Index: Melancholy - Reading of the symbolical meanings - Recognizing the values of invisible geometry
Harmony and beauty are gifts originating from a particular state of conscience. The inspirers of great spiritual principles have experienced it, but they are not the only ones. Although at a lower level, everyone has experienced in his life a flash of intuitiveness. It is what we call to understand without knowing why.
Thinkers, artists, scientists and observers have had the flash of intuitiveness that has enlightened them with sense of beauty and harmony.
The moment of illumination activates mental processes which are normally blocked, giving the impression that they come from another world. In reality it is a momentary access to a subtler level of conscience, where meanings multiply and reveal themselves, enlightening the observer's mind.
In intuition every distinction between thinking subject and idea thought disappears and the ùnion between thought and thinker exalts the potentiality of the mind. Indeed, the initiatory process aims most of all to make the link (bridge) between sensorial darkness of the physical conscience and the perceptivity of its superior counterpart, long-lasting.
Artistic illumination as well is a moment of inner re-awakening that reveals the deep meanings of what is perceived through the senses. For this reason the true function of art is to reveal the hidden beauty and the divine harmony in all things. The difference between the artist and its art and the craftsman and its craft is in being able to do it.
The genial vision is a virtue in which intuition and inspiration add up to the perceptive chrism of the artist and make it an extraordinary instrument for creative synthesis.
It is important to study the aspects of creativity in all its forms because it helps to recognize the fundamental aspects that will be used as a model.
An extremely advanced perceptivity, though, can cause suffering when the thinker's personality lacks a suitable inner alignment. In other words, the creative energy becomes suffering (see “Analysis of the creative fever”) when it is not guided by a powerful mind. Self-control is usually short in too independent spirits.
The processes of activating intuition (dynamic-masculine perception) and to receive inspiration (attractive-feminine perception) are activated through the sensitivity of the thinker.
When sensitivity, intuitiveness and inspiration are balanced they are used to give a concrete form (the work) to thoughts otherwise perceivable only to the inner vision.
Perceptive sensitivity is a spontaneous aspect close to empathy that finds its development in empathic intelligence, able to grasp the hidden side of every idea. It gathers a vision, then, that allows a link to a meaning with many others. Here's the importance of analogy.
The links between different physical and mental representations are channels of communication that the thinker learns to know and use as a proper initiatory language. To recognize the connections among many meanings (analogy) is the start of the geometry of thought that receives ideas, feelings and emotions. The result is that what is understood can be reproduced in a conventional form through principles, codes, methods or symbols that amplify and become languages; in their most particular forms they become proper initiatory languages (see “Initiatory languages”)
The purest forms of beauty and harmony originate from the thought, the deed and the word of their creators. The most refined forms of art reflect in the purity of principles that shine for divine reflection; therefore art as well is a language that we must learn to understand because, together with the symbolic language (see
“Examples of hermetic-symbolic language”) it is a deeply esoterical instrument.
Both architectonic and pictorial art are based on geometric relations invisible to an inexperienced eye. From these relations originates harmony. It is easier to recognize beauty, although when we are overwhelmed by admiration we miss the meanings or we omit to understand the language of the artist. This is what happens for Temples and Cathedrals, which are not symbols of faith as many people think; they are real books of stone that we must learn to read in order to grasp the meanings that great initiates and Master masons engraved in them. (see “Mysteries of the Builders”).
Together with the symbolic language, the artist uses the language of emotions to communicate ideas, sometimes even very complex ones. For someone who doesn't recognize its principles, though, the work keeps only its formal representations, maybe relevant, but still only a figurative appearance. This is why the principles of art are at the fundament of the language of art.
We will look at a unique work in order to give a practical example.
It is called «Melancholy» and it was realized in 1514 by the German master Albrecht Durer.
He is one of the artists who used their work to transmit initiatory principles and for this reason they have been compared to books of great symbolic value.
The esoterical meaning of “melancholy” is: “The man who is put through the trials of Saturn”.
