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The Periodic Table of the Light

Wednesday, July 20th, 2011

This writing is based on my work and also the work of Walter Russell, a man who in 1927 already knew all about the concept I have called “the Conscious Field”; which he referred to as the ” Universal One” or “the One Mind”. His writings are quite remarkable. I have included his work in my earlier writing:

http://www.alexpetty.com/2009/09/07/the-universal-one/

Below is a listing of the known elements of matter which make up the physical universe.

Listing of the known elements of matter. *Note that Density of elements with boiling points below 0°C is given in g/l

In 1871 Medeleev organized these elements into a table now well known as the Periodic Table of the Elements.

Medeleev’s first published version of this table is shown below:

Mendeleev's 1871 Periodic Table of the Elements

The elements are presented in the periodic table by increasing values of their atomic numbers which refers to the number of protons in their atomic nuclei.

The modern periodic table is arranged as follows:

Table 1. - Standard periodic table of the elements as of the year 2011

The standard periodic table is rectangular in general with counter-intuitive gaps in the horizontal rows (called periods) to keep elements with similar properties together in vertical columns (called groups), such as alkali metals, alkali earth metals, halogens and noble gases.

A wide, expanded view of the standard periodic table is shown below.

Table 2. - Wide view of periodic table of the elements in 2011

What is the true order of periodicity for the elements of matter? An order wherein no illogical or counter intuitive gaps may appear?

Before proceeding further, we must review some of the basics of Foundational Theory.

According to my work, Creation is caused by the subdivision of the conscious field into manifold parts through a constructive or destructive act of Mind.

This act results in the apparent existence of a universe of separate parts, ie., it gives rise to plurality.

I have discussed this idea which is central to my work in many of my past writings, notably:

http://www.alexpetty.com/2010/06/06/mapping-the-terrains-of-consciousness-with-foundational-mathematics/

Energy is the native aspect of Mind which allows effect to flow from Mind-ignited cause so that a desired outcome may arise.

Energy is the Mind’s force of intention.

The physical expression of the conscious field is the empty space that underlies all material form.

The mental expression of the conscious field is the empty space that underlies all thought form.

This underlying empty space in both cases; outward (i.e., physical) and inward (i.e., mental) is one and the same space.

Everything perceived in Creation is manifested in the conscious field as an effect of the force of Mind (i.e., constructive or destructive will).

Light is the primary effect.

Light is exerted by the Mind-force upon the conscious field itself.

Light produces vibratory pressures within the conscious field.

We perceive these pressures as vibrations of light in empty space exhibiting a wide range of frequencies.

Our eyes can perceive a slim band of these frequencies as visible light which our Mind translate into the Human experience of sight and so the effect of the primary cause manifests visibly to our range of experience.

Many other frequencies of light exist which are beyond our ability to sense directly however, certain ranges can harm us, while other may heal us. Still others can alter our states of consciousness.

Table 3. - The electromagnetic spectrum - lower light vibration

When light – which is always imbued by the intention of mind – imparts oscillation and potential to empty space, this is the creation mechanism for the physical universe.

This mechanism is directly linked to primary causality – the will of Mind.

The vast intelligence which has sustained by will the Creation (and of which the Mind of each human being is an inseparable part) has produced vast amounts of “material substance” or ”matter”. This has provided the basis for the existence of the entire physical universe, including the physical form of the Human Being.

These myriad gases, liquids and solids serve as a further medium for the movement of energy through apparent space and time, i.e., power transference.

Energy passing through material mediums yield second order effects, cascading into further degrees of effect which quickly fan out into seemingly endless orders of complexity, apparent chaos.

An example of this is the transference of energy through the medium of atmospheric gas atoms (air). This results in a pressure wave traveling through the air medium. If the air pressure waves possess frequencies ranging between 20 to 20,000 cycles per second, then human ears can translate these into the experience of sound in the Mind. Here, cause and effect have come full circle.

Energy moving through the medium of a conductor (e.g., copper wire) produces a charge pressure wave in the copper material lattice that can be used to create useful electronic devices. Here the cause and effect interaction is facilitating human inventiveness.

The elements of the Periodic Table are also an artifact of consciousness, of light.

One way to empirically analyze this is by carefully studying the atomic absorption and emission spectra for all known elements. The spectra provide unique “light signature” for each element. The light signatures are lower harmonics of the much higher frequencies of matter.

I have included the complete listing of light signatures for all stable matter:

Figure 1. - The light signature of Hydrogen

Figure 2. - The light signature of Helium

Figure 3. - The light signature of Lithium

Figure 4. - The light signature of Beryllium

Figure 5. - The light signature of Boron

Figure 6. - The light signature of Carbon

Figure 7. - The light signature of Nitrogen

Figure 8. - The light signature of Oxygen

Figure 9. - The light signature of Fluorine

Figure 10. - The light signature of Neon

Figure 11. - The light signature of Sodium

Figure 12. - The light signature of Magnesium

Figure 13. - The light signature of Aluminum

Figure 14. - The light signature of Silicon

Figure 15. - The light signature of Phosphorus

Figure 16. - The light signature of Sulfur

Figure 17. - The light signature of Chlorine

Figure 18. - The light signature of Argon

Figure 19. - The light signature of Potassium

Figure 20. - The light signature of Calcium

Figure 21. - The light signature of Scandium

Figure 22. - The light signature of Titanium

Figure 23. - The light signature of Vandium

Figure 24. - The light signature of Chromium

Figure 25. - The light signature of Manganese

Figure 26. - The light signature of Iron

Figure 27. - The light signature of Cobalt

Figure 28. - The light signature of Nickel

Figure 29. - The light signature of Copper

Figure 30. - The light signature of Zinc

Figure 31. - The light signature of Gallium

Figure 32. - The light signature of Germanium

Figure 33. - The light signature of Arsenic

Figure 34. - The light signature of Selenium

Figure 35. - The light signature of Bromine

Figure 36. - The light signature of Krypton

Figure 37. - The light signature of Rubidium

Figure 38. - The light signature of Strontium

Figure 39. - The light signature of Yttrium

Figure 40. - The light signature of Zirconium

Figure 41. - The light signature of Niobium

Figure 42. - The light signature of Molybdenum

Figure 43. - The light signature of Technetium

Figure 44. - The light signature of Ruthenium

Figure 45. - The light signature of Rhodium

Figure 46. - The light signature of Palladium

Figure 47. - The light signature of Silver

Figure 48. - The light signature of Cadmium

Figure 49. - The light signature of Indium

Figure 50. - The light signature of Tin

Figure 51. - The light signature of Antimony

Figure 52. - The light signature of Tellurium

Figure 53. - The light signature of Iodine

Figure 54. - The light signature of Xenon

Figure 55. - The light signature of Caesium

Figure 56. - The light signature of Barium

Figure 57. - The light signature of Lanthanum

Figure 58. - The light signature of Cerium

Figure 59. - The light signature of Praseodymium

Figure 60. - The light signature of Neodymium

Figure 61. - The light signature of Promethium

Figure 62. - The light signature of Samarium

Figure 63. - The light signature of Europium

Figure 64. - The light signature of Gadolinium

Figure 65. - The light signature of Terbium

Figure 66. - The light signature of Dysprosium

Figure 67. - The light signature of Holmium

Figure 68. - The light signature of Erbium

Figure 69. - The light signature of Thulium

Figure 70. - The light signature of Ytterbium

Figure 71. - The light signature of Lutetium

Figure 72. - The light signature of Hafnium

Figure 73. - The light signature of Tantalum

Figure 74. - The light signature of Tungsten

Figure 75. - The light signature of Rhenium

Figure 76. - The light signature of Osmium

Figure 77. - The light signature of Iridium

Figure 78. - The light signature of Platinum

Figure 79. - The light signature of Gold

Figure 80. - The light signature of Mercury

Figure 81. - The light signature of Thallium

Figure 82. - The light signature of Lead

Figure 83. - The light signature of Bismuth

Figure 84. - The light signature of Polonium

Figure 85. - The light signature of Astatine

Figure 86. - The light signature of Radon

Figure 87. - The light signature of Francium

Figure 88. - The light signature of Radium

Figure 89. - The light signature of Actinium

Figure 90. - The light signature of Thorium

Figure 91. - The light signature of Protactinium

Figure 92. - The light signature of Uranium

Figure 93. - The light signature of Neptunium

Figure 94. - The light signature of Plutonium

Figure 95. - The light signature of Americium

Figure 96. - The light signature of Curium

Figure 97. - The light signature of Berkelium

Figure 98. - The light signature of Californium

The Tones of Matter

Jelaleddin Rumi, a Persian Sufi mystic who lived from 1207 to 1273 century AD once said:

“In the rhythm of music a secret is hidden; If I were to divulge it, it would overturn the world.”

