In this article we will continue our discussion of the geometry of DNA.  In the last article we saw the importance of hexagons and pentagons in DNA structure and bonding.  Remember that the golden ratio is embedded within the pentagon.  Wherever there is 5-fold regular geometry, there is the golden ratio.

We discuss the golden ratio in extreme detail in other articles.  In this article we want to point out how the DNA molecule is built upon the golden ratio, pentagons and dodecahedra.

# DNA & the Golden Mean

1.618 is the ratio of the DNA structure.

a + b = 1.618 and a = 1

or a = 1.618 and b = 1

It is the only ratio that allows complete information or geometry to cascade down the harmonic series without destructive interference achieving perfect fractal data/wave compression.

A “Phi” Flower composed of golden spirals

This can be referred to as ‘implosion’ (as Dan Winter calls it).  This is the spin path to zero point.  (Zero point is the entrance/exit point between time/space and space/time.)

“The law of compression states that living systems follow a path [in which organization increases with time].  Evolution is the organization of information through time.  Life is evolution.  Life is increasing the organization of information through time.  In other words, the amount of information if life is increasing with time, and this trend is accelerating…

The existence of information leads to the formation of more information and thereby increases the overall information of the system.  It is a positive feed-forward loop.

The center of the phi flower is the entrance/exit point from time/space to space/time.  Credit: Marshall Lefferts – www.cosmometry.net

Another way to see this concept is by realizing that life seeks compressible information.  It uses this form of information for storage, and it decompresses this information for usage, just like a digital camera.

Another example of this is a human zygote.  A zygote can be thought of as the compressed information for generating a more complex organism, but where is the information that is needed to turn this cell into the final organism? ”1

We discussed implosion previous articles when we discussed time, space and gravity related to the Aether.  The DNA molecule comes from the same source and is built upon the same principles.  In order for the DNA to be able to interface with life in the way it does, it needs to be able to oscillate from time/space to space/time without losing information.  In fact, it needs a way to do this allowing for an infinite amount of information to be instantaneously available to time/space and space/time simultaneously.  This is an important part of the consciousness/matter feedback loop.

Consciousness/Matter Feedback Loop.  The ‘infinite’ center of the torus is the entrance/exit point from time/space (consciousness) to space/time (matter).

DNA is a carrier of a massive amount of information that is used as continual input into the metaphysical source reality, and through the DNA, an output of information from time/space flows back to space/time, re-configuring the life-form, or changing the activation of certain genes, of which the DNA is part.

The golden ratio is the only way the DNA can be organized to allow for this feedback loop to occur, so that information can be compressed to an infinite point to flow into time/space (implosion) and back out again.

The golden ratio structure of the DNA makes this infinite data compression and feedback loop possible.

Dr. Mark White says it best, “The genetic code stores information in highly compressed formats within DNA.  The code decompresses this information into complex protein populations through a complex sequence of molecular events that include DNA, RNA and protein, operating within a backdrop of time and space.”2

One 360 degree turn of DNA measures 34 angstroms in the direction of the axis.

The width of the molecule is 21 angstroms.  34 and 21 are both Fibonacci numbers.

Credit: Bruce Rawles – The Geometry Code

Each DNA strand contains periodically recurring phosphate and sugar sub-units (as discussed in the previous article).  There are 10 such phosphate-sugar groups in each full 360 degree revolution of the DNA spiral.  Thus the amount of rotation of each of these subunits around the DNA cylinder is 360 degrees divided by 10, or 36 degrees.

This is exactly half the pentagon rotation (of 72º), showing a close relation of the DNA sub-unit to the golden mean.

The double helix as a ratcheted dodecahedra.  Credit: Mark White

The braided thread of the DNA helix is a ratcheted dodecahedron.

The double helix as a ratcheted dodecahedra.  Credit: Dan Winter

The DNA double helix is made of a 32 degree tilted cube into a dodecahedron at the 4th axis of rotation.  Five spiraling cubes equals one dodecahedron.

Note here how the cube relates to the dodecahedron.  A cube can be inscribed in a dodecahedron.

Each of the different colored lines (red, blue, green, black, yellow) represent one of the five different cubes found in the dodecahedron.

Each of the 12 faces of the dodecahedron contains one of the 12 edges of the cube.  The cube’s edges are diagonals of the pentagons.  So, a 32 degree tilted cube can spiral along a path in this way to form stacked dodecahedra.

