Mathematics

# The 13 Digits of Pi

In Pi, the universal constant of periodicity, there are 13 digits separating the digits 26 equal to 2 x 13. Would it be a coincidence then that there are 13 averaged lunar phases in a year and a 13:8 resonance cycle between Venus and Earth. Read More...

# Derivation of Phi from Pi in a Standing Wave

There are many numerical and geometrical ways to connect the golden ratio Phi with Pi, but the easiest and most natural way is to sum the amplitude displacement of a standing wave fundamental at the node of its fifth harmonic partial. Measuring in radians, there are three steps to derive Phi from Pi. Read More...

# The DNA Egg Model

There are two geometric models found in DNA that help explain the geometry of the human body. The first is the Yang Quasi-28-gon Eggshell and the second is the White G-ball Yolk. Read More...

# Reflective Gaussian Geometry in Life

The harmonic interference pattern of two tones diverging over an octave produce the same geometry in polar coordinates as that of the human eardrum and brain. Read More...

# Planetary Spacing Model

Many planetary and moon resonances are known to exist in our solar system. However, any explanation on how this happened is difficult to find. Read More...

Social coherence can be modeled after the physics of a standing wave and harmonic self-organization. Read More...

# Mutually Orthogonal Isometric Hexagons

The geometric figure on the cover of INTERFERENCE was part of a graphic art series entitled Cubing the Human Archetype. Read More...

# The Fourier Series & Harmonics

After conquering Egypt in 1798 at the Battle of the Pyramids, the French fought and lost to the British a week later in a naval battle known as the Battle of the Nile. Stranded in Cairo, Napoleon set off on a three-year expedition across Egypt. With him was Joseph Fourier, a mathematician and trusted friend. It was during this journey that Fourier discovered that waves of any kind could be decomposed into a superposition of sine and cosine waves. Read More...

# Golden Spiral of a Flower

Given that every form of life on Earth grows out of a spiral and that indeed weather systems, planetary systems, solar systems and galaxies also form out of spiral formations, why is it that spirals are excluded entirely from the study of geometry and in fact much of the study of mathematics? Read More...

# Standing Wave Structure of the Human Body

One of the most egregious omissions in modern education is the fact that the body is a liquid carbon-water crystal that evolved harmonically according to the physics of a standing wave. Read More...

# Relationship of Pi to Phi in a Standing Wave

Most people interested in the Golden Ratio know that it is derived from the square root of 5, as Φ = (1 + √5) / 2. However, it is a little known fact that PI (or π) can also be derived from the number 5 corresponding to the fifth harmonic in a standing wave precisely where a Golden Ratio amplitude occurs. Read More...

# The Fine-Structure Constant as Resonance

In physics, the fine-structure constant α is a fundamental physical constant characterizing the strength of electromagnetic coupling. This interaction is a function of resonance and harmonic physics.

# Phi-damping Wells

When energy reflects into a resonating standing wave, Fibonacci vortices form around golden sections of the 2π period. Read More...

# Forbidden Apple of Harmony

The Apple of Knowledge symbolism is very old and appears to be related to the ancient belief that all life is harmonically organized. Here is a simple illustration showing how the golden mean is at the bottom of both horizontal and vertical geometries of the apple. Read More...

# Constructing the Vitruvian Man

Reverse engineering the geometry of the human body. Read More...

# The Harmonic Jupiter Hypothesis

The Harmonic Jupiter Hypothesis… Read More...

# Recursive Bio-Harmonic Ring Model

This is a chart of frequency associations for the human body based on the ring model described near the end of my book Interference. Read More...

# The Keyboard Models

This is something like what I visualize when I improvise jazz piano, only with additional layers and wave sets that unfold rapidly in time. I imagine sticking my hands into an oscillating web of harmonic waves floating over the keyboard and guiding the waves to shape different geometries. Read More...

# The Harmonic Lattice

According to quantum theory, space is not empty as we are all taught, but instead structured in the form of a very fine cubic lattice of quantum perturbations. For convenience, this lattice can be defined as a 3D grid of mutually orthogonal standing waves. Read More...

