Re: Fractal Foundations of mathematics: Axioms notions and the set FS as a model

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Relativity

I opine that the notion that is encapsulated in the word relate is the most fundamental notion that can be adduced!

Both sequence and form exhibit it as apriori, and like communication we cannot but relate subjectively, in subjective processing. Thus, even though we may declare that 2 objects or sequences are unrelated, it will be a statement that is a matter of opinion and not an incontestable fact. We may always find some way to relate every form and every sequence.

I will explore the notion of "relate"

The motion of light is not straight. It is very fast, but it is not straight. Or to put it another way: if our idea of straightness is based on light, then it is "bent"!

Etymology of the English word relate
the English word relate
derived from the French word relater
derived from the Medieval Latin word relatio (laying of matter before Senate, such motion; referring back case to magistrate; narration, relating of events, recital; reference to standard; retorting on accuser; giving oath in reply)
derived from the Late Latin word relatus (narration, telling of events; utterance in reply)
derived from the Medieval Latin word referre (bring, carry back, again; give, pay back, render; it matters, makes a difference, is of importance; report , bring back news; record)
derived from the Latin word ferre (to carry; to bear; bring, bear; tell)
derived from the Proto-Indo-European root *bher-
using the Latin prefix re-
derived from the Latin word relatum
derived from the Medieval Latin word referre (bring, carry back, again; give, pay back, render; it matters, makes a difference, is of importance; report , bring back news; record)
derived from the Latin word ferre (to carry; to bear; bring, bear; tell)
derived from the Proto-Indo-European root *bher-
using the Latin prefix re-
Date
The earliest known usage of relate in English dates from the 16th century.
Derivations in English
corelate, related, relating
Usage
Word found in Modern English

Etymology of the English word relative
the English word relative
derived from the Old French word relatif
derived from the Latin word relativus (relative; referring; having reference)
derived from the Late Latin word relatus (narration, telling of events; utterance in reply)
derived from the Medieval Latin word referre (bring, carry back, again; give, pay back, render; it matters, makes a difference, is of importance; report , bring back news; record)
derived from the Latin word ferre (to carry; to bear; bring, bear; tell)
derived from the Proto-Indo-European root *bher-
using the Latin prefix re-
derived from the Latin word relatum
derived from the Medieval Latin word referre (bring, carry back, again; give, pay back, render; it matters, makes a difference, is of importance; report , bring back news; record)
derived from the Latin word ferre (to carry; to bear; bring, bear; tell)
derived from the Proto-Indo-European root *bher-
using the Latin prefix re-
Date
The earliest known usage of relative in English dates from the 16th century.
Derivations in English
corelative, relatively, relativeness, relativism, relativist, relativity, relativize
Cognates
Dutch relatief, French relatif, German relativ, Italian relativo, Norwegian relativ, Spanish relativo, Swedish relativ
Usage
Word found in Modern English

Mathematicians and physicists and Philosophers seized upon this word in an existential frenzy, and gave it a new referent: a comparative process in which all were judged by each others standards. No one had supremacy or right to impose there standards on others as the coercive force of authority, but all were of equal authority and all had freedom of speech to voice their opinion, including their opinion of others and their actions.

This was not a democratic process, in which the mob or the people decide who has stirred them most, and thus they decide, nor is it a debate in which the aim is to win the approval of the audience as victor of the field of discourse. It was rather an intellectual and academic freedom to propose and suppose what honest opinion or devil's advocate opinion a proponent held, regardless of moral or political or even social censure. In open society these censures were and are endemic, but within certain clubs, societies and guilds each member was allowed to relae his opinion and position,

Thus relativity and relationships are bound together by these freedoms that are not public, but which nevertheless are expressed between parties, when closely observed.

The notion of dependency is also crucial to relativity, the sharing of matters which require advice or opinion or a decision from others.

Other notions take it back in History but forward into the future"Harmonias, Summetria, sunthemata and crucially, sumbola

Now i have exposited the strong subjective motives for the words, using it as an anchor we can look at how the nonverbal behaviour of the notion is utilised to connote ,by analogy, spatial and ultimately temporal dispositions.

In order to relate one must position oneself. Thus every preposition of space becomes a utility to describe this positioning or disposition while relating. Relating thus has a strong subjective motive,and thus emotional tie and a concomitant strong positional requirement. Thus the word itself has a powerful synaesthesia, which promotes its use as a term or denotation of spatial and temporal disposition. Add to that the compounding effect of family spatial bonds and temporal bonds and the absolute value of the notion is grounded. Thus "relate" in all its forms has a clear utility and flexibility of meaning which allows it to signify both spatial, temporal,subjective and objective, lingual and familial dispositions; ie "relationships"!

Thus we may begin to see the physical bond or tie as indicative of a binding relationship, regardless of the subjective feelings of the participants bound by the tie. Similarly a Boundary is significant as a tie that binds those within in it in a relationship. The first relationship is denoted as intra, the second as extra or external.

Relationships thus typified, strongly support internal and external coherency as indicative of bonded or boundary relationships(sunthemata)

When an object possesses an attribute of harmony it is because the external or internal relationships produce a subjective response that suggests fitting('ar) and oneness(monias). Such notions are direct derivatives of this bonding and binding and bounding perception of relationship.

There are levels of harmony: surface, where everything looks great on the outside, but internally may be complex, chaotic and disordered; ans internal, where everything looks great on the inside and may or may not look great on the outside. A particular value is something which has both external and internal harmony attributed to it. The relationships in these harmonious situations vary in complexity,

The attribute of summetria represents a subjective apprehension of an object as itself. It is a reflexive notion of relationships, and we develop these types of notions because we do not use referents external to the subject matter, that is we do not analogise.

When i study any formi compare. If i compare the form with itself or elements of itself i use the notion of summetria. The powerful result of doing this is not tautology, which of itself is fundamental, but identity. The ability to identify and have a notion of identity is crucial to so many systems, Thus self reflection and self referencing and selfishness is crucial to identity, and to boundary issues. The bonds, the bindings and the boundaries in summetria all relate to one nother, lead to and from on another and confine to one another. The notions of group or set or collection even sequence are not possible without summetria, the ability to define and denote belongingness, what is part of something and what is not.

Sumbola is that process that allows us to compare complex systems by means of a representative form or mark or subjective notion. By doing this i combine the summetria the sunthemata of a form into some representative form and then look for the relationships between the notions. From this i derive the above distinctions again, in a fractal pattern which is self similar, almost, and repeats at increasing scales of complexity of forms/symbols in relationships. One additional emergent notion from this comparison is analogy.

Analogy is where i compare a form with some other form that seems particularly close in its sunthemata and summetria of relationships. The Harmonias of the comparators may extend between the comparators, and thus a greater sense of harmonias is achieved. Disharmony may be evident from the comparison, and thus a bound is set on the analogy . These experiences form the bedrock foundations of aesthetics.

Thus through a lifetime of interacting with space and engaging in these comparative processes and refining the subjective notion of relationships i obtain to a certain aesthetic wisdom that may guide my behaviours at all levels and my perceptions a all leves, and my expectations and anticipations of the future.

Wholeness in the idea of relate is based on the notion of summetria, with only inductive empirical evidence. It is thus a subjective decision to accept the designation of whole for anything. Thus unity has no basis and is entirely a subjecive choice as to where that designation might apply. However, once we have established a referent for uniy certain relationships apply without variance! These invariant relationships are the subject of philosophical enquiry and discovery.

The "scatter pattern" of sensory intensities in space are processed and sequenced in the raww form up to the highly structured related form which i perceive as my current world. By building my world on these invariant relationships i aam able to maintain identity in a changing land and sound -scape(old German skapaz) that is a set of sensory relationships. If however one of these accepted invariants changes, either in value or significance or position or dominance, or even out of the processing loop, then i experience profound change. Such sets of invariants are sometimes termed paradigms.

Thus relate and relativity have a deep and abiding influential power on my subjective processing of sensory information, and the structure of relationships forms who i profess to be as and according o how i Accept them.

Acceptance is the final choice power i have over everything, and the structure of my experiential continuum is the structure of those relationships i accept and how i relate to them.

Within Shunya "i" relate,compare,contrast,describe,iterate and experience the outcomes

In his seminal work on Couples a science of pure time Sir William Rowan Hamilton ably demonstrates the power of the Eudoxian trichotomy, and wit it establishes the fundamentals of Euclidean gematria, as far as he understands it. His intention was not to develop spatial gematria but a temporal one which was nevertheless , per force, analogous. It is a pure vector analogue as well as a "number line" analogue. but this is simply because he chose to emphasise those analogies. His demonstration is of far greater applicability.

The basis of the analogy is the sequential stement above, which is of high probability to be the same for most animates- the "i".

Relating is in fact a spaciometric activity between the subjective and objective experience of sequenced attentional focus, with intentional relational or relativistic interaction with the shunya field. Thus i may objectify a region by location. This is a semiotic act. I may then objectify again region by location, and ascertain that there are in fact differences in location relative to "me", and infer differences relative to each "other", and thus settle upon the notion that i have regions in my experience that differ by location, multiple region which i might describe as 2 in this instance.

Re iterating with this new description enables me to approach a settles set of descriptors. Essentially the relae process has provided me with more than just a semiotic location, but with a language description of a compaison and contrast process i have automatically engaged in.

If i do not focus attention on an external "object", my attention turns inwarde and follows exactly the samr courses of action.

Thus i follow this process on one or multiple attentional "targets".

The comparison and contrast aspects become increasingly more complex and convoluted and interesting. We often hear that it becomes confusing, but in fact w are well able o unconsciously handle the task, if we understand that the process involves generating new language, not utilising old language . It is the attempt to use old language "correctly", that hampers my creativity.

Thus we come to Eudoxus who in his heory of proportions looked at this very issue. If i exclude the subjective region from the discussion some say that the discussion becomes objective. However this is a tutology. The point of view i adopt is a s subjective as anything else, but it does help to focus the attention on the "objects" and to highlight the comparison and contrast topic. In this case one object only seems to invite description. This of course is a subjective description of an "object".

Two objects invite description relation and comparison and contrast and finally language distinctions by iterating through the experience with different outcome products.

So why does this not happen with one object? Well it does, as a subjective description which we have just specifically excluded! We cannot avoid these types of processing no matter how much we want to be objective.

Eudoxus now takes the comparison and relation through another iteration, by moving the 2 objects together spatially and laying one down on the other. This process is called katmetreese. It is a fundamental "action " of FORM comparison, and spawns the whole of empirical Science.

By analogy i can now describe the subjective, "mental" comparison of objects as a type of form comparison done using the sensory processing networks within my biological frame. For this to happen it is necessary to have a "memory". a fundamental consequence of a sequencing space that imposes sequence, as discussed in an earlier post. These memory object comparisons are the basis of "logos", that is symbola or symbolic representation, and a manifestation of kairos that is direct proportion.

When i have come to a settled description and language about an object, after iteration, i have then to live my life interacting with these subjective objective representations. These provide me with additional comparisons and relations particularly the combinatorial ones. Thus the sunthemata and the summetria become subjectively significant from empirical experience and my inherent operating system, the logos kairos sumbola sunthemata summetria reponse is revealed .

This OS is in fact the basis of my initial reactions to the shunya field, which i have characterised by the title.

Now Eudoxus method applies to more than 2 Objects. However to apply it we have to recognise the objects in a higher level form or summetria. We tend to call these a group in modern mathematics, but fail to really explain what is being done. Euclid in fact in his teaching material sets out these comparisons in a readily apprehended form. These comparisons are set out as geometrical constructions. Thus if i hve 3 things to compare, i can compare them 2 at a time and draw a conclusion that way, but i can also compare them as a single unit, monad, a triangle of things and draw conclusions that way.

Thus i first have to subjectively describe the new unit consisting of 3 objects. This means that not only do i describe each individual object, but also each pair, and all their relations as part of a description of this 3 object unity. Having done that for 2 such 3 object unities i am now in a position to compare at the levl of the 3 objects, or at the level of the pairs of objects, or at the level of the individual objects.

It is clear that s more and more things re compared together the complexity of the comparison, potentially , seems to increase. However, utilitarian objectives make short work of what relative comparisons need to be made, and unconsciously many of the comparisons are made in processes we have come to call aesthetic.

At ach level there is an overarching simplicity covering an underlying complexity and an iterative convolution. Because these are sufficiently complex relations we experience greater degrees of freedom of choice as to how we may proceed, and process, and these degrees of freedom relate directly to the complex synaesheias we experience in our sensory mesh processing systems.

Thus when it comes to 3 dimensions the distinctions are qualitatively different from the Epihaneia that Euclid introduces the class to , and so in his later books he begins to explore how the gematria is derived in 3 dimensions. Of course, at this stage the set of comparisons, combinatorially can be very rich and interesting, and thus provides a means to capture the complexities experienced in "Nature", and a true theurgy toward any demands a god may place on a mere man!

Whether it be Gods or the State or the President, the theurgical nature of science is set by external parameters to which some of us respond with our whole lives!

http://www.enotes.com/topic/Sequence_theory
http://blog.aaronwalser.com/2009/12/sequence-theory/

http://math.stackexchange.com/questions/20277/graph-theory-proving-that-a-degree-sequence-is-graphical-havel-hakami

http://www.gametheory.net/mike/applets/Random/

http://www.purebits.com/mlsteo.html

http://cslipublications.stanford.edu/site/1575862174.shtml

Time Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison

David Sankoff and Joseph Kruskal

Time Warps, String Edits and Macromolecules is a young classic in computational science, scientific analysis from a computational perspective. The computational perspective is that of sequence processing, in particular the problem of recognizing related sequences. The book is the first, and still best compilation of papers explaining how to measure distance between sequences, and how to compute that measure effectively. This is called string distance, Levenshtein distance, or edit distance. The book contains lucid explanations of the basic techniques; well-annotated examples of applications; mathematical analysis of its computational (algorithmic) complexity; and extensive discussion of the variants needed for weighted measures, timed sequences (songs), applications to continuous data, comparison of multiple sequences and extensions to tree-structures. In molecular biology the sequences compared are the macromolecules DNA and RNA. Sequence distance allows the recognition of homologies (correspondences) between related molecules. One may interpret the distance between molecular sequences in terms of the mutations necessary for one molecule to evolve into another. A further application explores methods of predicting the secondary structure (chemical bonding) of RNA sequences. In speech recognition speech input must be compared to stored patterns to find the most likely interpretation (e.g., syllable). Because speech varies in tempo, part of the comparison allows for temporal variation, and is known as "time-warping". In dialectology Levenshtein distance allows analysis of the learned variation in pronunication, its cultural component. Levenshtein distance introduces a metric which allows more sophisticated analysis than traditional dialectology's focus on classes of alternative pronunciations. A similar application is the study of bird song, where degrees of distance in song are seen to correspond to the divergence of bird populations. A final application area is software, where Levenshtein distance is employed to located differing parts of different versions of computer files, and to perform error correction.

12/1/99

ISBN (Paperback): 1575862174

Subject: Computer Science; Sequences; Pattern Perception

http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.aos/1176350045

The Logos Kairos Sumbola Sunthemata Summetria Theurgigical Response

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 derive Pythagorean metaphysics.

One of the important corollaries of this axiom is the formation of the neurological "we" and the corresponding subjective "I". Both these subjective constructs arise out of the interaction of the biological frame interaction with the social and environmental interactions within the shunya field.

Pythagoras:The Universal Kairos

I have not shied away from the mystical and the mythical roots of mathematics and geometry. My appreciation of the significance of mysticalbthought and philosophy as a driver to scientific research has made that an inane thing to do.having, therefore, full freedom to explore all sources provides many moments of serendipity.

By now I amused yo the myths promoted in childhood education being disappointingly shattered by a more adult investigation, and so it is with Pythagoras and karos.

The notion of kairos indeed justifies the teaching of children fairy tales and myths, but equally coerced the shattering of those myths in the adult! What is " appropriate" as judged by some judge, being an individual or a group or a god or a system is what " kairos" is about. Thus the notion has no single referent , because it is a derived subjective one, and an abstract principle.

How do we come up with such abstractions? The process interested the Greek philosophers who thoroughly researched and expounded upon it, and over the course of time refined it. But such a treatment is not without it's ethnological differentiation, and this in fact is ra key element in abstraction: that is how a word or notion may be separated from it's referent and be given different or additional referents and thus significances.

Kairos would seem to start with a spatial referent which had great and vital significance: the very vital organs of the body. From this would be derived the full balance of life compared with a small region of vulnerability. This comparison is natural and of desperate importance, giving hyperbolic significance to the notion of kairos. By analogy of comparison the proportionate significance is established, and once established is free to be applied in comparative situations. Thus kairos is significantly linked with analogy and comparison with regard to the germane proportions or ratio.

The connection to logos derives solely from it's rhetorical contexts, that is : it's frequent use in rhetoric as a notion to be relied upon to convey proportionate, apt, and appropriate comparisons of significance. It's relation to time relates to its referencing those sequence which are of crucial significance in the sequential outplay of a sequence of events. The significance of such sequence is in the defining moment, that is the encapsulate a moment from which a measure of time may be made or by which an epoch of time may be divided or proportioned. Kairos therefore was a significant rationalising and proportioning notion, and it fell into the hand and mind of Pythagoras with unusual and powerful alacrity, becoming a fundamental principle of order, organisation, summetria, arrangement,architecture and form. As a behavioural principle it conjoined proportionality in action and reaction and promoted ratioed thought, proportionate language, levitate justice, proportionate dictatorship,etc. This received the cognate term " moderation", and thus moderation connotes proportionality not abstinence. There is no equality in kairos, but there is a notion of fairness based on proportion.

Pythagoras, as a mystic, clearly sought to promote this notion of kairos into a principle of living, and he had great influence in his time through his consistent application of this proportional principle. The welfare state is based on a kairotic principle: from each according to his means, to each according to his needs.

Pythagoras's scientific interests were not excepted. He sought and expected kairos in the environment and found it. He demonstrated some relationship between the counting numerals, the units or monads of measure on a string/ tape measure and the juxtaposition of square areas, or square columns of equal height: provided they could be arranged around a right gnomon the areas or volumes summed. In fact he was able to show that this applied to all proportionate figures or columns. These proportionate figures were called similar.

The pythagoreans were interested in these forms called arithmoi and studied there proportions extensively, developing many distinctions such as proto arithmoi, static and dynamic form etc.

I believe that the defining moment for Pythagoras was when he discovered the musical tones within a measuring cord called a mono chord.

The monochord is a measuring cord or a tape measure stretched across a bridge to make a musical instrument. In line with kairos Pythagoras sought to measure proportion in music.

The significance of Kairos is its "vital" nature. Thus it is a vital proportionality that is being conveyed, with such synonyms as just, right, apt. apro pos,correct, judged measured and moderate etc being employed as adjectives. thus the power of the notion of Kairos was in its adjustability to fit: it was not just any proportionality, it was the right, or necessary or apt proportionality, and in this case, the natural or divinely enthused proportinality.

Music was not unexplored before Pythagoras. It, of all the art forms relied on the subjective judgement of a skilled artisan, and the lore that such artisans developed through experience. This subjective skill was called a muse, connecting it to the divine inspiration that originated it: thus music.

By this subjective judgement and skill and religious and mystical sympathies and analogies the 7 stringed instrument was adopted as the aesthetic standard against which to measure all stringed instruments, and the music derived therby was the muses prompting toward a pleasing sound, and the conveyance of mood and emotion. The tuning also was at the whim of the muse.Like wise rhythm and tempo, dynamical range were similarly governed.

Pythagoras therefore, prompted by his belief in the universal principle of Kairos was the first to carry out a scientific investigation of musical sound. That he started with a measuring cord is not an accident. The idea was to find out what proportions of a musical string are involved in producing the pleasing musical sounds, the sounds of the muse. What rules of proportion did the muse use?

We have a direct connection between the physical instrument and the divine agency that inspires its aesthetic use. There is no irrationality therefore in applying these rules to the treatment of mood "disorders", to realign the proportions of the mood faculty . The word mood here is the greek psyche also translated soul. Thus this is a psychotherapy devised by Pythagoras on a basis of kairos and the ratios derived by empirical scientific means.

Pythagoras had a mythical apprehension of the naming of things. Thus to him the number names had significance, the main part of their significance was in the geometrical arithmoi. However this made number subject to geometry. When Pythagoras found the relationships of the muse acting on a measuring chord, he found that they were whole monads in the proportions. This immediately raised the status of the number names to a divine significance, and made them prior to geometry. Thus Pythagoras had an epiphany, in which the muse communicated to him the absolute primacy of numbers, and thus arithmatic, and within numbers the whole numbers were fundamental. He belieed he was shown that all things would have a ratio expressible in whole numbers. The number names became principles, abstracted from any earthly or (geometrical) significance and given a divine provenance and authority. That it seems has never been challenged fundamentally to this day.

However, i frequently challenge it. giving the preeminence to spaciometry and the human interaction with space through the Logos Summetria Response. I would modify the Logos to the Logos-Kairos summetria response, or even the logos Kairos Response, since Kairos implies a summetria.

Although it may seem that number took primacy, this in no way endorses the primacy of the numberline concept a later idea pioneered by Wallis an Dedekind. For pythagoras and all geometers ratio and proportion are the fundamental role of number, tha is numbers apply to comparisons and measurements. The measurinf cord was an instrument t provide numbrs, based on monads. Numbers did not exist without some monad, some divine inspiration of a unit, and that could be anything. Thus number was a principle and it was possible to divine the principles involved in everyday forms and relationships. In this sense information was encoded in forms and relationships, and this formed the the proper study of the more esoteric pythagoreans.

One can easily see , now, how many scientific, philosophic, metaphysic, and geometric, psychic, psychotherapeutic principles may be laid at the feet of pythagoras. Pythagoras did one thing with his measuring chord of music, he measured how the muse adjusted the natural sounds in a string to make pleasant music. He made one significant change in the natural tonal pattern within an octave to produce our familiar tonic scale, but more fundamentally he added an 8th string. This alone made him more than conqueror of nations! Establishing the octave as the fundamental tonal structure, he was able to show audibly the fractal structure of tones used by the muse. He was able to show the infinite iteration of the octave from before hearing to above hearing. He showed how tones outside the octave had counterparts within the octave. He showed how the octave contained everything in proportion that was needed for pleasant and affective music. It also contained horrendous discord, but the ratios of whole numbers were the secret code that kept you in tune with the muse.

The notion of Kairos informed Nwton, and everyone who seeks universal laws: they seek the correct proportionality to derive cosmos out of chaos. The success of the Newtonian philosophy and proportioning made many scientists forget that order is being picked out of chaos, that a mechanical universe is not all there is, but rather a space in which a kairos derives order, and not just any order, but a fractal order based on the music of the monochord.

When i began my research into the fractal foundations of mathematics, it was to reconceive modern mathematics in the light of fractal geometry. In many ways that has been a refiguring of Pythagorean philosophy, reinterpreting and apprehending misleading comprehensions of secret knowledge from the past. All in all Pythagoras left us a great legacy, but his conclusions, like mine are open to question and reevaluation.

On Reflection in a Centre Of Rotation

Complex Vector algebra has to have the property of reflection in a centre of rotation to fully model my experiential continuum.

i consider a spherical surface. A plane through the centre traces a great circle with the surface. The diamaeter of that circle is the path of a "reflective" translation. the path of the great circle is the path of rotation in the plane.

Consider ND on the great circle. translating ND along the diameter while my Subjective gnomon remains in afixed relative position to the sphere produces the result ND i diameter further, with perspective transformations accordingly.

If i rotate along the great circle it puts the ND upside down by the time it rotates a semicircle, and the perspective transforms accordingly. To get the result of a translation the ND needs to rotate relative to its own gnomon, in synchronicity with the spherical rotation along the great circle.

Without this rotation at the local gnomon to the ND the translation is different to the rotation.

Without local rotation then the rotation along a great circle produces different results. Vertically rotating tips ND upside down |/|), horizontal rotation flips ND round to (|/|. There ia no rotation or axial twisting That transforms it to a reflection. This can be seen by reflecting 2 figures place sequentially on the diameter, translating 2 items along the diameter and rotating the 2 items, with and without local gnomon rotation.
A reflection is a different transformation to a rotation or a combination of rotations, but a reflection in a aggregate of centres and then in the reflection of the aggregate of centres is equivalent to a rotation. This can be seen in a set of mirrors placed orthogonally to each other.

It would appear that rotations cannot "make" reflections, but can be decomposed into reflections. That is, reflections can aggregate to some rotations, depending on the relationships of the centres of rotation in which the reflections occur.

Now the real question is: is reflection an artifact of perception? Consider echoes and the way when one pushes on an object it feels as if it is pushing back.

I am in good company. Everyone who investigates these things at some stage ponders on light.

I have the advantage of that pondering. Light travels so fast that it is inevitable that it seems to travel in straight lines. Nobody had quite developed the notion of a field and consequently magnetic and electric fields seemed different things, But the undulatory theory of light waves and Maxwell's vorticular based equations soon defined the electromagnetic field that encompassed both magnetic, electrostatic and electric current behaviours.

Fields are warped space, light is a field effect, and fields are not about straight lines but dynamic space warping.

Consider the effect of space on light: refraction, absorption, emission, reflection. The same effects exist in sound, and also in solid compounds for the whole range of electromagnetic and nuclear and gravitational field effects.

The wave particle duality of electromagnetism is a classic dual description, dual analogy of what is dynamically moving in my experiential continuum. The question of which one is irrelevant as both are analogical. the question of which one is the most useful is decided by the weight of opinion, but for me the most fruitful description is relative rotational motion: this includes circles spheres closed paths open paths ,near straight lines etc in short trochoidal motion which includes full and partial trochoids and 2d,and 3d surfaces in trochoidal motion.

Saying light travels in straight lines like billiard balls is useful to work out a theory of lenses, but the same theory can be worked out using wave fronts. What however is missing is the subjective computation of the information in the wave fronts. Everything i experience is a computational output and so the information in a mirror reflection is revealing. Very little information is lost in the light signal from a mirror , and my computation of the output is almost the same as if the light was not reflected, i still compute distance and perspective from the interference pattern derived from the 2 eyes, but i compute what we eventually learn to recognise as a "reflection"

Why is it a reflection? Because we first perceive it as another person, then as a cop of ourselves, and then a mirror image of ourselves with everything not in the correct position. Correct here means "the rotated position". All my experience teaches me that i could only get into that position by rotation, but if i rotate i do not rotate "into that image".

The image is a computational output derived from the interference pattern from the signal from 2 eyes thus it matters which eye receives which signal as to what the final output is. Although patently the same information is received the same process does not occur, and it is the difference in processing that produces the difference in output. This is a powerful lesson observed again and again in the description of physical behaviours. The order of processing matters.

Thus to think that non commutativity is somehow odd is not to pay attention to the predominate condition of reality. It is commutativity which is special, and a rare thing for the order of an action or process not to make any difference to the outcome. Quite often the difference is small , but it is equally likely to be a large difference unexpectedly. Thus we experience narrow margins of stability with large margins of instability, or we might experience sudden flips in stability to stability without warning. Things, motions may appear to move chaotically or require certain quanta to exhibit a change. All of this is a consequence of the special relationship of commutativity in a non commutative set of actions or operations.

The mirror image difference is seen easily if a stereoscopic depiction is drawn and then the observer rotated into the direct viewing position. the two triangular ray diagrams go into different eyes to the reflected ray diagrams. The interference pattern produced in the brain leads to a computational output that accords with the subjective gnomons signal experience. This at once highlights the amount of perceptual processing that occurs with any signal, and the amount of information stored in a signal.

Can a complex vector algebra be expected to produce a similar computational output? only if it includes an additional step in the process which takes account of the observers relative position to the output signal, and the observers processing constraints on that output signal in that relative position.

The initial translations and rotations i was attempting take no account of observer processing and thus appear wrong. the correction is as described above.

Hamilton accomplihes the reflection by establishing a positive step, taking one mentally in a relation from precedent to consequent, having thoroughly established the terms in the previous paragraphs.

Thus he immediately establishes the contra positive as going from the relation to its antecedent. He established a null relation and thus was then able to precede to antecedent relations in reflection of proceeding to consequent ones. this was all done mentally, and again highlights the mental processing that is involved in achieving this output.

Of all the optical illusions that we may experience, the mirror reflection is the most intriguing. As an illusion it reveals the workings of our mental processing . in its action of assigning reality to our sensations. It reveals that this assignment is rule bound, and the rules are bound to the processing sequence

Whichever way it is approached mirror reflection is a mental creation. In the real world we have reverse translation or rotation. Thus to avoid getting it wrong we must accept mirror reflection as an analogy of rotation or reverse translation. In other worde mirror transformation does not exist except as a mental product applicable to abstract things called points. We are constrained in reality to rotation or translation, either of which we may alter or reverse.

http://aleph0.clarku.edu/~djoyce/java/compass/

http://aleph0.clarku.edu/~djoyce/java/compass/compass1.html

Parallelism: postulate 5 and reality and parallax.

Grassmann gives me hope, but i am still troubled.

The notion of a reference frame is only a basis for constructing a reference frame system, It is the reference frame system that holds the information about reality in invariant forms. In other words we have a system of reference frames and the invariant interference of their influence on our subjective experience is what we recognise or regard as eternal verity, truth, reality. Grassmann's linear algebra method and praxis makes it so straightforward that it is hard to believe that we have had to struggle to comprehend it. It is an apprehension of the interaction i have with space, the relationship i have in deriving a model (FS) of notFS from interacting with notFS.

It is at once far more general than any other conception while being far more specific. It convolutes with the wau i have to perceive things remarkably well, so that for the first time i feel i can notate my experience concisely but transparently. The reason why i believe is that Grassmann looked at the convolution and realised that we had a way of assessing it through combinatorics. Doing the work made clear to him the limits of the applicability of his conceptio. He then designed rules to stay safely within these limits and in that way provided us with a map of a land he had already explored in general . We are now able as he attempted , to fill in the detail.

That it is a map and not reality, and not the last word on reality, nor even the most sensitive map is shown by Cliffords immediate generalisation of Grassmann into Bi quaternions. linking immediatelyy Graswsmann's "map" with Hamilton Sketch map. I put it that way because Hamilton derived an abstract notion and applied it as much as he could to geometry, whereas Grassman Started with the full Euclidean geometry and "streched it". And before doing it he worked out all the ways he could sensibly stretch it. Thus his notion of a "vector" is indeed a elastic geometrical fo, a dynamic euclidean form. What his genius is was to take the "found" or inherent vectors in Euclidean geometry, the natural ones geometers us without realising and to make them explicit and accessible. by doing that he revealed the language we use when we manipulate space as being notable: that is we can denote a spatial manipulation action or intention explicitly and so write down precisely what we are doing or intend to do concisely and what that results in. "Numbers" or rather trig ratios then become coefficient or adjectives and adverbs of these new verbs or s we call them vectors.

This is Grassmann's conception, and this is why he was not understood in his time. His 'Zweig" was in fact not a twig or a branch but a foundational trunk of geometrical thinking specifically but logical and linguistic thinking generally.

For example it took millenia to end up with 26 letters in the english alphabet, but combinatorially and including punctuation and rules of grammar we can describe every aspect of our experiential continuum. However , we still know that this facility as flexible and fluid and essential as it is is still only providing approximate communication information, and different rules provide different maps of the same thing, ie the different languages!

The link to language is fundamental and deep, but as i have explained the Logos Summetria response undelies it all, so that it is not what is a subset of what but rather what is the relativistic structural foundation our neurology supplies in which we may begin to compare and contrast and distinguish? For it is that which leads to both language and geometrical mathematics, or as i refer to it spaciometry.

I have discussed before that in a reference frame parallelism is the notion of independent reference , not orthogonality, which carries the same idea but relates it to our perpendicularity sensory organ: it senses perpendicularity. Cartesian coordinates rely on the independence of the measurements and it is was natural to think that was related to the unique orthogonality of the 3 axes, but in fact Grassmann demonstrates powerfully that it is in fact parallelism that confers independence, and thus any reference frame can be established using that as an ordering rule for measurement. Thus we establish any number of non parallel directions, take the point of intersection of these orientations as a centre of rotation and an origin, and then order the measurements by rotation writing them down in an ordered set. This set of n measurements is now a generalised coordinate system relative to that centre of rotation and origin, We can then make independent measurement anywhere in space by measuring parallel to any or all of these reference orientations

This is why Grassmann is so straight forward, and why his method is so general, and of course there are geometrical relationships based on trigonometric ratios between all of the orientations.

Now the ordering of the set of coefficients/coordinates of the orientations actually follows a locus. In the plane it is a closed boundary,usually but not always a circle. It could also be an open boundary like a spiral and the interplay between the 2 is precisely what defines modularity. Now in 3d space we need 2 things a surface closed or open that surrounds the centre of rotation/origin and a path closed or open on that surface. Thus we could have a spheroidal surface on which a circle is drawn through the poles. but in that case we need other such loci to ensure we can reference all of space. The choice then is usually either great circles hat intersect at the poles ,ie radials from the poles or parallel circles parallel to a reference great circle. These choices section the coordinates into ordered sets which themselves are relatively ordered reflecting the geometry and the reference system chosen.

There is another alternative set of loci and that is the set of trochoids. One in particular the cornu spiral or the spherical helix going from pole o pole provides the possibility of an infinite set as a coordinate system: that is one long string of coefficients as it orders all the radials. Of course it seems clear that we could only ever approximate such system, and it remains to be shown that a single helix could order all the radials. Peanno's curve could do it and so that is another possible locus for a coordinate system.

Its funny, but Peanno was one of the first mathematicians to really grasp what Grassmann was expositing.

So parallelism and postulate 5 in Euclid really have a bearing on Reference systems that hold information about reality.

The minimum such system consists of my subjective gnomon and a local gnomon/ Although a reference frame requires a second arbitrarily small region to establish an axis in point of fact reference frames are mutual things and that is what is meant by relativity: my subjective gnomon and the local gnomon could equally well be referenced by each other,BUT the subjective gnomon is unique in that every reference gnomon relates to it and has a relative position that moves as it moves. This is the problem of parallax and incidentally why i think Einstein has got part of his theory wrong because he excludes the subjective gnomon. I tend to use gnomon because it relates directly to euclid and indeed carries the implication of trigonometric ratios in the reference frame.

So the problem with postulate 5 is parallax and perspective. I am sure that Euclid had not intended to say anything about infinity, but rather about an iterative process, Thus if the local measurement is that the lines are parallel that was good enough, He was well aware that lines which are locally parallel appear to meet in a point in the distance, his point was that they may meet, but they do not cross. Thus postulate 5 really states that any lines that meet bur do not cross are parallel. This applies equally well on a spherical surface and with regard to a straigtht line and a curve. The notion of parallel like the notion of an"angle" is much more general in Euclid than we are commonly taught. The tangent was devised just for this purpose of dealing with parallelism in curves, and the behaviour of tangents define the limit of parallelism. Thus if a curve has a tangent that never crosses a another line or tangent then that curve is parallel at the pont of that tangent.

The sophistication of the thought of the greek fathers is often underestimated. Very very often Newton borrowed ideas directly from the greeks in his formulation of the calculus, and indeed the calculus is applied trigonometry, and extension to trigonometry, just as Grassmann's Ausdehnungen are his elastic forms,stretchable geometry,bendable Euclid!

Thus the issue is that to apprehend reality we need not just one vector reference frame but a system of vector reference frames which define the notion of relativity and, most important this ,include the effect of the subjective gnomon.

Grassmann seems to me to be the best and safest way forward. As Clifford has combined it with Hamilton it seems Clifford algebras will light the path.However the light shines more brightly from Grassmann.

What is Place?

In a motion field theory, in which AR as motion sequents are computed in the Logos Summetria Response to the interaction with that motion field, there are broadly three descriptions of invariance : static equilibrium in a relative reference frame, dynamic equilibrium in a system of relative reference frames and "explosive" distribution. The last is a wide unexplored field and it is not helpfully described as chaos! Stochastic procedural dynamics is more useful, the basis of which is some aggregation of trochoidal motion sequents.

In any case the notion of place derives from some combination of the former two.

Thus place and its attendant reference frames inheres within its apprehension the perceptions of static and dynamic equilibria. The uniqueness of the combinations of these states of equilbria both in spatial and intensity-spatial distribution define the uniqueness of the sense of place.

It has to be pointed out that this sense of place is a "local" sense, which is more immediately apprehendable, and the notion of space is then constructed from aggregations of these local senses or magnification of a local sense, giving at once both the macroscopic sense and the microscopic sense of the experiential continuum.

Place and space are thus related , but in no way different except by aggregation and magnification. The "degree" to which there is any sense of difference between the two notions is a mark of the individuals perception of the relative weights of aggregation and magnification.

Intensity-spatiality is the computed intensity distribution of a signal in space and thus includes all the other responses within the Logos Summetria Response which are aggregated with the visual.

The Logos Summetria Response

The foundation of all my mathematics is the logos response. And the foundarional attribute i give to the logos response is the summetria response.

The summetria response is the organisation of the/my sensate responses into a relationship response set. And the first relationship is connection.
By connection i mean the logos response starts with an activity of connecting. All is in motion, all is dynamic and so we are forced to connect, to latch onto something from which to form A Summetria of our sensations of this dynamically motile experiential continuum.
From that set of sequenced connecting that no doubt originates for an individual at the moment of conception a summetria arises by a sequenced motion set of incredible iterative and convolutional motions. This is connecting at its most basic and where any notion of connecting comes from.

The formation of a connected sensate animate is the foundation of the logos response with its attribute summetria. So i have to recognise that the logos response is in fact the logos summetria response.

As i stated logosummetria is essentially a connecting response. The connecting of sensarions provides the following: Kinesiometry- the comparison of internal and external motion sequences including what we call pressing motions

On top of that and drawing upon it
Gustatiometry- the comparison of taste and smell of predominantly external motion sequences, at least external to the main mass of the animate organism

Sequentially and spaciometrically on top of the former (2) divisions is
Audiometry- the comparison of motion sequences predominantly in the environment of the aural sensory system including what we call pressing motions. The interpretation of the aural system in processing terms relies very heavily on the previous 2 divisions. Thus the aural Measure is essentially a representation of kinesiometric ans gustatiometric summetrias.

Finally the summerria on top is the spaciomerric summetria. This not only relies on the previous 3 divisions but also isolates itself from them in ways i can only reference as visual. In this sense each of the summetria has its own uniqueness that isolates it from the others. Thus the comparisons reveal similarities, congruencies, contrasts, unions and intersections, commonalities and distinctions, differences and sameness coherence and incoherence, adherence, consonance and dissonance, patterns, assonance rhythm, rhyme, beat, stress.. Etc.

It will not have escaped your notice that the foregoing list is a working definition of summetria in terms of its component distinctions.

Thus logosummetria seems a reasonable foundation to build upon in terms of modelling a dynamic experientoal continuum and The Logos Summetria Response an adequate descriptive title for a class of summetrias arising in a unique way in any animates experiential progress in this dynamic, motile "void" i refer to as Shunya (sunya) or not FS.

Building manipume on this basis must be a fuller richer experience than the way mathematics has been built.
Thus logosummetria means that i will no just derive algebra from spaciometry, but a logosummetric algebra from and or for the summetrias. The essential nature of this algebra will be those notions that define summetria: the connective relations, the commonalities, the intersection of all the summetrias in kinesiometry etc.

This logosummetric algebra is essentially called group theory today. But because it has arisen unnaturally from the twisted womb of a corrosive matthematics it is mutton dressed up as lamb. It is a mind twisting imposter!

Logosummetric algebras arise naturally and good examples are Euclids elements, Brahmagupta's siddhantas, Lai Zhu's Taijitu and the Tai Chi especially as revised by Lai Zhide.
I may of course be being harsh on western group theory, especially when you read the translations of some of the other logosummetric algebras. However, apart from Hamilton western logo smmetricf algebras do not start in everyday observations like the others do.

It is the naturalness of these algebras that is disguised in western representations of them, and that is the reason that we disconnect from western conceptions so readily and take up more naturally based ones.

The gain in apprehension is palpable, but essentially does not give the seeker a deeper understanding, just a more accessible one.

For each of the cultures i have menyioned i advise a recasting of modern group yheoretic structures into your own more natural logosummetric algebras.
Good luck with that.

Group Theory Or Analogous Thinking

"Crap!"

I looked at the text and thought, "This is utter crap!"

So i thought maybe i ought to try and make some normal approach to this abstraction called Group Theory after Galois.

First i am getting into Hamilton so i know how easy it is to create more and more distinctions. Secondly i have spent x years trying to find the foundations so i certainly do not want to build crap on them, And in addition the humanity of what we do and how we think is not to be "dissed" in this way! we all can think and we can all appreciate analogy. We do not need to have our brains warped in this way, or jump through hoops to please somebody elses "vanity", or "insight" or "mystery" or "deeper" or "higher" or "whatever" degree of thinking another might believe they have .

If you cannot explain it to a child then it "ain't right". Now maybe if your pet does not understand it you need not worry, but then again some times the way my cats look at me make me wonder!

So my friends the spiders do not talk crap. They do not do crap! They do n dimensional geometry and their point is it is not only beautiful, it is practical. Their webs are not only elegant, they are approximate, cos they have still got to eat!

So i start with The Logos Response. I give you some material by N.J. Wildberger, and i refer you to Euclid, Brahmagupta ands the sutras, Klein, singingbanana, Eudoxus,some simple etymology of dimension and parameter, Chinese Taijitu and analogical thinking in the Yi of the Yin and Yang, and Early Babylonian bicamerality and development of recorded analogical thinking.

We are born with measure, through measure and in measure to measure. It is innate within me to measure. So measuring is comparison, distinction and description(denotation or naming as a response). We only have language because of this innate imperative. (By the way this implies all animates have some form of response that communicates).

I call this The Logos Response after finding that the greeks named it similarly as "Logos". From this analytical notion flows all apprehension of the kosmos in greek thinking. This is an analytical start with the greeks because etymologically in the Indo European languages we can see traces of the measurement and manipulation and thinking "notions" prior to greek "Logos", based around, man-, me-,m- and cognates in sanskrit and other root languages.

We can go back as far as the Sumerian/Babylonians and find in their records of measurements and valuations based on 60 the recognition of ratio, reciprocity, human scale accounting and neasurement, and human scale analogical thinking. 60 seems to be based on the number of phalanges in the 4 "hands" of man. These were collected from dead skeletons and used in rituals as well as in accounting. There are other striking "similarites" between the human form and the number 60 including the factorisation into 1*2*2*3*5, giving 1,2,3,4,5,6 as factors, etc.

The Babylonians are the first to record analogical thinking, myths, stories,rules, regulations theorems etc.

The habit collecting small bones and sea shells etc for decoration, ritual and accounting, along with pebbles and clay media for inscription was widespread,and there is certainly a land link as well as a sea link and trade link to china and the far east. So we find many of the Babylonian notions mirrored in Chinese cultural history and development.

The Yin and the Yang are two small bones used in rituals of divination. Chinese culture developed these into astrological significance analogising them with many celestial markers, particularly the sun and moon, but not exclusively.

Brahman culture through Buddhism spread into china and chinese culture spread back into Brahman/Indian culture thus facilitating Brahmagupta's conception of "symmetry" in the siddhanta, and his advices on "fortune" and "misfortune" as an accounting structure.

Both Brahman and Chinese thinking is highly analogical. Sutras for example advise on much much more than what their literal words entail. The subtlety of the sutras and indian analogical thinking is what impressed the Arabs as well as the chinese. Lai Zhide completely revised the Tai Chi reflecting a more scientific estimation of the astronomy as well as the astrology of the Brahman's . Lai Zhide's "YIology" was recognised as consumate and definitive, and "YI" is the chinese equivalent of "analogy".