DNA is a fractal attractor because of its self-similarity – its inner structure is a mirror of its outer structure.

Dan Winter teaches that DNA is a biofeedback device to tell us when we have consciously chosen the appropriate thoughts and behaviors that make us sustainable [healthy & balanced as opposed to unsustainable or unbalanced].

He goes on to say, “DNA ultimately folds itself forging a ring torus in order to get the compression angles correct to cause the light acceleration [through space/time to time/space – the fluctuation between states of existence and non-existence or the physical and the metaphysical].

Randall Carlson notes, “Every cell in our bodies carries a copy of the DNA master code, inherited from the single fertilized egg that initiated our existence as individuals.”

DNA illustrates a very physical concept of the fractal-holographic nature of reality and life and the importance of the spiraling, oscillating torus that allows for the inward centripetal spiraling flow of Aether towards time/space and the simultaneous outward centrifugal spiraling flow of Aether back out into space/time.

These ideas are the basis of quantum physics as they are the basis of the DNA molecule’s structure and function.

# Genetic Geometry Takes Shape

Fractal geometry plays an important role not only in the structure of the double helix, but also in how the extremely long strand of DNA fits into a cell.

Fractal Geometry makes it possible for all that DNA to fit into a cell without tangling.

“Inside the cell’s nucleus, the double helix folds up in myriad loops and twists.

The genome packs into the nucleus in a manner consistent with the structure of a fractal globule, shown here – a polymer state that is extraordinarily dense, but entirely unknotted.”3

Olena Shmahalo/Quanta Magazine. Globule courtesy Miriam Huntley, Rob Scharein, and Erez Lieberman Aiden

Job Dekker, molecular biologist at the University of Massachusetts Medical School in Worcester says, “Scientists have made much progress in mapping the genome, but “this information-storage view reveals almost nothing about what makes a specific gene turn on or off at different times, in different tissue types, at different moments in a person’s day or life.

The beauty of the [double helix DNA structure] made people forget about the genome’s larger-scale structure.  Now we are going back to studying the structure of the genome because we realize that the three dimensional architecture of DNA will tell us how cells actually use the information. Everything in the genome only makes sense in 3-D.”4

“The increasingly detailed hierarchical picture of the genome that researchers like Dekker, Misteli, Aiden and their colleagues have been building goes something like this: Nucleotides assemble into the famous DNA double helix. The helix winds onto nucleosomes to form chromatin, which winds and winds in its turn into formations similar to what you get when you keep twisting the two ends of a string. Amid all of this, the chromatin pinches off here and there into thousands of loops. These loops, both on the same chromosome and on different ones, engage one another in subcompartments.”5

“The architecture of the genome is consistent with one-dimensional curves such as the Hilbert curve and the Moore curve that densely fill higher-dimensional space.

Hilbert curve: Miriam Huntley, Rob Scharein, and Erez Lieberman Aiden; Moore curve: Robert Dickau via Wikimedia

Recall from previous articles about the photon and how the photon loops and loops in various ways to form subatomic particles of various natures.  Now recall how everything in physical reality is made of light – that is, photons.  DNA is nothing but photons confined to a certain geometric pattern that allows for information compression and activation.

The looping structure of the DNA on a large scale parallels what is happening on a quantum scale as photons loop and loop to form the subatomic particles, atoms and molecules that form the DNA.

We have the same principle occurring on different scales.

Now we will take a closer look at the DNA molecule itself.  This is from UK artist and mathematician, Mark E. Curtis, from 1997.

# The Geometry of DNA: A Structural Revision

Mark Curtis suggested a slight revision to the DNA model of Watson and Crick.

When he tried to translate their theory from two into three dimensions he ran into considerable topological problems because their structure does not conform to geometric principles.

Without compromising the essence of their structure (the double helix), he proposes a resolution of the geometrical inconsistencies by means of a simple change in the position of alignment between the purines and pyrimidines.

“This realignment is founded entirely upon geometric principles and further investigation revealed a series of mathematical equations that describe a 3-D geometric helix that conforms to the known ratios of DNA.”6

# The Double Helix

The structure of the salt of deoxyribose nucleic acid is a double helix, with ten bases to each turn.

The diameter of the helix = 21 A (angstroms)

The base height = 3.4 A

The helix extension = 34 A

34 and 21 are two consecutive numbers in the Fibonacci series.  Therefore their ratio, 1.6190476 closely approximates the Golden Ratio φ=1.6180339.