# Phi-Recursive Heterodyning

This is an illustration of "phi-recursive heterodyning" demonstrating how harmonics emerge from the golden ratio by following the Fibonacci series backward. Read More...

# Golden Powers in the Fibonacci series

The Fibonacci series converges to more than just the golden ratio. It also converges to powers of the golden ratio. Read More...

# The Galaxy that Laid the Golden Egg

Our schools and churches do not tell us everything. They don’t tell us even the simplest things; things like the Earth-Moon system matches the geometry of a hen’s egg and that both are a containment property of the golden mean, Φ = (5 + 1) / 2. Read More...

# How Nature counts

Imagine, if you will, a time before numbers. A time when people had not yet created symbols to represent quantity and order objects in the world. In this primordial, prehistoric world we might ask if numbers still existed, waiting to be discovered. If so, does Nature itself count and, if so, how? Read More...

# Embryonic Geometry

Thought I would post a more direct illustration of the geometry of an embryo prior to it resonating into the characteristic geometry of a human body.

# The Tetraktys

Here are a few words about the Tetraktys and its relationship to harmonic physics.

# The Twin PIllars of Hercules

After finishing my last article Eleven that described my experience (and apparent widespread phenomenon) of 'seeing elevens', I watched this excellent video about this same subject. Avia Venefica's comments about the symbolic meaning of the double ones of eleven and its duality are right on target, which prompted me to further connect this phenomena with the physics and mythology of harmonic resonance.

# Earth-Moon proportions from the Vescia Piscis

Here is a quick sketch demonstrating how the Earth-Moon system is a harmony between maximum resonance and maximum damping, then approximated in a simple equation using only Fibonacci numbers. Read More...

# Gaussian geometry of the human head

The geometry of the human head continues to intrigue me. In the book I examine the geometry of the entire body and propose a method by which atomic resonance and damping works to guide cell growth. I named the resulting model Burningman, partly because it appears as if it was burning through fractal recursion and partly because I see it representing a new mythology that might return some day through the simulated reality of cyberspace. In this post I examine the harmonic interference fields apparently behind the geometry of the human head -- layers of polar Gaussians applied within a recursive spherical phi-damping framework. Read More...

# An Isometric View of Space

So, I have been having various conversations related to the relationship between the perfect solids, the quantum lattice and my harmonic lattice / matrix. I really want to get a 3D modeling program and do it up right, but attached is a 2D illustration relating to all of this. The basic idea is that space is a very fine field of tiny black holes that let it "breathe." These holes perforate space and thus warp it into a cubic grid. Within this grid light and other EM energy flows along the lines of the cubes while crystallized energy or particles collect inside the cubes around the black holes. These comprise atoms which all have different harmonic properties and geometries that resonate in the lattice, bonding with neighboring elements depending on harmonic compatibility. Space itself acts as a subtle resonator (zero-point energy) to keep electrons moving and to help atoms bond into larger crystalline structures. Read More...

# Fine-Structure Constant is harmonic

The inverse fine-structure constant is known to define the electromagnetic force in an atom.  This constant has been measured to be 137.03599907098, but no one can adequately explain where it originates. It originates in the harmony between odd and even harmonics. Read More...

# Experimental evidence of harmonics in human head geometry

Yesterday, I received an email from Tom Roth who is in the middle of reading my book. He sent me an analysis he had done comparing a composite human head with the Vesica Piscis. I was very excited when I opened up the graphics he sent me because it uses a random population sample to experimentally prove that human proportions follow the models proposed by Harmonic Interference Theory. Take a look... Read More...

# Water as a pentagonal damping structure for life

Recent research has found that water takes on a pentagonal molecular structure that then combined further into an icosahedral form - exactly as the Greeks suggested over two thousand years ago. Water is a damping agent for carbon-12, combining to create life... Read More...

