Kabbalah and holons
A fractal is close to the idea of holon, as it is a part that represents a whole at the same time.
A holon is something that is simultaneously a whole and a part. The word was used by Arthur Koestler in his book The Ghost in the Machine (1967, p. 48) and the phrase to hólon is a Greek word preceding the Latin analogue universum, in the sense of totality, a whole.
A holon is a system that is an evolving self-organizing dissipative structure, composed of other holons, whose structures exist at a balance point between chaos and order. It is sometimes discussed in the context of self-organizing holarchic open systems (or, SOHO systems).
The cosmos can best be understood as an endless sequence of wholes within wholes, each one a complete entity – a stable and intermediate form both autonomous and integral to another holon within a hierarchy.
Karen French posits the Holon of concentric circles as a representative of the dynamics of time.
Infinite tetrahedron grid
(See more about fractals below)
The infinite-dimensional infinite tetrahedron grid is made up of lower-dimensional infinite tetrahedron grid fractals which are made up of lower-dimensional infinite tetrahedron grid fractals and this repeats infinitely until it reached the 0th dimension and this is a representation of a holon.
Infinity
The infinity in infinite tetrahedron grid is 9xen which is the biggest infinity that is possible, 9xen is an infinity that is always growing it is a fractaling infinity therefor it is a holon. 9xen is a growing equation where it is 9 recurring which is infinite 9's and each 9 is 9 recurring and then all those 9's are recurring and this fractals 9xen times and never stops.
Creation of Holons
The dynamic membrane background can be understood as a Riemann Space.
All started with a zone (sphere) with an unbreakable dynamic membrane. On the left is shown how a HOLON is created. It is fact very simple. Two parts join in a new unity. But that Unity is a UNION. In the image on the left you see how the yellow active (male) tube penetrates the blue passive (female) tube. The result is a new zone B(a). That zone is called a HOLON. That holon has "structure" and is a "3D-Space".
Till we introduced this holon engineering concept the holons were a type of abstraction which explained a hierarchic interconnectivity. Interconnectivity is an important aspect in all religions. General Jan Smuts described an abstract holistic connectivity. In 1967 Arthur Koestler described the Holon - still an abstraction - as a "self-assertiveness tendency" (wholeness) as well as an "integrative tendency"(part). We proposed an engineering picture, an infolding gravity mechanism, to explain a holon, and a concept that proves the complete interconnectivity in our Universe, and thus also between humans and all aspects of nature.
The dynamic membrane background can be understood as a Riemann Space.
The holon concept can explain topologically the essence of Kabbalah. The Kabbalistic ABSOLUTE (or Hinduist Brahman) can create by penetrations of itself a three-layered holon. That gives the three Ain Voids, namely Ain, Ain Soph and Ain Soph Aur. The dynamic interactions between those three - still powered by the Absolute (Parabrahman) and still being Membrane - will caused from and/or between these layers a progressieve chain of more complex sub-holons by pelastration (penetration) actions.
In the holon concept "ALL" starts with a 2D-zone (sphere) with a non-breakable membrane. From experience and observation we know that our universe is a moving, highly dynamic system. This Prior-geometry has no shape, only oscillating boundary. You can say that it is chaotic and fuzzy. This Prior-Geometry is NOT a Holon, because it doesn't contain structure, nor history, not time. It is the potency of Everything. It is genderless.
In the top image we explained how the yellow active (male) tube penetrates the blue passive (female) tube. The result is a new zone B(a). So FROM a GENDERLESS system new ENTITIES WITH EMBEDDED DUAL ASPECTS are created.
Starting from an unbreakable and almost infinite stretchable membrane several zones are created. These peaks can penetrate each other in zillions of ways.
Since the membrane is unbreakable a new multi-layered zone is formed on every pelastration. A holon contains always the values/structure of the previous zones which created him. Holons can interact and combine to more complex holons. Under influence of internal oscillations between the layers new inside sub-holons can be made. This can also happen due external outside holons. The below image shows the holon B(a) can create five different types of new holons in which B(a) is the active holon. Very important is that we see something unexpected: The number of layers may differ!
