The new data has enabled me to set out a better proportion of 256: 21 for the proton-neutron : electron radii . In addition the line spectrum data for hydrogen gives me better frequency bounds. Trotorted has four linked Quaternion spheres so that it represents 3d on the screen by orthogonal axes which form a tangent plane to some sphere and two radii relative to that phere which take the sine dials. It would be nice to have circles in the faces of a tetrahedron but I have not even begun to investigate th mathematical calculations required for that! If Bill Shanks would talk to me then maybe?

Any way the 8 dimension controls for a pair of quaternions are reduced to 4 shared controls which in the case of hydrogen is manageable to encode most data for strongest lines. But for helium I can not really begin to do more than suck it and see what it looks like! In the hydrogen gas case I set the two hydrogen atoms in a proton electron proton pattern. The proton proton pattern with electron electron is different but not markedly so . The dynamic beats are however more noticeably wobbly in that pattern than the firs!.

Some thought needs to be given regarding these synthesis trials as a lot of assumptions like angular momentum for example are misleading in this context. Mre in another post.

Just a reminder: I am not advocating a particle model of the proton. Here I am reusing the data in a Trochoid application based on spherical coordinates to see what frequency and mplitude and phase do to calculated locii. These also end up , by the surface estimation as sketching trochoidal surfaces, and it these urfaces I am considering as representing curvilineal once surfaces within which curvilineal forces act as curvilineal lines.

So while you can not feel the magnetic behaviour you can see a magnetic patterning in space that is dynamic .

I am pushing my old computer o the limits of the application and inevitably it can't cope with the number of processes involved.

Let us consider the circle. The disc which fill in the circle perimeter has certin topological properties under rotation about the centre. Firstly , the disc rotating as a whole hides physical differences that appear when it is used asvavwheel. The perimeter becomes a dynamic region worthy of its own measure.

Firstly we have to understand arc length/ magnitude and angle.. We may be familiar with the neglect measure called degrees after the Babylonians that invented I. Like all measures we take them as granted, but in fact they are created by the weights and measures authorities in each civilisation or empire. The degree marked the daily precession ofnthevZodiac in the skies over Bbylonia/ Sumer. The Zodiac is a system of seemingly fixed stars in the night sky. We now know these are not ll stars, but contain galaxies of stars and intergalactic dust clouds nd water vapour and organic materials all moving in extremely fast celestial orbits around one mass or another. Amongst these we cn include the wanderers or planets.

The degree was therefore a fixed notion, but not relative to a fixed background. It was the very dynamic of rotation that made fixed proportions so interesting to Astrologers, particularly Eudoxus of the Pythagorean school. His theory of proportions , parts, multiple forms , in particular double forms, triple forms etc , inverted logoi or ratios and several others rests on the notion of logoi as dynamically related pairs of magnitudes linked only by the human observer! Thus these logoi are not necessarily physically related in space or time! However one requirement made by Eudoxus for his logoi, : topics of study if you will rather than ratios although the Latin means the same a topic of study , and thus we divert into all rational thought and rationality, not through magnitude but through consideration, comparison, contrast measured readonings etc.

It is fair to sy thatbthebPythagoreans excelled in. This kind of thought and in particular in regard to magnitude, which they quantified systematically.

So now in this manner Eudoxus set out the various ways two or more magnitudes may dynamically vary in a developmental process, providing they were Homognous, that is of the same kind. In fact it is not even kind, but rather genus or generative power! In this way what may be said of one part is said of all parts under discussion in this way a saying becomes a rule for all under discussion.

In this circumstance certin outcomes are inevitably true. This thn was the basis for logic the systematic rhetorical skill of argumentation.

Nevertheless I digress because the various things under discussion whether they be proportions squared forms( double forms) or cubed forms(triple forms) or any general multiple forms in structures that may be called analogous, or double or triple or inverse etc reveal one thing; Isis, or duality. And that is rather duplication or Isakis( multiplication by replication) in general. There was thus a constant form or quantum that was multiplied by replication and that constant form could be used to describe all replicants.

This is the true nature of the degree and indeed any invariant quantity in any measuring ystm that treats of dynamical magnitude.

Thus for centuries hidden behind the degree and planar geometry were the stringencies of spherical geometry and the real impetus for the centuries long calculation of the ine tables. The sine being that right triangular ratio of greatest interest to astrologers.

The arc length itself was a separate problem which led to the interest in the ratio we call Pi, the circumference to the diameter ratio or logos. Many approximate proportions hav bernnrevealed throughout the calculation with the rough and resdy3 being the most popular for artisans who made basins, or basket weavers.

These Two ratios were pursued for pragmatic reasons, but lately simply for academic pleasure!

It was Sir Roger Cotes who realised the usefulness of settin the numerical approximations of pinto the semi perimeter of a circle, his work,Harrmonium Mensuram may well have set this out had he not died. It is Euler therefore we give credit to for developing the same themes in his own inimitable way .

There is no physical necessity for pi to be set o the semi perimeter, but mathematically the work of De Moivre and Cotes on the roots of unity make this a Particularly convenient assignent.

In making this assignment Euler preserved the ratio betweenn the arc length and the radius that made the ratio of the circumference to the diameter work outno,pi in the unit circle.

The unit circle was the most asthmatic lily convenient circle for the quarter arc on which Pythagoras theorem is based.,,and the semi circle is what Thales theorem is based upon .

We may then harmoniously treat of the angle measure for the sine tables or the arc length for astronomical and astrological discussions.

