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The Logos Kairos Sumbola Sunthemata Summetria Theurgigical Response arises out of the visual, auditory gustatory kinaesthetic (proprioceptive) neural network interaction with the Shunya field. This neural network is maintained and enabled  by the cellular microbiological interactions with the shunya field, maintaining a regional distinction between the biological field effect of the shunya field and the environmental field effect.

The Logos Kairos Sumbola Sunthemata Summetria Theurgigical Response is the main component of the subjective  conscious process within the  biological frame of the neural network, with the subjective  unconscious processes arising within the biological structure as an evolutionarily determined outcome of shunya field interactions.

On an environmental objective subjective description, the biological framework arises from the  interaction between, and exists within a macro structure consisting of, similarly formed biological units. The macro structure is evolutionarily determined and environmentally bound within the shunya field.

On a Shunya field perspective, the environmental boundaries  for each subjectively distinct regional product within the field form a fractal distribution of the essential subfield structures of the multi-polar shunya field.

This is a first draught of axiom 1 and it is a derived Pythagorean metaphysics.

Axiom3
The experiential continuum is a subjective experience that arises developmentally within the subjective process both consciously and unconsciously through the interaction with the shunya field iterative process.

The earliest stage of the development is the formation of the experience of self , followed by the selection and amalgamation of the neural networks in the construction of "i" and "me". The interaction of the "i" and "me" with the interactive process within the iterative shunya field construct and develop the experiential continuum, as a model of objective space subjectively experienced with "me" in it.

Self is an emergent subjective process experience that arises out of the interaction between a dense sensory boundary( sensorially dense), and a niche environment within the wider shunya field. The dense boundary is a fractal product of micro shunya field processes within a biological frame that is a macrofield fractal product, of a relatively local shunya field process structure.

 underpinning this development as an inherent scaffold is the logos  summetria  kairos  sumbola sunthemata response.

I sense, therefore I am.
I am therefore i subjectively process objective sensory signals and output a model of my experience, that constitutes my experiential continuum.

Axiom 5: The Shunya Field  in Axiom 1 is not constructed or definable within my model but is perceivable by "me" by a iterative process of negation of all elements within my model.
Basically i can't say what the Shunya Field is but i can say what it is not by recursive means.

Axiom 6: I stabilise "my" model by an iterative process of "acceptance".

"My" experiential continuum changes with what i "accept" as a basis for the iterative processes of perception and recognition. The cultural forms which i accept from conception are numerous and pervasive and as i alter these my perceptions change as does my experiential continuum. "not altering" then is a nascent notion of acceptance.

Axiom 7: The Set FS is the "universal" set within which my model/ experiential continuum is defined and has a rule:- all processes on its elements are iterative /recursive and all its elements are determined by iterative processes.

notFS will be the recursive definition of the Shunya Field in axiom 1. However there is a mapping from notFS onto FS such that FS is a model of notFS.

Axiom 8: Iterative/recursive processes operating on notFS are perceivable.

These processes will be compared with energetic transfomations within FS.

Axiom 9:All perceived boundaries involve an iterative process or processes.

Definition: Infinfite is unbounded and large Infinitesimal is unbounded and small.

Euclid defined the term boundary and that is what i have used here without alteration. The axiom as i state it is a clarification of the definition of boundary and boundarisation.

Axiom 7 has an interessting corollary. Energy and motion are by it recursive or iterative processes. This leads on reflection to the notion that a set wide iterative process may be a hypothesis worth making with regard to the notions of energy and motion in FS. This set wide process will only be worth making if the energy and motion laws that Einstein derived can be shown to be consistent by every measure with the axioms of the set FS. If this can be done then starting with a suitable fractal rule if recursive processes can be shown to generate Einstein like motions and energy equivalents then a convincing case may be made for the recursive action of space. If space has this recursive action it may then be possible to relate each iteration to a notion of sequential statuses which may be similar to the notion of "time" in modern physics. I will be more rigorous in a following post, but essentially the elements of the set FS are many and varied but for it to be useful FS must explain the nature of space or rather have an equivalent/analogous  definition of space to what is in notFS.

Axiom 7 requires some careful handling. Axioms 1 - 6 lay out an underpinning framework for 7 but do not define a set or set notation. This is in fact assumed to be the standard mathematical definition and usage. However, the axiom itself is attempting to draw together axioms 1 -6 under a mathematical notation system. Thus axiom 7 is a tautology expressing a symbolic representation (set FS with rule ) of axioms 1 - 6. Tautologies like this are indicative of the iterative nature of my consciousness, and the question arises if the generalised notion of iteration does not preclude me from coming to any other description.

