Concept of Harmony Mathematics

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Concept of Harmony Mathematics

Unread postby junglelord » Sun Oct 12, 2008 8:09 pm

My quest to identify geometry of nature and to relate structure and function with a proper understanding of natural process and fractal relationships is missing something in modern math. APM showed me what I had been looking for since about the year 2000, a quantum structure system based on pi and phi. I found this Harmony Mathematics to be a natural extension of that thought process. Cheers.

Concept of the Harmony Mathematics
The golden ratio along with the numbers of pi and e have to occupy the prominent place in mathematics.
Thus, the neglect of the golden section and the harmony idea is one more strategic mistake not only mathematics but also theoretical physics. This mistake originated a number of other strategic mistakes in the mathematics development.

Concept of the Harmony Mathematics

The humanity became aware of a long time that it is the participant and the witness of huge number of different "worlds" surrounding it. And their own laws act in every from the "worlds". First of all there are the "mechanical world" and the "astronomical world" where "Newton's gravitation laws" act, the "electromagnetic world" where "Maxwell' equations" act, the world of "living nature", the world of "information", the world of "business", the "social world", the world of the "Art" and so on.

And the human science created the corresponding mathematical theories adapted very well to modeling of processes flowing in that or another "world". And this was the answer of mathematics to the "social need". The calculus created for modeling the "movement processes" and "gravitation laws" of mechanical objects was the brightest example of this. The electromagnetic theory created by Maxwell for modeling of the electromagnetic processes is the other brightest example.

We have described in our Museum a big number of examples where Fibonacci numbers and golden section play an important role. And the botanic phenomenon of phyllotaxis is the brightest example of this. And there arises a question: possibly there exist some "Fibonacci's world" subjected to Fibonacci numbers and golden section? Most likely the world of plants, animals and the man as the biological object is "Fibonacci's one". Recently the Ukrainian architect Oleg Bodnar showed that the geometry of living nature is the hyperbolic one. At that the growth processes are subjected to the hyperbolic Fibonacci and Lucas functions (we will tell about Bodnar' discovery more in detail). But possibly is the "world of business" the "Fibonacci world" too? And the highly unusual investigations of the American scientist Ralf Elliott ("Elliott's Waves") confirms this.

And like to the fact that the investigation of the "movement problem" brought into creation of the calculus, the most important mathematical apparatus of modern mathematics, and the investigation of the electromagnetic phenomena brought into the "Maxwell's equations", the modern scientific discoveries based on Fibonacci numbers and golden section demand on development of the corresponding mathematical apparatus adequate to the studying physical phenomena.

We showed in our Museum that the Fibonacci numbers theory was supplemented recently by some new mathematical results (the generalized Fibonacci numbers following from Pascal Triangle, the generalized golden ratios, the hyperbolic Fibonacci and Lucas functions being the extension of Binet's formulas to continues domain and so on). The algorithmic measurement theory being the generalization of Fibonacci "weighing problem" and also Bergman's number system and its generalization, "Codes of Golden Proportion", which, in essence, is the new number definition, play a special role in Fibonacci's field. These new mathematical results extend the topic of Fibonacci numbers theory and demand on systematisation of these new Fibonacci directions in the framework of some general idea. And just such attempt to systematize the different "Fibonacci's theories" was made by Prof. Stakhov in his lecture "The Golden Section and Modern Harmony Mathematics" delivered by him at the Seventh International Conference on Fibonacci Numbers and Their Applications (Austria, Graz, July 1996).

The hyperbolic Fibonacci and Lucas functions are the heart of the new phyllotaxis geometry (Bodnar's geometry), which presents by itself the brilliant confirmation of the effectiveness of the Fibonacci and Lucas hyperbolic functions for simulation of biological processes.

Thus it follows from this consideration at least two important modern applications of the Fibonacci numbers and the golden ratio theory namely:

Simulation of biological processes (Bodnar's geometry).
New computer theory (Fibonacci and "golden" computers).

As is well known the classical mathematical analysis based on the pi- and e-numbers was developed as the mathematical theory for simulation of mechanical processes (Newton's theory of gravitation). From comparison of the classical mathematical analysis with the Harmony Mathematics it follows that the latter, based on the golden ratio, is the interesting complementary to the classical mathematical analysis, its extension for simulation of biological and informational processes. Thanks to this approach the golden ratio along with the numbers of pi and e have to occupy the prominent place in mathematics.

Applications of the golden section in the Art are widely known. The Harmony Mathematics generates the new geometric proportions (the golden pi-ratios), which will be quite applicable to the art works. One may assume that the progress of the Harmony Mathematics will be able to influence to the progress of modern art.


Table 1.

Foundation of the "Classical Mathematics"
1. Euclidean number definition, natural numbers, number theory
2. Classical measurement theory, irrational numbers
3. Fundamental mathematical constants, the pi and e-numbers, elementary functions

Foundation of the "Harmony Mathematics"
1. New number definition based on generalized golden sections, generalized Fibonacci numbers, Fibonacci numbers theory
2. Algorithmic measurement theory, new number series following from the algorithmic measurement theory
3. Golden section, generalized golden sections, hyperbolic Fibonacci and Lucas functions

The main mathematical ideas and theories that underly the Harmony Mathematics:

1. Investigating the diagonal sums of Pascal triangle, the author came to the generalized Fibonacci numbers or Fibonacci p-numbers (ð = 0, 1, 2, 3,...), generalized the well-known Golden Section problem and developed the concept of the Generalized Golden Sections or the Golden ð-Sections (ð = 0, 1, 2, 3, ...) [2]. The author formulated a new scientific principle, the Generalized Principle of the Golden Section. This one includes in itself as special cases the "Dichotomy Principle" (ð = 0) and the classical "Golden Section Principle" (ð = 1) that came to us from the ancient science [3]. The Generalized Principle of the Golden Section underlies the following mathematical theories, which form in total the "Harmony Mathematics":

2. Algorithmic Measurement Theory [4] is a new direction in the mathematical measurement theory. In its origin this theory goes back to the problem of the best weights system choice (Fibonacci, 13th century). Its basic result is an infinite number of new, unknown until now measurement algorithms and new positional methods of number representations. They have practical and theoretical interest for modern computer and measuring systems. Fibonacci measurement algorithms based on the Fibonacci p-numbers, Fibonacci codes and Fibonacci arithmetic are one of the unexpected scientific results of the algorithmic measurement theory.

3. Theory of number systems with irrational radices is stated in author's book "Codes of the Golden Proportion" (1984) [5]. These number systems are a principally new class of the positional number systems that changes a correlation between rational and irrational numbers and concern to foundation of number theory [3]. New theory of number systems has fundamental interest computer science and can be used for creation of new computer projects. The ternary mirror-symmetric arithmetics [6] that is a synthesis of the classical ternary notation and Bergman's notation is one of the new results in this field.

4. Hyperbolic Fibonacci and Lucas functions [7-9] are a new class of hyperbolic functions. The Golden Section is the base of these functions. These functions have a "strategic" interest for theoretical physics if we take into consideration a role of the hyperbolic functions in Lobachevsky's geometry and Minkovsky's geometry (hyperbolic interpretation of special theory of relativity).

5. Fibonacci Matrices [10] that are based on the generalized Fibonacci numbers and the "Golden" matrices that are based on the hyperbolic Fibonacci and Lucas functions are a new class of the square matrices that have theoretical interest for modern matrix theory.

The "Golden" Projects:
1. New coding theory [11] that are based on the Fibonacci and "Golden" matrices can become the basis of new information technologies.
2. New theory of computers [4, 5, 6, 12] that is based on the Fibonacci codes and Codes of the Golden Proportion.
3. New theory of metrology and measurement systems [4, 5] that are based on the "golden" resistor dividers.
4. A reform of mathematical education based on the Golden Section.
5. Museum of Harmony and the Golden Section [13] (http://www.goldenmuseum.com/) as unique collection of all Nature, Science and Art works based on the Golden Section.

Concepts of Harmony Mathematics
http://www.goldenmuseum.com/1108HarmMath_engl.html

"Harmony Mathematics and its Application in Modern Science"
http://www.goldenmuseum.com/2204McMaster_engl.html


Doctor of Sciences in Physics and Mathematics, Professor
Gennady Shypov (Moscow):

In 1996 the author delivered the lecture "The Golden Section and Modern Harmony Mathematics" [1] on the 7th International Conference "Fibonacci Numbers and Their Applications" (Austria, Graz, 1996). This lecture was repeated by the author at the meeting of the Ukrainian Mathematical Society (Kiev, 1998) and then at the seminar "Geometry and Physics" of the Theoretical Physics Department of the Moscow University (Moscow, 2003).

