Journey to the Heart of Venus (III)

 

SIDEREAL ROSE

The Cosmic Dance Between Venus and the Earth

© Xavier de la Huerga 2023

Venus is the closest planet to Earth, not just in terms of distance, but in size similarity. So much so, that some consider Venus the Earth´s "planetary twin". Out of its orbital period and that of the Earth, arises an exquisite harmonic relationship in the shape of a pentagonal pattern, suggestive of what we could call a rose of hearts; an elegant spatial configuration where two universal symbols of beauty and love appear intertwined. Hence, it is suggested that more than a twin pairing, the relationship between Earth and Venus is that of lovers.

The orbital pattern generated by Venus, from a geocentric perspective. Ilustration by James Ferguson from his book Astronomy Explained Upon Sir Isaac Newton’s Principles (1756).

What we can see in the two images above and below this paragraph, is the pattern created by the synodic cycle of Venus from a geocentric viewpoint. The 5 central loops (marked by pink dots in the image below) describe the moments of maximum proximity between Earth and Venus; the so-called inferior conjunctions. While the 5 points where the lines touch the external perimeter of this floral mandala (in green), depict the moments of maximum distance, or superior conjunctions. It takes Venus 8 years to draw this figure, during which it goes around the Sun 13 times. As we have seen in Part II of this series of articles, 5, 8 and 13 are members of the Fibonacci series; a numerical expression of Phi.

Venus' orbital pattern, computer generated graphics. Inferior conjunctions are marked in pink and superior ones in green. (Image from A Little Book of Coincidences. Copyright John Martineau 2001)

Let's remember here that the two flowers traditionally assigned to the goddess Venus are the  rose and myrtle, both with double pentagonal geometry since they have 5 petals and 5 sepals. (All roses possess 5 petals originally*, it's only when hybridising naturally or for the creation of cultivar varieties that pistils and stamens mutate, becoming petals and resulting in the popular ornamental roses that nowadays can reach up to 100 petals). *Rosa Sericea is the only exception, with four petals.

The rose is without doubt the most archetypal, mystical and mythical of all flowers. It comes down through time surrounded by a perfumed aura of mystery, appearing in the traditions of gnosticism, sufism, alchemical and hermetic emblems, the Roman festival of Rosalia, the Christian Holy Rosary, as symbol of the Rosicrucian Order, in the science of heraldry, or in the ancient latin expression "sub rosa", that was used to denote the highest secrecy.

Myrtle flowers                     Rosa Canina                Heraldic Rose                        Rosycross

The more than 3,000 species in the botanical family rosaceae include not only roses, but many of the most appreciated fruits, such as strawberry, pear, blackberry, plum, cherry and many others. But only one among them enjoys a comparable status to the rose in as much fame, mythical renown and for being a symbol consecrated to Venus Aphrodite and to the feminine principle. This is the apple, a fruit with a "genealogical tree" that goes back to the biblical Genesis, with a reputation that grants it the power to bestow both immortality and death, together with divine knowledge of good and evil, upon those who eat from it. Interestingly, its seeds are arranged in the shape of a pentagram. 

An apple sectioned transversally reveals at its core the pentalpha star.

An apple sectioned transversally reveals at its core the pentalpha star. 

The apple; a fruit predestined to an allegorical relationship with the force of gravity. First, in provoking the Fall from Grace and expulsion from the Garden of Eden. Thousands of years later,  through its own fall upon Newston´s head, triggering the eureka moment that instigates the birth of the scientific rationalism paradigm; kick-starting the mad rush for the Industrial Revolution, the desacralisation of reality and the process of ecological destruction bound to reach its climax during our dysfunctional age.

This fruit, forbidden to mortals and giver of eternal youth to the gods, not only appears as a  central element in various mythological narratives related to Venus Aphrodite (Hesperides Garden, Atalanta and Melanion, Helen of Troy), it is also found in other cultural contexts; in Arthurian romances and fairy tales, Nordic sagas and cosmogonies, Celtic and Caucasian traditions... Always orbiting around feminine archetypes: Kore, Idun, Freya, Sin, Persephone...

The Venus Octave

 

Returning to the astronomy and to the harmonious geometry danced in space by Venus, we are going to see next that the Rose of Hearts can also be represented as a series of ten points symmetrically placed over two concentric circles in relation to the ecliptic or zodiacal band. 

