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Endless Octaves of Light

Sunday, October 16th, 2011

To begin to understand energy, it is necessary to develop an understanding of harmonics. How convenient is it that the underlying infinite intelligence has endowed humanity with senses that can be used by the astute to intuit energy’s true nature, to thus arrive at a higher understanding by an analysis of light and sound?

Energy manifests on the stage of space and time as what we perceive as vibration; waves of pressure (the force of intention) imparted by light (which emanates from and is received by Mind) onto the stage of the conscious field. The quintessential nature of unmanifested energy (the intention of Mind) is refracted by the prism of space and time thus, thought finds its path to form. It is very much like when the octave of visible light (Octave 50) is refracted, by the orderly geometry of a material crystalline lattice, into its 7 major tone components. In both cases, precisely the same thing has happened: expressions of Unity have fallen into less perfect pluralistic states so as to be made “digestible” for the witnessing “physical” presence.

Energy is mind-ignited causality.

Space and time are the stage where the effects of this causality unfold.

This refraction of energy through space and time is seen to be vibratory, its oscillatory results emanating spherically whether perfectly or oblately.

The scale (or length) of each oscillation is related to the number of oscillations the energy wave produces in a given unit of time. Though every octave may be infinitely divided (or at least very minutely divided indeed) into ever finer shades of semi-tones, there exists a direct correspondence between the Golden Ratio, Phi, and the 12 major and minor tones. These 12 tones fall into natural agreement with the universal human aesthetic for sight (color) and sound (pitch). These seminal tone positions within each octave are represented below. I have clad them in the terminology of western music theory together with the Phi generated mathematical ratios which cause them.

Figure 0. - 12 tones of C

Notice how the Major Tones “point” to the Northeast and the Minor Tones point to the Southwest. Notice also the opposing symmetry between the grey and white shapes.

The relationships between the Perfect Fifth intervals are instructive.

Figure 0.5 - Equilateral Fifths

The 12 tone series of charts below provides specific frequency and wavelength data about 100 octaves of light. The series ranges from Octave 1 (starting from the tone produced by a single oscillation in one second) up through Octave 100 (starting with the tone produced by 1,267,650,600,228,229,401,496,703,205,376 oscillations in one second).

