To find our deepest connection to nature, we need look no further than the geometry of the human body. It is at the apex of creation, reflecting the beauty of the cosmos and embodying the order of its physics. Yet in spite of this self-evident truth, we still have very little understanding about why our bodies are shaped the way they are and how that might be related to perception and human consciousness.

The contemporary Darwinian view from the fields of biology and anthropology hold that the appearance of life on Earth was driven by chance from the molecular level up then adapted over time to survive in a hostile environment. [1] Indeed, the accepted theory of evolution depends exclusively on natural selection and survival of the fittest (with the occasional mutation) to explain the shapes of the tiniest plants and organisms up to the largest animal. [2] This theory can be summed up by the oft-repeated phrase:

If we could somehow restart life on Earth or some other planet from the beginning, it would probably turn out completely different.

But what if there is a less obvious yet universal property in nature that physically guides evolution from beneath the environmental process of natural selection? What if life is as much a function of the way atoms bond into specific patterns, as it is genetic mutation and survival of the fittest? And what if all of this revolves around the Divine Proportion?

Phi as a Framework for Life

Life on Earth is composed mostly of carbon and water. This is the case because carbon-12 bonds or resonates with more simple elements than any other element in the universe, gluing together hydrogen, oxygen and nitrogen into the building blocks of life.

The way in which carbon-12 resonates is important because it tends to form into regular polyhedral cages, especially icosahedrons and dodecahedrons, which unfold into the shape of a pentagon (Fig. 1). It is the golden ratio in the diagonals of this pentagonal molecular geometry that help stabilize resonance and promote carbon bonding.

The C20 fullerene molecule is one such example. Shaped like a dodecahedron, it unfolds into a pentagon made up of twenty carbon atoms. Larger carbon molecules do the same thing – always balancing around the Divine Proportion.

Figure 1. Carbon and water polyhedron structures with identical pentagonal connectivity maps.

When mixed with water and nitrogen, carbon atoms then resonate into endless chains of sticky amino acids capable of crystallizing into DNA. This idea of DNA as a liquid crystal is a good one because just as minerals align under pressure into lattices, coils of amino acids fold under pressure into three-dimensional protein structures to create the familiar helical lattice of DNA. It is the pressure of hydrogen atoms in water that help create the lattice and give DNA its twist.

In recent molecular studies of water, biochemist Martin Chaplin found that liquid water organizes itself naturally into a lattice of icosahedral clusters compatible with carbon. The water lattice begins as 4-fold tetrahedral units of 14 water molecules, which then align into 20 clusters to create the geometry of a 280-molecule water icosahedron. This structure assumes a variety of stable geometric sub-structures (including the dodecahedron) before crystallizing into even larger superclusters. At this mesoscopic scale of liquid water, H2O molecules arrange themselves into a 2-dimensional connectivity map of a regular 5-fold pentagon just like carbon. [3, 4]

When these icosahedral superclusters of water are then combined with carbon-12 clusters, the pentagonal framework of life is born. Here again the Divine Proportion acts as a stabilizing constant to keep everything from over-resonating and falling apart. There is nothing random or arbitrary about this and natural selection is not involved. It is an inevitable outcome of the physics of atomic resonance.

The role of carbon resonance in creating organic geometry was confirmed recently in a study demonstrating how carbon molecules are able to fold into an egg. In 2006, a combined team from the University of California, Virginia Polytechnic and Emory and Henry College reported that a large fullerene C84 allotrope constructed its own egg-like cage when two adjacent pentagons in the carbon molecule fused together in a reaction with terbium. This was the first ever indication that the soccer ball geometry of a large carbon fullerene would wrap itself into an egg-like cage from the damping effect of another atom (Fig. 2). [5]

Figure 2. Endohedral carbon-84 fullerene egg collapsing into the geometry of a common hen's egg.

This discovery could answer a lot of questions. For instance, it could explain how amino acids, the building blocks of protein, react with water and other elements to form protective boundaries against the environment. At the earliest stages of gestation, it would explain how large carbon cages form around embryos, how craniums develop around brains and how ribcages enclose around vital organs in vertebrate animals. And, since carbon reactions favor pentagons over hexagons, it could even explain why eggs tend to approximate the golden ratio in their dimensions. [8] Now we know it was the egg that came before the chicken and that it was indeed golden.

Each of these studies shows how the Divine Proportion enables geometric bonding at the mesoscopic scale of carbon and water, just underneath DNA. But how could this geometry have become encoded in the DNA molecule? And what proof do we have that this helped guide the evolution of life?

The Divine Proportion in DNA

In a 2007 paper entitled The G-ball, a New Icon for codon symmetry and the Genetic Code, physician Mark White proposed that the codon table of the genetic code follows the shape of a 12-faced dodecahedron. Since there are exactly four nucleotides in DNA that combine in sequences of three to produce 64 codons (43 = 64), White suggested that the genetic code first folds into the shape of tetrahedrons that then combine into the shape of a spherical dodecahedron or its dual icosahedron (Fig. 3). [6]

Figure 3. Mark White’s ‘G-Ball’ DNA model showing the 20 standard amino acids organized in space according to water affinity.

Following the equilateral genetic structure predicted by Russian physicist and cosmologist George Gamow, White goes on to explain how the 20 connecting lines of the dodecahedron correspond to the 20 standard amino acids in DNA. Each amino acid assumes a location in the geometry according to their water affinity (how much they like or dislike water). From this, the dodecahedral sequence of amino acids is twisted by hydrogen around a fixed polar axis to create the 10-step spatial symmetry of a DNA molecule (Fig. 4).