Figure 7 shows a more complex combination of C(ba) pelastrating B(a), but the inverse B(a) pelastrating C(ba) will give a different layering. The attentive reader will say that the latter is impossible since B(a) is already embedded in the middle of C(ba) ... which is correct ...but ... the tube A may create a second tube on it's surface and that can pelastrate B on another location! We can say that unique pelastration combinations in cosmology can be expressed by the Catalan numbers.
These principles of building up of holons gives us after only 5 steps next 22 unique holon types. Each of these holon type has a unique layering, so they vibrate each in a unique way.
This image is based on the basic holon 2* on the inside of the membrane sphere. That gives 22 possible different holons. There is also a self-pelastrating basic holon 2° on the inside but this is not represented on the image. That 2° holon type gives also 22 possible different holons. Then there are two other basic holons (2' and 2") at the outside of the membrane sphere. They also can create each 22 different holon types. We can say that some of these 88 basic holons make the fundamental particles. The more layers they have the more mass they will have, and less flexibility they will have.
Next image shows on the inside and the outside the first 8 different holons the basic holon 2* can make after 4 building steps + the basic holon 2°. So holons prove us the interconnectivity of everything with everything ... a full holistic approach.
Kabbalah
The central picture in Kabbalah is the Tree of Life containing 10 sefirot and 22 paths. This design was derived from concentric circles (The Bahir). The concept of the tree is to represent how universal energy (Kether) transforms by emanations into the World (Malkuth). The Tree is about the "manifested" Universe, which is in Kabbalistic view - based on three voids (unmanifested) which come from The Absolute.
How can we translate this ancient abstract or mental images of Kabbalah using the engineering design of topological holons ? Firstly the Kabbalistic ABSOLUTE (or Hinduist Brahman) can self-create by a penetration of one of it's other parts a local three-layered macro-holon. The three layers are the 3 Voids, namely Ain, Ain Soph and Ain Soph Aur.
This is the fundamental IMAGE of the GENESIS (Creation). This "image" (engineering design showing an energetic process) will be repeated in ALL lower (more complex) emanating systems. This is the process of genesis (formation). This is ,in example, how fundamental unions ( called particles) like photons, are created. This is the fundamental universal energy coupling process, or the fundamental entanglement process. This is what Quantum mechanics tries to explain with magic quantum entanglement.
Secondly, there are four different types of such macro-holons possible on the spherical membrane. In each of these four worlds dynamic interactions happen. They are caused by the dynamics of superiour membrane. On and/or between these three Ain-layers of each world - and still powered by the Absolute and still being Membrane - a chain of progressive more complex sub-holons can be "made" by pelastrations. Next image shows that there are 22 possible sub-holons possible.
Genesis 1:26 - God said, 'Let us make man with our image and likeness. Let him dominate the fish of the sea, the birds of the sky, the livestock animals, and all the earth - and every land animal that walks the earth.' 1:27 - God [thus] created man with His image. In the image of God, He created him, male and female He created them.
But how can be visualized the Tree of Life? The above image shows the most simple combinations, from which more complex (more-layered) holons can deploy.
The Tree? After a certain analogy with the three derm-layers developing in the human embryo's - endoderm, mesoderm and ectoderm - we can look to the middle Ain, the Ain Soph, as the most important creation-layer - similar to the mesoderm (middle layer). Or it's possible to call the Ovum (embryo itself as a manifestation on the Ain Soph positioned inside the Womb (Ain Soph Aur). There is a lot to say here, and I will do it later, but I limit myself now to state that the Ain Soph is essential.
In the holon realm the Tree can be seen as a union of dynamic multilayered tubes which start from one or more of the Ain-layers, and where these tubes - by progressing - receive more and more layers. The penetration through the Ain Soph layer by the three superior sefirot (together one three-layered tube) gives an extra cover over this tube with is then called Daath (the Abyss), or the secret sefira. We looking from below cannot see behind. From the Ain Soph layer another 3-layered tube (three sefirot) will descend, which is penetrated by the middle (4-layered) tube, adding six extra covers. After two additional penetrations (adding 6 + 6 Layers) the Malkuth sefira (The World) is "made", having 22 covers (Paths). This is our actual Universe where the tree gives fruits (sub-holons), which have inside "seeds" again.
