Living Singularities
O#o van Nieuwenhuijze

We, as living organisms, operate a very interesting aspect of mathematics:
Shifting the Stability of the System Singularity Set.

How important this is, can only be understood by a summary understanding of the “Singularity”, a mathematical concept to describe the link between the part and the whole.

In a singularity, the system connects to the context: both the system and the context determine the system behaviour. The logic at this level is (at least) Dual, and the response of the system at this level is Fractal.
It is this level that determines the life and vitality of the integral system.

• The following gives some introductory ideas to this concept.

Starting point for this story is the first cell of your body: the Zygote.
As any sphere (or object) it is part of its context.
Mathematics describes this as: the system has a singularity.
The singularity determines the (dimensional) existence and (phase state) functioning of the system in its context.

Once the first cell divides, the situation becomes - literally - more complex.
The cell unfolds, and thereby creates a muti-layered (multi-plexed) system.
Crucials is that all the singularities of the system are interrelated.
The relationship between these singularities determines the continued existence and functioning of the system.

• Singularity Constellations

We can describe this as the System Stability Singularity Set; with its specific patterns by which the system singularities are interrelated.
This is the Constellation of the System Singularity Set.
It determines the stability and suppleness of the system.
The stability of the System Constellation determines the Health of the system.

Chinese medicine is one of the forms of healing which understands this, and makes use of this in order to re-stabilise the integrity of the system with/in its context.

• The math of Health

The body is an information processor. Its main capacity is to compute its phase state; literally. Compared to a computer, the computer itself is the output, the result of the calculations. In terns of science, the internal state of the body is determined by the shift in balance, equilibrium, between the body and its environment. The difference between a living organism and a dead object is: a living being can transform its internal state. Or rather, more appropriately (in traditional terms) the living body can transmute from one phase to another, to maintain its integrity within its environment.

• Our being is not physical by phasical

Living bodies are quite special: they are not composed of physical materials, but if information processing substance. The body is composed of liquid-crystal, piezo-electric, megneto-hydraulic semi-conductor materials. All the materials in the body are regulated to suit the ongoing process. This includes the structure and stability of the bone, the muscles, the organs, the fats, and even the body water. Each of these components has properties known as Intelligent Gels. All of these materials serve as wave guide, antenna, condenser and power source. Each in their own way. The body materials are phasical (phase relevant).

This ongoing computation, adaptation (thus learning and living) involves the shift of balance between materials: oils transform into fats, liquids into crystals, phase into state and vice versa. State and Phase interchange via phase-states and state-phases. All, in compatibility with the context. The phase changes of the body are all very precisely accounted for, and any shift in balance is balanced, compensated, counteracted and reinforced by changes elsewhere. This can only be well understood in systems theoretical terms. (Which requires a transcendental complex modelling, based on open system functioning in a closed system perspective (and v.v.).

• Health is being integral part of the whole

These shifts in balance can be plotted as topological changes; the work of Thom, Seeman and others is indicative for the way the thresholds of balance and shift of equilibrium can be charted as critical frontiers (cf. Dimensional Analysis) through/out the body. The changes involved are expressed as shifts n singularity: the body itself is a singular system (in wave mechanics, a Soliton is the most suitable term: a wave of which the wave envelope is also the wave field of the single contained wave.)

The system singularities are the nodes by which the local closed system is embedded in its context. Whereas Classical Science aims to reduce the system complexity, and eliminate the system singularities (by i.a. Dedekind Cuts, and Loop Integrals), living bodies as based on constellations of singularities. Not just single singularities, to relate the closed system to the open context; but whole systems of related singularities which, together, make it possible for the system to have a definite defined internal coherent dynamic (Autopoiesis) by which it can continue to exist (in basically very similar, thus stable, ways), although the environment may differ. (Our body metabolism is based on this concept.)

• Our body is the whole universe, in inverse

In this transition dynamic, the body changes in order to remain the same. The underlying dynamic is that of the Möbius Loop, cq. the Klein Bottle (depending on the way in which the system is regarded: as an interfacing surface, or as a coherent continuum volume.) It is the basic dynamic of Total System Inversion.

The singularities of the system are not singular: they are related, concatenated, nested and embedded: they themselves follow the principles (and descriptions) of complex systems. Herein, the degrees of freedom are determined by the way the singularities are linked; the patterns involved determine the degrees of freedom, but also the dynamics of coherence: 1) whether the dynamics is singly recursive (inertial of fixed or Material), 2) whether they have an added degree of freedom (thus operate at the level of process dynamics, and variational system dynamics), or 3) that there is a second degree of freedom involved (allowing for variations in a plane, i.e. interfacing potential, and gaseous material behaviour, of 4) if there is yet another degree of freedom, and thereby the potential of the system to function seemingly independently in the Dynamic context.