By connecting those ten points, two pentagrams are formed, as we can see in the image below, although this is only an approximation. In reality, the two pentagrams formed by Venus are not perfectly symmetrical. The point in space where Venus arrives to its eleventh conjunction doesn't close perfectly the double pentagram, but instead gives rise to a new sequence of ten points, which means that the two pentagrams slowly rotate along the ecliptic, at a speed of roughly two degrees every eight years. This open-ended progression is comparable to what occurs in the progression of a musical octave, whose last note is in fact the first note of the next octave. Continuing with this musical analogy, the period for the double pentagram of Venus to fully revolve around the zodiac is twelve centuries and there are twelve notes in an octave (seven whole tones and five semitones).

The double pentagonal geometry created by the conjunctions of Venus in regard to the zodiac. This image shows the next conjunctions in Leo, Gemini, Aries, Capricorn and Scorpio. Point number one marks the inferior conjunction on 6th June 2012 in Gemini; point number two marks the superior conjunction on 28th March 2013 in Aries, etc.

The harmonics of Venus with number five are not limited to the pentagram and the rose. From remote antiquity, the fifth day of the week was dedicated to Venus; Friday's etymology comes from Freya's day. Freya is the goddess that in northern European mythologies equates Venus. Spanish and French languages also keep that memory alive in their calendars since their words for Friday (viernes and vendredi) come from latin 'veneres', which is the etymological root of Venus. A further resonance is found in the cycle of twelve centuries during which the two pentagrams complete a full revolution around the zodiac, since there are five solar transits of Venus during this 1,200 year cycle.

Octaeteris: Venus, Sun and Moon

 

The cycles of Venus, Sun and Moon become synchronised after a period of eight years (with a small discrepancy of around one day), during which ninety-nine lunations and five synodic cycles of Venus happen. For example, on the 5th November 2005 the lunar crescent and Venus appeared in close conjunction just after sunset in the sign of Saggitarius. Eight years later, the same crescent Moon and Venus are seen again in close proximity in the same region of the sky right after sunset on the 6th November 2013 (that is, just one day difference). This astonishing coincidence between the solar year, the lunar phases and the synodic cycle of Venus was taken advantage of for calendrical use since very ancient times.    

  

Within this eight year cycle, known as the octaeteris in the Greek world, the double pentagon structure described by Venus in its orbit leads naturally to its subdivision into two shorter cycles of four years each. It is this bipartition of the octaeteris that determined the four year sequence of the Olympiads. And since this cycle was sacred to Aphrodite, its celebration was imbued with her archetypal attributes; resulting in the conciliatory, concordant, harmonious character that Olympic Games have always promoted; during which truces were decreed, prisoners released and all disputes banned. Nowadays, this four year cycle, although its astro-mythological origin is forgotten, is still in use through the celebration of the Olympic Games and other sports competitions, as well as political elections and the duration of presidential mandates, etc.

  

The Vitruvian Woman. © Xavier de la Huerga 2007-2023

Summmary and Interpretation 

Let's stop here to recap and obtain a glimpse of the greater picture. 

 

Once the impurities that time and man have attached to the original meaning of these symbols and archetypes are removed, a dense web of correspondences and reciprocities starts to emerge. The metaphor of Indra´s Net comes to mind, a net that extends throughout the universe with jewels hanging at every junction of the threads - an infinite cosmic cobweb covered in star dew drops - . On the surface of every single jewel a reflection of all the other jewels and in every reflection a further reflection of the whole. Throughout the entire Cosmos, Venus, the Golden Ratio, phyllotaxis and roses, apples and pentagrams, planetary orbits, galactic spirals... a beautiful infinite tapestry, tracery and knot-work without beginning or end... Microcosm in Macrocosm.

 

What is the meaning of this fascinating cluster of correspondences and complementary connections? Can it all be attributed to serendipity, coincidence and random chance? Or is there some other organizational principle in the universe that must be taken into account in our description of reality?

