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Important to add arcs, ropes and filamentary jets to these physical vectors . Non physical vectors or rather Invisible vectors are things like displacement of an object or the path (locus) of an object usually made visible by a trace.
It is also important to grasp the distinction between orientation( arc measure in a unit standardised circle) and direction( travel route in a specified orientation)
Where are some nitty gritty details which make a model work, and be useful, be transparent, or misleading. For example, the rules of vector addition are supposed to be commutative. But in fact when the directions are traced out it is clear that the paths taken are completely different, although the resultant is the same. The therefore the idea of commutativity is in regard to the symbolic manipulations rather than to the physical actions or movements. We glossed over these distinctions in practice, and as a result we often make some fundamental mistakes and interpretation. The additional notion of parallel translation is often not explained, or it is depicted as freedom to move in an unbounded manner. This is due to the general ignorance of what a vector is what a vector field is and how they apply in physical description. The lineal algebra was worked out in great detail by the Grassmanns. Few have got beyond the versions of it which have been promoted by Heaviside,Gibbs Hamilton and others.
I make no claim to be an expert in these matters, nor do I claim to be an expert in gyre or the addition of curvilineal vectors. I use Will Shank's trochoidal software in order to properly understand the summation or addition of such vectors. And there is a learning curve, because the addition of curvilinear vectors is not as straightforward as the addition of lineal vectors which are Rectilineal lines,
First of all, curvilineal vectors create,or define or distinguish an associated point called a centres centre is a point around which any circle may be drawn . A circle is a curved line drawn around the point, called the centre, in such a way as to be equidistant from that point for every point in the curve. Essentially a circle is a depiction of action at a distance. Distance is the distance between the centre and curve.
It turns out that semi and quarter arcs are of particular significance in the analysis of a circle. We may project these arcs on two straight lines so as to depict the movement which is trigonometric points along it. .
These arcs become the basis of curvilinear vectors. Therefore how we couple them becomes of great importance. Two main ways of coupling have been exploited so far. The first way is by beginning point to endpoint.
The whole notion of point now comes up for analysis. What is a point?
Suffice it to say that we will find it much easier to define a point is a segment of a line or an intersection of two lines rather than to define it as an independent entity. This is because the line as a primitive entity can be drawn or depicted whereas a point cannot. It makes more sense therefore to talk about a point "vector" as opposed to point, and a point as a section or indelibole element of a line. That drawn line may of course be curvilineal.
If we draw a line and call it bold a then we may call the end point the pointvector 1 a. The beginning point vector then actually becomes 0 a.. In starting at 0 a. and travelling to 1 a. we describe or draw the line a., when we introduce fractional notation it becomes easy to understand that along this "route " there are many fractional point vectors.
The centre is a point vector which is not on the curvilineal line c. The curvilinear line c. has also a point vector 1c., the centre as a point vector is the beginning point of any line between the centre and any point vector in the line c. if I draw a rectilineal line r. between the centre and the vector point 1 c. then I might call 0 c. the centre and 1 c. same as 1 r.
As the circular arcs extend around the circle the resultant vector point T traces out a trochoidal curve.
It is to be noted that all the radial an trochoidal vectors are dynamic in orientation and or extension or both. Thus1r(ø) would be a vector point that moves around a circular path governed by ø and nr(ø)would be a vector point that moves along a curve governed by n and ø. The curve is called a Trochoid or roulette.
These Trochoids or gyres show imperfectly the resultant Trochoid locii for different ø represented as frequency and fixed radii. The phase is also important to obtain these results.
The results constitue a dipole pattern for combinations that are in train or in opposition . The basket weaves are for those in train ( N-S) whatever orientation. . The opposition patterns are planar .
It is also important to understand that arcc1,c2 are in a plane P while circular arcs d1,d2 are in a different plane Q. P and Q intersect so as to give a common origin for arcsc1 and d1 , and may or may not be orthogonal.
Will Shanks software limits me to just 2 dipoles with the same cross sectional rotation Trochoid,
The animation shows the rotationa dynamics at the level of replicating thebDNA and the RNA. This indicates how the magnetic patterning powerfully shapes our very structure and demonstrates magnetic current punching through viscous space with incredible dynamism.
