System Stability Singularity Set
The description of Health requires mathematical formulation. Mathematics has offered languaging for fundamental properties of Physics. Physics has offered the realisation that matter originates out of Phase Space. Systems Theory has offered ways in which we can relate their findings.
Introduction
In order to understand the Unknown, we need to look beyond what is known. The best places to find the unknown, is there where the known no longer seems valid. These are the places of ‘madness’ and ‘taboo’, which in science are called ‘Anomalies’ and ‘Singularities’. By studying these singularities we can come to understand beyond our normal understanding.
This is especially valid for all those occasions where the normal continuously changes: life. At present there is no theory for life, because there is no theory for change beyond what is known. The following makes use of Singularity Theory of Mathematics, to come to a science of Life. Below the need to do this, and the way to do this, are described.
In order to understand the functioning of our body and health, we need other knowledge than medicine offers. Modern Medicine is obsolete in still adhering to the tenets of classical material science. To understand Health, we need to go beyond the findings of modern quantum Field science. We need to include the characteristic of Freedom of Choice, which discerns life from dead matter.
The properties of Freedom of Choice operate with/in Phase Space. For medicine we need to understand how they determined the origination of living beings. For healing we need to understand how information relates to EMfield, chemistry and physical matter. For Health we need to understand how our experience of Freedom of Choice affects the integrity of our body, in itself, and in its integration with/in its context.
The following description of the System Stability Singularity Set combines finding of mathematics and physics. Those are used to help formulate the interconnectedness of all cells in a body; and all life forms on the planet. The Systems Theoretical formulation helps realise that we need to combine, and integrate, different types of formulation; and relate them to experience also. The Singularity Theoretical description helps to understand how integrity in context originates; and is lost (See: The Equation of Health).
For medical doctors it may seem strange to make use of mathematics to understand medicine. Yet they are very aware that medicine offers no understanding for life, nor for consciousness. Also, they are very aware that the emergence of life cannot be explained by models of ‘dead matter’. A different approach is needed, making use of those insights by which we can understand the origination of newness, and life, in terms of models and language that we have available at this moment.
Moments of newness are seen as sites where the known behaves in unknown ways. These are locations where the local system is linked to the larger metasystem. With respect to each other the local system is called Closed and the metasystem Open. Such settings are called Mad (psychology), Taboo (sociology), Anomalies (physics) or Singularities (mathematics).
The principle is always the same: the known processes and forms are replaced by unknown behaviour. The unknown behaviour thus indicates the existence of a different kind of processes operating by a different kind of logic. By seeking the sites of singularities, it is possible to identify how a local system forms part of its environment (meta system). Singularities also help understand how the principles of manifestation form part of deeper, more fundamental principles of manifestation; with more universal meaning.
“Singularities” are all those event which are called 'strange', ‘out of the common’, 'unusual'. ‘mad’, The term ‘abnormal’ indicates that the observers do not want to acknowledge that what they see is in fact normal, in a larger sense. “Singularities”, “Anomalies”, “Taboos”, “Madness” all happen, thus comply with natural law; even though they do not comply with manmade models of nature. These events show that not the events are strange, but the models; and (specifically) that the rules would determine reality, instead of reality determining the rules.
Example of such strangeness has been well describe by Ilya Prigogine, in the situation 'far from equilibrium'. At the equilibrium point, you experience two (or more) fields, in (dynamic) balance. Far from equilibrium you experience on the one hand the one field; on the other hand: the other., Evidently the far from equilibrium (Boundary) conditions must different: they pertain to different Fields.
In this way every Singularity, Anomaly or Taboo shows an underlying reality which otherwise remains hidden from view. In this text, this is the core understanding which will lead to the definition of System Singularity Sets. Every singularity of a system, is a site where the system connects to the context. That what is held to be odd, abnormal, or sometimes even held to be forbidden, is the gateway to a larger/meta realm.
This is fundamental for understanding the complex stability of system singularity sets. Any singularity  every singularity  always pertains to a domain of larger importance. If this were not the case, the singularity would be just another point, agreeing with the properties of that specific local domain. Every Taboo, anomaly and singularity alerts to the fact that local understanding of local rule is incomplete.
