Harmonically Guided Evolution

This paper proposes atomic resonance as a structural guide and predetermining condition for Darwinian evolution theory. Recent studies on the mesoscopic structures of water and carbon, together with the latest geometric DNA mapping theories, suggest that life emerges and grows according to predictable harmonic patterns found in organic chemistry, preserving and propagating specific atomic geometries into living organisms.

Based on this and relevant neurophysiological research, a harmonic Gaussian interference model for cellular entrainment is presented to explain the origin of common organic geometries, including cardioid, ellipsoid and spiral primitives, as well as 3-fold exo- and 5-fold endo-skeleton structures. From this, a recursive harmonic Hilbert space is defined for use in evolutionary classification, physiological analysis and organic simulations. Examples are provided, including a step-wise analysis of the human body.Avenues for additional research are discussed, including application of harmonic Gaussian interference models to cosmology, cognition, medicine, social theory and philosophy.

1. Introduction

To find our deepest connection to Nature, we need look no further than the geometry of the human body.  (Fig.  1)  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  connected with the evolution of 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  better  in  a  hostile  environment.  [1] Indeed, the theory of evolution depends exclusively on natural selection and survival of the fittest (with the occasional random mutation) to explain  the  shapes  of  the  tiniest  plants  and  organisms  up  to  the largest animal. [2, 3] The theory is probably best summed up by the rallying cry of the neo-Darwinist “If we could somehow restart life  on  Earth  (or  another  planet)  from  the  beginning,  it  would probably turn out completely different.”

As  things  stand  today,  Darwin  natural  selection  combined with  Mendelian  inheritance  has  become  the  only  generally accepted scientific explanation for life on Earth. Without a better explanation, most scientific-minded people choose this theory as is, defending it without question in spite of the fact that it cannot tell us, for instance, why we have five fingers instead of six or a wave-like spine rather than a straight  one.  Everyone knows instinctively that something is missing in evolutionary theory  to answer such questions, but what could it be?

Re-thinking Evolution

What  if  there  is  a  less  obvious  but  universal  property  in Nature that physically guides evolution from somewhere  beneath the  environmental  process  of  natural  selection  to  carve  the  basic shapes of life? What if life is as much a function of the way atoms bond with one another as it is genetic mutation and selection?

Common  sense  alone  tells  us  that  for  natural  selection  to be  the  only  explanation  for  why  life  appears  as  it  does,  the fossil  record  should  show  many  times  the  variations  found.  For instance,  since  eight  legs  work  so  well  for  a  spider,  shouldn’t we  find  fossils  of  higher  organisms  with  eight  legs  capable  of outrunning,  outmaneuvering  and  even  out-boxing  their  four-legged predators?

Or,  how  about  only  three  legs,  which  might  have  enabled  a more efficient cardiovascular system? Where are all the “failed” animal  fossils  with  entirely  different  appendages,  re-arranged internal organs, extra joints that offer greater flexibility or even eyes in the back of their heads? Wouldn’t some of these have been more survivable than many animals today?

Yet for some unexplained reason, fish, reptiles, amphibians, birds, mammals and even dinosaurs all ended up with the same basic skeletal structure consisting of a wave-like spine, cardioid- shaped rib cage, single head and four limbs. While natural selection does imbue each of these creatures with a particular anatomical variation or morphology, this basic 5-fold archetype was the one and only internal skeletal template that emerged as life evolved in and out of the sea.

Similarly, insects are a morphological adaptation of a single 3-fold  exo-skeleton  template  comprising  a  head,  thorax  and abdomen. These, too, appear to have occurred during the transition to land and air from simpler sea creatures.  As for invertebrates like jellyfish all the way down to bacteria and viruses, all manifest a morphology of simple periodic geometries, such as spheres, rings, toruses, tubes, helixes, stars and even icosahedrons.  Plants and fungi are much the same, branching  or  spiraling  as  groups  of  about  62%  and  38%  into  the extruded regular geometries of fruits, vegetables and flowers (Fig. 2).

But  for  natural  selection  to  favor  survivability,  shouldn’t we  expect  to  see  fossils  of  plants  that  once  branched  randomly (or  equally)  or  land  animals  with  much  more  diverse  features?

Shouldn’t  the  animals  alive  today  have  descended  from  more efficient and fiercely competitive, anatomical archetypes?

The fact is there is nothing in the theory of evolution and the fossil  record  that  can  explain  any  of  this,  any  more  than  it  can explain why leaves are not square or why fruit assumes the shape of regular geometries. So, what else could be at work to guide the evolution of life?

