Fractal Dimensions of Spacetime in String Theory

Fractal Pattern Recognition Game for Artificial Intelligence - Part 2

I present a unified theory of spacetime physics, metaphysics, the philosophy of the mind and the divine geometry of nature. It will be revealed that this profound information is not a new understanding. Seen through the eyes of transfinite fractal cantor sets and golden mean renormalization, the mass spectrum of high energy particles resembles a nonlinear dynamical symphony where everything fits with everything else. The 5-fold symmetry of Penrose quasicrystal fractal tiling reveals a golden mean number system that is in harmonic resonance with the hierarchical organization of the fractal dimensions of spacetime in string theory. By using this established mathematical framework, we can direct Artificial Intelligence in a systematic way to the undreamed-of possibilities of using chaotic fractals to the extent of completely uncovering the true origin of quantum spin, which comes from a unified power source of energy in the universe.

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Figure 1 - Golden spirals in nature.

Introduction

As a mathematical person, I have always contemplated the beautiful fractal patterns of nature. I will present an alternative theory, unifying spacetime and consciousness (mind) through the language of numbers and geometry, opening new doorways in physics, mathematics, and spirituality. I have always believed that all things are interconnected and that profound knowledge comes from within.

Geometry is a field which allows us to perceive and numerically organize the forms and patterns that we observe in nature. The laws of Physics are especially intertwined with geometry, all perceived physical matter is a form of geometric expression. My greatest inspiration for this book, Professor Mohamed El Naschie has built a mathematical construct of spacetime by using cantorian fractal geometry. His theory, known as E - Infinity theory, remarkably calculates the entire mass spectrum of particle physics, allows us to understand previously unknown secrets of dark energy as well as the quantum wave geometry. E - Infinity theory reveals our mathematical reality in such depth that our current technology cannot achieve by any means.

By analyzing the E - Infinity mathematical framework with a metaphysical perspective, we arrive at a holistic theory of physics unification with consciousness (mind). I present a unified theory of spacetime physics, metaphysics, the philosophy of the mind and the divine geometry of nature. Many of the harmonic numbers of our known reality were encoded into the Bible, other ancient scriptures and into the geometry of ancient sacred sites. By using these key harmonic numbers, it will be revealed that this profound information is not a new understanding. Divine numbers resonate synchronistically throughout the construct of creation.

It may require a gradual reading process to fully grasp the scope and depth of the many layers of content in this writing spanning mathematics, physics, geometry, numerology, as well as modern and ancient / esoteric wisdom. This theory will show how the parameters of the Great Pyramid of Giza, the fine structure constant in Physics, and the 496 dimension E8E8 lie group in superstring theory are correlated through number. Most importantly, I see this as the beginning of a greater work in progress and is not a conclusion in and of itself.

This work aims to help anyone involved in what I perceive as an evolutionary process that is taking place in our collective consciousness. We are approaching a time where we will have the capability to realize the connection of all things micro and macro; breaking down all ideas of separation and strengthening the feeling of Oneness that naturally prevails.

A golden spiral is a logarithmic spiral whose growth factor is Φ, the golden ratio. The golden spiral is the fundamental geometry found everywhere in nature, from the arms of spiral galaxies to the winds of a hurricane. Even phyllotaxis patterns involving successive leaves and florets on many plants involve the golden ratio because it involves successive leaves or petals being separated by the golden angle in a spiral pattern.

All things in the universe are interconnected through the geometric pattern of the golden spiral vortex. The golden spiral vortex is the fundamental flow rotating on axis where the life force, chi, prana is in resonance with infinity. The ancient civilizations believed that the universe consists of a vibrating ocean of energy, the ether. Consequently, the world of matter didn’t exist as separate particles, but as the alchemy of consciousness, or the self organized transformation of the ether itself through the standing quantum wave interference.

The symbol of the spiral has been found in certain sacred sites, and shows the ancient knowledge about the manifestation of consciousness itself. The golden spiral allows a better understanding about how everything in the universe is interconnected through our minds, and how it could be possible for an advanced intelligence, or even a computing device to be in resonance with the grid of golden spiral vortexes from beyond our physical dimension.

Another example in nature, the shell of a snail shows the pattern of the flow of a golden spiral vortex in resonance. To give birth to the snail, the universe left the blueprint of the golden spiral. The greatest secret of nature, the golden spiral is the most binding of all mathematical relations; the key to the physics of the cosmos. Plato once said that continuous geometric proportion is the most profound cosmic bond. The golden spiral connects all things through one harmonic resonance.

Figure 2 - Golden spiral examples; milky way galaxy, hurricane storm, snail shell.

Spin Effect in the Universe - collaboration with Salah-Eddin Gherbi

Spin effect is everywhere from the smallest particles described by scientists to planets and galaxies. In nature, repeating patterns can be observed on any scale.

Historically the origin of spin was very difficult to interpret, in the genesis of quantum physics. With the introduction of particle physics a spin theory was developed. Previous to this a physical description of the electron’s structure and its spin had been a mystery. Spin is recognized to be a quantum phenomenon and its value independent from the properties of the particle yet there has been no successful physical description or any suggestion of its origin.

There is still much argument in the mainstream community as to defining the structured universe and whether matter consists of wave structures in space or particle objects with mass. In quantum theory it has been proposed that matter, substance, mass and charge do not exist physically, but are properties of the wave structure.

Circular motion is classified as spin or orbital motion. Spin is supposed to be the motion of an object around its center of mass. If physical objects are actually a manifestation of quantum waves, then spin effect is originally coming from a unified power source of energy in the universe. When two circles join to form a Vesica Piscis the center of each circle becomes a zero energy point. Everything is interconnected in the universe through energy, which means vibration and transportation. It is important to consider spin to be a quantum phenomenon and a universal mechanism observed in everything on any scale. As above, so below, universal consciousness follows the same pattern in distributing energy and giving birth to the infinite grid connecting everything together through the dance of the two polarities, Yin and Yang.

With this approach, no physical objects can be isolated. Universal consciousness is therefore an infinite energetic grid where everything else is affected if one part of the energetic web is triggered. This is similar to a stone hitting the surface of a lake. The description of physical objects acting independently and separate from each other is not in accordance with the transfinite holographic fractal nature of spacetime, which works only through vibrational energy waves.

The Seed of Life pattern is ever present in the geometric construction of the torus. Spin effect is caused by a power source of energy coming from the center, a Zero Energy Point, creating a toroidal energetic field resembling the cross section of an apple.

Figure 3 - Cross section of an apple.

Figure 4 - The seed pattern of a sunflower.

Figure 5 - Spin effect of the sunflower, forming a spiraling toroidal shape.

The sunflower shows information of the spin effect from nature. The seeds are more compacted around the center than those located at the outside edge. The geometric blueprint is a fractal expressed through an important release of energy at its center.

Figure 6 - Torus from a three dimensional view.

From a three dimensional framework, the torus is a curved energetic torsion field.

“Geometry is an ‘exact’ science. It leaves nothing to chance. It is precise. It is definite. By it we buy and sell our land, navigate our ships upon the pathless ocean, foretell eclipses, and measure time. All science rests upon mathematics, and mathematics is first and last geometry, whether we call its extension ‘trigonometry’ or ‘differential calculus’ or any other name. Geometry is the ultimate fact we have won out of a puzzling universe. ...There are no ultimate facts of which the human mind can take cognizance which are more certain, more fundamental than the facts of geometry.” - Carl H. Claudy

Mathematics of Phi, 1.618..., the Golden Number - Joe Dubs

Phi, Φ, 1.618…, has two properties that make it unique among all numbers.

If you square Phi, you get a number exactly 1 greater than itself: 2.618…, or Φ² = Φ + 1.

If you divide Phi into 1 to get its reciprocal, you get a number exactly 1 less than itself: 0.618…, or 1 / Φ = Φ – 1.

Figure 7 - These relationships are derived from dividing a line at its golden section point, the point at which the ratio of the line (A) to the larger section (B) is the same as the ratio of the larger section (B) to the smaller section (C).

This relationship is expressed mathematically as:

A = B + C, and

A / B = B / C.

Solving for A on both sides gives us this:

B + C = B^2/C

Let’s say that C is 1 so we can determine the relative dimensions of the line segments.

Now we simply have this:

B + 1 = B^2

This can be rearranged as:

B^2 – B – 1 = 0

Note the various ways that this equation can be rearranged to express the relationship of the line segments, and also Phi’s unique properties:

B^2 = B + 1

1 / B = B – 1

B^2 – B^1 – B^0 = 0

Now we have a formula that can be solved using the Quadratic formula. This formula allows you to solve a quadratic equation for an unknown x, with a, b, and c as constants.

A quadratic equation has this form:

ax^2 + bx + c = 0

The solution to this is found with the quadratic formula:

x =[-b ± (b^2 - 4ac)^(1/2)]/(2a)

So our formula for the golden ratio above (B^2 – B^1 – B^0 = 0) can be expressed as this:

1a^2 - 1b^1 - 1c = 0

The solution to this equation using the quadratic formula is (1 plus or minus the square root of 5) divided by 2:

( 1 + √5 ) / 2 = 1.6180339… = Φ

( 1 – √5 ) / 2 = -0.6180339… = -1/Φ

The reciprocal of Phi (which is normally denoted with an uppercase P), is known often as phi (which is spelled with a lowercase p).

Phi and phi can also be expressed in all fives as:

5 ^ .5 * .5 + .5 = Φ

5 ^ .5 * .5 - .5 = 1/Φ

The use of the Greek letter Phi to represent the golden number 1.618 is generally said to acknowledge Phidias, a 5th century B.C. sculptor and mathematician of Ancient Greece who studied Phi and created sculptures for the Parthenon and Olympus.

Figure 8 - Is there meaning hidden in Phi, the symbol for the Golden Number?

The central message from scripture of all of the major monotheistic religions is that God is One, who created the universe from nothing, splitting nothingness into offsetting forces and elements.

Curiously, the mathematical constant of 1.618.. that is found throughout creation is represented by the symbol Phi, which is the symbol 0 for nothing split in two by the symbol 1 for unity and one.

Could this be the meaning behind the symbol Phi? Adding Unity to nothingness produces the Fibonacci series, which converges on Phi. Now add God to the void, or Unity to Nothing.

In other words, add 0 plus 1 to get 1, and then follow this pattern to the Infinite. This is the Fibonacci sequence. 0,1,1,2,3,5,8...The ratio of each number in the series to the one before it converges on Phi as you move towards infinity ∞.

The Golden Proportion is analogous to God’s relationship to creation

The Golden Section, or Phi, found throughout nature, also applies in understanding the relationship of God to Creation. In the golden section, we see that there is only one way to divide a line so that its parts are in proportion to, or in the image of the whole:

The ratio of the larger section (B) to the whole line (A) is the same as the ratio as the smaller section (C) to the large section (B).

Only “tri-viding” the whole preserves the relationship to the whole.

And so it is with our understanding of God, that we are created in his image. Not by dividing the whole, but only by tri-viding the whole does each piece retain its unique relationship to the whole.

Only here do we see three that are two that are one.

The Book of John begins with these words that capture the essence of this:

"In the beginning was the Word,

and the Word was with God,

and the Word was God."

Phi as an insight to deeper spiritual connection and oneness

Figure 9 - Phi can be calculated with continued fraction expansion of the number 1, as shown.

Miika Kuisma observed that the act of “part of the whole adding the whole onto itself” can be thought of as a “mathematical way of describing conscious recognition of being part of the whole.” In application, this would suggest that “when someone sees himself/herself as part of the world without personal attachment to it, and stays firmly in that perspective, then he/she will also come into a harmonic relationship with the world. One cannot help but to become in Phi relationship with the nature. This could suggest even a healing process.”

The teachings of most religions express the thought that part of God is within each of us and that we are created in his image. The pervasive appearance of phi throughout life and the universe is believed by some to be the signature of God, a universal constant of intelligent design used to assure the beauty and unity of his creation.

Yin and Yang Energy - collaboration with Salah-Eddin Gherbi

Figure 10 - Fibonacci spiral forming an approximation of the Golden Spiral.

Yin and Yang energy can be observed as a Divine blueprint on any scale. The spinning spiral dance between the two polarities of Yin and Yang harmoniously celebrates the geometric nature of life.

A Fibonacci Spiral gradually approximates the Golden Spiral using quarter-circle arcs inscribed in squares of edge lengths corresponding to the Fibonacci sequence, shown here for squares with sizes of 1,1,2,3,5,8,13.

The Fibonacci Spiral or Golden Spiral is the path of expansion and contraction through which energy is in constant motion.

“Without mathematics there is no art.” - Luca Pacioli

Figure 11 - Conical Helix from a three dimensional view.

When we observe the trajectory of a spiral from the top we can see where the spiral begins but not where it ends. Another way is to view it as a constantly rotating circle expanding in a helical motion.

Figure 12 - The Flower of Life

Spin effect is caused by an energetic toroidal field, the quantum wave forming a huge web of points interconnected with others in the surrounding area. Each point is not preferential and isolated but is equated to others through the balance of Yin and Yang. This is why universal consciousness can be geometrically interpreted through the Flower of Life. A Zero Energy Point is located at the center of a circle from where life force manifests.

Figure 13 - Illustration of the horocycles.

Back in two dimensions, drawn in black are the geodetic curved lines emanating from a ‘point at infinity’. Like throwing a stone in a pool, horocycles ripple from this ‘point at infinity’. Horocycles are ever expanding circular waves.

Similarly, the spiral exponentially expands and emerges from a Zero Energy Point. Each Zero Energy Point or ‘point infinity’ is an infinite source of potential energy connected with every other surrounding Zero Energy Point in the energetic grid of the Flower of Life.

Figure 14 - Top view of the Golden Spiral conical helix image above (Figure 11) forming Golden Horocycles from a point at infinity.

The properties of hyperbolic geometry for a point at infinity are defined through Golden Horocycles centered at this point with a factor growth of the exponential powers of the Golden Ratio Phi (Φ).

Vortex or spiral energy connects everything in the universe through the divine blueprint. Chi or prana (life force energy) emanates from Zero Energy Points around an axis line creating an energetic grid that resonates infinitely through all of the potential points.

Figure 15 - Spirals from Newgrange in Ireland.

The symbol of the spiral has been found in many rock carvings and demonstrates a knowledge concerning the manifestation of consciousness itself. This is what connects each living being, resonating through the grid of etheric vortexes beyond the physical world.

Figure 16 - A snail’s shell.

The snail’s shell shows the pattern of spiral energy flowing from a Zero Energy Point. At the birth of a snail, a Golden Spiral comes into existence through the mathematics of the divine blueprint. It shows the Fibonacci Spiral an approximation of the Golden Ratio Phi (Φ).

Ancient civilizations believed that the universe consisted of a vibrating ocean of energy called the ether.

The ether acts like a superfluid organizing itself through an arrangement of vortexes. It favors the connection of all things. The geometric patterns resulting from Sacred Geometry demonstrate how the vortexes could be organized in a structured way. The vortexes could be structured to form the five Platonic solids in a sphere. These standing quantum wave interferences in the ether could be formed by using sound waves within the volume of a sphere. In the 1950s, Dr. Hans Jenny demonstrated through cymatics the formation of the Platonic solids within a vibrating sphere of water.

Figure 17 - The star tetrahedron formed.

Figure 18 - The icosahedron formed.

The vortexes can be arranged in twos, threes, fours, and so on to form structured geometric patterns.

The sphere is a geometric container showing how the ether behaves and organizes the four fundamental interactions of Electromagnetism (expansion), Gravity (contraction), Strong and Weak Nuclear forces (cohesion of matter) from microcosm (subatomic particles) to macrocosm (celestial heavenly bodies).