It was also anciently said by the great Alexandrian master Hermes Trismegistus, “As above so below”.

See: http://www.alexpetty.com/2009/09/15/the-emerald-tablet/

Both of these statements refer to the nature of energy.

The cycling aspect of energy can be relied upon at any octave.

Every octave of energy is identical to all others.

The only variation in comparing one octave to another is scale.

As the wavelengths grow longer, frequencies decrease – the energy and scale decreases.

As the wavelengths grow shorter, frequencies increase – the energy and scale increases.

We can experience this reliable, regular quality of energy when we hear the 7 major tones of the musical scale in the audio frequency range.

Do – Re – Mi – Fa – So – La – Ti

The human ear is capable of perceiving a range of 10 octaves of energy.

We can also experience this reliable, regular quality of energy when we see the 7 major tones of color in the frequency range of visible light.

Violet - Indigo - Blue - Green - Yellow - Orange - Red

There is a direct correspondence here: as above, so below.

We see “Violet” in the higher octave, we hear “Do” at the lower octave.

We see “Indigo” in the higher octave, we hear “Re” at the lower octave.

We see “Blue” in the higher octave, we hear “Mi” at the lower octave.

We see “Green” in the higher octave, we hear “Fa” at the lower octave.

We see “Yellow” in the higher octave, we hear “So” at the lower octave.

We see “Orange” in the higher octave, we hear “La” at the lower octave.

We see “Red” in the higher octave, we hear “Ti” at the lower octave.

The human eye is capable of perceiving but a single octave of energy.

We experience this reliable, regular quality of energy as the 118 tones of known matter which span across 7 octaves.

In other words, at an extremely high rate of vibration, in the wavelength range of perhaps 0.01 Å to 10 mÅ or shorter, light “condenses” into that which we perceive as matter.

Table 4. - The light spectrum - extending into higher vibrations of light

In this way, light produces the “material” sense stimulus for the experiences of touch, taste and smell.

According to the gigantic conceptions of enlightened genius Walter Russell, there are 10 full octaves of matter. I have adopted Russell’s conventions in my work as his ideas are very well aligned with mine and I believe his conclusions on many counts are correct.

The complete set of 10 octaves as given by Russell are:

1) The Alphanon Octave

2) The Betanon Octave

3) The Gammanon Octave

4) The Hydron Octave (which contains Hydrogen)

5) The Helium Octave

6) The Neon Octave

7) The Argon Octave

8 ) The Krypton Octave

9) The Xenon Octave

10) The Radon Octave

With the exception of Hydrogen, no tones in Russell’s predicted first four octaves have yet been observed in nature.

Russell named these predicted tones as follows:

Alphanon Octave: Irenon – Vijaon – Marvaon – Tomion – Alberton – Blackton – Boston

Betanon Octave: Jamearnon – Erneston – Eykaon – Athenon – Barnardon – Delphanon – Romanon

Gammanon Octave: Marconium – Penrynium – Vinton – Quentin – Tracion – Buzzeon – Helenon

Hydron Octave: Hydrogen – Ethlogen – Bebegen – Carbogen – Luminon – Halanon – Helionon

It should also be noted that by 1927, Russell had already predicted the existence of a significant number of then unknown elements in the 9th and 10th octaves which have since been discovered. In fact in 1941, the American Academy of Sciences conferred a doctorate on him, after several laboratories had isolated the elements which he had foreseen: Deuterium, Tritium, Neptunium and Plutonium.

The figures below show how light cycles through the higher energy octaves appearing as matter at major tones and certain semi tones.

I have indicated the semi tones in “cents” between 0 and 1000. For example a semi tone falling half way between “Mi” and “Fa” would appear as “Mi500″.

The tones of Walter Russell's first octave of matter

The major tones of Walter Russell's first octave of matter

Figure 104. - Light Absorption for the 1st Octave of Matter

Figure 105. - Light Emission for the 1st Octave of Matter

The tones of Walter Russell's second octave of matter

The major tones of Walter Russell's second octave of matter

Figure 106. - Light Absorption for the 2nd Octave of Matter

Figure 107. - Light Emission for the 2nd Octave of Matter

The tones of Walter Russell's third octave of matter

The major tones of Walter Russell's third octave of matter

Figure 108. - Light Absorption for the 3rd Octave of Matter

Figure 109. - Light Emission for the 3rd Octave of Matter

The tones of Walter Russell's fourth octave of matter

The major tones of Walter Russell's fourth octave of matter

Figure 110. - Light Absorption for the 4th Octave of Matter

Figure 111. - Light Emission for the 4th Octave of Matter

At man’s present level of knowledge, the first octave of light in which all of the major tones have been identified is the The Helium Octave. This includes the tones:

Lithium – Beryllium – Boron – Carbon – Nitrogen – Oxygen – Fluorine

Note that the Noble Gases are at equilibrium and produce no physical vibration. In this way, there is a relationship between Noble Gases and Prime Numbers.

See earlier writing for more on my research into the nature of primes: http://www.alexpetty.com/2009/11/15/on-numeric-magnetism-and-the-fundamentals-of-primality/

The tones of Walter Russell's fifth octave of matter

The major tones of Walter Russell's fifth octave of matter

Figure 106. - Light Absorption for the 5th Octave of Matter

Figure 107. - Light Emission for the 5th Octave of Matter

The octave above The Helium Octave is the Neon Octave and it includes the major tones:

Sodium – Magnesium – Aluminum – Silicon – Phosphorus – Sulfur – Chlorine – Neon

The major tones of Walter Russell's sixth octave of matter

Figure 108. - Light Absorption for the 6th Octave of Matter

Figure 109. - Light Emission for the 6th Octave of Matter

From the 7th Octave of matter, Semi Tones of light manifest as stable elements.

The listing of these Semi tones for the 7th Octave of matter (The Argon Octave) including their associated Major tones are:

Potassium – Calcium – Scandium | (Major tones)

Titanium – Vanadium – Chromium – Manganese – Iron | (Semi tones)

Cobalt | (Major tone)

Nickel – Copper – Zinc – Gallium – Germanium | (Semi tones)

Arsenic – Selenium – Bromine | (Major tones)

The semi tones of Walter Russell's seventh octave of matter

The major and semi tones of Walter Russell's seventh octave of matter

Figure 116. - Light Absorption for the 7th Octave of Matter

Figure 117. - Light Emission for the 7th Octave of Matter

The listing of Semi tones for the 8th Octave of matter (The Krypton Octave) including their associated Major tones are:

Rubidium – Strontium – Yttrium | (Major tones)

Zirconium – Niobium – Molybdenum – Technetium – Ruthenium | (Semi tones)

Rhodium | (Major Tone)

Palladium – Silver – Cadmium – Indium – Tin | (Semi Tones)

Antimony – Tellurium – Iodine | (Major Tones)

The semi tones of Walter Russell's eighth octave of matter

The major and semi tones of Walter Russell's eighth octave of matter

Figure 118. - Light Absorption for the 8th Octave of Matter

Figure 119. - Light Emission for the 8th Octave of Matter

The listing of tones for the 9th Octave of matte, The Xenon Octave are:

Caesium – Barium – Lanthanum | (Major tones)

Cerium – Praseodymium – Neodymium – Promethium – Samarium – Europium – Gadolinium – Terbium – Dysprosium – Holmium – Erbium – Thulium | (Semi tones)

Ytterbium | (Major Tone)

Lutetium – Hafnium – Tantalum – Tungsten – Rhenium – Osmium – Iridium – Platinum – Gold – Mercury – Thallium – Lead | (Semi Tones)

Bismuth – Polonium – Astatine | (Major Tones)

The semi tones of Walter Russell's ninth octave of matter

The major and semi tones of Walter Russell's ninth octave of matter

Figure 120. - Light Absorption for the 9th Octave of Matter

Figure 121. - Light Emission for the 9th Octave of Matter

The listing of Semi tones for the 10th Octave of matter (The Radon Octave) including their associated Major tones are:

Caesium – Barium – Lanthanum | (Major tones)

Cerium – Praseodymium – Neodymium – Promethium – Samarium – Europium – Gadolinium – Terbium – Dysprosium – Holmium – Erbium – Thulium | (Semi tones)

Ytterbium | (Major Tone)

Lutetium – Hafnium – Tantalum – Tungsten – Rhenium – Osmium – Iridium – Platinum – Gold – Mercury – Thallium – Lead | (Semi Tones)

Bismuth – Polonium – Astatine | (Major Tones)

The semi tones of Walter Russell's tenth octave of matter

The major and semi tones of Walter Russell's tenth octave of matter

Figure 122. - Light Absorption for the 10th Octave of Matter

Figure 123. - Light Emission for the 10th Octave of Matter

In the same way that the “number line”

the number line

is more rightly constructed as a “number spiral”

the numeric spiral

and in the same way that the growth and contraction structure of numbers themselves cycle internally with “breathe-like” ebb and flow,

breath cycle of the numeric spiral

so too is the periodic table more closely representative of matter’s true nature with all its periodicities when represented using a spiral rather than today’s less perfect rectangular periodic table.