2. Atomic resonance as a framework for life

All life on Earth is composed mostly of carbon-12 and water. This is the case because carbon-12 bonds or resonates with more simple elements than any other element in the universe. It is for this very reason  that  carbon-12  is  the  international  standard  for atomic weight and all other elements are measured against it. With 6  protons  +  6  neutrons  in  its  nucleus  and  6  electrons  orbiting  in two shells, carbon-12 exhibits the lowest possible energy of all the elements  and  is  said  to  be  ‘unbound’,  thereby  creating  the  most stable atomic geometry possible (Fig 3). When mixed with water, carbon-12 creates endless chains of sticky amino acids capable of crystallizing into life.

This  idea  of  life  as  a  crystallization  process  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, aligning into the familiar helical lattice of DNA. It is the geometric pressure of hydrogen atoms in water that helps create the lattice and give DNA its twist.

In  recent  molecular  studies  of  water,  biochemist  Martin Chaplin  found  that  water  organizes  itself  naturally  into  a  lattice of icosahedral clusters, just as Greek philosopher Plato proposed more than two millennia ago. Water really does resemble the 12-pointed, 20- faceted geometry of an icosahedron.

The  water  lattice  begins  as  4-fold  tetrahedral  units  of  14 water molecules, aligning into 20 clusters to create the geometry of  a  280-molecule  water  icosahedron  (Fig  4).  This  structure  then assumes  a  variety  of  stable,  geometric  sub-structures  (such  as its  complementary  dodecahedron)  that  form  into  even  larger superclusters. At this mesoscopic scale of water, molecules arrange themselves into a 2-dimensional connectivity map of a regular 5-fold pentagon. [4a-f]

When the 5-fold icosahedral superclusters of water is then combined  with  the  complementary  dodecahedral  structures of  carbon,  something  very  interesting  occurs  -  they  resonate with  one  another  to  produce  the  characteristic  geometry  of life.  There  is  nothing  random  or  arbitrary  about  this  –  it  is  an inevitable  outcome  of  the  physics  of  harmonics  acting  at  the atomic  level.  Carbon  vibrates  or  resonates  with  itself  and  other simple  elements  to  form  a  wave-like  spine  while  water  acts  to deaden  or  ‘damp’  everything  into  a  pentagonal  framework.

The role of atomic resonance in creating organic shapes was demonstrated in another recent study showing the first step of enclosure needed for a living cell occurs from a geometrical folding of carbon molecules. In a 2006 publication of the American Chemical Society entitled, Tb3N@C84: An Improbable, Egg-Shaped Endohedral Fullerene that Violates the Isolated Pentagon Rule , it was reported that a  large,  Fullerene,  carbon-84  allotrope  constructed  its  own  egg-like  cage  when  two  adjacent  pentagons  in  the  carbon  molecule became  fused  together  in  a  reaction  with  terbium  (Fig  5).  [5]

Discovered by a combined team from the University of California,  Virginia  Polytechnic  and  Emory  and  Henry  College, this was the first indication that the regular soccer ball geometry of hexagons and pentagons in a large carbon Fullerene could wrap itself into an egg-like cage by reacting with another atom, thereby producing a uniquely organic geometry known as a quasi-crystal.

This discovery could help answer a lot of questions.  It may explain how amino acids ‘learned’ to form cellular containers to protect themselves from the environment.  It could even offer a reasonable  explanation  for  how  ribcages  came  to  form  around vital organs in all vertebrate animals. It suggests that the atomic balance between pentagonal and hexagonal molecular geometry is the primary cause for the enclosure process of life, rather than some mysterious external selection process. The egg clearly came before the chicken!

In  each  of  these  studies,  we  can  begin  to  see  how  evolution could be guided by geometric harmonies at the mesoscopic scale of carbon-water bonding. The 5-fold inward-damping  geometry of water  provides  a  kind  of  pressurized  container  for  the outward-resonating carbon-12 atoms, bonding out of inanimate elements into living harmonic crystals. The entire process could be described as a kind of biological music resonating out of a finely tuned atomic framework contructed primarily from water and carbon atoms.

From the perspective of atomic resonance, Darwinian evolution becomes a veneer of adaptation that depends on pre-existing and universal harmonic laws intrinsic to Nature.  Simple animals resonate into uni-body  and  3-fold  carbon-12  shapes  while  more complex forms succumb to the 5-fold damping pressure of water, branching  out  at  approximated  Golden  Sections  into  pentagonal clusters, such as roses, starfish and the human anatomy. As the most resonant life form of all, we humans exist at the razor’s edge of  atomic  harmony  -  perfectly  balanced  in  12:5  proportions  by Nature – to achieve consciousness and ponder our own existence.