Octave 1

Figure 1. - Octave 1

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Octave 2

Figure 2. - Octave 2

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Octave 3

Figure 3. - Octave 3

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Octave 4

Figure 4. - Octave 4

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Octave 5

Figure 5. - Octave 5

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Octave 6

Figure 6. - Octave 6

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Octave 7

Figure 7. - Octave 7

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Octave 8

Figure 8. - Octave 8

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Octave 9

Figure 9. - Octave 9

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Octave 10

Figure 10. - Octave 10

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Octave 11

Figure 11. - Octave 11

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Octave 12

Figure 12. - Octave 12

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Octave 13

Figure 13. - Octave 13

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Octave 14

Figure 14. - Octave 14

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Octave 15

Figure 15. - Octave 15

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Octave 16

Figure 16. - Octave 16

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Octave 17

Figure 17. - Octave 17

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Octave 18

Figure 18. - Octave 18

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Octave 19

Figure 19. - Octave 19

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Octave 20

Figure 20. - Octave 20

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Octave 21

Figure 21. - Octave 21

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Octave 22

Figure 22. - Octave 22

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Octave 23

Figure 23. - Octave 23

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Octave 24

Figure 24. - Octave 24

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Octave 25

Figure 25. - Octave 25

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Octave 26

Figure 26. - Octave 26

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Octave 27

Figure 27. - Octave 27

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Octave 28

Figure 28. - Octave 28

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Octave 29

Figure 29. - Octave 29

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Octave 30

Figure 30. - Octave 30

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Octave 31

Figure 31. - Octave 31

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Octave 32

Figure 32. - Octave 32

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Octave 33

Figure 33. - Octave 33

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Octave 34

Figure 34. - Octave 34

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Octave 35

Figure 35. - Octave 35

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Octave 36

Figure 36. - Octave 36

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Octave 37

Figure 37. - Octave 37

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Octave 38

Figure 38. - Octave 38

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Octave 39

Figure 39. - Octave 39

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Octave 40

Figure 40. - Octave 40

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Octave 41

Figure 41. - Octave 41

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Octave 42

Figure 42. - Octave 42

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Octave 43

Figure 43. - Octave 43

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Octave 44

Figure 44. - Octave 44

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Octave 45

Figure 45. - Octave 45

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Octave 46

Figure 46. - Octave 46

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Octave 47

Figure 47. - Octave 47

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Octave 48

Figure 48. - Octave 48

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Octave 49

Figure 49. - Octave 49

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Octave 50

Figure 50. - Octave 50

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Octave 51

Figure 51. - Octave 51

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Octave 52

Figure 52. - Octave 52

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Octave 53

Figure 53. - Octave 53

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Octave 54

Figure 54. - Octave 54

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Octave 55

Figure 55. - Octave 55

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Octave 56

Figure 56. - Octave 56

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Octave 57

Figure 57. - Octave 57

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Octave 58

Figure 58. - Octave 58

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Octave 59

Figure 59. - Octave 59

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Octave 60

Figure 60. - Octave 60

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Octave 61

Figure 61. - Octave 61

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Octave 62

Figure 62. - Octave 62

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Octave 63

Figure 63. - Octave 63

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Octave 64

Figure 64. - Octave 64

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Octave 65

Figure 65. - Octave 65

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Octave 66

Figure 66. - Octave 66

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Octave 67

Figure 67. - Octave 67

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Octave 68

Figure 68. - Octave 68

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Octave 69

Figure 69. - Octave 69

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Octave 70

Figure 70. - Octave 70

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Octave 71

Figure 71. - Octave 71

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Octave 72

Figure 72. - Octave 72

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Octave 73

Figure 73. - Octave 73

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Octave 74

Figure 74. - Octave 74

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Octave 75

Figure 75. - Octave 75

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Octave 76

Figure 76. - Octave 76

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Octave 77

Figure 77. - Octave 77

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Octave 78

Figure 78. - Octave 78

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Octave 79

Figure 79. - Octave 79

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Octave 80

Figure 80. - Octave 80

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Octave 81

Figure 81. - Octave 81

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Octave 82

Figure 82. - Octave 82

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Octave 83

Figure 83. - Octave 83

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Octave 84

Figure 84. - Octave 84

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Octave 85

Figure 85. - Octave 85

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Octave 86

Figure 86. - Octave 86

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Octave 87

Figure 87. - Octave 87

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Octave 88

Figure 88. - Octave 88

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Octave 89

Figure 89. - Octave 89

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Octave 90

Figure 90. - Octave 90

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Octave 91

Figure 91. - Octave 91

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Octave 92

Figure 92. - Octave 92

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Octave 93

Figure 93. - Octave 93

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Octave 94

Figure 94. - Octave 94

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Octave 95

Figure 95. - Octave 95

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Octave 96

Figure 96. - Octave 96

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Octave 97

Figure 97. - Octave 97

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Octave 98

Figure 98. - Octave 98

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Octave 99

Figure 99. - Octave 99

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Octave 100

Figure 100. - Octave 100

All energy cycles through countless octaves of light.

There is a correspondence between the quality of mind-generated causality and rate of light vibration produced by that mind.

A mind generating high vibrational causality will be perceived on the stage of effects as the author of kindness and love.

A mind generating low vibrational causality will be perceived on the stage of effects as the author of shades of darkness and hatred.

Each octave is like every other except for in scale.

As above, so below.

A mind generating extremely high vibrational causality will be perceived on the stage of effects as the author of the “miraculous” for such a one is no longer bound by the ordinary constraints of physical existence. Such minds, through persistent effort, have become able to work natively with extremely high vibrations of light, vibrations so high as to be beyond the range of ordinary human experience. Such experiences transcend the senses and these minds are able to work consciously with Astral light by intention alone.

Though this eventuality is the aspiration of all major spiritual teachings, I have set out to show that one can reach these conclusions (and experiences) by scientifically following where the clues of light and sound harmonics lead which is to the inner study of one’s own mind and the eventual understanding that all minds are in fact Unified as One Mind in the cosmic vastness of the Conscious Field.

.:.

Posted in Foundational Analysis, General, Harmonics | No Comments »

The Music of Matter

Sunday, August 14th, 2011

The principles of harmonics which are well-known to the musician are the very same principles which govern the laws of physics, though this is very little realized at present. All octaves of energy, whether within the range of human investigation or beyond it, are the same. Each octave varies from the next only in scale and the amount of energy required to sustain the oscillation.

