Fractal Matters Soience of Life (c) SIG, the Foundation for advancement of  Integral Health Care

The Bones of Belief - Roberto Renout - Hypermandala linking Atoms and Molecules

Atoms are considered to be the building blocks of the universe.
Matter is composed of molecules composed of atoms composed of phase information.
This uniVerse is a form of information in formation; this is a.k.a Creation.
The underling principle of creation can be represented by a Vortex.



Figure 1. The Vortex, linking 3D, 2D, 1D and 0D (Energy perspective)

We need to formulate the basis of creation by a Vortex, because…
We must not only explain the existence of atoms, but also their origin.
We must not only think in terms of matter, but especially in terms of information.
We need to be able to describe how the various material phases are related.

Alchemists already realised this to be the case.
In alchemy, the four elements (phases of matter) are related by the "Quintessence".
This "fifth Essence" deals with the ability to change from one phase state to another.
Nowadays this change of state of phase is call the internal degree of freedom.

We find the relationship between these degrees of freedom in the Vortex.
A vortex unifies a Volume with a Plane, a (stream) Line and a (transition) Point.
In the zero/transition point, the 3 dimensions of space, time and energy are connected.
Together this specifies the relationship between 4 Dimensions, in creation.

The Vortex is the instrument by which a Boundary connects to its context.
Lawrence Edwards explained how this is shown by a line inverting on itself.
The form which results is the vortex/egg: a unifying dynamic in Nature.
The Vortex is a Singularity, by which a Part connects to a Whole.

Characteristic for the dynamic of the Vortex is: "Total System Inversion".
For a living being to (continue to) exists in context: this is its dynamic.
The system must be able to reset its boundaries; i.e. invert upon itself.
This is why Lawrence Edwards entitled his book "The Vortex of Life".

The dynamic of the Vortex is based on the linking of 4 dimensions.
The 3D Volume, 2D Plane, 1D Line and 0D Point geometries are therein unified.
These can also be represented in the form of the shape of a Tetrahedron.
Therein too, we see a relationship between point, line, plane and volume.



Figure 2. Tetrahedron, linking 0D, 1D, 2D and 3D (Space perspective)


This has been long known (since antiquity) as the Platonic Solids.
These are categorised by the properties of degrees of freedom.
These operate by a very definite sets of rules; a logic.
"Logic" is the mathematical formulation for organisation of information.

The use of Logic ties in directly with the operation of "beliefs".
This is made most explicit in Dimensional Analysis.
Therein it can be seen that our assumptions determine our perception ("critical boundaries").
This is also expressed by quantum theory as "the collapse in the vector of state".

Quantum theory came to this realisation by a shift of perspective.
Such shifts of perspectives are commonly know as a Paradigm Shift.
This is a different way of looking at reality, by using a different assumption.
This is done by a change in Logic: how we describe/relate to our observation.

"Reality is a Realisation"; we must add our involvement to understand that.
This requires a model which addresses, defines our involvement in creation.
One of the models created for this is that of Astrology: links in process cycles.
All objects in reality were created by a process; all those processes are related.

This means that "reality" is not defined by the specific shapes of objects.
The dynamics of the processes that create them are defined by cycles.
The re-organisation of those processes is done by how they (un)link.
This means that these cycles must be determined by how their ORIGINS relate.

The way to do this is by relating the cycle to the zero/transition point of the system.
This is done in Relativity by looking at the electric-magnetic wave crossing.
In Quantum Theory this is done by looking across this same wave crossing.
Both models are therein complementary - the technical term for this is "dual".




Figure 3. Astrology, linking 0D, 1D, 2D and 3D (Time Perspective)

The relationship between a cycle and its origin is expressed by a Vortex.
In discrete mathematics, the equivalent formulation is a Tetrahedron.
Therein, a point, line, plane and volume are interrelated in one model.
In Astrology, it is expressed as the relationship between a circle and its centre.

Roberto Renout has elaborated this model and its underlying meaning.
In the HyperBoule ( he showed a discrete model of a sphere.
The HyperBoule is an approximation to a sphere, as in a mathematical series.
In this case it can be seen that the sphere unifies the various platonic solids.

