 and 2 or between a and b. We notice that the divine laws (such as the karmic law) fully respect the principle of analogy and proportion: always, the karmic answer is proportional with our deed. We always obtain results according to the actions we have done. Everything in the universe “flows” according to the law of analogy and proportion. The “mathema”-tic model of proportion only establishes this universal truth through a symbolic mark, much more synthetic and concise and, necessarily, more abstract. It leaves us to awaken our attention more and more and to notice the overall presence of the proportion in our life. This will help us understand that nothing happens at random in the world, that everything has a cause and it is according to the divine rules. In this way, we will always be able to act correctly and to be perfectly integrated.
The proportion with four terms - a, b, c, d (which today is written a/b=c/d), which was called “disjunctive” by the Greeks, in fact represents the model of quaternary development, the model of projection of the Principle at the level of the Earth. The extreme terms (a and d) and the median terms (b and c are polarized two by two, complementing each other and at the same time being symbols of the opposite manifestations - “discordant”, according to the Pythagorean expression. The divine harmony naturally implies “the approval of the discordant”, meaning the unification of the polarities. Its model is that of One-into-Three, of the Middle - essence which unites the opposite ends (principles) through the law of Trinity. Here is how Plato introduces, in Timaios, the notion of ideal proportion, which unites three terms: “… it is not possible for two separated terms (and thus, broken from the Harmony of the Whole) to form a beautiful composition without a third. Because a secret connection must exist between them that brings them closer to one another. And out of all connections, the most beautiful is the one that gives the most perfect Unity to the terms it connects. This is the proportion that connects in the most beautiful way.”
The consonance between parts taken two by two and, respectively, between each part and the Whole, is thus the harmonious result of the connection of the things that make the Whole. Coming back to the proportion with four terms, complementary two by two, a/b=c/d or a, b, c, d, its harmonization is done through the fusion of the denominator of the first fraction and the numerator of the second into one unique factor of connection, according to the scheme of the middle, which unifies the extremities through the power of Trinity.
Thus, the proportion with four terms transforms into “continuous” proportion, with three terms
which, in an enumerative notation, becomes the series a, b, c. Here a and c are the symbols of the “discordant” terms, as the Pythagoreans call it, or of the polar opposed forces, of the complementary phenomena, feminine and masculine, Yin and Yang, + and -, while b is the symbol of the median term and at the same time of the essence which realizes the balance and the harmonization or the “accord of the discordants”.
Maybe many have wondered – reading about “The Golden Ratio” – why is it marked with ? and why it equals 1.6180339…, where does this value come from and what is the guarantee that beauty has any connection with it. The notation with the Greek letter ? (phi) was adopted as a sign of homage to the Greek sculptor Phidias, who was harmonizing the effects of his works of art using the Divine proportion. Regarding the numerical value 1.6180339…, it comes from the continuous proportion. The “Golden” proportion (and at the same time the most beautiful proportion) is, according to Plato, the one to which the “connection”, the median term, gives the most complete Unity. Here we speak about that ideal beauty that the Creator insufflates through the likeness with Him, meaning through reflection and analogy, to the entire Creation. Any emanating process starts from the unique Being of the Creator, which is also called the non-separated godly Whole; because of this, we will make a scheme of the calculation (symbolic, of course, and with metaphysical implications) which allows us to find what is, in fact, the numerical expression of the most beautiful, ideal, harmonious, perfect connection between the Creative Whole and the created part.
In chapter III of this book we will show (using the means of elementary mathematics) the way in which this condition of complete unity leads us to the Divine Proportion and to the Golden Ratio. Thus, these appear as being intimately related to the idea of middle and perfect mediation between two things (or two beings), as well as to that of core, essence which connects, knits together, unites. Etymologically speaking, the term “middle” comes from Latin (medius + locus) or, in other words, “the location” of the core, of the essence.
The calculations are not strictly necessary for understanding the idea of Divine Proportion. But they make the above principles more concrete in a numerical form. Those who have forgotten the way in which such calculations are made must only remember that the divine law of analogy and unity of the Creation – as well as the principle of Unity in Trinity exposed by Plato – allows us, as a concretely numerical application, to find again the value ?=1.6180339… Practically, all we do is rediscover the symbolic explanation of the reason why such a long line of Pythagoreans present this Proportion and this rapport (and not another) as the absolute canon of Beauty in a modern context. Thus, instead of being, like many contemporary “Pythagoreans”, just enthusiastic about the idea of Golden Proportion, we also have the metaphysical key of the principle upon which it is based, even if this is not in itself a demonstration with hypothesis and conclusion, as in academic mathematics.
