Experimental Mathematics: Finding Number Patterns

Let's see which geometric shape encapsulates this relationship.
At a given iteration, every new prime number needs to be connected to all the primes preceding it.
1746655635059.png

From left to right, we obtain:
  • a point (1 vertex, no edge),
  • a line segment (2 vertices, 1 edge),
  • a triangle (3 vertices, 3 edges),
  • a tetrahedron (4 vertices, 6 edges),
  • a 5-cell (5 vertices, 10 edges)
Going a bit further, a way to geometrically map primes would be to associate each prime to a vertex using barycentric coordinates.
In geometry, a barycentric coordinate system is a coordinate system in which the location of a point is specified by reference to a simplex (a triangle for points in a plane, a tetrahedron for points in three-dimensional space, etc.). The barycentric coordinates of a point can be interpreted as masses placed at the vertices of the simplex, such that the point is the center of mass (or barycenter) of these masses.
  • Prime 1: (1)
  • Primes 1,2: (1,0), (0,1)
  • Primes 1,2,3: (1,0,0), (0,1,0), (0,0,1)
  • Primes 1,2,3,5: (1,0,0,0), (0,1,0,0), (0,0,1,0), (0,0,0,1)
  • Primes 1,2,3,5,7: (1,0,0,0,0), (0,1,0,0,0), (0,0,1,0,0), (0,0,0,1,0), (0,0,0,0,1)
  • ...and so on.
1747496062446.png
source (image): simplex in nLab

Finding the coordinate of the next prime is very easy, because the next prime occupies a new dimension and embeds the preceding primes into that new dimension. For example, the prime 11 (the 6th prime) would have the coordinate (0,0,0,0,0,1) in six-dimensional space.

But given a coordinate, how would we deduce the numerical value of the prime? The geometry of a simplex seems to put each vertex on equal footing with the other vertices. Remember, when we drew the graph, the edges were directional in order to show the dependence between each vertex. As you can see, the prime 2 doesn't depend on the prime 5, but the prime 5 depends on the prime 2.
1747497961077.png
But we could also say that the prime 1 "gives birth" to the prime 2, which, in turn, "gives birth" to the prime 3, and so on. And so, by transitivity, the prime 1 "gives birth" to all the other primes.
1747499415847.png
If we add both graphs together, we obtain an undirected (no arrows) graph, because the direction of travel is unrestricted, i.e. we can travel back and forth from each point to all the other points.
1747499590623.png
Q: Now, the other night, in front of the psychomantium, I did not exactly have a vision, but something came into my head, and the idea was that prime numbers are important because, the principle that they are only divisible by themselves and by one is indicative of the fact that they are direct links, channels, or conduits to seventh density, or first density, or something...

A: How about all densities?


Q: Okay, that is sort of what I mean, that they are, in a sense, gateways - would that be a good term?

A: Close.
"All is one and one is all," as the C's said.
 
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Found another way to generate Pascal's Triangle.

Step 1: Initialize a matrix with a column of 1's on the left, and row of variables in this manner.
1753126363773.png

Step 2: Multiply two elements diagonally to find the next element(s).
1753126071505.png

Step 3: Add more variables and 1's, and repeat Step 2 until the table is filled.
1753126159708.png

Step 4: Pick a variable, say x, and only keep the exponent of this variable in each expression.
1753126197288.png

Pascal's Triangle strikes again!
1753127253498.png
 
Going a bit further, a way to geometrically map primes would be to associate each prime to a vertex using barycentric coordinates.

  • Prime 1: (1)
  • Primes 1,2: (1,0), (0,1)
  • Primes 1,2,3: (1,0,0), (0,1,0), (0,0,1)
  • Primes 1,2,3,5: (1,0,0,0), (0,1,0,0), (0,0,1,0), (0,0,0,1)
  • Primes 1,2,3,5,7: (1,0,0,0,0), (0,1,0,0,0), (0,0,1,0,0), (0,0,0,1,0), (0,0,0,0,1)
  • ...and so on.
View attachment 108574
source (image): simplex in nLab

Finding the coordinate of the next prime is very easy, because the next prime occupies a new dimension and embeds the preceding primes into that new dimension. For example, the prime 11 (the 6th prime) would have the coordinate (0,0,0,0,0,1) in six-dimensional space.

But given a coordinate, how would we deduce the numerical value of the prime? The geometry of a simplex seems to put each vertex on equal footing with the other vertices. Remember, when we drew the graph, the edges were directional in order to show the dependence between each vertex. As you can see, the prime 2 doesn't depend on the prime 5, but the prime 5 depends on the prime 2.
View attachment 108575
But we could also say that the prime 1 "gives birth" to the prime 2, which, in turn, "gives birth" to the prime 3, and so on. And so, by transitivity, the prime 1 "gives birth" to all the other primes.
View attachment 108580
If we add both graphs together, we obtain an undirected (no arrows) graph, because the direction of travel is unrestricted, i.e. we can travel back and forth from each point to all the other points.
View attachment 108581

"All is one and one is all," as the C's said.

This is great. That tetrahedron (0,1,2,3) appears to be the topology that informs various domains. This uses the dimensional value system you touched on, which appears to be a kind of rosetta stone. But here, we'd consider the centroid (5) a kind of no-local modulating function, more on that.

In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. The simplex is so-named because it represents the simplest possible polytope in any given dimension. For example,
- 0-dimensional simplex is a point,
- 1-dimensional simplex is a line segment,
- 2-dimensional simplex is a triangle,
- 3-dimensional simplex is a tetrahedron, and
- 4-dimensional simplex is a 5-cell.

Consider how the classical elements might map to this:
  1. 0-dimensional (fire - nascent > potential)
    - 1-dimensional (air - discrete > autonomy)
    - 2-dimensional (water - ancillary > relational )
    - 3-dimensional (earth - form > experiential)
    - 4-dimensional (aether - blueprint > coherence regulator)

Screenshot 2025-07-22 at 11.42.54 am.png

For example, mapping to Genesis:
Zz9GH--insert-title-here-.png

The Genesis story gives us an initial 10 step progression of recursive functions. Rightly as a progressive "breath" cycle of 0 (inward) and 1 (outward), the basic binary off and on. This gives us a kind functional breath (btw YHWH denotes breath). This becomes a live operator to and from the centroid (5):
  • Compression (1→0→5) + (1→2→5) inhale raw potential into a stable lattice.
  • Expression (5→1→0) + (5→3→0) exhale coherent form into the world.
  • Stabilisation (3→0→5) + (3→2→5) strain becomes the signal for update.
  • Emission (5→1→2) + (5→3→2) release into the next coherent state.