It isbwhennwe come to deal with the arc in orbital or celestial mechanics that we realise the angle measure imposes an impossible constraint

One of the reasons I post videos from this site is because of the curvilineal force vectors on the wind maps. They are not infrequently associated with magnetic columns or ropes called properly Birkland Currents. In particular, looking closely at the so called anode tufts on the sun shows them to be vortices in dynamic rotation

We also see how the sunspots represent these vortices leaning into a powerful magnetic vortex as if feeding it, Finally we see in solace many novae and galaxies exhibiting trochoidal dynamic topologies. We know magnetic behaviour is universal. We are not so sure about gravity . Therefore it is a Magnetic Universe. Com!! Xxx

We may see how heat is represented by a rotational function, but not realise that that is induced by a magnetic behaviour that is fundamentally rotational.

We may hear that music is generated by a rotating surface and not grasp that magnetic behaviour is fundamentally a rotating surface behaviour. Shocking as that may seem, it is a fundamentally electric idea that sparks with potential! An idea that is magnetic . As an aside Norman Wildberger explains what are generally called linear combinations or spans. What that means is that prior to and fundamental to so called mathematics is Combinatorics. And we may combine anything, but it is more useful if we combine homogenous types. The exponential label for linear combination of ratios of variable sides of a right angled triangle obscures the none li rarity of the variable magnitudes, because it uses straight lines to measure the circular arc. To call it a linear combination is therefore misleading. As Grassmann described it: they are lineal combinations. That is a general an idea as an Mset! The articular lineal combination here is a Fourier series.

However Quaternion Hamilton-Fourier series also exist , and these I have defined as Grassmann twistors, in Fractalforums.com

We see how the diffraction grating is generated in the presence of paramagnetic materials, that are ferromagnetic. That means that they are many times greater than the background magnetic patterns. The nano particles are organised into an array that is curvilineal , and the rotation or chirality or rotationa polarisation of the light is altered accordingly.

Ok. Enough scientific speak. The magnetic behaviour is trochoidally dynamic. I can mimic tht dynamic result by certain ratios of circular arcs that are mutually and correspondingly acting on each other as force vectors. .

Where the orce vectors cancel an inertial region is created that resists all accelerative encouragement. Because of this inertia the force vectors are strained by a greater external pressure until pressure is equalised. The amazing thing about magnetic pressure is its regional containment.

Normally we use a container to generate high or low pressures, but magnetic behaviour allows high pressures to be generated in space with no known containment vessel.

We can think of this like compression of a spring, or use the fluid dynamic notions of viscosity nd relaxation in materials to explain this Boscovichian type of force. The nature of inertia when applied to curvilineal velocity and force vectors, naturally explains the intensification of curvilineal dynamics as radii are decreased.

It is still a. Mystery, but one to which we can attach a circular rule of thumb.

The thin ferro fluid coating inside th sphere can pick out the extended region of influence of the magnetic material. While it does not prove the rotational dynamic of that influence it does visualise such a dynamic naturally.

For me, this presents the history of the misunderstanding of trochoidal dynamics. It eulogises those who make breakthroughs with " crazy" ideas and at the same time reveals the stultifying effect of dogma and combatorial academics. The difficulties start with the particle conceived as a solid billiard ball. . The mechanical philosophers loved that concept. It was Leibniz who took a more organic view of the corpuscle as " squishy"

Later fluid dynamics was able to show complex"wave" behaviours come out of these squishy corpuscles, but in the course of that Boscovich generalised the notion of a force as a monodic entity, to set out how space itself has powered that generate pressures in discretizable regions. The concept of a particle and a wave had a theoretical " solution" in the works of Leibniz and Boscovich.

We see how Planck took Boltzmans ideas which were based on probability theory and statistics, which as I have hinted are derived from the study of the unit sphere for probability, and the counting of possible outcomes for organic products like peas, grain etc, all cyclically determined products.

And we have found how Maxwell despite the paradigm favoured vorticularly dynamic " corpuscles" as fluid dynamic particles of a medium for electric , magnetic and light behaviours.

The complexity of calculating Trochoids and rotational dynamics per luded any consistent model building. Instead a mish mash of ideas starting with Thompsons corpuscular atom, then Rutherfords atom and then finally Bohrs atom, all based on magnetic ordering, particularly the Bohr Magnetron, we're used to quantise materiality into discrete rotating regions defined as protons after the electron was first defined, and then followed by neutrons. Einstins massless electron, the photon had too be combined and the rings ofvSaturn inspired a planetary model that deemphasised Ritherfords discrete elliptical orbit model.

Yet I have shown that a trochoidal path model for a dynamic pressure urface is not only possible but feasible and removes many of the problems supposedly solved in QuantummTheory!

Well if you say so, and if you can get a straight answer from a Quntum physicist!.

The electromagnetic medium is an aether proposed by Maxwell. As logically and experimentally defensible , as opposed to the numerous theologically inspired notions of an aether , was always in his mind a fine grained vorticular structure in dynamic contiguity. Through such a medium a stress deformation could pass in the characteristic manner of a wave on the surface of the ocean.

It is best never to confuse the wave concept with the sine model of a wave, because it is known that real surface waves take on other trochoidal forms too! A sine curve is but one of many trochoidal curves, and really has no preeminence over any other Trochoid in a general rotational dynamic.

The three experiments that supposedly establish the granular nature of light as distinct from a wave that is supposedly continuous do nothing but show the ignorance of trochoidal dynamics! De Broglies pilot wave theory simply extends the range if trochoidal oscillations beyond the sine curve formulation!

The particle that sits above a concentric wave is a well known trochoidal dynamic that has simply been not believed.