The sheer rotation itself generates a charge in the electric mode of magnetic behaviour ,mans the cavities ( ribosomes and enzymes) create a chamber where Masing currents cn be formed and released as RHA . These are charged molecules full of agnetic current
Think about this question when you turn the tap water flows out and fills the bowl, when you turn the tap off the bowl remains full of water. When you turn the light on light floods the room but when you turn the light off light disappears. Is it because it escapes or is there another reason?
As far as we know, and when we are stuck in a cupboard with all the doors locked with a light switch in it, then switching the light on and off floods the room with light and the light disappears. If we presume that the light has not escaped through any crack or any whole hole or any way that it may get out of the cupboard, then a good working explanation is that we have experienced a change in frequency of the materiality of the cupboard and ourselves just as sound disappears in a locked room due to amplitude and frequency decay.
This change in frequency them leads us to the understanding that the surface of materiality is vibrating or rotating at a certain frequency and amp,itude. It is these rotations and vibrations at these specific frequencies and amplitudes that we appreciate as light and colour.
By accepting this presumption our appreciation, and apprehension of materiality changes.
It takes awhile to apprehend that there are different frequencies at different layers or levels of materiality. It is these differences in the frequency, and the structure of the frequencies that create our experience of feeling sound heat light an radiation. The view of materiality as frequencies and rotations at different spatial positions, levels, relative interactions changes everything. The relative interactions we may describe as trochoidal dynamics, representable by Grassmann Fourier transforms, a type of quaternion Fofurier transform.
These thre dimensional rotations are what we identify as magnetic dipole gyres.
The curvilineal vectors are highlighted in red by packing density. Thre dipole gyre is in 2 p,anes. The N-S plane creates the latitudinal oscillation as the equatorial plane rotates the N-S plane in a trochoidal loop ( cardioid or more omplex)
Here the Crookes radiometer experiment is scaled up to the sun earth size.the anode emits both electrons and canal rays.that is catio s and anions. The sun does the same in a CME event, but here it is clear that magnetic perturbation is the driver, not electric current so called as the Electric Universe Paradigm posits. . The magnetic current paradigm is a sounder basis for all explanatory models of pressure and force expression, including gravity .
Of course magnetic field lines, embedded magnetic field lines are a nonsense. We start with magnetic current consisting of rotational dipoles generating contracting and expanding trochoidal surface patterns which surfaces are regions of magnetic force induction , in patterns that create charge effects ( attraction and repulsion) and behaviours( double layers) and structure in near vacuum but non empty fluidic space( gas and liquid)
We mow have several descriptions of the chromosphere. Chemists tend to understand the behaviour of materiality better than physicists.. The emission and absorption spectral lines are explained by some mathematical mambo jumbo, but in fact better elained by rotational dynamics. The frequency of these emission and absorption lines tell us something about the amplitude and phase dynamics of materiality as trochoidally dynamic surfaces of magnetic induction force modes. . Whether we identify these as chemical elements or structural magnetic dynamic patterning depends on what utility that expression is to us. Clearly for a chemist it helps determine the molar concentrations for reactions, for a physicist it blows their mind regarding the over simplifications they make regarding magnetic inducing force patterns.
The concept of MASING across a shock wave cavity/ boundary, is well descr.ibed but not identified by astrophysicists. Forced to talk as if everything were some particle or another. .
Whether the aether exists as a material or spiritual entity , the best we can know is in regard to models that give trustworthy measurable outcomes within the specified ranges.
A+xj=yi+zk
What I am expressing is a combination process .
I am combining a lineal point vector with 3 curvilineal point vectors in orthogonal planes XY,XZ,YZ .
The vectors join endpoint to beginningpoint.
These are arcs that combine directly, not through their associated centres of curvature.
If i!jk are circular quarter arcs we design multiplication to mean rotate a quarter arc in the factor plane. So ii means rotate the quarter arc i by a quarter arc in the XY plane after performing i, but ij means rotate the arc j by a quarter arc into the plane XY'after performing j. In both these cases we adopt a right to left evaluation of the process.
ijk means after performing k rotate it into the the XZ plane and perform j, and then rotate it into the XY plane and perform i.
So why do we equate it to -1?
Hamilton made this decision after realising he needed a calculation or evaluation axis to make sense of his Quaternion algebra. In effect he projected the arc travels orthogonally into the same or a parallel plane. By standardisation he equated the movement of a projected point along an axis from 1 to -1 . But ij and ji move the projected point into opposite quadrants on the plane or parallel plane.
How does this represent a general rotation?