Which btw provides us a possible functional meaning of the Svastika. See one of those "arms" mapped here:

Screenshot 2025-07-22 at 12.59.09 pm.png

This is only part of the mapping. Given say the esoteric maxim of what is above so below, we see the next "progression" through the sister tetrahedral topology in the star tetrahedron. More to come on that
 
This is great. That tetrahedron (0,1,2,3) appears to be the topology that informs various domains. This uses the dimensional value system you touched on, which appears to be a kind of rosetta stone. But here, we'd consider the centroid (5) a kind of no-local modulating function, more on that.



Consider how the classical elements might map to this:
  1. 0-dimensional (fire - nascent > potential)
    - 1-dimensional (air - discrete > autonomy)
    - 2-dimensional (water - ancillary > relational )
    - 3-dimensional (earth - form > experiential)
    - 4-dimensional (aether - blueprint > coherence regulator)

View attachment 110543

For example, mapping to Genesis:
View attachment 110544

The Genesis story gives us an initial 10 step progression of recursive functions. Rightly as a progressive "breath" cycle of 0 (inward) and 1 (outward), the basic binary off and on. This gives us a kind functional breath (btw YHWH denotes breath). This becomes a live operator to and from the centroid (5):
  • Compression (1→0→5) + (1→2→5) inhale raw potential into a stable lattice.
  • Expression (5→1→0) + (5→3→0) exhale coherent form into the world.
  • Stabilisation (3→0→5) + (3→2→5) strain becomes the signal for update.
  • Emission (5→1→2) + (5→3→2) release into the next coherent state.

Which btw provides us a possible functional meaning of the Svastika. See one of those "arms" mapped here:

View attachment 110547

This is only part of the mapping. Given say the esoteric maxim of what is above so below, we see the next "progression" through the sister tetrahedral topology in the star tetrahedron. More to come on that

To add these are the two-arm paths (1→0→5→3→2) & (3→0→5→1→2) that bear stricking similarity to the Svastika if represented in a 2D symbol. Also, notice the of the 10 possible node pairs (including the centroid)

Also, more detail to this progression, as a geometric topology, surfaces (faces) are distinct functions, and we could say, recursive patterns stemming from the first 4 points (0,1,3). This lead me to consider that 4-7 correspond to the faces and in Kabalistic terms - the 4 worlds. So if follow this through, symbolically at least, we have:

  1. "Day 0": Point: Fire (0) - inhale
  2. Day 1: Line: Air (1) - exhale
  3. Day 2: Surface: Water (2) - inhale
  4. Day 3: Volume: Earth (3) - exhale
  5. Day 4: Face 1: Fire (0,1,2) - Atziluth (emmanation) - inhale
  6. Day 5: Face 2: Air (0,1,3) - Beriah (creation) - exhale
  7. Day 6: Face 3: Water (0,2,3) - Yetzirah (formation) - inhale
  8. Day 7: Face 4: Earth (1,2,3) - Assiah (action) - exhale
Screenshot 2025-07-22 at 3.43.32 pm.png
Image above depicts how each "world" has a breath function too. This is further reiterated via next key events / function in Genesis: Tree of Knowledge and Tree of Life (inhale and exhale). So a decent into knowledge (1→0→5→1→0 fire and air) burns when not balanced with the exhale in life (3→0→5→1→2). We see that same metaphor in the Ark of the Covenant and the Holy Grail. In other words, truth without care, law without grace, structure without flow - is incomplete and casts us out of the garden of Eden.

Consider again the burning bush - it ignites without being extinguished, the breath YHWH that is fully "breathing". This is the complete 10 progressions (Decad / Tetraktys):

9. "Day 8": Arm 1 (Svastika): Fire and Air - via 4 connections - inhale (decent of strain to centroid - the 5th node / 5th element / Adam Kadman / Aether)
10: "Day 9": Arm 2 (Svastika): Water and Earth - via 4 connections - exhale (release of novelty from centroid)

This traces the 10 possible node pairs via this "breath cycle". Given both trees are fall on progression 9 and 10 (day 8 & 9) these "branches" might just be the 10 Sephira. But two of those remain "untraced". These are node pairs 1-3 (a double inhale) and 0-2 (a double exhale). Perhaps they are Keter - a crown (above head/body) - sometimes said to be "Ayin" - nothing. And Yesod - the foundation and transparency of transmission. Serving here more of "silent" function?

So back to the idea of the star tetrahedron. If the first tetrahedron is something like the most basic topology / consciousness unit / monad, then a mirror / shadow / polarity completes it (as above so below; STO/STS; action and equal and opposite reaction; peak is balanced by a trough, heartbeat and breath itself etc.). This provides then an additional 10 progressions across all nodes, faces and connections "sephira") (via 6 edges + 4 to centroid):

Screenshot 2025-07-22 at 4.47.26 pm.png

As you can see this foms the 3-4-3-4 cuboctahedron, an Archimedean solid, also known as ‘vector equilibrium’ coined by Buckmister Fuller. He called that the zero starting point for happenings or nonhappenings.. "it is the empty theater and empty circus and empty Universe ready to accommodate any act and any audience". This describes how the "centroid" (Aether, Adam Kadman etc.) is no actually a point but a non-local, 4th dimensional geometry. So the "breath cycle only ever moves towards the centre but never full entering it.

The star tetrahedron also forms a cube. This provides a cubic boundary of 6 new faces and x,y,z directional space + growth vectors (inhale and exhale): up, down, left, right, forward, back If we follow the inhale/exhale it transpires as follows:

...11-20 (day 10-19) the phases of the mirror tetrahedron: from Kaf (כ) to Resh (ר) that ends with an "exhale"
21. Shin (ש): Up
22. Tav (ת): Down
23. Kaf Sofit (ך): Left
24. Mem Sofit (ם): Right
25. Nun Sofit (ן): Forward
26. Pe Sofit (ף): Back
27. Tsade Sofit (ץ): Seed growth in 6 directions.

There's a bunch of other fascinating connections that seem to unravel from this too. Will add more.
 