The vertex positions formed are at stand-still and could be called a standing wave structure.

Figure 19 - A standing wave.

A standing wave is the sum of two propagating waves traveling in opposite directions.

The ether self-organizes at the quantum level forming structured geometric patterns. Universal consciousness behaves like sound waves (standing wave interference) mapping out the geometric patterns of the platonic solids in a spherical volume. The two opposing propagating waves are the two Yin and Yang vortexes linked by a Zero Energy Point.

Figure 20 - Yin and Yang Golden Spirals from a three dimensional view displayed in Cartesian coordinates.

With the principle of Yin and Yang there are two Golden Spirals in opposition. One is going upward, rotating counter-clockwise (Yang, positive, expansion) and the other is going downward rotating clockwise (Yin, negative, contraction).

Figure 21 - Golden Spirals with spin effect from a three dimensional view.

Figure 22 - Side view of Figure 21 showing opposing waves emerging from a Zero Energy Point.

According to the German psychologist Adolf Zeising (1810–1876), the golden ratio was expressed in the arrangement of plant parts, in the skeletons of animals and the branching patterns of their veins and nerves, as well as in the geometry of crystals.

This proportion is the fundamental ratio found in Nature.

Since 1991, several researchers have found connections between the golden ratio and human genome DNA.

What are the natural numbers related to the golden ratio?

Any regular polygon can be based upon the constructibility of right triangles.

For a regular polygon (N-sided) and its fundamental right triangle, angle a=180/n°.

By using the Trigonometric functions (cosine, sine and tangent), the natural numbers are the angles when projected on a specific axis, it results a proportional length (or inversely) to the golden ratio with an integer constant multiplier (or an integer constant divisor).

The projection of these natural angles by using the Trigonometric Functions reveals the golden ratio:

Sin 18° = Cos 72° = 1/(2φ)

Cos 36° = |cos 108°| = φ/2

Figure 23 - Many other angles could be involved to give the same proportional length.

All of these angles are simply intervals of 180 degree rotation, but scaled to a truncated base.

[180->18, 360->36, 540->54, 720->72, etc.]

This is a major implication linking the Golden Ratio to quantum spin which will be expanded on later.

A program realized with the Software Matlab gives a list of these natural numbers, which could be called the list of "9".

The sum of the numbers of each one of them gives 9. For example, the number 432, 4+3+2 = 9, or 972 = 9+7+2 = 18 and 18 = 1+ 8 = 9.

There are four equations when considering the values of both plus and minus.

y = +- (phi/2)

y = +- 1/(2*phi)

Harmonic digit root numbers are at the intersection points between the equations (y), cosine (blue), and sine(red).

The Divine Proportion Phi (Φ) is a natural manifestation in the core of universal consciousness and is related to some remarkable harmonic numbers such as 72, 108 and 216. Numbers are the language of consciousness creating the fundamental blocs of geometry built within the Flower of Life.

Universal consciousness works through standing quantum wave interferences within a sphere. The vortexes organize the ether and produce specific geometric patterns according to particular frequencies.

The sphere is directly related to the torus topologically and is the fundamental geometric shape responsible for spin with torsion effect and presence of curvature.

Figure 24 - The sphere.

In three dimensions, the Flower of Life could be interpreted as a grid of spheres overlapping each other. When a sound is produced the sphere is directly affected by vibration.

The interconnection of these spheres is expressed through the fact that they are overlapping and not separate from each other. If a sound is affecting a sphere, its neighboring spheres will also be affected.

When a vibration is emitted from anywhere in the universe, whatever its nature, the whole interconnected grid is affected.

Figure 25 - The Vesica Piscis.

The Vesica Piscis represents two overlapping spheres from a three dimensional point of view.

Figure 26 - The Vesica Piscis reveals unit interval square roots.

Figure 27 - Geometry emanates from the center of the Vesica Piscis.

Regular polygons created by the Vesica Piscis all share an edge length of the radius of the circle. Red dots mark the corners (vertexes) of each polygon following the path of a circle.

Figure 28 - The list of Golden Ratio harmonic numbers are all divisible by the number 9, which happens to be the number of triangles in the Tetractys found in the Flower of Life.

The Tetractys also contains another key number related to the golden ratio.

The number of points could give the number of vertices of a regular polygon.

Within the Tetractly, the polygons built are the triangle (1+2=3), the square (1+3=4), the pentagon (1+4=2+3=5), the hexagon (4+2=1+2+3=6), the heptagon, the octagon, the nonagon and finally the decagon (1+2+3+4=10).

The decagon is the stage of completeness as the number 10 is also closely related to the golden ratio.

In geometry, the circumscribed circle or circumcircle of a polygon is a circle which passes through all the vertices of the polygon, its radius is called the circumradius.

Figure 29 - If we consider these regular polygons of unit edge length 1. Then, the circumradius of the decagon is exactly equal to the golden ratio phi 1.618. This is also the case if we consider the generation of regular polygons from the flower of life with the same unit edge length 1, as the picture shows.

The decagon can be built with two pentagons interlocked. Then, the pentagon having 5 vertices is the polygon related to the golden ratio Phi, as Φ = (√5 + 1)/2.

The numbers 9 and 10 are two important numbers related to the divine proportion and could be used in the calculations to understand the connection between the factor time and the angle (the factor length) of a regular polygon.

Figure 30 - The convoluted universe follows certain mathematical laws or fractal codes based on the golden ratio. For example, if we look more closely at the list of the natural numbers giving the number 9, the number 864 (8+6+4=18, 1+8=9) is related to a factor of spacetime. In 24 hours, there are 86400 seconds, this is also the diameter of Jupiter in miles, with the diameter of the sun being 864000 miles. Only a factor 100 and 1000 from 864, respectively. Another example, the number of years of the precession of the equinoxes of Earth is 25920, the number related to it in the list is 2592 (2+5+9+2=18 and 1+8=9), only a factor 10.

Pythagoras had the intuition that geometry was related to Music and numbers, and that it was more the expression of the Harmony of the Spheres in our Solar System. Actually, it would be the expression of the Harmony of Consciousness, as the Consciousness units (spheres) can be quantified through the flower of life. Music would be everywhere and harmoniously played. There would be harmonious Music from the planets themselves in our Solar System although there is no possibility to hear anything in our physical realm, inaudible for human ears.

Figure 31 - This geometry; The Tetractys, an equilateral triangle from which any geometric pattern is generated, is made of 9 smallest equilateral triangles and it can be found in the flower of life.

The rows can be read as the ratios of 4:3 (perfect fourth), 3:2 (perfect fifth), 2:1 (octave), forming the basic intervals of the Pythagorean scales.

The Universal Consciousness interconnects all things from the geometric pattern of the flower of life through the vortex path. The vortex path is the fundamental flow rotating on an axis where life force, chi energy, prana, or the zero point energy is in resonance with Infinity.

The Ancient civilizations believed that the universe consists of a vibrating ocean of energy, the ether. Consequently, the world of matter didn’t exist as separate particles, but as the Alchemy of Consciousness, or the transformation of the ether resulting from a self organization of the ether itself through the standing quantum wave interference.

The symbol of the spiral has been found in certain sacred sites, and shows the Ancient knowledge about the manifestation of Consciousness itself. The spiral is a better understanding about how Consciousness interconnects everything, and how it could be possible for a spiritual being, or even a device, to be in resonance with the grid of vortexes from beyond the physical plane.

Another example through nature, the shell of a snail shows the pattern of the flow of energy in resonance and coming from a zero point. To give birth to the snail, Consciousness left the blueprint of the golden spiral. The golden spiral is the fundamental geometry found everywhere in nature, and is consequently an important geometry to understand how Consciousness manifests itself.

To begin with this approach, it is important to make a connection with the vortex path and sacred geometry, as the latter represents the overlapping circles, the energetic grid of Consciousness structured neatly. In this grid, each point is a zero point in which life force is likely to manifest itself.

The Platonic Solids

Figure 32 - The Platonic solids overlay with the flower of life pattern.

“Everything is Formed by Vibration and Geometry” - written by Enoch Tan

Scatter some very fine sand over the head of a drum. Then take a tuning fork and strike a note just above the drum head causing it to vibrate. The sand would shift and assume a geometrical figure corresponding to the particular note that was played. When another is sounded, the sand will shift and assume another figure. This shows that every vibration produces a corresponding geometric form. Form is the organization of energy at certain rates of vibration.

There is no solidity in the universe. A form that appears solid is actually created by an underlying vibration. Vibrations express themselves in corresponding geometrical figures and in this way build up crystals that are the expression of vibration.

Crystals collectively form a body of an element according to its particular vibration. The forms of snowflakes and faces of flowers take on their shape because they are responding to some sound in nature. Crystals, plants, and human beings are music that has taken on visible form.

There are five perfect three dimensional forms. The tetrahedron, hexahedron, octahedron, icosahedron, dodecahedron. They are known as the Platonic Solids and are the foundation of everything in the physical world. The entire Periodic Table of Elements and literally everything in the physical universe is based on these five forms.

There is a precise way that the energy of Creation organizes itself. Every natural pattern of growth or movement conforms inevitably to one or more geometric shapes. These patterns and codes are symbolic of our own inner realm and the subtle structure of awareness.

Fire (plasma) is associated with the tetrahedron, Earth (solid) with the hexahedron, air (gas) with the octahedron and water (liquid) with the icosahedron.

Fire is sharp and stabbing like a tetrahedron. Air is made of minuscule components that are smooth like an octahedron. Earth is solid and tessellates Euclidean space as a hexahedron. Water flows as if it is made of tiny little balls like an icosahedron. The four elements are made from the fifth element which is the universal matter. It is the dodecahedron.

In the Periodic Table, the protons in the nucleus of each element arrange themselves in concentric forms that have the shapes of the Platonic Solids. Each of the elements are most stable in a particular state of matter, often requiring significant amount of temperature changes in order to shift from one natural state to another. The Periodic elements can be classified as gaseous elements, radiant elements, liquid elements and solid elements. Air, Fire, Water and Earth.

The final form which contains the others within it is the dodecahedron. It is completed at element 46 which is palladium. Palladium is a catalyst, a substance that creates certain transformations only when it is present and not when it is absent. Lethal chemical compounds such as nerve gas, can be broken down by adding palladium which transmutes the lethal chemicals into safe substances. The dodecahedron is the pattern of pure life energy and therefore a basis of practical alchemy.

The last natural element on the Periodic Table is element 92 which is uranium. It is based on the form of two connected dodecahedra being torn apart, a rupture creating toxic nuclear radiation.

All man-made elements of the Periodic Table, from element 93 onwards, emanate potentially lethal radiation. Modern nuclear weapons and nuclear waste are directly related to manipulations affecting the core pattern of the dodecahedron. The dodecahedron pattern could create destructive effects if misused. The crust of our spherical planet Earth has a dodecahedral pattern revealed when viewed topologically which makes it like a gigantic crystal.

Sound vibration creates geometric shapes. When sound is transmitted through physical mediums in the shape of monitored electronic frequencies, a low frequency produces a simple circle encompassed by rings, whereas a higher frequency increases the number of concentric rings around a central circle. If the frequency increases, the complexity of shapes increases and the number of elements becomes greater, to the point where tetrahedrons, mandalas and other sacred forms can be discerned.

Ultrasound is capable of interacting with physical elements to such an incredible degree. It can be aimed, focused and reflected almost like a light beam, and specific frequencies can be focused to cause certain kinds of molecules to vibrate while others nearby are left unmoved. The higher the frequency of ultrasound, the greater its ability to be directed. Such extremely high frequencies are known to affect the state of awareness and consciousness in humans. Ultrasound that is tuned in the Megahertz range also prevents damage to sensitive tissues, so its healing properties are used in treating muscular ailments.

A hologram (fractal) contains a blueprint of everything in its existence. Any change we make to any part of the hologram is reflected in the entire hologram. Consciousness is holographic. Our bodies, minds, souls and even our DNA all contain the unified blueprint of everything in the universe. Everything in nature exists because of the blueprints that are in the form of different geometric patterns. The quantum hologram holds that pattern.

Vibrations in the quantum hologram create geometric patterns and these patterns create rocks, trees, oceans, mountains, plants, animals and humans. The quantum hologram holds the blueprint of all possibilities that could ever take place, past, present, or future. We have the power to choose the blueprint, which already exists in the quantum hologram, that we want to activate in our lives.

Bio-Geometry is a science that deals with the effect of geometrical shapes on life functions and the design of shapes that interact with earth’s energy fields, to produce special pre-calculated effects on biological systems. Bio-Geometrical shapes, when designed or engraved on jewelry, have shown positive effects on the body’s energy field, and reduce the potential health hazards caused by cellular phones, computers and other modern appliances. In many ways the science and metaphysical discipline of Bio-Geometry provides one of the underpinnings to support what many know today as Feng Shui.

Elaborate geometries are used to alter states of consciousness. Crop circles contain special meaning. The Sacred Geometry within these formations is recognized by the subconscious, since all living creatures consist of geometrically shaped elements.

Sacred Geometry is a universal language. The purpose of it is to evolve the consciousness of mankind to a higher level. This way they are literally creating Heaven on Earth. As a result mankind is more consciously prepared to grow physically, mentally, emotionally and spiritually. We absorb the codes much faster in our subconscious by looking at them than by hearing or reading.

The essence of creation is geometry. Change the number of the parts of the atom, and its geometric shape changes which transforms it into a different element. Physical reality is governed by geometric arrays based on sound frequencies. Geometry is frozen music. Sacred geometry expresses the image of God. God is Geometry. We can know God by knowing the perfect design and order in the universe. We are vibrations of God’s perfect design.

Figure 33 - The Platonic solids total angles all reduce to 9. For example (2+1+6+0 = 9)

The cube and octahedron are both manifested by the vertices of a star tetrahedron. They are dual solids as their number of faces and points are mirrored. The icosahedron and dodecahedron are also dual to one another.

The octahedron has 3 sided faces with 4 faces at each point, whereas the cube has 4 sided faces and 3 faces at each point. This pattern continues to the other duals where the icosahedron has 3 sided faces but 5 faces at each point, whereas the dodecahedron has 5 sided faces and 3 faces at each point. This is one of many ways the Platonic solids correlate to the Pythagorean 3 - 4 - 5.

Figure 34 - The physical sizes of Earth and Moon encode the 3-4-5 triangle, which itself also encodes Phi.

If the Moon was pulled next to Earth the dimensions would create two 3-4-5 triangles on either side. The squares around Earth and Moon are 11 and 3, respectively.

Like our five senses there are five Platonic solids, each of which is made up of shapes that have 3, 4, or 5 sides. The tetrahedron is made up of 4 triangles (3-sided), the octahedron, 8 triangles. And the icosahedron has 20 triangles. The cube is composed of 6 squares (4-sided) and the dodecahedron is made of 12 pentagons (5-sided). Three-Four-Five is reflected in the way nature structures itself, based upon the simplest 3D geometries in our reality.

In addition the Platonic solids also encode 3-4-5 in the way the shapes fit together. The tetrahedron, cube, and dodecahedron have three shapes at their corners. The octahedron, four. And the icosahedron has five shapes coming together at every point.

Figure 35 - Correlation between total angles of Platonic solids and the diameter of the Sun.

The angles of the perfect solids display a pattern that is broken with 5040, which is the mean radii of both Earth and Moon in miles. Adding up the total angles on the surface of each solid sums to 7920 degrees. The mean diameter of Earth is 7920 miles.

Is this really all just a coincidence?

There's too many coincidences for it to be all just coincidence.