Figure 4. DNA double helix modeled as G-ball dodecahedron resonating up around a central axis.

Once again, the Divine Proportion acts as a stabilizing constant in the DNA lattice. The axial view reveals a double pentagon very similar to the resonance pattern produced by a musical perfect fifth, both exhibiting golden proportions in their geometry. Even the DNA strands are spaced according to the golden ratio, making DNA not just a double helix but instead a golden double helix.

Another recent study by Chi Ming Yang, director of neurochemistry at Nankai University, found a quasi-periodic golden egg geometry encoded in the human genome that parallel’s White’s G-ball. Derived from the same building blocks of 20 amino acids and 64 tri-nucleotide codons in DNA, Yang found a cooperative ‘vector-in-space’ addition principle that stretches the molecule into an ellipsoid or egg-like shape called an icosikaioctagon (Fig. 5). Not surprisingly, he suggested this probably originated as five ‘stereochemical’ growth stages over a period of millions of years. [7]

Figure 5. C.M. Yang’s Quasi-28-gon model showing five stages of DNA evolution. When combined with White’s G-ball model, a golden egg is revealed n the space-time geometry of DNA.

When we now combine Yang’s Quasi-28-gon model with White’s G-ball model, the story of DNA can be told. As the G-ball protein ball resonates into a spherical yolk or fetus, water and other elements react with the outer carbon cage causing it to collapse into a protective boundary or shell. During gestation, the protein inside the egg boundary then resonates into a single harmonic standing wave to become the heartbeat of a new life. Throughout the process, the Divine Proportion in the DNA molecule acts to stabilize the overall geometry, guiding cellular reproduction and growth from the inside out. We can see this more clearly in the development phases of a human fetus.

Phi as a Biological Focusing Function

As a new human life grows, it takes the form of a Fibonacci spiral focused first around the eye and then the helix of the ear. In this way, the entire body resonates or unfolds outward from the center of the brain (like an idea). Here the Divine Proportion acts as a focusing function in the fetus for the development of sensory perception (Fig. 6). [9]

As the largest of the five sense organs, the body continues to unfold along the Fibonacci spiral now shifted to the front and centered on the navel. The skeleton and organs align at right angles to this spiral, proportioned according to Phi-spaced rings and the Vitruvian squaring of the circle. Here again, this is not a matter of natural selection and mutation. Rather, it is a simple matter of carbon-water geometry governed by the Divine Proportion. [10]

Figure 6. The Golden Egg: From embryo to adult.

Back inside the head, the Fibonacci spiral continues to swirl into its golden center, opening up the mouth to the sinus cavity and displacing inner cells forward to form the peculiar shape of a nose (Fig. 7). Human heads are indeed a fifth appendage winding around the ear canal into the jaw hinge, clenching inward like a fist or chambered nautilus instead of unfolding as our arms and legs do.

If heads were unwound like other mammals, they would form a perfect star geometry with the body that sequentially hears, sees, tastes, smells and feels as it narrows to a point. Add to this the fact that every human infant is born with a pentagonal cranium and it is apparent the human body unfolds from DNA as a pentagon in the anterior and dorsal dimensions and a Fibonacci spiral in the lateral (or side) dimension of the head.

So it is through a brief geometric analysis of human physiology that we can see how life evolves from DNA according to the Divine Proportion. Carbon resonates into regular geometry while water damps or crystallizes it into golden eggs, pentagons and spirals. From this one focusing function in nature comes our capacity for perception, response and the gift of human consciousness.

Figure 7. Human cranial egg as a Phi focusing apparatus.

Counter to the widely accepted theory that life was a fluke guided only by natural selection, carbon-water resonance has been guiding evolution all along even as entropy in the environment worked to tear it apart. The truth is, Darwinian evolution is but a veneer of adaptation on top of the preexisting patterning process of carbon and water.

As long as our theory of evolution remains incomplete, so do we. Without an understanding of atomic resonance and its primary role in evolution, people will never realize what they have in common with the rest of nature. Only through the acceptance of the Divine Proportion as a guiding principle can we as a society ever comprehend our deepest connection to the cosmos and fully embrace the divinity within.

Bibliography

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2. Williams G.C., “Adaptation and Natural Selection,” Oxford University Press, 1966.
3. Chaplin M.F., “Structuring and behaviour of water in nanochannels and confined spaces,” In: Adsorption and Phase Behaviour in Nanochannels and Nanotubes, Dunne L, Manos G. (eds), Springer, 2009, article in press.
4. Chaplin M.F., “A proposal for the structuring of water,” Biophys Chemist 2000;83(3):211-21.
5. Beavers C.M., Zuo T, Duchamp J.C., Harich K., Dorn H.C., Olmstead M.M., Baich A.L., (2006), “Tb3N@C84: An Improbable, Egg-Shaped Endohedral Fullerene that Violates the Isolated Pentagon Rule.” Department of Chemistry, University of California, J. AM. Chem. Soc. 128 (35), 11352-11353, 2006.
6. White M., “The G-ball, a new Icon for codon symmetry and the genetic code,” arxiv.org:q-bio/0702056v1 [q-bio.OT], Feb 26, 2007.
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8. Rojas, C.C., “From the Harmony of Nature to that of Architecture,” Web: http://vismath7.tripod.com/rojas/
9. Merrick R.S., “Interference: A Grand Scientific Musical Theory,” (self-published), Fairview, Texas, 2009. ISBN: 978-0-615-20599-1.
10. Merrick R.S., “Harmonically Guided Evolution,” Proceedings of the Natural Philosophy Alliance, Volume 7, June 2010.