The definition of iteration is clearly too specific to explain everyday usage as I recognise iteration not only on bounded regions but also on values and symbols. Turings machine for example is a symbolic iteration, and Newtons iteration is a value iteration. Then there are the iterations which can be seen in design modification, Editing, scientific inductive reasoning, the scientific method itself acting on a group behavioural process; cybernetic and feedback systems etc. Therefore for FS to represent axioms 1 -6 the rule of iteration must take a more general form which can not rigorously be defined and is subjective to my appreciation of iteration. This is not a new problem. I mention it to highlight the fact that my so called knowledge of set FS is more likely to be a knowledge of a partial or restricted subset of FS or subsets of FS which may or may not be cofactors of one another.

I have changed the lead title to reflect the metaphysical and philosophical nature of this thread. Perhaps it should now be moved to the Philosophy " channel" , Chris?

It is apparent that i should amend the heading of this Thread to the Logos Analogos... thus replacing Kairos.

But for the minute i will retain Kairos as the overall desired effectiveness of Astrological art, the advising of human souls on the opportune time at which to carry out their affairs and businesses!

There are several principles to our interaction with and inhabitation of space. At least I posit these are derivable from our intuitive Grammars which attempt to strap rules onto our unruly languages!

I will relate these to the 4 usual cases of the noun. There are more complex constructions of " cases" which I will ignore at this stage focussing only on the Nominative, accusative , dative and genitive cases.

The first thing we consciously do, and it is an action or rather a reaction to space, is to name space or form or some form within a space or constituted by space. This is the nominative case and represents simple recognition or perception( even though these, Reactions are by definition iterative and fractal! )

The next stage of our reaction deals comprehensively with the relativity issues of space. The accusative case reflects the relativistic relation between two objects in dynamic relation. The simple accusative places the object relative to the subject in the activity. The object is either fixed or motive.

Newton in his concept of relativity starts with a fixed or a uniformly moving object. This was done to provide a meaurable difference so that a system of measures could be derived. The accusative case is more complex and subtle than this however. Languages that retain the reflexive pronouns indicate the essential tautological nature of this case. Although English tries to straighten it out it cannot be straightened out without losing important properties and principles of relativity.

We next move to comparisons of relative forms and this is usually the function of the dative case. The comparisons are fundamentally spatial! Thr prepositions are the basic distinctions in this spatial relativity, but also they form the basic reference Frame for meaning and analogy.

The genitive case records how we flexibly adopt the relativistic viewpoint of another person or object. The aim is to experience what is fixed and what is motive from that position or point of view, in a dynamic situation.. The concept of solidity and fluidity is based firmly on this notion of fixity and motive. By adopting these viewpoints we compute a widespread notion of solid liquid and gas and plasma( fire!) .

One thing we do not compute without deep thought is the concept of pressure and pressure gradients. These concepts determine the relative fixity and motion of space. We recognise this as relative " density" , but are mislead into thinking this intensity of fixedness or motion is somehow independent of relative viewpoint. Density is measured and apprehended by our kinaesthetic sensors. These represent a relative assessment of durability based on pressure interactions. What we usually think of as solid is in fact a highly local pressure system. Within a higher pressure system these systems become fluid.

Within every solid system a fluid pressure system is in motion , and that motion is relative, not just to our conscious viewpoint, but also to objective reference frames.

The proto Indo European roots man* and me* underpin our Pre literate response to our interaction with space.

From a foetus we extend(metosis, meiosis) into space and that extension culminates in the limbs and the hand(manus)  and the foot, and the tongue. These instruments probe , prod and  explore space  proprioceptively, developing a map as a copy of that probing experience.

Thus me* denotes extension into and encompassing space, the proprioceptive intention of which is to " know" by comparing and contrasting results of the process.

In that regard the hand plays a particular role ,man* denoting manipulating, holding, turning everyway and ultimately considering , drawing to ones side for special scrutiny , to come to conclusions.

For these activities the Greeks coined the word Logos, but the idea is already present in the PIE roots and found in other linear B languages like phone in and Hebrew ( mamre).

Given this fundamental extensive beginning one can trace counting as a consequence of this proceeding.

Katametresee is bases on me* in combination with several other relevant notions, but fundamentally it is placing down and extensive body to cover a larger body . This is the act or activity of counting. It is literally a song and a dance: the dance rhythmically covers the form the song names each step.

The names of each step only have an order if the Metron ( the extensive body used to measure) is set down in a sequence..

Where fors that sequence come from? It is an internal necessity of our development and growth, but it is also a derived process from natural processes.

In this discussion no mention of points has arisen. That is because a point is a forml notion. Points do not have a real embodiment in some, although we can set out such a formal system.

Points arise from our contrasting Anlysis of objects in spae, as we analyse an object it is dissolved into parts . When we arrive at a part that can no longer be divided then we call such a part a point. It is the first fundmental element of a synthesis of such elements by a sequence of construction.

The calculus is portrayed as an advanced subject accessible to those with prior learnings. Nevertheless it is a fundamental restatement of the basic process of factorising space, and spatial objects.
We may as well drop the term calculus and use the familiar term bricks .