Prof. Stakhov's lecture is irreproachable both under the form, and under the contents, that is, satisfies completely to the "Golden Section Principle". The most impression is the fact that such serious mathematical research is executed by one person. Results of Prof. Stakhov's researches have fundamental importance for development of mathematics and a computer science. Prof. Stakhov work is executed at so high level, that quite deserves its promotion on the Nobel Prize.

Professor Alan Rogerson,
the scientific supervisor of the International Project
"Mathematical Education of the 21-th century"

Museum of Harmony and the Golden Section
MATHEMATICAL CONNECTIONS IN NATURE, SCIENCE, AND ART
THE CONCEPT OF HARMONY AND THE GOLDEN SECTION
http://www.fenkefeng.org/essaysm18004.html

Mathematical Models of the Hyperbolic Worlds
http://www.mi.sanu.ac.yu/vismath/stakhov/index.html

Knots and Everything
http://www.mi.sanu.ac.yu/vismath/sg/sta ... /index.htm

From Euclid to Contemporary Mathematics and Computer Science
http://www.worldscibooks.com/mathematics/6635.html
If you only knew the magnificence of the 3, 6 and 9, then you would have a key to the universe.
— Nikola Tesla
Casting Out the Nines from PHI into Indigs reveals the Cosmic Harmonic Code.
— Junglelord.
Knowledge is Structured in Consciouness. Structure and Function Cannot Be Seperated.
— Junglelord
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Re: Concept of Harmony Mathematics

Unread postby webolife » Tue Oct 14, 2008 2:45 pm

Yea, JL, two golden finds in a row!
Truth extends beyond the border of self-limiting science. Free discourse among opposing viewpoints draws the open-minded away from the darkness of inevitable bias and nearer to the light of universal reality.
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Re: Concept of Harmony Mathematics

Unread postby junglelord » Fri Oct 17, 2008 3:36 pm

Implosion physics
To understand the free zero point energy of the universe, is to understand the ancient cosmologies and the nature of our universe. The ancients believed that he universe consists of a vibrating sea of energy, the ether that is all around us. This means that the material world does not exist of separate particles, but instead matter is created from standing waves in the ether. This ancient view of our universe is best explained in a novel physics called ‘implosion physics’ by Daniel Winter, who is an expert in sacred geometry, an ancient science and philosophy that can be traced back to the Egyptians.

Daniel Winter’s implosion physics describes matter as a self sustaining arrangement of imploding vortexes in the ether. The atom is simply the geometrical arrangement of these vortexes. Each vortex corresponds with what mainstream physics regards to be an electron particle. When the imploding vortexes are arranged according to the Platonic Solids, the electron shells and their magnetic quantum numbers, the number of electrons in a shell (2, 6, 10, 14) emerge naturally from the symmetries of these geometrical forms. Nest these Platonic Solids one inside the other to form fractals, and we have a model of the atom existing of different electron shells = fractal or nested set of Platonic Solids.

The Platonic Solids were mentioned by Plato 300 BC and he equated these solids to the five elements fire (tetrahedron), air (octahedron), earth (cube), water (icosahedron) and the ether (dodecahedron). Remember that Plato equated the icosahedron to water and we’ll show you how right he was!

Now just for a moment image the universe to be electrical in nature and imagine all matter to actually exist of these imploding ether vortexes. This makes our observable universe basically a matrix consisting of electromagnetic waves all imploding into what we observe as matter. The matrix itself consists of interwoven Platonic Solids geometries spun by these waves. When waves are nested within waves from long to short wave lengths, everything gets interconnected, galaxies, planets, molecules, atoms and subatomic particles.

This matrix exists of spiralling electromagnetic energy waves that interfere non-destructively into a zero or still point within the atom. The imploding effect is what we observe as gravity as these waves not only pack together in the implosion to form matter, but also speed up to reach superluminal speeds.
To visualise an imploding vortex just imagine the little whirlpool that is created when you pull the plug in your bathtub, feel the suction of the whirlpool as it attracts everything into its funnel. This is what the imploding ether vortex of electromagnetic energy does; it sucks in matter creating gravity. It’s also the key to zero point energy, since in the zero still point the energy density has become infinitely high!

Torsion fields
According to Dan Winter this is the relation between electromagnetism and gravity that Einstein was looking for. Russian scientists call these imploding electromagnetic energy fields, torsion fields. The spiralling wave that spirals into the zero still point is the torsion wave. Tapping the zero point energy from the universe is tapping the energy from the matrix of energy that makes up our physical reality! It’s tapping the energy from gravity itself!

In the fifties Dr. Hans Jenny demonstrated with his Cymatics experiments using simple sound waves that all of the Platonic Solids emerge as standing wave interference patterns in spherical volumes. The Platonic Solids are the blueprint for the self organising universe. The spiralling imploding waves in a vortex also create these Platonic Solids as standing wave patterns. The implosion is simply a set of these nested or fractal Platonic solids as wave interference patterns.



Cymatics experiments icosahedron on the left, star tetrahedron on the right

This is the reason why geometric forms like the Platonic Solids are able to resonate with the energies of the universe. Russian science calls them passive torsion field generators. This is the secret of the Great Pyramid of Giza that is actually half an octahedron and is able to resonate with the torsion fields of the Earth. The Earth’s electromagnetic energy matrix, called the Earth grid consists completely of these nested Platonic Solids. The Platonic Solid energy grids of the atom simply locks into the larger Platonic Solids of the energy grid of the Earth, which in term locks in the energy matrix of the dodecahedral zodiac and the dodecahedral energy grid of the universe at large (from the latest Hubble space telescope observations). This makes up the matrix of our physical reality.




Pictures courtecy of Dan Winter (http://www.soulinvitation.com)


Imploding donut field with internal Platonic Solids

The ancients understood all of this very well. It’s the secret of geomancy, Feng Shui, the art of channelling and balancing the Chi energy of the universe. By creating geometrical patterns on the land, resonance is created with the geometrical patterns of the energy matrix of our universe!


Structured water
With this introduction into ancient wisdom and modern day implosion physics, we can now start to explore the properties of water and start to understand how water can harness this life giving cosmic energy from the vacuum of space. The secret of water is that it is able to conduct the Chi, Orgone or zero point energy from the universe using the same ancient geomancy principles, the art of Feng Shui: resonance through geometrical form! It’s most likely the secret to the ability of our own body cells to harness the life force, the Chi, zero point or Orgone energy from the universe using these resonance principles.

It has been known for quit some time that water can form internal structures when the hydrogen atoms of one water molecule start to bond with the oxygen atom of another water molecule. Although the water molecule is electrically neutral, its charge is not dispersed equally along the molecule. Water molecules are actually small dipoles since the bigger oxygen atom in the H2O water molecule attracts the valence electrons harder than the much smaller hydrogen atoms. The result is that the hydrogen becomes somewhat positively charged and the oxygen atom becomes negatively charged. This dipole effect allows water molecules to form chains of molecules. The positively charged hydrogen atoms bond with the negatively charged oxygen atoms of another H2O molecule. The hydrogen bonding in normal water is very instable and these connections last only picoseconds. So water is constantly dynamically rebuilding these internal structures as a result of the thermic vibrations of the water molecule. Only at temperatures below zero do the hydrogen bonds become stable enough to form ice crystals.

A recent theory by Martin Chaplin Professor of Applied Science Water and Aqueous Systems Research of the London South Bank University demonstrates that water molecules can arrange themselves in various structures and configurations based on the icosahedron. The most amazing structure is a super icosahedral structure that exists of 13 smaller icosahedral structures with a total of 1820 water molecules:


Icosahedral super water cluster of 1820 H2O molecules

Chaplin’s model of the molecular structuring of water is able to explain many of the anomalous properties of water, such as its expansion between 0 en 4 degrees, its high boiling point and many other strange properties that makes water such a rare fluid. So what this theory shows is that water dynamically creates these super icosahedral clusters to give water its exclusive properties.

Now here’s the secret of water in relation with Orgone energy, these icosahedral structures resonate with the zero point energy through form! They are the waveguides that allow the zero point energy to implode. The icosahedral water clusters simply, nest or fit recursively into the fractal matrix of imploding waves that sustains matter, i.e. the atoms of the water molecules. According to Daniel Winter, the implosion of this electromagnetic energy into matter is what we observe as gravity. So in other words the icosahedral structure is a wave guide for the imploding Orgone energy, allowing super conductance of these imploding waves, which is just another word for this non-destructive Golden Mean based electromagnetic implosion. What happens in the water is that a vortex of imploding electromagnetic energy is created, drawing in this Orgone, or Chi energy from the universe into the water. Just think of it as an ether vortex or whirlpool that is sucking in ether and it is this suction of the ether wind is that we experience as gravity.