This is the time to introduce a concept that depth psychology founder Carl Jung called synchronicity, defining it as "a coincidence of events that are related meaningfully between them, yet lack a causal connection". This definition can be expanded to include the occurrence of events not just in time, but in geometric and astronomical space and within the archetypal-mythical dimensions pertaining to consciousness. This is what we witness when we look back at all the acausal correlations, common themes and multi-dimensional correspondences explored in this succinct three-part article.

But we will have to leave this discussion until the publication of Rooted in the Sky, when the development of these ideas within a much broader context will allow for a better understanding of the far-reaching implications. Once there, we will probe into the relationship of the synchronicity principle to both the holographic nature of the Cosmos and the function of consciousness as an integral element of the equation that defines reality.

We must now go on with the journey to the heart of Venus. The heartbeats are already audible.

 

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Journey to the Heart of Venus (Part II)

 

THE GOLDEN RATIO 

Mathematical Nexus between the Physical and the Metaphysical

 © Xavier de la Huerga 2023

 

Also known as the Golden Section, Golden Number, Golden Mean, Divine Proportion, Extreme and Mean Ratio, Katatome Kanonos... Although its discovery is commonly assigned to the Pythagoreans, it was known thousands of years before in Egypt, Babylon and the megalithic cultures of Western Europe. From the beginning of the 20th century, it was agreed to denominate this mathematical constant with the Greek letter Phi (ϕ). Its numerical value is usually shortened to 1,618 or 1'62, but Phi is an irrational number and has an infinite decimal component (1'61803398874...).

Phi appears in the pentagram informing the proportional relationships between all of its segments, between the sides of its triangles and between all its angles. Indeed, the pentagram is a pure geometric expression of the golden ratio.

The proportion between the pink segment and the yellow segment; the yellow and the green; and the green and the blue = Phi. Likewise, in each of the five triangles, the ratio of the bigger to the smaller sides is also equal to Phi. And so are the ratios between all its angles.

To correctly understand the presence of Phi in the Cosmos, it is useful to familiarise ourselves with a fascinating numerical sequence; the Fibonacci Series, which arises from a simple sum starting with the number 1 added to itself and followed by the sum of the result to the preceding member (1+1 = 2, 1+2 = 3, 2 + 3 = 5, etc). The resulting sequence looks like this: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144... This progression has the property that whenever you divide any of its members by the preceding one, it gives an approximation to Phi (ej. 144 : 89 = 1'617).

Organic and Inorganic Gold

With this understanding of Fibonacci numbers as the numerical expression of Phi, we can commence our exploration of the Golden Ratio in nature with greater ease. Let's start up with the vegetal kingdom where we find the recurrence of Phi in the frequency and angle of distribution of leaves around a stem; the numbers of petals and sepals; the distribution of seeds, etc. As we can see in the following image, the presence of Phi is not limited to the vegetal kingdom.

  

An example of Fibonacci numbers in the human body. The lengths of the bones in every finger conform to the 2-3-5-8 sequence.

Phi is present throughout the whole human body in the proportions and configurations of its constituent parts, but this presence also extends to the physiology of countless species in the animal kingdom. Phi is also at the source of many beautiful spirals that appear in a myriad organisms, from the microscopic unicellular foraminifera, through molluscs' conchs, ruminants' horns and all the way up to the flight patterns of the pilgrim falcon.

The Phi Golden Spiral in the nautilus conch-shell and one of the geometric methods  to generate it from the triangular parts of a pentagram

The Phi Golden Spiral in the nautilus conch-shell and one of the geometric methods

 to generate it from the triangular parts of a pentagram

In fact, we can say with absolute certainty that Phi leaves its blueprint in the totality of the biological realm, since we find it in the turning angle of the double spiral that shapes DNA; the "molecule of life".

This brief list doesn't exhaust Phi's presence in nature, since this is not limited to the organic; the vortexes found in tornadoes and at the macrocosmic level, in galactic spirals, the Cassini division in the rings of Saturn and the orbital periods between the Earth and Venus (as we will see in the next part of this article), they all bear Phi's unmistakable signature.

Other examples of spirals generated from the Golden Ratio  

Phi in the Arts

The harmonious nature of the Golden Ratio has an aesthetic quality that has been applied to many fields of human activity over the ages. It shows up embedded in the composition of masterpieces in music, architecture, painting and poetry. Which entails a very enigmatic element since, apart from instances when Phi has been used intentionally, recent studies show that in some cases its integration in creative works is not conscious. To this respect, various hypotheses have been offered and in view of statistical evidence, pure coincidence must be discarded.