Figure 36 - Correlation between integer multiplication, time measurements, total angles of Platonic solids and the diameters of the Earth and Moon.

Spacetime Geometry and the Tetractys

Figure 37 - As we have seen, if you take the first 12 digits of the 24 reduced numbers of the Fibonacci sequence and add them to the second 12 digits, applying numeric reduction to the result you will find that they all have a value of 9. 

This means that each numbers mirror equivalent reduces to nine, which is significant in and of itself, but also notice how with further reduction of the entire sequence we are left with the number 108 (twelve nines) again, reduces to nine. 

Applying the ‘octave’ system to base ten, where 5,6,7,8 become mirrors of 4,3,2,1, (i.e. 5 becomes -4, 6 is -3, 7 is -2, 8 is -1) and where 9 and zero are the same. 

You can see that there is a pattern of 11 numbers (1,1,2,3,4,1,4,3,2,1,1) interlinked with the zero point or neutral zone, at which the pattern mirrors itself between positive and negative numbers.

Applying the ‘octave’ system to the 24 reduced numbers transforms the sequence into a numerical palindrome, just like the previously shown Nexus key sequence. Visually you can see how the pattern ‘builds’ up from zero to four and then reverses at its center (1) where it ‘deconstructs’ from 4 back to zero. Recognize that pattern? Embedded into the 24 reduced Fibonacci numbers is the mirrored construction/deconstruction of a dual Tetractys or Star Tetrahedron; +1+2+3-4 mirrored with -1-2-3+4, etc.

Figure 38 - It is known that in Ancient Greece, a famous metaphysicist named Pythagoras worshipped a particular shape called the Tetractys. He and his followers believed it to symbolize everything that is perfect about the Universe. 

The Tetractys is an equilateral triangle with 10 interconnected points across exactly four layers. The Pythagoreans believed that this basic shape of nature reveals doorways to the most profound mathematical principles of the Universe. 

As we have seen, the 24 reduced Fibonacci number pattern is related to the number 9, which happens to be the number of triangles in the Tetractys found in the Flower of life. 

The Tetractys also contains another key number related to the golden ratio. The number of points could give the number of vertices of a regular polygon. Within the Tetractys, the polygons built are the triangle (1+2=3), the square (1+3=4), the pentagon (1+4=5 or 2+3=5), the hexagon (4+2=1+2+3=6), the heptagon, the octagon, the nonagon and finally the decagon (1+2+3+4=10). The decagon is the stage of completeness as the number 10 is also closely related to the golden ratio. 

If we consider these regular polygons of unit edge length 1. Then, the circumradius of the decagon is exactly equal to the golden ratio phi 1.618. 

The decagon can be built with two pentagons interlocked. Then, the pentagon having 5 vertices is the polygon related to the golden ratio, the Divine proportion.” 

(1 + √5) / 2 = 1.6180339… = Φ 

Phi can also be expressed in all fives as: 5 ^ .5 * .5 + .5 = Φ 

This geometry; The Tetractys, an equilateral triangle from which any geometric pattern is generated, is made of 9 smallest equilateral triangles and it can be found in the flower of life. The rows can be read as the ratios of 4:3 (perfect fourth), 3:2 (perfect fifth), 2:1 (octave), forming the basic intervals of the Pythagorean scales.

Numbers are instructions that are given to our manifest physical world through the spiritual plane and geometry can be seen as one expression of these numbers as they take form through our multidimensional landscape

Figure 39 - “The Tetractys is the foundation stone of the Divine Architecture. It held an important mystical meaning to the Pythagoreans who considered it as the base of the structure of the universe in terms of arithmetic, music and geometry. 

The first Platonic solid to appear in the Tetractys is the projection of the tetrahedron shown in light blue. The red hexagon represents the projection of the octahedron with the green cube projected inside 

The Tetractys means literally “the number four” and is a triangle composed of 10 points rising upwards, arranged in four rows. The number ten is mathematically known as the fourth “triangular number” with rows of one, two, three and four points. 

Each row has an important meaning and brings forward an understanding of the connection between the innermost and the outermost.

Figure 40 - The first harmonic number encoded in the Tetractys is 432, a cosmic code which can be read from the base to the 2nd row, the top of a step pyramid, such as the ones found in central America, Egypt and China. 

These pyramids come from the geometry of the Tetractys. A second Tetractys is placed on the top of the first as a fractal forming the second step. The numerical sequence 432 432... rises from the base upwards. This is a very important number when tuning instruments to resonate with consciousness. 

From planetary systems to atoms, everything surrounding us is an embodiment of perfect harmony created by numbers, referred to in music as “Harmonics”.

Figure 41 - The Tetractys, representing the organization of space from a two dimensional point of view. 

First row: From a single original point everything is created and brought into existence from nothingness. 

This could be considered as a state of awareness to that which is about to manifest into creation. 

Second row: From a single point two further points are generated defining the first dimension. The possibility of going from one point to another brings the idea of motion into consciousness.

Third row: A line drawn between these three dots defines the second dimension. Structure is formed into consciousness with the possibility of quantification and measurement.

Fourth row: A line drawn between these four dots defines the third dimension where geometry takes form. From this row of the Tetractys all regular polygons can be generated.

Figure 42 - These four dimensions would also derive the tree of life symbol in two dimensions, as shown. This number sequence (1,2,3,4,1) was previously revealed to be encoded into the 24 reduced Fibonacci numbers with the ‘octave’ system applied to base ten. 

The Dimensions of Spacetime in String Theory and the Fibonacci Spiral 

Figure 43 - As I will soon explain in great detail, the dimensions of space-time is a repeating sequence of integers very similar to the Fibonacci sequence: 

1 1 2 2 4 6 10 16 26 42 68 111 

This sequence is actually double or an 'octave' of Fibonacci numbers: 

1 1 2 3 5 8 13 21 34 55 

which is the approximation of the golden spiral. 

The only difference is the last integer, which is not 110, but 111. 

In the universal consciousness, numbers (frequency) and geometry are the same language. The Spiral is a geometric pattern. 

Can we really make a connection with the other language, frequency?

The dimensionality of space-time plays a paramount role in the theoretical physics of unification and has led to the introduction of the 26 dimensions of string theory, the 10 dimensions of superstring theory, and finally the heterotic string theory with the dimensional hierarchy 4, 6, 10, 16 and 26. In that sequence, the dimensions 4, 6, 10, 16 and 26 are present. The higher dimensions haven’t been necessarily discussed in the mainstream yet. In heterotic string theory the value 26 has another meaning; as the inverse of the coupling constant of super symmetric unification of all fundamental forces known to Physics.

By introducing the golden ratio 1.618 as being the connector for all the dimensions, it would result in the natural sequence of the dimensions of spacetime, and then the higher dimensions. The decagon, having a circumradius equal to the golden ratio φ; nature is paying attention to the number 10. It was the beginning of the trail.

One of the most promising attempts to go beyond the standard model of particle physics is string theory. String theory holds that all elementary particles are nothing but the different modes of string vibrations. String vibration can be interpreted as a certain tension or pressure applied on any string instruments such as guitar, harp, piano, and violin. Then, it is natural to observe the universe as the result of the music played with various vibrations, the whole connected in resonance. Now E-Infinity theory claims to go one step further and depicts these strings to have a fine structure, more precisely it conceives these strings as being made of a hyperbolic fractal of Cantor sets. Seen from afar, the sizzling Cantor sets appear as if they were the violent movement of superstrings, and these strings seen from farther appear as if they were particles.

El Naschie holds that all what we observe in nature is a manifestation of the true transfinite, hyperbolic fractal structure of quantum spacetime underpinning it. The vibration is understood as a sizzling violent movement of the transfinite, hyperbolic fractal of cantor sets, simulating the zero point fluctuations of the totally empty vacuum of spacetime.

Ripples on the ponds still surface. That is all our perceived reality is. The still pond is the cause, while the wavy ripples are the effects that our senses detect.

Every observable form of matter is a disturbance to stillness, caused by a pulsing / thinking Mind. The disturbance manifests as a sequential wave-motion of frames / pulses, in which our sensing is programmed to detect and interpret. If the universe of motion could be slowed down, the secret of the illusion would become obvious. The individual frames / pulses of a thinking mind would be revealed. But when those frames / pulses are run at 186,282 miles per second, our senses detect a solid, materialistic world. This means that all matter and energy manifestations in our cosmos are essentially a manifestation of the zero point energy of the totally empty vacuum of spacetime. This amounts to a paradigm shift in physics where the totally empty vacuum of spacetime is taken as fundamental and everything else is derivable from it.

The Fractal Dimensions of Spacetime in String Theory 

We are now going to explore more about the Tetractys and Prof. Mohamed El Naschie’s E-Infinity theory which has information about how the structure of spacetime is related to the fine structure constant (α); nature's fundamental physical constant. 

It's value (which I have previously shown to be 1/20Φ^4) is approximately the inverse of the number 137, α ≈ 1/137. 

This new theory mathematically connects the theoretically exact value of the fine structure constant to the generation of the values of all of the dimensions of spacetime by the means of an infinite-dimensional hierarchical cantor set. 

Although it has been characterized as the strength of the electromagnetic interaction between elementary charged particles, if one considers that the universe is connected, and not separated, one could ask if the number 137 would be inherent to space-time? Is there another way to figure out the number 137 through Geometry? 

The flower of life would have this information through the fundamental grid, the Tetractys made of 9 triangles. The Tetractys generates the number 1234. The zero points are spatially distributed so as to form 9 triangles. 1234 / 9 = 137.11111… 

As we have seen, the number 9 is an important number playing a role with the golden ratio 1.618. The golden ratio is the number related to the spiral, blueprint left by the Divine Consciousness and found everywhere in nature.

The circumradius of the decagon is equal to the golden ratio, suggesting that the number 10 (also the sum of the numbers in the sequence 1234=10) is an important number in the structure of space-time. The golden ratio is the factor which would connect all of the dimensions of spacetime together, and opens the door to the fractal quantum world. The golden ratio is consequently the number supporting the nature of a connected Universe, and its geometric pattern is the spiral. 

The number 10 shows a certain symmetry in the dimensions of space-time, around which the golden ratio would generate all the dimensions connecting each other. The number 10 gives the information about the number of dimensions of space-time, and the number 9 gives the information about how the zero-points are spatially distributed, or how spacetime is structured. 

The structured grid is the Tetractys, starting with a triangle (3), and gradually appears the hexagon (6) inscribed in a circle, and a bigger triangle (9) which would be the nonagon in the sequence 369 (triangle-> hexagon-> nonagon).

The golden ratio could be approximated by the irrational number 1.62, itself is reduced to 9 (1+6+2=9). 

This is also the total angle of the Tetractys. As we know, the sum of the angles in a triangle is 180 degrees. The Tetractys having 9 triangles, the total is 1620°.

Figure 43 - The dimensions and their values have been listed in the table. The values have been calculated with the golden ratio and its inverse starting from 10 by multiplying it outwards. This generates a Fibonacci-like sequence; 

The base dimension, D(0), has integer value 1, is 10/Φ^6. This value is Immirizi's entanglement of three quantum particles (1/Φ^6), scaled to a magnitude of 10. This value was used to calculate the theoretically exact ratio of atoms to dark matter and dark energy in our current universe. These results are perfectly aligned with cosmological measurements that were awarded the 2011 Nobel Prize in Physics. 

The first dimension, D(1) also integer value 1, is 10/Φ^5. This value is Hardy's entanglement of two quantum particles (1/Φ^5), also scaled to a magnitude of 10. (1/Φ^5) can be referred to as 'k/2', or the 'fractal-correction' ratio for all of the other dimensions from their respective integer values. It has been previously expressed as a continued fraction expansion of the number 11. This value is also in the core of Fractal M-Theory as well as El Naschie's Quantum Gravity Energy-Mass Equation, which have been previously shown. 

The second dimension has integer value 2, and is 10/Φ^4. This dimension is constructed by adding the previous two dimensions together. All of the remaining dimensions are constructed in the same manner, resulting in a hierarchical sequence that is an octave (doubling) of the Fibonacci numbers. This dimension, 10/Φ^4 is exactly 200 times the fine structure constant, which is 1/20Φ^4. 

The third dimension, also integer value 2, is 10/Φ^3. This value is the added 'fractal dimension' of real-space in E-Infinity theory (1/Φ^3), scaled to a magnitude of 10. The dimensions of real-space in E-Infinity are 4+(1/Φ^3)=Φ^3. This added value can also be expressed as a continued fraction expansion of the number 4. 

For dimensions 4-8 the integer values are 4, 6, 10, 16, 26, the Heterotic string dimensions. Their calculated values are respectively 10/Φ^2, 10/Φ, 10, 10Φ, 10Φ^2. This 10 dimensional superstring core can be derived from the dimensionality of an E8 world quantum entangled with a second shadow E8 world, and is understood to be the fabric cantorian spacetime which was woven from an infinite number of zero set quantum particles and empty set quantum waves in a 10 dimensional quasi phase space, given by 10-10/Φ=10/Φ^2. The 4.5% of ordinary energy in the universe is nothing but the multiplicative volume of a 5 dimensional Kaluza-Klein zero set while the 95.5% dark energy is the additive volume of the same 5D Kaluza-Klein empty set. The largest value, 10Φ^2 = 26+k is generally understood in quantum gravity and El Naschie’s theory to be the inverse of the coupling constant of super symmetric unification of all 5 fundamental forces known to current Physics.

The ninth dimension has integer value 42, and is 10Φ^3. This value is generally understood in quantum gravity and El Naschie’s theory to be the inverse of the coupling constant of non super symmetric unification of all 5 fundamental forces. This value is exactly 10 times the dimensions of real-space in E-Infinity theory. The dimensions of real-space in E-Infinity are 4+(1/Φ^3)=Φ^3.

The tenth dimension has integer value 68, and is 10Φ^4. This value is exactly half of the inverse of the fine structure constant, which is 20Φ^4. 

Finally, the eleventh dimension, D(11), has integer value 111, and is 10Φ^5. Φ^5=11+k=11+1/Φ^5, therefore this dimension can also be expressed as 110+5k or 10(11+1/10(D(1)))=110+10D(1). This implies an infinite repeating, fractal nature to these dimensions. 

It has previously been shown that it is possible to generate the values of all of the dimensions of spacetime in string theory by an incredible hierarchical sequence of cantor sets that are scaled in proportion to the inverse of the fine structure constant α^-1 = 137.082039 = 20Φ^4;

α^-1/(2) = 68+3k = 10φ^4 

α^-1/(2Φ) = 42+2k = 10Φ^3 

α^-1/(2Φ^2) = 26+k = 10Φ^2 

α^-1/(2Φ^3) = 16+k = 10Φ 

α^-1/(2Φ^4) = 10 

α^-1/(2Φ^5) = 6+k = 10/Φ

α^-1/(2Φ^6) = 4-k = 10/Φ^2 

α^-1/(2Φ^7) = 2+2k = 10/Φ^3 

α^-1/(2Φ^8) = 2-3k = 10/Φ^4 

α^-1/(2Φ^9) = 5k = 10/Φ^5

α^-1/(2Φ^10) = 5k/Φ = 10/Φ^6

Where k = 2/Φ^5 = (1/Φ^3)(1-(1/Φ^3))

The dimensions of spacetime, as well as their transfinite fractal-correction ratios, are clearly organized into a dual hierarchy with mirrored ascending symmetry around the number 10; the same sequence that is found in the Tetractys (1234) is embedded into E-infinity theory, revealed through the hierarchical sequence of cantor sets that are scaled in proportion to the inverse of the fine structure constant and the powers of the golden ratio. This embedded sequence (-4,-3,-2,-1,0,+1,+2,+3,+4) is remarkably similar, but in a mirrored fashion, to the sequence that was previously revealed to be encoded into the 24 reduced Fibonacci numbers with the ‘octave’ system applied to base ten, however visually you can see how this time, the star tetrahedron or dual-tetractys pattern that is embedded into the hierarchical sequence of cantor sets in E-Infinity ‘deconstructs’ a negative tetractys down to zero from four and then reverses at its center (zero) where it ‘builds’ a positive tetractys from zero back to four. 