This is a metaphor where the planet Saturn symbolizes the divine thaumaturge who decides which trials the initiating will have to face and to overcome in order to reach the «victorious freedom».
Examples of trials are the twelve labors of Hercules.
During the time of trials which life subjects us to, the sense of neglect, loneliness and distress cause a pain of living that some traditions have called the dark nights of the soul.During these trials the soul can't intervene in the personality (physical reason) of the postulant or it would nullify his autonomy. The latter is not free will yet, but rather freedom of choice. The higher the goals the harder the task.
The trials express crisis that start with the process of transforming oneself. Inner transmutation follows the same principles of the initiatory metamorphosis* of old traditions and both mean to change inside in order to grow.
Inner transformation is a process limited in time, occurring completely in the physical conscience and accompanied by the sense of melancholy (feeling of neglect of the soul).
During the process of transformation we are melancholic because two forces seem to conflict and break us. A part of ourselves (the conscience linked to the physical senses) resists to the progress whilst another one (the evolving conscience non-related to physicality) pushes us to overcome any point of mental stagnation (habits, idleness). In these “shilly-shallying” called personal evolution the subject is confused because he doesn't understand where he's going (unclearness of the new). He leaves behind himself, memories and old habits. He regrets what he was and who is was with.
Everything seems lost. This uneasiness lasts until he realizes the advantages of the inner growth, such as an increase in the hidden potentiality, a widening of the boundaries of his conscience and therefore a higher ability to understand, farsightedness, extension of mental abilities and sensitivity. The previous mental vision will then become a memory not to be regretted.
* Initiatory transmutation or metamorphosis is based on the process of transformation and regeneration of the instinctive, passional and sentimental energies that are raised to psycho-spiritual energy.
The sulphur, salt and mercury of alchemists are symbols of the different aspects of the human psyche. The container (athanor) in which they are placed is man, or rather his conscience. The fire is called incendium amoris, the heat and transforming force of spiritual love.
Reading of the symbolical meanings
The larger of the two winged figures represents the soul, whilst the smaller next to it represents the individuality of material man who, as a forgetful child, engraves on his little book the memory of his short subjective present. It marks the experience of good and evil from which the plot of his destiny will originate.
The wheel on which personality is sitting is the Wheel of Generation and Re-birth that moves destiny.
The “Wheel” is part of the major arcana of the Tarot.
Its meanings, like the other 21 Cards of the God Thoth, are hidden by popular meanings that caused the loss of part of contents considered sacred. The Tenth Card, the Wheel, has been veiled by the coarse meaning of Wheel of Fortune. Perhaps because the profane doesn't know that destiny is the consequence of his decisions-actions (law of cause and effect) and therefore he imagines that good and evil depend on lucky or unlucky coincidences.
The motion of the Wheel of Generation and Re-birth* is connected to the temporal cycles that act and modify the physical plane and the rhythms of every living creature. Therefore, in good and evil, the cycles are the line of advancement of every kingdom of nature**.
* Wheel of Generation and Re-birth - The nine months of gestation are part of the Wheel of Life. This is a period where man's Ego thinks back through its experiences in order to rebuild its physical and mental appearance. The action of conception corresponds to the individualization of the race, whilst the birth corresponds to its first initiation.
From an esoterical Commentary: «many things will be clear when the astrological implication of individual life will be understood ...such as the motion around the Wheel of Life. The horoscope of the physical person is linked to the Wheel that rotates from right to left (from Aries to Taurus, Note of the Editor), whilst the horoscope of the soul runs on the Wheel from left to right.
The antagonistic ways of the Wheel “that revolves on itself”, as the Bible says, cause conflict in the life of the planet, the Humankind and the individual.» In man it shows through the alternation of destiny, through his joy and pain, difficulties and good chances caused by choices and personal deeds. Therefore motion of the Wheel and destiny are “minor” synonymous destined to widen with the development of the initiatory conscience.