Perhaps  it  is  time  to  update  Darwin’s  19th  century  theory of  evolution  to  include  atomic  resonance  acting  in  concert  with natural selection. And maybe the first goal for this new theory of harmonic  evolution  should  be  to  understand  how  carbon-water geometry is preserved in the genetic code.

3. Evidence of geometric encoding in DNA

A  recent  paper  by  physician  and  researcher  Mark  White, entitled  The  G-ball,  a  New  Icon  for  codon  symmetry  and  the  Genetic Code, proposed that the codon table of the genetic code follows the shape of a 12-faced pentagonal 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 organizes itself into the shape of tetrahedrons,  which  then  combine  into  the  shape  of  a  spherical dodecahedron – exactly like clusters of water molecules  (Fig 6).

Following the equilateral genetic structure predicted by Russian physicist and cosmologist George Gamow, White explains how the 20 edges of a dodecahedron (or 20 triangular faces of its dual icosahedron) can be used to represent the 20 standard amino acids in DNA. The amino acids are then assigned locations in the geometry according to their water affinity (how much they like or dislike water).

From  this,  protein  bonds  into  sequences  of  amino  acid tetrahedrons,  forming  into  a  12-sided  dodecahedral  framework that is then twisted by hydrogen around a fixed polar backbone to produce the 10-step spatial symmetry of the DNA double helix (Fig 7). [6]

Another study by Chi Ming Yang at Nankai  University  in China claims to have also found a quasi-periodic, egg geometry in the human genetic code, paralleling Mark White’s G-Ball model.

Derived  from  the  same  building  blocks  of  20  standard amino acids and 64 tri-nucleotide codons in DNA, Yang found a cooperative ‘vector-in-space’ addition principle that stretches into an  ellipsoid  or  egg-like  shape  called  an  icosikaioctagon  (Fig.  8).

Not surprisingly, this geometry was determined to have originated as five ‘stereochemical’ growth stages over a period of millions of years. [7]

So,  when  we  combine  Yang’s  quasi-periodic  model  with White’s  G-ball  model,  we  arrive  at  a  structure  common  to  all forms of biological life – a 5-fold ‘egg’ with a 12-fold ‘yolk’ inside. Through the harmonic physics of atomic resonance and damping, Nature has engineered DNA with its own eggshell container to protect the geometric resonance of life over time.

This can be understood a  a natural interaction between space and time. Water creates a spherical container for carbon-12 resonance, allowing only whole number harmonic structures to form in the yolk. Around this, a pentagonal water crystal forms to protect the yolk and gestation of life. This cage is then shaped into an egg as the pentagonal crystal recurses toward the square root of five and the yolk region is displaced along a polar axis. This causes the egg to assume the quasi-crystalline shell dimensions of Φ3 long x 2Φ wide, which reduces to Φ2 / 2 = 1.3090165.

While  the  idea  that  DNA  could  be  encoded  geometrically as  an  egg  may  seem  “improbable”  to  some,  the  idea  appears  to predate even Pythagoras. As a symbol of balance in all life, early natural philosophers seemed to understand the egg as an instance of the Golden Mean – cubed in its length and doubled in its width, derived from the square root of 5 in a pentagram.

As  an example,  Aesop’s  fable  of The  Goose  That  Laid  the  Golden Eggs, based on a much older Egyptian story, probably has more to do with how life grows harmonically inside a golden-proportioned egg  container  than  it  does  the  precious  metal.  In  an  ancient worldview founded on the physics of music, the golden egg  could have been seen as a pentatonic container for a dodecahedral yolk, creating  a  living  7-fold  diatonic  animal  in  between  (“dia-tonic” means “thru the body”).

But  even  with  the  growing  evidence  of  harmonic  structures in  DNA,  one  last  puzzle  remains  to  fully  understand  how  DNA unfolds  itself  in  space  during  reproduction.  How  exactly  do the  carbon  and  water  atoms  in  DNA  self-organize  into  larger organisms? And while the resonance of amino acids clearly start the  crystallization  process  at  the  mesoscopic  level  of  water  and carbon, what can we say enables this process to continue outward into the macro structures of highly evolved life?