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  • Screenshot 2025-07-22 at 3.43.32 pm.png
    Screenshot 2025-07-22 at 3.43.32 pm.png
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To add these are the two-arm paths (1→0→5→3→2) & (3→0→5→1→2) that bear stricking similarity to the Svastika if represented in a 2D symbol. Also, notice the of the 10 possible node pairs (including the centroid)

Also, more detail to this progression, as a geometric topology, surfaces (faces) are distinct functions, and we could say, recursive patterns stemming from the first 4 points (0,1,3). This lead me to consider that 4-7 correspond to the faces and in Kabalistic terms - the 4 worlds. So if follow this through, symbolically at least, we have:

  1. "Day 0": Point: Fire (0) - inhale
  2. Day 1: Line: Air (1) - exhale
  3. Day 2: Surface: Water (2) - inhale
  4. Day 3: Volume: Earth (3) - exhale
  5. Day 4: Face 1: Fire (0,1,2) - Atziluth (emmanation) - inhale
  6. Day 5: Face 2: Air (0,1,3) - Beriah (creation) - exhale
  7. Day 6: Face 3: Water (0,2,3) - Yetzirah (formation) - inhale
  8. Day 7: Face 4: Earth (1,2,3) - Assiah (action) - exhale
View attachment 110552
Image above depicts how each "world" has a breath function too. This is further reiterated via next key events / function in Genesis: Tree of Knowledge and Tree of Life (inhale and exhale). So a decent into knowledge (1→0→5→1→0 fire and air) burns when not balanced with the exhale in life (3→0→5→1→2). We see that same metaphor in the Ark of the Covenant and the Holy Grail. In other words, truth without care, law without grace, structure without flow - is incomplete and casts us out of the garden of Eden.

Consider again the burning bush - it ignites without being extinguished, the breath YHWH that is fully "breathing". This is the complete 10 progressions (Decad / Tetraktys):

9. "Day 8": Arm 1 (Svastika): Fire and Air - via 4 connections - inhale (decent of strain to centroid - the 5th node / 5th element / Adam Kadman / Aether)
10: "Day 9": Arm 2 (Svastika): Water and Earth - via 4 connections - exhale (release of novelty from centroid)

This traces the 10 possible node pairs via this "breath cycle". Given both trees are fall on progression 9 and 10 (day 8 & 9) these "branches" might just be the 10 Sephira. But two of those remain "untraced". These are node pairs 1-3 (a double inhale) and 0-2 (a double exhale). Perhaps they are Keter - a crown (above head/body) - sometimes said to be "Ayin" - nothing. And Yesod - the foundation and transparency of transmission. Serving here more of "silent" function?

So back to the idea of the star tetrahedron. If the first tetrahedron is something like the most basic topology / consciousness unit / monad, then a mirror / shadow / polarity completes it (as above so below; STO/STS; action and equal and opposite reaction; peak is balanced by a trough, heartbeat and breath itself etc.). This provides then an additional 10 progressions across all nodes, faces and connections "sephira") (via 6 edges + 4 to centroid):

View attachment 110553

As you can see this foms the 3-4-3-4 cuboctahedron, an Archimedean solid, also known as ‘vector equilibrium’ coined by Buckmister Fuller. He called that the zero starting point for happenings or nonhappenings.. "it is the empty theater and empty circus and empty Universe ready to accommodate any act and any audience". This describes how the "centroid" (Aether, Adam Kadman etc.) is no actually a point but a non-local, 4th dimensional geometry. So the "breath cycle only ever moves towards the centre but never full entering it.

The star tetrahedron also forms a cube. This provides a cubic boundary of 6 new faces and x,y,z directional space + growth vectors (inhale and exhale): up, down, left, right, forward, back If we follow the inhale/exhale it transpires as follows:

...11-20 (day 10-19) the phases of the mirror tetrahedron: from Kaf (כ) to Resh (ר) that ends with an "exhale"
21. Shin (ש): Up
22. Tav (ת): Down
23. Kaf Sofit (ך): Left
24. Mem Sofit (ם): Right
25. Nun Sofit (ן): Forward
26. Pe Sofit (ף): Back
27. Tsade Sofit (ץ): Seed growth in 6 directions.

There's a bunch of other fascinating connections that seem to unravel from this too. Will add more.
Forgot to add this too - that star of David could be thought of as a 2d representation of the star tetrahedron. A couple related signals is the Hebrew alphabet can be traced across the star of David:

Screenshot 2025-07-22 at 7.19.48 pm.png

We often see both symbols together in eastern religious symbolism too.
1752478260245.png


My understanding (as above is that they are essentially symbolic of dual aspects of the same topology - that is structure and flow; Ark (box) and Grail (curve); law and grace, truth and care. But coming back to the point of this thread - ℚₚ (structure) and ℝ (flow)
Overall it points to a dual-domain topology that fuses continuous flow with discrete structure – Reality = ℝ × ℚₚ.

ℝ as our informational sense making experience of reality and as an ultrametric, p-adic tree-like form in ℚₚ for fixed logical organisation of all properties that make up reality. I realise I'm taking a lot of liberties with Ostrowski's theorem! But it does give us a powerful analogy for seriously exploring the Adelic algebra as a real contender for a kind of TOE that accounts for how and what we experience / measure in one formalism.
 
Q: Is that the only thing you want to remark about the crossing of the comets in front of the eye of Medusa?
A: Can you not picture all reality as a curving and bobbing journey through a transparent, undulating matrix mosaic?
Q: Alright: 'mathematics converts to sound in geometric measurements.' When we set up these figures...
A: Imagine an interlocking triangular mosaic in three dimensions.
If we consider n-simplexes, i.e. the pyramid family, as the "building blocks" of reality, does their self-duality capture the relationship between matter and consciousness?
 
If we consider n-simplexes, i.e. the pyramid family, as the "building blocks" of reality, does their self-duality capture the relationship between matter and consciousness?
Be curious your thoughts on my build on your ideas. Even to hear this is completely off target or simply has little relevance to this.
Q: How does one utilize the energies inherent in prime numbers in this respect? Do they represent frequencies or frequency relationships?

A: Verities.

Q: Is there any formula, or any thing about prime numbers that makes it easier to find them... anything about them that is unique?

A: Pyramidal.

Q: Pyramid relationships would help one find prime numbers?

A: Graph.

Q: A pyramid type graph. Okay, anything else about prime numbers? When you said that they were the 'dwellings of the mystics' I had an idea that a prime number could be a dwelling of a mystic because the individual would express in some manner a frequency that related in some way to a prime number. Is that somewhere along the line...? That mystics can traverse all densities because of frequency?

A: Something like that.
 
Be curious your thoughts on my build on your ideas. Even to hear this is completely off target or simply has little relevance to this.
I appreciate your contribution. However, it's difficult for me to assess the validity of your ideas, especially the mapping between mathematical structures and esoteric symbols. Generally, I try to avoid fitting esoteric symbols into my own reasoning, because I don't have enough knowledge to distinguish truth from obscure structures. It is very easy to be led astray. I want to stay as objective as possible, and hopefully derive some of these symbols a bit later (if possible), once I have built a stronger logical foundation.
 