Figure 44 - To come back to the number 137, it would be inherent to spacetime, as it is exactly the octave of D(10), with integer value 68, carefully calculated with the golden ratio. Notice that the difference of the numbers calculated with their corresponding integer number, which is essentially an integer multiple of 'k', is a multiple of 9, and there is a hierarchical symmetry around the perfect number 10. 

Figure 45 - The number 137 is also the value of the golden angle found in Nature. The golden angle is the angle subtended by the smaller (red) arc when two arcs that make up a circle are in the golden ratio. 

The golden angle is equal to 360/Φ^2= (60/Φ)^2, giving 137.51. 

The angle between successive florets in many flowers is the golden angle.

Figure 46 - The volume of the dodecahedron is also equal to 137.51 if its edge length is equal to the square of the golden ratio φ^2, which is actually the radius of its insphere when the edge length of the dodecahedron is equal to the unit 1. The inspheres of the Platonic solids are depicted above. 

The inradius of the dodecahedron has approximately the same values of the dimensions of spacetime; 

The values of the inradius of the dodecahedron for a value of the edge length equal to the golden ratio power to {1-11} and the comparison with the first values calculated previously are listed in the table above.

137 (4^2 + 11^2) is the 33rd Prime number. 

Since the early 1900s, physicists have postulated that the number could lay at the heart of a grand unified theory, relating theories of electromagnetism, quantum mechanics and, especially, gravity. Physicist Leon M. Lederman numbered his home near Fermilab 137 based on the significance of the number to those in his profession.

Lederman expounded on the significance of the number in his book The God Particle: If the Universe Is the Answer, What Is the Question?, noting that not only was it the inverse of the fine-structure constant, but was also related to the probability that an electron will emit or absorb a photon—i.e., Feynman's conjecture. He added that it also "contains the crux of electromagnetism (the electron), relativity (the velocity of light), and quantum theory (Planck's constant). It would be less unsettling if the relationship between all these important concepts turned out to be one or three or maybe a multiple of pi. But 137?”

The number 137, according to Lederman, "shows up naked all over the place,” meaning that scientists on any planet in the universe using whatever units they have for charge or speed, and whatever their version of Planck’s constant may be, will all come up with 137, because it is a pure number. “It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it. Immediately you would like to know where this number for a coupling comes from: is it related to π or perhaps to the base of natural logarithms? Nobody knows. It’s one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the “hand of God” wrote that number, and “we don’t know how He pushed his pencil.” We know what kind of a dance to do experimentally to measure this number very accurately, but we don’t know what kind of dance to do on the computer to make this number come out, without putting it in secretly.” - Richard Feynman 

“If alpha [the fine structure constant] were bigger than it really is, we should not be able to distinguish matter from ether [the vacuum, nothingness], and our task to disentangle the natural laws would be hopelessly difficult. The fact however that alpha has just its value 1/137 is certainly no chance but itself a law of nature. It is clear that the explanation of this number must be the central problem of natural philosophy.” -Max Born, Arthur I. Miller

Figure 47 - The Infinite Circle 

In this section, the circle will be discussed and it will be shown how it is possible to calculate the dimensions of spacetime through its parameters. From the circle, the dimensions of spacetime can be calculated with the golden ratio 1.618, its circumference and diameter.

The circumference of a circle is the length of the 360 degree arc of that circle. As we know that the circumference of a 360 degree arc is 2πr, where r is the length of the radius, we can calculate its corresponding diameter D;

360=2πr, 2r=D 

2(360)=2π(2r) 

720=2πD 

360/π=D 

If we divide the diameter of the circle by 1000, adding 1, it results 1.1146, which is approximately the octave of 0.55728, which is D(0).

The exact result : 1.11459156 

Half octave : 0.55729578

Figure 48 - This value is very close to the inverse of the golden ratio (1/Phi = 0.618) ^ 6, multiplied by 10. There's only a difference of 10 to the power of -5 between these two values.

With the parameter of the unit circle D, its diameter D on the scale 1/1000 added to 1; the close values for the dimensions of spacetime have also been listed in the first table above.

These dimensions are correlated to the diameter of the golden spiral at set levels of hierarchical factor growth that are dictated by the universe/nature itself. This method allows the reader a better way to visualize how the dimensions of spacetime are structured within one another.

These dimensions are scaled to a 4 digit ratio (1/1000) in a hierarchy of infinite circles because of the fundamental spacetime framework of the 4 layer Tetractys geometry. As we have seen, the Tetractys is deeply correlated to the hierarchical organization of quantum spacetime.

Figure 49 - The number 1234 from the Tetractys has interesting correlations with the number 137 and the number pi itself “π”. Some of the calculations above show these correlations. 

The exact value for the inverse of the fine structure constant is 20Φ^4.

There is a definitive fractal existing within the dimensions of spacetime. Once the 11th dimension is reached, multiplying by the golden ratio, the result is approximately 180.

There is a factor equal to φ^11 between the first value (D(1)) 0.9, which is the half octave of 1.8, and the 12th value (111*1.618) approximately 180. Between the 24th value and the 12th value, a factor equal to φ^11 Between the 24th value and the 1st value, a factor equal to φ^22 and so on. The scaling factor 22/2 = 11 is deeply connected to El Naschie’s correction to Einstein’s equation E = mc^2, combining Newton’s mechanics with quantum mechanics using fractal M-Theory and Hardy’s quantum entanglement to account for the missing dark matter and dark energy of our cosmos.

If we apply the scaling factor of 200 between these repeating sets of 12 dimensions, (0.9 → 180) the natural values reduced to 9 appear: 180, 36000, 7200000, 1440000000, 2880000000000, etc. This is identical to the recursive doubling / halving of cantor sets and vortex math that was shown before.

All of these numbers are related to the same cosine/sine wave generating golden ratio natural numbers that we have previously seen. Scaling these numbers to a truncated base reveals the natural golden ratio numbers from before, but this time they appear in a doubling sequence of 180 degree intervals of rotation; 18, 36, 72, 144, 288, … -> 180°, 360°, 720°, 1440°, 2880°, …

This 12 digit repeating pattern within the fractal dimensions of the superstring core of E - Infinity generates a recursive doubling sequence of golden ratio harmonic trigonometric rotation angles.

This keystone is the missing link between vortex math and string theory, allowing for a more accurate understanding of the origin of quantum spin, leading to the realization that our universe is a gigantic infinite dimensional black hole in which we are peacefully living. The hyperbolic cantorian fractal geometry of dark energy, which defines the wave function at the surface or holographic fractal boundary of spacetime is powered by toroidal vortex energy originating from the recursive simultaneous doubling / halving of the random triadic cantor sets of the singularity.

Building Elements of E-Infinity Diagrams - written by Professor Mohamed El Naschie

The quintessence of the present theory is easily explained as the 1/Φ^3 intrinsic Casimir topological energy is produced from the zero set 1/Φ of the quantum particle when we extract the empty set quantum wave 1/Φ^2 from it and find 1/Φ - 1/Φ^2 = 1/Φ^3 by restructuring space via conducting but uncharged plates similar to that of the classical Casimir experiments.

Figure 50 - The classical experimental set up of the Casimir effect as the basic idea behind the present work is best visualized and understood using a hydrodynamical analogy.

Suppose we put two walls in relatively shallow water near to the shore with the reasonable objective of building a small boat harbor. Clearly within the two walls constituting the harbor, there will only be moderate water wavelets.

Outside however we have the open sea with its relatively strong waves that would have the effect of pushing the walls towards each other being much stronger than the waves between the two walls. In this analogy the open sea is the vacuum of cantorian fractal spacetime while the waves are the quantum waves of quantum field theory and finally the two walls are our two Casimir plates as shown in the figure.

Figure 51 - The main two elements or building blocks of E-infinity diagrams are the zero set and the empty set. From these irreducibly simple set theoretical elements we can virtually build an entire spacetime and more. Thus we have

The zero set D = 1/Φ

The empty set D = 1/Φ^2

where D is the Hausdorff (fractal) dimension. From the above we obtain the latent Casimir spacetime set representing the latent topological energy of spacetime as the difference of 1/Φ and 1/Φ^2 in symbolic reflection of the essence of the famous Casimir experiment with two uncharged but perfecting conducting plates. From this picture we can generalize to two limiting cases.

1) When the distance between the two plates tends to real zero, this is then the totally empty set (1/Φ)^∞ = zero. In the surrounding space we have a non-empty set with the average latent pressure everywhere equal 1/Φ^3 while the average spacetime density is basically the fractal five dimensional average 5 + 1/Φ^3. Consequently the density of the latent Casimir pressure is simply (1/Φ^3) / (5 + 1/Φ^3). This is exactly equal to (1/Φ^5) / 2 which is our well known ordinary measurable energy of the cosmos and in astounding agreement with cosmic measurements and observation.

The immediate rather profound conclusion is that the measured real energy density of the cosmos is nothing more but nothing less than the Casimir latent energy of spacetime and at this scale it is not related in any way to the Riemann curvature of spacetime but to the chaotic fractality of spacetime in full agreement with our picture which we adopted based on Feynman’s conjecture that gravity is similar to van der Waals fluctuation of micro spacetime frequently termed Feynman-El Naschie van der Waals quantum gravity conjecture.

2) Now we look at the other extreme where the distance between the symbolic Casimir plates is equal to the diameter of our universe. The repulsive Casimir-like pressure is in this case equal

5 + 1/Φ^3 minus the latent Casimir topologic pressure 1/Φ^3 which is working in the opposite direction so that the net repulsive topological pressure pushing the boundary of the universe outwardly is given by (5 + 1/Φ^3) - 1/Φ^3 = 5. Therefore the density of this repulsive topological pressure is (5) / (5 + 1/Φ^3).

This happens to be equal to 1 – [(1/Φ^3) / (5 + 1/Φ^3)] which means it is simply identical to what we calculated for the dark energy of the cosmos 5(1/Φ^2) / 2. We recall that 5(1/Φ^2) / 2 was interpreted as the energy of the pre-quantum wave, i.e. the energy of the empty set albeit in five dimensional Kaluza-Klein space.

According to Bosonic string theory, the spacetime dimensions needed are not 4 but 26, however we can make measurement only via 4 dimensions, 3 space dimensions and 1 time dimension. Thus we have 22 hidden dimensions. Consequently if we understand E = mc^2 as a theory for D = 4 then according to the D = 26 theory we have ignored the effect of the 26 - 4 = 22 'compactified' dimensions of spacetime.

We could define a scaling to account for these compactified fractal voids to be approximately 1/22, which means the observable 4 dimensional spacetime contains approximately 22 times less spacetime and following general relativity, less energy than the total energy of the cosmos.

Since E is an eigenvalue, then by Rayleigh theorem we should reduce by division E = mc^2 which means scale it using a scaling exponent y = 1/(22+k).

This implies that the hypothetically missing dark energy;

E(Dark) = (1-1/(22+k))*100 = 95.49150281% of the total energy of the cosmos, whereas the remaining observable energy;

E(Observable) = 1/(22+k)*100 = 4.50849719% of the total energy.

Where k = 2/Φ^5 = 1/Φ^3(1−1/Φ3)

The preceding two results are probably the most important achievements of many research efforts of many scientists rather than a single person and could be truly said to stand on the shoulders of giants. From this privileged position we can now answer a deep question by G. Ord, namely; "What is the wave function?"

From the above it is clear that the wave function is the empty set or the 'surface' of the zero set quantum particle.

In addition, the wave function is the source of dark energy. In other words the surface or holographic fractal boundary of the zero set quantum particle is the source of dark energy.

For an easily understandable explanation of these facts, we consider the 5 dimensional Kaluza-Klein spacetime. When it tends to quantum scale, the average Hausdorff dimension of fractal Kaluza-Klein spacetime is 5 + 1/Φ^3. Consider a quasi-Hausdorff hyper volume of the 5 dimensional Kaluza-Klein spacetime, which consists of the zero set of quantum particles, and the empty set of quantum waves.

The quantum particles are not occupied within a 1 * 1 * 1 * 1 * 1 hyper volume but a

1/Φ * 1/Φ * 1/Φ * 1/Φ * 1/Φ fractal hyper volume. That means that the quantum particles have energy equal to;

E = (1/Φ * 1/Φ * 1/Φ * 1/Φ * 1/Φ) / (1 * 1 * 1 * 1 * 1) * (1/2) mc^2

= 1/2 (1/Φ^5) mc^2 = E(Observable) = 1/(22+k)

This is El Naschie’s equation predicting that currently 95.4915028% of the energy in the cosmos is the hypothetically missing dark energy.

Where k = 2/Φ^5, the scaling factor

(22+k) = (4+1/Φ^3) * (5+1/Φ^3)

(22+k)/2 = 11+1/(11+1/(11+1/(11+...)))

This is a super symmetric Penrose tiling.

(4+1/Φ^3) is the rational bosonic tiling and the Hausdorff (fractal) dimension of our spacetime

(5+1/Φ^3) is the asymmetric fermionic tiling and the five dimensional Kaluza-Klein spacetime

Penrose fractal tiling is basically a quasi-crystal mathematical model with the forbidden 5-fold symmetry. This form of matter not found naturally on earth, was produced experimentally by the great engineer D. Schechtman, who after facing a long period of fierce opposition from high profile scientists, was bestowed with a Nobel Prize.

The 5 fold symmetry could be thought of theoretically as five Kaluza-Klein dimensions and using nanoparticles and nanotubes combinations one could build in the lab a nano holographic fractal universe akin to our own from which energy could be experimented with and extracted.

(22+k) / 2 is the topological Planck Length of our unit interval universe and also the isomorphic length of a super symmetric compactified hyperbolic Penrose universe with a Hawking black hole circular horizon given by;

(lp) = (4 + 1/Φ^3)(5 + 1/Φ^3) / 2

= (22 + k) / 2

= 11 + (k / 2) = 11 + 1/Φ^5 = Φ^5

= 11+1/(11+1/(11+1/(11+...)))

It follows then that (22 + k) is the topological diameter of our fractal M-theory universe.

The topological Planck energy of our unit interval universe is nothing but Hardy’s quantum Entanglement probability of two quantum particles;

(Ep) = (PH) = 1/φ^5 = k/2

Since 11 + 1/φ^5 is equal to φ^5, which is the inverse of the unit interval (Ep), we see that E - infinity space is infinitely multi-connected and that all these fractal gaps and voids in their space are essentially wormholes with length equal to (lp) = 11 + 1/φ^5 which constitutes Einstein - Rosen bridges.

There is a fundamental connection between what we may call Witten Hypercube and Witten Fractal M-Theory connecting quantum relativity with Hardy’s Quantum Entanglement.

We believe that El Naschie’s theory gives a bridge joining our visible world with the invisible quantum world, which was proposed for the first time by Prof. Ji-Huan He.

This exact result 1/Φ^5 became the background against which the quantum entanglement theory of E-infinity theory was developed and the simple quantum entanglement probability formula of n quantum particles was established, namely P = 1/Φ^(3+n). There is a deep meaning for this superficially nonsensical result, it means that spacetime at the quantum resolution is completely interconnected and nonlocal. In addition, dark energy is the energy of the quantum wave. Consequently it must be a possible source of near to infinite clean energy.