When a cycloid moves beyond a certain radius, loops form that are characteristic of the radial proportions . If a curvilineal force extends beyond the non slip boundary of a rotating disc, that force, providing it retains its association to the non lip rotating centre will loop back on itself apparently. Physically it will pinch off part of the rotating fluid into a droplet. Providing no other forces act on that droplet( air pressures for example) that droplet I'll seamlessly recombine with the rotating mas from whence it cme.

The application of this dynamic alone to the photoelectric effect is sufficient to demonstrate that a wave particle duality is not a conundrum but a consequence of trochoidal dynamics at given relative frequencies.

How weirdness is eulogised! Here the mystery is in ignoring the Boscovich theory through complicated math! Some naive assumptions about corpuscularity and a general ignorance of Trochoids.

Thompsons plum pudding model at last explained and critiqued, as are the Rutherford and Bohr models. The classical simplicity while appealing makes assumptions that are rarely questioned. Why do spatial objects move kr remain still? Or rather How?

The relative motion goes hand in hand with absolute motion, but motion in general is always, perperpetually happening. And that motion is always perpetually curvilineal.

So Thompson only considered vibration about a mean , Rutherford o ly considered c irculating about a centre and Bohr o ly considered circulating in a concentric system .

Not one of them considered trochoidal motion.

And when further co side ration was given, it was almost exclusively mathematical and algebraic to boot. Thus trochoidal dynamics as a general solution was hidden behi d arcane symbols, and weird explanations.

And the fundamental fluid dynamic as magnetic behaviour was pushed aside into o security.

When it comes to materiality, to restrict o es paradigm to solid characteristics is to ignore the viscoelasticity, the fluid dynamicity of materiality , and to create pro lens where there are none.

The uniqueness of e ery data set regarding periodic table elements can best be described by trochoidally dynamic pressure surfaces that give rise to and govern curvilineal force lines or lineal segments

These dynamics radiate by default , and the radiation of these dynamics does not deplete trochoidal motion at any point it merely promotes dynamic equilibrium at. Point chosen by the observer.

But since promoting equilibrium in a given region says nothing in general about what is occurring outside that region, the complexity of trochoidal motion in and of itself does not tend to equilibrium, but rather to a perpetual and ever changing aperiodicity dynamic!

Despite our concept of invariant laws, that does not mean invariant stasis! In fact we observe that Panta Rhein! And so what synthesises will over time disintegrate and synthesise into a new form.

Do waves scatter? Trochoidal waves do! And every surfer knows the scattering of waves , and the scattering of the wind . And the supernovae we see show the scattering of magnetic behaviour just as CME's show the scattering of solar material.

Rotational dynamics is far more comp,ex than the sine wave model.

The wind maps show how a pressure boundary is associated with curvilineal force lines or lineal segments. It is a lesson to be learned that the lower the viscosity of a material medium the more dynamically these force lines play out.

Pause for a moment and consider that as a material medium becomes less viscous the more rotational behaviours become evident, and then realise that around any material is a vapour boundary of that material. Within that vapour boundary electrical and magnetic behaviours or rather differing magnetic modes of behaviour exhibi. . And now considervRutherfords scintillation experiment on a gold lattice.

One may assume that a dynamic alpha ray would be reflected, refracted, dispersed and diffracted , and indeed scattered. The tiny holes in a supposedly continuous foil begs the question: does the scintillation experiment create a diffraction grating that alters the recorded patterns?

These are very difficult experiments to carry out, and there is disagreement over the results obtained by different methods, the reoeatability of thevrutherford results when the same methods are used is heartening but not convincing that a robust phenomenon has been uncovered. .

So the 99.9% myth remains suspect.

The pressure produced by a scintillator is not uniform or stable. Using electrified surfaces and grids does not guarantee uniformity, and in fact measurements around a microwave transmitter show that. close to the source the variation is no uniform. However at a certain distance polarised microwave are strongly evident.. Rotational damping and resonance are factors that come to mind here.

Again, the photoelectric effect comes to mind as a model of this scintillation dynamic.

As a powerful polarised disturbance approaches a regional trochoidal dynamic, the resultant combination can be as follows: increase/ decrease in the trochoidal dynamic, absorption or or emission of the trochoidal dynamic, splitting of the trochoidal dynamic , absorption of the disturbance, refraction of the disturbance, reflection of the disturbance, change of phase of the disturbance change of polarity/ chirality of the disturbance , diffraction / dispersion of the disturbance, change in amplitude and or frequency of the disturbance.

These are known and measured effects in many dynamic situations. They constitute what Newton generalised as: action and reactions. He claimed or asserted that every action somewhere had an equal and opposite action, called a reaction. This general idea extended to chemical affinities although mechanical philosophers generally only applied it to Force and inertia situations.

When a student is introduced to inertia it is usually to discount it in some way from the solution to a given problem . However Newton spent some time exploring the property of inertia and did not discount it. Consequently the assertion of the existence of an equal and opposite reaction is not limited to an equal and opposite force. For examp,e, wrongly, friction is portrayed as a force . The viscous reactivity between surfaces is more co plrx than a simplistic representation of roughness by a coefficient of friction ! Obscured behind that coefficient are many complex chemical and electromagnetic interactions, not the least of which is viscosity in a fluid interface between two definite surfaces.

I have often wondered how a moving object is slowed to stop and then reversed! The general explanation is not given in terms of equal and opposite forces , but in terms of the energy balance or the work function. Without realising it many physicists except this mathematical explanation without the severe questioning it deserves.

The complex force and inertia interactions are ignored , the deformation of materials and viscosity and relaxation times set aside, the Youngs modulus, the plasticity and separation forces the Dirac impulse measure are all ignored in this simplistic explanation of dissipation of energy by friction! In addition, the wave like nature of the interactions is simply not addressed.

When a car crashes we instantly see the wave of interactions that occur, and the speed at which viscosity, elasticity and relaxation times act. In addition the plasticity and breaking strain limits of materials under impulsive forces operating at extremely high amplitude and frequency are revealed. Corresponding to these effects are magnetic disturbances in many modes which result in many magnetic, once, thermic and electric anomalies around the materials. Sparks for example, taken for granted may not only result but contribute to chemical reactions within the flammable materials, compounding the mechanical outcomes of the crash. Therefore the simple idea that a force can be stopped and reversed is materially inaccurate. A force inertia system may change its dynamic so that the expressed force is absorbed into the internal dynamic of a material thus changing its inertial characteristic. A hot body does not interact with its surroundings in the same way as a cooler one. Thus thrust from a propellant is much greater when that propellant is in its explosive phase and it's inertia suddenly becomes a radially active pressure as opposed to a reactive resistance to an external pressure.

The uniformity of Boscovich's force theory is perhaps best seen in how it provides a singular theory for most of these instances based on measurable phenomena, evn if th phenomena are not simply and translucent ly explainable

Equipotential surfaces usually are theoretically associated to normal or radial forces. The tangentially force within an equipotential surface is usually obscured by an explanation of the centripetal/ centrifugal radial force. For example the tangential force may be measured as a constant , that is brake horse power, or the velocity tangent may be measured as a constant , rotational velocity, but in both cases the inertial forces that maintain the circularity of the equipotential surface or rather it's curvature are ignored or not explained.

For example an orbit is not maintained by a centripetal force! Rather a centripetal force actsvagainstva complex inertia. We may represent this as an inertial force because it changes the curvature of the velocity tangent along with the centripetal force decomposition.. You may never of wondered how a weaker force can curve an object into a circular path if that object is supposedly moving only tangentially! The inverse square law is not stable on its own in a dynamic situation . As an object moves further away the force becomes less and so a tangential force would never do more than bend slightly. It would never go into orbit. A tangential velocity is therefore a nix description of a curvilineal velocity. Curvilineal velocities are obscured by this misdescription. If a straight line velocity takes the object closer to a centripetal source or into a centrifugal force ( a higher pressure) then orbital behaviour may be satisfactorily explained by such means, but in fact that still obscures curvilineal forces and velocities as the general force and velocity motion laws .

Thus around a current guiding wire the equipotential voltage lines depict the curvilineal magnetic force lines or line segments . The radiall Force lines described as electrostatic lines of force indicate the resultant pressure on a material that is susceptible but not ferro magnetic ( that is in the ferromagnetic range) . The susceptibility orients the material by the curvilineal fotces distributed throughout the matrial, twisting the material in space so that the magnetic polarity follows the equipotential surface and the rotation of the vortices or skymions are maximal at 90° to that surface. This maximal dynamic is called the electric force, but here I claim it is the magnetic rotational behaviour aligned in this radial aspect about a magnetic material with a high paramagnetic coefficient, or a high dielectric coefficient.

The Thompson model started the rot! The electron was considered to be the oscillator within the generally positive nucleus! However the nucleus is Aldo an oscillator! And so the concept of the spectral lines coming solely from electron energy level changes s misleading to say the least.

The concept of quantised energy levels indicates only that stable ratios exist for the frequencies of all oscillations around a circular perimeter. Every circular perimeter is a natural u it of oscillation , so quantised ratios are expected, evn if the circles are incommensurable either in perimeter , radius or both. Resonance means that these measures are in some commensurately proportion to each other.

The ultraviolet catastrophe is avoided by commie durable proportions , which in turn founds the notion of quanta.

There are proportions that are incommensurable, but these are beyond our capability of measurement, because we ultimately measure using finite metrons and counting. Quanta is just the Latin term for a finite system of finite magnitudes

In explaining tornados I drew attention to the downdraft and updraft sheets that counter rotate in a system . At the time I was not able to describe a curvilineal force dynamic as magnetic. But now I do so without hesitation.

It is known , and shown in a beautiful shot that the storm system generates spiral waves in the ground revealing the variation in the pressure sheets , but then I did not know that the height variation in the ocean associates to a magnetic disturbance. The ocean is now mapped as a magnetic phenomenon.

There is now so much evidence tha magnetic dynamics are not secondary effects to electrical differences but primary and causal to electrical phenomena.

Again, the collision of particles to generate triboelectric effects a) ignores tribomagnetic effects andb) is not necessar as curvilineal forces reveal the cause of pressure urfaces, hich as my previous post discusses are dynamic surfaces of acceleration and velocity in an inertial medium. .the inertial medium itself responds by oscillating at frequencies that are sufficient to represent the electric mode of agnetic behaviour, the fractal pattern of the park reveals not only the breakdown stresses in the medium, but also that intensely high frequencies of rotation are involved , intensely high magnetic oscillations. Lichtenberg fractal patterns shw where these stress patterns due to high frequency oscillations in a viscous material form, and high speed tornadic winds press air gases into a highly viscous form.

By the way we know tha the Bernoulli effect in moving gases apparently involves a lower pressure , but in fact the effect is better explained by the work function. The work required to lift a column of still water above a moving jet is not available , showing that force surfaces and pressures do not act orthogonally to each other but within the material sustaining the pressure surface

How Dirac presented a mathematical model that founded quantum Mechanics,

Despite the weird notation this example simply uses the rational trig values for angles. The use of probability relies on DeMoivres derivation of probability from the sine or trig tables. While those who do not know Newtons wide ranging work through his students might be amazed that Quantum Mechanics works , the plane fact is QuantumMechanics is just the group Theory on the unit circle .. It is purely mathematical and interpreted to the hilt. ! . The link to probability is the reason why Dirac set out this weird model. .