Triangular numbers, which arise after summing natural numbers up to a number n, can be expressed in terms of a binomial equation.

a(n) = binomial(n+1,2) = n*(n+1)/2
1,3,6,10,15,21,..

So I experimented with binomial parameters to see what equations and sequences they would yield.

a(n) = binomial(1,0) = 1
1,1,1,1,1,1,...

a(n) = binomial(2,0) = 1
1,1,1,1,1,1,...

a(n) = binomial(3,0) = 1
1,1,1,1,1,1,...


a(n) = binomial(n,0) = 1
1,1,1,1,1,1,...

a(n) = binomial(n,1) = n
1,2,3,4,5,6,...

a(n) = binomial(n+1,1) = n+1
2,3,4,5,6,7,...

a(n) = binomial(n,2) = (1/2)*(n-1)(n)

0,1,3,6,10,...

a(n) = binomial(n,3) = (1/6)*(n-2)*(n-1)*(n)
0,0,1,4,10,...

Then, I tried to express prime numbers in terms of binomial equations such that, when an equation is evaluated at n=1, it outputs a prime. An interesting pattern appeared!

for p = 1: bin(n, 0)
for p = 2: bin(n+1,1)
for p = 3: bin(n+2,2)
for p = 5: bin(n+3,3) + bin(n,0)
for p = 7: bin(n+4,4) + bin(n+1,1)
for p = 11 bin(n+5,5) + bin(n+2,2) + 2*bin(n,0)
for p = 13: bin(n+6,6) + bin(n+3,3) + 2*bin(n,1)
for p = 17: bin(n+7,7) + bin(n+4,4) + 2*bin(n+1,2) + 2*bin(n,0)
for p = 19: bin(n+8,8) + bin(n+5,5) + 2*bin(n+2,3) + 2*bin(n,1)
for p = 23: bin(n+9,9) + bin(n+6,6) + 2*bin(n+3,4) + 2*bin(n+1,2) + 2*bin(n,0)
for p = 29: bin(n+10,10) + bin(n+7,7) + 2*bin(n+4,5) + 2*bin(n+2,3) + 2*bin(n,1) + 2*bin(n,0) + 2*bin(n,0)
for p = 31: bin(n+11,11) + bin(n+8,8) + 2*bin(n+5,6) + 2*bin(n+3,4) + 2*bin(n+1,2) + 2*bin(n,1) + 2*bin(n,1)

Notice how each equation has a higher degree compared to the previous one. Take for example the equation for p=7, bin(n+4,4) + bin(n+1,1), which equals (n^4)/24 + 5(n^3)/12 + 35(n^2)/24 + 37(n)/12 + 2. This is a polynomial equation of degree 4.

Now consider the equation for p=11, bin(n+5,5) + bin(n+2,2) + 2*bin(n,0), which equals (n^5)/120 + (n^4)/8 + 17*(n^3)/24 + 19*(n^2)/8 + 227(n)/60 + 4. This is a polynomial equation of degree 5, one degree higher than the equation for p=7. Each successive prime increments the degree of the equation by one! This is consistent with my hypothesis that each prime "opens a new dimension," like successive n-simplexes.

I added a bit more equations/evaluations (up to prime 53) so that we can see the pattern more clearly. Let's evaluate the equations at n=1. Here is each prime (on the left) with its corresponding numerical composition (on the right) based on the evaluation of its binomials.

1 = 1
2 = 2
3 = 3
5 = 4 + 1
7 = 5 + 2
11 = 6 + 3 + 2*1
13 = 7 + 4 + 2*1
17 = 8 + 5 + 2*1 + 2*1
19 = 9 + 6 + 2*1 + 2*1
23 = 10 + 7 + 2*1 + 2*1 + 2*1
29 = 11 + 8 + 2*1 + 2*1 + 2*1 + 2*1 + 2*1
31 = 12 + 9 + 2*1 + 2*1 + 2*1 + 2*1 + 2*1
37 = 13 + 10 + 2*1 + 2*1 + 2*1 + 2*1 + 2*1 + 2*1 + 2*1
41 = 14 + 11 + 2*1 + 2*1 + 2*1 + 2*1 + 2*1 + 2*1 + 2*1 + 2*1
43 = 15 + 12 + 2*1 + 2*1 + 2*1 + 2*1 + 2*1 + 2*1 + 2*1 + 2*1
47 = 16 + 13 + 2*1 + 2*1 + 2*1 + 2*1 + 2*1 + 2*1 + 2*1 + 2*1 + 2*1
53 = 17 + 14 + 2*1 + 2*1 + 2*1 + 2*1 + 2*1 + 2*1 + 2*1 + 2*1 + 2*1 + 2*1 + 2*1

If we collect the terms in bold, we obtain:

1 = 1
2 = 2
3 = 3
5 = 4 + 1
7 = 5 + 2
11 = 6 + 3 + 2*(1)
13 = 7 + 4 + 2*(1)
17 = 8 + 5 + 2*(2)
19 = 9 + 6 + 2*(2)
23 = 10 + 7 + 2*(3)
29 = 11 + 8 + 2*(5)
31 = 12 + 9 + 2*(5)
37 = 13 + 10 + 2*(7)
41 = 14 + 11 + 2*(8)
43 = 15 + 12 + 2*(8)
47 = 16 + 13 + 2*(9)
53 = 17 + 14 + 2*(11)

At first sight, it seems like we can infer the next prime from the previous prime(s). For example, if we follow the pattern, the prime after 53 will need to have this configuration:

P = 18 + 15 + 2*(X), X >= 11

We have an equation with two unknowns. However, we know that X has to be at least 11, but how do we find X? It turns out that the sequence 1,1,2,2,3,5,5,7,8,8,9,11,... corresponds to the number of odd composite numbers less than n-th odd prime.

The first few odd composite numbers are: 9, 15, 21, 25, 27, 33, 35, 39, 45, 49, 51, 55, etc. If we pick a prime, say 37, then X=7, and the equation is 37 = 13 + 10 + 2*(7), because there are 7 odd composite numbers below 37, namely 9,15,21,25,27,33,35. The paradox is that we first need to know that 37 is a prime number!

One way out is to find a formula which generates the next odd composite number and which doesn't depend on primes, but this is a tall order. Prime numbers are prime for a reason!
 