** Circadian Cycles - «... the Cycles rule the appearance and disappearance of great energies that flow in and out of the universe. They are limited and opposed by the quality of the forms on which they have an effect.
To understand the flow of the Cycles means to understand the fundamental laws of evolution that rule the rhythms of regeneration.
Vital impulses are affected by the flow and re-flow of energy and the alternation of periods of “light” and “darkness”. Energy re-appears with the sunlight and goes quiet with the darkness of the night.
The cycles reflect in the light and dark periods of planets and in the good and evil period of humanity. Both in times of emersion and immersion of every living creature (birth, growth, death and re-generation) and in times of progress and fall that characterizes the stages of development of every race and nation...».
At the bottom of the image we can see other symbols. A light is irradiated from a point representing the exit from the world, final goal of the incarnated soul. A bridge stands above the waters of a quiet sea, crossing them.
The water represents the emotiveness that rules the human soul and the world it has built. The latter is shown by the artist through the manufactured products he's placed on the sides. The houses mark the world built by man; the trees represent the vegetable kingdom whilst the mountains represent the mineral kingdom.
The bridge is a passage that crosses the waters of desires and passion. It represents the superior conscience, whose flow is not affected by the signs of the world and its presence is expressed by the light irradiating from the point that expresses the presence of the Divine conscience above all.
On the head of the angel is placed an evergreen garland symbol of victory.
In the earthly world as well (the conscience) the angel is pre-destined to victory because he is the only one made up by the spiritual substance of his creator. The victory of the soul is not his freedom because it is never completely fixed in his matter. His victory is the ascent of the small personality (small because his earthly existence is short) that is his “shadow on earth”. In simple words: if the soul is the celestial shadow of spirit, physical man is the earthly shadow of soul.
The ascent of the earthly personality is represented by the Ladder placed next to him, on the walls of the building representing the inner Temple erected by human evolution (ascent). In order for this to happen, some tools are hanging from the walls.
The Scales are the symbol of Balance and Justice, virtues that we discussed earlier on.
The graduated Sandglass represents the cycles of life associated to the universal motion and kept in the symbol of the Great Zodiac.
The Bell is ritually rubbed to obtain the vibrating note (sinusoidal wave) that recalls the attention of God and his messengers. This is the representation of the “silent and sacred sound” that every man must learn to re-sound in himself to recall the attention (law of affinity) of the divine particle that animates us.
Esoterical memories talk about this inner sound as the Substituted Word (the physical voice) and the Lost Word*, projected by an act of conscious will.
The act of will generates an energetic alignment between conscience, heart and mind and it causes the resounding of the soul that “replies” by producing a vibrating note (law of magnetic attraction). It is a tone that “precipitates” in man's conscience, filling it with an energetic motion that “electrifies” the three levels of its manifestation:
1) the energy that personalizes the physical mind;
2) the energy that individualizes the superior mind;
3) the energy that, lacking corporeal characterizations, expresses the spiritual will in the mind**.
* Lost Word - the note below is taken from a bigger essay.
The evocating Words are based on the principle that all words are symbols with the power to stimulate and cause the activity associated to them. It consists in choosing the word that expresses the quality we want to evocate. It can be evocated through a written text to look at, a word to repeat (see mantram), or an image to visualize. The important thing is to repeat properly the technique. The visual or auditive image produces an impression on the plastic unconscious and it gradually affects it. The rhythm to use for evocating Words can be continuous, periodic, repetitive, cyclic or rotational.
The Lost Word is an essentially destructive energy. It is a sonorous emanation in the shape of a spiral and it becomes conical when it is closed, if it is properly projected and with the help of visualization. It becomes attractive when the sonority has dissolved all the “existing forms” in the space of action, where is therefore created a prolonged vortex. In the higher vacuum of order created, energetic forms relating to the quality of that Space (see eggregore) are attracted.
