The discovery by Arago of magnetic behaviour in a non magnetic disc rotating near a magnetic object lead to many consequences . First it lead Lenz to formulate a law of induction which modified Faradays prior law. Then it lead more careful researchers to recognise a charge differential between the centre of the disc and the edge during rotation, which lead to the concept of a generator. It was never compared to the Wimhurst generator in those days but it should be recognised equivalent under the larger principle of tribomsgnetic behaviours. Faraday and others investigated the notion of diamagnetic polarity as a consequence of Lenz observations and Ampères law of currents. It was shown that all materials are susceptible to magnetic induction. However certain materials iron cobalt and Nickel were permeable to an extraordinary extent. It was conceived as environmental magnetic flux soaking into these materials .

Of those that were susceptible some showed what came to be proven as diamagnetic polarity, and like Aragos disc opposed the direction of magnetic induction in ferromagnetic materials : Those that showed parallel tendencies to ferromagnetic induction were called paramagnetic .

On another track researchers into Aragos disc phenomenon realised that reversing the homopolar generator by applying a current between the centre and the edge created a homopolar motor. Decades later Hall realised that applying a current to a semi conductor but diamagnetic material induced by a magnet pole would generate a measurable side voltage,as if the material was twisting in the magnetic field producing piezzo electricity.

During that time magnets became downgraded to current loops and research on the magnetic field structure stopped . It was not until Ed Leedskalnin that magnetic theory was revived and not until Howard Johnson that Eds findings were richly corroborated. But Ed did not describe diamagnetic polarity nor did Johnson. However the electronic characterisation of diamagnetic materials was completed and taught as fact.

I have to recant the particle theory for a rotational dynamic fluid theory . Vortices become the primitive structures but trochoidal vortices , dynamics unfamiliar to all but a few.

Howard Johnson’s magnetic poles as double vortices model. With like vortices attracting and unlike repelling provides a direct link to diamagnetic polarity in materiality and itsbrelation to the magnetic mode called electric charge and electric current.

Further NMR and all magnetic behaviours can be understood by his model including chemical bonding and nuclear fusion and fission . It explains why the so called neutron is unstable and why hot bodies like the sun are intensely magnetic.

Finally gravity is a demonstrable mode of magnetism in which induced magnets cling to one another when in a larger magnetic field .

]]>**absorbs or draws in energy before reacting to the initial action . And finally pressure acts curvilineally not just in straight lines .**

**https://youtu.be/mril0zFVJXQ in general the notion of a force should be derived from an expansion and contraction pressure in an inertial medium, which is why a fluid dynamic description of motion is crucial and something Newton advocated keenly . Einstein’s geometrical version or equivalence of force was an attempt to define an aethritic medium purely by data points and is naturally curvilineal. Unfortunately his students confused the reference force with a universal notion called gravity which still is not known or understood to this day by Academics . The reference force for earth or the solar system does not work for galaxies and galactic clusters which is why dark matter was invented . That dark matter is increasingly being found to be unaccounted for dust and water in the interstellar medium . The contraction and expansion of this and all materiality is governed by magnetic rotational dynamics of a fluid aetheric medium .**

**How does light propagate?**

**The first mistake is to teach young children and people that light travels in straight lines . The way like troubles is as a radiating disturbance from the point source. The radiating disturbance is A trochoid surface that expands from the point source. A light source or a reflecting source is made up of many point Sources. So the wave front is made up of an interference pattern of spherical Trochoid surfaces.**

**When this interference pattern hits a surface it is absorbed and then re-transmitted either as a Reflection or as a scattered pattern of light. Where the interference pattern meets a translucent material it becomes absorbed and re-transmitted through the material in the way which we call Refraction.**

**However if the lightht continues hrough a small openings and in the same medium The interference pattern becomes Diffracted near the Boundary of the small pin hole, The interference pattern is absorbed and re-transmitted at the Boundary, and the retransmission interferes with the existing interference pattern which is passing through. The Result is that the hole becomes a new point source. This source now transmits a complex interference pattern onto a surface which we can interpret as an inverted image.**

**If instead of a pinhole a small slit is used then the image becomes blurred because the interference pattern from the top of the slit to the bottom of the slip is made up of multiple overlapping point sources. The rotations will therefore interfere in a wavelike motion which we interpret as a blur.**