We may not all have played with bricks or in the sandpit when children but the logos response derives from there.

The construction of forms we now give the grand name topology. When topology was first coined in the late 1950s the forms were morphable . This was in recognition to the overwhelming static nature of formal analysis hitherto. Classicists revered the Greeks codification of ideal forms and proportions based on aesthetic sensibilities. However we can see that different cultures had differing aesthetic values based on their sensibilities in particular thevindian Shunyasutras or trochoidal topologies, promulgated into Mongolia, China and Japan.

So the mosaic patterns collected from the world cultures by the Arabic empires provides a rich topological set of bricks to choose from.
Harriot, according to Wallis formulated a topological treatment of these forms and differences which the young genius DesCartes absorbed from the Jesuit scholars who instructed him. While plagiarism was not strictly defined at this time, it was a major concern among scholars who often obscured findings in coded descriptions to prevent others claiming authorship.
With authorship came scholarly authority and that made a financial difference because expertise was valued and attracted patronage. And scholars urvived on patronage! Disciples or students are a meagre source of income but a wealthy patron could facilitate research and development of expertises for mutual benefit of the patron and scholar.

In addition a scholars social standing was closely tied to their patrons. We therefore should not be surprised that scholars would imbibe each others ideas without giving due credit. DesCartes was notorious for this.

Nevertheless his genius is not questioned even if his morals might be.

DesCartes encouraged the study of differences . Differences here means differences in topology. Sticking to the Greek ideal forms often made topological geodesics difficult. In particular the curved forms of the eastern cultures were difficult to describe. However factorising the forms into smaller nd smaller regular nd recogniseble forms not only was a fractal process, but alo a differences process. Many series were devised by this method and the logarithmic and sine tables were derived by these differences methods expressed as calculation process formulae.

The methods were expressed in a symbolic notation which stood for countable or measurable quantities. These expressions were later lumped under the term Algebra, by Wallis even though they had little to do with the Arabian Al Khwarzimi and his interest in finding the square and the roots of quadratic types of expressions .

Bombelli is perhaps the earliest western author to publish on Alvebra as opposed to Arithmetic., but they constitute the same topic area, that is methods of calculating sums, areas and quantities and finding squares nd roots. The symbolic notation of Algdbra merely highlighted its status as ymbolic arithmetic.

So the differences in algebra and the formulaic expressions of these difference processes became known by later students as differentials. These differentials were well studied by Newtons time but not well organised. We can trace two streams of organising this material to Newton And Leibniz, even in the face of the great works of the Bernoullis.

The same core idea of factorising ino infinitesimal differences informed both, and both communicated with the others involved in the Mersenne correspondence community sharing scholarly ideas. However a difference in application and notation transpired between the two. I might briefly state it as Leibniz apprehended at last the principles of differential topology , the methods of calculating measurements of spatial forms. This is often caled differential geometry.

However Newton apprehended the principles of differential dynamics ! There was no real equivalent to it . However that is not to say that Mechanics did not have all the required precursors. Mechnics is the application of topology to the methods of obstructing durable forms that can transmit and receive force or living force!

These concepts of applying morphable forms to constructions Is not new, and in particular in understanding dynamics of motions or Kinematics morphable forms are the staring point. However, whereas Leibniz and others were studying the topological morphology, newtonwas studying the dynamic morphology. He was therefore studying forms that were Not static. To signify this he called his measures and symbols fluents.

We may think the term amiable covers this, but it of ourse is too general. What istinguishesbabfluent from a variable is the time property of the magnitude.
Up until then no one gave a Metron a time property. It was regarded as fixed.fixed by mental ecessity granted, but also later deemed to be fixed by the Gods or Musai. Newtons dynamical innovationnwasvto give all extensible and intenive magnitudes an inherent time property, that made them fluent.

From this notion he derives the Fluxion, that is the small fluid change in topology over an infinitesimal Time change.
Panta Rhei.
All things flow with time!

While this realisation is certainly obvious now, the pragmatics of scholarly analysis then denied this elemental philosophical truth. All scholars then looed for eternal fixed forms, even Leibniz. Only Newton looked for and expressed an eternal dynamic flow. Hence his terminology of fluents and Fluxions.

In taxonomical terms classical geometry even differential Grometry is the geometry of a fluxion . All such geometry depicts an instantaneous topology , that is a topology at one instant in Time. Newtons method of fluxions thus deals with a dynamically flowing universe mom only called space-time . Space-time calculus originates with Newton and his method of Fluxions . Einsteins credit is to realise that nobody in his time had really read Newtons principles for Astologers or his papers on motion or the method of Fluxions.  Those that had did not apprehend how to apply it to modern physics. He therefore redacted and resurrected it for his work on gravity.
By thenn4 dimensional Algebras were common  And Netons principles could be restated in these terms. The topology of space dynamically morphed could be equated to forces measured in space.