Figure 124. - Spiral Periodic Table of Light

The mapping between the Spiral Periodic Table of Light and the Vortex Glyph is as follows:

Figure 125. - Mapping of the Spiral Periodic Table with the Vortex Glyph

In 1931, Max Planck who is considered the founder of Quantum Theory, said ”I regard consciousness as fundamental. I regard matter as derivative from consciousness. We cannot get behind consciousness. Everything that we talk about, everything that we regard as existing, postulates consciousness.”

In 1932, he also said, “Science cannot solve the ultimate mystery of nature. And that is because, in the last analysis, we ourselves are part of nature and therefore part of the mystery that we are trying to solve.”

I agree with Max Planck, and others who have deeply understood this. It is from this perspective that my work is rooted.

.:.

Posted in Foundational Analysis, Foundational Technology, General, Walter Russell | 10 Comments »

Vortex Math Based Computing

Saturday, September 11th, 2010

Consciousness Modeled Computational Paradigm

Conceived of by Alexander S. Petty

Creation, by its nature, operates the systems which arise within it in the most efficient manner possible. Only Creation is so economical in its every expression. Wisdom compels the thoughtful to observe and learn from nature’s miraculous ingenuity and employ these methods in the development of technology whenever it is possible to do so.

The system that Creation has devised for encoding and transmitting information is known as genetics whose base units of currency are RNA and DNA. I believe that the time has come to employ nature’s own information management system in the field of modern computer science.

It is the goal of this project to bring about this transformation in the state of art for computing machines.

Brief Summary of DNA Structure

DNA is a four bit system using the following nucleic acids as units for storing and conveying data.

These are:

Adenosine (A)

Formula C10H13N5O4

Figure 1. - Adenosine

Thyamine (T)

Formula C5H6N2O2

Figure 2. - Thyamine

Cytosine (C)

Formula C4H5N3O

Figure 3. - Cytosine

Guanine (G)

Formula C5H5N5O

Figure 4. - Guanine

By virtue of their geometry, which is governed by magnetic/numeric polarity, these nucleic acids will always pair such that Adenosine binds with Thyamine and Cytosine with Guanine. These units are referred to as base pairs.

Possibility of a DNA-Modeled Computing Paradigm

The basis of modern computer science is binary in nature, which is to say that it is based upon whether the voltage in a given transistor is off (zero) or on (one). These zeros and ones are rolled up into a base 2 number system which is operated to encode information “digitally”. By convention (e.g. standards like ASCII or UTF8), the letters of the English alphabet, for example, are digitally encoded by 8 bit phrases of zeros and ones called bytes.

DNA is also digital, but it is not limited to positions 0 and 1. DNA uses 4 possible bit positions and is therefore a quaternary digital system:

Figure 5. - Assigned numeric value for nucleic acids in DNA

By convention, a binary digital byte is 8 bits in length, providing 256 possible different values per byte.

A “byte” of DNA is called a codon. A codon is 3 bits long (e.g., AAA or GCT). Each bit can be one of 4 possible values (0, 1, 2 or 3) and so the DNA quaternary encoding system provides 64 possible values per codon.

Binary 8 Bit Byte

Figure 6. - Binary 8-bit byte

Any value between 0 and 255 can be expressed within this binary system.

For example, the number 73 would include 1 bit from 2^6, 1 bit from 2^3 and 1 bit from 2^0.

This binary value looks like:

01001001

and can be expressed in base 10 as:

64 + 8 + 1 = 73

Quaternary 3 Bit Byte (aka. Codon)

Figure 7. - Quat 3 bit byte, or Codon

Any value between 0 and 63 can be expressed within this quaternary system.

For example, the number 53 is represented by a 3 bit in the 4^2 ordinal, a 1 bit in the 4^1 ordinal and a 0 bit in the 4^0 ordinal. This is represented as 310 in base 4. Chemically, DNA would express this with the use of the following nucleic acids:

TGA which would pair with ACT.

Complete listing of codon bit pairs (All sum to 9)

The positive side (left) and negative side (right) sum to neutrality (9). This polar balance provides the underlying framework dictating DNA’s physical form. This is of course an expression of vortex mathematics in biology. It is the magnetic relationship between the base pairs which enables the compression of DNA in biological systems. The very same principles, however expressed by numeric polarity, provides the under-pinning for a DNA-modeled compression algorithm.

Figure 8. - Base pairs are magnetically neutral

Keyboard Encoding Standard

ASCII standard encoding with DNA translation

The long time standard for keyboard encoding is known as ASCII. Since ASCII is a base-2 8-bit standard, it supports 256 unique values. Just as a 16-bit binary standard requires 2 bytes to cover a range of 512 characters, a DNA-based keyboard encoding standard, with its limit of 64 values per codon, requires multiple codons to support the ASCII standard. This can be implemented as follows:

Codon 0

Figure 9. - ASCII CODON 0

Codon 1

Figure 10. - ASCII CODON 1

New Foundational Standards

It would be ideal to deprecate many of the legacy ASCII character codes such as ENQ, RS, EM, etc in a new DNA based standard.

In developing a new Foundational Encoding Standard, UTF8, UTF16, etc. should be considered. It may take as many as 8 codons to capture all of the needed keyboard codes for world-wide requirements.

Simple Encoding Example

Figure 11. - Textual "Genetics"

Only one half of the codon pair needs to be stored since the other half can be inferred and applied by an algorithm at compression runtime.

Figure 12. - Genetic modeled text encoding

The ability to persist only half the bit pair provides a fundamental efficiency quotient of 3 to 8 (62.5%) over the current binary paradigm before compression is even considered.

Numeric Polarity based Helical Compression Algorithm

Using these methods, data can be compressed in a manner identical to that of DNA. It is possible to utilize the principles of numeric polarity to compress information into a kind of “chromosomal superstructure” just as with physical DNA.

Furthermore, it appears that DNA modeled compression offers performance curves allowing large amounts of information to be more tightly packed then smaller amounts of information. This agrees with the observation that fruit fly DNA is physically much larger then human DNA and yet it contains many orders of magnitude LESS data.

DNA Runtime Environment

32 bit PC architecture allows the CPU to address four 8-bit bytes of data per clock cycle. Since a quaternary system is not compatible with today’s hardware, a translation layer is required which may be implemented as a runtime environment.

Figure 13. - Mapping Bytes to Codons in a VM

Bit position 9 is reserved for technical overhead in support the virtual run-time environment. The 9th bit can be reclaimed when implemented on quaternary based hardware.

I should also note that, while I am proposing a system of bits based on 0, 1, 2, 3 for the sake of feasibility of implementation. The system nature itself uses appears to rely on the following pairing system :

1 pairs with 8

2 pairs with 7

and 4 pairs with 5

Nature reserves 9, 3 and 6 for higher purposes.

9 is connected with the causal intention of Mind that underlies all observable force driven events.

3 and 6 are connected are expression of polarity aspect of force which we observe everywhere in our subject and object human experience.

CMYK Data Transmission

The subtractive CMYK four-state color description system appears to operate in a manner similar to that of how nature uses light within physical RNA/DNA. It stands to reason that the “technical access” to use of 1-8, 2-7 and 4-5 pairs may be achievable by using a light based system. It may be possible to input and output quaternary digital information to DNA-modeled machines using light harmonics in the form of a subtractive 4 color standard.

C = Cyan

M = Magenta

Y = Yellow

K = key (Black)

Figure 14. - CMYK

It is interesting to note that chromosomes (tightly packed DNA superstructures) naturally reflect these very colors (thus their name). See image of chromosome below.

Figure 15. - Chromosome exhibits CMYK subtractive color dynamics

Posted in Foundational Technology, Number Theory | 5 Comments »

Mapping the Terrains of Consciousness with Foundational Mathematics

Sunday, June 6th, 2010

I wanted to take a moment to thank everyone for the steady stream of kind and gracious feedback and the general show of support for my work. Please know how very thankful I am for that.