There are alternative designs possible. But all enfoldings/layerings - representing levels of increasing energy compactification - are composed and caused by the upper dynamic Membrane. In example, in next alternative design is shown how a descending "snake" creates Malkuth.
Another design - I personally prefer - is next one. It shows that Malkuth is positioned inside /centered into a womb that is made by the fermionic snake. There are 22 paths which are the merger of bosonic actions (the straight decending pillars) and the fermionic snake. You see that always the same Universal Principle (The universal CROSS, the mathematical addition) is used, which is that of merging by dividing. Straight down motion can be called a bosonic action (energy related), and a lateral motion can be called a fermionic action (matter related).
In this image the Letter Bet (a Container, a House) is essential. The Large Bet is the first letter of the Bible. Above three designs show in essence how two type of forces - an active one and a passive one create the World by their different orientation. In this topological approach by adding more and more layers - thus by having more complex holons - mass (weight) is created and parts of universal energy is locally stored (like in capacitors/batteries). When a holon decays - depelastrates (dies) - the unified energies become again separate energies of an higher level. More complex holons - above a certain measuring threshold (like these of the human sensing systems) - will be called 'Photons and electrons" and "Matter" and will be visible or measurable. Below the threshold the hidden elastic connections can be called Attraction (Gravitational effects).
Finally I give here in next animated image my topological interpretation of the first two days of the Genesis, namely Genesis 1:1 till 1:8.
At the end of the animated image I show that the First (neutral) Energy can be split in two types: Enm (Energy not manifested) + Em (manifested Energy). So E = Enm + Em. Where Em = M (massa) x C^2. However the two C's are not the same. One C is the hidden "dark" energy/light, the other the light (photons) we see and observe.
This topologic approach is in the line of the original geometrical thinking of Riemann, Clifford (Energy and matter are just different types of curvature of space) and Einstein (deformations of spacetime) , but now - for the first time - explains how the emanations in the Tree of Life can happen, where the membrane is the mediator of vibrations and all holons and sub-holons are still Membrane. In religious terms: "God is everywhere and we are part of God." or in more scientific terms: "We are enfolded/layered Membrane"
Fractal
Holograms, tori and the vector equilibrium matrix found by Buckminster Fuller all relate with holons and with the irrational but economically distributing spiral built on phi. Organisation is how the different parts of the system and arranged in relationship to each other. In the natural world, while organization might appear to be chaotic, broad underlying patterns based on fractals and on what some call "sacred geometry" emerge. A holonic map is a fractal map of perceptions represented as holons, forming a holarchy of perceptual information. A holarchy is a connection between holons, where a holon is both a part and a whole.
If we wish to understand the universe, we’d better grok how it’s structured. However unfathomable its energies, processes and outcomes, the whole scheme of life can be understood in terms of patterned repetition. An example of the fractalated nature of the Universe is that the structure of an atom, with electrons orbiting its nucleus, is exactly that of the Solar System, with planets orbiting the Sun. The universe is nested, not unlike Russian dolls, holon within holon within holon — from the Pure Intelligence of Life to the fullest expression of Life (That’s where we come in!). Each level has its own vibratory band, meaning its defining density, with Earth-density being the limit of Reality’s manifestation — which is why the wise have throughout time referred to human beings as “the crown of Creation.” Thus is Creation’s pristine architecture achieved — from its most rarified inner stratum to its most expressed stratum — each stratum holonically whole. Creation is arted/crafted — from nebulae to quarks — in unbelievable perfection of design. Our Universe is omni-directional, inter-connected, inter-penetrating and ultra-holographic.
Sacred geometry fractals
There is a wealth of good literature on this subject; it’s always fascinating how nature propagates the same essence regardless of the magnitude of its expression…our spirit is spaceless yet can manifest aspects of its individuality at any scale.
