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.

The second method for combining circular arc vectors is a radius vector r1 end point 1r1joined to the beginning point 0r2of a radius vectorr2. Both vector points1r1 and 1r2 are vector points1c1 and 1 c2 on the arc vectors / curves c1,c2.

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

Where does the light go when you switch off the light?.

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.

## Comments

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

athen we may call the end point the pointvector 1a. The beginning point vector then actually becomes 0a.. In starting at 0a. and travelling to 1a. we describe or draw the linea., 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 linec. 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 linec. if I draw a rectilineal liner. between the centre and the vector point 1c. then I might call 0c. the centre and 1c. same as 1r.r1end point 1r1joined to the beginning point 0r2of a radius vectorr2. Both vector points1r1and 1r2are vector points1c1and 1c2 on the arc vectors / curves.c1,c2As the circular arcs extend around the circle the resultant vector point

Ttraces 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. Thus1

r(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 arc

c1,c2are in a plane P while circular arcsd1,d2are 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+zkWhat 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

Arepresents 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!