**A translucent lens is not a pinhole, however when it focuses the light to a point then the point acts like a point source and so acts like a virtual pinhole.**

**By focusing to a pin hole the image appears on the screen or Retina. However past that focal point light will continue to expand. The interference pattern becomes increasingly blurred, and the image is lost in a flood of non collimated light. This does not occur in a pinhole camera. The pinhole is fixed so the pattern emerges from a fixed position in space.**

**Collimator takes a “pinhole focus “ and prevents the light from expanding. It directs the light in a given direction onto a screen.**

**It is known that certain energetic sources form interference patterns which are too powerful to be focused by any optical lens. In this case a collimator is used to provide multiple point sources. The reduction in power allows the point sources to create an interference pattern which can be detected clearly on the screen. The multiple sources act like a single point source if the diffraction pattern is set up to interfere correctly.**

**We need to understand the collimating effect of an impedance surface in the magnetic flux**

**we also need to understand how a translucent lens through its dispersion effect by refraction enables the collimated interference patterns to align correctly in the magnetic flux.**

**The second refraction in the lens collimates the interference pattern in a certain direction, And those second refraction points sources act as a diffraction grating**

**How appoint source can be colimated Buy a lens, and why refraction is associated with diffraction.**

**Absorption and retransmission associated with diffraction at the LHC**

This is an electrified dielectric object. It is called a capacitor. Another electrified dielectric object that is called an inductor. A capacitor can store energy for much longer than inductor can. An inductor is a dynamic store of energy whereas the capacitor can store energy when it is not connected to a capacitor circuit. However, Ed Leedskalnin showed that if you make an inductor into a U-shaped loop then the inductor can store energy when that loop is magnetically closed with a bar when it is not connected to the circuit. This inductor which stores energy is called a PMH

A capacitor stores its energy in a dielectric. A PMH stores its energy in the magnetic current in the magnetic material. The ferromagnetic material is also a dielectric but it is a very poor one. It is therefore necessary for the ferromagnetic material to take the form of a closed loop. When in the form of a close loop the energy circulates around the ferro magnetic material in what Ed Leedskalnin called a magnetic current.

If we connect capacity to a PMH we should expect an oscillating Or alternating current flow in the circuit until it disappears.

This gives insight into what happens in the battery. The battery stores energy in both these forms within the chemical reactions that occur within the battery. However, as we know,a battery is not needed to charge a capacitor inductor circuit. We could use a generator.

Thus we can see that Energy can be stored within the PMH or within a capacitor which is a dielectric form in which the dielectric is a poor conductors or it can be stored within a PMH or it can be stored in a capacitor inductor circuit itself. The implications for transformer design, and transformers within any electric circuit, great . This means that if a transformer is disconnected from a circuit it will still carry a magnetic correct. Reconnecting such a transformer back into circuit will cause a flow of magnetic charge which could burn out a generator. In addition trying to disconnect a transformer in alternating current circuit will lead to flashback of energy .

The implications for storage of energy in the sun it’s also great. When are PMH is situated within the surface of the sun the magnetic current will flow smoothly. When the PMH breaks the surface of the sun then the magnetic current will form a loop of plasma involving several ferromagnetic / magnetic materials . This loop may discharge violently. We call such discharges coronal mass Ejections.

It also gives a better explanation of the so-called magnetic reconnection. NASA has shown that where so-called magnetic reconnection events occur magnetic bubbles are also present. These magnetic bubbles are what we call PMH . They are closed magnetic loops within the magnetic aether.

And finally, this has great implications for the understanding of plasmoids.

]]>Kens terminology can be confusing.

He combines insights from Eric Dollard with insights from some other observant specialists. The result can be gobbledygook . However, a little patience is rewarded by an insight into what Ken is pointing out .

First let’s explain what is a dielectric. The term derived from Latin refers to the fact that materials can hold separated charge. This refers back to the two fluid theory of electric charge on all or in materials.The term dielectric is a generalisation of the idea of a dipole. The words Paul and charge refer to points. Dipole is two separated points each. Believed to have different charges. These charges often characterised as opposite; that is plus and minus. In the more general theory separated points can just be at different “potential “

Dielectric is a region which consists of different charges the charges are believed to be points. Again the charges can be opposite, plus and minus, or different potentials.