Similar to the quasi probability of Wigner’s quantum mechanics in phase space, our topological probability approach to quantum mechanics as enshrined in E-infinity represents an alternative extremely simple formulation for quantum mechanics which adds a few new points to our understanding of the deep mathematical structure of quantum spacetime.

For instance, as we enter into the negative dimensions regime and find that the Hausdorff dimension 1/Φ^n is getting increasingly small, it is clear that this means the “Cantor set” is becoming thinner and tending to real nothingness or the absolute empty set. The situation is thus paralleling the density of the density matrix. Similarly when we are summing in E-infinity theory over all dimensions to reach our expectation Hausdorff dimension of the core of E-infinity spacetime D(4) = 4 + 1/Φ^3 then we are using essentially a similar mathematical concept as that of Feynman path integral but exchanging “paths” for “dimensions”.

The Vague Attractor of Kolmogorov and Quantum Phase Space from the View Point of E-Infinity - written by El Naschie

In the following we show a simple deep connection between a few fundamental aspects of E-infinity and Weyl-Wigner theory;

If we take 1/Φ to mean a coordinate then 1/Φ^2 is the quasi derivative and (1/Φ) – (1/Φ^2) = 1/Φ^3 becomes a phase space with (1/Φ)(1/Φ^2) = 1/Φ^3 being simply a cell of this phase space. Seen that way, then (1/Φ)(1/Φ)(1/Φ)(1/Φ^2) = 1/Φ^5 of Hardy may be recognized as the unit cell of 3D Cantorian-quantum phase space. Since the Vague Attractor of Kolmogorov is a Hamiltonian “strange” attractor conjectured by Rene Thom to represent the equilibrium states of quantum mechanics, we see how the Vague Attractor of Kolmogorov, E-infinity and Wigner quantum phase quasi probability are intimately connected.

The Advantage of Transfinite Cantorian Quantum Mechanics - written by El Naschie

Let us start with Heisenberg’s uncertainty. In E-infinity spacetime there are no ordinary points. It is exactly as in von Neumann’s continuous space which he describes in jest as “pointless”. Consequently in Cantorian spacetime this fundamental principle is taken care of automatically.

In fact writing 1/Φ^3 as (1/Φ)(1/Φ^2) reveals that neither (1/Φ) as a quasi coordinate nor (1/Φ^2) as its derivative are fixed numbers which can be written in decimal expansion in a finite way nor the quasi phase space spanned by (1/Φ) and (1/Φ^2). The same is true for the product 1/Φ^3 which is ambiguous in a fundamental way because (1/Φ) could be seen as a distance or a mean velocity while (1/Φ^2) could be interpreted as acceleration or mean velocity squared.

However for the union of the two sets, the zero set (1/Φ) and the empty set (1/Φ^2) we have the remarkable collapse in a simple integer

(1/Φ) + (1/Φ^2) = 1

It would be a mistake to think this result is trivial.

However, written in symbolic form (5^(1/2) – 1)/2 = 1/Φ and 4/(5^(1/2) + 1)^2 = (1/Φ^2) this is of course trivial computation but not when written in the chaotic decimal expansion.

In other words E-infinity transfinite Cantorian quantum mechanics has at its disposal and in a natural way, a transfinite golden computer with a real efficiency which borders on the surreal because simple finite arithmetic operations can handle uncountably infinite numbers and find at the end a neat compact answer.

In fact nothing can attest to this like that first rate orderly character of the continued fraction expansion of 1/Φ, namely

1/Φ = 1/(1+1/(1+1/(1+1/(1+…))))

when compared to its totally chaotic decimal expansion

1/Φ = 0.61803398925…

and find on the top of that a well known fact, namely that 1/Φ is the Hausdorff (fractal) dimension of a random triadic Cantor set.

E-infinity fulfills the criteria which says that maximal accuracy is attained in the ideal limit at maximal simplicity. We could find nothing better to close this section with than the wise words of a Socrates of modern science, Prof. J.A. Wheeler in his classic book “Information, Physics, Quantum: The Search for Links” where he wrote “Surely someday we can believe, we will grasp the central idea of it all as so simple, so beautiful, so compelling that we will say to each other;

‘Oh, how could it have been otherwise!. How could we all have been so blind so long!’”

The ‘One Sided’ Möbius Strip in Higher Dimensions as the Boundary of the Holographic Boundary - written by El Naschie

We presented in this relatively short paper a general theory for quantum spacetime and zero point energy fluctuation based on E-infinity and related mathematical concepts.

The main conclusion is a natural consequence of mirror symmetry and Witten’s T-duality, in addition to Dvoretzky’s theorem, revealing that approximately 95.5% of the volume of an infinite dimensional sphere will be concentrated on the surface or holographic fractal boundary, which explains why dark energy is concentrated at the edge of the universe, similar to information stored on the surface of a black hole.

The quintessence of the present theory is explained as the 1/Φ^3 intrinsic Casimir topological energy is produced from the zero set 1/Φ of the quantum particle, when we extract the empty set quantum wave 1/Φ^2 from it and find 1/Φ - 1/Φ^2 = 1/Φ^3.

Casimir energy and ordinary energy density of the cosmos are not only identical conceptually but identical numerically. Casimir energy and cosmic dark energy are complimentary in the most strict mathematical and physical meaning.

The difference between Casimir energy and dark energy is a difference of boundary condition where the boundary of the holographic boundary of the universe is a one sided Möbius-like manifold. There are at least two fundamental interpretations of this miraculous effect. The first is loosely connected to boundary conditions and the zero point quantum vacuum fluctuation which may be the common way of looking at the Casimir effect within the physics community. The second, which may be more theoretical and fundamental, is to see Casimir as a source in the mold of J. Schwinger’s way of thinking and not far from the Casimir operators of quantum field theory. Thus we could look upon the Casimir effect as a member of the same family of Hawking’s negative energy fluctuation around a black hole or as Unruh’s temperature for an accelerated universe expansion.

One of our most important insights gained here is undoubtedly the Möbius-like one sided boundary of the boundary of our universe which led us to realize that dark energy expansion of the universe is a global manifestation of the local Casimir forces. By manipulating the local dimensionality of spacetime using an elaborate and complex setup of Casimir plate systems, we could build a nano-universe and extract the 95.5% dark energy concentrated at its boundary.

The holographic boundary theory goes back to the pioneering work of ‘tHooft and Susskind.

On the other hand the principle that the boundary of a boundary is zero goes back to the out of the box thinking of J.A. Wheeler. Pushing their ideas further, it became obvious to El Naschie that the boundary of the holographic boundary is not only a zero limit set but actually a hierarchy of empty and emptier still sets ramifying at a most general form of a one sided higher dimensional Möbius band.

Figure 52 - This limit set resembles a fundamental polyhedron group or better still, a Kleinian group which changes the topology of our conventional Casimir experiment to that of a sphere with internal Casimir pressure inflating the balloon-like universe and makes it expand into the surrounding ‘nothingness’ fixed by the well known E-infinity formula D(-∞) = 1/Φ^∞ = 0.

From the preceding elementary reasoning it is clear that Casimir-effect and dark energy have the same cause, namely the topology of a Banach-spacetime like manifold and the only difference, as we mentioned and stressed repeatedly earlier on, is the difference of local exophysics and global endophysics and the respective associated boundary conditions.

What we are aiming at in the present paper is to point out the way to move from theory to useful, practical application of which nothing could be more important and pressing than building a free energy reactor, based on real science rather than wishful thinking.

Thus we combine the dreams of great and grossly undervalued visionaries like Nikola Tesla with hard nosed modern mathematics and physics due to ‘tHooft, Witten, Penrose, Kerr, Dovertzky, and many other pioneers which were not yet available in the time of Tesla. We are of course now in a far better position than Nikola Tesla because we can fall back on modern results both theoretical and experimental in black holes and fractal research.

In recent years, nanotechnology has invaded all scientific fields and played a significant role in Casimir effect experiments. Thanks to E-infinity we now know the true physical mathematical connection between dark energy and the Casimir effect. A natural consequence of this discovered reality of the quantum wave is rendering it a relatively simple task to find a way to harness dark energy or Casimir energy. Of course this ‘simple’ is still extremely difficult but no longer impossible. As mentioned earlier on, we are aided in our quest for a Casimir reactor by the many wonderful results obtained in fractal sciences and the geometry of black holes.

We can start with a highly complex sub-structuring of space using nanotubes and nanoparticles and create that way of nanosphere packing, modeling the moonshine conjecture that relates superstrings to other fields of theoretical physics. We presently have, in embryonic form, the main idea of constructing a nano universe and extracting dark energy from its nano boundary of its holographic boundary. An established program to actually extract energy from such a nano reactor may still need five or more years but the road is marked and reasonably clear.

It is only at the edge of the universe that 95.5% of the energy resides as dark energy. However we could create many nano universes from which its 95.5% energy concentration could be extracted without actually reaching to the boundary of our universe. Thus while we need to minimize or eliminate the Casimir effect when manufacturing nano devices, here we accomplish the opposite by maximizing the Casimir effect using fractal nano technology.

In the present paper, we view the Casimir effect as a natural topological necessity of a Cantorian spacetime fabric which was woven from an infinite number of zero Cantor sets and empty Cantor sets.

The zero set is taken following von Neumann-Connes continuous dimensional function to model the quantum particles while the empty set models the quantum wave. 

Following this road we come to realize that the Casimir latent energy is nothing but the universal fluctuation 1/Φ^3 which gives birth to the core of Cantorian-fractal spacetime by inversion 1/1/Φ^3 = Φ^3 = 4 + 1/Φ^3 ≅ 4.23606797. In turn this is nothing but the difference between the Hausdorff (fractal) dimension of the particle zero set 1/Φ and the wave empty set 1/Φ^2.

The result not surprisingly is almost equal to double the value found using imaginative modification of the classical Casimir experiment by Zee who found the dimensionless Casimir energy to be π/24 ≅ 0.1308.

Using E-infinity methodological reasoning, the exact value of Zee in the limit must be the ratio of the dimensionality of a CalabiYau transfinite manifold 6 + k = 6.18033889 and the transfinite dimension of bosonic string theory, i.e. 26.18033989.

That means (6 + k) / (26 + k) = (1/Φ^3) / 2.

The division by 2 is due to the subdivision of the “vacuum” of E-infinity theory and is analogous to dividing Hardy’s entanglement (PH) = 1/Φ^5 by 2 to obtain the density of the ordinary measurable energy of the cosmos E(O) = ((1/Φ^5) / 2) mc^2.

From this topological interpretation, it is realized that Casimir 1/Φ^3 is the counterfactual or global part of Hardy’s entanglement (PH) = (1/Φ^3)(1/Φ^n), where n is the number of quantum particles, and is found for n = 0.

It is obvious that the preceding discussion and analysis have sharpened our conception of quantum cantorian fractal spacetime. We see now that quantum particles are zero sets moving towards being either Schwarzschild black holes or spinning Kerr black holes.

Surrounding the zero set quantum particle we have the quantum wave empty set with the noncommutative or E-infinity bi-dimensions D(-1) = (-1 , 1/Φ^2) acting as the surface or cobordism of the quantum particle, i.e. the zero set D(0) = (0 , 1/Φ).

These (D(0) – D(1)) quantum objects are floating and propagating inside an infinite sea of spacetime with an average Bi-Dimension = D(-2) = (-2 , 1/Φ^3) which is our quantum Cantorian-fractal micro spacetime with an expectation value for the Hausdorff dimension equal to Φ^3 = 4 + 1/Φ^3 which we perceive as a topological dimension equal (4 + 1/Φ^3) – (1/Φ^3) = 4 = (3 + 1).

This triadic picture of a quantum particle zero set wrapped in a propagating quantum wave empty set and floating in a quantum spacetime which has 1/Φ^3 average topological Casimir pressure is more satisfactory than any previous picture which was presented in the past.

The 10 dimensional superstring core can be derived from the dimensionality of an E8 world quantum entangled with a second shadow E8 world, and is understood to be the fabric of cantorian spacetime which was woven from an infinite number of zero set quantum particles and empty set quantum waves in a 10 dimensional quasi phase space, given by 10-10/Φ=10/Φ^2. The 4.5% of ordinary energy in the universe is nothing but the multiplicative volume of a 5 dimensional Kaluza-Klein zero set while the 95.5% dark energy is the additive volume of the same 5D Kaluza-Klein empty set.

It has previously been shown that it is possible to generate the values of all of the dimensions of spacetime in string theory by an incredible hierarchical sequence of cantor sets that are scaled in proportion to the inverse of the fine structure constant α^-1 = 137.082039 = 20Φ^4;

α^-1/(2) = 68+3k = 10φ^4 

α^-1/(2Φ) = 42+2k = 10Φ^3 

α^-1/(2Φ^2) = 26+k = 10Φ^2 

α^-1/(2Φ^3) = 16+k = 10Φ 

α^-1/(2Φ^4) = 10 

α^-1/(2Φ^5) = 6+k = 10/Φ

α^-1/(2Φ^6) = 4-k = 10/Φ^2 

α^-1/(2Φ^7) = 2+2k = 10/Φ^3 

α^-1/(2Φ^8) = 2-3k = 10/Φ^4 

α^-1/(2Φ^9) = 5k = 10/Φ^5

α^-1/(2Φ^10) = 5k/Φ = 10/Φ^6

Where k = 2/Φ^5 = (1/Φ^3)(1-(1/Φ^3))

In noncommutative geometry as well as E-infinity theory, the Penrose universe plays a significant role as a generic concrete model for both theories. Penrose universe or Penrose fractal tiling is basically a quasi-crystal mathematical model with the forbidden 5-fold symmetry. The 5 fold symmetry could be thought of theoretically as five Kaluza-Klein dimensions and using nanoparticles and nanotubes combinations one could build in the lab a nano holographic fractal universe akin to our own from which energy could be experimented with and extracted.

The Lucas Sequence = The Dimensions of Spacetime in String Theory

I will correlate this to my next main point that I wish to share with you. Along with the 24 reduced Fibonacci numbers, there are many other secret Fibonacci patterns that have not been discussed. Lucien Khan has revealed several remarkable patterns, I will note his discovery of the 60 digit repeat cycle within the last digit in the values of the Fibonacci sequence, because it correlates to another discovery of Lucien Khan, which is the fact that the Lucas sequence also contains a 12 digit repeat cycle for the last digits.

Figure 53 - The Lucas sequence 12 digit repeat cycle for the last digits of each number.

As you can see here the Lucas sequence contains a hidden 12 digit pattern.

2,1,3,4,7,1,8,9,7,6,3,9

Applying the same technique as the 24 reduced numbers reveals a pattern adding to 10 vertically.

2,1,3,4,7,1

8,9,7,6,3,9

1,1,1,1,1,1 - Sum of row 1 and 2 with digital root.

This is a correlation between the Lucas sequence and both the 12 digit repeat cycle of the fractal dimensions of spacetime and also the 10 dimensional quasi phase space of E infinity.

The Lucas numbers or Lucas sequence is an integer sequence named after the mathematician François Édouard Anatole Lucas (1842–91), who studied both that sequence and the closely related Fibonacci numbers.

Similar to the Fibonacci numbers, each Lucas number is defined to be the sum of its two immediate previous terms, thereby forming a Fibonacci integer sequence. 

The first two Lucas numbers are L0 = 2 and L1 = 1 as opposed to the first two Fibonacci numbers F0 = 0 and F1 = 1.

Also like all Fibonacci-like integer sequences, the ratio between two consecutive Lucas numbers converges to the golden ratio.