The Lost Word can be sonorously emitted to cause the vibration of the physical field and silently (much more powerful) emitted to cause the vibration of the mental field.But let's not go further. Once it is projected it frees by destroying, it is the Sound of Liberation, the Great Note of spiritual Resurrection and elevation of Humanity to the Secret Place of the Highest.
** see Plato, the divine monad (within us).
Another concept the artist wanted to transmit is the idea of Numbers engraved in the magic Square. The magic Square is made up by Numbers which must be never repeated; therefore they can appear only once. Furthermore, the sum of the numbers on the horizontal, vertical and diagonal lines must always give the same result.
Apollonius of Tyana taught how a magic Square held energy becoming a powerful talisman. Since the times of Pythagoras, Ficino and Paracelsus, this sacerdotal art, which goes back beyond the Temple of the Mysteries of Osiris, was promoted for research and therapy. It is well known the relationship between Number-Sound-Color hidden in the magic Squares*.
*The magic Square - Through this Square, the artist shows the Number 34, which is the numerical value of the Planet Jupiter; the latter vibrates at the same energetic sound of the Sun (Do), the same octave but 1 and a half tone lower. The same octave vibrates the planet earth going down one tone. These theories find confirmation in the Lessons on the Monochord by Pythagoras, the universal harmonics by Fludd, the “De Musica Mondana” and “The Harmonies of the super-mundane Monochord” and in the modern studies on Harmonics by H. Kaiser.
The fundamental note of the Solar System corresponds to a sound of octave, in which the planets create in vibrations the intervals, in tones and semitones; it is shown that the sum of those intervals equals the six complete tones of the octave.
Another important element is in the meaning given by the hermetic Tradition to the Planet Jupiter, Logos indicated as the one the Ritual Magic and the Ceremonial Order are emanated from.
«…the Soul in its descent into the matter is fixed to the cross of the form with the four nails of the elements...»
The meek and domestic looking animal that lies at the feet of Durer's work represents the animal kingdom, but in this instance it takes on a particular value: the animal whose physical conscience and part of the soul are immersed.
The artist underlines the concept of incarnation by adding below on the right 4 nails that represent the 4 Elements that fix the divine conscience to the physical world. The earth, the physical body, the water, emotions, the air, the thought and the fire, the spirit; they are the matrix of human form.
Not very visible next to the four nails is placed a chisel, an instrument used to engrave and make signs on various materials (complements of the matter). The chisel, this time, could be interpreted as the pen of life.
Going back to the bottom of the work, we can see two far away images. The first one represents a wooden boat sheltered on the seashore.
In esoterical iconography it represents the physical and rational mind of man who, plowing through the water of the sea of emotions, crosses the horizontal plane of mind, the two dimensional comprehension. Also, the wings of the two main images symbolize the mind that produces an intellectual and intelligent vision in its abstraction*.
The psyche advanced through a continuous intuition develops the three dimensional vision (verticalization of the mind that links the reason to the intelligence of the superior Ego). Man will then abandon the habit of observing reality with the characteristics of the profane**, which reflects only in the lower planes of his mind
*Intelligence - According to spiritual Alchemy, intelligence is the Silver of Wise men. It corresponds to intuition, penetration and information. It gives us the discerning of the spirits and the possibility to perceive, under the aspects or physical forms, their link to the poles of Good and Evil, Light and Darkness. Intelligence allows us to penetrate the occult meaning of words, formal representations, esoterical letters and texts and their superior meaning. It connects us to the hidden sense of the Sacred Scriptures and the Holy Books. It reveals the superior symbolism of the Sensitive Signs, Rites, Symbols, Sacramental Objects and Matters. It allows us to grasp the presence of spiritual realities in the imperfect reflections of appearance. It shows us the consistence of the causes that produce effects and phenomena.