I have developed the chart shown below in Figure 1 to help you appreciate this more deeply. In it you can examining a full range of 100 octaves beginning from 1 cycle per second all the way up through 1,267,650,600,228,229,401,496,703,205,376 Hz (or a million billion billion cycles per second).

I have not tuned my chart to Standard Pitch where A = 440Hz. I have instead used Scientific Pitch (also known as Philosophical Pitch) where Middle C = 256 Hz and where A = 426.|6| Hz. (Note that some add the closed cycle 6 to the open cycle portion and call this, erroneously, A = 432Hz). I have shifted down from Standard pitch because the mathematics underlying Scientific Pitch are perfectly aligned with Foundational Mathematics while Standard Pitch produces many irrational values suggesting a kind of dissonance or lack of alignment with the fractality of the Conscious Field itself.

Figure 1. - 100 Octaves of Light

In high octaves of light, far higher then Gamma Rays, light condenses into the 10 Octaves of Matter. For more about this topic, see my earlier writing:

http://www.alexpetty.com/2011/07/20/the-periodic-table-of-the-light/

Beyond the Octaves of Matter begin the Octaves of Lower Astral Light. This point in the energy scale marks the borderline between human spirituality and western science.

“As above, so below”.

As the vibrations of light oscillate to ever higher rates, light extends further and further into subtler levels of the conscious field, which is to say that it extends into ever higher vibrations of consciousness.

–

In what follows, I will be working from 256 cycles per second as my root tone.

.:.

Posted in Foundational Analysis, General, Number Theory | 5 Comments »

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 »

Long Division and Euclid’s Lemma

Friday, May 20th, 2011

Do you remember the “long division” you once learned in grade school? Even though it seems now a rather quaint method to the microchip wielding man of today, long division is actually a very powerful procedure. It allows one to very efficiently determine the internal fractal structure of integers without introducing the cumbersome aspects of floating point arbitrary precision.

What we call Long Division is actually the Division Algorithm developed thousands of years ago in ancient Greece. The Division Algorithm is not really an algorithm as much as it is part of a theorem which assures the ability to divide integers and natural numbers known as Euclid’s Division Lemma.

But first, some basics. I will step you through the Division Algorithm.

Suppose you want to find out how many times a number “goes into” another number. For example, imagine that you have 128,654 grains of rice that you wish to distribute to 12 people. So then the question becomes, how many times can 12 be divided among 128,654.

In this case, we refer to 12 as the divisor, to 128,654 as the dividend and the number of times that 12 can be divided among 128,654 as the quotient. When the divisor can not be distributed equally to the dividend, the left over balance is referred to as the remainder.

Long Division (ie. the Euclid’s Division Algorithm) is a procedure that can be used to determine the quotient and remainder for a given divisor and dividend.

Here is how it works:

Arrange the divisor and dividend as shown below.

We address the dividend starting from its significant-most digit.

In other words, we start from the left side of the dividend and perform the long division procedure working from left to right.

We first ask ourselves whether 12 can be distributed evenly to 1.

When we realize it cannot and that 12 requires at least 12 in order to be distributed, we mark a zero in the quotient and we expand our consideration of the dividend one position to the right (which is 2). So now we are considering 12.

We now ask how many times can 12 be distributed to 12?

The answer is that 12 can be given to 12 exactly one time with nothing remaining. We express this by arranging our mathematical statement as shown below.

We then expand our consideration of the dividend out to the third digit (which is 8), asking how many times can 12 be distributed to 8? Since 8 is smaller then 12, 12 cannot be distributed among 8 and so we mark a zero in the quotient. Also, because we are considering the 8, we “bring it down” into the working area of the mathematical statement as shown below.

Since 12 cannot be distributed among 8, we expand our consideration of the dividend to include the fourth number (which is 6) by bringing it down into the working area of the mathematical statement. We then arrange our mathematical statement as shown below.

We now ask, how many times can 12 be distributed to 86?

The answer is that 12 can be given to 86 seven times with a remaining balance of 2. We express this by arranging our mathematical statement as shown below.

Next we ask how many times can 12 be distributed to 2?

Since 12 cannot be distributed among 2, we expand our consideration of the dividend to include the fifth number (which is 5) by bringing it down into the working area of the mathematical statement. We then arrange our mathematical statement as shown below.

Next we ask how many times can 12 be distributed to 25?