I’ve been away from the blog in recent months quite busily working on advancing my energy research and the physical implications of Foundational Mathematics. I am pleased to report that I am making steady and surprising progress in developing this area and have accomplished some very exciting results, yet, much work remains. Each answer I achieve begs many new questions!

My writing efforts in the last few months have been mostly directed into the completion of my first book, “The Nature of Numbers –Mapping the Terrains of the Conscious Field”. The book is almost completed now and I am very pleased with how it has unfolded both as a process and as a work.

.:.

Today I’d like to give you a taste of the main subject matter covered in my upcoming book which is at its heart an exploration of the archetypal terrains of the conscious field. I believe the method I have developed amounts to an important new way to visualize the underpinnings of consciousness. It is a potentially revolutionary channel for enabling an intuitive working understanding of how subject and object (particles) relate to one another on the illusory stage of light (or state of mind) into which humanity is born.

In the fractal glyph plates I have drawn below, I have used red lines to denote a positive or clockwise path and gray lines to denote a negative or counterclockwise path. Where positive and negative flows overlap, a color mixture of red and gray (a sort of light peach-brown) results. Darker brown colors correspond to a greater number of overlapping fractal paths. For prime sequences I have used yellow for positive and green for negative. In the same way, overlapping of prime fractal paths results in a kind of olive color. A darker olive color correspond to a greater number of overlapping prime fractal paths.

.:.

The Nature of Numbers

In my theory of Foundational Mathematics, numbers can be sorted into 3 classifications:

Structural Numbers (Primordial Numbers)

Structural numbers are few. These fields are the basic building blocks used to create the universe within the conscious field.

Polar Numbers (Closed Cycle Numbers)

Polar Numbers shepherd the world of form by imparting force. These include negative, positive and neutral polar number fields. These fields are in the world but not of it.

Form Numbers (Open Cycle Numbers)

Form Numbers obey the effects of polar forces and comprise the visible elements of the Creation.

I will explain these classes of numbers more in depth in what follows.

Structural Number Fields

1, 2 and 5 are archetypal. They are fully Foundational to consciousnesses in its plural aspect. When Unity, through an act of Mind falls into a plural state, the fields of 1, 2 and 5 appear automatically. Note that Unity and 1 are not the same. Unity is an expression of the absolute oneness of the universal whole, while 1 is an expression of “subject” in a “subject and object” world.

Zero

The zero field has no physical component. It represents the unmanifested Mind. It represents infinite potential existing apart from the physical Creation. The singularity is where the physical world and the zero field “touch”.

Unity

The field of one or the unity field represents the Universe in stillness. It is all that is without any distinction imposed upon it by the activity of Mind. Within the unified field there are no vibratory perturbations. Here, no effects have been caused.

foundational field of 1, unity

unity

Plurality

The field of 2 is Structural. This field is the archetypal expression of plurality.

The elective action of Mind to fall from unity into plurality spawns the basis of dualistic human experience. In this act, subject and object, the space between, the time to traverse and the power of force is born. The image below shows how the vector fields from two point particles form interference patterns on the stage of consciousness that is the magnetic dipole form itself. It is in this very manner that magnetic fields are born. It is when the mind elects to produces plurality that the stage of consciousness gives rise to the self evident experience of distance and force.

dipole interference patterns arising spontaneously from the intersection of offset point field. the cause of force in space and time is a manifestation of consciousness

See my earlier writing: http://www.alexpetty.com/2009/10/04/relative-motion-of-vectors-produces-fields/

When duality arises, consciousness sets up some basic “plumbing” to facilitate this state: 1, 2 and 5.

Whenever the field perturbation represented by 2 appears in the conscious field, the field perturbations represented by 5 automatically also appear. You must understand that numbers represent very specific energetic perturbations signatures and are not merely abstractions as is commonly supposed.

It should also be noted that in my theory of Foundational Mathematics, further vocabulary is needed to distinguish separate concepts of one. The “high concept” of Unity and the “lower concept” of a one as apart from two, ie. the first element of Unity divided.

foundational field table of 2

foundational field glyph of 2

So then, 2 gives rise to 1 and 5 and then spontaneously sets up the following ratios.

In the case of expansion into a higher enumeration, this relationship is constructed:

phi, the operator of enumerative expansion

In the case of contraction to a lower enumeration, this relationship is constructed:

phi, the operator of enumerative contraction

This expression provides the underpinnings for how the conscious field will use 1, 2 and 5 to enable any level of enumeration. The resulting magnetic interactions produce force and form which gives rise to the the universe we experience as human beings.

The conscious field possesses a kind of elasticity. Phi is the mechanism that consciousness uses to control the expansion and contraction of the conscious field into myriad parts. It allows the conscious field to experience itself in any number of divisions the Mind can conceive of. In this way, numbers themselves represent the elastic nature of the conscious field, that aspect which responds automatically to the constructive or destructive will of Mind.

The field of 5 is structural as it is an essential element for allowing the conscious field to experience itself dualisitically. Perhaps counter-intuitively, 5 appears in the field before 4 since it is a field perturbation that arises automatically whenever the primordial instance 2 occurs.

foundational field table of 5

foundational field glyph of 5

Polar Number Fields

Polarity is established automatically the moment that Unity falls into Plurality. There are three classes of Numeric Polarity: Positive, Negative and Neutral.

The chart below shows how polarity cycles around the circle of nine. Note that as the very first iteration of nine is cycled through (the Primordial Cycle), consciousness is bootstrapping the building blocks it uses to manifest The Physical Creation.

numeric polarity

For more on numeric polarity see my earlier entry: http://www.alexpetty.com/2009/11/15/on-numeric-magnetism-and-the-fundamentals-of-primality/

Postive Polarity

The field of three is the first example of what I have called “closed cycle fields”. Any field which is closed cycle is an element of polarity. This is as opposed to elements of physical expansion and contraction (ie. elements of form) which are all “open cycle fields”.

Polarity guides the direction and magnitude of the expansion and contraction of the world of form and it does so in accordance with the elective will mind, communicated by the field perturbations which the mind produces as a feature of its natural function. Consciousness itself is the long elusive underlying basis of electricity and magnetism.

foundational field table of 3

foundational field glyph of 3

The closed cycle field of 3 produce two circular paths |3| and |6| yielding clockwise flow 3-6-9 (or 3-6-0) and a counter-clockwise field 6-3-9 (or 6-3-0). The deflections of these flows form two overlapping, offset and opposed equilateral triangles. Much ancient symbology comes from this archetype including the Star of David.

Three is the positive pole and related directly to the concept of the proton.

The field of 12 is the second occurrence of a “layered cycle field” which means it simultaneously contains both closed and open cycles field elements (6 is the first such occurrence).

12 is the positive pole on the second iteration of the circle of 9. Twelve is also the field which marks the half way point for the the magnetic sequencing of the Fibonacci series. To see this sequencing refer to plates from my earlier writings:

http://www.alexpetty.com/wp-content/uploads/2009/11/fibonacci-in-mod9-with-polarity-mapping.png

http://www.alexpetty.com/wp-content/uploads/2009/12/fibonacci-converging-on-phi5.png

This topic is explored in depth in my coming book.

foundational field table of 12

foundational field glyph of 12

The field of 21 is a closed cycle field. The 21 field is the positive pole on the third iteration of the circle of 9.

foundational field table of 21

foundational field glyph of 21

Negative Polarity

The field of six is another very important “closed cycle field”, but it is also the first occurrence of a “layered cycle field” as it simultaneously contains both closed and open cycles. This means that within the field of six is both polarity and form all at once. Thus we see that it is the negative pole around which physical form arises. This is consistent with our experience. The electron is understood to be the carrier of negative charge flow. Since almost the whole of physical human experience is tared around net flows of negative charge, it is for this reason that physical interactions in our world are observed to center around electrons seeking equilibrium states. (In normal experience, we rarely observe positronic charge – so called cold current – except through exotic circuits which manifest non-linear effects.)

foundational field table of 6

foundational field glyph of 6

The closed cycle portion of the field of 6 produces two circular paths of |6| and |3| yielding counter clockwise flow 6-3-9 (or 6-3-0) and clockwise field of 3-6-9 (or 3-6-0). Just as with the field of 3, the deflections of these flows form two overlapping, offset and opposed equilateral triangles however the circular flows in 6 are opposite of 3.

Six is the negative pole and its nature gives rise to the concept of the electron. Human experience is very much about the perception of net flows of charge and the electron is understood to be the carrier of charge. It is for this reason that we interact with negative charge flows in the course of normal experience and rarely with positronic charge or cold current (which is related to 3).

It is also worth noting that within the field of 6, we see first hints at an entirely new method of computation. My book spends a lot of time on this topic.