Issue here is that in standard electrostatics the charges are assumed to be in static equilibrium. Thus in standard electrostatics the dynamic stage in which the charges rearrange themselves into separated regions is totally ignored.

Are these charges electric or magnetic? So William Gilbert and Ampére believe them to be magnetic. Later theorists, including Maxwell, separated the charges into two sorts. The first sort was magnetic and the second sort was electric. The justification for this was the observed differences in behaviour of so-called charged objects. However it is clear that the process that was being observed was, is called induction on an object or material. The nature of the charge is indeterminate.

You’re able to build a theory therefore, on the idea of an electric charge or on the idea of a magnetic charge. The Ideas are indistinguishable because the observed behaviour is behaviour of induction

Because the dynamics of the situation is ignored in electrostatics, and in Magnetostatics, the notion of induction is also ignored until much later. The velocity of induction for a magneto static or electrostatic situation differs. In the so-called electrostatic situation, according to the material, induction appears to take place at a very rapid rate. In fact rapidity of the rate is described by the term conduction. Maxwell determined that the induction in certain materials is so rapid that they would be called conductors. However we are looking at the same process the process of induction into different materials.

Because the fields were determined to be static, by that I mean the fields of study, the rate at which the in juicer was brought near to the inductor, that is material that will be induced, the rate of induction caused by the movement of the inducer was ignored until much later.

What Ampére noted was that statics was the wrong way to consider magnetic phenomena. Therefore he coined the term electrodynamics. This is not a tall to say that he believed in little points called electrons. In fact he considered many options but his favourite was dynamic circuitous movement which generated magnetism in a north south pole orientation. He believed that in a copper wire, or copper rod there were small regions which were in this dynamic. Beyond that he could not give any account of is notion, Ampére observed when the battery is connected in a circuit a magnetic North Pole alignment is generated within the circuit . So therefore some circular dynamic is causing this dipole or dielectric arrangement.

Later on Faraday noticed when the magnetic field was changing, that an induction was noticed within the circuit. So both a battery or a moving magnetic field induced this behaviour within a circuit. Equivalence of a battery and a changing magnetic field, the dynamic situation, should not be ignored at any scale or any dynamic or changing situation including chemical reactions.

Because of the belief in electrons, or magnetron the movement of the magnetic field was ignored. Movement was therefore placed only n the so-called electrons or magnetrons, this movement represented both induction and also generation of the magnetic field. It is much simpler to represent the changes as different modes of the same thing. Therefore the movement of a magnetic field generates a different mode of magnetic behaviour. The rate of induction by the movement of the magnetic field is equally as fast as the rate induction by the so-called electric charge in a conductor. The rate of induction in the conductor is therefore the same weather is induced by so-called battery or that induced by removing magnetic field. “Field quote is just a shorthand expression for the region around a magnet which influences material which is in its environment.

Is the field steady? Magnetostatics that it would have you believe that it is. However magneto statics like electrostatics ignores the dynamic stage of induction. When iron filings are sprinkled onto a magnet it is obvious to the eye and findings are in motion. When they achieve a state of rest they settled quickly into a state of equilibrium. When the paper is tapped get moved and they then also move into a different state of equilibrium. So therefore it is hard to think of the “field “as being static, it is easier to think of it as being in dynamic equilibrium.

Because the field is in dynamic equilibrium Ken is right poles as static entities do not exist. Instead we have dynamic regions where the dynamism concentrates.

When we discuss attraction and repulsion we are talking about these dynamics within the “field “.

Kens use of the word counterspace is misleading. The idea of counterspace comes from Steinmetz. It is a mathematical term and it refers to the fact that the field that we use to count or measure the strength of rotation within a magnetic field is an exponent or power or a logarithm . The term field or space here is the mathematical one. That is it is a set of numbers.

When objects are “drawn “together it is a moot point. The objects are either drawn by some spring or they are pushed together by some spring externally. This is mechanical explanation of what is observed. However it is more useful in thinking that space is somehow disappearing into some dimension. We can replace a spring by a dynamic pressure of expansion and contraction in a fluid.

Bloch wall, which appears between the north and south polarities when they brought together, indicates where the dynamic is nUllified. When we mhttps://youtu.be/LzdsRu1zscseasured this Bloch wall by means of a test dipole we find that there is a region where the torque is balanced on the dipole. So that we can talk about the alignment of the dipole with the alignment of the larger magnetic type as being parallel.

