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.
 | |
|
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:
- Singularity and Uniqueness. Like God, Phi is unique and incomparable.
- Immeasurability. Since, as an irrational number, it is infinite.
- Trinity. As it is defined by three components.
- Omnipresence. Because Phi is a universal constant.
- 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)
< Journey to the Heart of Venus (I)
Initiation into Appplied Astrogeomancy courses in Spain.
No comments:
Post a Comment