It is not that reality is weird, it is our measurement method that is weird!

## Comments

In addition the line spectrum data for hydrogen gives me better frequency bounds.

Trotorted has four linked Quaternion spheres so that it represents 3d on the screen by orthogonal axes which form a tangent plane to some sphere and two radii relative to that phere which take the sine dials.

It would be nice to have circles in the faces of a tetrahedron but I have not even begun to investigate th mathematical calculations required for that! If Bill Shanks would talk to me then maybe?

Any way the 8 dimension controls for a pair of quaternions are reduced to 4 shared controls which in the case of hydrogen is manageable to encode most data for strongest lines. But for helium I can not really begin to do more than suck it and see what it looks like!

In the hydrogen gas case I set the two hydrogen atoms in a proton electron proton pattern. The proton proton pattern with electron electron is different but not markedly so . The dynamic beats are however more noticeably wobbly in that pattern than the firs!.

Some thought needs to be given regarding these synthesis trials as a lot of assumptions like angular momentum for example are misleading in this context. Mre in another post.

Just a reminder: I am not advocating a particle model of the proton. Here I am reusing the data in a Trochoid application based on spherical coordinates to see what frequency and mplitude and phase do to calculated locii. These also end up , by the surface estimation as sketching trochoidal surfaces, and it these urfaces I am considering as representing curvilineal once surfaces within which curvilineal forces act as curvilineal lines.

So while you can not feel the magnetic behaviour you can see a magnetic patterning in space that is dynamic .

I am pushing my old computer o the limits of the application and inevitably it can't cope with the number of processes involved.

The disc which fill in the circle perimeter has certin topological properties under rotation about the centre.

Firstly , the disc rotating as a whole hides physical differences that appear when it is used asvavwheel. The perimeter becomes a dynamic region worthy of its own measure.

Firstly we have to understand arc length/ magnitude and angle.. We may be familiar with the neglect measure called degrees after the Babylonians that invented I. Like all measures we take them as granted, but in fact they are created by the weights and measures authorities in each civilisation or empire. The degree marked the daily precession ofnthevZodiac in the skies over Bbylonia/ Sumer. The Zodiac is a system of seemingly fixed stars in the night sky. We now know these are not ll stars, but contain galaxies of stars and intergalactic dust clouds nd water vapour and organic materials all moving in extremely fast celestial orbits around one mass or another.

Amongst these we cn include the wanderers or planets.

The degree was therefore a fixed notion, but not relative to a fixed background. It was the very dynamic of rotation that made fixed proportions so interesting to Astrologers, particularly Eudoxus of the Pythagorean school. His theory of proportions , parts, multiple forms , in particular double forms, triple forms etc , inverted logoi or ratios and several others rests on the notion of logoi as dynamically related pairs of magnitudes linked only by the human observer! Thus these logoi are not necessarily physically related in space or time! However one requirement made by Eudoxus for his logoi, : topics of study if you will rather than ratios although the Latin means the same a topic of study , and thus we divert into all rational thought and rationality, not through magnitude but through consideration, comparison, contrast measured readonings etc.

It is fair to sy thatbthebPythagoreans excelled in. This kind of thought and in particular in regard to magnitude, which they quantified systematically.

So now in this manner Eudoxus set out the various ways two or more magnitudes may dynamically vary in a developmental process, providing they were Homognous, that is of the same kind.

In fact it is not even kind, but rather genus or generative power! In this way what may be said of one part is said of all parts under discussion in this way a saying becomes a rule for all under discussion.

In this circumstance certin outcomes are inevitably true. This thn was the basis for logic the systematic rhetorical skill of argumentation.

Nevertheless I digress because the various things under discussion whether they be proportions squared forms( double forms) or cubed forms(triple forms) or any general multiple forms in structures that may be called analogous, or double or triple or inverse etc reveal one thing; Isis, or duality. And that is rather duplication or Isakis( multiplication by replication) in general.

There was thus a constant form or quantum that was multiplied by replication and that constant form could be used to describe all replicants.

This is the true nature of the degree and indeed any invariant quantity in any measuring ystm that treats of dynamical magnitude.

Thus for centuries hidden behind the degree and planar geometry were the stringencies of spherical geometry and the real impetus for the centuries long calculation of the ine tables. The sine being that right triangular ratio of greatest interest to astrologers.

The arc length itself was a separate problem which led to the interest in the ratio we call Pi, the circumference to the diameter ratio or logos. Many approximate proportions hav bernnrevealed throughout the calculation with the rough and resdy3 being the most popular for artisans who made basins, or basket weavers.

These Two ratios were pursued for pragmatic reasons, but lately simply for academic pleasure!

It was Sir Roger Cotes who realised the usefulness of settin the numerical approximations of pinto the semi perimeter of a circle, his work,Harrmonium Mensuram may well have set this out had he not died. It is Euler therefore we give credit to for developing the same themes in his own inimitable way .

There is no physical necessity for pi to be set o the semi perimeter, but mathematically the work of De Moivre and Cotes on the roots of unity make this a Particularly convenient assignent.

In making this assignment Euler preserved the ratio betweenn the arc length and the radius that made the ratio of the circumference to the diameter work outno,pi in the unit circle.

The unit circle was the most asthmatic lily convenient circle for the quarter arc on which Pythagoras theorem is based.,,and the semi circle is what Thales theorem is based upon .

We may then harmoniously treat of the angle measure for the sine tables or the arc length for astronomical and astrological discussions.

It isbwhennwe come to deal with the arc in orbital or celestial mechanics that we realise the angle measure imposes an impossible constraint

Trochoids I general

One of the reasons I post videos from this site is because of the curvilineal force vectors on the wind maps. They are not infrequently associated with magnetic columns or ropes called properly Birkland Currents.