Each Platonic Solid is a geometrical structure with a specific own coherence.
The coherence of these ' solids' is defined by relationships in degrees of freedom.
In Quantum Theory, this is is formulated by the interaction of wave fields.
These wave fields can be represented by stacked geometries of Platonic Solids.

In the HyperBoule, Roberto Renout modelled such stacked series of patterns.
Each platonic solid represent a specific geometry, logic, of system coherence.
Each form of system coherence if defined by organisation of degrees of freedom.
The core concept therein is that of relating Nodes (O) to Branches (|); (Rods & Rings).

Most significant is that these stacked geometries represent a fractal system.
Astrology models the linking between system (feedforward-feedback) cycles.
This is a formulation for a system of time fractals, as defined by Suzy Vrobel.
This fractal concepts can be applied also to the model itself; as the Hypermandala implies.




Figure 4. Our Body, linking 0D, 1D, 2D and 3D (Participation perspective)


The model of the HyperBoule can thus itself regarded to be a seed for a fractal.
This is equivalent to comparing the HyperBoule to a cell, in cell division.
This formulation can however be used in both senses, or directions.
That means that the HyperBoule lends itself to atomic and molecular organisation.

For atomic model, the HyperBoule represents a nested/embedded organisation.
Atoms can be regarded as resonant nodes superimposed on a concentric core.
Molecules can be regarded as expressions of lateral linking: concatenation.
This is where the HyperBoule shows 'rods' and 'rings' of primary geometrical shapes.

Within the HyperBoule, different layers of geometry/logic shapes are integrated.
Dan Winter has shown how such complexes form coherent yet simple patterns.
This means that the organisation of matter can be understood in one integral pattern.
The HyperBoule unifies the role of ' photons', 'electrons', ' protons' and 'neutrons'.

Traditionally, physics regards the (quantum) jumps of electrons in atom orbits.
Traditionally, photon exchanges between atoms orchestrate electron jumps within atoms.
However, in case atom orbits are synchronised, inter-atomic proton exchanges are possible also.
The correlation between neutrons between atoms is consequence of the combined possibility of photon/electron/proton exchanges.

The HyperBoule comes in 4 versions; with spin- and counter-spin, and a male and female version.
Between them, they represent the orientations of a vortex, before and after zero-transition.
Together, they represent, in discrete form, the feedforward and feedback dynamic into the vortex.
The coherence between these 4 dynamics, lie at the basis of the formation of matter.

    Atoms are NOT "Perpetuum Mobiles"; they do not exist forever.
    The origin of atoms is tentatively described as from 'the big bang'.
    There is however not a theoretic description for the origination of atoms.
    The HyperBoule offers an expression in time space, for time space coherence.

Few people realise the importance of a formal formulation for time dynamics.
Astrology offers such a description, for Modulo time-base cycles.
The model is formulated in terms of planetary cycle dynamics.
The principle however applies also to cell cycles, and all process cycles.

System Theory has advanced our understanding from space- to time organisation.
Classical, relativistic, quantum and field theory therein all complement each other.
Each, respectively, addresses the dimensional coherence of space, time, energy and phase.
We experience this in our body as anatomy, physiology, regulation and information integration.

Astrology in that sense does not refer to the planetary motions, and our life 'fate'.
Astrology describes the patterns of/for linking/unlinking process cycles.
This is the underlying fundamental dynamic of the creation of Nature; and the food chain.
It thereby describes, and links, our internal/external time-based process cycles.

Time cycles can be internally linked (concentric: embedding/nesting); stable.
Time Cycles can be externally linked (concatenated), for transient dynamics.
The concentric harmonics ("rings") form the basis of the model of "Atoms".
The concatenated harmonic cascade ("rods") forms the basis for "Molecules".

    The work of Roberto Renout can be found at
    It unifies the models of astrology, i Ching, Kabala and Platonic Geometry.
    The descriptions serve to help us make choices in process-switching.
    The HyperMandala is the matrix for interfacing, using choices and options.

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