The Parthenon in Athens. Its facade, ground plan, interior chamber, columns, etc are all imbued with Phi. In fact, it is Phidias, the name of its architekton or master builder, that is behind the choice of Phi to refer to the Golden Ratio.

The Divine Proportion

It's not surprising that artists and philosophers have found the Golden Ratio to have metaphysical, spiritual or transcendent properties. In 1509, contributing to the climax of the Renaissance with an influential treatise; De Divina Proporzione - illustrated with 52 engravings by Leonardo Da Vinci -, Franciscan monk Luca Pacioli described various equivalences between Phi and the attributes of divinity (his conception of divinity owed much to that of Plato's), who led him to give to Phi the epithet of The Divine Proportion. A concise summary:

1. Singularity and Uniqueness. Like God, Phi is unique and incomparable.
2. Immeasurability. Since, as an irrational number, it is infinite. 
3. Trinity. As it is defined by three components.
4. Omnipresence. Because Phi is a universal constant.
5. Creative Principle. The dodecahedron is the twelve-sided Platonic Solid whose geometry is a pure tridimensional expression of Phi and symbolises God's Creation, the Cosmos.

The Golden Ratio defined upon a line as three lengths. 'a+b' = 1, 'a' = 0,618 (Phi) and 'b' (Reciprocal of Phi) = 0.382. So, the relation of 'b' to 'a' is the same as the relation of 'a' to 'a+b'

Golden Ratio and Self-Reflective Consciousness

Pacioli´s theist terminology might be unpalatable to some, but it is still possible to formulate another analogy with identically profound metaphysical implications, in less theological terms. This is the correlation of Phi's properties of recursion and self-similarity with the self-reflective capacity of human consciousness.

The conventional meaning of recursion is that of "a sequence in which each term is defined as a function of former terms". Here, this definition is extended to refer to the capacity of Phi to reflect itself in scalar increments or reductions ad infinitum, without losing its self-similarity. In modern physics this property is known as "fractal". 

 The recursive, self-similar geometry of fractal shapes resembles organic patterns, hinting at the underlying order behind chaotic systems in nature (Image: https://www.fractal-recursions.com Copyright 2001-2008 by Jock Cooper)

Fractal pattern based on the Golden Ratio. (https://commons.wikimedia.org/wiki/File:Phi_glito.png)

On the other hand, self-reflection (also called metacognition) is the ability by which consciousness is conscious of itself; so to speak, "capable of seeing itself seeing", as in the act of looking into a mirror. This is the characteristic that defines the highest order of intelligence, which only a few species, other than human beings, possess to a similar degree. So, Phi's recursion and self-similarity can be conceived of as a mathematical expression of this capacity, by which consciousness is conscious of itself. 

The Golden Ratio is therefore, one of the mathematical expressions of the great mystery of existence that underlies the manifestation not just of life, but of consciousness. As such, its universal recurrence displays the three characteristics of Cosmos simultaneously exemplified in its essence; the Beautiful (aesthetic qualities), the Good (it has an intrinsically ethic function, as it supports the generative processes conducive to life, its growth and evolution into self-reflective conscious beings) and the True (as it offers proof of a greater purpose and intelligence at play in the universe, through the exact languages of number and geometry).

A great digital animation by Cristóbal Vila shows several examples of Phi in Nature (Note: the last part of the video showing the structure of dragonfly´s wings doesn't show Phi, but Voronoi tessellations).

We are not going to dive further into these waters, in the hope that this concise introduction has been enough to illustrate the importance of the Golden Ratio, its intimate relation with pentagonal geometry, its ubiquity in Nature and its role as a link between the physical and the metaphysical. Next in this series of articles, we are going to see how Venus seamlessly integrates within this multi-dimensional tapestry of correspondences, interweaving its beautiful movements and its cosmic melody. Going from its purely astronomical, planetary and physically measurable aspect to a perfect counterpoint with its mythological, archetypal, metaphysical and immeasurable facets. Let's go on with our Journey to the Heart of Venus!  >(Part III)

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