Aside from this, we can also metaphysically interpret the fact that the median term of the continuous proportion is geometrical mean of the extremities (b2 = a.c). In this way, the idea of Unity appears more and more clear, expressed in multiplicative marking (which, symbolically, is the correspondent of the creative process that leads from Unity to Multiplicity).
The Law of Trinity governs Creation doubly: thus, we have a transcendental Three, immovable and unchanged, Three-in-One, which corresponds to perfect Balance, Stillness and Repose and actually constitutes the archetypal Unity and Harmony of the principle, in which no part is separated from the Creative Whole; at the same time, we also have an immanent, dynamic Three, which expresses the growth and asymmetric Movement of life in Manifestation through the number ?, constantly related to the unchanging Pole of perfect Divine Harmony and Symmetry.
The Divine Proportion exactly reflects that unique superior force which creates and in the same time reabsorbs, which gives life and destroys, which materializes and sublimates, which ascends and descends, which unites and divides, most often represented through the model of Three in One and of One in Three of the Holy Trinity. This is present in Christianity, in the Sri Vidya tradition or in the Trika school of Kashmir, in different specific visions, of course, which can not be assimilated or overlapped mechanically. The divine Logos, the secret creative Word, is the median term, therefore being represented in manifestation by the Golden Proportion. This can be understood as the vivid, all-present and perfect connection that mysteriously governs all harmonious relationships. Philo of Alexandria said very beautifully that “God the Father gave Logos both the power to mediate between Him and the Creation, as well as the power to make the difference between Him and the Creation.” This means that actually the Logos is the seed of the Divine Consciousness from the belly of the Manifestation, the threshold between Transcendence and Immanence, the Point in which the universal emanation and resorption merge. It is profoundly significant that we find the line in the Bible: “Where Two or Three are gathered in My Name, I will be with them!” (Matthew, 18:20)
Symbolically, and not at random, the Hindu tradition places Brahma the Creator in the Navel of the World, and the ancient Greeks were worshipping the Omphalos as the Centre of the World, from the same metaphysical considerations.
Fig. O5 – The diagram from the Hermetic manuscript of Giorgi allows the construction of the succession of musical octaves, quadruples and quintuples that form the harmonic system given by Plato in the Timaeus dialogue (a modern representation is shown on the right side)
The notion “mean” (the geometric – harmonic – arithmetic triad) is closely connected to the Divine Proportion and the Tetraktys, the Perfect Decade. Dividing a segment in the Golden rapport also implies the geometrical mean: the rapport between a/b and b/c leads to the formula b2=a.c. In fact, this means that b is the geometrical mean between a and c.
Fig. 0.6 The Lambda from Plato's Timaeus
Fig. 07 The numbers that complete the Lambda by keeping the law of formation unaltered
When Plato suggested dividing the primordial Mixture (the Triad of the Identical, the Different and the Being) through the Number (Resonance) (Timaeus, 35b-c), he also presented the scheme that was later on called Lambda (see figure 0.6). On the left side we have the powers of 2 and on the right side, those of 3. The Feminine, Earth (2) and the Masculine, Sky (3) merge together in the Unique Principle (1) and thus they emanate the three levels of the World that complement each other. The division of the Soul of the World is a profound subject in itself, so we will not develop it further here, but those who want to deepen it can find it in the Timaeus dialogue, together with the way of forming the musical chords (see figure 0.5). What is amazing is that, without much difficulty, Lambda appears as being “extracted” from Tetraktys, the fundamental archetype of the Pythagoreans, thus starting the formation of the Tetraktys by adding the three missing “stones”. Now our problem is what numbers complete the Tetraktys, at the same time keeping its law of formation unaltered. The answer is a new confirmation of our hypothesis and it is provided by the very law of triangular growth, a real archetype of fractal development (which reproduces a unique model through the quality of so-called “auto similarity”, repeated over infinite iterations) or holographic (in which the parts are copies on scale of the whole): The original triangle 1-2-3 must be reflected (proportionally) in all the others. Thus, between 4 and 9 appears 6, because the progressions 2-4-6 and 3-6-9 both hide the triplet 1-2-3. They are obtained from this by multiplying the terms with 2 and 3, respectively. In the bottom line, out of similar reasons, we complete with 12 and 18 (4-8-12), 6-12-18 and 9-18-27 also keep the 1-2-3 rapport). In this way we obtain the scheme from figure 0.7.