The field of 15 is a mixed cycle field. The 15 field is the negative pole on the second iteration of the circle of 9.

foundational field table of 15

foundational field glyph of 15

The field of 24 is a mixed cycle field. The 24 field is the negative pole on the third iteration of the circle of 9.

24 is also the field which completes the magnetic sequencing for the Fibonacci series.

Again, you can review this sequencing in the plates included in my earlier writings:

http://www.alexpetty.com/wp-content/uploads/2009/11/fibonacci-in-mod9-with-polarity-mapping.png

http://www.alexpetty.com/wp-content/uploads/2009/12/fibonacci-converging-on-phi5.png

foundational field table of 24

foundational field glyph of 24

Neutral Polarity (The Number 9)

The field of 9 is the third polarity, it is the neutral pole which has no physical aspect in creation – and yet it gives rise to the elements which make up nature. Nine is both 0 and 9. It is the Alpha and the Omega. It is the beginning and end of the circle whose 9 divisions resonant with Nature.

The field of nine is composed of eight closed cycle fields.

foundational field table of 9

Interestingly, the harmonic overtone series for sound (an expression of energy traversing the medium of air as a compression wave) is definitely connected to this.

See: http://www.alexpetty.com/wp-content/uploads/2009/11/harmonics-of-each-harmonic-in-mod9.png

foundational field glyph of 9

Take a moment to review the beautiful degree of balance and symmetry which is contained by the field of nine, the neutral pole.

The field of 18 is a mixed cycle field. It is the neutral pole on the second iteration of the circle of nine.

foundational field table of 18

foundational field glyph of 18

Operators of Neutral Polarity (Primes)

The field of 7 indicates magnetic neutrality, 7 is therefore by the definition I have set forth in Foundational Mathematics, the first true prime field.

foundational field table of 7

foundational field glyph of 7

I here offer The Foundational Definition of Prime Numbers as follows:

A number is prime only when all elements of the number’s field possesses a closed cycle internal structure and when each of these closed cycles sum to zero (using clock math) for any arbitrary base.

All primes exhibit neutral numeric polarity!

I have discovered that primality is the result of magnetic neutrality in fields of numeric polarity.

The observation that primes are divisible only by themselves and one is purely an effect of their numeric polarity, since primes are internally balanced, they are magnetically inert and therefore unable to combine geometrically with other numeric fields. This is the actual basis for the “atomic” nature of primes. Furthermore, I hypothesize that the chemically inert nature of the Noble Gases is a directly related to this quality of prime numbers.

Primes fields possess an incredible and very beautiful degree of palindromic symmetry and cyclic resonances. It is my view and the view of Foundational Mathematics that all primes are made up of fractal series which possess the characteristic of closed cycle rotation, palindromic symmetry and net numeric neutrality.

It is my further view that the fields of 2 and 5 can not truly be considered prime as they are neither magnetically neutral nor do they possess a closed cycle nature. Instead I regard 2 and 5 as Structural numbers. I also do not regard 3 as prime since its closed cycle has a net positive polarity rather then a net neutral polarity.

All primes are closed cycle which means that despite their magnetic neutrality, they are indeed instruments of polarity, a kind of neutral “Divine” Polarity. The chart below shows the manner in which this neutral polarity is distributed and how the conscious field extends its tendrils of neutral polarity throughout the channels of expansion and contraction.

petty foundational chart of the primes

The field of 11 is the second magnetically neutral field and therefore it is considered in Foundational Mathematics as the second prime number. Again, in Foundational Mathematics, we consider that 2 and 5 are not Prime but Structural and that 3 is also not Primes but a Structural Archetype of Polarity.

foundational field table of 11

foundational field glyph of 11

Observe that the field of 11 it is composed of five separate sequences, each which sum to nine (again, a quality of the primes alone).

The first 5 sequences flow in a positive direction while the other 5 flow in a negative direction.

09, 18, 27, 36 and 45 are palindromic with the latter 54, 63, 72, 81 and 90.

These sequences are perfectly opposite flows. In my energy physics experiments, I have observed that numeric flow reversal relates directly to charge spin reversal in capacitors.

The field of 13 is the third magnetically neutral integer and therefore it is the third prime number.

foundational field table 13

foundational field glyph of 13

Observe that it is composed of two separate sequences, again, each sum to nine (a quality of the primes alone).

The first rotating closed sequence is 076923.

The second rotating closed sequence is 153846.

The field of 17 is the fourth magnetically neutral integer and therefore it is the fourth prime number.

foundational field table of 17

foundational field glyph of 17

This prime contains one rotating closed sequence of 0588235294117647 which again, sums to magnetic neutrality.

The field of 19 is the fifth magnetically neutral integer and therefore it is the fifth prime number.

foundational field table of 19

foundational field glyph of 19

The field of 23 is the sixth magnetically neutral integer and therefore it is the sixth prime number.

foundational field table of 23

foundational field glyph of 23

I have studied thousands of prime fields and without exception, they all possess neutral pole closed cycle rotation, (ie. all fractal elements of primes sum to nine.)

In this, I have arrived at a deeper, more causal definition for primes and the precise reason *why* these numbers, in a diamagnetic sense, can not be geometrically reduced by other numbers.

In my book, I have rigorously addressed the topic of primes as understood from the higher perspective of Foundational Mathematics.

Here are a few more Foundational Prime Tables for good measure. Watch in particular how the magnetic orientation in the fields become ever more elaborate and beautiful.

The perfect balance is always struck in the following manner:

0 (Neutral) pairs with 9 (Neutral)

1 (Neutral -) pairs with 8 (Neutral +) creating Form Neutrality around the neutral pole at 9

3 (Pole +) pairs with the 6 (Pole -)

7 (-) with 2 (+)

5 (-) with 4 (+)

Form Positivity is the result of 2 and 4 proximity to 3.

Form Negativity is the result of 5 and 7 proximity to 6.

As you consider this, you may find it helpful to study this plate:

http://www.alexpetty.com/wp-content/uploads/2010/04/numeric-polarity.png

foundational field table of 29

foundational field table of 31

foundational field table of 37

foundational field table of 43

foundational field table of 47

foundational field table of 51

The World of Form

The field of 4 is an open cycle field. Open cycle fields always represent the world of form in growth or contraction shepherded by the closed cycle forces of polarity.

foundational field table of 4

foundational field glyph of 4

Form always progresses in a doubling or halving pattern. Consider an embryo developing in the womb (the initiation of a consciousness being) follows this pattern during mitotic division:

1 cell doubles to 2

2 cells doubles to 4

4 cells doubles to 8

8 cells doubles to 16 (which compresses to 7 in mod9)

16 cells doubles to 32 (which compresses to 5 in mod9)

32 cells doubles to 64 (which compresses to 1 in mod9, completing the cycle around the circle of 9)

doubling and halving on the walls of the vortex

Within every process, from embryonic cellular division to complex fluid dynamics, the progression of all manifestations of form always obey this archetypal pattern.

In the second iteration of 9, one observes that:

64 double to 128 (mod9: 1 doubles to 2)

128 doubles to 256 ( mod9: 2 doubles to 4 )

256 doubles to 512 ( mod9: 4 doubles to 8 )

and so on.

doubling and halving on the walls of the vortex

The doubling and halving is governed by the closed cycle forces of positive, negative and neutral polarity ever guiding form in accordance with the will of conciousness which govern the shape and form of the Physical Creation.

The field of 8 is an open cycle field.

foundational field table of 8

foundational field table of 10

The field of 10 is an open cycle field.

foundational field table of 10

foundational field glyph of 10

The field of 14 is mixed cycle field:

foundational field table of 14

foundational field glyph of 14

The field of 16 is an open cycle field:

foundational field table of 16

foundational field glyph of 16

The field of 20 is an open cycle field:

foundational field table of 20

foundational field glyph of 20

The field of 22 is a mixed cycle field:

foundational field table of 22

foundational field glyph of 22

If you find that you are interested in my work, please keep an eye out for the release of my book this summer.

“The Nature of Numbers, Mapping the Terrains of the Conscious Field” in which I explore this subject in its depths.

Posted in Foundational Analysis, Foundational Technology, General, Number Theory, Prime Numbers | 8 Comments »

The Golden Ratio

Sunday, January 10th, 2010

The Golden Ratio, also known as Phi.

What is Phi?

Phi is a ratio of lengths which possesses many remarkable characteristics.

To me, perhaps the most telling unique feature of Phi is that if you add 1 to its value the result is Phi squared. Equally strange, if you subtract one from Phi the result is 1/Phi (ie. the reciprocal value of Phi).