**Profanum - Profanum, pro-forward, fanum-temple; it is the non-initiate that stands in front of the Temple and doesn't dare to enter on his own, in order not to violate its sacredness or not to be hit by the effects of the impious deed. It is profane the man who is considered undeserving to hear the secret teaching and to touch the sacred ritual objects. Superficially, it might seem that to the idea of “profanity” follows the idea of ignorance; it is not so. It is true that ignorance determines the profane being but it is also true that it regards a relative level of knowledge; therefore even in the highest formulas of human initiation there is a part of “not knowing”. In order to characterize the profane we must look elsewhere. According to the principles of spiritual Alchemy gluttony is worse than ignorance.
Gluttony will lead the profane to devour in excess all the documents, books, essays and schemes he will have access to. He will keep the most different doctrines, even opposed teachings. The strangest mixtures attract the greedy man. Eager for all that flatters his curiosity and his hunger for knowledge, the greedy man will swallow down any strange mixture; his avarice will lead him to a total and sterile isolation. The mean man will consider it painful and distressful to teach and transmit all that he has received and learnt from others. He will pile up books and manuscripts, documents and symbolical initiations, but he will never accept he is only an instrument for the transmission of an order he will never understand.
He will try to extract a personal doctrine for his personal pride and he will fill in the missing parts with fantastic ideas. Otherwise, if idleness accompanies his obtuse hunger, he will give back the excess of all his mixed knowledge, poorly digested by an idle mind. He will then go back to materialism that he finds safer and more relaxing.
Gluttony corresponds to Water. It is the opposite of Temperance whilst it is linked to avarice. Avarice corresponds to the Earth and it is the opposite of Caution.
The big vase with handles placed in front of the little boat reminds us of the alchemic athanor , and the flames coming out of it, fed by a fire of wood or coal, suggest the idea of a fire revived by natural elements. It is a mind that, through the purifying fire of the spirit, eats away and burns the dross of one's own conscience (see Flaming Pentalpha in “Secret numbers in masonic catechisms” and “The Pentalpha and the 5 Kingdoms of Nature”).
The minor adept doesn't yet have the resolving power of the Act of Will, represented by lightning. Therefore he resorts to the use of the minor will. He turns to his obstinacy, which is rhythmic and repetitive as it is symbolized in the repeated strokes of the hammer he gives on his stone until it's smooth and thin. As the metaphor of the initiatory transformation reminds us, consistent and rhythmic obstinacy in hitting the same spot again and again, breaks the hardest rock and the sturdiest obstacle.
On the ground we can see an incensory; it reminds us of the importance of fumigations and the Ritual use of Perfumes in the Temple. This symbol is an occult memory of the sense of smell* that implies the sense of the inner vision. This perception is represented in the East through the metaphor of the Third Eye.
*The sense of smell, in its inferior and astral counterpart, is called instinct.
In his 1973's “lessons on psycho-synthesis”, R. Assagioli states that inspiration is the process of passage or descent in the field of conscience of more or less elaborated contents of the super-conscious; artistic, literary and musical inspiration are guide and help of the Self or superior Ego. Sometimes the product reaches the conscience already formed and complete, whilst some other times it is in a gross and incomplete state and requires work from the conscious self (personality) in order to have a proper shape.
When we refer to a man who lives through his perceptions still immersed in the emotional and astral plane, we say that he proceeds through “guesswork”, meaning that he follows the animal instinct. This perception, that foresees the time when the Adept will have the clear-vision of the Psyche, also occurs thanks to the instinct of the soul. Both in states of ordinary conscience and in the inner silence, the man who lets himself being reached by the breath of the Soul, will receive it instinctively as inspiration. This man is then called “inspired”.
Still on the ground we can see a tape measure. It represents the logic that provides the workman-speculative (minor initiate) the sense of measure that, together with the saw (sense of discrimination), allows him to give the right proportions to the products of the thought. The harmony of the thought is increased furthermore through the symbolic use of the planer, the balance that annuls (tolerance) any superficial diversity (ephemeral diversities).