I appreciate your contribution. However, it's difficult for me to assess the validity of your ideas, especially the mapping between mathematical structures and esoteric symbols. Generally, I try to avoid fitting esoteric symbols into my own reasoning, because I don't have enough knowledge to distinguish truth from obscure structures. It is very easy to be led astray. I want to stay as objective as possible, and hopefully derive some of these symbols a bit later (if possible), once I have built a stronger logical foundation.

Thank you for your thoughtful feedback! I completely understand your preference for staying grounded in objective, logical foundations, and I appreciate your commitment to rigour. My exploration, while incorporating esoteric symbols, is primarily an attempt to unpack the "riddle’s" clues - by that I mean... prime numbers as “verities,” their “pyramidal” relationships, and the idea of a “graph” as a relational structure. I approached it through a lens that looks to connect mathematical structure to broader patterns.

But let me clarify how I see this tying back to the riddle and why I think it might offer value, even from a strictly mathematical or logical perspective...

The transcript detail points to prime numbers as fundamental “energies” or “verities,” suggesting they’re more than just counting tools... they might encode structural principles of reality. The mention of “pyramidal” and “graph” led me to consider geometric and relational frameworks, specifically the tetrahedron, as it’s the simplest 3D structure that forms a fully connected graph. This aligns with your observation about primes depending on preceding primes, forming a relational network where each new prime adds a “dimension” or vertex to the system. Your coordinate-based approach (e.g., mapping primes to vertices in higher-dimensional simplices) is a fantastic way to formalise this, and I see my tetrahedral model as complementary - it’s a specific geometric realisation of that relational logic in 3D, with the centroid potentially acting as a harmonising node.

By mapping 0, 1, 2, 3 (and the centroid as a stand-in for 5) to a tetrahedron, I’m exploring how these fundamental values might define a minimal, stable structure for encoding information or relationships, which ties back to the riddle’s hint about primes as “frequencies” or “frequency relationships.” The tetrahedron’s four vertices and six edges provide a concrete way to visualise dependencies, much like your directed graph where each prime relies on those before it. The “breath cycle” I described (inhale/exhale through node connections) is an attempt to model dynamic interactions within this structure, which could be interpreted as a purely mathematical process of information flow or transformation.

Where I diverge into esoteric territory (e.g., mapping to classical elements or Kabbalistic concepts) is an attempt to test whether this mathematical structure might resonate with patterns observed in philosophical or symbolic systems, as the riddle’s mention of “dwellings of the mystics” and “traversing densities” suggests a metaphysical dimension. I agree that this can feel speculative, and I share your caution about avoiding ungrounded assumptions. My goal isn’t to assert these mappings as definitive but to use them as a heuristic to explore whether the relational logic of primes and geometry might scale to describe broader systems - be they physical, informational, or even experiential.

For example, your insight about primes forming a simplex where each new prime adds a dimension is a powerful, objective foundation. My tetrahedral model could be seen as a low-dimensional case of that, with the centroid representing a meta-point that stabilises the system - a purely mathematical concept that doesn’t require esoteric framing. From there, we could ask: does this structure suggest a way to encode “frequencies” (as per the riddle) in terms of graph properties, like edge weights or connectivity patterns? Could the tetrahedron’s symmetry hint at a minimal unit of relational organisation, akin to how primes are indivisible building blocks?

I’d love to hear your thoughts on how we might further formalise the “pyramidal graph” idea in a way that stays grounded in mathematics but remains open to the riddle’s broader implications. For instance, could we define a function that maps prime dependencies to geometric properties (e.g., edge lengths or angles in a simplex)? Or explore whether the tetrahedron’s structure could model “frequency relationships” in a graph-theoretic sense? Your coordinate system is a great starting point, and I think combining it with a geometric or topological approach could yield some exciting insights into the riddle’s meaning.
 
I’d love to hear your thoughts on how we might further formalise the “pyramidal graph” idea in a way that stays grounded in mathematics but remains open to the riddle’s broader implications. For instance, could we define a function that maps prime dependencies to geometric properties (e.g., edge lengths or angles in a simplex)? Or explore whether the tetrahedron’s structure could model “frequency relationships” in a graph-theoretic sense? Your coordinate system is a great starting point, and I think combining it with a geometric or topological approach could yield some exciting insights into the riddle’s meaning.
Thanks for clarifying your intentions. If we consider primes as verities, then we should be able to combine them to build even more complex structures. This is where combinatorics enters the picture.
Q: (A) 1 2 3 are the first three prime numbers...

A: Yes, thank you Arkadiusz!!!! Laura is dancing around in wonderland, meanwhile all of creation, of existence, is contained in 1, 2, 3!!! Look for this when you are trying to find the keys to the hidden secrets of all existence... They dwell within. 11, 22, 33, 1/2, 1/3, 1, 2, 3, 121, 11, 111, 222, 333, and so on! Get it?!?!
The mysterious sequence given by the C's is a good starting point, but it's not clear how it continues. The numbers 1/2, 1/3, and 121 muddy the waters in the sense that it is not obvious how they fit with (1,2,3), (11,22,33), (111,222,333), etc. We are left with more questions than answers.

If we turn our attention to geometry, the problem becomes more tractable.
Q: (A) Okay. That answered my question. So, we are using the same thing, but for you it is more adequate or so. Now, I want to ask about mathematical modelling of gravity. The gravity that we know about is modelled by geometry of a curved space. Is the gravity that you are talking about, which is an expansion of this concept, capable of being modelled in a similar way: by geometry?
A: Geometry is the correct model.
Q: (L) Well... (A) What was this answer 'yes' to the changing of density and how it relates to what Sakharov was working on and how it connects to Kaluza Klein theories?
A: Both.

Q: (L) Well, I guess we are going to have to wait until I type it to make any sense out of it...
A: Geometry... pentagon and hexagon, algebraic equations...

Q: (A) Pentagon and hexagon algebraic equations... (L) What is the connection between the pentagon and hexagon?
A: Discover.
Q: (Ryan) Could sufficient chi flow organise not just the geometry of molecules, but also the subatomic structure of individual atoms, effectively transmuting elements?
A: Yes.
I think we are missing a general theory of shapes which would allow us to predict the energy or electromagnetic flow through each geometric arrangement.
Q: (L) Do the tetrahedrons spin within the sphere? Do these power points of the tetrahedron spin?
A: Energy fields flow in balance.
Q: (T) It describes a physics that transcends the densities.
A: So is pentagon.


Q: (T) So is the Pentagon? (J) A pentagon. (T) The pentagon shape. These are part of what humans describe as the sacred geometries.
A: Yes.
Q: (T) So, in that 'Bear' book that I have...