By standardising the planes to the octants of a sphere a general spherical rotation can be identified.
Nevertheless the A represents the scale size of the sphere or circular arcs. Thus this type of Quaternion represents in dynamic mode a general trochoidal surface.
If we express a Quaternion in the form
Exp(A+ xi+ yj +zk)
We express a trochoidal surface dynamic in dynamic mode , but a more complex dynamic which emphasises frequency phase and amplitude in 3 orthogonal plane dimensions. The arcs are combined by radiii from associated centre to associated jcentre to arcpoint,
.
However we express them they represent trochoidal motions either by direct arc combination or by radial vector combination.
However the exp() form helps us the model a dipole more easily.
The magnetic cage looks familiar!
Why would a sphere or circle be appropriate as a centre of virticity?
Circular motion can represent power and force : contraction and expansion . These can not be achieved by a single circle , combination of circular spiral dynamics.is needed
At first the citcle or sphere seems to simple, but when adding 2 cir les gives a resultnt larger citcle . It is apparent that any circle can be resolved into 2 primitive circles: a dipole!. In addition one circle larger than the other provides distinctions readily identifiable no matter what orientation.
So a dipole is representable by a circular gyre with distinctive characteristics.
With this fundamental dipole, frequency and amplitude and phase may weave any manner of dynàmic surfaces in a 3 dimensional structuring in volvong cross sectional dipoles, in other words in the sphere .
The phere is a structure resolvable into two primitive spheroidal regions, a dipole of spheres.
Theoretically a pole iscabprimitive , loosely constrained region of virticity / pressure/power/potential.
Because early chemists wanted a singular notion the electron concept was devised and defined on a corpuscular stream of plasma. The stream was quantised by a ratio. In other words it looks like and behaves like a fluid but we conceive it as made up of particles separated by empty space! Discrete particles not contiguous or continuous materiality. .
Thus a pole can be combined with another pole to give a dipole. . The closer the poles in a dipole are the more they appear like a single pole .
But in fact this is unphysical. We find only dipoles and double layers!
Now consider that we also find that a dipole combined with another dipole forms a larger expanded or a smaller contracted ipole. . This is physical and observable. .
So founding our theories on dipoles brings us one step closer o a useful expertise.
The vector combination of dynamic spheres with varying relative phase mplitude and frequency models the physical behaviour nd observables of dipolar virticity / potential/ power. .
In this light I can now interpret trochoidal patterns as indicative of dynamic dipolar behaviour. I addition a dipole can be resolved fractally into more primitive dipoles.
I can illustrate a simple ipole dynamic formed fom 2 primitive dipole dynamics interacting.
Watch closely
https://arxiv.org/pdf/1802.08646.pdf
The gyre is in all planes
Another realisation that has crystallised in. My minds eye is the Quaternion as a polar coordinate system constructed from lineal and curvilineal vector arcs.
I resolved the polar coordinate version of the Mandelbulb in my thread with Kali found on the archive Fractlforums,com , and the thread introducing Quasz presentations.
So using the polar coordinate idea I can link Will Shanks Citca and Trochoid apps to the Quaternion sculptures of Quasz in the corresponding slice through the Quaternion block .
Thus I have apps that can model magnetic trochoidally dynamic surfaces,
(exp(ix)+ exp(-ix))/2. (a)
(exp(ix) - exp(-ix))/2. (b)
The primitive dipoles that are being composed to make these dipoles ( a) and ( b) are 2 circles in the XY or XZ planes of radius magnitude 1. The direction of the radius rectilineal vectors is initially in the Primcipal direction denoted by X . However the i indicates we are using quarter turn arcs so the x is a scalar magnitude of a quarter arc( Pi/ 2 radians)
So this scalar starts at 0 indicating the radius is initially in the X direction, but as it increases the radius moves to point circular vectors along the quarter arc.
When x is 1 the radius vector points in the Y or Z direction accordingly.
Now you may be more familiar with x being called a radian measure, and i an imaginary quantity. However we do not need to perpetuate this historical nonsense!
The - in front of the i reverses the direction of rotation around the circular arc vector.
Now combining the two primitive dipoles/ circles is done by attaching the endpoint of a radial point vector to the beginning point of the second radial point vector. When the combination involves a - sign this reverses the direction of the radius vector on the X direction. We still connect end point to beginning point in the combination.
