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Author Topic: Principles of The Logos Kairos Sumbola Sunthemata Summetria Theurgigical set  (Read 6479 times)
Description: Revised and Philosophical version of the axioms for the set FS
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« on: October 11, 2011, 07:51:25 AM »

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.
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« Reply #1 on: October 22, 2011, 11:37:43 PM »

Axiom 2

The shunya field is a variable density driven rotational motion field, in which the multipolar structure forms the centres for the rotations of the spatial intensity. The spatial intensity is distributed according to the dual nature of the poles as either condensing or rarefying of space. The poles if they do collide merge to a uniform spatial intensity within the shunya field, but a uniform spatial intensity is not a equilibrium state, the shunya field is a dynamic equilibrium of poles. The spatial rotation is also dual, either it is one way or the other and is described relativistically by 4 states for any 2 poles, and in general 2^N states for N poles.

The rotation is driven by the density dynamic of space as space condenses around some poles and rarefies around others ,but is spatially distributed in any 2 poles by the 4 states.

The 4 states between any 2 poles doubles to 8 for the dual nature of the poles. Within these 8 states the rotational structures encapsulate the emergent properties of the Shunya field as subfield attributes.

The Macro effect of the relative rotation multipolar field is an  infinite iteration process and subprocess fractal structure that produces fractal  Forms and dynamic iterative processes.
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« Reply #2 on: October 24, 2011, 02:05:23 AM »

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.
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« Reply #3 on: January 13, 2012, 10:56:07 AM »

Axiom 4

My fundamental apprehension of space relies upon the assignment of semeia to regions of space, relative to my subjective processing centre, which provide a fundamental scatter pattern of semeia which may then be sequenced freely. Each sequence constitutes an output system status, and a synthesis or spatial relationships within the sequence. The complex of such systems i have synthesised under the notion of a network of vectors which dynamically vary orientation, in relationship to one another, and act as information conduits to the subjective processing centre.

The dynamic information feed to the centre enables the system to be updated and the output to be changed iteratively. One essential output process is switching of relativity between the semeia by moving the apparent processing centre reference. This is a subjective and intriguing facility of the processing system, and is accomplished by iterative computation and reverse tracking of the information feeds in the sensory network systems.

I establish the most effective model of these processes as the tools developed by The Grassmanns (Justus, Robert  and Hermann) but principally organised in the Ausdehnungslehre. I acknowledge the debt these ideas owe to the Pythagorean school of Philosophy, and in particular the Fundamental Teaching Material of Euclid.
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« Reply #4 on: March 03, 2012, 10:38:00 AM »

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.

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« Reply #5 on: April 01, 2012, 11:07:10 AM »

Axiom 10 i sketch out here as: large scale and small scale iteration procedures in FS are fractally entrained at any scale size i wish to examine.

When i take a large scale iterative process such as a solar cycle as a standard or the rotation of the earth about its axis, i can then subdivide it into smaller and smaller segments and use it as a measure or metric. Measures or metrics are some of the most obvious fractals that i can create or design in FS, but as such they are subjective attributes. Each iteration process i use as standard has to include the sub iterations within its "orbit" to imply any useful iteration link. So to become so "abstract" that a metric is applied "outside" of its defining iteration procedure is likely to lead to problems of scale.

When i experience a fractal zoom it reminds me so strongly of the differences in structure which scale changes reveal and therefore it is a wisdom to me not to generalise in an assumption of a "smooth" continuous development beyond a certain iteration , procedures  defining region of operation. Rather i should expect discontinuity and discrete regionalised developments. So for example the quantum physics and classical physics are fractally entrained by axiom 10 so they will operate on each other,but there will not be a smooth continuous link between them.

The reason why Quantum and classical do not combine smoothly is because the number systems are different. Quantum uses an extension of the natural number system called Complex, or even quaternionic. There is no smooth transition between these two systems by design. They are adjugate or conjugate systems.

The second issue is the scale of the forces. Gravity is often called space time curvature and a comparatively weak force toelectro magnetism. Thus it is approximately disjoint between these forces, as far as the data is concerned.


Whatever descriptions we have of vorticular procedures should have a "fractal" nature if it is a "universally found" iteration, and boundary conditions will need to be generalised to reflect the wada nature of all boundaries in a fractal.

So to follow on, a vortex process operating in an iterative way in set FS leads me to re emphasise newtons laws of motion in FS. A body continues in a state of vorticular motion iteration by iteration unless impressed upon by a force. A body impressed upon by a force changes its motion in proportion to the force and along the vorticular path of the force. And finally the impressed or drawn force is opposed by an equal and opposite force acting on the bodies involved  .

Newton accepted the states of motion and rest, but in set FS the iteration  vortex is the source of all motion by fractal entrainment. A body is only at rest to an observer with the same vorticular motion, and i will discuss this more when i consider equilibrium and inertia.