A: You as Atlanteans knew this, and lived by it in many ways. For example, the pyramid recharges by capturing exactly half the energy points, thus allowing a positive imbalance buildup to be captured, then expended.
Geometry seems to be intrinsically tied to sound. Concepts like tuning, resonance, and frequency suddenly have a deeper meaning!
A: In prime numbers, you will find resonance.
A: Mathematics converts to sound in geometric measurements. Why do you think the pyramid became a pyramid?
Q: (L) Multiple user necessity implies that a number of people must do the spiral. Is that correct?
A: No. Must hear and feel and understand precisely the same thing. The molecular structure of the rock, when properly sculpted sing to you.
Q: (L) Is it construction work?
A: Yes except that they are using sound waves to disintegrate rock in the crust under the ocean. This disintegration causes the atomic structure of the particles being disintegrated to completely disappear which has something to do with why those sounds are heard in that particular rhythm.
And we are back to gravity.
Q: (L) Does sound produce gravity?
A: Yes.

Q: (L) Can sound manipulate gravity?
A: Yes.

Q: (L) Can it be done with the human voice?
A: Yes.

Q: (L) Can it be done tonally or by power through thought?
A: Both.

Q: (L) Then, is there also specific sound configurations involved?
A: Gravity is manipulated by sound when thought manipulated by gravity chooses to produce sound which manipulates gravity.
Coordinates are one way of interpreting differences between shapes, but it would be great if we could describe the energetic flow passing through each geometric configuration. Bridging algebra with geometry would be helpful.
1753276710674.png
Geometers (like Schläfli and Coxeter) have invented ways of classifying shapes, but the meaning of the combination of these shapes with respect to electromagnetism remains a mystery. However, gifted dowsers (like T.C. Lethbridge) have been able to quantify energetic waves surrounding objects. Unfortunately, their insights have not been formalized into mathematical theories.
1753276074822.png
 
Thanks for clarifying your intentions. If we consider primes as verities, then we should be able to combine them to build even more complex structures. This is where combinatorics enters the picture.

The mysterious sequence given by the C's is a good starting point, but it's not clear how it continues. The numbers 1/2, 1/3, and 121 muddy the waters in the sense that it is not obvious how they fit with (1,2,3), (11,22,33), (111,222,333), etc. We are left with more questions than answers.

If we turn our attention to geometry, the problem becomes more tractable.



I think we are missing a general theory of shapes which would allow us to predict the energy or electromagnetic flow through each geometric arrangement.



Geometry seems to be intrinsically tied to sound. Concepts like tuning, resonance, and frequency suddenly have a deeper meaning!




And we are back to gravity.

Coordinates are one way of interpreting differences between shapes, but it would be great if we could describe the energetic flow passing through each geometric configuration. Bridging algebra with geometry would be helpful.
View attachment 110585
Geometers (like Schläfli and Coxeter) have invented ways of classifying shapes, but the meaning of the combination of these shapes with respect to electromagnetism remains a mystery. However, gifted dowsers (like T.C. Lethbridge) have been able to quantify energetic waves surrounding objects. Unfortunately, their insights have not been formalized into mathematical theories.
View attachment 110583

You’ve raised an really important point - it’s one thing to map a few numbers to a few shapes and call it meaningful, but that doesn’t yet give us a real framework for understanding energy flow through form. I agree too - without some underlying theory that ties the algebra to the geometry to the dynamics, it’s easy to stay in the realm of metaphor.

But here’s the thing I keep coming back to: if we take those numbers seriously (1, 2, 3, 11, 22, 33, 1/2, 1/3, 121, 111, 222, 333) they don’t look like random curiosities. They look like states. Modes of something deeper.

Because these numbers aren’t just values, what if they are actually positions!

Take 1, 2, 3: these are the most basic “keys” - single points, lines, planes. In geometry, they’re the vertex, the edge, the face. In music, they’re the base tones of any resonance system. They’re the foundations.

Then we look at 11, 22, 33: these are doubles, not just bigger numbers. Doubling here is interesting... in resonance it means the same frequency amplified, a standing wave reinforcing itself. In geometry it often means parallelism or nesting - again: two tetrahedra forming a star tetrahedron, two edges reinforcing a frame. It’s the difference between a lone tone and a chord.

Now add 1/2 and 1/3 - why could the sequence suddenly invert? Maybe they are like damping modes - subharmonics that slow or stabilise the flow. If you think of it like a breath (that I talked about above) this could be the “still point” between inhale and exhale, where energy compresses before it changes direction.

And then 121, 111, 222, 333: these are the cascades. 111, 222, 333 are tripled harmonics. Think about in sound, the third overtone. In structure, they’re recursive nesting - so a tetrahedron inside a tetrahedron inside a tetrahedron. But 121 is different. It’s a square of the doubled state (11²). It’s the balanced centre of Pascal’s triangle at depth two. In that sense, 121 feels like a hinge - it's possibly there as the state that allows the amplified system to settle into higher coherence.

So rather than being arbitrary, the numbers might sketch out that breath cycle:

Amplification (11, 22, 33) → Stabilisation (1/2, 1/3) → Grounding (1, 2, 3) → Expansion into higher coherence (121, 111, 222, 333).

It’s not a sequence of size but possibly it’s a "breathing" sequence of transformation.

Why does that matter? Because as you've been getting at - it should be measurable

So it could be modelled as a pyramidal graph - a tetrahedron with weighted edges and a centroid then compute its graph Laplacian. The Laplacian’s eigenvalues literally give us the vibrational modes of that structure. If the numbers in the sequence line up with those eigenmodes (or their harmonics), then its more than riddling - it could show that this “mystical list” matches the natural resonances of a simple polyhedral system.

From there, there's possibly more... Map each number to a Schläfli class (tetrahedron, square pyramid, star polyhedron). Use those binomial paths you talked about to describe how these modes combine (Pascal’s triangle, prime factors). Relate them to sound and field dynamics but not just metaphorically, but as actual wave‑modes of the shape.

Where does that leave us? Might not yet be a “general theory of shapes and energy flow,” but we can see the scaffolding of one?
- primes and binomials set the weights (algebra)
- tetrahedra, pentagons, hexagons provide the frames (geometry)
- laplacian spectra give us the flow modes (dynamics)

Perhaps starting to answer your point - how do we make sense of the energetic wave through a shape? We treat it like a resonant network - a structure whose numbers tell us how energy moves, amplifies, stabilises, and cascades. It’s not a complete solution, but it’s a real path forward:
- modelling the graph.
- compute its resonant modes.
- test them against the sequence.