The answer is that 12 can be given to 25 two times with a remaining balance of 1. We express this by arranging our mathematical statement as shown below.

Next we ask how many times can 12 be distributed to 1?

Since 12 cannot be distributed among 1, we expand our consideration of the dividend to include the sixth number (which is 4) by bringing it down into the working area of the mathematical statement. We then arrange our mathematical statement as shown below.

Next we ask how many times can 12 be distributed to 14?

The answer is that 12 can be given to 14 one time with a remaining balance of 2. We express this by arranging our mathematical statement as shown below.

So now we have found out that if we have 128,654 grains of rice to distribute evenly to 12 people, each person would receive 10,721 grains of rice (our quotient) and that there would also be 2 grains of rice left over (our remainder).

If we wanted to be very precise, we would then determine how many portions to split the remaining 2 grains of rice up evenly amongst the 12.

Since we have run out of digits in our integer dividend, we now must add a decimal point and continue the long division procedure as shown below. Since we are free to add as many zeros to the right of the decimal point as we wish without changing the value, we can continue long division indefinitely. Therefore, it is said that we may continue producing numbers in the quotient to any arbitrary degree, a quality known as arbitrary precision.

So then, let’s continue.

Next we ask how many times can 12 be distributed to 20?

The answer is that 12 can be given to 20 one time with a remaining balance of 8. We express this by arranging our mathematical statement as shown below.

Since 12 cannot be given to 8, we add another zero and “drop it down” as shown below.

Next we ask how many times can 12 be distributed to 80?

The answer is that 12 can be given to 80 six times with a remaining balance of 8. We express this by arranging our mathematical statement as shown below.

With the remainder again being 8, we see that the solution will repeat 6 in the quotient forever.

Thus, the quotient for 128,654 / 12 = 10,721.1|6|

The above has been a particular example of long division. Now let’s consider the general procedure of long division.

Suppose we wish to divide an integer a by a positive integer d.

Let a = a_na_n-1…a₁a₀ in decimal representation.

Since a has n+1 digits, the long division will have n+1 steps as each digit of the dividend generates exactly one step and gives exactly one digit of the quotient.

At step i, we do this:
Look for the largest integer q_i so that d × q_i does not exceed B_i, where B_i is defined as follows:

B_n = a_n and

B_i = 10(B_i+1 – d × q_i+1) + a_i, 0 ≤ i < n.

Write q_i to the right of q_i+1in the quotient row.

After we reach i = 0, what remains is r, the remainder.

Why does long division work?

In the long division procedure, the dividend must equal the sum of the remainder and all the numbers that have been subtracted.

But the numbers subracted are d×q_i with place value 10ⁱ. So

a = (d × q_n)10ⁿ +(d × q_n-1)10^n-1 + … + (d × q₁)10¹ + (d × q₀) + r, where 0 ≤ r < d

= d × (q_n10ⁿ + q_n-110^n-1 + … + q₁10¹ + q₀) + r

= d × q_nq_n-1…q₁q₀ + r

= d × q + r, 0 ≤ r < d.

Here is where we need Euclid’s Lemma.

According to it, q and r must be unique. That is, the q we have found in the long division is indeed the one and only value possible, namely the quotient of a when divided by d.

Now that we know why long division works, it is easy to extend to dividends that are not integers.
Suppose a = 758.9 and d =5. Then a/5 = (1/10)(7589/5) so that we carry out the long division involving two integers and then divide the answer by 10 which is accomplished by moving the decimal point left.
Finally, noting that the Division Algorithm is valid in any base, we can extend these arguments to any base just as well as we can for base 10.

Below is an example of Euclid’s Division Algorithm in action.

Euclid's Division Algorithm in Animation

More about Euclid’s Division Lemma

The Division Lemma of Euclid assures us that each result obtained at every step of the Division Algorithm is absolutely the correct unique value for every possible dividend-divisor pair.

Here is how Euclid derived the Lemma:

For example, if you are given 13 and required to divide it among 4

Figure 15. - Euclid's Division Lemma, Step 1

Euclid thought about this in terms of 13 small spheres.

Figure 16. - Euclid's Division Lemma - Step 2

He then imagined the spheres being partitioned into 3 groups of 4 with 1 remaining ungrouped sphere left over.

Figure 17. - Euclid's Division Lemma - Step 3

Next Euclid arranged these spheres into the following mathematical relationships.