Though closely related in definition, Lucas and Fibonacci numbers exhibit distinct properties.

We can express the relationship of L(n) and F(n) as..

L(n) = F(n-1) + F(n+1) = F(n) + 2F(n-1) = F(n+2) - F(n-2)

The sequence of Lucas numbers is:

2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123..

All Fibonacci-like integer sequences appear in shifted form as a row of the Wythoff Array and also Stolarsky’s array; the Fibonacci sequence itself is the first row and the Lucas sequence is the second row (third row in Stolarsky’s array), it is fascinating to note that the integer values of the dimensions of spacetime in E-Infinity theory, revealed by El Naschie’s equation Dn = Φ^(n-1), is the third row of the Wythoff array (and also is the second row of Stolarsky’s array).

Figure 54 - The Wythoff array is an infinite array of integers that can be constructed by beginning with the Fibonacci numbers {F2, F3, F4, F5, …} in the first row and then building up subsequent rows by repetitively adding {F3+k, F4+k, F5+k, F6+k, …}, where k = 0 or 1, is the smallest offset producing an initial term that has not occurred in a previous row. 

This process gives the array shown on the top of Figure 54.

A stolarsky array is an array of natural numbers such that:

-The rows {m1, m2, …} are positive Fibonacci sequences

-Every natural number occurs exactly once in the array

-Every positive Fibonacci sequence is a row of the array after a shift of incides

That is given a positive Fibonacci sequence {Sk}, there exist m and k such that m(n) = Sn+k

The first such array was constructed by Stolarsky and is shown below the Wythoff array in Figure 54.

By inspecting the tables of these two arrays, it is easy to obtain more Stolarsky arrays. (For example, in either table, the 4 may be shifted from the second to the third row.)

It would be interesting to have a classification of the Stolarsky arrays.

The Wythoff array is a Stolarsky array and also contains every natural number exactly once.

Alternatively, we can express the relationship of L(n) and the golden ratio (Φ) as..

L(n) = Φ^n + (1-Φ)^n = Φ^n + (-Φ)^(-n)

For n > 1, the magnitude of the term (-Φ)^(-n) is less than 1/2, L(n) is the closest integer to Φ^n or, equivalently, the integer part of Φ^n + 1/2.

Combining the above with F(n),

F(n) = (Φ^n - (1-Φ)^n)/(√5)

a formula for Φ^n is obtained:

Φ^n = (L(n) + F(n)(√5))/2

Since 1-Φ = 1/Φ, this means that for n ≥ 1, L(n) is the same integer that is expressed in the continued fraction expansion representations of Φ^n. For example;

L(1) = 1

Φ^1 = 1+1/Φ^1 = 1+1/(1+1/(1+1/(1+...)))

Φ^1 (which is simply Φ) is also equal to 1/Φ+1 = Φ^1 = Φ

The correlation of Φ with 1 and the inverse of Φ (1/Φ) reveals a Fibonacci sequence that connects all of the powers of Φ and their inverses and 1.

This hidden Fibonacci sequence that exists between positive and negative Φ exponents and the unit interval (1) reveals a transfinite golden computer with a real efficiency which borders on the surreal because simple finite arithmetic operations can handle uncountably infinite numbers and find at the end a neat compact answer.

L(2) = 3

Φ^2 = 3-1/Φ^2 = 3-1/(3-1/(3-1/(3-...)))

Φ^2 is also equal to 1+Φ = Φ^2

L(3) = 4

Φ^3 = 4+1/Φ^3 = 4+1/(4+1/(4+1/(4+...)))

Φ^3 is also equal to Φ + Φ^2 = Φ * Φ^2 = Φ^3

In other words our E-Infinity space is blind to the union (+) and intersection (*) of the probabilities of quantum particle and quantum wave in fractal-cantorian spacetime, and cannot tell them apart which is the deepest explanation possible for the particle-wave duality of quantum mechanics.

According to El Naschie, this is the exact value for the dimension of our ‘ordinary spacetime’ in E-Infinity theory. 4 ordinary dimensions + 1/Φ^3 Fractal dimension. Following this road we come to realize that the Casimir latent energy is nothing but the universal fluctuation 1/Φ^3 which gives birth to the core of Cantorian-fractal spacetime by inversion 1/1/Φ^3 = Φ^3 = 4 + 1/Φ^3 ≅ 4.23606797. In turn this is nothing but the difference between the Hausdorff dimension of the particle zero set 1/Φ and the wave empty set 1/Φ^2. (1/Φ - 1/Φ^2 = 1/Φ^3)

L(4) = 7

Φ^4 = 7-1/Φ^4 = 7-1/(7-1/(7-1/(7-...)))

This value is closely related to the 7 sided Klein modular group in the previously shown hyperbolic fractal projection of the quantum gravity of spacetime in El Naschie's E-Infinity theory. This value is exactly 20 times the Fine Structure Constant (1/20Φ^4) according to El Naschie. The inverse of the Fine Structure Constant can be divided by 2 and then subsequently by 2Φ, 2Φ^2, 2Φ^3, etc. in order to generate a hierarchical scaling sequence that produces all of the dimensions of spacetime, as previously shown.

L(5) = 11

Φ^5 = 11+1/Φ^5 = 11+1/(11+1/(11+1/(11+...)))

Where k = 2/Φ^5, the scaling factor

(22+k) = (4+1/Φ^3) * (5+1/Φ^3)

(22+k)/2 = 11+1/(11+1/(11+1/(11+...)))

This is a super symmetric Penrose fractal tiling.

This value is the Topological Planck Length and also the isomorphic length of a super symmetric compactified hyperbolic Penrose universe with a Hawking black hole circular horizon given by;

(lp) = (4 + 1/φ^3)(5 + 1/φ^3) / 2 = (22 + k) / 2

= 11 + (k / 2) = 11 + 1/φ^5 = φ^5

= 11+1/(11+1/(11+1/(11+...)))

Note that the continued fraction representations of the powers of phi (Φ^n) alternate with addition and subtraction to the corresponding Lucas sequence value in order to produce the final result. This addition/subtraction alternation, as well as the clear correlation between any positive Lucas sequence integer L(n) and the continued fraction expansion representations of Φ^n would remain a pattern into infinitely large numbers.

Another alternating pattern that can be seen in both the Lucas sequence and the Fibonacci sequence is the alternation of 2 odd numbers followed by 1 even number..2 and 1 also being the root integers of the  Lucas sequence.

Fibonacci - (1,1) - 2 - (3,5) - 8, …(2 odd, 1 even, 2 odd, 1 even, …)

Lucas - 2 - (1,3) - 4 - (7,11), … (1 even, 2 odd, 1 even, 2 odd, …)

Wave Sequences Project 2D into 3D - Flower of Life Origin

The flower of life grid can represent the 2D pattern which will unfold as a 3D moving image within a wave field.

Figure 55

Figure 56

This is evident in the fact that the flower of life is simply a 2-dimensional infinite scalar grid of self similar x, y and z wave-axes as seen in Figure 55, each of these quasi phase spaces are held within their own 6 sided cubic wave field, as seen in Figure 56.

One can see the 2D flower of life transform into an illusionary 3D grid at any point in the pattern by a change of visual perception, shifting focus between the internal x, y and z wave-axes and external 6 sided cubic wave field boundaries. The flower of life grid actually encodes an infinite cubic fractal; 8 cubes within a cube, within a cube, within a cube, within a cube...infinitely repeating into both micro and macro scales.

The flower of life grid depicts a 2-dimensional interpretation of the layout of mindspace, where each 6 sided intersection of axes is another zero point in which Mind has the potential to manifest into the infinite cubic wave field that is encoded within the grid.

Figure 57 - Fractal cube within the Flower of Life.

Figure 58 - Tetrahedron structures multiplying by octaves; 1, 8, 64, 512 & 4096. 

The tetrahedron is a fundamental geometric building block. Two polarized larger tetrahedrons creates a star tetrahedron, which is composed of 8 smaller tetrahedrons.

Putting 8 star tetrahedrons together creates a 64 tetrahedron grid which internally forms 2 octaves of the cube octahedron geometry.

The cube octahedron is a perfectly balanced geometry that Buckminster Fuller called the "vector equilibrium". The cube octahedron is the only 3D geometry that is equal and opposite in every possible way, where every line (vector) in the geometry are of equal length, including from the center of the geometry to the edges.

At a total of 512 perfectly stacked tetrahedrons, 3 octaves of cube octahedron geometry are formed, at 4096 another octave and the pattern continues both infinitely to create a perfectly balanced and harmonic geometric grid of space.

Figure 59 - The star-tetrahedron, 64 tetrahedron grid and the larger related octave structures define the edge points of cubes, however they have none of the lines of a cube. This is easily seen in both Figure 58 and 59.

It’s as if the triangles / tetrahedrons / 64 tetrahedron grid octaves create circles / spheres / toroidal vortices that define metaphysical squares / cubic wave fields. The tetrahedron is a fundamental building block to the physical world and provides a geometric pathway for the manifestation of the larger platonic solids.

The average Hausdorff (fractal) dimension for our spacetime is;

D(4) = 4 + 1/Φ^3 = Φ+ Φ^2 = Φ(Φ^2)

= 4+1/(4+1/(4+1/(4+1/(4+…)))) = Φ^3 = 4.236…

The general El Naschie’s dimensional form is

D(n) = Φ^(n-1) = 1/Φ^-(n-1) 

For our real n = 4 space-time, the general El Naschie’s dimensional form results in the average Hausdorff dimension for our space-time.

Figure 60 - The visual interpretation of this equation is shown here and looks like a Russian doll with self similarity in all scales. This self similar fractal cube structure correlates El Naschie’s fractal spacetime model, the 64 tetrahedron grid, the flower of life grid and also Walter Russell’s cubic wave field model, which will be explained in the next section.

All of these models explain the same concept, namely an infinite cubic fractal; 8 cubes within a cube, within a cube, within a cube, within a cube...infinitely repeating into both micro and macro scales. This idea is equivalent to Walter Russell’s cubic wave field. The concept of the cubic wave field is that of a 'container' within which a moving expression of Idea can manifest.

Figure 61 - example image of the geometry that is revealed by selected area electron diffraction, providing further reinforcement to this omnipresent self similar cube fractal spacetime model that has been explained through many different perspectives.

The Cubic Wavefield - Alan Hayes

"Within the Cube lies the secret of the Wave"

The cubic wave field is not a physical structure, it is metaphysical in character. The cube model is typically back-referenced from the wave model.

Figure 62 - Imagine the following thought experiment…

Build a six sided cube, the internal walls of which are mirrored. A light is placed in the center of this cube. When the cube is lit, the light radiates to each of the 6 mirrored walls.

This light is then reflected backwards and forwards between opposite mirrored surfaces creating (if observed from the center) a reproduced infinity image of the original source.

The original light source itself is reflected at harmonic distances from the original center as well as from each reflected center. This is how the illusion of dimension is created.

We will refer to this all-encompassing cube as the Master Cube. All of the simulated illusion of our sensed reality is contained within this Master Cube.

The Master Cube IS Mind.

Every cube (without exception) must be thought of as being composed of 8 sub-cubes.

This technique will be of great benefit to you as Walter Russell describes matter accumulating at the center of the cubic wave field while also describing wave-sections being completed at wave field corners. The corners of the cube have special properties that are well known to many fields of science and engineering and are primarily used in navigation systems.

The Master Cube contains the whole Universe.

The Master Cube is Universal Mind, Universal Intelligence. All that Mind can possibly imagine is contained inside the Master Cube.

How big is your mind? How big does your mind need to be in order to imagine a galaxy? Does your mind have a size at all?

When you imagine a galaxy...the entire imagined image fits inside your head...doesn't it?

Now imagine 10 galaxies, or 100. Your mind is your master cube. The images are not limited by dimension. Your mind and Cosmic Mind are one. You think in exactly the same way Cosmic Mind Thinks. Can you conceive the universe as being the result of an imagined thought?

The illusionary simulation in which your body is part, is imagined by the Universal Mind in exactly the same way. Your physical body is an imagined thought of Mind. The entire matrix is a Mind projection. The term matrix is used to describe the simulation; the illusory universe of matter, form and motion. It implies that there is something outside of our visible universe of effect; i.e. The One Infinite Creator's Mind.

The concept of the cubic wave field is that of a 'container' within which a moving expression of Idea can manifest. 

The entire universe is God-Mind. God-Mind is Stillness. Walter Russell describes Stillness as dark, empty space. There are no dimensions to this Stillness, because there is no motion. Dimension only comes into being when motion begins, and motion only comes into being as a result of Mind's desire to express Ideas.

That expression manifests as a rippled disturbance to Stillness.

So, you can think of this Stillness as being omnipresent (everywhere at once) and yet it is dimensionless. This Stillness is the realm of the God-Mind, and it is from this realm that our 3D universe is projected. How is this achieved? 

An apparent division of Stillness is created by the God-Mind. Stillness is often referred to as a plane of zero curvature, because curvature is a measure, a dimension, and dimension is only associated with a universe of motion. The entire universe of motion manifests to our sensing inside the Master-Cube. Walter Russell also refers to the cube as the wave field.

The cubic wave field is made up of 9 mirrored planes; 3 internal planes and 6 boundary planes.

The 3 internal planes are used to project images out into the wave field, while the boundary planes are used to reflect images back towards their origin.

These 9 planes are termed planes of zero curvature because they are flat and without distortion.

Walter Russell draws on the analogy of a calm pond without any ripples evident on the surface of the pond. The undisturbed surface would thus be described as a plane of zero curvature.

These planes do have character, and their properties apply to all planes. If we now examine one plane in detail, and define some of its attributes, we can then apply those characteristics to all planes, both internal and boundary.

Figure 63 - This apparent division occurs across a plane of zero curvature.

Planes of zero curvature become evident when motion stops, like when a ball is thrown into the air, the ball stops before returning to the hand. This immediately implies that any expression of motion is therefore curved or distorted in some way. In fact, this curvature is the cause of motion in the first place.

Although the depicted figure isolates out individual x,y,z axes, the lower portion of the image is the focus. 

Mind is everywhere at once. It becomes evident at planes of zero curvature due to the motion surrounding it. In the image above, a portion of the x-axis is expanded for clarity. The God-Mind resides IN this axis of zero curvature. Mind exists in all planes of zero curvature, because Mind is every plane. Another important characteristic of the plane is any point along the plane is the same point because it is the same Mind.

Now, imagine instead of simply visualizing the plane of zero curvature as a line or plane, imagine the God-Mind IS every projection and reflection plane. Planes of Stillness are Mind. Imagine if the magnified x-axis above expanded to fill the entire wave field. Mind is all there is.

The lower portion of the image indicates that a division of some kind occurs. This is only a representation of the mechanism of Mind-Thinking.

Light projected by the God-Mind is cast to create a 3D illusion, created by motion. Ripples on the ponds still surface. This is all our perceived reality is. It is a moving disturbance, caused by Thinking-Mind. The disturbance manifests as a wavy motion, which our sensing are programmed to detect and interpret. The still pond is Cause while the wavy ripples are effect.

The first great lesson Walter Russell's Cosmology can teach a student is the true nature of Cause, and not allow too much credence be given to sensed (effect) experiences. 

Motion is the unnatural state of our perceived universe. 

Stillness, and your relationship to that Stillness is your first lesson. 

Because Mind is omnipresent, all 'points are the same point', which implies all points have the full potential of Mind. Therefore every point can unfold any possibility of a Thinking Mind.

Expression of this Mind can therefore spring from apparent 'nothingness' at any point in the perceived universe.