And perhaps they match, this may begin to turn what looks like a puzzle into a principle. Still all speculative, but also where the excitement is - not in declaring we know what these numbers mean, but in building a bridge between number, form, and flow that can actually be tested.
 
You’ve raised an really important point - it’s one thing to map a few numbers to a few shapes and call it meaningful, but that doesn’t yet give us a real framework for understanding energy flow through form. I agree too - without some underlying theory that ties the algebra to the geometry to the dynamics, it’s easy to stay in the realm of metaphor.

But here’s the thing I keep coming back to: if we take those numbers seriously (1, 2, 3, 11, 22, 33, 1/2, 1/3, 121, 111, 222, 333) they don’t look like random curiosities. They look like states. Modes of something deeper.

Because these numbers aren’t just values, what if they are actually positions!

Take 1, 2, 3: these are the most basic “keys” - single points, lines, planes. In geometry, they’re the vertex, the edge, the face. In music, they’re the base tones of any resonance system. They’re the foundations.

Then we look at 11, 22, 33: these are doubles, not just bigger numbers. Doubling here is interesting... in resonance it means the same frequency amplified, a standing wave reinforcing itself. In geometry it often means parallelism or nesting - again: two tetrahedra forming a star tetrahedron, two edges reinforcing a frame. It’s the difference between a lone tone and a chord.

Now add 1/2 and 1/3 - why could the sequence suddenly invert? Maybe they are like damping modes - subharmonics that slow or stabilise the flow. If you think of it like a breath (that I talked about above) this could be the “still point” between inhale and exhale, where energy compresses before it changes direction.

And then 121, 111, 222, 333: these are the cascades. 111, 222, 333 are tripled harmonics. Think about in sound, the third overtone. In structure, they’re recursive nesting - so a tetrahedron inside a tetrahedron inside a tetrahedron. But 121 is different. It’s a square of the doubled state (11²). It’s the balanced centre of Pascal’s triangle at depth two. In that sense, 121 feels like a hinge - it's possibly there as the state that allows the amplified system to settle into higher coherence.

So rather than being arbitrary, the numbers might sketch out that breath cycle:

Amplification (11, 22, 33) → Stabilisation (1/2, 1/3) → Grounding (1, 2, 3) → Expansion into higher coherence (121, 111, 222, 333).

It’s not a sequence of size but possibly it’s a "breathing" sequence of transformation.

Why does that matter? Because as you've been getting at - it should be measurable

So it could be modelled as a pyramidal graph - a tetrahedron with weighted edges and a centroid then compute its graph Laplacian. The Laplacian’s eigenvalues literally give us the vibrational modes of that structure. If the numbers in the sequence line up with those eigenmodes (or their harmonics), then its more than riddling - it could show that this “mystical list” matches the natural resonances of a simple polyhedral system.

From there, there's possibly more... Map each number to a Schläfli class (tetrahedron, square pyramid, star polyhedron). Use those binomial paths you talked about to describe how these modes combine (Pascal’s triangle, prime factors). Relate them to sound and field dynamics but not just metaphorically, but as actual wave‑modes of the shape.

Where does that leave us? Might not yet be a “general theory of shapes and energy flow,” but we can see the scaffolding of one?
- primes and binomials set the weights (algebra)
- tetrahedra, pentagons, hexagons provide the frames (geometry)
- laplacian spectra give us the flow modes (dynamics)

Perhaps starting to answer your point - how do we make sense of the energetic wave through a shape? We treat it like a resonant network - a structure whose numbers tell us how energy moves, amplifies, stabilises, and cascades. It’s not a complete solution, but it’s a real path forward:
- modelling the graph.
- compute its resonant modes.
- test them against the sequence.

And perhaps they match, this may begin to turn what looks like a puzzle into a principle. Still all speculative, but also where the excitement is - not in declaring we know what these numbers mean, but in building a bridge between number, form, and flow that can actually be tested.

..but in a nutshell

Combinatorics
Sequence can be seen as binomial pathways - 1, 2, 3 as vertices, 11/22/33 as double‑paths, 111/222/333 as full nested combinatorial sums.

Geometry
Each number corresponds to a class of polyhedral forms:
  • 1/2, 1/3: Inversion / fractional scaling - these represent contractions of the base form, like the inner scaling steps in a self-similar fractal (shrinking modes that prepare for re-expansion).
  • 11, 22, 33: Resonant doubling - these are parallel or mirrored structures, akin to nested tetrahedra forming a star‑tetrahedral frame (edges or planes reinforcing each other in phase).
  • 121: Squared coherence - this is a bridging lattice, where doubled edges are orthogonally reinforced, like forming a square‑pyramidal or layered tetrahedral lattice that balances two amplified states.
  • 111, 222, 333: Harmonic cascades - these describe recursive nesting, where the base tetrahedral unit proliferates into higher‑dimensional compounds (e.g., Coxeter’s {3,4,3} cuboctahedral lattice - the filling geometry inside a star‑tetrahedron).
Energetic flow
Treating the tetrahedral graph as an oscillator network, these numbers aren’t just labels but mode identifiers. Each mode has a different energy flow pattern, which could in theory be modelled using the graph Laplacian (eigenmodes = natural frequencies).
 
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But here’s the thing I keep coming back to: if we take those numbers seriously (1, 2, 3, 11, 22, 33, 1/2, 1/3, 121, 111, 222, 333) they don’t look like random curiosities. They look like states. Modes of something deeper.
A: Yes, thank you Arkadiusz!!!! Laura is dancing around in wonderland, meanwhile all of creation, of existence, is contained in 1, 2, 3!!! Look for this when you are trying to find the keys to the hidden secrets of all existence... They dwell within. 11, 22, 33, 1/2, 1/3, 1, 2, 3, 121, 11, 111, 222, 333, and so on! Get it?!?!
Initially, what confused me is that this sequence was not ordered. 1/2 and 1/3 suddenly appear and then 121, followed by 11 again, which break the monotonously increasing logic I assumed. The C's suggested that using a number system based on primes is preferable, and that zero was an optional symbol that wasn't required to be explicitly part of the number system.
Q: (A) I have a question that goes back more than a year ago when you were speaking about numbers 1, 2, 3; how important they are. You gave some examples: 1,1; 2,2; 3,3; 1,1,1; 2,2,2; 3,3,3; 1 over 2 or 3; 111, 222, 333; the point probably being that everything of significance is related or will come out to 1, 2, 3 or combinations thereof. However when I tried to understand this mathematically, I noticed that you never used zero. In math, any number system, uses zero. 101 is also a way to code something. Why did you omit zero? What was the reason?
A: The self-cancellation factor allows zero to appear in any sequence if needed. What does 0 represent?