Figure 18. - Euclid's Division Lemma - Step 4

Then Euclid considered a wider set of data points.

In the examples included in figure 19 below, let’s refer to:

all of the dividends as ‘a‘

all of the divisors as ‘b‘

all of the quotients as ‘q‘

all of the remainders as ‘r‘

Figure 19. - Euclids Division Lemma - Step 5

Careful analysis begins to reveal that a pattern is emerging. We are getting unique combinations of quotients and remainders for any given pair of dividends and divisors. Furthermore, we see that in every case, remainder r is always greater then or equal to zero, but is always less then divisor b.

Figure 20. - Euclids Division Lemma - Step 6

Thus, Euclid’s Division Lemma may be stated as:

Given integers a, b with b > 0, there exist unique integers q, r
with 0 ≤ r < b such that a = bq + r.

To really be sure that the combinations are unique however, we need proof. So here it is:

Proof of Euclid’s Division Lemma is given as follows.

The proof consists of two parts — first, the proof of the existence of q and r, and second, the proof of the uniqueness of q and r.

Part 1: Existence of q and r

Consider the set:

We claim that S contains at least one non-negative integer. There are two cases to consider.

1) If a is non-negative, then choose n = 0.

2) If a is negative, then choose n = ab.

In both cases, a – nb is non-negative, and thus S always contains at least one non-negative integer. This means we can invoke the Well-Ordering Principle, and deduce that S contains a least non-negative integer r. By definition, r = a – nb for some n. Let q be this n. Then, by rearranging the equation, a = qb + r.

It only remains to show that 0 ≤ r < |b|. The first inequality holds because of the choice of r as a non-negative integer. To show the last (strict) inequality, suppose that r ≥ |b|. Since b ≠ 0, r > 0, and again b > 0 or b < 0.

If b > 0, then r ≥ b implies a-qb ≥ b. This implies that a-qb-b ≥0, further implying that a-(q+1)b ≥ 0. Therefore, a-(q+1)b is in S and, since a-(q+1)b=r-b with b>0 we know a-(q+1)b<r, contradicting the assumption that r was the least non-negative element of S.

If b < 0, then r ≥ -b implies that a-qb ≥ -b. This implies that a-qb+b ≥0, further implying that a-(q-1)b ≥ 0. Therefore, a-(q-1)b is in S and, since a-(q-1)b=r+b with b<0 we know a-(q-1)b<r, contradicting the assumption that r was the least non-negative element of S.

In either case, we have shown that r > 0 was not really the least non-negative integer in S, after all. This is a contradiction, and so we must have r < |b|. This completes the proof of the existence of q and r.

Part 2: Proof of the uniqueness of q and r

Suppose there exists q, q’ , r, r’ with 0 ≤ r, r’ < |b| such that a = bq + r and a = bq’ + r’ . Without loss of generality we may assume that q ≤ q’ .

Subtracting the two equations yields: b(q’ – q) = (r – r’ ).

If b > 0 then r’ ≤ r and r < b ≤ b + r’ , and so (r – r’ ) < b. Similarly, if b < 0 then r ≤ r’ and r’ < -b ≤ -b + r, and so -(r – r’ ) < -b. Combining these yields |r – r’ | < |b|.

The original equation implies that |b| divides |r – r’ |; therefore either |b| ≤ |r – r’ | or |r – r’ | = 0. Because we just established that |r – r’ | < |b|, by trichotomy we may conclude that the first possibility cannot hold. Thus, r = r’ .

Substituting this into the original two equations quickly yields bq = bq’ and, since we assumed b is not 0, it must be the case that q = q’ proving uniqueness.

–

The question then occurs to me. Is it possible to further generalize Euclid’s Division Lemma using Foundational Mathematics? Can we, when armed with the ordering clarity offered by The Foundational Mathematics, develop a method based on it to allow us, like a mathematical spider, to glide effortlessly and steadfast over the seemingly infinite labyrinthine web of numbers?

With this goal in mind, I have produced the following charts.