Recent discoveries in biology now show that the water inside a biological cell is highly structured. This is the secret as to why the Chi or life force energy of the universe animates all biological life.



Orgone and consciousness
Human consciousness seems to have an effect on the clustering of the water molecules.

In the late fifties, Russian scientist, Nikolai Kozyrev has proven that human thoughts and emotions relate to torsion fields. Torsion fields or vacuum domains as the Russians tend to call them are the equivalent of the electromagnetic imploding vortexes in the vacuum of space.

At Heart Math institute Daniel Winter has proven that e-motion is actually an implosion of electromagnetic energy from the heart and mind when coherence is reached between the EEG and the ECG. Feelings of love will harmonically entrain brain and heart waves by Golden Mean ratio related frequencies in the frequency spectrum of the EEG and ECG. This will create an imploding vortex in the energy field around the person. This effect which creates Kozyrev’s conscious torsion field, may also explain why Masaru Emoto’s water crystals are influenced by thoughts and emotions. Masaru Emoto is a Japanese scientist who has proven that the formation of ice crystals from water samples can be altered by human intention.

It’s noteworthy that all of Masaru Emoto’s water samples that stem from natural and unpolluted water sources as well as those that have been administered positive human intentions, form ice crystals with a hexagonal core. It’s only from pure, natural spring water or water that has been treated with love that these beautiful hexagonal ice crystals can be created. In all other cases, the ice crystals are chaotic.

The ice crystals with a single hexagonal core have fractal structures at the vertices of the hexagon, often hexagonal structures themselves. In reality the hexagon in Masaru’s water crystal is the top view of an icosahedron:



The hexagon in the icosahedron

Masaru Emoto research on this hexagonal or icosahedral structured water has shown that this water has abilities to transfer what he has coined ‘Hado’ or the vital energy of the universe. Now isn’t Hado just the Japanese term for Orgone that Wilhelm Reich discovered? Masaru Emoto’s research seems to acknowledge the abilities of water to act as a superconductor for this cosmic energy once the water itself gets structured. Masaru Emoto’s research has shown that:

Hexagonal structured water appears in natural clean water sources
Ordinary water such as tap water can be changed into hexagonal structured water by positive and loving human intentions.
Hexagonal structured water can be artificially created using scalar waves or torsion fields.


There is a Dutch psychic woman by the name of Woutje Winkler-Prins who’s been paranormally receiving information from her spiritual guides about geometrical forms that supposedly impose ‘healing faculties’ on water. She’s been creating her ‘structured water’ using geometrical forms drawn on paper for at least 20 years now and the latest geometrical form that she has been using to create her Donave trademark water is this:



Woutje’s geometrical form icosahedral super water cluster

The similarity between the two images is striking. Pay especially attention to the number of rings in both diagrams and the trapezium like shapes in the outer ring with the double loops.

Could it be that this woman has been intuitively receiving information about hexagonal or icosahedral structured water?

I think it’s not a coincidence.
http://www.soulsofdistortion.nl/water4.html
If you only knew the magnificence of the 3, 6 and 9, then you would have a key to the universe.
— Nikola Tesla
Casting Out the Nines from PHI into Indigs reveals the Cosmic Harmonic Code.
— Junglelord.
Knowledge is Structured in Consciouness. Structure and Function Cannot Be Seperated.
— Junglelord
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Re: Concept of Harmony Mathematics

Unread postby junglelord » Fri Oct 17, 2008 3:57 pm

Platonic Solids & States of matter:
What's so important about them?
http://blazelabs.com/f-p-solids.asp

An excellent read on how standing waves in the shape of platonic solids is the best way to understand distributed charge.
Pretty cool as I finally figured that out today as I was messing around with my Stator and Rotor idea.
:D

This would be a real simple yet profound fractal idea. The entire universe is electric motor fractals with standing waves of distributed charge in the geometry of platonic solids, nestled one in another. Thats how I see it now. Nestled electric motors, each one driven by a pump, ie a push/pull. The primary push pull would be the Gforce which we can see as we look at the orbit of the hydrogen electron. It makes I believe pointed vertices and not perfect circles or curved radius, but rather immediate change in height based on the effect of the Gforce.

On Geometry and Advanced Energy Conversion
http://www.padrak.com/ine/ONGEOMETRY.html

The Joe Cell.
Water and energy with platonic solids, via specially combined water into icosahedron shapes
http://www.soulsofdistortion.nl/downloa ... nation.pdf
Capacitors
Now here’s a radical shift from our current understanding of capacitors which has
not yet been accepted by mainstream physics.
A capacitor creates a classical static electrical field when charged. According to
Tom Bearden this classical static electrical field is not static at all! In reality the
charged capacitor creates a dynamic electromagnetic field that radiates from this
capacitor and dynamically interacts with the vacuum energies, the zero point
field. The ‘static’ electrical field is simply a dynamic equilibrium of virtual photon
emissions with the vacuum. What is perceived as a static electric field is therefore
a steady state dynamic flow of electromagnetic energy exchanged with the
vacuum.
Daniel Winter takes Bearden’s interpretation of charge as a dynamic
electromagnetic interaction with the zero point field of the vacuum even further.
Winter adds the required geometry for these electromagnetic waves and shows
us how the charge compression of this capacitor is created from the implosion of
these electromagnetic waves. It’s the charge compression or the electromagnetic
implosion that creates the voltage in a static electrical field.
According to Dan Winter the electromagnetic energy of a capacitor arranges itself
in Golden Mean ratio frequencies of EM waves along Platonic solid geometries that
allow these waves to implode to a zero still point. Winter’s calls this implosion of
electromagnetic energy a charge compression. The electron in Winter’s implosion
physics is an imploding vortex in the atom. These vortexes are aligned in Platonic
Solid symmetries and their funnels all join in the nucleus of the atom. The charge
compression is from negative charge to positive charge when imploding in the
electromagnetic vortex. In Winter’s implosion physics there are no particles, no
electrons and no protons, the electron-proton pair is this imploding
electromagnetic vortex. Since the charge compression in the vortex takes place
from negative charge to positive charge, from outside the atom towards the
nucleus, this is why the positive ‘proton’ particles are found in the nucleus and
the negative ‘electrons’ are found in the shells of the atom.
The Joe Cell is just one big capacitor creating an internal vortex field when
initially being charged with 12 Volts.

Structured water
With this introduction into ancient wisdom and modern day implosion physics, we
can now start to explore the properties of water and start to understand how the
Joe Cell may harness this free energy from the vacuum of space. The secret of
water is that it is able to conduct the Chi, Orgone or zero point energy from the
universe using the same ancient geomancy principles, the art of Feng Shui:
resonance through geometrical form! The Joe Cell mimics the ability of our own
body cells to harness the life force, the Chi, zero point or Orgone energy from the
universe using these resonance principles.
It has been known for quit some time that water can form internal structures
when the hydrogen atoms of one water molecule start to bond with the oxygen
atom of another water molecule. Although the water molecule is electrically
neutral, its charge is not dispersed equally along the molecule. Water molecules
are actually small dipoles since the bigger oxygen atom in the H2O water
molecule attracts the valence electrons harder than the much smaller hydrogen
atoms. The result is that the hydrogen becomes somewhat positively charged and
the oxygen atom becomes negatively charged. This dipole effect allows water
molecules to form chains of molecules. The positively charged hydrogen atoms
bond with the negatively charged oxygen atoms of another H2O molecule. The
hydrogen bonding in normal water is very instable and these connections last
only picoseconds. So water is constantly dynamically rebuilding these internal
structures as a result of the thermic vibrations of the water molecule. Only at
temperatures below zero do the hydrogen bonds become stable enough to form
ice crystals.
A recent theory by Martin Chaplin Professor of Applied Science Water and
Aqueous Systems Research of the London South Bank University demonstrates
that water molecules can arrange themselves in various structures and
configurations based on the icosahedron. The most amazing structure is a super
icosahedral structure that exists of 13 smaller icosahedral structures with a total
of 1820 water molecules:

Icosahedral super water cluster of 1820 H2O molecules
Chaplin’s model of the molecular structuring of water is able to explain many of
the anomalous properties of water, such as its expansion between 0 en 4
degrees, its high boiling point and many other strange properties that makes
water such a rare fluid. So what this theory shows is that water dynamically
creates these super icosahedral clusters to give water its exclusive properties.
Now here’s the secret of water in relation with Orgone energy, these icosahedral
structures resonate with the zero point energy through form! They are the
waveguides that allow the zero point energy to implode. The icosahedral water
clusters simply, nest or fit recursively into the fractal matrix of imploding waves
that sustains matter, i.e. the atoms of the water molecules. According to Daniel
Winter, the implosion of this electromagnetic energy into matter is what we
observe as gravity. So in other words the icosahedral structure is a wave guide
for the imploding Orgone energy, allowing super conductance of these imploding
waves, which is just another word for this non-destructive Golden Mean based
electromagnetic implosion. What happens in the water is that a vortex of
imploding electromagnetic energy is being created, drawing this Orgone, or Chi
energy from the universe into the water. Just think of it as an ether vortex or
whirlpool that is sucking in ether and it is this suction of the ether wind is that we
experience as gravity.
It’s my hypothesis that when the Joe Cell is electrically charged using a 12V
battery, the cylindrical charge field will create an electromagnetic vortex that will
act as a catalyst and stimulate the formation of more of these naturally appearing
icosahedral super water clusters. When a critical threshold is reached and enough
of the water molecules have bonded into these super clusters, the ‘cosmic
charging’ of the Joe Cell becomes self steering. In reality no energy is stored
inside the Joe Cell; the Joe Cell merely acts as a super conductor of this free
energy, the Orgone, Chi or zero point energy of the universe that will freely flow
through the water. It has become a superconductor of this energy. The Joe Cell
most likely mimics a biological organic cell that draws the same Orgone energy
into it using the same mechanisms. Science has proven that the water inside a
biological cell is organised differently from the water outside the cell. This is the
Chi or life force energy of the universe that animates all biological life.
If you only knew the magnificence of the 3, 6 and 9, then you would have a key to the universe.
— Nikola Tesla
Casting Out the Nines from PHI into Indigs reveals the Cosmic Harmonic Code.
— Junglelord.
Knowledge is Structured in Consciouness. Structure and Function Cannot Be Seperated.
— Junglelord
User avatar
junglelord
 
Posts: 3693
Joined: Mon Mar 17, 2008 5:39 am
Location: Canada

Re: Concept of Harmony Mathematics

Unread postby junglelord » Fri Oct 17, 2008 5:57 pm

The periodicity of the atomic volumes of the elements (the ratio of their atomic weight to density) - a measurement of structure compactness guided Lothar Meyer in the 19th-century in developing the periodic table. The maxima in the graph at atomic numbers 3, 11, 19, 55, and 87 identify the Group 1A elements that begin each period. However, minima occur in the same graph at or near the atomic numbers 8, 14, 26, and 46, which mark the completed platonic shapes of this nucleus model.

Moon equated each vertice in his model to a proton. Eight protons, corresponding to the Oxygen nucleus, occupy the vertices of a cube which is the first nuclear shell. Six more protons, corresponding to Silicon, lie on the vertices of an octahedron which contains, and is dual to, the cube. The octahedron-cube is contained within an icosahedron, whose 12 additional vertices, now totalling 26 protons, correspond to Iron. The icosahedron-octahedron-cube nesting is finally contained within, and dual to, a dodecahedron. The 20 additional vertices, now totalling 46 protons, correspond to Palladium, the halfway point in the periodic table.

Beyond Palladium, a second dodecahedral shell begins to form as a twin to the first. After 10 of its 20 vertices are filled at Lanthanum (atomic number 56), a cube and octahedron nesting fill inside it, accounting for the 14 elements of the anomalous Lanthanide series.

Next, the icosahedron forms around the cube-octahedron structure, completing its 12 vertices at Lead (atomic number 82), which is the stable, end-point in the radioactive decay series. Finally the dodecahedron fills up, and the twinned structure hinges open, creating the instability which leads to the fissioning of uranium.

The completed shells of the Moon model, correspond to the elements whose stability is attested by their abundance in the Earth’s crust: Oxygen, Silicon, and Iron. These elements also occur at minima in the graphs of atomic volume, and of other physical properties (viz. compressibility, coefficient of expansion, and reciprocal melting point) as established by Lothar Meyer in the 1870s to 1880s. Palladium, which is an anomaly in the modern electron-configuration conception of the periodic table because it has a closed electron shell, but occurs in the middle of a period is not anomalous in the Moon model. Further, all four closed-shell elements in the Moon model occur at maxima on the graph of paramagnetism (versus atomic number), as reported by William Draper Harkins.

The Moon model is thus consistent with much of the same experimental data which underlies the periodic table of the elements, and explains additional features not explained by the modern, electron-configuration presentation of the periodic table. However, it seems to be inconsistent with the evidence from spectroscopy (upon which the electron-configuration conception rests) which suggests the periods of 2, 8, 18, and 32; it is also not consistent with the older law of octaves, which was developed to explain the phenomena of chemical bonding, and was subsumed in Mendeleyev’s conception. So, although Moon's model has introduced important geometric ideas, its accuracy is not good enough to match with experimental evidence. This means that his basic assumption - that vertices correspond to particles - may not be quite right.

At this point, we may have a look at what might be happening in a bose-eintein condensate (BEC). What happens when such a platonic structure is cooled down to zero Kelvin and screened from all external energies, does the structure collapse? The effect of external EM radiation, such as heat, on a standing wave structure, is exchange of momentum. It is a known fact that EM radiation exerts momentum on matter. Such impacts of heat energy upon the platonic arrives randomly from its surroundings, but gives the same average momentum impulses to each edge, which results in rotation of the platonic about its centre. In this way the platonic vertices will be able to span a whole sphere over time. The whole integral of momentum over the time taken to span one whole sphere is zero. Indeed if we lower the temperature to absolute zero, and shield our atom from all EM radiations, the atom will no longer rotate, and there will be no more volume of space trapped between any two spheres, hence no electron cloud, but the structure does not breakdown, it simply becomes one huge entity made up of stationary platonic standing waves. In 1995, Ketterle cooled a gas made of sodium atoms to a few hundred billionths of a degree above absolute zero and created the first Bose-Einstein condensate. In such condition, the atoms do not need the spherical boundary between them, since they are not rotating. This means that the atoms will eventually pack side by side to each other forming a single compact standing wave structure. No wonder that since all platonic shapes have an even number of vertices, BEC are only possible with atoms with even number of electrons + protons + neutrons, normally referred to as bosons. The Bose Einstein plot shown here (top) shows the distribution of atoms in volume as temperature is decreased from 400nK to 200nK down to 50nK, in the order from left to right.
Another variation of this state of matter is the fermionic condensate (lower plot). This substance has been created by cooling a cloud of 500,000 potassium-40 atoms to less than a millionth of a degree above absolute zero. In a BEC, the atoms are bosons. In a fermionic condensate the atoms are fermions. Bosons are sociable; they like to get together. Fermions, on the other hand, are antisocial. Any atom with an odd number of electrons + protons + neutrons, like potassium-40, is a fermion. To overcome the antisocial problem in the fermionic condensate, an external magnetic field has to be applied.

http://blazelabs.com/f-p-swave.asp
If you only knew the magnificence of the 3, 6 and 9, then you would have a key to the universe.
— Nikola Tesla
Casting Out the Nines from PHI into Indigs reveals the Cosmic Harmonic Code.
— Junglelord.
Knowledge is Structured in Consciouness. Structure and Function Cannot Be Seperated.
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Re: Concept of Harmony Mathematics

Unread postby junglelord » Fri Oct 17, 2008 6:50 pm

I have to say that the blazelabs site is a perfect combination of APM, Fuller and Tensegrity, Fractals, Harmony Math, Standing Waves, almost all the aspects of APM are presented the same way. The idea I had today of the Platonic Solids and standing wave EM, was fully realized as I read through this web page. Truly the best way to understand these issues for myself has come to pass.

The relationship between electron binding energies and the magic numbers is clearly a result of em standing waves with the geometry of platonic solids.
http://blazelabs.com/f-p-develop.asp
http://blazelabs.com/f-p-magic.asp

Magic numbers derived from variable phase nuclear model.
http://blazelabs.com/magicnumbers.pdf
If you only knew the magnificence of the 3, 6 and 9, then you would have a key to the universe.
— Nikola Tesla
Casting Out the Nines from PHI into Indigs reveals the Cosmic Harmonic Code.
— Junglelord.
Knowledge is Structured in Consciouness. Structure and Function Cannot Be Seperated.
— Junglelord
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Re: Concept of Harmony Mathematics

Unread postby junglelord » Fri Oct 17, 2008 9:42 pm

The etymology of the term nucleus is from 1704, meaning “kernel of a nut”. In 1844, Michael Faraday used the term to refer to the central point of an atom. The modern atomic meaning of the term was proposed by Ernest Rutherford in 1912, following the detection of a central massive entity by the scattering experiments of Hans Geiger and Ernest Marsden, carried out under his own supervision[1]. To the present day, this important component of the atom has been bombarded by more energetic probes in an almost desperate attempt to reveal its internal physics. Today, almost a century after its discovery, both mechanism and phase of matter of the nucleons are still an enigma. Various models have been developed to understand selective properties of the nuclei. Some of the most popular are the shell [2], liquid drop [3] , cluster[4], Moon’s[5], and double tetrahedron[6] models, which assume a gas, liquid, semi-solid, platonic solid and tetrahedral solid phase for the nuclei respectively. It is interesting to note that each of these models is able to describe very successfully certain selected properties of the nuclei; however, none of them is able to give a comprehensive description. Most of the characteristics of the different phases are mutually exclusive. I shall here introduce the Variable Phase Model of the nucleus[7], based on the projection of a hypertetrahedral nuclear structure into our view of perception, which is limited to the observation of three dimensions. In this model, the phase of the nucleus varies between the various phases of matter according to the angle of projection of the hyper dimensional nuclear entity, thus redefining mass as a physical parameter having both real and imaginary components.