Credit: Mark E. Curtis

# The Pentagons of DNA

Credit: Mark E. Curtis

Curtis tells us, theoretically, it is possible to construct a helix from almost any series of polygons, though only one polygonal formation fulfills the necessary criteria: ten regular pentagons orientated about a decagon.

When translated into 3-D space, these pentagons would become prisms with all equal lengths.

A complete turn of the helix is formed by progressive rotation and extension of the ten regular prismatic pentagons.

It follows that the diameter of the helix (HD) and the height of the helix extension (HE) have a direct and constant proportional ratio to the pentagon length (PL) and pentagon diameter (PD).

His results (shown in his paper) cohere with the known dimensions of DNA, as revealed by x-ray diffraction data.

See his construction of an exact dimensional composite of the DNA double helix below:

Credit: Mark E. Curtis

He used single prismatic pentagons to illustrate the 3-D helix.  To ensure stability in the structure as it would exist in reality, it is necessary to place adjacent pentagons on each plane and stack accordingly, creating the double helix.

# Application of Geometry to the DNA Molecular Structure

Curtis’s modification requires adjacent pentagons at the heart of the base pairing.

He re-oriented the established molecular pairing so that the pentagons of adenine and guanine form hydrogen bonds to the hexagonal structures of thymine and cytosine.

This enables the necessary adjacent second pentagon to become viable.

It also accords with our understanding of molecular bonding and maintains the specificity of G with C and A with T.

Credit: Mark E. Curtis

# Implications

“This proposed structure for DNA is wholly founded upon mathematical principles. Although the geometrical modification to the base pairings is relatively minor, the resulting double helix manifests a clarity altogether distinct from that offered by Crick and Watson and would appear to shed light upon a number of areas of continuing uncertainty.”7

Curtis goes on to tell us, “Geometric equations predict the dimensions of DNA’s structure.  Not only does the pentagonal geometry predict the helical dimensions but it would also demonstrate ‘principle causation’.”

“The pentagonal geometry provides the dynamics required to build a consistent, stable and uniform helical structure and also establishes why there should be consistently ten bases contained within a single turn of the helix.”8

“Both the hollow center and side-by-side structural formation ensure instant access at any point within the helix.  This would permit the DNA (even circular) to open and close during its replication functions without entangling itself.”9

“The modification to the base pairing would appear to be able to exist in either the enol or keto formations.  (Guanine and thymine may exist in either enol or keto configurations and are believed to pass through tautomeric shifts from one to the other – in other words, an indiscernible and spontaneous leap by the hydrogen atom from a specific oxygen atom to a specific nitrogen atom or vice-versa.  The Crick and Watson proposal requires the keto formation, whereas this alternate proposal would appear to be viable in either of the formations.)”10

“While the sugar-phosphate backbones will undoubtedly prove integral to the stability of the helical structure, it is the geometry of the base-pair molecules themselves that is ultimately responsible for the formation of the helix.”11

Credit: Mark White

To end with a quote featured on Curtis’s website:

“…the choice between competing paradigms regularly raises questions that cannot be solved by the criteria of normal science.  To the extent, as significant as it is incomplete, that two scientific schools disagree about what is a problem and what a solution, they will inevitably talk through each other when debating the relative merits of their respective paradigms.  In the partially circular arguments that regularly result, each paradigm will be shown to satisfy more or less the criteria that it dictates for itself and to fall short of a few of those dictated by its opponent…the normal scientific tradition that emerges from a scientific revolution is not only incompatible but often actually incommensurable with that which has gone before…Because it has that character, the choice is not and cannot be determined merely by the evaluative procedures characteristic of normal science, for these depend in part upon a particular paradigm, and that paradigm is at issue.”

~ Thomas Kuhn: The Structure of Scientific Revolutions

1. White, Mark, MD, Four Laws of Biology Used to Locate the Genetic Code, Rafiki, Inc. 2008, http://www.codefun.com/Genetic.htm
2. ibid.
3. Amato, Ivan, Genetic Geometry Takes Shape, Quanta Magazine, February 25, 2015, https://www.quantamagazine.org/20150225-genetic-geometry-takes-shape/
4. ibid.
5. ibid.
6. Curtis, Mark E, The Geometry of DNA: a structural revision, 1997, http://www.curtisdna.com/markecurtis_dna_art_geometry/DNA_geometry.html
7. ibid.
8. ibid.
9. ibid.
10. ibid.
11. ibid.