Said another way, add 1 to this value and you produce an additional dimension. Subtract one from this value and you arrive at something very transcendental indeed which I will discuss later on. I do believe that this number, Phi, is a structural essential within the “operation” of the conscious field.

Want to see Phi? How can one construct it? It’s easy!

1) Draw a pentagon

2) Connect two of its corners as shown below

simple construction of phi

Phi is the ratio of lengths AB:BC

The diagram below shows some other key geometric constructs based upon the “Golden Ratio”.

the golden triangle

Some points of note:

1) The angles a, b and c all reduce to 9 on the circle of 9.

2) All three sides of the triangle formed by points A, B and C are divided by the various intersections of the circle and pentagon into the Phi ratio and other directly related lengths.

Below is another diagram showing some interesting Phi based geometric relationships.

phi based geometry

So, how may one compute the value of Phi with arbitrary precision?

This is also fairly easy to do provided you remember your basic Algebra. Start by taking the ratio of lengths given by AB and AC as shown below.

how to derive the value of phi using basic algebra

My own theory of mathematics (The Foundational Mathematics) is that the conscious field, of which all realms of existence are an inseparable part, in reality only makes provision for values between 0 and 1.

The distance between 0 and 1 may be divided and made vastly manifold to any arbitrary extent that the consciousness field of mind can conceive of. What we perceive as integers are just a play of the 5 human senses.

Think of it this way.

You look at your hand and you see 5 fingers. From the quantum mechanical perspective however, there is no differentiation between your body and the surrounding space. There are not five fingers there at all, only an undifferentiated field of energetic vibration. From this level one can see that the idea of fingers is a construct of the mind only – as is the business of counting them. The senses of our body provide a sort of lens through which we experience the conscious field. It is the case that the conscious field connects everything that is together. This is because everything in existence emanates as a manifestation of the One Conscious field. The lens of the physical body creates an apparently solid physical experience from this field but the dualistic reality of subject and object, however convincing it may be, is merely illusion.

Here is another way to see what I am trying to express. The integer 5 is really a universe of 1 being considered in 5 parts.

So then for counting integers one through five:

0 , 1 , 2 , 3 , 4 , 5

In reality we are counting fractional areas of one:

0.0

0.2

0.4

0.6

0.8

1.0

As another example let look at counting integers one through seven:

0, 1, 2, 3, 4, 5, 6, 7

again, here we are counting fractional areas of one:

0.000000

0.142857

0.285714

0.428571

0.571428

0.714285

0.857142

1.000000

When one develops an understanding and working knowledge of this basis, then suddenly mysteries such as the nature of primes become much easier to comprehend and work with. This discovery enables for the first time in more then two millennium ground for traction in significant forward progress within the field of number theory. It will of course be no small challenge to convince the majority of scientists in the world of the unreality of integers and the illusory nature of sensual experience. Still, this important paradigm shift is the path down which our technological evolution lies.

So how does this relate to understanding Phi?

In Foundational Mathematics numbers do not represent ratios of lengths but rather they correspond directly to scale in terms of growth and contraction. The number 1 enjoys the distinction of representing the unified whole. The Uni – Verse, Creation’s One - Song. The number One is all that consciousness has manifested into apparent being while zero represents the dimensionless infinite potential of the unmanifested Mind.

Generally when people refer to the number 2, what they think they are referring to is the idea of 2 portions of 1. But in reality the act of counting as it is understood today, while certainly useful in ordinary experience, would see us manifest an entire second universe with the stroke of 2, and a third universe with the stroke of 3 and so on.

What is actually meant by counting two, is the consideration of a single universe of mind as two parts. When one counts to three, perhaps without knowing it they have just created 1 of 3 parts in the conscious field, NOT 3 portions of 1.

3 means 3 parts of 1 concious field

I know that many of you who read this will think that such an assertion is beyond absurd. I hear you saying, “Of course I can count to 3, it’s one of the first things I learned how to do!”. But I am telling you that from the perspective of Foundational Mathematics, you can not. The universe simply won’t cooperate with you on this forever. It will present you with such mischief as infinities beyond the range of comprehension and oddities such as Prime Numbers which defy all explanation and myriad other problems akin to chasing shadows. Nature will not tolerate people trying to count into being whole new Universes!

Perhaps Phi’s inverse value should be named after the Greek numeral 6, “Stigma” or “Ϛ” since it is itself an important value for the Foundational Mathematician. Stigma, Ϛ = ~ 0.618033

Phi is about controlling the growth of conscious fields into ever more divisions while Stigma is about controlling the contraction.

In the algebra Phi tells us more about itself.

the geometry of squaring phi by adding one

To get another perspective on this situation, we can re-arrange the equation a bit and think about it from a slightly different vantage.

the curious geometry of phi

I will elaborate more fully in a subsequent post.

Phi and the Fibonacci Series

In the late 1100′s, Fibonacci noticed something peculiar about the following series of numbers (now called the Fibonacci Series).

1 , 1 , 2 , 3 , 5 , 8 , 13 , 21 , 34 , 55 , 89 , 144 , 233 … and so on

In case you don’t see it, the sequence builds upon itself by always adding the most recent result with the previous. For example, the next value in the sequence above would be found by adding 233 with 144 which is 377.

Fibonacci took a close look at the ratios produced by this series as given below:

1/1 = 1.000000

2/1 = 2.000000

3/2 = 1.500000

5/3 = 1.666666

8/5 = 1.600000

13/8 = 1.625000

21/13 = 1.615385

34/21 = 1.619048

55/34 = 1.617647

89/55 = 1.618026

144/89 = 1.617978

233/144 = 1.618056

and so on.

As is plain to see from the above listing, what Fibonacci found is that the higher you are in the series, the more the value of the ratio converges with Phi.

I have developed a chart showing this. I have color keyed this chart in accordance with my numeric polarity theory showing how the interlaced positive and negative magnetic polarity cycles in the Fibonacci series.

the fibonacci series converging on phi

For those interested, below is the error term of the convergence taken to 243 significant figures. Again, my Numeric Polarity is indicated.

chart showing diminishing error term as the fibonacci series approaches phi

The table below expresses the Fibonacci series values as points on the circle of 12 within the incrementation they appear. 12 is relevant here because the Fibonacci sequence itself naturally cycles from zero to zero through 12 completing the full cycle of polarity in 2Pi (ie. 24)

the fibonacci points on increments of 12 (granular view)

It is quite astounding to see that when you increase your “altitude” from this chart, you can see that the numbers have organized themselves into a very regular double helical pattern.

the fibonacci points on increments of 12 (high level view) showing the Fibonacci/Petty Double Helix

More to come!

Posted in Foundational Analysis, Foundational Technology, General, Number Theory, Prime Numbers | 9 Comments »

The True Foundation of Arithmetic

Saturday, January 9th, 2010

Breath.

Here is the process:

1) The in-flow of fresh air from outside space into the lungs. This is Yin flow.

2) With lungs fully expanded, the body is satiated and nourished with essential life force. When the breathing action reaches its in-flow boundary (ie. its upper limit or boundary interaction with positive polarity), the flow of breathe passes transiently through zero resulting in a reversal of directional flow. (ie. boundary crossing)

3) The out-flow of spent air back to space. This is Yang flow.

4) With lungs depleted, the body hungers desperately for more air. A physical being is at great peril of bodily death after only a few minutes of being deprived of air. When the breathing action reaches its out-flow boundary (ie. its lower limit or boundary interaction with negative polarity), the flow of breathe passes again transiently through zero resulting in another reversal of directional flow. (ie. boundary crossing).

5) The Yin flow begins again with a new breathe. The cycle of giving Yin to the Yang and Yang to the Yin by way of the polarity boundaries repeats itself so long as a being lives.

Through the course of my analysis, I have discovered that the principle of breathe is as much a reality for mathematical abstraction as it is for the evident physiology of respiration in biological systems.

The chart below is matrix style listing of how numbers 1 through 2016 are position on the radial of a circle divided into 9 parts.

Also indicated in the chart below is the numerological compression of each value listed. When ever a base10 sum changes by an order of magnitude, the color is alternated between blue and gold.

On each radial, the number represented by the radial oscillates in a palindromic manner. For example, in the 500 range of the One radial (values 505 through 595) you see the following patterns:

** yin palindrome **
505
514
523
–
532 (32 is the mirror of 23)
541 (41 is the mirror of 14)
550 (50 is the mirror of 05)

** yang palindrome **
559
568
–
577
–
586 (86 is the mirror of 68)
595 (95 is the mirror of 59)

These patterns are consistent everywhere in the system. The pattern that governs this behavior completes a full cycle after 223 incrementations around the circle of 9.

petty foundational table of arithmetic

When this matrix is plotted along a circular system, the result is the chart shown below.