History of the magic numbers

"Magic numbers" were first discovered by physicist Maria Goeppert-Mayer[8]. Careful observation of the nuclear properties of elements showed certain patterns that seemed to change abruptly at specific key elements. Mayer noticed that magic numbers applied whether one counts the number of neutrons (N), the atomic number (Z), or the sum of the two, known as mass number (A). Examples are Helium Z=2, Lead Z=82, Helium N=2, Oxygen N=8, Lead N=126, Neon A=20, Silicon A=28. Magic numbers in the nuclear structure have been coming up during all this time, but no plausible explanation for their existence has ever been given. Interestingly, there are peaks and dips for binding energy, repeating every fourth nucleon. This periodicity is one clear indication of a geometrical structure within the nucleus. In particular, those nuclei that can be thought of as containing an exact number of alpha particles (2P+2N), are more tightly bound than their neighbours. This effect is more pronounced for the lightest nuclei, but is still perceptible up to A = 28. For those nuclei with A > 20, the number of neutrons exceeds the number of protons, so some sort of distortion occurs within the cluster, as we shall discuss.

It is found that nuclei with even numbers of protons and neutrons are more stable than those with odd numbers. This comes from the fact that the physical structure must have an even number of vertices. A type of regular polyhedron would satisfy this condition, since no regular polyhedron exists with an odd number of vertices. These specific "magic numbers" of neutrons or protons which seem to be particularly favoured in terms of nuclear stability are:

2,8,20,28,50,82,126
Note that the structure must apply to both protons and neutrons individually, so that we can speak of "magic nuclei" where any one nucleon type, or their sum, is at a magic number.

We find magic numbers in the elements most abundant in nature:

2H1 (Hydrogen, 1st most abundant - 74% of the universe) 1+1 = 2 = magic
4He2 (Helium, 2nd most abundant - 24% of the universe) 2,2 = both magic
16O8 (Oxygen 3rd most abundant - 1% of the universe) 8,8 = both magic

Maria Goeppert-Mayer proposed that magic numbers should be explained in the same way as the electron shell model applies to electrons. So, in such a nuclear shell model, when a nuclear shell is full and the structure is formed (equivalent to saying that the nucleons have used up all of the possible sets of quantum number assignments), a nucleus of unusual stability forms. This concept is similar to that found in an atom where a filled set of electron quantum numbers results in an atom with unusual stability, usually an inert gas. When all the protons or neutrons in a nucleus are in filled shells, the number of protons or neutrons is called a "magic number." Visualizing the densely packed nucleus in terms of orbits and shells seems much less plausible than the corresponding shell model for atomic electrons. You can possibly accept the fact that an electron can complete many orbits without running into anything, but you would expect protons and neutrons in a nucleus to be in a continuous process of collision with each other. Despite the expectations, dense-gas models of nuclei with multiple collisions between particles didn't fit the data, and remarkable patterns like the "magic numbers" in the stability of nuclei suggested the seemingly improbable shell structure, which defines nuclei in layers similar to those of the electron shell model (Fig.1). In our model, a shell is built up of a structured layer.

Quoting Maria Mayer in "The shell model": "One of the main nuclear features which led to the development of the shell structure is the existence of what are usually called the magic numbers. That such numbers exist was first remarked by Elsasser in 1933. What makes a number magic is that a configuration of a magic number of neutrons, or of protons, is unusually stable whatever the associated number of the other nucleons. When Teller and I worked on a paper on the origin of the elements, I stumbled over the magic number. We found that there were a few nuclei which have a greater isotopic, as well as cosmic, abundance than our theory, or any other reasonable continuum theory, could possibly explain. Then I found that those nuclei had something in common: they either had 82 neutrons, whatever the associated proton number, or 50 neutrons. Eighty-two and fifty are magic numbers. That nuclei of this type are unusually abundant indicates that the excess stability must have played a part in the process of the creation of the elements..."



Doubly Magic nuclei

Doubly magic nuclei, are those nuclei which have both neutron number and proton number equal to a magic number. All such nuclei are particularly highly stable and are called "doubly magic".



Lead-208 is one such example of a "doubly magic" nucleus as it has both 82 protons and 126 neutrons. Calcium it yet another example of this exceptional stability quality since it has two of them. The existence of several stable isotopes of calcium is due to its magic proton count of 20. The two highlighted isotopes have neutron numbers 20 and 28 and a proton count of 20, all magic numbers. Atomic nuclei consisting of such a magic number of nucleons have a higher average binding energy than that calculated from the semi-empirical Weizsaecker formula, and also anomalously low masses and high natural abundances.
The existence of these magic numbers suggests some special shell configurations, like the electron shells in the atomic structure. They represent one line of reasoning which led to the development of a shell model of the nucleus. Other forms of evidence suggesting a geometrical structure include the following [9]

Enhanced abundance of those elements for which Z or N is a magic number.

The stable elements at the end of the naturally occuring radioactive series all have a "magic number" of neutrons or protons.

The neutron absorption cross-sections for isotopes where N = magic number are much lower than surrounding isotopes.

The binding energy for the last neutron is a maximum for a magic neutron number and drops sharply for the next neutron added.

Electric quadrupole moments are near zero for magic number nuclei.

The excitation energy from the ground nuclear state to the first excited state is greater for closed shells.

Tetrahedral stacking


Following the interpretation of Maria Mayer, the striking evidence for a structure in the nucleus was surprising at first, because common sense tells us that, a dense collection of strongly interacting particles should be bumping into each other all the time, resulting in redirection and perhaps loss of energy for the particles. This idea at first seems to violate Pauli's exclusion principle, but it does not. Keep in mind that the exclusion principle itself has been devised in the first place due to the lack of information about the geometrical structure of the electron shells.

Let us have a closer look at the nucleus. Assuming some sort of close packing arrangement for the nucleons, and assuming that the nucleus is perceived as a three dimensional object, it can be shown that the least number of nodes a three dimensional structure can have is equal to four, and that the simplest stable stacking structure is that of a tetrahedron (Fig.2). Four nucleons are thus required to fill the nodes of a tetrahedron. A nucleus with two protons and two neutrons would thus satisfy the most basic stable three dimensional structure, which would in fact give the nuclear structure of Helium 4 - otherwise known as the alpha particle.

Calculations of potential model, constrained by the hadrons spectrum for the confinement of the relativistic quark[10] and coloured quark exchange model[11], are also consistent with a tetrahedron formation of the nucleus. Also note that this tetrahedron structure is not something new, but dates back to 1964 in the work of Linus Pauling.[12] Once all four nodes of a tetrahedron are occupied, the next nucleon cannot be permitted at the same energy level, and the next spherical standing wave[13] (spherical tetrahedron) has to start forming. Recently, tetrahedron structures have regained interest in the study of the nuclear structure.[6] This theory also explains the emission of alpha particles from the nucleus. Many radio-nuclides achieve increased nuclear stability by emitting an alpha particle (a tetrahedral structure) rather than a single proton or neutron. This suggests that many isotopes contain one or more alpha particles in their nucleus.

If you consider every particle, being it a proton, neutron, or electron, as being restricted in space relative to its neighbour particle by the shape of a particular structure (spherical standing wave), there would be no need for any principle to show how and why these particles can never collide with each other, since they would be seating within the nodes of the frame. We know that collisions between electrons or nucleons in a particle are very infrequent. As I shall discuss later on, the possibility that matter exists in higher dimensions than three must not be excluded, in which case, two distinct three dimensional objects can overlap within the same three dimensional space without colliding. In fact from my own space time conversion system [14] one can easily deduce that mass is a three dimensional structure of energy, that is a six dimensional unit, and not a structure of point particles.
Note in the above diagram (Fig.3) that each nucleon is itself a spherical tetrahedron, each of which has three of its nodes touching the neighbouring nucleons, and one touching the external spherical tetrahedron of the formation. Thus the nodes of the spherical tetrahedral standing wave, are formed at the points where the stacked nucleons touch the external sphere. In a three dimensional nucleus, a tetrahedral stack consisting of four nucleons, such as an alpha particle, can accommodate an infinite number of stacked layers, while keeping the same properties of a tetrahedron. For example if six other nucleons are added at the base of a four nucleon tetrahedral stack, a new tetrahedral structure consisting of ten nucleons will be formed, having its three outermost nucleons touching a bigger external spherical tetrahedron.