This can be summarised by the notion that a singularity point is a gateway, hinge or navel where you see that the 'normal' system is part of a larger system. This can be difficult to discern, such as in observing living human body cells: can you identify 'the navel' by which it is part of the system (cell) from which it emerged? Sometimes these points of emergence (connection points, singularities) can not de identified in the form, or the function, but in the breakdown of interaction, or freak disintegration.
In all those instances you see that the local system goes in upheaval, collapses and dissolves, when the underlying larger realm state 'remerges'. In fact, what is seen in the 'death' of a system, is that the life of the system is based on, and determined by, a different reality to main which is not seen in seeing the system. This is the paradox which is characteristic for working with singularity set systems: as long as, e.g. you associate the life of a cell with the cell, then you cannot see that the cell is the result of a difference system of forces, operating from a different (meta) domain, out of which the form of life emerges. This paradox is well known to occultists: is you look at the Form, you do not, cannot, see the force by/dueto/out of which the form emerges.
System singularity sets make this principle more tangible, and more risky. At the moment that you approach the singularity of a system, you enter into a gateway by which the system connects to a metadomain. Like a black hole, or white source, the Singularity can be regarded as a site where the properties of the local domain space are lost, or gained into a pit (or out of the source) for which, in that domain, there is 'no' explanation. The explanation, however, is simple: the singularity is a connection point to another domain, with a different domain space configuration, and a different logic.
Singularities therefore are nut just simply passive gateways: they are (inter)active transformers. Singularities, anomalies and taboos are the only locations for learning, about other domains of existence. The singularity which may be taboo (black hole) for one person may be a sacred site (white source) for another. There is no difference in the singularity in itself; the difference lies only in the form of appreciation.
A simple taboo may serve as example: the difference between winged being, called devils of angels. Both represent, in symbolic form, another mode of reality that humans somehow, mythically, relate to. Devils are portrayed by reptilian earth like traits and characteristics (hoofs, scales, tails and batwings). Angels are portrayed by birdlike traits an feature (wings made up with feathers).
The question is angels or devils are your messenger of choice, is a matter of appreciation. Both forms are used by humans, indifferent cultures, and complement each other in their meaning. Both however are identical in their function: both represent contact with realms beyond our human being. Regardless of what people choose to belief about the topic: both are anomalies with respect to the form known as humans.
There are many different forms of taboos, singularities, anomalies and (the fourth, experiential, form:) diseases. Each of these forms  as mentioned above  is defined as, by, the breakdown of a situation held to be 'normal'. If however we choose to understand these 'abnormal' states as normal states for another situation... then we can learn about realms beyond our knowing and understanding. Diseases teach about health, taboos about culture, anomalies about physics, and singularities about mathematics.
This text focuses on the singularities of the system: mathematics offers more 'languaging’ to understand this than physics. Mathematic also enable more direct and details studies than (social) taboos and (bodily) diseases. Singularities also allows describing the transitions between domains of existence. Singularities, in mathematics, also allow for the description of change of systemic logic.
Singularity analysis thereby is the tool of choice to study anomalies, taboos and diseases, also.
1) Mathematics of Singularities
There is a long history of the emergence of the mathematics of Singularities. Initially mathematics was aimed at simply measuring (land size) and recording (taxes) as geometry and algebra. This led to the understanding or regularities in the symbols, codes, for description (magic). From this, emerged a systematic system of codes with their own rules, logic: mathematics.
With the emergence of mathematical formulae, there was a profound change in understanding. At first there was an insistent attempt to get rid of all ‘irregularities’ that emerged out of the description. ‘Rules’ were devised, such as the forbidding of division by zero, and the invention of Limit Numbers. But it became clear that the ‘magic’ of mathematics led to unexpected new insight, such as ‘unreal’ or otherwise strange ‘numbers’. (e, I, pi, phi, log, ln, root, infinity, and so on).