Petty Chart for Foundational Arithmetic (1X)

The numbers set themselves up as interlaced spirals.

The Yin spiral expands the system. The system grows as large as it can in as it moves through 2 Pi along the spiral path.

When it reaches 2 Pi (at 9), the system begins a kind of contraction, not in size but in movement back towards the initial polarity. It seems the system that governs creation, which is reflected by mathematics, never looses size once gained.

This is where I was reminded of the principles of breath.

breath of the spiral

Below I have provided various magnified views of this chart.

2X Magnification

Petty Chart for Foundational Arithmetic (2X)

4X Magnification

Petty Chart for Foundational Arithmetic (4X)

6X Magnification

Petty Chart for Foundational Arithmetic (6X)

8X Magnification

Petty Chart for Foundational Arithmetic (8X)

16X Magnification

Petty Chart for Foundational Arithmetic (16X)

32X Magnification

Petty Chart for Foundational Arithmetic (32X)

Here is a 1X view with the Vortex Glyph superimposed.

Petty Chart for Foundational Arithmetic with Vortex Glyph

The prime numbers fall on this chart as follows:

Petty Chart for Foundational Arithmetic indicating Primes

See earlier post http://www.alexpetty.com/2009/11/15/on-numeric-magnetism-and-the-fundamentals-of-primality/ to better understand the color coding being applied to the primes in the chart above.

Here is a closer look

magnified view of the primes on petty foundational table of arithmetic

More to come!

Posted in Foundational Analysis, Foundational Technology, Number Theory, Prime Numbers, Singularity | 4 Comments »

The Foundational Tables of Multiplication

Sunday, January 3rd, 2010

I wanted to share with you some of the foundational basics of arithmetic I have uncovered through my research. Incredibly, it seems that numbers have been widely misunderstood throughout time. I have found evidence that certain ancient people knew of the true nature of numbers, but by and large the information has been kept shrouded in secrecy or otherwise concealed and/or forgotten.

The time has come to clarify this information and its implications, as the lack of this clear understanding has for too long contributed to the hindrance of humanities continued development as a truly advanced technological civilization.

One of the first “truths” children are taught about mathematics is that all numbers exist on a construct called the number line.

the number line

The idea of a number line easily supports the apparent reality that adding and subtracting numbers is an exercise in traversing distances to the right and left along the line. If you want to involve higher dimensions (multiplication, exponents, division and square roots) then you turn 90 degrees for each dimension, create some more distance between points and begin measuring areas and volumes and the unit integers contained by these spaces.

All of this geometry works out just fine when dealing with life within the normal range of our ordinary human experience, however there are layers of important meaning lost by not taking into account the underlying information which the numbers themselves indicate to us about how they are actually positioned in relation to one another.

The reality is that numbers position themselves on a circle divided into nine parts, and so we live in a MOD9 universe. To be even more precise, numbers are positioned on the circle along the lines of a spiral whose growth is governed by the Golden Ratio, Phi. This spiral gives form to the vortex which has shown itself to be so fundamental in the physical creation. It is at this very place that the “abstract” counting numbers can first be seen as what they really are – the fundamental granularity of the “physical” Creation.

numeric spiral

Let’s take a careful look at what it means to multiply numbers together.

Here are the multiplication tables which have been typically taught to students.

tables of multiplication

Although the above table is a clear expression of the geometric growth of numbers in two dimensions, it fails to offer a true representation of how the numbers relate to each other in the two dimensional geometry. When one accounts for the reality of the circle of nine, one sees that the tables of multiplication are in reality as given below.

foundational tables of multiplication

We can derive universal structure from the table above.

table of the universal structures underlying geometric growth

Each multiplication table for the foundational numbers 1 through 9 posses a specific geometric signature. The one’s table chart is given below in the diagram below.

the one's table foundational chart

The two’s table chart is given below in the diagram below.

the two's table foundational chart

The three’s table chart is given below in the diagram below.

the three's table foundational chart

The path of the Three Chart traces the enclosed equilateral triangle 3 times.

The four’s table chart is given below in the diagram below.

the four's table foundational chart

The five’s table chart is given below in the diagram below. Note that between 4 and 5 lies the path through the singularity (the zero point). Once crossed the direction of the flow is reversed.

the five's table foundational chart

The six’s table chart is given below in the diagram below. Here again, the triangle is lapped three times.

the six's table foundational chart

The seven’s table chart is given below in the diagram below.

the seven's table foundational chart

The eight’s table chart is given below in the diagram below.

the eight's table foundational chart

The path of nine has no component and is therefore always zero. It is a perfect unperturbed circle.

the nine's table foundational chart

Again, the shapes formed in the charts above are derived directly from the foundational multiplication tables

color coded table showing geometric growth structures

The sequences that arise from the foundational multiplication tables are perfectly summarized by the vortex glyph

vortex glyph

Simply by organizing the numbers 1 through 9 and 0, we can see the doubling pattern, it gives rise to a polarity driven system which provides the framework for the expansion and contraction of systems within Creation.

I think it was said best by Fibonacci himself in 1202 AD:

“These are the nine figures of the Indians: 9 8 7 6 5 4 3 2 1. With these nine figures, and with this sign 0 which in Arabic is called zephirum, any number can be written, as will be demonstrated.”

This statement, although seemingly straight forward, is actually quite significant and layered with meaning.

For those interested, I would like to announce that I will be releasing my first book on the subject of Foundational Mathematics.

The Nature of Numbers
Mapping the Terrains of Conciousness

by Alexander S. Petty

(to be released in Summer of 2010 – target release date: 08/15/2010)

Posted in Foundational Analysis, Foundational Technology, General, Number Theory | 8 Comments »

Strange Vortex Appears In Sky Above Norway

Wednesday, December 9th, 2009

Last night an interesting vortex appeared in the sky above northern Norway.

This display of light in the northern sky was quite incredible.

Vortex clouds and light in the sky above Norway

Here is how the affected sky looked hours later in the morning light.

norway spiral next morning

A similar event occurred in China earlier this year.

Something similar also occurred over Russia in 2006.

Posted in Foundational Technology, General, Singularity | 3 Comments »

On Numeric Magnetism and the Fundamentals of Primality

Sunday, November 15th, 2009

I have never forgotten the moment I first learned that there existed such a thing as primes numbers. That moment impressed me deeply. It was in my third grade year of elementary school and I vividly recall how my teacher explained to us that certain numbers can only be divided by themselves and one, adding with dramatic emphasis that the reason for this has remained one of mankind’s greatest unsolved mysteries. She said that prime numbers have been an open question for the whole of human history. With gravity she added that who ever will reveal the enigmatic nature of the primes will surely in so doing also reveal an entirely new basis for understanding the universe. My young mind was struck with awe by her words and there began my life long fascination with the theory of numbers.

This fascination has manifested itself as a 30 year work in analysis, a fervent search for a fully satisfactory explanation of the distribution of the primes and the true nature of numbers. Over the decades, I have come to realize that numbers are no mere mental abstraction representing the physical world, but rather they are the Creation’s lowest level of “physical” granularity – the base currency of the physical expression of consciousness.

Through my research, I have formulated the view that mind creates the field we think of as numbers through the act of creative (or destructive) will. This contrasted with a mind at rest which experiences unity, that is, it experiences one-ness with all that is as an undifferentiated field of emptiness.

unity

A mind with a will to experience separateness through subject and object instantly brings numbers into being. These numbers are in reality a positive and negative perturbations (or vibratory pressures) in the conscious field itself. The interactions of these fields automatically set up polarity and thus magnetism arises.

negative numeric field

positive numeric field

plurality

Numbers then, which radiate from the mind itself (i.e., consciousness) are the conduit connecting cause to effect. For many years I have held the idea that those abstraction we call numbers are the fundamental granule of existence which, directed by the mind and tempered by a vast cosmological nexus of cause and effect, combine to manifest the physical Creation that we as Human Beings experience as life.

I believe that my theory of Numeric Polarity and the concepts I have grouped together under the heading of Foundational Mathematics are in harmony with the Creation, simple and yet rooted at the very border line of mind and matter. It is through numbers and by the simple set of self-constructive “rules” encoded within the Glyph plate below that the Universe organizes itself into myriad variation. Now more then at any other time in documented history, I believe that the primes are in serious danger of giving up their long guarded enigmatic nature in large part due to the entirely new perspectives being offered through emergent revolutionary patterns of thought.