What does an incomplete tetrahedron standing wave look like

Up to now we have considered filled up shells which equate to a complete spherical tetrahedron, equivalent to the Helium-4 nucleus (Fig.3). But what does the standing wave look like when the number of nodes is not equal to the number of vertices, for example in a Hydrogen nucleus? Does this result in a non-uniform structure within the spherical standing wave? How can a spherical wave contain one, two or three nodes? In the analogous situation of the electron shell model, chemists just put up the next shell and place the extra electrons orbiting around, but this picture is totally wrong.
Let us assume that a complete shell structure, say shell 's' has just been completed and a spherical tetrahedron has formed. We know that three similar spherical standing waves (known as subshell p) are now required until we have enough nodes to create a bigger tetrahedron shell. An analogous example to this process is with the case of using an oscilloscope trace while increasing the input frequency. If the wave signal frequency at its input matches exactly its time base frequency f, then, a single wave will appear at a standstill on the screen. If we double the input frequency to 2f , we see two standstill waves on the screen. But what do we see in between the two frequencies? If one increases the frequency slowly from f to 2f, the result is that the single wave will start moving across the screen until it slows down again and ‘morphs’ into the shape of two waves. This is exactly what happens at the nuclear level as extra nodes are added. This movement of the standing wave results in ROTATION or spin of the structure, until it builds up further nodes and 'slows down' into the new zero spin complete shells. Another analogy, this time mechanical, is that of a two spoke wheel being viewed under the light of a stroboscope. Slowing down the speed of the wheel will result in the observation of a stationary two, four, six, eight … spoke wheel. For revolutions which are not exact integer fractions of the stroboscope frequency, the spokes will appear to be either in random positions, or rotating and the observer cannot determine the actual number of spokes.
All incomplete, spherical, 3d standing waves have non-zero spin values and are pictured as various standing wave components. Zero spin and complete shells are achieved at the same time for the same reason - the number of nodes are equal to the number of nodes of a spherical platonic. Hydrogen(2) has a non zero spin since it has 1/2 the nodes required to complete the smallest and simplest spherical tetrahedron, which is achieved by a minimum of four nodes equivalent to the alpha particle, which in fact does have a zero spin. For many years, physicists have known that energy particles spin as they travel. For example, electrons appear to be continually making sharp 180-degree turns or half spins as they move through the atom. Quarks are often seen to make one thirds and two thirds spins when they travel. No one in the mainstream has provided a truly adequate explanation as to why this is happening. In our model, spin is just the movement of the spherical standing wave whenever the structure of nodes does not ‘lend itself’ to create a complete three dimensional structure.


What’s wrong with the standard model

The conventional 'bunch of grapes' nuclear structure (Fig.4) described in the standard model [15] has big flaws, and lacks to predict too many well known characteristics of the nucleus. One of its biggest flaws, is that it regards all elementary particles as point particles (zero dimension), which results in infinite energy when electric field energy is taken into account. However, it does give us a vague clue that multiple spherical standing waves can combine into another bigger entity, while maintaining themselves as separate identifiable similar structures. Evidence for this clustered structure comes from electron and alpha particle emissions from the atom.


However due to the lack of a defined structure, the conventional 'bunch of grapes' model tends to be an overly complicated model. In such a model, there is the need for the nuclear binding energy to overcome the tendency of the nuclear components to fly apart, because of the mutual repulsion of the positive proton charges. The mass deficiency of atomic nuclei has been hypothesized as the cause of this nuclear binding, and for this to take place, a new type of strong force has been hypothesized to exist in the form of 'exchange forces' between nuclear components. To complicate the issue further, a new class of particles like the meson have been invented to account for the force exchange mechanism. This hypothesis has in fact never been proved. The standard model also gives no hint to the existence of the nuclear magic numbers and no way to predict, or even explain the existence of its obvious shell structure. Since Bohr's orbiting electron model failed to describe the actual orbital distribution of the electron cloud, it had been concluded that the electrons motion is not governed by any ordered motion or structure, but is completely random. The standing wave shape is called an 'Orbital' - quite a misnomer considering nothing is orbiting inside! We usually learn that these represent the volume of space of probability distribution of an electron in an atom, and whose momentum and position cannot be determined at the same time. This is quite confusing since one would expect any moving object to have both momentum and position. It would all make sense if instead of probability distribution of point particles, we refer to orbitals as the real electromagnetic standing waves. Even if today we no longer learn about ‘orbiting electrons’, Heisenberg principle has unfortunately been established into mainstream science. The interpretation of such principle is that the atomic structure and the interactions of its electrons are random and can be discussed only statistically as probabilistic distributions of a random motion. On the other hand, we have nature, that shows us otherwise - crystal lattices[16] do not build up in random shapes, but in very specific shapes like simple cubic, body centred cubic, cubic close packed etc..
Unfortunately, to the present day, science gave up the search for a 'physical' model and most people prefer to ignore hard evidence in favour of an outdated principle, referring to electromagnetic radiation patterns (Fig. 5) as probabilistic distribution of electron ‘clouds’.

One can solve the binding force problem, by showing that the most stable nuclei, are tightly bound due to being in the stable nodal positions of a spherical standing wave. Before going into the actual hyper geometric structure model of the nucleus, we shall first hack the magic number sequence into a predictable three dimensional configuration.

Deriving the Magic Number sequence using a physical model

The first attempts to hack, or reverse engineer, the Magic number sequence into a geometric progression by the use of a physical model, date back to 1964 during Pauling's research[12]. From his records we can see that today’s magic numbers are exactly the same as those listed under his 'Observed' values. Unfortunately it seems that Pauling never got a solution to generate the correct sequence.

An interesting characteristic of the collection of protons and neutrons is that a nucleus of odd mass number A will have a half-integer spin and a nucleus of even A will have an integer spin. This highly suggests that the real structure is based on pairing of nucleons. The suggestion that angular momenta of nucleons tend to form pairs is supported by the fact that all nuclei with even Z and even N have nuclear spin I=0. In this section, we will need to stack pairs of tetrahedrons in our nuclear structure, so I shall first cite the triangular and tetrahedron number sequences. [17,18] These are very simple numerical sequences which are very useful for this study.

Hacking the Magic Number sequence using a physical model

The first attempts to hack or reverse engineer the Magic number sequence into a geometric progression by the use of a physical model, date back to 1964 during Pauling's research. From his records we can see that todays magic numbers are exactly the same as those listed under his 'Observed' values. Unfortunately it seems that Pauling never got a solution to generate the correct sequence.


Let's now see how these two number series apply to our tetrahedral pack of nucleons. Level n=1 is the top level - the black sphere, level n=2 is the red, n=3 is the yellow and so on... The first equation for the triangular numbers at n=3 gives us the number 6. So, 6 is the number of spheres in the yellow layer. Putting n=3 in the tetrahedral equation, gives us the number 10, and that is equal to the total of spheres making up the tetrahedron whose base is formed by the yellow spheres, that is the total of yellow, red and black spheres. If one wants to find the number of spheres required for the whole 5-layer tetrahedron, it will be the fifth number in the tetrahedron number series, that is 35. If you subtract the 4th triangular number from 35, you get the number of spheres of the whole tetrahedron, less the blue slice, which will be 35-10=25.

Next we will apply two other facts, already described in the this section to hack the magic number sequence. Fact no.1 is that nuclei up to magic number Z=20 have equal numbers of protons and neutrons, whilst for Z>20, the balance is lost. Fact no.2 is that the nuclie build up as a double structure. From fact no.1 we deduce that up to the formation of the structure containing 20 nucleons, the nucleus will look as a perfectly symmetrical structure, in electromagnetic terms, a perfect dipole. From fact no.2, we deduce that each tetrahedron level, builds up in pairs, and the next level tetrahedron is not started unless both pairs of the previous stage have been completed. Applying these rules we can now start from level n=1 until we get to Z=20 at n=3.

For n=1 (black sphere) the Tetrahedron number=1, the double tetra structure closes at 1x2 = 2
For n=2 (red and black) the tetrahedron number=4, the double tetra structure closes at 4x2 = 8
For n=3 (yellow, red, black) the tetrahedron number=10, the double tetra structure closes at 10x2 = 20
You may have already noticed, that these are the first 3 of the magic number series:

2,8,20,28,50,82,126

Now that we are at Z=20 (n=3), we know that the geometrical symmetry from here over is lost, that is the double structure (or 3 dimensional dipole) will no longer act as two perfect tetrahedron structures and so, we can no longer assume a simple symmetric double tetra structure. However, things do not complicate much, because what happens from here is that the two terahedron pairs now couple or hinge together much like covalent bonds are known to 'hinge' in chemistry. In electromagnetic terms, the dipole will no longer act as a purely resistive electromagnetic standing wave, but become slightly reactive due to their overlap.