A body at rest is in a state of force equilibrium which is to say that all forces acting on the body cancel out. Only when this condition fails does a net force impress upon or draw upon a body in a "right" direction in the newtonian sense. This right direction is not a straight line but a perpendicular direction to the place of contact of the force. In a vortex field this approximates to a straight line as a first order approximation, but it is more accurately a logarithmic motion.
Axiom11
 Vorticular Iteration is the fractal entrainment underlying motion : a basic axiom of the set FS and a development of axiom 3

to be edited
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« Reply #6 on: May 28, 2013, 07:49:45 AM »

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?
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« Reply #7 on: July 14, 2013, 03:20:19 AM »

Recent research on Euclids Stoikeioon book 5 has developed my insight into Logos as a humanist response to the experiential continuum within and without.

As I have always said Logos is our response to the comparison of magnitudinal experiences. This is a ratio. But when I was taught raios it was always explained in terms of quantity. Numerals were then placed in front of me as symbols of quantity. No one explained magnitude to me. I had to figure that out myself 4 decades later!

I book 5 a magnitude is placed in front of me. It is a straight line segment. Different magnitudes are apparent as different line segments. Mekos derives from mega, that is a general greatness. Mekothes is this general greatness as a description of a form, and it applies to any form open or closed, surface or stereoscopic. These are different kinds of magnitude.

But then immediately , just as logos is defined it takes on the role of a model, a proto type which is used as an exact mould, something against which another logos is compared. Ana-logos, a new different logos in corresponding part to corresponding part, similar arrangement to similar arrangement. This exact copy is called an analogos even if the magnitudes are different, but only if the 2 logoi are equal or dual.

The exactness of the copy is a subjective opinion. If the copy is almost exact this arrangement is formally defined by Benoit Mandelbrot as a fractal! Thus the notion of Fractal is based on Analogia, but ones where the analogos fails. The genius of Mandrlbrot's definition of almost self similarity defines intuitively analogos that is arbitrarily close to duality or equality.

The analogos is a formal system. We subjectively sequence the form. The way to objectively see this is again based on the prior sequencing of an arbitrary mosaic. Within any mosaic, I subjectively identify four parts in a sequence. These four parts and their sequence are set in the mosaic! Now by using the language of distinctive order, protos, deuterons, tressaros, that is first, second, third, fourth I formally set those parts as positions in the language of rhetoric.

Now actually on the mosaic part I may draw any line segment magnitude. If I do this for the four parts I have four line segment magnitudes in a formal sequence. The definition of a logos is the first and the second part compared. That means I compare the line magnitude drawn on the first part of the mosaic with the line magnitude of the second part of the mosaic.

Already you see and feel the complexity of the rhetoric! The actual drawing could not be simpler!

This sense of communication complexity is physically manifested. The subjective processing of the rhetoric causes a meditative or hypnagogic state of mind to enfold, while the eyes dart this way and that as each listened to word is visually and kinaesthetically processed. To an outside observer, this kind of response is simply called "thinking!". I call it internal and subjective processing. Hermann Grassmann called it Denken Akt.

How would a blind person process this kind of mosaic based information?  My answer is that such a person would have to process it kinaesthetically. Their proprioception would be entirely physical muscle memory, where each of the sequenced positions would have a muscle pattern say to the left and right.

I mention the blind person because too often we ignore the contribution of our other senses to our "intuition". Also it helps to explain why rhetoric, or words are so slippery. If the word does not access the proper representational system, then the response of the processing is such that we call it " confusing". To overcome this, elementary rhetoric is strict, repetitive and highly referential. We do not find it pleasant to listen to this kind of rhetoric unless we are in "imprinting mode".

Every newborn animate has a neurological set up which maximises information uptake, called imprinting. During the time of this set up most of the fundamental orientation learning takes place. What is learned at this time can help or hinder progress. Few realise that when they get to understand this process, they can go back and alter their imprinting. This involves meditative techniques which I will not go into here.

So the mosaic pattern of four defines first a logos. The next 2 in the sequence define an ana logos!. Thus this is simply another logos, sequentially at the side of the protos logos, that is the first logos. But the relationship has to be fully defined to get the title Analogos. This definition is an algorithm. It defines an algorithm which essentially is a process of correspondence and comparison, after the second logos has been defined.

I will not repeat the algorithm in this post, because I have written too much already!
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« Reply #8 on: July 27, 2013, 12:23:44 PM »

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!
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« Reply #9 on: August 02, 2013, 07:15:34 AM »

Research into the Eudoxian  definitions show how this method has a specific framework set up. or algorithm. but that essentially it can be laid out in a pattern on the floor called a Sxesis, very similar to the word Sketch, or even Schematic. For me, this is yet further evidence of the imaginative use of the mosaic that the Pythagoreans made in their grasping into the nature of experiences.

http://jehovajah.wordpress.com/2013/08/02/eudoxus-on-logos/
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« Reply #10 on: July 15, 2014, 12:27:57 PM »

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.
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« Reply #11 on: January 23, 2015, 09:53:29 AM »

The Axiomatic approach was a weird take on Euclidean philosophy so called but taken as  a Platonic Philosophy rather than what it is a Pythagorean philosophy primer. Thus Kant based on some  traditions and Legendres redaction of Euclids Stoikeia declared the postulates as Axioms. The Greek is not "axee " but "Aitema" which means demand. The word postulate means to demand or request, or beg.