4. Space as a resonant container

It is a well-known fact that sound will produce regular geometric patterns when particles of powder are vibrated on plates or inside liquid  containers.  Known  as cymatics   (from  the  Greek  word  for ‘wave’), researchers such as Ernst Chladni in the 18th century and Hans  Jenny  in  the  20th  have  shown  how  harmonic  waves  will reflect in containers to form circles, triangles, pentagons, hexagons and other, more elaborate, mandala-like patterns (Fig 9).

As  might  be  expected,  the  simplest  cymatic  patterns  occur inside a circular or spherical container, always aligning to a single line of symmetry. As waves resonate into standing waves, different harmonic frequencies combine to form regular patterns by crossing one another at whole number proportions. The same thing can be said to occur in the atomic substratum of DNA as harmonics guide cell mitosis. The only difference with DNA is space (together with gravity  and  atmospheric  pressure)  act  as  the  cymatic  container.

According to quantum chromodynamics, the vacuum of space is structured as a non-compressible, stationary cubic lattice.

One  interpretation  of  this  lattice  is  as  a  field  of  nominal Schwarzschild  black  holes  comprising  a  field  known  as  the Schwarzschild  lattice .  Within  this  definition  of  quantized  space, atomic  particles  (bosons)  are  said  to  center  on  spiraling  vortices (called  a Flamm  paraboloid)  in  a  given  cell  of  the  lattice,  forming geometrical  patterns  in  its  nucleus  and  orbiting  electron  shells.[8]

So, when we now consider carbon and water atoms resonating together  inside  a  geometrical  space  lattice  –  pressurized  into spherical bubbles by Earth’s gravity and atmosphere – the atoms and molecules in living tissue would naturally entrain and resonate synchronously into larger and larger cymatic patterns.For  life,  it  must  be  the  quantum  structure  of  space  and  the pressure  of  its  gravitational  “egg”  that  together  have  the  ‘know how’ to arrange vast numbers of resonating molecules into life-size crystalline structures. In this way, living cells would dynamicallyself-organize  into  stable  geometries  much  like  powder  vibrated inside a spherical water container.

In  the  container  of  a  human  body,  the  energy  of  resonating atoms, molecules and cells would have little choice but to entrain into a reflected harmonic standing wave, rippling outward from the 12 x 2 = 24 vertebrae of the spinal column with less and less energy to the tips of our 5 x 2 fingers and 5 x 2 toes. Here again we find the body described as a 12 : 5 dodecahedral proportioned carbon-water crystal resonating under intense gravitational pressure into the  container  of  the  quantum  chromodynamic  lattice.  It  is  not  a matter of metaphysics to say that life is crystallized light formed by spherical harmonics in a structured space.

The universal harmonic pattern of life

This discussion now brings us to a definition of life based on the physical process behind the formation of harmonics in a circular or spherical container. Properly defining this process is essential in understanding the physics guiding evolution and the patterning process of organic growth. As we will see, the geometry of life can be traced back to one universal pattern of harmonic interference.

Not too surprising, this universal pattern can be easily found using  a  “Blackman  spectral  analysis”  of  two  musical  tones diverging at a constant rate from unison upward to an octave (Fig. 10). Reproduced here with a built-in function in  Adobe Audition®, the  analysis  reveals  the  spacing  and  size  of  resonant  gaps  that form naturally according to small whole number harmonic ratios, just as Pythagoras had discovered over 2,500 years ago. Each gap corresponds to a simple musical proportion, such as the 3:2 ratio of a perfect fifth, 4:3 perfect fourth and the highly resonant 5:3 major sixth – the widest gap of all.

To be clear, this is not a random, variable or contrived pattern, but  the  one  universal  pattern  of  interference  produced  by  all harmonic  standing  waves  as  they  vibrate  through  any  medium.

This  spectral  pattern  is  not  limited  to  sound  only,  but  exists everywhere  harmonics  form,  including  electromagnetic  fields, laser  light,  musical  tones,  natural  vibrations  in  the  Earth,  the spacing and sizes of planets in our solar system and the coherent cellular  structures  of  life.  We  can  represent  it  mathematically using a statistical curve called a first-derivative Gaussian distribution  (shown in red in Fig. 10).

You  will  probably  never  learn  in  school  how  important  this harmonic curve really is, but it is present everywhere in Nature. It  approximates  the  change  in  the  number  of  spots  on  the  Sun, describes  the  change  in  diameter  of  blood  vessels  in  living organisms  and  estimates  the  thickness  of  tree  bark  as  it  reduces upward  in  a  tree,  to  name  but  a  few. As  a  representation  of  the velocity  change  in  a  Gaussian  “normal  distribution”  (or  “Bell Curve”), this one function is the foundation of probability science and the very cornerstone of modern statistics.