The lowest values 2, 8, and 20 agree with independent nucleon motion into a single particle potential, like a harmonic oscillator. Nucleons' stacking positions occur at the vertices of the two spherical standing waves or the resistive configuration, shown above in Fig.9. Mathematically the sequence of complete shell nucleon numbers for Z<=20 is given by the same equation that gives the total number of spheres of two symmetrical tetrahedron stacks forming an ideal 3D dipole:

For 3 ≥n≥ 1: Z = Magic(n) = (n/3)(n+1)(n+2)

For 3 ≥n≥ 1: Magic(n) = (n/3)(n2+3n+2)
giving series: 2, 8, 20

The magic numbers 28, 50, 82, and 126 agree to those nuclei with a strong spin-orbit coupling (by Maria Mayer and Jensen) which have the mentioned nuclear co-valent bond type structure as discussed above. Nucleon stacking positions occur at the vertices of the two spherical standing waves shown on the right, or the reactive configuration of the above figure. So, for Z>20, the total number of nucleons is given by the above equation, less a pair of two triangular layers which represent the binding energy (or nuclear anomalous mass deficiency). In electromagnetic terms, this binding energy or missing mass is due to the reactive component of the capacitive dipole, a situation analogous to the real and apparent electric power in reactive loads we learn in electrical theory.

For n>3: Z = Magic(n) = (n/3)(n+1)(n+2) - n(n-1)

For n>3: Magic(n) = (n/3)(n2+5)
giving series: 28, 50, 82, 126, 184

Fig 9. - Resistive (left) & Reactive (right) dipole configurations
We have therefore finally hacked the magic number sequence into a physical model based on the double tetrahedron structure and simple dipole structure of the nucleus as proposed here. Not only do the above geometrical sequences derive all known magic numbers (2,8,20,28,50,82,126) but also derive the magic number 184, which is predicted by many scientists to be the next higher magic number. I have also showed how todays' classical 'bunch of grapes' nuclear model can be geometrically arranged while explaining the shells build up for the nucleus and giving a plausible explanation for the missing mass that is normally attributed to binding energy. This physical model also unveils a property of mass which is not so common in today's science literature - the imaginary component of mass. As is easily observed above, all magic number structures can be understood in terms of electromagnetic energy components, and since such components are complex in nature (complex means they have both real and imaginary parts), a structure which can be completely described in such terms will have the same properties of its constituents. Looking at the periodic table of elements, one should not only visualise nucleons simply bunching up as tetrahedral stacks of hard steel balls, but tetrahedral stacks of spherical electromagnetic standing waves with varying real and imaginary energy components. Only then, can one start to appreciate and predict the properties of the elements.


Deriving the Quantum theory nucleon and electron shell capacity

If we slice a stacked tetrahedron in two level layers, we find out that the total number of nucleons agrees with that predicted from Quantum Theory for each quantum shell, assuming that the number of protons and neutrons are equal.

Level n 1 2 3 4 5 6 7 8
Quantum Shell number N 1(K) 2(L) 3(M) 4(N)
TRI(n) 1 3 6 10 15 21 28 36
Nucleons in Quantum Shell =
Nucleons in two level slice =
TRI (2N) + TRI(2N -1) 4 16 36 64
For the case Protons= ½*nucleons 2 8 18 32

Table 2

If we define each principal quantum shell number N, as a two level slice of a tetrahedron, then, the number of nucleons per slice = TRI(n) + TRI(n-1) where n=2N. As already mentioned, the sum of two consecutive triangular numbers is always the square number of the highest triangular level.

The total number of protons or electrons in such a slice = ½ * total nucleons in slice
So, Zmax = ½ [TRI (n ) + TRI (n-1) ]
Zmax = ½ n2
Zmax = ½ [ 4N2 ]
Zmax = 2N2 , giving the sequence 2,8,18,32,.. for principal quantum numbers 1,2,3,4…

This is the well known empirical formula which defines the maximum number of electrons in the set of orbitals, also known by their spectroscopic designation K, L, M, N, etc. ). We now reconfirm, that each quantum shell, is made up of two sub shells, or a two layer slice of a tetrahedral structure, which is composed of the triangular levels TRI(2N) and TRI(2N - 1). It thus follows, that the electron structure is closely related or simply a direct effect of the nuclear structure. This is the same as saying that the far field radiation pattern of a radio antenna, can be directly deduced by knowing either its near field pattern, or its dipole structure[20].

Nuclear structure of inert gases

Two independent tetrahedron stacks will each generate Zmax sequence 2, 8, 18, 32 …. A tetrahedron stack pair would generate Zmax sequence 2, 2, 8, 8, 18, 18, 32, 32 …. A simplex stack pair having their top simplex projected over the same space in 3D, will thus generate Zmax sequence 2, 8, 8, 18, 18, 32, 32 …. and be like two tetrahedral stack structures with their uppermost tetrahedrons overlapping the same space. It will also be equivalent to a conventional electron shell structure: s, sp, sp, spd, spd, spdf, spdf.

Building up the dual overlapping stack, gives the element sequence 2, 2+8, 2+8+8, 2+8+8+18, 2+8+8+18+18, 2+8+8+18+18+32, 2+8+8+18+18+32+32 which results in elements 2, 10, 18, 36, 54, 86, 118 - well known as the inert gases (including the recently discovered Unonoctium - element 118!). Again, the sharing of the top tetrahedron indicates higher dimensional entities. Taking into account both protons and neutrons, the structure will look like four tetrahedral stacks, sharing a common central tetrahedron. For the sake of clarity, figure 10 shows only two of the tetrahedral stacks, the other two would be stacked over the other two faces of the central tetrahedron.


Fig. 10
This physical model also unveils a property of mass which is not yet conceived in today's science literature - the reactive or imaginary component of mass. As is easily observed above, all magic number structures can be understood in terms of electromagnetic energy components, and since such components are complex in nature (complex means they have both real and imaginary parts), a structure which can be completely described in such terms will have the same properties of its constituents. Looking at the periodic table of elements, one should not only visualise nucleons simply bunching up as tetrahedral stacks of hard steel balls, but (hyper)tetrahedral stacks of spherical electromagnetic standing waves with varying real and imaginary energy components. Spin and angular momentum are direct effects of the imaginary components. Only when we take these components into account, can we start to appreciate, predict and master the properties of the elements.

Tetrahedral or Hypertetrahedral stacking?

The structure for the pair of tetrahedrons for Z>20, shown in Fig.8, leads one to consider a hypertetrahedron (simplex or higher dimension) type of stacking, in favour of the simple tetrahedron stacking. To understand why, let's analyse a simpler situation with a pair of three dimensional spheres, as shown below in Figure 11:


Fig.11
You can see two different cases, showing the 3D spheres at a different angle of projection onto a 2D plane, one at say, time=t, and another at time t=t+Dt. The relation of their position with respect to the 2D projection plane is described by the projection or phase angle. In real life we can see the 3D view with no problem. If one takes photos from underneath them however, or simply projects their shadows on a screen, the result would be that shown in the 2D projection. Now, if one has got only a photo of the 2D projection, it will be confusing, since it will appear that two individual circles (lower left) are merging into two overlapping circles (lower right). The surface area of the two circles on the right is less than that of two separate circles, and can diminish to the surface area of a single circle, at which point the observer cannot even know whether there is one or two circles. The observer will call the effect as missing area, and if density (in a 2D world like Flatland) is defined as mass per unit area, the effect would be that of a missing mass. Now, you do not really have to imagine what a 4D hyper sphere would look like (it is impossible, even if you try), but just apply what you understood for the lower dimensional case, to the case, where the spheres exist in 4D, and the projection is on a 3D kind of screen. Two hyper spheres separated at a distance greater than their diameter, would look like two independent 3D spheres, and the image would look like it is the real thing. But when their horizontal distance is decreased, or the phase angle increases, strange things start to happen. They seem to be overlapping into the same space, until you can see only one sphere! One would actually see the two separate masses combining into a single mass, sharing the same space until their mass becomes that of a single sphere. The observer will call the effect of the missing volume as missing mass - a ‘mass defect’, as Einstein called it, accompanied with a respective increase in internal or binding energy. In the macro world, the effect will show as a decrease in density, or change of phase of matter from solid to liquid to gas to plasma and finally to vacuum, accompanied with a respective increase in internal energy. As you can surely understand, when such effect is observed, it is a clear indication, that your image is not the complete picture, and that the real thing is operating at a higher dimensional level. One cannot really know if it's just one or many levels up, but it is certain that the observed dimension is a limited projection of the entity being observed. And that's exactly what's happening with our tetrahedral stacking within the nucleus. For Z<20, we see pairs of 3D tetrahedral stacking operating as normal 3D stacks would do. Only as Z increases further, we realize that strange things start to happen, the pair of tetrahedral stacks overlap and partly share the same space, resulting in a mass defect. At that stage, it becomes clear that a tetrahedral nuclear model is just a limited projection in 3D, of a higher dimensional entity - a hypertetrahedral stack. You will now clearly understand, that if we define mass as a 3D entity, it will always be a shadow effect. In other words, the term mass refers to the apparent component of a much complex entity. This is the reason of the long time failure of generating a 3D physical model to represent the complete list of known elements. The variable phase angle is the reason for which a nuclear model cannot assume any single specific phase of matter. Similarly to electronic components, where in practice, no component can be assumed purely resistive or purely reactive, the phase of matter and hence of the nucleus, cannot be considered to be either purely solid, or purely vacuum energy, both of which are purely theoretical limits. Such model must be considered as a hyper dimensional structure, otherwise, all those elements which do not happen to project into a simple enough 3D structure like the case for magic numbered nucleons and inert gases, will have spin, which will result in a rotating/overlapping three dimensional projection of hypertetrahedral stacks popping in and out of the 3D ‘screen’.