At the feet of the main character we catch a glimpse of some pliers. In a metaphorical sense it represents tenaciousness; it is the firmness in extracting the nails of physical elements that crucify the part of conscience of the soul materialized in the animal body. It is another reference to the human conscience subjected to sensuality and illusions of mother land, widow because lacking the light of the spirit (the father).
The small wooden rule is the metaphor of experience that is useful to define the corners of the stone and therefore the style of character and personality.
Lying on the lap of the angel we can see two other meaningful objects.
The Book of Laws kept by the soul.
The Compass with its graduation is the symbol of mental openness, where the completely awake intellect corresponds to its extreme opening. This is the highest aspect a physical mind (personal self) can reach. The complete mental opening is the condition where the super-conscious Ego (result of the activity of the soul on the physical level) can connect with its physical counterpart, pouring into it part of its thought energy. In short this is the process that leads to illumination* called Pure Reason and that produces the Gold of the Wise Men**.
*Illumination - «...we usually live and see through our eyes and listen through our ears, stimulated by senses, moved by the abilities of the body; we receive only the spiritual knowledge that can reach us momentarily through the purity of our being. On the mystic way we create our light; at first we fight, blind and deluded, without seeing anything, unable to think and to imagine. If we carry on for weeks and months, the state of astonishment disappears. Our faculties re-adapt, work the way we want them to and the way they've never worked before. The dark caves of the brain start becoming bright, because we're creating our own light. Through the heat of will and aspiration we transform what is gross in the subtle ethers that make our mind work. In the same way that a dark bar of metal starts enlightening becoming red at first and then white; in the same way ice melts and becomes liquid and then steam and gas; and eventually radiating energy, where ethers purify and become luminous essences; they create a new event for the soul and connect us to a medial world towards the sky, where their true place is» George W. Russel.
**The Gold of Wise Men - For spiritual Alchemy the Gold of Wise Men is wisdom and it consists of the choice of the best among the data accessible to Intelligence. Intelligence is Knowledge and wisdom is the use we make of it.
Wisdom allows us to judge everything according to the Highest of the causes (Archetype One) on which all the others depend, whilst it doesn't depend on any other.
We must now consider the two solids. The sphere has a particular meaning because inside it the bodies of all the regular solids can be inscribed; like the circle that, in its two dimensional expression, contains all the regular shapes of plane geometry. It is therefore a form that represents the idea of “universal”. In the mental contest this word is used to indicate a point of conscience, such as the personal sphere, the sphere of conscience, the sphere of influence, etc. In other words the sphere represents the idea of mental habitat. The seat of personality (mental habitat) can have several characteristics. It can be a liberating or restrictive center; natural or artificial; sacred or profane; spiritual or infernal. All this is connected to the spherical form, as well as the philosophical value of the metaphysical zero.
We have now come to the main symbol in the work: the dodecahedron.
Pythagoras was the master of hyper-solids* that, like the decahedron, constitute the geometry of the 4th dimension.
* Hyper-solids - «... when we try and understand the idea of a Euclidean space with four dimensions, we are helped by imagining the efforts that a hypothetical “being” with two dimensions should do to visualize our three dimensional world.» - op. cit. Abbot, from “Ordinary Polytopes in Higher Space”
For a more in-depth research of the graphic study of the hyper-solids and the 4 th dimension, we suggest the essays: “A Primer to Higher Space” by Bragdon; “Regular Polytopes” by the mathematician H. S. M. Coxter.
Representation of two solids
Duodecedron Planus Vacuus and Ycocedron Planus Vacuus , work by Leonardo da Vinci from “De Divina Proporzione” by Luca Pacioli. A.D. 1509 (Ambrosian Library)
Nobody knows who first discovered that whilst the number of regular polygons is infinite, the regular solids in the three dimensional space are 5.
Limiting our short study to the western mathematical tradition, we can mention what the historian and mathematician C. Boyer wrote:
«...the scholiast Suda refers that Theaetetus, a friend of Plato 414-369 B.C. was the first one to write about solid forms...it seems believable that Theaetetus studied the 5 regular solids more than any other mathematician».