The physical universe is fundamentally divided into 9 parts.

vortex glyph

The number 9 represents the seat of the creative or destructive will. The numbers 3 and 6 extend from nine as polarity which imparts motive force from the creative will into the Creation. It is for this reason that the poles of duality are reflected in every facet of existence; subject and object, night and day, good and evil, sweet and sour, hot and cold, plus and minus, up and down, east and west, Yin and Yang and so on. This functioning of the principles encoded in the vortex glyph create space, time and force through interactions with the poles at 3 and 6, which are “powered” by their connection to creative or destructive will at 9.

9 is never “physically” present in the system but ever guiding it

The idea of balance in stillness on a circle of 9 is not possible since 9 is by its unpaired nature inherently unbalanced. This confers upon the cosmos a basic state of “restlessness” which is the root cause of the vortex from which arises the physical Creation. Nothing in the range of the physical human experience is ever at rest.

The Yin Yang symbol however points to the aspiration of balance at rest, perfected stillness. To obtain this level of stillness, one must transcend physical (or mod9) based existence altogether and transfer consciousness to the higher sphere, the circle of 8. Eastern and Western spiritual traditions have both pointed towards this aspiration with concepts like enlightenment and atonement. The s-curve in the Yin Yang symbol contains the potential of Creation, but as there can be no “movement” in this perfect state, the potential remains unexpressed until an act of creative will sets the system into motion.

yin yang in stillness (circle of 8)

Once the system is set into motion, the expression of Yin Yang takes on another form.

yin yang in motion (circle of 9)

The glyph I have constructed above illustrates how the rise of polarity sets into motion a magnetic vortex which is at once a balance of positive and negative polarity. When this balance exists through equilibrium, a third neutral force can be observed in the system. The glyph above represents the subtle mechanics of this flow.

It seems to me that the field glyph shown below may represents this same idea.

crop circle showing balanced motion in terms of ying yang

field glyph showing balanced motion

The Aetheric Vortex which gives rise to physical existence is powered by the cosmological trait of in-flow and out-flow shepherded by polarity. I believe that this principle produces all physical phenomenon at every scale: the “atom”, the breath of the human body, and spiraling arms of galaxies. We have here put our finger on the basic underlying principle which governs the mechanics of the physical Creation.

Here is a brief outline of my idea of Numeric Polarity:

Since 2 and 4 are both even (or paired numbers), I think of them as being “complete”. I therefore refer to these as having an inherently positive polarity. Since 5 and 7 are both odd (or unpaired numbers), I think of them as “incomplete” and say that they have inherently negative polarity. Here, I am borrowing the existing conventions around negative particle behavior.

To better understand the polarity of numbers, consider the diagram below.

petty numeric polarity map

The numbers 2 and 4 “insulate” the positive pole at 3. No primes will ever occur along the 3 radial which passes through 3 from the center of the circle of 9.

The numbers 5 and 7 “insulate” the negative pole at 6. No primes will ever occur along the 6 radial which passes through 6 from the center of the circle of 9.

The numbers 8 and 1 “insulate” the neutral pole at 0 / 9. No primes will ever occur along the 9 radial which passes through 9 from the center of the circle of 9.

I think that the prime numbers are the result of particular interference patterns between the vector fields produced by the numbers themselves. I refer to these as “Numeric Field Interactions” and define Numeric Fields to be the quantum field produced by the mind wherever there is a conscious will differentiating unity into plurality. The term Quantum is defined as:

—-

quan·tum(kwntm)n. pl. quan·ta (-t)

1. A quantity or amount.

2. A specified portion.

3. Something that can be counted or measured.

—-

I find it amazing that the definition of this term is so highly conformant with the ideas being expressed in this writing. It makes one wonder how well the fathers of Quantum Mechanics understood the important significance of the numbers themselves.

The growth and contraction of all physical systems is expressed through the doubling pattern which ranges infinitely in any direction from (dn_small), …, 1, 2, 4 through 8, 7, 5 , … , (dn_large), where 7 = 16 or 1 + 6 and 5 = 3+2 or 32. Since distance is illusory, as has been shown through the non-linear transmission of charge through circuits exploiting super-luminal effects, the universe is able to act at any scale that the creative will desires and always follows the rules set forth by the Numeric Polarity.

The first 7 primes (with the range 0 to 27) are indicated with purple circles. Note that I do not consider 1, 2 or 3 to be prime as my definition of primes is built upon a theory of field interactions rather then the coinciding (but surely related) effect of prime factorization. Note that I refer to each complete cycle around the circle of nine as an incrementation.

primes on incrementing circle of 9

In some cases the primes insulate both sides of the negative or positive polarity line, in other cases they only insulate one side of it. The more one increments around the circle of nine, the fewer occurrences of primes one encounters. I think this is because higher incrementations are further from the center of the vortex and therefore causes a diminishing strength of interaction between the numeric fields.

Below is a listing of all of the first 720 incrementations around the circle of nine. The table indicates numeric polarity and the position of the primes.

: table of numeric polarity

An analysis of the table above will indicate that there is a magnetic attraction between the alternating columns conferred by the poles at 3 and 6.

The table above collapses magnetically as follows.

: Collapsed View of Petty Numeric Polarity Table

If you overlap all of the numbers sorted according to their numeric polarity, you will see that no positive prime ever overlaps with a negative boundary prime. You will also see that no negative prime ever overlaps with a positive boundary prime.

My discovery is that the primes interact in a conscious field which is undergoing contraction or expansion in a manner precisely in accordance with the principles of magnetism and diamagnetism!

I have also found that analysis of the numeric polarity for the Fibonacci sequence reveals an infinitely repeating cycle of interlaced magnetic polarity.

fibonacci in mod9 with polarity mapping

A far more expanded view of this can be seen in my writing: http://www.alexpetty.com/2010/01/10/the-golden-ratio/

Of particular interest are the so called prime quintuplets which are defined as places on the circle of nine where the closest possible density of the primes are manifest. According to Jeremy Stride’s deep analysis of the art work at the Grand Masonic lodge in Philadelphia (http://www.pagrandlodge.org/tour/360images.html), and of Ed Leedskalnin’s remarkable achievement at Coral Castle (http://www.leedskalnin.com/CoralCastlePhotos.html) , prime quintuplets are apparently a major key in understanding the operation of a pyramid which I believe to be an instrument which can act as a conduit for light from higher spheres (extremely high vibrations of light) into this one (the range of light oscillation corresponding to velocities below 186,000 m/s).

Stride’s research indicates that prime sums placed on a circle in a specific configuration as identified by Stride prescribe the pyramidal geometry itself!

I have included a table of the first 39 prime quintuplets.

table of first 39 prime quintuplets

Below are the 3 possible prime quintuplet configurations and associated polarities.

neutral prime quintuplets

positive prime quintuplets

negative prime quintuplets

quan·tum

(kw

m)n. pl. quan·ta (-t

)

1. A quantity or amount.

2. A specified portion.

3. Something that can be counted or measured.

Posted in Foundational Analysis, Foundational Technology, General, Prime Numbers, Pyramids, Singularity | 10 Comments »

Numeric Field Interactions in Square-based Pyramid

Saturday, November 14th, 2009

As part of my continuing work with pyramids, I have illustrated the various key interactions of Nelson’s numeric field map of the square pyramid in terms of Numeric Polarity Theory.

: 3 and 6 on the pyramid

: 234 on the pyramid

: 567 on the pyramid

: 9 on the pyramid

: 819 on the pyramid

Posted in Foundational Analysis, Foundational Technology, General, Pyramids | No Comments »

Numeric Fields of a Square Base Pyramid

Monday, November 2nd, 2009

Recently I have been working to map the form of the square base pyramid to Vortex Mathematics through a process of analyzing the interactions of the pyramidal field lines. I recently encountered a paper written by Scot Nelson who has already figured this out. The link to Nelson’s brief but powerfully insightful paper is http://docs.google.com/nelson. I have included the Nelson’s mapping of the square base pyramid below. I have colored in using my usual color encoding scheme. See below.

pyramidal energy map

It is quite interesting to find that the NW/SE diagonal of the pyramid has encoded in to it in MOD9 the harmonic series for the key of C in Hertz! Here are the 16 overtones of the harmonic series.

the harmonic series

Here are the overtones encoded on the pyramid starting from the center and going up the NW diagonal.

pyramidal harmonic series

I think what may be happening at the cap stone is that the harmonic overtones (mod9) 2, 6 and 1 are summing to 9. Furthermore, it seems to me the mod 9 sums below this point define the levels of the Seal of Solomon “zone”, the King’s Chamber and the Queens chamber respectively. The base of the pryamid rests on a mod9 foundation of 7. See table below: