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

[jehovajah]

So iguess just to finish the thought, that 3d Fractal generators are some kind of Tensor sculptor and tensor manipulator algorithms with the formula being the relational link to all differential elements of the tensor. These differential elements at least in Quasz are related in the form of a quad block.


So what i am delving into now is a spaciometric understanding of rotation which is not based on the euclidian tool "angle" but rather on some more topological notions.

I am fairly certain that i can distinguish two types of rotation which are discontinuous to each other but linked by topologically based limit processes, In addition i want to begin the analysis based on the "logos" response to see how much easier that makes intuitive mathematical thinking. All sensors are involved but the two i think i have to use in a TOTE analysis of spaciometric rotation are a visual region or boundary as a mrker for axiomatic visual orientation and an auditory linked sonar map with the auditory canal orientation sensors switched on. A Test Operate Test Exit (TOTE) is a basic , the basic cybernetic algorithm for traversing a self regulating system. This also happens to be the most basic iterative process that can be devised. Thus iteration and comparison and distinction are at the foundational level of any self regulating conscious intelligent system.

Again if this means my apprehension of the fractal nature of everything is inevitable because of this or that this is evidence that the fractal nature of the iterative processes in the universe are universal and always acting at every scale i cannot possibly distiguish.

[M Benesi]

  That is way intensor than I thought it would be. 

  I didn't read the whole thread (maybe at a further date), the 3rd page, than 62% of the 5th, and perhaps most of this one, so don't know if you mentioned it...  Kaluza Klein theory could be considered one of the precursors to modern multi-dimensional theories (not that it isn't modern, as it is post-relativistic, but perhaps pre-Copenhagen).  I ended up, long ago, coming up with it on my own (based on reading about relativity) and then mentioning my idea to a physicist I know (slightly) who told me my idea sounded like Kaluza Klein theory (which really isn't that hard to come up with, if one has a basic understanding of trig and special relativity).

  So I named this quick paper I threw together (a long time ago) KK math tricks... and I know you like math tricks.

kk math tricks at google docs

[jehovajah]

Hiya matt, got to run but great to have some input. I am hoping Charles Wehner will return and give his insight. Will read your post link later.

Just to note that if i use P(ø,r) where r= n*ø and ø is in radians i have a reference frame which i can apply to a plane using 1 parameter ø and scalars n which are elements of the hyperreals as another parameter.

So now i am waiting to see if i can intuit a frame that works spaciometrically like this. This is inspired by plant leafing patterning, how plant spatially organise their leaves. Yep, i have been in the garden again!

[jehovajah]

So i was going to write about the probabalistic nature of my experiential continuum, but aside from the fact that it is a personal response to the uncertainty of induction and prediction it was only to note that our culture has measured it by chance, luck, likelihood, and probability and gaming odds. This combinatorial and permutational ratio map has brought the binomial theorem and the binomial series(discovered by Newton) into an important juxtaposition with a more computational approach to probability and a wider application of the probability model to physical/motion events, that is relativistic events; provided they can be represented by a compound interest type formulation. Thus  second order Taylor Expansion with all its conditions provides a basis for a probabilistic formulation of the event described by the initial formula .

any way i guess i should flat out just define a unch of terms related to the logos response. These tems are all based on the comparison of sensor signals as measured by a iteratively structured array system with massive parallel processing functionality, i.e. me!

So i am going to have i think visiometry, audiometry, gustatiometry,kinesiometry which has an important subdistinction proprioceptiometry. Some of these words are pretty ugly huh? I might come up with some cooler ones later.

So basically there is in each of the major sensory systems in the central nervous system/ central neural network a process of ratio distinction and storage, which constitutes the comparison or measurement response of that system to raw signal input. Thus an initial sensor array has its raw signals processed and stored as a ratio response: the signal at its sensor locations compared to all the sensor locations and their differing signals. Immediately the concepts of Area , Focus , and attention become nascent and emergent along with relativity in location. All these factors as well as the raw signal are stored or inherent in the structured array system, available for the system to utilise at different levels of processing and iteration.

This is the logos response technically desceibed an the above terms enable me to focus on describing the functioning of one of the systems or a synesthesia of the systems.

[jehovajah]

When i listen to music the fact that it is an experience of ratio variation is immediately apparent,but when i look at a visual scene the symphony of ratios in it are tuned out because that is a musical metaphor. a patchwork quilt of ratios comes to mind. And the sensations of texture and touch are a "thrill" of sensational ratios of hard, soft smooth; just as the gustatory responses produces a bouquet of flavours all ratioed to one another.

~It seems obvious to me that our logos response is  ratioed response that is the source of all our language distinctions and grammars and syntax as well as our mathematics.

[jehovajah]

A bit of fun which may help me to apprehend a relativistic reference frame.

How to build a binary tree.

And then

How to build a hanging binary tree mobile .

Some homework

Which leads to a computer storage and processing analogy.

Which almost gets to my idea of a binomial tree mobile with the notion of a binomial heap.

Here is an application of a binomial tree to stock price evaluation. Essentially it is a tensor for a stock market movement over a given time frame. It is a good example of a dynamic tensor which can map dynamically scale variations in the quantities of interest, and show that a tensor is a store of relationally linked differential quantities in a relational way and does not have to have a spaciomeric form linked to it. In fact the tensor "form" as an array is a convention or set of conventions because the form for an array is physically different as one moves through different ways of representing it; eg. on paper,as a solid object, as a computer memory allocation, as a mobile...

So finally a binomial tree mobile can be simply made by hanging two binary tree mobiles from the same yoke.

My question is do i make a trinomial tree mobile by hanging 3 binary trees from the same yoke?

Have a play and enjoy

[jehovajah]

When thinking about the history of polynomials, as such there really is no early history devoid of the general equation solving that seems to start early with the development and expansion of civilsation. But it is noticeable that such equation solving has a common history with matrix history and thus my feeling that the more general notion of tensor is a suitable  vehicle to frame the development of many related strands of mathematical thinking, arithmetic algorithm formation, and geometric notions in algebraic form.

The logos response enables me to see that the tensor has been at the back of all mathematical quantification of the set notFS; and the piecemeal development of the setFS has a unifying factor in the Tensor notion and in the logos response notion, which essentially denotes everything as a ratio distinction: My language response is essentially a collection of ratio distinctions with syntax rules and grammars that reflect the ratio relationships perceived through my CNS, in interaction with the set notFS. Because My CNS is an iterative processing system, the products of this system are fractals stored within the system in the set FS: a distributed memory system which of course is accessed iteratively and produces fractal results to consciousness (have you ever had that tip of the tongue experience? that is fractal consciousness).

Thus the CNS system holds many ratios distributed in a tensor form which themselves have been derived from structural array sensors in a tensor format. which are massively parallel processed to produce a tensor output fractally, which tensor is invariant under certain processing operations; Chiefly the affine transformation operations; but which same tensor of tensors is updatable and malleable to the iteration of notFS and set FS.

Thus when it is said that our initial response to the world was to name its elements and then to number them, i do not see it in that order. Rather we measure the world and name those distinct measurements which in fact are ratios. The development of mathematical thinking then has been the development of thinking language, and only when the language was develoed to specify quantitive information distinctly by numeralising it, did the syntax of language take a commensurate course to reflect the grammar of these numeral quantities. Our early history shows great mysticism around the concept of number because number was a name not a numeral. Over time through successive development and revision of specific language and then notation and the feedback feedforward loop between language and notation, specific mathematical lnguage and grammar and syntax was isolated. But because it is the logos response it was not isolated to die in its own obscurity! Rather in an intensely human response to notFS the language scope and facility and function of the mathematical thinking process language, was extended by exploration, and above all play.  

Diophantus (3rd century AD) is sometimes called "the father of algebra" in greek mathematics but it was With the collation and dissemination of the knowledge of maths at the time by al jabr"s author Muhammad ibn Mūsā al-Khwārizmī (c. 780-850) that modern maths arises. He learned Indian mathematics and introduced it to the Muslim world through his famous arithmetic text, Book on Addition and Subtraction after the Method of the Indians. He later wrote The Compendious Book on Calculation by Completion and Balancing, which established algebra as a mathematical discipline that is independent of geometry and arithmetic, with his parameterisation model of explanation, based on indian thinking at the time, in which even a colour could represent a parameter( hows about that you colour algorithmists!) .

Descartes was eventually able to begin the process of notating the tensor. With that it soon became possible to notate the difference between scalars and matrices after an extensive development of yes you guessed it polynomials!

Researchers now are able to identify the early matrix form in china and japan and the early binomial forms even the binomial theorem in india. Each instance of these forms is language based and purposed for a civilised, cultural outcome, so in a very real sense Descartes notation began the release of mathematical language and notion from purely group or cultural concerns with their mystical overtones.

However modern practitioners have gone too far the other way and so lost contact with the societies in which they live leading to the danger og mathematicians disappearing up their own backsides! (That is a topological joke if not a topical one)

So really now we can trace the development of the tensor to LEVi and Ricci in its full blown modern form, and not before time too as Einstein needed Levi to tutor him in Tensors to be able to describe his Theories. Up until then one supposes his wife was more than adequate to the job!

So What of Newton and his Erstwhile collaborator Leibniz? My view is that had Leibniz not been so far away in terms of communication times that they would have been direct collaborators and even friends, but as it was Leibniz received his information second or third hand or late, but could  have known also from their source,  the brilliant but secretive Newtonian mind. In fact it almost seems that had not Hooke mentioned a notion of his, to find the orbits of planets by compounding tangents, that we may not have ever had Pricipeae Mathematica!

Newton and Leibniz indisputably established polynomials as a secure mapping tool of the real world that is those elements in FS which have to do with change and motion in notFS. Thus polynomials are the basis for the success and accuracy of calculus when it wants exactness rather than ratios. But calculus is in fact all about ratios. The differential elements that support these ratios are in a one to one mapping with the differential elements within a tensor form

That to me leaves William Hamilton in this brief synopsis of mathematical development. As an engaging algebraist Hamilton in his theory of couples put the complex plane and all of complex mathematics on a sound an rigorous basis. He then went on to extend the basis to the third dimension and found he could not do it satisfactorily because it always seemed to demand a 4th basis element. Thus he solved it for 4 in a general way and got 3 as a bonus. Hamilton was seeking a description of time, and consequently and subsequently proved his theorems without the use of Descartes coordinate system, thus showing that the field he was in was unaffected by reference frame transformation, the defining characteristic of the modern tensor concept. Hamilton although the first to coin the phrase space time was to early to define a tensor as it is now thought of, but who really knows? Just a many topics :Finite differences, Power series expansions, infinitesimal numbers; were thought of and utilised by Newtn in his quest to describe the motions of the planets accurately, without elaboration or even publication, so Hamilton may have such notions unrecognized in his works because they were a means to an end not a subject in itself to him.

[jehovajah]

Relativistic reference frames. Just to note that these reference frames are exhibited in social and group rule behaviours found in the herd instinct behavours, group dynamic behaviours in gregariously organized group structures, and small group interaction models for space filling.

Specific examples are: filling seats in a bus, or positioning of individuals using an open toilet in which positions are clearly delineated by design (eg individual urinals) or not (troughs). Cockroaches in their gregarious social structures are good models for liquid and gas phase  dynamics, whereas the social structure of bees would model solid liquid gas phase dynamics. The general herd behaviours in fish shoals, locust swarms, bat swarms, wilderbeast and other animal migrations model liquid vapour dynamics.

Now the important thing is that some scientists and companies have developed algorithms to model this dynamic in the larger groups which have a high accuracy, and are impressively predictive.

This suggest to me that the Cartesian Tensor (cartesian coordinates), Polar Tensor and the Hamiltonian Tensor are reference frames that need slight tweaking to become relativistic reference frames, but even then may not be flexible enough to describe liquid and gas Phase. There are the more general Clifford Tensors to mention and there may also be, eventually a Musean Tensor if someone can work out what he was on about exactly.

 I am proposing that  a binary or binomial reference frame may be more applicable. However Binary or Binomial Tensors are unlikely to be affine transform invariant and so i will call them Flexors and Growors!

Flexors should help to model liquid, gas and plasma phase dynamics and Growors should model Growth dynamics of flexible non lattice structures, i think.

Just a note about other Tensor reference frames: Spherical, Cylindrical, Toroidal, Tetrahedral, Conic Sectional etc.

It looks like Dirac's Equation is going to be quite a journey! 

[jehovajah]

Have to say that reading other peoples musings highlight the difficulty of communicating with others. This is why playing together and collaborating is so important. The marks we scratch on bits of paper or tap into computer screens are just marks. The wonderful thing is that by sharing time together we can share a common reference for these marks. So I think it behooves all mathematicians to be kind playful souls full of patience and endless barrels of strong liquor! A kindly disposition did no one any harm and is a force for good.

It seems to me that Dirac and Hamilton have one thing in common an ability to explore abstract relations algebraically as let's and couples are essentially the same things.

Hamiltons quaternions are a positive development in mathematics because to me the method of their derivation is based on Hamiltons abstract algebra of time which he called couples. In this exploration it is clear to me that he tried to look at two related events and the algebra that governed those he derived by exploration. So all the while he was looking at relativity, relatedness, relationship. He used the line or vector to denote this relationship and some the inherent geometrical ideas which are thus independent of Cartesian constraints to place complex math on a secure footing. However I think that despite his wish to be free of Descarte's reference frame he used polynomials in a way that implies a reference frame just not a Cartesian one.

We cannot avoid a reference frame or geometry/spaciometry when thinking algebraically or mathematically. This is one of the unavoidable consequences of the logos response

[jehovajah]

I made a mistake. I explain it this way; I took a look at where i was going! Where possibly could all these ideas be coming from and leading too? I found Schroedinger, and then Dirac, and now Feynmann and his group, Add to that Haramein and it is inescapably looking like it is some kind of theory of everything?

But this is in line with the Axioms, so why the mistake? I don't want to do all their math!

Do not get me wrong, i am sure it would make an interesting read, and would even educate the pants off me but i don't want to do it that way, so i won't. I like going in my wifes garden and seeing the spaciometric ratios, the tensor reference frames and the topological phenomenon that catch my eye. For example Dirac's string "trick" [ realise is a topological function of spirals especially hose pipes. Why do they always kink when i roll them onto a garden hose spiral? I call it potential twist which becomes actual mechanical twist if the ends of the hosepipe are moved apart in opposite directions.
<a href="http://www.youtube.com/v/CYBqIRM8GiY&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/CYBqIRM8GiY&rel=1&fs=1&hd=1</a>

When i found this video i was stunned to think that an idea i had was actually one fully worked out by others! So i know i am on the scent and i will follow it down to the core, but i will let others do the notation in their way cos i am too bogged down to learn their way as well as discover my way.

My thoughts on this and vortices are well laid out beforehand, but in addition i see how these systems can represent "pixel"s in a plankian lattice structure with soace deformable in this way representing on and off in the sense of a density energy tensor for this pixel. Or put it another way when the vortex is at its most definite and strongest the pixel is on as a dense form of matter, when at its weakest and least definite the pixel is off as a vacuum energy  form. Spin thus is functional as a determinant of matter phase state or as i want to call it relativistic form.

I am only writing this because it is apparent that the wave particle / wavicle debate is now a dead duck and we need a way of describing space so that it can exhibit all possibilities. The Quantum field theory purports to do this and my only observation is that the field is a substantive one  that is in vorticular motion continuously and in what seems like a quantized way, but really is a result of the binary nature of our sensor systems in making comparative distinctions. By this i mean that the cycle time for my sensory system to recognise and compare is such that i will only compute a sampling of what is happening in notFS and not an analogue. This is a generalisation of the uncertainty principle applied to compute cycles for information processing. As a result i am only aware of the set of information that my sensors have sampled and on the basis of this i have responded with my measurements and comparisons and distinctions.

It would seem apparent to me that many of the issues in high energy physics will have their natural counterparts in the digitisation of signals for inputting information into a processing system, and indeed the binary storage systems look attractive to me as more general reference frames for relativistic motion tensors .

Here is Feynman explaining what i am feeling!

  <a href="http://www.youtube.com/v/lr8sVailoLw&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/lr8sVailoLw&rel=1&fs=1&hd=1</a>

[jehovajah]

I was going to write about the logos response in the context of an intuitive notion of tensors, but my mind has just been blown away by an alternative algebra and some topological representations of a "space" its properties and motions in the space holding information that changes. Then there is the starting notion of representing geometrical shapes and directions by a contiguous notation and developing an algebra from the geometry. It is called  higher dimensional algebra.
Any way it put me in mind of Hamilton a congenial and loyal algebraist of the 19th century and particularly his theory of couples  and conjugate functions. There is no doubt that Algebra was viewed in his time as a source of meditiation rule of thumb and formal language expression. The logos response was felt but not idenified, but Hamiltons 3 part distinction is revealing in that it describes the shape of a mathtematics athe time: Arithmetic, Analysis, and an Algebra of symbolic manipulation and notations which was a language exercise, just like grammar.

The logos response in my mind simplifies everything. There is a not fs there is an interface of sensors arranged in some system capble of responding to interactions with notFS, and both storing information about and imparting information to notFS. The stored information is stored and processed within a set FS which is defined by the iterative processes in the sensory system interacting with not FS.

The primary response of the system of senses with the processing within thew sytem and the memory store is the logos response: the system measures by comparison of responses from individual sensors in a binary or binomial or even polynomial very very large array stucture or set of structures;it then distiguishes by contrast(same or not same) and this gves rise to a "language" response. The language response is the notion of the interaction with the set notFS and is a pure ratio. What the ratio signifies is relative to each individual, thus it is relativistic form the get go. The vocal expressions i give to this ratio is what i call words. Some of the ratios are about spaciometric  considerations, others are about spaciomtric actions and still others are about details in spaciometric forms stuctures surfaces, boundaries etc.. certain uses of this language have been fashioned as tools to identify relations , objects, plurality and actions. Further specialism have lead gradually to the identification of the action of proportining , placing a portion of something pro to another portion. That is placing a quantity pro to another quantity. This is completely general : placing q pro to w. pro means before or next to or by. Q by w then is a proportioninig of quantities and it was called a ratio. A ratio of quantites. It is also a relation of quantities, a model or ideogram of the spaciometric relationship of quantities, an ordering and even a ranking, an array, an arrangement, a sequence.an ordinal with each quantity being a cardinal. And yes even a tensor.

Ratios were usually arranged into equivalences that is proportions were lined up or arrayed ingroups or classes each proportion(ratio) being in a ratio with the other proportions defined by the equivalence, the smallest quantities in proportion that have the same proportion as every other proportion gathered into the class.

[jehovajah]

Well this is neat. Lying in bed jotting down ideas.
Sa ratios were proportioned too especially if they were equivalent .this notion of equivalence is an inherent function ofbthe sensory system structure through comparison. Physicallybratios are different but a similar pattern goes into the proportioning of equivalent ratios, it is this similar pattern of activate which is used to define the equivalence.

So 4pro8 can be packaged by bundling 4 lots of 1 pro 2 together. This bundling is of course multiplication but it is built up from adding ratios so I have both addition and subtraction and multiplication of ratios right off the pat providing the ratios are the same, and repeated subtraction of the same ratios is the same as an operation called cancelling or factoring . Now factoring is a precursor to a more general operation called division. In fact providing the ratios are equivalent  can show that the equivalence class is an algebra group called a field.

So now we have a algebra with an obvious extension into non equivalent ratios.

A less obvious structure of the equivalence classes is the polynomial,but the great curiosity to find the rules and structures that enabled the "solving of proportions" would eventually lead to the discovery and reorganisation around these ratios which we call polynomial series and polynomials in general.

Notation lagged behind facility because language took time to develop these distinctions first orally then scripturally/pale ontologically. Only when the first civilizations arose do we see the development of scripts. Before that signs landmarks on various surfaces can be found which definitely show the oral languages were distinguishing ratios, which is not suprising as this is the logos response anyway. What the development of civilization clearly shows is that the use of ratios and proportions and portions was well advanced by the time any cities are evidenced, and especially in Egypt but probably in the Indus valley region first the use of a simple tool called a ruler conferred great economic and cultural power on individuals who could master it. Howevere this did not preclude having to coerce others to ones ways and educating ones offspring in those ways to ensure power remained with ones family and tribe.

[jehovajah]

I have to write this as i know from experience that the bon mot does not last with me long.
 It is clear to me that my culture and language have obscured this notion: the set notFS whatever it is is undeniably an iterative space, a recursive space if you will, that is a repetitive space and  a periodic one which is active at all scales and self similar at all scales.it is a space of generalised boundaries that surround generalised regions in which periodic and cyclical change occurs and from which periodic and cyclical rotation arises; that is it is a space of motion; pure motion that is vorticular motion and  vorticular at every scale and in every boundarised region. That is it s the universal fractal generator of a fractal spaciometry and a fractal self awareness which i call the experiential continuum, my experiential continuum.

Thus a fractal formula that is iterative, rotational in a vorticular motion and self similar will be a necessary description of the elements of the set FS and should provide an approximation to the activity in the set notFS as we iteratively uncover it. Such a formula as an approximation will be achieve through a Taylor expansion of the Einstein field equation of general relativity and special relativity such that the additional terms ar identifiable with the Dirac equation and the Feynman field computation schemes common in quantum theory. The additional terms will be subject to Clifford algebras and symmetries and will formally be equivalent to adding a spin term to the Einstein field equations, but a relativistic spin component that reflects the fourier nature of the vorticular motion. in quaternion space.
 Progress should be made though the taylor expansion of the tensor formalism, and a modification of the harmonic oscillation model to a fourier modeling of a vorticular motion field with a lattice type structure initially that is relativistically in motion as if changing into a liquid or gas phase.
 

[jehovajah]

What this means for string theory is that the strings need o be open and in fact parts of of a spiral. The strings are not closed but do get close to closing through the spiral completing a revolution but the pitch of the spiral may be quantised but small, so that it overaps as close as possible. The second condition that determines this will be to replace the harmonic oscillations with fourier modeled vorticular motion of the strings. Thus the pitch of the spiral segment will allow for the maximum amplitude of the vorticular string. A closed string will represent a special mode that is probably stable like absolute zero or something like that, or possibly even the vacuum stable state for "zero point energy", the moment of the big bang!

The other point for electromagnetic theory is to do with the electomagnetic wave in fact any wave. We are used to waves being harmonic oscillations of a string and phase shifting in the waves, but i have yet to hear of a vorticular wave transport along a string as a model of an electromagnetic wave giving the pitch of the wave vortex as half a wavelength.

This would give a conical wave transport for radiation and a helical wave transport for lasing and masing. Focusing and refraction and diffraction and interference will need slight modification but may explain why light is bent when it goes through a slit in a barrier. The interaction of light as  "particle" with a slit does not seem explained by saying it is just bent. How is it "bent",do the particles bounce around in the slit channel? Is that how they spread out when they leave the split? When a wave transfers through a slit it oscillates the space in some way so the slit becomes a wave source, and the resultant wave source emits the transferred light wave as a coupled "light resonator".

[jehovajah]

So now i venture to state that the laws of thermodynamics are incomplete.  I venture to say this because i have sufficient comprehension of what i am about to notice that this is an obvious missing area in our understanding of notFS.I do not claim to have full apprehension of the details only to comprehend that details are missing. It is obvious to me that the increasing "order" in living biological and zoological systems flies in the face of the thermodynamic description of relativistic motion. I might add that now i am encountering "fellow souls"  using this term that i use it in its relational sense and not in the sense of being  coherent with Einsteins postulates in his theory of special and general relativity.

The vorticular nature of notFS is only partially described by the current expression of thermodynamic laws. It seems clear from the Dirac analysis and the Feynman analysis that a symmetry has to be expected and looked for in all things. Thus when we look at radiation into the vacuum we need to look for a radiation from the vacuum into the region that is the focus of our current interest. The uncertainty principle of Heisenberg means that in effect by focusing on one aspect we exclude other aspects, obvious i am sure when stated in these terms but nevertheless impactful on our theory making.

There is therefore to be expected a thermodynamic principle of increasing order with decreasing relativistic motion. That is to say quite naturally that as relativistic motion decreases in a region relativistic order increases in that region and vice versa. Clearly relativistic motion should be modifed through any rules for relativistic motion transfer, and such rules need to be symmetrical allowing transfer both ways. This is where i think thermodynamic laws have missed something.

We already have this relationship in phase states and phase state transformations of matter so it is not hard to point to examples highlighting the missing details in the thermodynamic description of notFS.

As a vortex spirals in it will also spiral out, but each event in sequence and in relation to boundary conditions. Thus a vortex may spiral to a "point region" as in translating to the "point" and then spiral out of the "point" either continuing the translation or reflecting or diffracting the translation depending on the boundary conditions and the "point region" permeability properties to the relativistic vortex motion. Alternatively the "point" may remain where it is but increase in relativistic potential motion, and or relativistic spin motion, that is rotational relativistic motion transfer may take place to the "point". The "point " thus may appear to grow in some ratio/tensor sense or intensify in again some ratio/tensor sense. So as examples it may increase in spaciometric mass or in mechanical mass, or it may increase in spaciometric density or mechanical density. or it may increase in spaciometric rotation( yet to be defined but it is on its way!) or mechanical rotation. Contrariwise it may appear to shrink or diminish in intensity if the vortex spirals out of the point.

So what am i to say about the fact that vortices usually have a low pressure area at their core in fluid dynamics? Well it could be as simple as saying the vortex is spiraling out from the low pressure region  in some sense, which is counter intuitive i know but interesting nonetheless.