Somehow the word got lost in translation and became equivalent to proposition! It would be more difficult to trace how that happened but essentially I assume that Aristitelian paradigms based on his logic of grammar and syllogistic forms was adopted first by Islamic scholars who then translated Euclid accordingly and mistranslated postulate as proposition.

The result was that for nearly a millennia Arabic and Persian scholars attempted to derive the 5th postulate as if it were a proposition. This ultimately led to a crisis in Western European mathematics in the 1800s and the downgrading of Geometry, but just prior to that Kant and other Prussian philosophers had raised Axioms to a logical level of premise that cannot be demonstrated as true but are necessarily true.

This is again an example of the profound difference between Aristotelian and Pythagorean thinking.

The Pythagorean type of thinking is called rational, the Aristotelian is called Logical. One is based on Spatial interaction and the other one is based solely on grammar structures.

On the face of it Aristotle had based his system on the " gatekeeper" position, because as far as he understood all thinking was done in and through language structures. Thus his taxonomy was derived by grammatical considerations , and his ontological categories was similarly derived.

Rational thinking by Pythagoreans is based on spatial forms , but the system is reduced to ratios of line segments on a single line segment. This reduction is obtained by rotating line segments onto a given line, using circles. In fact one of the first propositions is about precisely this.

This spatial and intuitive form of interacting with space engages the observer in what Grassmann called a real Expertise, whereas the Aristotelian logic only engages the observer in a Formal expertise!

Why were the two " confused" for do long?

The word Logis, a Greek Philosophical word obscured the 2 differing trains of thought
  For the Pythagoreans a logos was a description of a  comparison, a ratio. The point being that in the presence of solely one thing nothing can be spoken or stated. A word begins in comparison .

However Aristotle took Logos to be a word and the fundamental unit of language and grammar. He did not begin at the primitive nonverbal elements of space, but rather starts with words as primitive referents to objects and ideas.bthus his system was incapable of resolving beyond the formal definition of a word.

The formal definition should admit more fundamental elements, but these are excluded by the insistence or the assumed equivalence of words to experiential objects.

In the Pythagorean system the referent is not a word but on the text version a drawing, and in the course any number of physically sensible objects. Thus is revealed the basic structure of synthesis and analysis for real objects, the way real structures come into or go out of being in the observers experience and spatial location and at the moment of the observer reifying it.

Aristotelian logic has difficulty in describing this experience and so calls them Axioms of their systems..

The two thought patterns thus do not fundamentally match so combining them leads to anomalous positions., so logic and Rayionality are in a tension that has to be managed, and this was best explored by Hegel who introduced a dilrcticsl procees based on comparing contrasting and concluding/ resolving. He later went on to redefine Logical Categories and ontological categories based on Kant's system but revised in the light of this dichotomy and Hegels rigorous and holistic analysis and synthesis.
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« Reply #12 on: February 17, 2015, 08:27:56 AM »

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.

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« Reply #13 on: August 16, 2016, 12:17:15 PM »

It has been a while since I asked the question: where do sequences and series come from?

It is apparent that they arise from our human analytical and synthetical response to our interactions within space.

Norman Wildberger had spent some time arcanely reinterpreting the foundational basis for a subject called mathematics to fit it for the computational age, but he has not tackled the origin question for these thought forms or " logical" structures.
The word logic derives from Logos, but particularly in the context of methods of debating that " win" using logoi or symbolic patterns of expression. We do not often think of the words of our language as symbolic patterns because we interpret these patterns on the fly and not always accurately !
 However it is usually the graphic symbols we utilise in astrological analysis and mosaic analysis. ( Arithmoi)

The Stoikeion book 5 begins the instruction on how to analyse by means of Logos Analogos , a pattern of comparisons that highlights the duality of forms with different divisors / factors.

Book 6 particularly takes this method to some sophistication, but it is in book7 that Eudoxus/ Euclid  describes the Arithmoi constructed by the Euclidean highest common factor Algorithm. Book 7 forms a bridge between counting on line segments to counting using any type( genus) of magnitude . Again homogeneity as demanded in book 5 is crucial.

The Algorithm reveals that the factoring process may have no natural end, and thus may not give a finite count. This was dealt with by declaring factors that had this result as protos, that is first in a new line of magnitudes! Proto Atithmoi often called prime numbers represent the deconstruction of magnitude into factors that are whole counts. Even so called irrational magnitudes are just re named prime magnitudes in the rational setting.

It is from this factorising algorithm that we derive sequences of magnitudes by" Analysis" and in synthesis we construct "series" of these analytical elements to find the total count .

Sequences and series arise from this analytical synthetical process of logos analogos comparison when factorising .

http://m.youtube.com/watch?v=T_UAj92_hRY

Unfortunately most mathematicians are used to putting multiplication preeminent to division . The Stoikeioon position is counting and factorising are the fundamental responses, the Logos ..
Nevertheless this is an example of Normans systematic approach which makes sense.
« Last Edit: August 16, 2016, 04:27:38 PM by jehovajah » Logged

May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
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« Reply #14 on: August 23, 2016, 10:53:56 AM »

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.
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May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
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