# The Solfeggio Scale

I have been getting a lot of email concerning the Solfeggio scale. It seems there have been several popular books about its healing effect on the body. Some have even purchased tuning forks tuned to its specific frequencies, which are higher than today's system. This post discusses the good news and the bad news about this scale. Read More...

# Relationship between geometry and wave interference

This is a summary of my philosophy regarding geometry as a function of wave interference. Read More...

# 5-fold temporal symmetry as an isometric projection of 12-fold space

Subsequent to the publishing of an article I wrote for NEXUS magazine, I was contacted by one Einar Thorsteinn, a geometer and modern artist outside of Berlin. He introduced me to his 5-fold geometry system, which we called FANG, and a unique star-like geometry he called Thorsteinn's Star. After corresponding for a while, he sent me a DVD-ROM filled with information about this system which he had published some years back with a Foreword written by his friend Buckminster Fuller. I have just begun to review this fantastic geometry, but it appears to me to be a way to view 5-fold geometry (a pentagram) from an isometric angle. Read More...

# Tetrahedral recursion as a model for space resonance

In communicating with Icelandic geometer Einar Thorsteinn living in Germany, I shared what I consider a very important ratio related to resonance in harmonic interference. Specifically, a couple of years ago I had found the ratio 1:81 = 0.012345679... built into the dimensions of Rosslyn chapel. I found that its repeating digits represents a natural resonance proportion in any harmonic standing wave, specifically as a 2:81 halo gap around the proportion of 5:3 (a musical major 6th) between any two coherent standing wave sources (tone, light, atoms, whatever). This is discussed in detail in my book.

But Einar pointed out that this proportion also represents the volume of a tetrahedron placed inside a larger tetrahedron such that its four points touch the incenter of each of the faces of the outer tetrahedron, assuming that the larger tetrahedron is inside a cube with volume equal to one... Read More...

# Have a Happy Winter Solstice

It suddenly occurred to me that a Christmas tree is a pagan symbol because it grows in the shape of a golden triangle found in a pentagram. Take a look at the fun Christmas card you can make out of it... Read More...

# Decoding the "Ghost Whisperer" crystal ball puzzle

Dan Reed sent me a link to this puzzle:

http://www.cyberglass.biz/customflash/ghostwhisperer/

Be sure to try this before you click to learn how the crystal ball "reads your mind."

# Life as Crystalline Music

While working on a new Flash animation to illustrate some new aspects of the golden ratio, I found the Rojas egg geometry described the orbital pattern of Pluto. This led me back to do a new analysis of the Rojas egg model and its application to life and the harmonic lattice. Read More...

# Possible New Mathematical Constant connecting Pi and Phi

While working on the harmonic lattice described in the book, I discovered that Phi (the golden ratio equal to 1.618033...) and e (the natural logarithm equal to 2.71828...) have a common factor of almost 1.68. I mentioned then that I thought that Napier used this number instead of the golden ratio to avoid offending the Church, who knew it to be a pagan number). As a result, modern science bases all of its study of nature on e instead of Phi, though it could have just as well used Phi as I did in my calculations. There in another interesting relationship between these two irrational and infinite numbers... Read More...

# What do a bug and an egg have in common?

In trying to explain the role of harmonic damping in both the formation of our solar system and life on our planet to a graduate astrophysics student about a year ago, I offered a simple question. The question was "What do a bug and an egg have in common." Mainstream science does not normally discuss such things because there is no unifying theory that explains why life takes the shapes it does. This entry is an attempt to show a connection between these two natural life formations in the behavior of standing waves. Read More...

# The first heartbeat of InterferenceTheory.com

This blog is intended as an exploration of some of the more exotic and controversial ideas related to harmonic science. The views expressed do not necessarily represent my decided opinion about a given topic - only areas of interest that I am exploring that could eventually lead to something useful. I have found that staying open-minded to even the strangest (and silliest) ideas will sometimes lead to valuable insights and discoveries.

To kick things off, I would like to explore the idea that a human heart functions harmonically according to the recursive Mandelbrot Set fractal.

- Richard Merrick, October 11, 2008 Read More...