The resultant Trochoid for(a) is a trochoid straight line along the X direction between -1 and 1. That corresponds to the value ranges of cos(ix) or cosø if you can apprehend the congruency.
Similarly (b) results in a Trochoid straight line between -1 and 1 in the Y or Z direction accordingly. , corresponding to values of sin( ix) or sinø if you apprehend that better.
These famous dipoles are clearly dipoles in orthogonal juxtaposition . When amplitude frequency and phase are introduced we get to apprehend how dipoles may be represented by complex patterns of force/ induction interaction. .
You may wonder bout sinh(ø) and Cosh(ø) as more general representations. They clearly refer to lineal torque rotations or swings not closed rotational dipoles. Consequently the do not represent magnetic behaviours
Another realisation that has crystallised in. My minds eye is the Quaternion as a polar coordinate system constructed from lineal and curvilineal vector arcs.
I resolved the polar coordinate version of the Mandelbulb in my thread with Kali found on the archive Fractlforums,com , and the thread introducing Quasz presentations.
So using the polar coordinate idea I can link Will Shanks Citca and Trochoid apps to the Quaternion sculptures of Quasz in the corresponding slice through the Quaternion block .
Thus I have apps that can model magnetic trochoidally dynamic surfaces,
This is how they enforce the electric current as a cause of magnetic behaviour. But the two dipoles are indistinguishable .
Can we isolate an electric monopole?
NO
So dipoles are sources of magnetic induction force , but the field pattern shows the equi polarity magnetic force induction. In paramagnetic materiality. Where the material is fixed by "friction".. In a ferro fluid the dynàmic rotation is revealed and the filaments form a structure along which materiality moves by rotational translation at varying speeds governed by Reynolds number and viscosity. And magnetic induction force per volume.
Note the flattened spheroid shape. . When I model a dipole using a circle the trochoidal forms conform to a spheroidal shape, how flat in the middle depends on how many dipoles are between the 2 major poles.
Another realisation that has crystallised in. My minds eye is the Quaternion as a polar coordinate system constructed from lineal and curvilineal vector arcs.
I resolved the polar coordinate version of the Mandelbulb in my thread with Kali found on the archive Fractlforums,com , and the thread introducing Quasz presentations.
So using the polar coordinate idea I can link Will Shanks Citca and Trochoid apps to the Quaternion sculptures of Quasz in the corresponding slice through the Quaternion block .
Thus I have apps that can model magnetic trochoidally dynamic surfaces,
This is how they enforce the electric current as a cause of magnetic behaviour. But the two dipoles are indistinguishable .
Can we isolate an electric monopole?
NO
So dipoles are sources of magnetic induction force , but the field pattern shows the equi polarity magnetic force induction. In paramagnetic materiality. Where the material is fixed by "friction".. In a ferro fluid the dynàmic rotation is revealed and the filaments form a structure along which materiality moves by rotational translation at varying speeds governed by Reynolds number and viscosity. And magnetic induction force per volume.
Note the flattened spheroid shape. . When I model a dipole using a circle the trochoidal forms conform to a spheroidal shape, how flat in the middle depends on how many dipoles are between the 2 major poles.
We only get the iron filing pattern if the paramagnetic material is static/ very viscous ( resistive / friction)
I used to be enamoured of technological progress until I realised the spin doctors and marketing people were taking advantage of a certain level of gullibility .
Ah, but it was ever thus!
This particular report contains physical evidence of Trochoidal dynamic surfaces called Alven waves. Also the galactic magnetic field profiles are 3 d trochoidally dynàmic structures.
I can create similar structures using Will shanks TroTorted app.
It has taken a while to intuitively apprehend these trochoidal forms at all scales in 3d . The simple process of exploring amplitude,frequency and phase ratios between curvilineal force vectors is more satisfying than making up fancy names like relativity theory or quantum mechanics or String theory.
Why do objects attract and repel? I can, using a Boscoich pressure/curvilineal force vector represent a magnetic force induction , thereby simulating a magnetic inductive force by a curvilineal dynamic surface interaction.
Of course then I can simulate materiality by fractal distributions of these regional local interactions which I may point up as "particle- like" and their interaction as physical, chemical and microbiological .
As the scale size increases so do the forms and structures I can build / model from these magnetic " Lego bricks"
In the end it is the technological utility of any model or theory that gives it credibility. Credibility is not Truth . But if a methodology or system is true to any individuals experience of mechanically altering materiality then it is useful to comprehend it.