In particular, looking closely at the so called anode tufts on the sun shows them to be vortices in dynamic rotation

We also see how the sunspots represent these vortices leaning into a powerful magnetic vortex as if feeding it,

Finally we see in solace many novae and galaxies exhibiting trochoidal dynamic topologies.

We know magnetic behaviour is universal. We are not so sure about gravity . Therefore it is a Magnetic Universe. Com!! Xxx

We may see how heat is represented by a rotational function, but not realise that that is induced by a magnetic behaviour that is fundamentally rotational.

We may hear that music is generated by a rotating surface and not grasp that magnetic behaviour is fundamentally a rotating surface behaviour.

Shocking as that may seem, it is a fundamentally electric idea that sparks with potential! An idea that is magnetic .

As an aside Norman Wildberger explains what are generally called linear combinations or spans. What that means is that prior to and fundamental to so called mathematics is Combinatorics. And we may combine anything, but it is more useful if we combine homogenous types. The exponential label for linear combination of ratios of variable sides of a right angled triangle obscures the none li rarity of the variable magnitudes, because it uses straight lines to measure the circular arc. To call it a linear combination is therefore misleading. As Grassmann described it: they are

linealcombinations. That is a general an idea as an Mset!The articular lineal combination here is a Fourier series.

However Quaternion Hamilton-Fourier series also exist , and these I have defined as Grassmann twistors, in Fractalforums.com

We see how the diffraction grating is generated in the presence of paramagnetic materials, that are ferromagnetic. That means that they are many times greater than the background magnetic patterns. The nano particles are organised into an array that is curvilineal , and the rotation or chirality or rotationa polarisation of the light is altered accordingly.

Ok. Enough scientific speak.

The magnetic behaviour is trochoidally dynamic. I can mimic tht dynamic result by certain ratios of circular arcs that are mutually and correspondingly acting on each other as force vectors. .

Where the orce vectors cancel an inertial region is created that resists all accelerative encouragement. Because of this inertia the force vectors are strained by a greater external pressure until pressure is equalised. The amazing thing about magnetic pressure is its regional containment.

Normally we use a container to generate high or low pressures, but magnetic behaviour allows high pressures to be generated in space with no known containment vessel.

We can think of this like compression of a spring, or use the fluid dynamic notions of viscosity nd relaxation in materials to explain this Boscovichian type of force. The nature of inertia when applied to curvilineal velocity and force vectors, naturally explains the intensification of curvilineal dynamics as radii are decreased.

It is still a. Mystery, but one to which we can attach a circular rule of thumb.

The thin ferro fluid coating inside th sphere can pick out the extended region of influence of the magnetic material. While it does not prove the rotational dynamic of that influence it does visualise such a dynamic naturally.

For me, this presents the history of the misunderstanding of trochoidal dynamics. It eulogises those who make breakthroughs with " crazy" ideas and at the same time reveals the stultifying effect of dogma and combatorial academics.

The difficulties start with the particle conceived as a solid billiard ball. . The mechanical philosophers loved that concept. It was Leibniz who took a more organic view of the corpuscle as " squishy"

Later fluid dynamics was able to show complex"wave" behaviours come out of these squishy corpuscles, but in the course of that Boscovich generalised the notion of a force as a monodic entity, to set out how space itself has powered that generate pressures in discretizable regions.

The concept of a particle and a wave had a theoretical " solution" in the works of Leibniz and Boscovich.

We see how Planck took Boltzmans ideas which were based on probability theory and statistics, which as I have hinted are derived from the study of the unit sphere for probability, and the counting of possible outcomes for organic products like peas, grain etc, all cyclically determined products.

And we have found how Maxwell despite the paradigm favoured vorticularly dynamic " corpuscles" as fluid dynamic particles of a medium for electric , magnetic and light behaviours.

The complexity of calculating Trochoids and rotational dynamics per luded any consistent model building. Instead a mish mash of ideas starting with Thompsons corpuscular atom, then Rutherfords atom and then finally Bohrs atom, all based on magnetic ordering, particularly the Bohr Magnetron, we're used to quantise materiality into discrete rotating regions defined as protons after the electron was first defined, and then followed by neutrons.

Einstins massless electron, the photon had too be combined and the rings ofvSaturn inspired a planetary model that deemphasised Ritherfords discrete elliptical orbit model.

Yet I have shown that a trochoidal path model for a dynamic pressure urface is not only possible but feasible and removes many of the problems supposedly solved in QuantummTheory!

Well if you say so, and if you can get a straight answer from a Quntum physicist!.

The electromagnetic medium is an aether proposed by Maxwell. As logically and experimentally defensible , as opposed to the numerous theologically inspired notions of an aether , was always in his mind a fine grained vorticular structure in dynamic contiguity. Through such a medium a stress deformation could pass in the characteristic manner of a wave on the surface of the ocean.

It is best never to confuse the wave concept with the sine model of a wave, because it is known that real surface waves take on

othertrochoidal forms too!A sine curve is but one of many trochoidal curves, and really has no preeminence over any other Trochoid in a general rotational dynamic.

The three experiments that supposedly establish the granular nature of light as distinct from a wave that is supposedly continuous do nothing but show the ignorance of trochoidal dynamics!

De Broglies pilot wave theory simply extends the range if trochoidal oscillations beyond the sine curve formulation!

The particle that sits above a concentric wave is a well known trochoidal dynamic that has simply been not believed.