Q: (A) In any number system, we use zero because any number system is based on zero and some digits. So, whenever we code numbers...
A: But what does it represent?

Q: (A) It tells us that, at any given place we have zero of the given unit. For instance, when I have 10, it means that I have one ten and zero ones. Without zero, ten would not exist.
A: But can one not insert 0 where one needs to?

Q: (A) Of course one can insert zero where one needs to the same as one can insert 3 or 1 or 2 when one needs to.
A: No. Zero is what?

Q: (A) Zero is one of the integer numbers. (L) Zero is not a number. (A) Zero is a number. (L) No it's not. (A) Yes. Zero is a number. Minus 1 is a number, plus 1 is a number... (L) But zero is not. (A) Zero is a number. (L) Zero represents 'not.' (A) When you subtract 1 minus 1, if you say zero is not a number... (L) But that is an example of self-cancellation!
A: Yes. When one subtracts one from one, one is left with nothing. Therefore, in real terms, zero is potentially evident everywhere.

Q: (A) How would I write 10 without using zero? Without using zero, 10 would be 1. (L) Or ten ones.
A: Or 9 + 1. 11 - 1.

Q: (A) But the point is that 11 - 1 is the same as 12 - 2, is the same as 13 - 3, and it is very silly to just pretend that it does not exist!
A: Nobody is pretending that it does not exist, it is everywhere. Another numerical system could represent "10" just as accurately by inventing another number to represent that quantity.

Q: (A) So, when you were using this 11, 22, 33, and so on, were you having in mind binary number system based on two numbers or ternary number system based on three numbers?
A: Either/or.


Q: (A) Could it have also been a decimal system?
A: Decimals represent the "floating factor."

Q: (A) I was asking whether you had in mind binary or ternary and you say either/or. So it's not so important, I understand, whether it is either. But, perhaps, when you say 'either/or' about my question, you could also say either/or about anything else. For instance, a number system based on 4 numbers.
A: Yes.

Q: (A) What's wrong with 4?
A: Because 4 is not prime.

So here is a bijective base-3 system in comparison with our standard base-10 system.

Base-3
(no zero)
Base-10
(with zero)
1
1
22
33
11
4
125
136
217
228
239
3110
3211
3312
11113
11214
11315
12116
12217
12318
13119
13220
13321
21122
21223
21324
22125
22226
22327
23128
23229
23330
31131
31232
31333
32134
32235
32336
33137
33238
33339
111140

11 (one-one) is equal to 4 (four). 121 (one-two-one) is equal to 16 (sixteen). In our standard base-10, 11^2 (eleven squared) is equal to 121 (one hundred twenty-one), but 11 (eleven) isn't a square compared to 11 (one-one) in base-3.

11 (one-one, i.e. 4), 22 (two-two, i.e. 8), and 33 (three-three, i.e. 12) keep the same ratios if we translate them to base-10, i.e 11 (eleven), 22 (twenty-two), 33 (thirty-three). 4/12 = 11/33, 8/12 = 22/33.

Then, if we consider the transcripts, much is said about 11, 22, 33... and it seems to strangely apply to both bases until the C's say "both times 2 is your square, my dear. In other words, perfect balance," which is confusing. Did they mean "both times 2 is your square" as in "2 x 2" which equals 4, which translates to 11, a square number in base-3? Or did they mean 11 (eleven) times 2 which is 22 (twenty-two)... but how is 22 (twenty-two) a square?
Q: First of all, this session on 11/11/95, the question was asked - you were talking about matrixing Gemini and Aquarius, the 11th and 3rd houses of the zodiac - and I made the remark that 33 could represent... giving my idea... and you answered 'Medusa 11.' I'm assuming loosely that your answer, Medusa 11' was to the question of what 33 represented. So, Medusa 11 was the answer?
A: 1/3 of 33.

Q: Medusa was 11 of the 33. So that means that there was 22 of the 33 that was represented by something else, is that it?
A: If you wish to perceive it as such.

Q: Okay, well then, is my perception erroneous?
A: The pathway chosen is fruitful, but do not suppose the terminus to have been reached.

Q: Well, Medusa 11 is one third of 33, what are the other two thirds. (A) I believe, that in general, they will try to take you out of this idea of 33. They never, by themselves - I am not sure that the 33 is right...
A: 33 is right, but what it means is complex and fluid in nature.
Q: Okay, one interesting thing that we just discovered was that Hyakatuke and Hale Bopp both crossed the eye of Medusa, the star Algol, on April 11th exactly one year apart. What is the significance of this?
A: You must remember mosaic, matrix... When you are on the verge of quantum changes or discovery, the realities begin to reveal their perfectly squared nature to you.

Q: Is that the only thing you want to remark about the crossing of the comets in front of the eye of Medusa?
A: Can you not picture all reality as a curving and bobbing journey through a transparent, undulating matrix mosaic?

Q: Well, do you have anything else to say about Andromeda? (It's VERY HOT in here!) Okay, Medusa 11. So, this was 11 of the 33, and assuming that you were not saying that there were 11 heads, but that Medusa was one of three heads, is that what we are getting at here, that there are three heads and Medusa was one?
A: Or both times 2.

Q: What do you mean? I don't understand.
A: Both times 2 is your square, my dear. In other words, perfect balance.

Q: Okay...
A: No! Ponder, do not jump around so much, lest ye lose the chance to learn!

Q: So, Medusa represents both heads times 2, and that is the square and balance. But that is only 22 or 121. So where does the 33 come from?
A: All these 1s 2s and 3s... hmmm...
Finally, the number 12 (twelve) is apparently also significant, and when we translate it to base-3, we get 33 (three-three)... talk about symbolism!
Q: (L) See! You could save my reputation! Okay. Ark is ready to meet with Santilli and we think we should be able to offer him a few clues derived from the sessions to inspire greater confidence so could you give us said clue. (A) In this session with Santilli there was repeated at least twice the term 'matrix.' Laura made a comment that maybe it was a three dimensional matrix. So I was thinking about this matrix and I have two possibilities. If it is related to the number 3, it can be a matrix that is flat and 3 by 3. Or, it can be any matrix that is three dimensional rather than flat. Which of these, if any, is the concept mentioned in the session?
A: Three dimensional 12 by 12.

Q: (A) 12 by 12 by 12?
A: Yes.


Q: (A) Why number 12? What is so particular about number 12?
A: Try it and see.
 
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