With the creation of Differential Calculus, a new experienced emerged: the equations themselves led to different kinds of contradictions. Again, at first, rules were imposed curbing the type of formulae that could be created. Later it was seen that such limitations themselves implied contradictions (Euclid’s Axioms one by one crumbled). Eventually this led to greater insight in relationship with/in context; in the relationship between Differentiation and Integration.
Out of the mathematics involved with Integration, it became clear that every calculation (formula) needs to be understood within a larger context. The Integration Constant became a standard procedure for (re)fitting local findings achieved by Differentiation, into such a larger context. This later led to strange and disquieting insights: these operations of (re)contextualisation sometimes led to even stranger insights. Out of this came a branch of mathematics involved with Loop Integrals, Dedekind Cuts, and other descriptions trying to resolves local nodes of “Strangeness’ which fell outside of the otherwise usable equations.
In the meanwhile mathematics had also managed to operate at a more complex level of understanding. Numbers had already been transformed into fractions, transcendental and irreal numbers. Numbers had already changed to variables, functions and Functors. Numbers had evolved from Scalars to Vectors, Matrices, and MultiD matrices.
Descriptive mathematics (algebra, geometry) had more and more been transformed into Functional Mathematics, Operator Mathematics, and to Dimensional Analysis. Mathematics was no longer only about description, but more and more related with our understanding of understanding. This was also seen in the development of science: physics, chemistry, and electromagnetism became more and more determined by the descriptions of mathematics. For some it even seemed as if mathematics was not just a language for realisation, but a formulation of reality …
In practice however the story is quite different. Mathematics, more and more, became related to the understanding of Logic. The different forms of mathematics were practical and (once understood) easy; but all of them were human creations. One of the examples of complexification followed the approach seen in the unfolding from number to vector to array to matrix.
Likewise the mathematics of Series (Taylor Series, Fourier Series) led to an extreme version of this approach: Fourier Integrals. This approach made use of a method called the Series Limit, and Limit Integrals, in which patterns were explored to their farthest limits. The mathematics of Limits led to the formulations of Gödel, and Cantor: “how can we imagine the limits of our imagination?”. All that was described, in terms of mathematical rules and systems, was still all a human mental artefact; created by our own mind.
Yet, in the course of thus elaborating the understanding of mathematics – thinking about relationships, it had been possible to come to a new kind of insight. The characteristics of “Strangeness’ which first had been smoothened out, denied, disallowed or swept under the carpet seemed to form a pattern. After the loop integrals, there came fractals, Mandelbrot Sets, Feigenbaum numbers, strange attractors, and even names such as chaos theory. More to the point however were the insights of System Theory and Dimensional Analysis.
Dimensional Analysis was described by Langhaar, as a means to account for differences of scale in the making of model boats and aeroplanes. It was found that such models all have specific characteristic limits where the behaviour drastically changes; depending on the parameters selected by the observer! System Theory was formulated by biologist von Bertalanffy, making use of the relationships between what Mathematics described as Systems of Equations. It turns out that such systems – in themselves – make use of the relationship between Object, Process, Interaction and Subject.
In the developments of Topology, René Thom created Catastrophe Theory, specifying the different types, stages, phases and form of transtion of Boundary Systems. Together with Christopher Seeman he demonstrated many applications of this approach; also for the understanding of embryological development.
This means, that mathematics had already come to a method of formulation where Systems can be linked to the understanding of Dimensional Analysis: the limitations of the equations reflect those of its makers. It also showed that mathematics had no longer a descriptive role; it was much more interactive. In the equations this was seen in the used of sets of variables, with functions, with Weighing Functions, and their coparameters. This had led to a category of mathematical formulations where the formulations could be changed – fundamentally – while being used in making a description. At this level, mathematics as a whole functions in an interplay as seen between a river and a bedding. The formula (and its parameters) define a specific mode of description and prediction. The weighing equation and coparameters redefine the interpretation and the outcome.
At this level of description mathematics is no longer a mechanical function, a calculation. At this level it can be seen that mathematics is a purely mental operation. This makes clear that Mathematics always is, always has been, a mental operation. Mathematics is an expression of a purely mental function.