When a cycloid moves beyond a certain radius, loops form that are characteristic of the radial proportions . If a curvilineal force extends beyond the non slip boundary of a rotating disc, that force, providing it retains its association to the non lip rotating centre will loop back on itself apparently. Physically it will pinch off part of the rotating fluid into a droplet. Providing no other forces act on that droplet( air pressures for example) that droplet I'll seamlessly recombine with the rotating mas from whence it cme.

The application of this dynamic alone to the photoelectric effect is sufficient to demonstrate that a wave particle duality is not a conundrum but a consequence of trochoidal dynamics at given relative frequencies.

How weirdness is eulogised!

Here the mystery is in ignoring the Boscovich theory through complicated math!

Some naive assumptions about corpuscularity and a general ignorance of Trochoids.

Thompsons plum pudding model at last explained and critiqued, as are the Rutherford and Bohr models.

The classical simplicity while appealing makes assumptions that are rarely questioned. Why do spatial objects move kr remain still? Or rather How?

The relative motion goes hand in hand with absolute motion, but motion in general is always, perperpetually happening. And that motion is always perpetually curvilineal.

So Thompson only considered vibration about a mean , Rutherford o ly considered c irculating about a centre and Bohr o ly considered circulating in a concentric system .

Not one of them considered trochoidal motion.

And when further co side ration was given, it was almost exclusively mathematical and algebraic to boot. Thus trochoidal dynamics as a general solution was hidden behi d arcane symbols, and weird explanations.

And the fundamental fluid dynamic as magnetic behaviour was pushed aside into o security.

When it comes to materiality, to restrict o es paradigm to solid characteristics is to ignore the viscoelasticity, the fluid dynamicity of materiality , and to create pro lens where there are none.

The uniqueness of e ery data set regarding periodic table elements can best be described by trochoidally dynamic pressure surfaces that give rise to and govern curvilineal force lines or lineal segments

These dynamics radiate by default , and the radiation of these dynamics does not deplete trochoidal motion at any point it merely promotes dynamic equilibrium at. Point chosen by the observer.

But since promoting equilibrium in a given region says nothing in general about what is occurring outside that region, the complexity of trochoidal motion in and of itself does not tend to equilibrium, but rather to a perpetual and ever changing aperiodicity dynamic!

Despite our concept of invariant laws, that does not mean invariant stasis! In fact we observe that Panta Rhein!

And so what synthesises will over time disintegrate and synthesise into a new form.

Do waves scatter? Trochoidal waves do! And every surfer knows the scattering of waves , and the scattering of the wind . And the supernovae we see show the scattering of magnetic behaviour just as CME's show the scattering of solar material.

Rotational dynamics is far more comp,ex than the sine wave model.

The wind maps show how a pressure boundary is associated with curvilineal force lines or lineal segments. It is a lesson to be learned that the lower the viscosity of a material medium the more dynamically these force lines play out.

Pause for a moment and consider that as a material medium becomes less viscous the more rotational behaviours become evident, and then realise that around any material is a vapour boundary of that material. Within that vapour boundary electrical and magnetic behaviours or rather differing magnetic modes of behaviour exhibi. .

And now considervRutherfords scintillation experiment on a gold lattice.

One may assume that a dynamic alpha ray would be reflected, refracted, dispersed and diffracted , and indeed scattered. The tiny holes in a supposedly continuous foil begs the question: does the scintillation experiment create a diffraction grating that alters the recorded patterns?

These are very difficult experiments to carry out, and there is disagreement over the results obtained by different methods, the reoeatability of thevrutherford results when the same methods are used is heartening but not convincing that a robust phenomenon has been uncovered. .

So the 99.9% myth remains suspect.

The pressure produced by a scintillator is not uniform or stable. Using electrified surfaces and grids does not guarantee uniformity, and in fact measurements around a microwave transmitter show that. close to the source the variation is no uniform. However at a certain distance polarised microwave are strongly evident.. Rotational damping and resonance are factors that come to mind here.

Again, the photoelectric effect comes to mind as a model of this scintillation dynamic.

As a powerful polarised disturbance approaches a regional trochoidal dynamic, the resultant combination can be as follows: increase/ decrease in the trochoidal dynamic, absorption or or emission of the trochoidal dynamic, splitting of the trochoidal dynamic , absorption of the disturbance, refraction of the disturbance, reflection of the disturbance, change of phase of the disturbance change of polarity/ chirality of the disturbance , diffraction / dispersion of the disturbance, change in amplitude and or frequency of the disturbance.

These are known and measured effects in many dynamic situations. They constitute what Newton generalised as: action and reactions. He claimed or asserted that every action somewhere had an equal and opposite action, called a reaction. This general idea extended to chemical affinities although mechanical philosophers generally only applied it to Force and inertia situations.

When a student is introduced to inertia it is usually to discount it in some way from the solution to a given problem . However Newton spent some time exploring the property of inertia and did not discount it. Consequently the assertion of the existence of an equal and opposite reaction is not limited to an equal and opposite force. For examp,e, wrongly, friction is portrayed as a force . The viscous reactivity between surfaces is more co plrx than a simplistic representation of roughness by a coefficient of friction ! Obscured behind that coefficient are many complex chemical and electromagnetic interactions, not the least of which is viscosity in a fluid interface between two definite surfaces.

I have often wondered how a moving object is slowed to stop and then reversed! The general explanation is not given in terms of equal and opposite forces , but in terms of the energy balance or the work function. Without realising it many physicists except this mathematical explanation without the severe questioning it deserves.

The complex force and inertia interactions are ignored , the deformation of materials and viscosity and relaxation times set aside, the Youngs modulus, the plasticity and separation forces the Dirac impulse measure are all ignored in this simplistic explanation of dissipation of energy by friction! In addition, the wave like nature of the interactions is simply not addressed.