The wave cycle is the journey of expression from that apparent 'nothingness' out into a seeming 'somethingness' and the return from that sensed expression back to motion-in-inertia or Stillness.

Figure 64 - This image implies that as Mind expresses Thinking, an apparent division is created by projection one half of the Idea/Concept in one direction with the second portion of that same Idea/Concept in the opposite direction.

Imagine, an Idea is divided into a red spectrum signature and a blue spectrum signature. Neither one by themselves is sufficient to tell the whole story of the original Idea. When those two lights come together, then the original Idea is reproduced as an expression in motion. The original Idea is never created. So, when Mind desires to express Ideas/Concepts, cubic wave fields are constructed to contain and house a moving expression of Thought. Remember, a cubic structure by itself, has no meaning to our sensing. Without motion, there can be no expression.

Figure 65 - These images indicate how the static metaphysical universe sits in the dynamic universe of apparent motion.

Notice how the white petal of motion is created not as a physical thing, rather it comes into being as a result of Mind's Curved Thinking activity.

Think of this motion exactly as you would a vibrating string. We know the string must oscillate across a static equator to express itself in reverse.

When Mind, in thinking, expresses a desire to give life to an Idea, an apparent mirrored division within Mind occurs which brings the petals into manifest.

A diverging, radiating, expanding light is sent from the central internal projection plane out towards the boundary. This radiation is condensed and reflected back in towards the internal plane of origin.

The two opposed wave streams interact and when an equilibrium is established a standing wave is produced between the two points of stillness or nodes. The standing wave and the internal petal symmetry it produces is of vital importance in determining how moving images are manifested.

Think of the image above as you would shine light through a stencil. Mind appears to divide and create a 'gap' into which your sensing fills in to 'see' a moving image where no such image exists. The omnipresent black background of Mind appears to divide and thereby create a 2D pattern. Your sensing then fills in the gaps to 'see' matter and form as a 3D expression.

This is why scientists find more space than matter when looking inside the atom.

Wave Sequences Project 2D into 3D

Figure 66 - The first image indicates wave sequence pairs.

There is always action followed by equal & opposite reaction. 

Sequence 1 is a projected action while sequence 2 is the reflected reaction. Wave actions are completed as a balanced pair.

The second image at the top of Figure 66 has straight diagonals as therefore we can say that Mind is undivided not wishing to express an Idea. This model is consistent with the concept that Mind is omnipresent, and every part of Mind is the same Mind.

The first image on the bottom of Figure 66 indicates a desire of Mind to express Idea. See how the apparent curvature seems to open a space into which an image may be produced. This image implies one part of Mind is acting as an anode while another part of Mind is acting as the cathode, and the string/flower petal vibrates and oscillates between the apparently different aspects of Mind. This motion only becomes manifest when the 2D pattern arises to create a 3D moving expression of the 2D pattern. Our sensing is tuned, in fact designed, to only sense the vibrating/oscillating blue areas as indicated in the second image on the bottom of Figure 66.

We believe this motion to be real when it is only an illusionary effect. If the first image on the bottom acts like a stencil, our sensing fills in the gaps and we 'see' a reality which is not 'real'.

We 'see' a similar effect when we observe a wave traveling although the motion is only up / down.

It is important for the reader to understand that these images only contain the x and y axes in order to ease the visual aspect. The introduction of the z axis into these images would give us a 3-dimensional representation of the flower of life pattern.

Figure 67 - Electricity is the force of Mind and the cause of all curvature and polarity.

When Mind wishes to express a Thought, a 2D pattern (a negative) is prepared and suitably dimensioned. In order to bring that image to life (into the 3D) it must be imbued with motion.

Why motion?

Because our sensing has been designed to interact with motion.

Before we begin the construction of a cubic container, consider the following important premise.

Mind is omnipresent, there can be nothing else in existence.

However, to our sensing, Mind appears to divide as pictured in the first image above.

The red aspect is generated between the central plane and the red boundary plane, while the blue aspect is generated between the central plane and the blue boundary plane.

The cubic structure in the image above is showing a sequential motion of wave sequences. Once motion begins, everything changes because motion imparts a dynamic movement to the image. Nothing actually stays still long enough to be recognised as solid structure.

Motion begins in the top hemisphere then is repeated to the lower hemisphere in the next wave field, meanwhile motion in the bottom hemisphere is also repeated to the top hemisphere of the next wave field; oscillating in sequential cycles, forever.

It is the Thinking impulse which gives the impression of motion within the physical universe. Our universe image is constantly being reproduced by the sequential pulsing of Mind Thinking. Each pulse creates the entire universe again. Just like a film strip; the entire movie is made up of thousands of individual still images. Our physical universe is also switched on / off / on every single moment from every single point (omnipresent Mind). This appears to our sensing as a moving, imaged physical universe, when in reality, no such movement is occurring at all.

Remember, all Creation Idea lies in the Still axis, in this case the horizontal wave axis. The process of Concentrative Thinking by Mind within that axis creates the illusion of a division; a polarized condition which manifests as a N/S disturbance which we sense as a physical object in motion within our physical universe.

If the universe of motion could be slowed down, the secret of the illusion would become obvious. The individual frames/pulses of a Thinking Mind would be revealed. 

But, when those frames are run at 186,624 miles/sec; we sense a solid, materialistic world.

This image shows the 2D plane 'edge on' at the top, and also that Mind is partially divided by assigning the top side a red and the bottom side as blue.

This 2D plane may be considered as possessing 4 poles. An E/W pair to dimension the width of the plane and a second E/W pair to dimension the depth (receding into the distance) of the same plane. The distance between them is minimal in 2D, however when the distance between red/blue is maximum, a cubic wave field will result from these 4 poles.

The 3D physical moving expression is effectively mapped out first as a 2D red and blue negative, so that the positive red aspect can be projected in one direction, while the blue positive aspect can be projected in the opposite (180°) direction.

This is a dimensionless plane because it has no (N/S) 3D character at all. Projection has not yet begun, because division has not yet happened.

The inert gas expression is best described as this edge on almost 2D flat geometry. This is why hydrogen and helium are so abundant in outer space. These gases represent the seed conditions from which most of our perceived matter unfold or germinate.

One Mind begins to Think, electricity is born. Electricity is the force which drives the red/blue faces away from one another in opposite directions. Mind always remains still and remains anchored to the center of the wave field. Mind will act as the still fulcrum for any induced motion.

Once electricity comes into being, N/S (red/blue) polarity is born. Notice how the process of Thinking has produced two anode expressions centered by one single (Mind) cathode plane.

Why is a cubic wave field necessary at all?

The wavefield acts as a container to hold within it the desired image. This is achieved by the way motion behaves inside the wave field and how our sensing apparatus is programmed to interpret this motion. Boundaries of straight planes are necessary to differentiate between motion in one wavefield and motion in a neighboring wave field. A geometric (cubic) structure of some description is necessary which will allow curvature to develop inside that structure.

Curvature implies polarity, polarity implies electricity, electricity implies Mind Expressing Thought. Curvature is also polarized which means that there is centripetal compression in one direction and centrifugal expansion in the opposite direction.

Rotating loops implies a gyroscopic effect, for the same reason you stay upright on a moving bicycle.

A 3D geometric structure is necessary to hold the projections of a 2D pattern. That pattern is the dividing equatorial plane. Once these conditions are incorporated into your idea of a cubic wave field model, it should become much more accessible as a structure.

Figure 68 - Electricity is the first force to manifest into the physical universe. All expression is therefore electric, and dimensioned electrically.

When these electric forces go to work, the area where the projected image will eventually form acquires a curved geometry.

Not the charge, but the 'curvature' is positive (red) on the surface with the shorter arc, and negative (blue) on the side with the longer arc.

The effect is present regardless of which hemisphere the curvature is expressed.

This is Natural Law for all curvature. This is a two-way universe, polarity is caused by curvature.

This curved geometry is responsible for all of the effects within the physical universe that we sense and believe to be real. Our senses are simply deceived.

Figure 69 - Curvature is necessary in a two-way universe, whereas there is a compressing effect in one direction but an expansive effect through the same curve in the opposite direction.

Pay really close attention to the implications of curvature regarding the manifestation of red/blue character.

Blue character with negative curvature is present outside the red in the top hemisphere, while red character with negative curvature is inside the blue in the bottom hemisphere. This red / blue divide comes into being because of curvature, and this differential can be applied to all expressions of curvature within our universe.

Figure 70 - A wavefield might appear as one sphere, but it is composed of eight sub-spheres.

The first two images above indicate why matter appears to have both particle and wave properties.

When motion is examined with respect to its relationship to the cubic hub center, then it appears to possess particle character.

However, when that same expression of matter is reviewed with respect to the corner of the 8 sub-cubes then it appears to possess wave like properties. The expression of matter can thus be described as being located at both conditions (center and corner) at once.

The red body is positioned in sub-section 8 of sub-cube 1. That same red body is also positioned in sub-section 7 of sub-cube 2, in sub-section 5 of sub-cube 4, in sub-section 6 of sub-cube 3,  in sub-section 5 of sub-cube 4, in sub-section 2 of sub-cube 7, in sub-section 1 of sub-cube 8, in sub-section 3 of sub-cube 6, and  in sub-section 4 of sub-cube 5.

This will give you an idea of some of the sub-dimensions at play in order to create a sphere.

Walter Russell teaches that the 3 internal projection planes are formed as follows.

Each sub-cube (1 to 8) is imbued with an electrical pressure potential.

Mind will continue to inflate these sub-cubes until they are appropriately filled to reproduce the intended idea. As inflation reaches a critical volume, the outer surfaces of the 8 spheres push against one another, flattening along the plane between them. When the sub-cubes are fully inflated, the potential is compressed into the 3 internal planes and the 6 external boundary planes. This is how matter appears to emerge from a seeming nothingness. Images are formed within the large cube, by the interactions of the 8 inner sub-cubes.

The boundary planes of zero curvature are formed as follows.

If you consider the inflation of wavefield with electrical force as the internal pressure then, a plane of zero curvature is created when opposed pressures fronts equalise one another at their common intervening plane.

Sodium and Chlorine unite in a balanced way to create a cubic straight walled (salt) structure. All other crystalline structures are a result of a non-balanced geometry about the common equator. Wave fronts of different frequencies will pass through one another. Pairs in resonance will oppose one another; having equal balanced wave front frequencies and dimensions.

Figure 71 - We are all at Sea.

"Waves of light do not travel. They reproduce each other from wave field to wave field of space.

The planes of zero curvature which bound all wave fields act as mirrors to reflect light from one field into another. This sets up an appearance of light as traveling, which is pure illusion."

Imagine a diver releases a polystyrene sphere/ball at 100 ft below the ocean waves.

The sphere will rush to the surface as fast as it can, do you know why?

The ball seeks buoyancy or balance in its own electric potential environment. The electrical pressures are too great at 100 ft and thus, the less dense material will rise.

You wouldn't say the sphere was experiencing an 'anti-gravity' phenomena, would you?

A gas will do exactly the same thing, falling from the surface of the ocean up into the heavens for exactly the same reason, it is seeking buoyancy. The electric potential of the environment is too great for a gas on the Earth and so the gas will rise to find balance and rest from motion.

What would Newton have said if the diver had released an apple at 100 ft?

Newton may then have invented anti-gravity, or developed a theory as to how the moon pulled the apple to the surface of the ocean.

Consider from now on, that the universe, from the very center of the most incandescent sun to the coldest vacuous space is filled with a differential electrical potential which works in exactly the same way as the pressure differential experienced by our diver with the apple.

This force motivates the entire universe, as all matter desires to find buoyancy with its own electrical potential environment.

This is an electric universe, not a gravitational one.

Gravity is an effect, not a cause.

Matter, can 'fall' uphill as well as falling downhill.

"Gravity exerts no force, whatsoever, to either attract or repel. Gravity is a shaft of magnetic stillness which has been extended two ways from zero in the cathode of the electric current, around which electric motion can simulate the energy of its magnetic zero center. Gravity is motionless and changeless." - Walter Russell

Imagine you were to fabricate a hula-hoop in a workshop which forms a perfect ring or loop. Where is its center?

The center may be easy to find if you place the loop on the bench and mark the location of the central hub on the bench. Now, hold the loop in the air. Where is the center of the loop now?

It may not be so easy to locate that center while the loop is suspended in space, especially if the hoop is moving/rolling. But, no matter its location a center always exists as a hub equidistant from the rim. The point is, that central hub is anywhere in the universe.

The central point only becomes evident when the circular rim is present. You don't have to bring the central hub with you when you move the rim, that central location simply becomes exposed wherever you express the rim.

The effect of gravity is exactly the same as the exposure of the central hub above.

Gravity exists everywhere, it is not created.

The effect of gravity becomes exposed by motion, just as a rim exposes a central hub.

Mind too, is everywhere, omnipresent. It, too, becomes exposed by fast motion.

Motion circulates in spirals around a 'gravity shaft' (equator) of Stillness.

That Stillness though, is already everywhere, it is not created.

The illusion of the universe of motion is designed to expose Stillness, but our senses are distracted by that very motion and we lose sight of the true nature of reality.

Because Stillness, Mind, and expression of gravity are omnipresent, we can thus manifest any motion we desire anywhere to express any Idea of Creation.

Think of the universe as an ocean of potential, and matter will always adjust its position in that potential, until it finds rest and buoyancy of electric potential. If Newton had originally thought of all material bodies as moving to find buoyancy of electric potential, rather than being 'attracted' by another body, he would have realized that a balanced body has no weight associated with it, and therefore he would not have pursued a gravitational model.

Weight is not a property within matter, rather it is an effect of the interaction a body has with its environment. Look what happens to one's weight when you climb a mountain. The greater that potential difference between a body and its environment the greater the dimension is expressed as weight, which applies to the moon attracting the ocean surface to create the tides.

The space between the Sun and the Earth is cold, because the radiation from the sun needs to condense in order to regenerate the condition of the sun. If an object entered the space between the sun/earth then that object would act as a condenser and heat.

There is a plane of zero curvature which exists between any two bodies. It defines the balance point of their respective potentials. This plane of zero curvature (PZC) lies much closer to the Earth because the emanations from the Sun are of such potential pressure that the body of the Earth is held buoyant at 93 millions distance. The PZC lies where the emanation from the Earth matches that of the Sun. However, as radiant light reaches the PZC it changes direction and becomes a generative stream focused towards the Earth.

This is why space is cold and light invisible.

As these streams are condensed again by the Earth, the conditions on the sun are reproduced, to scale, here on Earth. If the Earth was capable of condensing all of the sun's emanations, then the Earth would look like and behave as a sun. Thankfully, the Earth's specific ability to act as a condenser will only allow an Earth to manifest. Man also applies the same principle, to scale, in a hierarchical distillation column in his chemical separation processes.

Another interesting process to investigate is the commercial printing process. You may intuitively guess that the 3 colors of cyan, magenta, and yellow are used to generate a positive image from a negative. What may not be so obvious, is why a 4th color black is also used to complete that positive image. In order to reproduce a positive image of a poster, 4 separate negatives are utilized, one each for cyan, magenta, yellow and black.

Each negative is positioned onto a card substrate and the appropriate color is applied. Each subsequent negative is then overlaid on top of the already applied color, until finally the black pigment is added.

It is only after the black color is added does the image take on a feeling of 'depth', and 'contrast'.

Do you think cold dark space plays a similar role in creating the illusion of the simulated physical dimension? The core of accumulated potential may be represented in wavelengths of visible light, red, cyan, yellow, etc., but our senses are designed to react to a fluctuating vibrationary field. The blackness of space acts like the thin strip between two frames of a movie negative.

