Mapping the Terrains of Consciousness with Foundational Mathematics

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.

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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.

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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.

field of 1

foundational field of 1, unity

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.

plurality

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 table of 2

field 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 ennumerative expansion

phi, the operator of enumerative expansion

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

phi of contraction

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 table of 5

field 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

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 table of 3

field 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 table of 12

foundational field glyph 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 table of 21

foundational field glyph 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 table of 6

field 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 table of 15

foundational field glyph 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 table of 24

foundational field glyph 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

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

field of 9

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 table of 18

foundational field glyph 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 table of 7

field 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.

foundational chart of primes

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 table of 11

field 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.

petty foundational field table 13

foundational field table 13

field of 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 table of 17

foundational field glyph 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 table of 19

foundational field glyph 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 table of 23

foundational field glyph 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 29

foundational field table of 31

foundational field table of 31

foundational field table of 37

foundational field table of 37

foundational field table of 43

foundational field table of 43

foundational field table of 43

foundational field table of 47

foundational field table of 51

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 table of 4

field 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

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

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 8

field of 8

foundational field table of 10

The field of 10 is an open cycle field.

foundational field table 10

foundational field table of 10

field of 10

foundational field glyph of 10

 

The field of 14 is mixed cycle field:

foundational field table of 14

foundational field table of 14

petty foundational field glyph 14

foundational field glyph of 14

The field of 16 is an open cycle field:

foundational field table of 16

foundational field table of 16

foundational field glyph of 16

foundational field glyph of 16

The field of 20 is an open cycle field:

foundational field table of 20

foundational field table of 20

foundational field glyph of 20

foundational field glyph of 20

The field of 22 is a mixed cycle field:

foundational field table of 22

foundational field table of 22

foundational field glyph 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.

8 Responses to “Mapping the Terrains of Consciousness with Foundational Mathematics”

  1. mAt says:

    I’ll take some time to read it well, but wow! well done…
    Keep going.

  2. Cora says:

    Lovely work….what a treat to “happen” on your thinking.

  3. Biggs says:

    Wow. I am really grateful that you shared this information with us. Amazing! I have a lot to think about now. Thanks again.

  4. Raymond Burchard says:

    Pythagoras observed numbers as archetypes rather than mere numerals. In addition to Pythagoras’s observations is the fact that inverse numerical sequencing lends a smaller to larger directional flow to an archetypical, zero sum game, then seen as life’s Mobius band as a countrapositive logic.

    Then when conjugation of the Hebrew inspired mathematics. Within multiplicity in so much as requiring multiple 0 through 9 sequencing, beginning with 00.0 (purpose, calculable resolve mathematics designed to measure and calibrate the fractionalized parameters of the whole of infinity) conjoined with its innate dichotomy, the early Greek digit root mathematics within its own corresponding parameters of singularity (purpose visually demonstrating symmetrical balance, while simultaneously exampling whole numbers behavioral modeling) as a zero sum game/gain mathematics, starting from and returning to a composite 9.

    The purpose of the intertwined innate (quadric) dichotomy as demonstrated by alternating odd and even plus even and odd numbers and values culminating with a single composite value of nine, is in visually modeling the dual, inverse and intertwined symmetries of the double helix and thereby exampling homoscedastic coupling. Men, testosterone/estrogen and women, estrogen/testosterone. Where man’s testosterone is inversely sequenced with regards to the women’s sequenced testosterone, then as well their estrogen sequencings.

    Given; Wherein, 9+9+9+9+9 = 45 = 9. Then 02468 as a five digit, but four numerical values, smaller to larger even numbered/number sequenced left to right with a root digit number value of an even number 2 , 0+2+4+6+8 = 20 = 2. …

    Which when 02468 is subtracted from 99999, leaving a remainder of 97531 as a five digit, five numerical value, as the counter sequenced, smaller to larger odd numbered/number right to left sequence with a root digit number value of an odd 7, 9+7+5+3+1 = 25 = 7. Therefore an even 2 plus an odd 7 equals a composite 9.

    Then too, see even numbers sequenced oppositely as 86420 from right to left. Then when 86420 is subtracted from 99999 the remainder is an odd number/numbered 13579 sequenced from left to right, also totaling a root digit composite 9.

    Where as 9999999999 = 90 = 9, and/or 09 , esoterically speaking nine more than ninety. Therefore 0123456789 totaling 45 as an even/odd (depending on viewing vantage point) number equaling a composite 09, Then when subtracted from 9999999999 totaling 90 equaling 09, then leaves 9876543210 totaling 45 as an even/odd 09, innately quadratic sequencing.

    Key is root digit element and placement of odd/even number and the smaller to larger, and vice versa of first and second digit as set and thereby, group sequencing. Given; … 0+9 = 9 and 1+8 = 9 and 2+7 = 9 and 3+6 = 9 and 4+5 = 9, then reverse the compared numerical odd/even set and group sequencing within followed lineage congruency, 5+4 = 9, 6+3 = 9, 7+2 = 9, 8+1 = 9 and 9+0 = 9. This represents creating a visual symmetrically whole iterative fractal with alternating, odd, even and even, odd numerical balance where magnitude does not necessarily reign supreme, but also lends credence too directional flow.

    The following models the matrix of an iterative fractal from its center out.
    Given; each 3 digit sequence conforms to these root digit and digit value traversing disciplines. 099, 198, 297, 396, 495. Where each 3 digit sequence conforms to this example, 099 equals 0+9+9 = 18 = 9. While continuing, but with inverse digit sequencing 584, 693, 782, 892, 990. Therefore 099+990 = 1089 and 198+981 = 1089 etc totaling the palindrome 5445 plus inversely sequenced 990+099 = 1089 and 981+198 = 1089 etc again totaling 5445, where 5445+5445 = 10890 and bigger and bigger etc … “Whole” number resolve where 1089 equals 33 squared, while its sequenced reverse 9801 equals 99 squared, there is much more on this eventuality.

    Then too, visually modeling Aristotle’s stated, “the whole is greater than the sum of its parts” Given; archetypically 01+10 = 11 and 045+450 = 495, therefore 495 divided by 11 equals a whole 45, but when 045 and 450 are separately divided by 11 and the results added the answer is 44.9999… As the fractionalized equivalence of 45. Not so coincidentally adding all 2 digit numbers from 01 through 99 gives a total of 4950, where 495+4950 = 5445. Try dividing 099 by 11 and then divide each 09 and 90 by 11 and add the results or try 198, then as 018 and 180 or 297, then as 027 and 270 or 396, then as 036 and 360. Then too when 495 is then 135 plus 360.

    08 26 44 62 80 = 220 , 19 37 55 73 91 = 275, where 220+275 = 495
    220 divided by 11 = 20 plus, 275 divided by 11 = 25 and 20+25 = 45 But when 90 72 54 36 18 = 270 , 81 63 45 27 09 = 225, where 270+225 = 495. Then when 270 is divided by 11 = 24.5454… Plus when
    225 is divided by 11 = 20.4545… Then 24.5454 + 20.4545 = 44.9999… Why?

  5. rich says:

    I am a beginning student in math and geometry and the star tetrahedron/merkaba. The math on your website is over my head ,but thankyou for giving me alot to think about and learn. I like your website. rich.

  6. Gerd Zimmermann says:

    Hallo Alex

    vielen Dank für Deine wunderschönen Seiten.

    So genial kann eigentlich nur einer sein. Der/ die (es) mit der Gesamtidee.

    herzliche Grüsse Gerd

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