The first chart shows the unique euclidean lemma value matrix which I have generalized using Foundational Mathematics for ranges:

Dividend (a) = 1 for Divisors (b) = 0 through 9

Dividend (a) = 2 for Divisor (b) = 0 through 9

Dividend (a) = 3 for Divisor (b) = 0 through 9

Dividend (a) = 4 for Divisor (b) = 0 through 9

Dividend (a) = 5 for Divisor (b) = 0 through 9

Dividend (a) = 6 for Divisor (b) = 0 through 9

Dividend (a) = 7 for Divisor (b) = 0 through 9

Dividend (a) = 8 for Divisor (b) = 0 through 9

Dividend (a) = 9 for Divisor (b) = 0 through 9

Figure 21. - Petty Foundational Division Lemma for a equals 1 through 9

To see my work which led to these charts, review the follow document:

http://www.singularics.com/docs/petty-foundational-lemma-sequences_draft.pdf

Note that zero and nine are the Alpha and Omega. The end is the beginning. This is an expression of infinity.

9 is the intention of Mind to either constructively expand (multiply if the expansion in spatial) or to destructively contract (divide is the contraction is spatial).

3 and 6 are the force of Mind’s intention (extending thus from 9) exerted upon the conscious field as a vibratory pressure of light.

1, 2, 4, 8, 7 and 5 are the archetypal vibrations of form, shepherded through space and time, arranging themselves with respect to one another in accordance with the laws of polarized force and sacred geometry.

zero and nine are the alpha and the omega

Note also that every incrementing number that occurs where the spiral intersects with radials always compresses back to the radial’s initial value. For example, 546 is on the 6 radial because 5+4+6=15 and we then compress 15 as 1+5=6.

To develop a working understanding of this and other Foundational Mathematics concepts, please refer to my earlier writings:

http://www.alexpetty.com/2010/01/09/the-true-foundation-of-arithmetic/

Focus particularly on this rectangular table showing radial compression in base 10:

http://www.alexpetty.com/wp-content/uploads/2010/01/fae2016_small.png

You may also wish to review this circular version of the table:

http://www.alexpetty.com/wp-content/uploads/2010/01/fns-circle-chart-round-1×1.png

To see this principle at work in numerous other bases (indeed any arbitrary base), please review my earlier writing:

http://www.alexpetty.com/2010/08/23/the-effect-of-base-on-numeric-fields/

Can this characteristic of numbers help us more deeply understand what it means to divide?

Can we say that for any arbitrarily sized divisor, that “Foundational Radial Compression” assures that we can rely on the values listed in figure 21 for the general case?

.:.

Posted in Computer Science, Foundational Analysis, Number Theory, Prime Numbers | No Comments »

Euclid Elements – Book 1 – Proposition 2

Tuesday, May 17th, 2011

euclid elements: book1 proposition 2 in greek

To place a straight line equal to a given straight line with one end at a given point.

Let A be the given point, and BC the given straight line.

book1 - proposition2 - step1

It is required to place a straight line equal to the given straight line BC with one end at the point A.

Join the straight line AB from the point A to the point B, and construct the equilateral triangle DAB on it.

book1 - proposition2 - step2

Produce the straight lines AE and BF in a straight line with DA and DB.

book1 - proposition2 - step3

Describe the circle CGH with center B and radius BC,

book1 - proposition2 - step4

and again, describe the circle GKL with center D and radius DG.

book1 - proposition2 - step5

Since the point B is the center of the circle CGH, therefore BC equals BG.

Again, since the point D is the center of the circle GKL, therefore DL equals DG.

And in these DA equals DB, therefore the remainder AL equals the remainder BG.

But BC was also proved equal to BG, therefore each of the straight lines AL and BC equals BG.

And things which equal the same thing also equal one another, therefore AL also equals BC.

Therefore the straight line AL equal to the given straight line BC has been placed with one end at the given point A.

book1 - proposition2 - final

.:.

Posted in Euclid, Foundational Analysis, General | No Comments »

Analyzing Magnetic Fields

Friday, September 10th, 2010

I have noticed that the progression of my energy research is linked to my ability to intuitively think about the moving form of magnetic fields and the ability to anticipate how these fields are affected by the systems they are part of.

Below are a couple of basic fields of interest.

Cross-section of Spherical Magnetics Fields with NSNS Arrangement

Cross-section of Spherical Magnetic Fields with NSNS Arrangement

Cross-section of Spherical Magnetics Fields with NSSN Arrangement

Cross-section of Spherical Magnetic Fields with NSSN Arrangement

I will be sharing more of these kind of field plots as I think they are very beautiful.

Posted in Foundational Analysis | No 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 »

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