Harmonically Guided Evolution

Scientific Paper
Title	Harmonically Guided Evolution
Read in full	Link to paper
Author(s)	Richard S Merrick
Keywords	Harmonics, Evolution, Resonance, Golden Ratio, Structure, Consciousness
Published	2010
Journal	Proceedings of the NPA
Volume	7
No. of pages	14
Pages	318-331

Read the full paper here

Abstract

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.

Overview

Merrick's proposal is that natural selection is not the whole story of evolution and is not even the deepest part of it. Beneath selection, he argues, lies a physical patterning process — harmonic resonance and damping — that fixes in advance the small set of body plans life can take, leaving selection to work as "a veneer of adaptation" on shapes already determined by physics. The paper is the biological arm of a larger project set out in his self-published book Interference: A Grand Scientific Musical Theory (2009).

The argument opens with a challenge to the fossil record. If selection alone shaped life, Merrick asks, where are the eight-legged higher animals that would outrun and outmanoeuvre quadrupeds, the three-legged creatures with more efficient circulation, the animals with eyes in the backs of their heads? Instead fish, reptiles, amphibians, birds, mammals and dinosaurs all converge on one internal template — wave-like spine, cardioid rib cage, single head, four limbs — while insects converge on a single three-fold exoskeleton of head, thorax and abdomen. That convergence, he holds, is not explicable by chance and selection and requires a physical cause. His candidate cause is the resonance of carbon-12 against the damping pressure of water, propagated upward through DNA, cells and organs by a single recurring interference pattern.

The argument

Carbon, water and the geometry of life

Merrick builds from mesoscopic chemistry. Carbon-12, with six protons, six neutrons and six electrons in two shells, is taken as the most stable and most freely bonding element, which is why it serves as the standard of atomic weight. Water, following Martin Chaplin's work on structured water, is described as organising into 4-fold tetrahedral units of 14 molecules, twenty of which assemble into a 280-molecule icosahedron, which in turn forms superclusters that map two-dimensionally onto a regular pentagon. The 5-fold icosahedral geometry of water and the complementary dodecahedral geometry of carbon then resonate together: carbon vibrates outward to produce a wave-like spine, water damps inward into a pentagonal frame. Life is a crystallisation under that pressure.

He cites as supporting evidence a 2006 American Chemical Society report of an endohedral fullerene, Tb₃N@C₈₄, in which two adjacent pentagons fuse in reaction with terbium and the cage warps into an egg-like quasi-crystal — for Merrick, an indication that the balance between pentagonal and hexagonal molecular geometry, rather than any external selection, is what caused cells to acquire enclosing membranes and vertebrates to acquire rib cages. "The egg clearly came before the chicken!"

Geometry in the genetic code

Two prior models are recruited. Mark White's "G-ball" arranges the 64 codons and 20 standard amino acids on a pentagonal dodecahedron, with amino acids placed according to water affinity, and derives the ten-step spatial symmetry of the double helix by twisting that dodecahedron about a polar axis. Chi Ming Yang's vector-in-space model at Nankai University derives an ellipsoidal "icosikaioctagon" from the same building blocks. Merrick combines them into a structure he says is common to all life: a 5-fold egg with a 12-fold yolk. He assigns the egg the quasi-crystalline shell proportions Φ³ long by 2Φ wide, reducing to Φ²/2 = 1.3090165, and reads Aesop's golden-egg fable as a garbled memory of this proportion.

Space as a resonant container

To carry the pattern from molecules to bodies, Merrick appeals to cymatics — Chladni's and Jenny's demonstrations that vibrated powder forms regular geometric figures — and proposes that space itself is the container. He states that on one interpretation the Vacuum is structured as an incompressible stationary cubic lattice, a field of nominal Schwarzschild black holes in which particles centre on Flamm-paraboloid vortices. Living tissue, pressurised into spherical bubbles by gravity and atmosphere, entrains into progressively larger cymatic patterns inside that lattice.

The Reflective Interference Model

The central construct comes from a Blackman spectral analysis of two tones diverging from unison to an octave. The resonant gaps in that spectrum fall at small whole-number ratios — 3:2 the perfect fifth, 4:3 the perfect fourth, 5:3 the major sixth and widest gap — and the envelope is a first-derivative Gaussian. Merrick reformulates it "organically" as the squares of the first twelve harmonics {1, 4, 9, …, 144} divided by the first twelve Fibonacci numbers {1, 1, 2, 3, …, 144}, and glosses the result as π² divided by Φ, "the squaring of the circle". Squaring and folding this curve back on itself inside a circular container gives the Reflective Interference Model, which in polar form produces a cardioid with an almond-shaped "mandorla" at the centre, and in linear form a double-Gaussian. He identifies these shapes across anatomy: leaves, fruit, bones, brain, the heart nested in the mandorla of a chest MRI, shoulders, wings, tectonic plates, and the paired breasts.

The Harmonic Lattice and the human body

Section 6 proposes a Harmonic Lattice: orthogonal standing waves superposed over concentric damping rings spaced by the golden ratio, with outer radius 2π, offered as a recursive Hilbert space for organic growth. Ring n carries frequency n×. Applied to Leonardo's Vitruvian Man, Merrick reports that the point of maximum resonance (5:3) falls at the lower throat and top of the heart, maximum damping (Φ) at the lower heart, with further gaps at brain, navel, perineum and knees; that the fifth harmonic matches the curvature of the spine; and that the seven tones of the major scale align with the seven chakra locations, colours included.

The quantitative core is a "squaring of the circle" calculation. With R = 2π = 6.28318, the Vitruvian circle has area πR² = 124.0248; the Vitruvian square has side RΦ = 10.1664 and area 103.3555; their ratio is 1.1999 ≈ 12:10 = 6:5, which he matches to the 12:10 ratio of carbon-water resonance. Equivalently π : Φ² = 1.1999. Ring 5, at area π(RΦ⁻⁴)² = 2.64, is then combined with that ratio and its reverse (π² : Φ = 6.099) to yield a "torso split" of (2.64 : 1.2) × (6.0 : 2.64) = 5. The spine, a half-period in length, is partitioned into 24 vertebrae, each group of ten matching the golden-egg proportion.

Extensions

The remaining sections extend the model outward. The solar system is fitted geometrically by taking each semi-major axis as 1.6877 times the last, starting from Mercury, a constant Merrick identifies as 39^1/7 and also as e ÷ Φ ≈ 1.68, with residuals described as a Bessel envelope of cylindrical harmonics and a claimed cumulative average variance under 0.04 per cent. Perception is treated as harmonic focusing, citing the Gaussian-derivative model of spatial-temporal vision and Gaussian filtering in the auditory cortex and cochlea. Starlight and laser light are said to become more coherent with distance because the space lattice filters out enharmonic frequencies — so a living body, being "crystallized light", is a slow-motion biological laser tuning itself over time. Conscious self-awareness is proposed as a pre-existing property of space "tuned in" by the brain acting as a quantum transceiver, drawing on Karl Pribram and David Bohm's holonomic brain theory and on Evan Harris Walker. A closing section on social evolution calls for the recovery of Pythagorean musica universalis.

Assessment

The paper's real contribution is the question it puts, which is a legitimate one and older than Darwin: why is the morphospace actually occupied by living things so much smaller than the space of viable designs? Developmental constraint, physical self-organisation and the limited repertoire of reaction-diffusion patterning are active research topics, and Merrick is right that a theory of variation-plus-selection alone does not by itself explain the recurrence of a small number of body plans. He is also right that the first-derivative Gaussian is ubiquitous and that Gaussian-derivative filters genuinely appear in models of visual and auditory processing; the references at [9]–[11] are real work and are described accurately.

Against that, the paper's central mechanism is never made to do any work. Nowhere does a resonance frequency, a wavelength, a stiffness or an energy scale appear. The gap that has to be bridged is roughly ten orders of magnitude — from the ångström scale of a water cluster to the metre scale of a human spine — and the paper bridges it by asserting that space, gravity and atmospheric pressure act as the cymatic container. But a standing wave in a container has a wavelength set by the container's size and the medium's wave speed, and no such wave is identified. Without one, "entrainment" is a word rather than a mechanism, and the many shape resemblances catalogued cannot be distinguished from the general fact that smooth closed curves with one axis of symmetry look broadly alike.

Several of the specific arguments have problems that can be checked. The claim that carbon-12 "exhibits the lowest possible energy of all the elements" is not correct; binding energy per nucleon peaks near iron-56, and carbon-12 is the mass standard by convention, not because it is an energy minimum. The description of the vacuum as a cubic lattice of Schwarzschild black holes is attributed to quantum chromodynamics and referenced to Misner, Thorne and Wheeler's Gravitation; neither QCD nor that textbook contains such a proposal.

The Vitruvian calculation is where the method is most exposed. The arithmetic is correct — 124.0248/103.3555 does equal 1.1999 — but the result is an identity, not a discovery: the circle-to-square ratio with side RΦ is π/Φ² for any R whatever, so choosing R = 2π adds nothing and the "12:10" is simply the numerical value of π/Φ², which has no connection to carbon or water beyond the coincidence that it is near 1.2. The "torso split" is worse: (A : 1.2) × (6.0 : A) is 6.0/1.2 identically, so the area of Ring 5 cancels exactly and the answer would be 5 whatever the human body looked like. A calculation whose input drops out cannot be evidence about its subject. There is also a plain slip: having correctly given Φ = (1 + √5)/2 on the preceding page, the paper writes Φ = (1 − √5)/2 when introducing damping, a quantity equal to −0.618.

The solar-system fit is a geometric progression, and geometric progressions of this kind have been known since Titius and Bode to fit the planets moderately well while failing at the ends and predicting nothing; the quoted "cumulative average variance of less than −0.04 percent" is a statistic of a cumulative average, which can be small while individual residuals are large, and no per-planet residuals are given. The identification of the ratio with e ÷ Φ is numerically true to three figures (1.6801 against 1.6877) but is a second, independent coincidence stacked on the first rather than a derivation. Similarly, the observation that roadkill distances follow a Poisson distribution is correct and is exactly what any independent-events process gives; it is evidence of independence, not of harmony, and the inference that it shows harmonics guiding time inverts the standard reading.

Finally, the paper's method is fundamentally that of pattern-matching without a null hypothesis. When a framework can accommodate spines, breasts, tectonic plates, planetary orbits, brain wiring, chakra colours, Gestalt principles and word-frequency statistics, the question that must be answered is what it forbids — and no observation is anywhere identified that would count against it. The closing sections, which move from anatomy to consciousness outside spacetime, to religion transformed into "temples of natural learning", to world peace, take the argument well past anything the preceding evidence supports, and this weakens even the parts that are defensible. The narrower thesis — that physical and developmental constraints, not selection alone, restrict the body plans available to life — deserves a hearing; it would be better served by one quantitative prediction than by the breadth on offer here.

See also

• Richard S Merrick
• Proceedings of the NPA
• David Bohm
• Black Hole
• Vacuum