From: www.BillHowell.ca

To: Dan ...

Subject: RE: Overlapping circles in [myth, religion, math]

Date: Tue, 16 Apr 2024 20:04:18 -0600

NUTS! I forgot to include Edo Kaal's "Structured Atom Model, which actually USES non-overlapping proton spheres (with intervening electrons - he doesn't say of torus shape) as a basis of his concept to completely replace Quantum Mechanics and put the nucleus of the atom on a [rational, scientific] basis!

Kaal Structured Atom Model vs Quantum Mechanics

(in case that link fails, copy-paste the WHOLE text : http://www.BillHowell.ca/ProjMajor/Electric Universe/Kaal SAM nucleus/Kaal Structured Atom Model vs Quantum Mechanics.html

Also : NO neutrons, now [weak, strong] forces, electrostatic. He doesn't really discuss gravity, given his nuclear focus (for which gravity is irrelevant!).

I also mention on that webPage :

Sierpinski fractal tetrahedra: "... Things just seemed to blow up into fireworks this morning while doing a minor update to my draft webPage on Kaal's "Structured Atom Model" (SAM). I was trying to find my notes from circa 2012-2017 giving the name ("Hoh...?" or something), and references to an amateur's presentation to the Natural Philosophy Alliance" (before it became the "Natural Philosophy Society", I think). ... His concept was the early stages of an intent to replace Quantum Mechanics (QM). It only had 1 arbitrary parameter, if I remember correctly, compared to something like 20 for QM? ..." (taken from one of Howell's emails, 15Jan2024)

However, I suspect that I haven't updated my website since I made major changes to these webPages... plus I've probably forgotten many other key points.

Bill

-------- Forwarded Message --------

From: www.BillHowell.ca

To: Dan

Subject: Overlapping circles in [myth, religion, math]

Date: Tue, 16 Apr 2024 19:50:25 -0600

I did a quick webSearch on the topic of concentric circles in [myth, religion, math], which I hadn't heard of before. I really only looked at one webPage of direct relevance (and that was well put together), although there are many more:

12 Sacred Geometry Symbols & What They Mean:

Discover the ancient powers and uses of these geometric shapes

Co-authored by Sophie Burkholder, BA Reviewed by Joseph Meyer

Last Updated: April 3, 2024 Fact Checked

Sacred Geometry Symbols & Meanings |Understanding Sacred Geometry |Video |Tips

- Whether you’re aware of it or not, sacred geometry really is all around you.

Mathematically, historically, and spiritually, the impact of sacred geometry symbols on the ancient and modern worlds is irrefutable. While some people call it the language of the cosmos, the basic idea of sacred geometry is that certain shapes are the blueprint for all life in the universe. In order to fully understand sacred geometry symbols, their meanings, and how they came to be, read below for a comprehensive guide on these mystical mathematical shapes.

This page shows several symbols with circles, overlapping or not, plus a few other interesting ones. The webPage links four of these directly to Christianity (plus other faiths) :

- Vesica Piscis is related to Christianity as the "fish symbol".
- "...Seed of Life is made up of seven intertwined circles, creating a simple,
symmetrical pattern that’s reminiscent of a flower:
- In religious texts, the seven circles in the Seed of Life represent the seven days in which the world was said to be created.
- Consequently, the powerful symbol appears in prayer books and the architecture of religious cathedrals, temples, and mosques. ..."

- The Tree of Life is represented in a geometric pattern with ten interconnected circles,
with 22 linear paths connecting each one.
- This symbol has been used across many cultures and belief systems, especially in Jewish, Christian, and Hindu faiths.
- The Tree of Life can be found in religious symbols such as the Kabbalistic Tree of Life and the Biblical Tree of Life in the Garden of Eden.

- Metatron’s Cube is a highly complex symbol made up of 13 circles, all of which are
encompassed by a larger circle and lines linking the center of each circle.
- Metatron’s Cube borrows its name from an important archangel in Islamic, Judaic, and Christian texts.[10]
- Some believe that Metatron’s Cube holds the keys to the creation of the universe, just as the Archangel Metatron was thought to.
- By honoring and understanding Metatron’s Cube as a sacred symbol, believers hope to connect with the archangel’s deep wisdom and knowledge.

- The Grid of Life is composed of 64 individual tetrahedrons and serves as the masculine
counterpart to the Flower of Life. Some people believe that, if researched properly, the Grid of Life can reveal unknown information about the space-time continuum.[11]
- The Grid of Life is also significant because of its connection to the number 64 which, according to sacred geometry, symbolizes the interconnectedness of all things.
- This symbolism is largely due to the number 64’s reappearance throughout the natural world, technological advancements, and religious texts.
- 64 is the number of codons in human DNA, tantras in Hinduism, and generations between Adam and Jesus, to name a few of its notable appearances.

You specifically commented on 64 interlocking circles, not tetrahedra as described above, but perhaps other refeerences use interlocked circles?

I was not familiar with the symbols listed above, but other symbols that are listed amont the "15 most sacred" I have long known:

- The Torus symbol resembles a vortex-like structure that’s thought to appear in every part
and piece of the universe. Symbolically, the Torus represents a continuous flow and is associated with auras, chakras, energy flow, infinity, and the cycle of life.

The torus, although well known, is NOT central to conventional physics, but several authors that I follow use it fundamentally, notably:- Bill Lucas's "Universal force" theory attempts to replace all physics on a solid basis, but is not widely accepted. I put perhaps a full year of work or more into my work to re-deriving his equations, but am stuck becasue I was plagued by may errors and need a formal theorem prover that is [auditable, credible] (which is a tougher challenge than the physics!!). I still think his ideas (based on other people and his own interpretations) to be credible and serious, but confidence only comes from step-by-step re-derivations in detail. Embarassingly, I still haven't built a series of webPages describing my project on Lucas's theories.
- Both Lucas and a very few others over the last ~120 years (it would take time to find names that escape me now) use the torus as the structure of the electron, combined with the protons in strange 3D arrangements for each element (atom). There are NO neutrons - these do NOT exists as fundamental particles, but as nuclear associations of electron-proton pairs (sort of) which decay extremely rapidly outside of the nucleus.

- Platonic Solids have faces that are all the same size, edges that are all the same length,
and angles that are all the same degree.[16] There are five Platonic Solids in total, each of which is associated with a different element.[17]
- Cube: Six square faces, represents the Earth element.
- Tetrahedron: Four triangular faces, represents the Fire element.
- Octahedron: Eight triangular faces, represents the Air element.
- Dodecahedron: Twelve pentagonal faces, represents the Aether element.
- Icosahedron: Twenty triangular faces, represents the Water element.

- The golden spiral is a visual way to represent the Fibonacci sequence.
To calculate the Fibonacci sequence, one calculates each new number by adding together the preceding two integers.[19]
- This formula results in a proportion, also known as the golden ratio, that is seen throughout nature and used to design architecture and digital interfaces.
- In nature, the golden spiral or ratio can be found in flower petals, pinecones, tree branches, and, famously, seashells

**1872-2020 SP500 index, ratio of opening price to semi-log detrended price**), and**webPage.**(ongoing work maybe)

But the "Sacred-Geometry-Symbols" webPage leads me much [deep, broad]er into many themes that I don't know well. One exciting find via this path was Johannes Kepler (he keeps popping up!).

- There are five 4-D geometric shapes that are essentially the 4-dimensional versions of the Platonic Solids. These shapes, also known as regular convex polytopes, are called the tesseract (4-D cube), pentachoron (tetrahedron), the 16-cell (octahedron), the 120-cell (dodecahedron), and the 600-cell (icosahedron).