Mapping the Terrains of Consciousness with Foundational Mathematics

Today I’d like to share a method which I have discovered about how to think about the nature of numbers in terms of how numbers can offer a means to visualize the underpinnings of the conscious field. I have called this field of study the Foundational Mathematics. My hope is that this work may serve as a new channel for enabling an intuitive understanding of how subject and object (particles) relate to one another on the illusory stage of light (mind) into which humanity is born.

In the plates I have published below, I’ve 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 forming a a light peach-brown color. 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 corresponds 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 categories:

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 now explain these classes of numbers more in-depth.

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.


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”.


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


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 are born. The image below shows how the vector fields from two point particles manifest interference patterns in the form of the magnetic dipole. I suggest that is in this very manner that magnetic fields are manifested. Namely, 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:

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 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

Positive 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 underlying basis of electricity and magnetism.

foundational field table of 3
foundational field glyph of 3

The closed cycle field of 3 produces 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 magnetic sequencing of the Fibonacci series.  See some of my earlier writing for more about this.

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).

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.

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 directly connected to this field table; see plate below from my earlier writings.

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:

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 sums to zero using clock math for any arbitrary base. 

All primes exhibit neutral numeric polarity.

It appears to me that primality of integers is the result of magnetic neutrality in fields of numeric polarity.

The observation that primes are divisible only by themselves and one is a side-effect of their neutral numeric polarity. More fundamentally, 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 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 that all prime integers enclose fractal series which possess the characteristics 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 than 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, this is 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.

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

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:

numeric polarity
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 that the cells of an embryo developing in the womb follow this pattern during mitotic division; during the process of initiating a new concious being.

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

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

The doubling and halving are governed by the closed cycle forces of positive, negative and neutral polarity ever guiding form in accordance with the will of consciousness 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 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


Relative Motion of Vectors Produces Fields Foundational Tables of Multiplication 36 Point Rodin Coil Windings
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  • Alex… love your work/writings. I’m working on a paper (possibly a theory) regarding “information”, “It from Bit” and consciousness itself. I’m interested in talking with you. I can’t find your email anywhere though.

    • Hi Christopher. Feel free to reach out on linked in. Or, my email is my first name, Alexander, dot my last name, at Gmail.