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If you only knew the magnificence of the 3, 6 and 9, then you would have a key to the universe.
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Casting Out the Nines from PHI into Indigs reveals the Cosmic Harmonic Code.
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Re: Concept of Harmony Mathematics

Unread postby junglelord » Fri Oct 17, 2008 9:49 pm

The fundamental hybrid tetrahedral structure

I am now going to explain the real origin of subshells s,p,d,f and also show that Zmax for shells g and h are somehow different than those defined for the conventional theoretic subshells. It is also shown that the empirical equation for the maximum number of electrons in level n = 2n2 just happens to give the correct answers only to the first four shells and such equation has no fundamentals. In fact the conventional equation implies that we can have an infinite number of subshells s,p,d,f,g,h,i.... whilst our proposed structure limits the shells to h, at which point the model can handle 412 atomic numbers. We will also go further to explain why nature abhors the existence of elements with Z>120.

At this point we no longer need Pauli's exclusion principle to explain subshells, since the limit of two opposite spin electrons per 'orbit' is built in the structure of the tetrahedron. In no electromagnetic standing wave structure could we ever have two vertices touching each other, so this principle is built inherently in our new definition for matter. In the preceeding sections I have explained that a tetrahedron, having 4 vertices, is equivalent to an atom having 2 Protons + 2 Neutrons. We also know that the number of electrons of such a stable atom will be equal to the number of protons. So for example, a tetrahedron structure we have 2 electrons. For each platonic, we can work out the number of electrons which is equal to half the number of vertices Z/2, as shown in the table below. Note that at each complete shell stage, that is a formation of a complete platonic shape, one of the spherical standing wave will always be a complete sphere formed by the previous higher energy levels. For higher atomic numbers, one of the vertices of each complete platonic shell will always be formed by a spherical platonic, which in turn can nest other spherical platonics within it. It's a fractal build up. For example, in the above diagram, you can see that the inscribed tetrahedron is made up of 4 spheres, three of which are 2p spheres and one 1s' sphere. So for the formation of a tetrahedron (4 vertices), you only need to have three extra spherical tetrahedrons. In general, you will always need the formation of n-1 new spheres which together with the existing complete spherical standing wave, will form the new platonic with n vertices. The quantum number dictates the energy level, seperated by s levels, so for example a 3s, a 3p or 3d subshell spheres will have the same quantum number. In the example shown, we see that although each of the 4 vertices of the tetrahedron looks electrically the same, one of them will result in a higher equivalent mass due to its internal structure. The higher the atomic number, the higher is such imbalance, which results in deviation of the nuclear stability line from the curve N=Z, as shown further above. Thus this model accounts for another experimental fact, which is otherwise unaccounted for in the conventional model. On the last column, Zavail shows the available electrons for each complete structure. Zavail= 2,10,18,36,54,86 and 118 represent all the noble gases, namely: Helium 2, Neon 10, Argon 18, Krypton 36, Xenon 54, Radon 86, and the still unknown ultimate element 118. Being complete platonic structures, these are the most inert elements to exist in nature.



Level
(Quantum number) Lowest level Platonic Vertices No. of inscribed tetrahedrons No. of tetrahedron vertices P+N=Z Electrons in subshell= Z/2 Zsmax Zlmax Zmax Zavail
1 = s,s' Tetrahedron + 4 1 4 2 (s) 2 4 2 0
Tetrahedron - 4 1 4 2 (s) 2 4 2
2 = (p,s)(p,s)' Dual Tetrahedron + 4 3 12 6 (p) 8 16 12 10
Dual Tetrahedron - 4 3 12 6 (p) 8 20 18
3 = (d,p,s)(d,p,s)' Octahedron + 6 5 20 10 (d) 18 36 38 36
Octahedron - 6 5 20 10 (d) 18 56 54
4 = (f,d,p,s)(f,d,p,s)' Cube + 8 7 28 14 (f) 32 64 88 86
Cube - 8 7 28 14 (f) 32 120 118
5 = (g,f,d,p,s)(g,f,d,p,s)' Icosahedron + 12 11 44 22 (g) 54 108 174 172
Icosahedron - 12 11 44 22 (g) 54 228 226
6 = (h,g,f,d,p,s)(h,g,f,d,p,s)' Dodecahedron + 20 19 76 38 (h) 92 184 320 318
Dodecahedron - 20 19 76 38 (h) 92 412 410


Why 118 elements not 412 ?



In the above table we see, that we can model all known elements with the proposed fractal structure by just using the first four structures: Tetrahedron, Dual Tetra, Octahedron and Cube. The two 'extra' structures containing icosa & dodeca structures, which could result in a total of 410 elements, seem not to be applied in nature. Why? The answer is quite simple, and you may understand it better as you follow this section. I have hinted in various sections that our reality is just a 'projection' of a unified higher dimensional reality in our 3D vision of the universe. In simple words, those things that cannot be found in higher dimensions, are most probably unstable and usually abhored by nature. The tetrahedron, cube, and octahedron all occur naturally in crystal structures. These by no means exhaust the numbers of possible forms of crystals. However, neither the regular icosahedron nor the regular dodecahedron are amongst them! As we have discussed earlier during the introduction to platonics, the icosa & dodeca structures are limited to exist in 3D, whilst the first four, and ONLY the first four structures exist in all dimensions. The fact that no stable elements with Z>118 have ever been found in nature, is in itself a clear indication that atoms, of which the universe is known to be made of, exist as a projection of a higher dimension than 4. So our proposed model gets truncated to the 4th quantum level, and the shaded part of the chart is deleted.
If you only knew the magnificence of the 3, 6 and 9, then you would have a key to the universe.
— Nikola Tesla
Casting Out the Nines from PHI into Indigs reveals the Cosmic Harmonic Code.
— Junglelord.
Knowledge is Structured in Consciouness. Structure and Function Cannot Be Seperated.
— Junglelord
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Re: Concept of Harmony Mathematics

Unread postby Vincent Wee-Foo » Sun Nov 02, 2008 12:47 am

Hi junglelord,

I agree with harmony mathematics is essential to holistically understand the geometry of nature and to relate structure and function.

While blazelabs site is not new to me, I come to realize they also have a pushing in gravity theory through your posts here. ;) Was goggling for vortical universe previously and they are the only site found, was more into their article on dimension, did not explore the site entirely and therefore have missed out something so significant. Would have saved a lot of headache previously on planetary gravity effect in figuring out my own way describing with unconventional terminologies.

Liked the way they have described planetary gravity with electromagnetic radiation pressure, and unifies the three natural force field as below, all following the principle of inverse-square laws:
Electrostatic Force F = KQ1Q2/R2 .... K=1/4pieo, Q= charge, R = distance
Gravitational Force F = GM1M2/R2 .... G= gravitational constant, M= mass, R = distance
Magnetic Force F = UM1M2/R2 .... U=1/u, M= magnetic monopoles strength, R = distance
~ Vincent Wee-Foo

Enlightenment on the the paradoxical effect of nature enlightens.
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Re: Concept of Harmony Mathematics

Unread postby danwinter » Tue Jul 19, 2011 5:18 am

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Re: Concept of Harmony Mathematics

Unread postby seasmith » Fri Jul 22, 2011 3:17 pm

Dan,

So what is the point you are making ?

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