When a car crashes we instantly see the wave of interactions that occur, and the speed at which viscosity, elasticity and relaxation times act. In addition the plasticity and breaking strain limits of materials under impulsive forces operating at extremely high amplitude and frequency are revealed. Corresponding to these effects are magnetic disturbances in many modes which result in many magnetic, once, thermic and electric anomalies around the materials. Sparks for example, taken for granted may not only result but contribute to chemical reactions within the flammable materials, compounding the mechanical outcomes of the crash.

Therefore the simple idea that a force can be stopped and reversed is materially inaccurate. A force inertia system may change its dynamic so that the expressed force is absorbed into the internal dynamic of a material thus changing its inertial characteristic. A hot body does not interact with its surroundings in the same way as a cooler one. Thus thrust from a propellant is much greater when that propellant is in its explosive phase and it's inertia suddenly becomes a radially active pressure as opposed to a reactive resistance to an external pressure.

The uniformity of Boscovich's force theory is perhaps best seen in how it provides a singular theory for most of these instances based on measurable phenomena, evn if th phenomena are not simply and translucent ly explainable

For example the tangential force may be measured as a constant , that is brake horse power, or the velocity tangent may be measured as a constant , rotational velocity, but in both cases the inertial forces that maintain the circularity of the equipotential surface or rather it's curvature are ignored or not explained.

For example an orbit is not maintained by a centripetal force! Rather a centripetal force actsvagainstva complex inertia. We may represent this as an inertial force because it changes the curvature of the velocity tangent along with the centripetal force decomposition.. You may never of wondered how a weaker force can curve an object into a circular path if that object is supposedly moving only tangentially! The inverse square law is not stable on its own in a dynamic situation . As an object moves further away the force becomes less and so a tangential force would never do more than bend slightly. It would never go into orbit. A tangential velocity is therefore a nix description of a curvilineal velocity. Curvilineal velocities are obscured by this misdescription.

If a straight line velocity takes the object closer to a centripetal source or into a centrifugal force ( a higher pressure) then orbital behaviour may be satisfactorily explained by such means, but in fact that still obscures curvilineal forces and velocities as the general force and velocity motion laws .

Thus around a current guiding wire the equipotential voltage lines depict the curvilineal magnetic force lines or line segments . The radiall Force lines described as electrostatic lines of force indicate the resultant pressure on a material that is susceptible but not ferro magnetic ( that is in the ferromagnetic range) . The susceptibility orients the material by the curvilineal fotces distributed throughout the matrial, twisting the material in space so that the magnetic polarity follows the equipotential surface and the rotation of the vortices or skymions are maximal at 90° to that surface. This maximal dynamic is called the electric force, but here I claim it is the magnetic rotational behaviour aligned in this radial aspect about a magnetic material with a high paramagnetic coefficient, or a high dielectric coefficient.

The electron was considered to be the oscillator within the generally positive nucleus!

However the nucleus is Aldo an oscillator! And so the concept of the spectral lines coming solely from electron energy level changes s misleading to say the least.

The concept of quantised energy levels indicates only that stable ratios exist for the frequencies of all oscillations around a circular perimeter. Every circular perimeter is a natural u it of oscillation , so quantised ratios are expected, evn if the circles are incommensurable either in perimeter , radius or both. Resonance means that these measures are in some commensurately proportion to each other.

The ultraviolet catastrophe is avoided by commie durable proportions , which in turn founds the notion of quanta.

There are proportions that are incommensurable, but these are beyond our capability of measurement, because we ultimately measure using finite metrons and counting. Quanta is just the Latin term for a finite system of finite magnitudes

In explaining tornados I drew attention to the downdraft and updraft sheets that counter rotate in a system . At the time I was not able to describe a curvilineal force dynamic as magnetic. But now I do so without hesitation.

It is known , and shown in a beautiful shot that the storm system generates spiral waves in the ground revealing the variation in the pressure sheets , but then I did not know that the height variation in the ocean associates to a magnetic disturbance. The ocean is now mapped as a magnetic phenomenon.

There is now so much evidence tha magnetic dynamics are not secondary effects to electrical differences but primary and causal to electrical phenomena.

Again, the collision of particles to generate triboelectric effects a) ignores tribomagnetic effects andb) is not necessar as curvilineal forces reveal the cause of pressure urfaces, hich as my previous post discusses are dynamic surfaces of acceleration and velocity in an inertial medium. .the inertial medium itself responds by oscillating at frequencies that are sufficient to represent the electric mode of agnetic behaviour, the fractal pattern of the park reveals not only the breakdown stresses in the medium, but also that intensely high frequencies of rotation are involved , intensely high magnetic oscillations.

Lichtenberg fractal patterns shw where these stress patterns due to high frequency oscillations in a viscous material form, and high speed tornadic winds press air gases into a highly viscous form.

By the way we know tha the Bernoulli effect in moving gases apparently involves a lower pressure , but in fact the effect is better explained by the work function. The work required to lift a column of still water above a moving jet is not available , showing that force surfaces and pressures do not act orthogonally to each other but within the material sustaining the pressure surface

How Dirac presented a mathematical model that founded quantum Mechanics,

Despite the weird notation this example simply uses the rational trig values for angles. The use of probability relies on DeMoivres derivation of probability from the sine or trig tables. While those who do not know Newtons wide ranging work through his students might be amazed that Quantum Mechanics works , the plane fact is QuantumMechanics is just the group Theory on the unit circle .. It is purely mathematical and interpreted to the hilt. ! . The link to probability is the reason why Dirac set out this weird model. .

It is not that reality is weird, it is our measurement method that is weird!