The aforementioned developments of mathematics define a taxonomy of understanding, of an unfolding of a complexity of thinking. More important than the development of the various branches of mathematics, is the pattern that can be seen in the development of ‘new’ forms of mathematics. All the forms of mathematics reflect developments in our – collective – understanding; our ability to (collectively) use our mind in a different manner. In other words: mathematics is a form of ‘reverse engineering’ of our own thinking: a symbolic representation of our mind in action.
This is seen most clearly in the changes of the belief system underlying Mathematics. The classical axioms of Euclid have all been abolished; every local system description had to be replaced by its counterpart: an Open System formulation. This means that every form of formal logic had likewise had to be replaced by a logic which relates to both the closed and open system. It means that objective (object) science has ceased to exist; every description now needs to be based on the interface (the functor, ‘equation sign’) in the link between the closed and open system. That is the place of participation of the mathematician. The Mathematician is not an Outsider Observer, but participant, and ultimately (and originally) the Creator of mathematics, and every finding in it.
We are – here – dealing with a form of description which no longer describes reality, but realisation. Mathematics is not a language of models, but a reflection of our language of mind. The importance of mathematics thereby doe not lie in its capacities for description, but in its expression of the development of our capacities for understanding. The fundamental mechanism of our understand lies in the relationships between the changes of mathematical models: our capacity to create newness by creating changes in the Logic by which we function.
 The (change of) logic of mathematics has no other basis than the (change of) logic in our mind.
There is a very marked example where we can see both: the changes in relationship of logic, and the changes in functioning of mind. This example is the logic and mechanism of Cell Division. In changing from one cell (the Zygote) to a manycellular system, the operand logic of the body is changed. This also reflects in a change of logic for our mental capacity and function; it likewise calls for a change in the mathematical models (logic) for description.
There is great need to describe this in detail. The systematic of cellular division calls for a form of mathematics which is dimensionally compressible fractal. Fractal, because we are witnessing a system of cell division leading to multiplication of the number of cells; herein increase of quantity and increase of quality are directly related. Dimensionally compressible, because in the division of the unit, unity is maintained.
2) The system Singularity Stability Set.
The simplicity of the complexity therein is easiest shown by regarding the System Stability Singularity Set. Most of the concepts on which this is based have been (implicitly) mentioned above. The principle can be explained as based on the Loop Integral, Dedekind Cut (Figure 1) and Residue Vectors. The concept is based on a conclusion from Topology, one of the branches of mathematics. The core notion is that every object (i.c. a sphere) has 2 ‘poles’ which are related to its creation, thus relation, in its context.
The System Singularity Set is the linking of the Zygote, in its divisions, with the cells that are thereby formed. Every cell, ensuing from cell division, is thereby topologically linked, in a very logical manner, with all cells before it and after it (in time or origination).
 This topological set is a temporal fractal (Susie Vrobel).
 This topological sequence is a Dimensional System (O#o).
The concept of the System Stability Singularity Set is simple: every cell has 2 topological poles in spacetime (plus 2 more in energyconsciousness). The stability of the system depends on the connection/coherence between the singularities of the system. The system singularities operate by the coherence and complexity of their logic and organisation; this determines the quality of the life potential of the system. The pattern of organisation of The System Stability Singularity Set determines the vitality, and organic functions (including consciousness type) of a life form.
Each singularity represents a node of (total) system inversion. This is a moment (fulcrum point) for regulating the relationship of the part within/to the whole. This is a pivotal moment, comparable to a 4D version of the EM field line zerotransition. The functional singularitylinks are thereby moments of maximum potential of organismic reorganisation.
As pointed out by Arthur M Young, there is a modulo relationship between consecutive stages in the singularity set cascade organisation. Structurally and organisationally the operation of the System Stability Singularity Set is determined by the dimensional topological compressibility of the fractal.