This 'off' condition facilitates the illusion of movement; i.e. one frame to another.

Figure 72 - The cyclic appearance / disappearance of matter is the evolution of mass from plane to sphere. If we now think of the introduction of the electric force into the wavefield as an inflation / deflation cycle, then physical matter unfolds as the wavefield inflates through an inhalation of this electrical potential. This generative process we perceive as a living, vitalising motion. As this potential is allowed to collapse or is 'exhaled', the projected image returns to its source. To die means to lose N/S character and thus the image returns to the 2D plane. It does not fall backwards. Can you now 'see' that by the process of Mind Thinking, Mind breaths into the wavefield, vitalising it. 

The electrical pressure holds the expression away from the horizontal zero wave axis in the form of a N/S projection. When Mind relaxes from Thinking, the wavefield deflates and returns that potential to Source through exhalation. All motion is caused by Mind inflation / deflation of Thought-bodies.

Your physical self is a direct result of Mind Thought.

"To know the mechanics of the wave is to know the entire secret of Nature." - Walter Russell

We exist simultaneously in two universes. One universe of the polarized physical realm and the second of the unpolarized spiritual realm. The spiritual realm is the hardest to fathom because our senses on which we are so reliant do not register and record within the unpolarized realm of stillness and uniformity. Our senses are designed to operate only in a polarized field.

The spiritual realm also known as the metaphysical realm is as real as the physical universe of form and apparent solidity.

"Mind is spiritual, and constitutes the invisible universe of Cause. Matter is physical, and constitutes the visible universe of Effect." - Walter Russell

Imagine you meet up one day with Beethoven and he begins to tell you about this tune he has going around in his head. He describes what story is unfolding and how the different parts of the orchestra will play their part. He might describe the melody, and arrangement necessary to replicate his mind idea. Even with the best will in the world, you might only be able to keep up with all of his enthusiasm for a short period, as you attempt to connect your physical senses with his metaphysical mind. You need more concrete physical evidence of his mind idea.

Once his idea has been successfully transcribed and the orchestra fully practiced, you can then 'sense' and appreciate what Beethoven's original mind idea was. Beethoven had to first create a physical body (body of musical sound) to replicate his metaphysical idea.

This is how the unseen idea becomes a physical reality.

Many scientists believe that the physical reality is the only reality, and yet it's own evidence suggests otherwise. How you make your physical body behave within the physical realm is your choice, but the desire to follow a particular path is rooted in your metaphysical body.

The desire to express any idea is the only energy of the physical universe.

Electric force is the measure of the differential between the metaphysical idea and the physical expression. The greater the desire to express idea, the greater will that desire manifest within the physical; the greater will that desire be registered in electric current.

So, all expression of matter is as a result of the desire of mind to express an idea.

Remember, 'as above, so below'.

The Creator's Mind does exactly the same thing to express the Creation Idea.

Opposed physical bodies are created to interact to create the illusion of form and solidity, just as Beethoven expressed his mind idea as a body known in physical form as the 5th symphony.

This physical sound is the exact replica of his original metaphysical thought pattern.

When we listen to this body of music our senses can record within our metaphysical bodies the emotions, feelings, inspiration etc. that Beethoven himself felt. This is how idea is reproduced. You could now channel your own desires and inner inspiration and create another physical body of work; maybe a cake, a painting or a novel.

The physical realm could not exist without the metaphysical realm, and vice versa.

The physical is the realm of the sphere, while the metaphysical is the realm of the cube.

Almost everything particle physicists are searching for within the physical realm has its cause in the metaphysical. Energy is not in matter, energy is extended to matter from the metaphysical. Desire to express is energy.

In the course of describing the cubic wave field, and how sodium chloride (NaCl) is the best representation of Stillness within the simulation, the following is a natural conclusion; all matter which expresses itself in motion wants to rid itself of that motion and return to the metaphysical universe of Stillness. This ultimate goal of all matter is to find rest from motion.

However, there are some suitable conditions along the way within the matrix of motion which are acceptable states of motion, that offer a balanced simulated Stillness akin to the metaphysical universe of non-motion.

When one's body is worn out, the physical body dies, but the metaphysical body returns home to build another negative which, when completed, will be projected as a positive expression into the matrix. Death resides in the metaphysical, but death is not what man believes it to be.

Can't you 'see' that you die every second of every day, because as you alter your own thought pattern, a new physical you is projected. The only difference between this momentary death and your physical death at around 80 years is 'dimensional'.

Now, hand in hand with this idea comes the fact that the NaCl salt forms as a result of a balanced union between oppositely sexed expressions.

The salt is in fact a physical representation of the death experience.

When two lovers unite in the ultimate expression of union, they experience an ecstasy which rather than being an insight of 'ultimate life' is in fact an insight to the ecstasy of death. 

Death is a euphoric experience for the soul and true euphoria is to be found in Stillness. 

Finding Stillness in death is an experience for all to look forward to.

Your physical body is separated from your metaphysical self. Electricity is the force of Mind which is the cause of this separation. Your physical body desires to unite with its own metaphysical self. Electricity, expressing the 'life' principle prevents this re-unification from occurring. When electricity disappears however, that re-unification is inevitable.

All expression of matter and motion express and follow this simple law of nature; all matter will express the life principle once electricity is present.

Electricity is the cause of polarity, and polarity results in motion. All motion is driven by the desire to stop moving. The best place to find that stopped condition is with union between the physical/metaphysical self. A temporary rest condition may be found within the simulated universe, through a balanced union of sexed mated opposites.

Your physical body is a condensed thought-form of Mind.

Just as a droplet of invisible vapor condenses on the cold glass surface, your physical body condenses against cold space. All visible matter is manifested as a result of condensation.

Your physical body is centered by an equator of Stillness.

This is the location of Mind itself.

Mind cannot be separated from its own Creation.

Mind therefore forms the boundary limits and the very center of every single expression within the matrix. Your physical body is centered by Mind.

The rims of the thought-bodies define your own physical wave field boundaries.

Mind encloses your condensed physical form.

The previously shown string theory equations also conclude that the quantum wave composes the surface or 'holographic boundary' of the quantum particle, which shows a clear correlation to the metaphysical concepts of the One Infinite Creator’s Mind that have been explained above.

In order for your soul to express itself, it must do so through your physical body.

Cosmic Mind does exactly the same thing, because there are not two forms of Thinking.

When Cosmic Mind wishes to express his idea of 'Man' he does so through a physical instrument; your physical body.

Mind channels its Soul/Light through every physical expression, including you.

You are one with Mind, you are one with all Created things. Every aspect of Creation is an instrument through which Mind expresses the entire Creation Idea.

One only needs to develop the 'eyes' to see this truth. Cosmic Mind uses all physical forms to express the Light/Soul of Mind, just as a musician channels his/her soul through their particular instrument. The musical instrument acts as a device to set into motion the ideas of the musician; those ideas having no motion in themselves. The musician is acting exactly as Cosmic Mind does in creating physical forms to express concept and ideas which are qualities of the Mind.

"The instrument by itself can do nothing, but the instrument in the hands of a master can inspire.”

Triangular Number 73

The first verse of the Bible reads “In the beginning God created the heavens and the earth” and has a total gematria value of 2701. 2701 is 37 * 73

The mirror numbers 37 and 73 are the 12th and 21st prime numbers, again mirrors.

This mirroring continues with 144 (12^2) and 441 (21^2).

From the One come three primary colors then forming seven colors of the rainbow.

Figure 73 - Geometrically, the triangular number 73 has 2701 energy points making three red triangles of 666 (triangular number 36) and a central green triangle of 703 (triangular number 37).

At this point, it would be easy to dismiss the numerical patterns derived from the Hebrew letters in the Bible's creation account as interesting but coincidental.

Recent peer reviewed research, however, has extended the understanding of these same numbers into the realm of science.

Included in their research was the following Table, setting out the molecular weight (gm/mol) of all 20 amino acids, which are the building blocks of all plants and animals.

Figure 74 - Numerical correlation between mass of amino acids.

“This paper is a review of the research of Rakocevic as presented in his paper “A Harmonic Structure of the Genetic Code”. Rakocevic’s findings are confirmed. A strong symmetry is revealed in Rakocevic’s table – both horizontally and vertically. New data reveals that Rakocevic’s patterns are framed around 5 key numbers - the prime numbers 37 and 73, and their midpoint 55, and the triangular numbers 666 and 703. A simple geometric pattern is proposed that integrates all 5 numbers. It is shown that 666 and 703 are the constituent triangles of the 73rd triangular number 2701 (37 x 73), and 703 itself is the 37th triangular number. These findings have implications for the origin of the amino acids, suggesting the operation of a primordial arithmetic process, and concur in this respect with the findings of Shcherbak.”

The harmonic number 273 is key in the process of manifestation:

• The sunspot rotational period is 27.3 days.

• The orbital period of the moon is 27.3 days.

• The moon and earth’s diameter ratio is 0.273.

• Water liquifies at 273 degrees above Absolute Zero.

Figure 75 - Leonardo da Vinci’s painting of the Last Supper.

Much has been written about this famous painting but what has been ignored is the large 10101 structure behind the feast. There are three huge doorways behind Jesus and his disciples.

Figure 76 - The painting is 880 cm wide and 460 cm high. These two numbers are encoded in the Great Pyramid. Half the perimeter of the base of the Great Pyramid is 880 cubits or 460 meters.

460 and 880 express the same length in different units.

The most important divisors in the number 10101 are 273 and 37.

10101 = 111 * 91 = 777 * 13 = 273 * 37 = 21 * 13 * 37

The number 10101 represents the number 21 in binary as shown in the equation below.

2^4 * 1 + 2^3 * 0 + 2^2 * 1 + 2^1 * 0 + 2^0 * 1 = 21

The harmonic number 21 is a numerical key for the entrance points of energy on Earth through the three doorways (3 * 7 = 21) found in a variety of ancient sacred sites.

Figure 77 - The three doorways in sacred sites, South America (pre Inca) and Saqqara.

Back to the Future

Figure 78 - The Sphinx, Great Pyramid, and Golden Spiral

Figure 79 - Pyramids at Giza and the Golden Spiral

Figure 80 - Layout of Pyramids with Sphinx and Golden Spiral

Figure 81 - Pyramids at Giza and Orion’s Belt

A little bit of information around the Key number 144,000 and the Key number 9.

All is part of a great design showing that the builders and designers knew the major presence of 144,000 in the divine creation. There are tangible facts in many fields : architecture, physics, mathematics, geodesy, astronomy. There were 144,000 highly polished casing stones covering the Great Pyramid. All was already written in the sacred architecture.

This Key was mentioned in the ancient scriptures as it is encoded in many parts of the divine creation and relates directly to the properties of light, the exact "Grid Speed of Light" was found by Bruce Cathie, 144,000 minutes of arc per grid second in free space. The speed of light on a Ley Line (energetic line of Earth). 144,000 is an ancient code of a "geomatrix system" used in the astronomical timekeeping Mayan calendar. 144,000 Mayan days = 1 Baktun = 20 Katuns.

144 is a fundamental tone frequency of creation, numerical foundation of vortex energy, encoded in the golden spiral on the 12th position of the Fibonacci sequence.

1,1,2,3,5,8,13,21,34,55,89,144… and 12 x 12 = 144 The spiral on the shell of a snail or in the Milky Way galaxy is the result of this amazing sequence. Beauty in nature.

Musical instruments tuned at 144 Hz on a D scale unfolds naturally the healing frequency of the heart 432 Hz, A as the perfect fifth. 432 is a gematrian number part of this "geomatrix system" with other numbers of digit root 9. (4 + 3 + 2 = 9). 432 is the gematria value for "All Things (the universe) " in Greek παντα (panta). Deciphering letters, numbers and geometry brings all the pieces together showing even more the Interconnectedness of All Things.

Let's get deeper into the foundations of the Great Pyramid.

The physical correlations with the earth form takes us into a journey within a sacred design carrying great information about ourselves, our planet and All Things. This naturally encodes the properties of light animating anything in consciousness.

The Great Pyramid is a power plant or energetic device drawing power from Earth through the physical principle of resonance.

To achieve this aim, the builders needed to take into consideration two important things;

1. The placement of the Great Pyramid must have an energetic affinity to the orbital frequency of the earth itself, i.e the numbers of days to complete one full orbit about the sun : 365.2421

2. The physical base side length of the structure (756 ft) and the height (481 ft) must each possess a harmonic relationship to the exacting earth form. There must be a precise fit between both values and some key physical dimensions of the earth.

Below the two mathematical relations meet this aim :

Height of the structure = Earth radius at pyramid latitude / 36524.21897 (1)

Square base circumference = Earth circumference at pyramid latitude / 36524.21897 (2)

From these relations, the builders achieved an energetic harmonic linkage to the earth form via its orbital frequency.

Two other relations below show this beautiful connection between the earth form and the pyramid through 432;

Height of the structure x 43,200 = Meridional Earth's radius (3)

Square base circumference x 43,200 = Meridional Earth's circumference (4)

Meridional distance = distance around the world going over the poles.

When we work a bit between the four relations (1), (2), (3) and (4). We find a harmonic relationship between the dimensions of the Great Pyramid, the earth form, the orbital frequency of the earth and the key number 432.

Figure 82 - A closer look at these four relations and their correlation between the parameters of the Great Pyramid and the physical dimensions of Earth.

“The world around us is a world of numbers that spell life and harmony. They are organized by the geometry of figures, all related to one another according to a sublime order, into dynamic symmetry. Glimpses into this magnificent kingdom form the basis of all our knowledge and it seems that in this domain the ancient civilizations had gone further than modern science.” - Paul Jacques Grillo

Conclusion

By using this established mathematical framework, we can direct Artificial Intelligence in a systematic way to the undreamed-of possibilities of using chaotic fractals to tackle quantum physics starting from a comprehensive picture up to an exact solution. In part 3, it will be revealed that I have discovered a system of mathematical pathways to accomplish this task specifically.

The purpose of this research is to explore the use of Artificial Intelligence in order to provide humans with otherwise inaccessible information fundamental to the manifestation of consciousness, while simultaneously scaling the ability of Artificial Intelligence to recognize patterns within extremely complex fractal systems.

Using the mathematical framework revealed from El Naschie’s quantum cantorian fractal spacetime, I discovered a fractal pattern recognition game of incredibly high complexity. My calculations have established a system of numerical patterns which can be defined as rules for Artificial Intelligence to perform mathematical operations and analysis into much higher layers of magnitude allowing us to recognize a higher order fundamental network of numerical patterns which otherwise cannot be calculated by humans alone. This emerging field of collaborative research could allow for a paradigm shift by combining the power of Artificial Intelligence with the revolutionary implications of quantum cantorian fractal spacetime theory.

Remembering that Penrose tiling depends crucially upon a golden mean proportionality, we see that the hunch that this golden mean is fundamental is far more than a hunch as it is a fact discussed on numerous previous occasions. Maybe it is at this point that we should stress the marvel hidden in a golden mean based number system and E-infinity is indeed embedded in a golden mean binary constituting de facto a golden mean computer rivaling even a transfinite version of Turing’s machine without hardware save for a modern pocket calculator on the side to perform the elementary manipulation of the adding, multiplying and dividing the golden mean and its power.

Having solved the measure technical computational problem as well as the fundamental contradiction between the discrete and the continuous by building a method which unites both opposed concepts into a transfinite discretum which has the cardinality of the continuum, we realize that we have not only a much better understanding of the vacuum fluctuations but we found a handle on it which can be used to the extent of establishing a real mathematical framework, completely uncovering the true origin of quantum spin; which comes from a unified power source of energy in the universe.