Besides, we notice that 6 is the geometrical mean and middle of the pairs 2-18, 4-9, 3-12, in the centre of which it is (62=2.18=4.9=3.12) and at the same time for the triads 1-8-27 (63=1.8.27), 2-12-9 (63=2.12.9) and 3-4-18 (63=3.4.18).
It is indeed unexpected, but the respective “coincidences” only strengthen the idea of an extremely coherent metaphysical-mathematical system (for the initiates) of Pythagorism. Here is another impulse for a better reflection upon the significance of the arithmetical operations and to a more profound focus upon the numeric symbolism, which can open unexpected gates for us.
Coming back to the Divine Proportion, we notice that in fact the complementarity of the Identical and of the Different is fulfilled through the unifying Principle of the Being, and after portioning Unity through the powers of 2 and 3, the sequence 1, 2, 3, 4, 9, 8, 27 is obtained. Plato describes the filling of the intervals through the use of arithmetic and harmonic mean. Thus, they regulate the proportional (comm)union of the extreme terms, becoming “representatives” of the mediating principle (connected to psyche – the soul) between the spiritual – causal (intelligible) domain and the physical one (sensitive). In this direction, it is significant that the means correspond analogically to the three Worlds. Thus, we can say that the Causal world corresponds to the arithmetic mean, the Astral world corresponds to the harmonic mean and the Physical world corresponds to the geometrical mean.
Therefore, we have outlined a specific way of metaphysical interpretation, which allows very special correlations between Arithmology and the Golden Proportion, all these being revealed to us as the elements of a structure that is impossible to break.
For the ancient Greeks the Trinity (truly Holy) was the carring force of the Concordia, Harmony and “marriage”. At the same time, it was the cohesive, unifying factor of the opposite and discordant pairs of terms. Homer (Iliad, 15.189) said that “Everything was divided into three”; according to Nicomah of Gerasa, the virtues were somewhere in the middle between two vicious states (one through excess, the other one through the lacking) and reciprocally opposite. The virtues are under the incidence of the monad, thus being something wise and defined – because the mean is one – while the vices are governed by the dyad and are indefinite and meaningless.
Expression of the Great Cosmic Power TRIPURA SUNDARI, the Trinity of the Divine Proportion appears as being the unique Canon of Harmony in the three worlds, each fundamental level reflecting its light, as much as it given through the Universal Order.
As far as we are concerned, we must know how to apply this canon in different ways, because if in the physical level we can use the measure of lengths and the value 1.618033… in order to outline the harmonic rapport, at the emotional level we must live fully and to integrate inner states. With regard to the causal level we must reveal within ourselves, as intensely and profoundly as possible, an ineffable overview which secretly synthesizes and unifies the ideas. The arithmological model for this way of acting is the mean, which corresponds, analogically speaking, to “the middle way”. Not by chance, Jesus said of Himself that he is “the Way, the Truth and the Life”, and Buddha found the “median way”. Also, in folklore there is the wise saying: “The Truth is in the middle”. Therefore, for the lover of wisdom, the arithmetic, harmonic and geometric means are tools which symbolically evoke the integration of all tendencies and latent imprints of the being, as well as of the inferior tendencies (corresponding to the extremes, and to the discordant) through the cultivation of the state of neutrality (which corresponds to the Mean, Balance, Harmony and Unity).
Though it might appear ordinary, the simple measurement and comparison of some relations to the 1.618033… value is a good start, because even if this constitutes a minor application of the Divine Proportion, it has the power to gradually awaken something mysterious within us.
Quoting the inspired words of the apostle Paul, we could say that by doing this, “[now] partly we know, and partly we foretell. But when that which is divine and perfect will be revealed to us COMPLETELY, than that which is offered to us as part will transfigure us.” Knowing all this, we just have to get involved with our entire being, body, soul and mind in this fruitful search that gradually leads us to finding our essential Unity. In this way, at one point we will fully, completely and profoundly experience the inspired saying from the ISA UPANISHAD:
“That is perfect. This is truly perfect. Perfection brings perfection. Beauty calls for beauty. Take perfection from perfection and thus you will see that what is left is perfection.”
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