The System Stability Singularity Set thereby contains the key of, and to, life; and consciousness, as operated and experienced in the body. Although the System Stability Singularity Set itself can not be physically nor functionally seen in the body, there are organisational derivative equivalents in the form of the frequency cascade of intra/intercellular communication, the metabolome cycle cascade, the metabolic pathway circuits, and the system stability in the PathoPsychoPhysiologyProcessing in our body.
The above formulation makes use of:
 the principles of PathoPhysiology, described by Bert Verveen,
 the principle of zeropoint potential amplification, described by Bill Tiller,
 the principle of zeropoint inversion optimisation, mentioned by Charles Rowlatt,
 the principle of coherent system harmonic cascade, illustrated by Dan Winter.
Formally every sphere has a topology with two poles. Consider a cell in this manner: it will have two poles. In splitting, a cell will also split its singularity nodes. Where the first cell has two nodes, the (2) second cells will have four poles, of which 2 coincide.
This produces a very precise mathematics of cell division. In the maintenance of cellular coherence, all these singularities will ‘line up’. The (organisational) connection point of two cells will be based on the linking of two singularity poles. We find ourselves looking at a model of coherence very similar to that of magnetic poles.
There is however a great difference: In the splitting and merging of singularity poles we see that division relates to rotation. The singularity poles are nodes of System Inversion; that is how cells multiply by dividing. This is easiest portrayed by a chain reaction of vortices, all related, unfolding in forming the body.
This defines the Time base of the organisational structure (dynamic) of the living body. The architecture of cell division, in cascade, can be represented by vortices linking in on another. The System Singularity Stability Set is determined by the interrelated vortices, of the cell divisions. Each of these divisions adds another node in the unfolding of the organism, and expands its coherence.
Each of these nodes however is based on the superposition of two poles; which requires a different consideration. The coincident nodes are the basis of a very precise mechanism of higher order attunement. Here we are not looking at a simile of a magnet, but an electromagnetic waves. In the Electromagnetic wave we see what this means: as the Zero Energy of the system.
Figure 5: Zero Node Transition in EM Wave Representation
In the electromagnetic wave, the magnetic component and electric component move at right angles. These waves meet at the same point, the zero point; which we van look at in detail. What is seen as the crossing point of the two waves, can in another representation be shown as a crossing. This means that we can use the description of a Light Cone, to represent what happens in this crossing.
Figure 6: Zero Node Transition in Light Cone Representation
This means that we now have four different but related images for the same concept:
 Cell division  Lemniscate model
 Stacked Singularities  Vortex coincidence description
 EMField Zero transitions  Light cone
 Dimensional (un)Foldment Fractal Cascade
Each of the models specifies that very small changes in the (non)coincidence of the systemic organisation. Minute wobbles will affect not only the local nodes, but also the holosystemicharmonics. In this way, the stability of the singularity node, will determine the stability of the whole system set. What is needed is a method of/for description of the coherence of this (growing) spatial organisation.
By using this Singularity node description, we can specify the large scale coherence in small scale coherence. Because of the formulation in terms of a vortical system, the coherence is defined in terms of a vortex fractal. Due to the detail of the singularity/singularity junction, changes can be described in terms of changes in the light cone (zero node). Small scale variations in the precise moment of intersection, will have large effects (‘reverberation’) on the whole system.
 From a mathematical perspective, the Singularity System Stability Set requires:
A complex number notation in cyclic transcendental space A fractal notation for the division cascade in spacetime and energyphasespace, A vortex spin rotation integration formulation, operating total system inversion. A dimensional (de)compression logic of the topological unfolding (and cusps) of cell division.
In other words: what we are dealing with is a fractallic spatially unfurling logic of dimensional reorganisation.
This is beyond the scope of contemporary mathematics (though, it is being worked on). And this is beyond the scope of contemporary medical understanding (although traditional healing understands this).
It however all boils down to one simple image: that of the aligned system singularity set, of cell division. This logic, of unfolding and cancellation, is the basis of the calculus of of addition and negation, multiplication and division. From this logic follows the structural organisation of branching, concatenation, nesting and embedding; i.e. structural organisation. The metric is based on the interface, and determined by the 4DD Logic.
To be continued ...