Referring to Plato's Work he wrote:
«It is not ruled out that the Pythagorean cult for the geometrical form of the dodecahedron induced Plato to consider this fifth and last regular solid as a symbol of the universe».
Proclus 485-410 B.C. writes in his “Comment to the first book of Euclid's Elements” also called “Resume” that «…Pythagoras transformed this study into a liberal form. Researching through his principles and studying the theorems both abstractly and intellectually, he discovered the irrationals and the construction of the cosmic forms».
In the west Plato (427-348 B.C.) was the first one to express interest for the study of those forms, so much so that he left a relevant testimony in his Work "the Timaeus".
The platonic cosmogony
«When God began to get the universe into order, fire and water and earth and air ... were altogether such as everything might be expected to be in the absence of God ... God made them as far as possible the fairest and best, out of things which were not fair and good, this we will say of everything forever».
«… is evident to all, fire and earth and water and air are bodies …»
The mathematical generation
«... and next we have to determine what are the four most beautiful bodies which are unlike one another, and of which some are capable of resolution into one another; for having discovered thus much, we shall know the true origin of earth and fire and of the proportionate and intermediate elements. And then we shall not be willing to allow that there are any distinct kinds of visible bodies fairer than these.
Therefore we must endeavor to construct the four forms of bodies which excel in beauty, and then we shall be able to say that we have sufficiently apprehended their nature».
The mathematical generation of the 5th solid, the dodecahedron
«...the most beautiful of all the many triangles is that of which the double forms a third triangle, which is equilateral». [*]
[*] A rectangular scalene triangle with a cathetus equal to half the hypotenuse.
«Four equilateral triangles, if put together, make out of every three plane angles one solid angle, being that which is nearest to the most obtuse of plane angles; and out of the combination of these four angles arises the first solid form which distributes into equal and similar parts the whole circle in which it is inscribed».
The hyper-solids and the 4 Elements
«...it is the tetrahedron (fig. A) element and germ of fire ...the second kind, then, is formed by the same triangles, joined together in eight equilateral triangles ... and say the second by generation that of air; it is the octahedron (fig. B). The third species is formed by a hundred and twenty solid triangles joined together and twelve solid angles, it is that of the water; the icosahedron (fig C). But the isosceles triangle originated the nature of the fourth species so to form an equilateral tetragon ... and the figure of the resulting body became cubic ... attributing this form to the earth; it is the cube (fig.D).
There was a fifth combination left and God used it to decorate the universe; the dodecahedron (fig. E).»
Recognizing the values of invisible geometry
What is hidden in the images is the invisible and silent relationship between the elements that make the work. Like Pythagoras taught, they are the geometry of the world.
In the relationships that link the parts making the inner space of the work, originates the science in which the geometry of the relationships is synthetized by the “Number”, that is the soul of every Form.
Going from the two dimensional condition of the figures to the three dimensionality of the solid, we reach the study of the relations of inner spaces. This science has obvious analogies with the study of harmonics and their mathematical relations.
The “Science of Harmonics” (H. Kaiser) is a derivation of the Science of the Sound by Pythagoras, that himself taught through the use of an instrument he invented, called Monochord.
Here the attention goes from the work to man because man as well contains inner spaces; this postulate is acknowledged by modern science. We know that the space produces a number and this has value of sound and that the movement of sound produces color. This equation of form, number, sound and color becomes threshold of the sacred science that we thought lost but is only forgotten.
This is the occult teaching that the master (but not only this master) has taught us. If geometrical relations reduced to numbers express sounds, intervals, tones and semitones, that are then translated into colors (chromatic scale) the same process occurs for man. Pythagoras put this as a doubtless assumption.
We don't want to lead our reader to specialistic notions, but only show an itinerary.
Today sonorous harmonics are part of science, psychology and medicine. But also of mathematics. We can see that in the Sinergetic Mathematics by H. B. Fuller.