The Arabs, influenced by Brahman/indian thought completely developed the field of "Al Jibr"! This was a method of accounting by balancing and so coming to a"solution", that after the indian style was "general" in that it applied to many analogous situations

We have to bear in mind the influence of the greek empire on India, and that greek culture including Euclid flowed into indian thought. Thus Euclid's analogical thinking was a contributor to indian analogical thinking and vice versa.
summetria was at the heart of greek thought and science. Like the Babylonians whom they learned much from they also used human scale thinking,analogising from human "proportions"

It hs been said that Euclid did not "measure". Of course he did measure but he did not parametrise! Euclid dimensioned: that is he "cut" space in order to measure by comparison, and so every cut every dimension became an edge of a solid form or rather was analogous to an edge of a solid form. Thus his definitions are analogies of vertices, edges and his basic form in greek is called an arithmoi, that is a plane figure having "ar" that is area or amount of space, the first object in his scheme to have magnitude that was apprehendable.

Having dimensioned space into arithmoi Euclid leaves it to the reader to paramatrise that is uses some devised fractal scale "alongside" the "dimensions" or cuts in space he has drawn.

What drops out of Euclid then is symmetria: overwhelming symmetries, similarities, congruences, distinctions etc, a most general categorization and ontology of space and spatial forms.

Of course we rarely get to see Euclid's full work so we would not know would we!

There are others who extended the generality or dealt with specifics which required measurement using some kind of fractal scale, but the generality of Euclid has always been prized in all cultures that he influenced as "Truth". I have to say "True" in my estimation.

"Euclid" drew on previous greek and other cultures empirical knowledge and measurement to abstract these relations, particularly the Egyptian, and Babylonian sequential data, and processing of that data analogically: using circles and star charts, and images of animates and objects, and gods. He focused on what he perceived as a symmetria, a set of postulates which connected all else together.

He was not the first to do this, even in Greek culture. I think that honour goes to Thales, but certainly whichever thinkers and expositors in whichever cultures he drew upo, he is certainly proved to be the most influential geometer of all time. Even Isaac Newton has a few thousand years to go to catch up with him.

So from the very beginning animates have used analogy and some have found within that mode of thinking a kind summetria, an economy of thought and similarity of thought, action and expression, which analogy allows, which afforded the most general of description of actions we might take to measure, or perceive through the Logos Response as we compare.

The absolute jewel in this crown is Eudoxus. Without Eudoxus the notions of proportion, ratio, proportioning, comparison, establishing unity would not have had such a robust and strong theoretical base. Of course Euclid included his theory within his elements, and this is perhaps why they have had such a long lasting appeal. There is no technological or scientific or even commercial enterprise that does not rely upon it fundamentally.

So when we come to group theory we come not to anything new, but rather a reworking of what is old, and that is symmetria as discussed particularly by Eudoxus, but more generally by Euclid in the Elements, drawing it out by postulation and definition and axiom, and displaying it by theorem or proposition. Finally, constructing the demonstration of what hitherto were mere words on the page.

Since for a time the western world lost all reason and light, they embarked anew on many things guided by snippets of information allowed through by a repressive ecclesiastical establishment. Thus in the notions of Geometry and trigonometry, they reinvented the wheel and many times with fundamental mistakes that the arabs had s carefully avoided or expunged! Thus we find ourselves heirs of the ludicrous "imaginary numbers", not put right until Hamilton, and even less understood. Whereas we could have been heirs to the summetria of the trigonometric ratios and the unit circle of the greeks to which we needed inly to add reflection in a point as Brahmagupta envisaged.

Never mind, we have what we have. However to then go on to dismiss geometry and replace it with"abstract" algebra as if Euclid was not the most general conception is absurd. We have reinvented the wheel again and i for one do not propose to suffer for it.

The few new distinctions in group theory may usefully be added to Euclid to make a most satisfactory and complete and by and large more accessible analogical system for the study of all space, and motion and sequence.

Time Has No Direction

, , , ...

Thanks to Hamilton's careful "analysis" ; that is his systematic exposition of the fundamental relationships of all thinking about comparisons, spaciometry, motion and temporality i am suddenly aware what the distinction between time and motion is.

The " problem with time" is that it has no orientation, no motion, and therefore no direction.

If i examine the more fundamental notion of sequence i find it is indissoluble from orientation and from direction but only in its attributable mode. By this i mean i or an observer has to attribute sequence yo my experiential continuum . Since i attribute it , where do i get it from? It is an innate intuitive sense that inheres in me and physically derives from the motions of tiny self organising structures called nanozoe by me of which my immediate example would be an enzyme.

An enzyme functions like a battery powering an electrolytic circuit: some molecules it lyces, other molecules it combines. This is done at the level of electrostatic / chemical bonding or loosing. These structures are molecular and dynamic exhibiting conformative behaviour. Simply put they move. We also believe that electrons move.

I tend to believe that electrons tend to "shuffle" so the action is that the electron at the end of the wire "falls out" and it is the shuffle wave that travels at the speed of light.
Anyway this motion at the level of nanozoe translates to a notion of motion sequence that is innate within me and in particular within my sensor action. And within the sensory meshes there is a state structure which is called memory. This memory is also necessarily sequential by this construction. That is not to exclude massive parallel action, but such action is fundamentally sequential because it is based on motion. The motion it has at its basis i surmise as the production of protein strings in an enzymatic action. That is a guess so do with it what you will.

Hence i have an innate sensory mesh for sequence, and in interracting with shunya i attribute sequence to shunya consequentilly. In Manipume term the set notFS has an attribution of sequencing by me which appears in my model the set FS.

Because i attribute it to shunya sequence has orientation and direction in dynamic space, but none of these in "non spatial" situations. Therefore when i use sequence or attribute sequence to comparisons i tend to lose the sense of direction and orientation. I may replace it by a "local" spatial analogue say a sequence of symbols on a page. These have a local spatial distribution and i can use that to attribute direction an orientation.

So what about aural experience? We have no spatial referrent for aural experiences and yet audiometry is a fundamental spatial measure! What we actually do is synaesthesia. I kinda "borrow" the visual processing system to make sequential sense of auditory signals. I also key into the proprioceptive sensory mesh so i get a "close" geometry in which to reference sequence. This is why rhythm and dance are so linked to music: these are the primary sequencing modes of the auditory sensory mesh.

If time is going to have an existential form it has to be linked to the audiometric response and to rhythm dance and music. Time therefore is fundamentally a sensation of "endurance" not visual flow. I may experience time as a tactile flow of motion throughout and about the kinaesthetic sensory mesh. With that as a basis i may then attribute that sensation to spatial motion, such as the motion of a pendulum or of the stars relatve to the ground on which i stand, sensate and alive with a beating heart.

Lets dance!
December 2013
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