• Alchemy: The dynamic logic of phase change

This is known as The Fire Element in Alchemy. The other degrees of functioning, and modes of operation, verse to relate this seemingly autonomous functioning to/with/in its context. This involves the Air, Water and Earth elements of Alchemy. These are the gaseous, fluid and solid modes of functioning of/in the body.

• Dimensional Analysis

Although these singularities may seem to be very complex in their interrelationships, they are in fact very simply related. No matter how large or great the complexity of the body, within context, it still emerged from one cell. This means that the whole system of body singularities is in fact one coherent network.

• Singularity Theory

Topologically this involves each cell. According to topology each sphere (e.g. a cell) will have two poles: each with a different orientation. This can be compared to a battery with a + and a - pole; determining its charge potential. (In this sense, it determines the loop integral and residue vector components of each cell in the system).

• Variational Calculus

As the first cell splits and doubles, the number of singularities splits and doubled; but does not necessarily increase. Although each doubling adds a cell, thus a + and - pole, these poles can be grouped, this linked (concatenated, nested or embedded). The result is that the number of singularities does not necessarily increase, at the functional/operational level. Each “+” singularity that is couples to a “-” singularity may be balanced and not operate as a singularity within the system. (cf. the work of Spencer Brown, and Parker Rhodes); nondistinguishable boundaries can exist is a coherent system of coupled and balanced singularities.

• Those singularities that are balance will be invisible in the system (there is no phase gradient/change, thus no discernible boundary in/for the system).

• Phase States

Each cell division will thus create a new internal boundary, with opaque/translucent/trans-parent/black boundary characteristics, dependent on the amount of phase change in the boundary. This can be expressed as the amount of spin or curl, of the curvature of the singularity or its loop integral. This means that the geometry of the arrangement of the system singularities determines the system complexity, the nature of the system boundaries (and compartmentalisation) and the material substances of the body; together with its dynamics with/in its context.
Physicality is the result of a a logical ordered entanglement (embedding, nesting, concatenation, isolation) of the phase relationships of the system.

• The constellation of system singularities thus determines all of the levels of system state, by the way it determines the system phases, at all levels.

Each cell forms part of the pattern of system singularities; together they define and determine the singular system. Living organisms thereby determine their InnerPhasing, their interfacing, their system state and their system dynamic, within their context: all are interdependent. (This requires a systems theoretical, thus mathematical, rather than a medical perspective, for understanding the vital difference between a living system and physical objects.)

• The physical nature of our body is thus always a dynamic computational process, in which the phase field (in a four fold interpretation of the word phase: physical, mathematical, material and wave specific) are all interrelated.

The properties of the living being are thereby determined: organically, psychologically, socially and existentially (cosmologically/spiritually). (I.e., the phase dynamic singularity formulation at once integrates the somatic, psychological, social and transcendental aspects of our being; thus spans all disciplines of human research.

• The formulation of the system singularities is thus essential for the understanding of its capacities and potentials, and a much more detailed description of the system singularity organisation grid dynamics is needed, to fully understand what a living being is and can be/do.

This requires a full computation of all the phase state shifts during embryological development. At present this information is not available (Mainly because many people think the body is a medical object, while in fact it is an information processor.)

With a more precise understanding of the patterns of organisation of the singularity poles of the individual cells, it is possible to understand how the cellular organisation functions in groups, membranes and individual cells, to define the operation of the body as a whole (singularity cluster). In extenso, this also specifies how all humans relate in the meta-organism known as humanity, the meta-meta-organism of all life forms, and the meta-meta-meta-organism known as all life on/of Earth. I.e.: by looking at the singularities and their concatenation, the interconnectedness of all life forms is a logical result. This however requires a much more specific and detailed understanding of living organisms in terms of their system singularities; and their co--ordination/organisation.

The system singularity states are not invariant but dynamic. The singularity poles of each cell (of which there are 2 in the real, and 2 in the imaginary domain) can be compared to spinning tops: with rotation, nutation and precession; and their higher harmonics. They can be expressed in wave phase, thus frequencies of the system. (In which the time base or loop length is determined by each system event horizon (i.e. the loop integral or curvature of the event of each cell). In order to understand the overall system, de variational dynamics, and all the fluctuations and harmonics involved, need to be understood. By the relationships between the 4 levels of phase, the singularities, per cell, and the relationship to other cells, can be expressed in terns of resonance entrainment; and its higher harmonics. The coherence of the system (including all scaled of higher harmonics) relate to the health of the system. The loss of integrity, integration of these 'vibrations' and all their harmonics, relate to the system disease. Health and disease are thus logical consequences of a formulation of the system in terms of phase wave coherence.

• The organisation of the system singularities in patterns of coherence is thus the basis of our body (Meta) physical state(s).

To be continued, on request, addressing:

• Amplification
• Reset
• Insulation
• Layers
• Geometry
• metaplexity
• ...

O#o