A Fractal is a repetitive geometric pattern that can be scaled to any size, extremely small to large. The scale may change but the ratio remains constant. The same repetitive patterns that are found in the Platonic Solids that fit within each other are fractals. That fractal pattern is what shapes the atom, the smallest unit of matter that defines the chemical elements. That same atomic structure behind the fractal pattern is what shapes our planets, stars and the Universe. The inner structure of a fractal is reflected identically in its outer structure, it is the same geometric pattern repeated. A fractal means fraction which indicates that it is a fraction of the all, each piece is holding a reflection of the part of the whole. The fractals of the Electromagnetic Field energy interconnect with everything through multiple layers of Morphogenetic Fields repeating their fractal pattern in many dimensions within the Universe and are the basic building blocks of the Holographic Universe.
Sacred geometry and fractal geometry are energy patterns that can show us how life and reality work at the supernatural level. If you comprehend how these geometries are used to create matter and life at the fundamental levels, you should know that the Universe wasn’t the result of an accident; rather it was created by the Prime Creator. The fact that sacred geometry and fractal geometry contain simple and complex mathematical formulas is strong evidence that reality and life are possible because of the Prime Creator. These mathematical formulas weren’t created by scientists. Instead, they were rediscovered when scientists started playing with mathematical formulas.
Sacred geometry and fractal geometry are some of the blueprints of Creation. These geometries are used to direct light (energy) into specific patterns, and therefore allowing them to shape matter into specific forms. On every scale of reality, whether it is the atomic world or the material world, everything is affected by sacred geometries. The structures of our DNA, the shapes of clouds, the patterns of snow flakes, the cornea of our eyes, the shapes of crystals, the star we spin around, the galaxy we spiral within, and all life forms emerge out of geometric patterns and codes.
Fractal waves
Fractals can be turned into waveforms and if we apply this to the universal wave function we would get the infinite tetrahedron grid fractal which would be one face of the higher dimensional infinite tetrahedron grid which is the infinite curve superstring fractal membrane.
Why 12 keys/12 vibrational dimensions?
12 Note Subdivision
If you take any note and play 12 perfect fifths in any one direction you come back to the same note (albeit in a different octave and with a tiny tuning difference). We have Pythagoras for this discovery to thank.
7 Note Subdivision
If you play any note and then stack 6 additional perfect fifths on top you get the notes of the major scale (Ionian). They’re super spread out but if you bring them into one octave then you have the major scale. Sure depending on WHICH note you start on this scale can be the Ionic (Major), Doric, Phygian, Lydian, Mixolydian, Aeolian (Natural Minor) or Locrian. These seven scales can also be referred to as ‘Heptatonia Primera’. When you play though any of these Heptatonia Primera Scales it takes you seemlesly from one octave to the next. Of important note: you use a mixture of half and whole steps, otherwise known as hemitonic.
Why the major scale
Because you can create three triads using it forming the three musical functions: Tonic, Sub-Dominant and the Dominant. Those chords are the basis of most western music. The tonic is the 4,5 and 6th partial of the overtone series, i.e. the ‘home’ chord. The dominant is the chord which when played in it’s seventh form uses the tritone to ‘force’ resolution back to the tonic and the sub-dominant is the reflection of the dominant triad chord on the undertone series. The purpose of the subdominant chord is to allow music to be lead astray from our ‘home’ tonic area - this provides a bit of drama. The purpose of the dominant chord is to provide a way back to the tonic.
Anyways, long explanation, the major scale (Ionic) is the only scale which gives us the notes to be able to play these three chords.
Why 7 white and 5 black
So once you’ve got the major scale you can see/hear that the scale has two different kinds of steps, whole and half steps. If you fill in all of the whole steps with additional half steps you get the chromatic scale - which is the other way to get around all of the notes. The first way was to play 12 fifths on top of each other. When you’ve filled in these half notes you can then be able to play 12 different major scales. The 7 white keys correspond to C major for several reasons. White with superimposed black notes is easy to see. The C major scale is the one which we’ve decided to notate with no flats/sharps. This probably became standard around the time of Guido d’Arezzo. So it makes sense to give the non-accidental scale the white keys for simplicity.
Why 5 black
When you fill in the whole steps with half steps 5 half steps get contrasting looking keys which are black.
Extra information
Thoughts
As I was making this post I thought maybe we could explain the holons as toruses coming out of a star tetrahedron which would be the other part of the structure.
Source
mu6.com
Peter Land- Quora answer