But while most scientists accept and use this distribution and its strange equation without question, some of us might still wonder what physical process is at work underneath it to cause harmonics to always self-organize in this way. How can we understand what this Gaussian equation is trying to tell us about Nature?

When  we  stop  to  consider  the  curve  from  a  philosophical perspective,  we  can  begin  to  understand  the  basic  principles underneath  it,  driving  the  harmonic  patterning  process. A  more intuitive and organic description of the resonance pattern can be expressed as the square of the linear harmonic series as it is curved (one might say  carved ) by the Fibonacci series (Fig. 11).

As we see in the figure, the interference curve is a natural byproduct of harmonics as they resonate and damp one another. It results from the square of the first twelve frequencies of the harmonic series, as {1, 4, 9, 16, …, 144}, divided by the first twelve Fibonacci frequencies {1, 1, 2, 3, …, 144}. This is summarized by the Harmonic Interference function  in the figure, expressing the balance between  spatial  resonance  and  temporal  damping  in  a  simpler,  more beautiful symmetric form.

With  this  one  equation,  we  can  see  how  Nature  balances itself between the finite and the infinite, harmonizing a closed resonating circle or harmonic wave with an open Fibonacci spiral. It represents nothing less than the geometric harmony of  π-squared divided by the golden ratio Φ, otherwise known as the “squaring of the circle.”

While this may all seem a bit abstract at first, its relevance to understanding how harmonics guide the evolutionary process will begin to become clearer after a minute or two. Consider first the fact that spherical stars and planets form out of spiraling clouds of plasma. Then consider that life also grows out of a spiral. We see this in the unfolded Fibonacci spirals of tree branches, the spiral of a chambered nautilus and the spiral of a human embryo. In a very real and physical way, everything emerges out of infinity as a spiral, eventually stabilizing into a harmonic wave or sphere.

So  when  we  now  take  this  harmonic  interference  pattern and  geometrically  square  it  again,  folding  it  back  upon  itself  as if reflecting inside a circular container, we arrive at perhaps the most  important  geometry  in  the  universe  and  the  one  guiding pattern at work in the evolution of life – the symmetrical Reflective Interference Model  (Fig. 12).[9]

Formed from the harmonic mean between a circle and a spiral, this organic-looking curve is the shape life assumes as it evolves into higher and more complex organisms. We can prove this by observation.First of all, DNA and all forms of life always orient around a polar axis (see Fig 13). In humans and other animals the primary axis becomes the spine while for plants it is the trunk or stem.

As  cells  grow  and  resonate  outward  from  their  polar  axis, the  Polar Reflective Interference Model tells us that they resonate or explode outward (in slow motion) as a circle or sphere, but then begin to lose energy and damp back inward, spiraling and twisting back  toward  the  polar  axis.  As  this  reflects  in  two  opposing directions,  a  heart  or  cardioid  shape  forms  with  an  intersecting almond-shaped  region  called  a  “mandorla”  in  the  center.  We see this geometry in such things as plant leaves, fruit, bones and internal organs, such as the brain and cardio-respiratory system.

A MRI cross-section of the chest is probably the most impressive example, revealing how the heart nests inside the mandorla.Sometimes this harmonic pattern runs along a line instead ofaround a polar axis. Examples of Linear Reflective Interference  can be found in such things as wings, shoulders and even the Earth’s spherical  tectonic  plates  (stretched  at  the  equator  and  narrowed near the  poles). The most noticeable  example of linear harmonic geometry  is  the  double  Gaussian  shape  of  human  breasts.  As the  organ  that  generates  more  energy  during  lactation  than  any other organ (including the brain), female breasts act as a damping container  for  cellular  resonance  either  side  of  the  heart.  Nipples are  a  function  of  this  resonance,  forming  near  the  apex  (or  max velocity) of the interference curve, opening at golden ratios to the surface of the body (Φ and – Φ in previous Fig. 12). All sentiment aside,  mother’s  milk  is  a  physical  expression  of  the  heart’s harmonic resonance.

This same harmonic interference pattern is found repeated at different scales and orientations throughout the entire human body. Yet, it is not immediately apparent why the pattern configuresitself the way that it does. Is it strictly random, a result of mutation and natural selection as the Darwinian theory of evolution claims, or is there an even larger harmonic pattern involved?

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