However when we look at magnetodynamic we do not get a static equilibrium of the dipole, instead we get the rotation of the dipole as it mous relative to the inducing magnet. We need to understand that in general magnetic behaviour generates rotation not static equilibrium. That’s what we see as attraction and repulsion as part of this general rotation relative to each other. At one end of the so-called polls rotational be observed t at the other end attraction will be observed as there is and is it a rotating away from each other will push the other end together.

This the analogy of a gyroscope is apt and is useful. It’s utility comes in acknowledging that the “field “ is dynamic, it is a torque or Rotating field , and therefore gyroscopic motions with in dynamic fields or torque fields need to be considered.

It is important to realise that the dynamics of rotation are not usually properly understood. The best handle on the general idea of rotation is Study Trochoidal dynamics.u

]]>It is the combinatorics of arithmetic. In combinatorics we pay attention to the sequence and arrangement of elements. In arithmetic these elements tend to be objects that we call numbers and symbols that we call operations. In fact in the written form arithmetics is totally symbolic. By this I mean that the marks that we call numerals are symbols, and the symbols that we use for operations are symbols, and any other signs marks or elements or brackets that we use in arithmetic are symbols.

What distinguishes algebra from arithmetic, is that we tend to use general symbols for everything. if we do not have a typeface for a particular operation or expression of something that we are trying to perform or process that we are trying to depict then we can create a new symbol and give it a precise definition.

Historically algebra was developed by an Islamic scholar called Al Khwarzim. and the symbolic methods or processes that he wrote down our more correctly called algorithms. Algebra was devised from a common term in Arabic Al Jibr which referred probably to the swinging of a balance. The balance would have two sides in which different objects replaced and the object would swing until it achieved a balance. however there was a more vernacular meaning to the word al Jibr and from there we get the idea that algebra was a “mindfuck” involving twisting and contorting the mind or brain in order to obtain some meaningless (apparently ) solution. Also from this connection we derived the word gibberish.https://en.m.wikipedia.org/wiki/Gibberish

Underlying algebra therefore is the fundamental nature of combinatorics, in which elements which might be objects or items or ideas are placed together in some kind of sequence or pattern. These sequences of patterns might be visual objects or they may be auditory objects or Tones ,musical notes; they may also be patterns of movement or patterns of flavours and tastes. This combinatorics is not limited to visual objects but can include every aspect of our interaction with our experience( experiential continuum).

How do we combine things?

The methods and systems and objects and elements that we used to combine help us to define the boundaries of certain subjects. So if we use mostly symbols then we may define our subject as logical or mathematical. If we use mostly the elements of nature and the environment that we may define our subject as chemical and if we use mainly the elements of the zoetopia then we might define our subject as zoology.

The common Underlying idea is our language the language of our mind and the ideas of our mind. The symbolic representation of our language may then take on the position of being symbols in our combinatorics and thus form an algebra. And as you have seen combinatorics might be the algebra of mathematics or of social sciences or of biology or chemistry.

Thus as Justus Grassmann pointed out, we must found all subjects in a more fundamental combinatorics, and then define an Algebra from these combinatorics rules and structures.

If we do so we remove Mathematics to its proper place in philosophy and computational sciences.

You may weep now understand why methods and systems are prominent in the sciences and mathematics and why Pythagorean scholars say first the Arithnoi and then the Geometree or Gematria or Numerology or Quabballah. It is general combinatorics of sequences and patterns of ideas, objects, processes and elements tha give rise to the algebras found scattered among all subjects.

]]>The inner smile

You smile at your heart

You love yourself inwardly

You grow your soul and spirit like a baby inside you

. Then you love and hug those persons around you even if you can’t see

]]>As a magnetic theorist i postulate an aether that is in rotational dynamism on every scale.

https://arxiv.org/pdf/1808.01967.pdf

This technical paper shows in practical radio Astronomy. A magnetic universe is unavoidably demonstrated.

Any of the mathematical techniques employed to solve linear view problems are mathematical evidence that a linear assumption is non utilitarian in cosmic and quantum scale dynamics. .

Such an aether ,as proposed,develops necessarily dipole characteristics and characteristic trochoidally dynamic surfaces.

The most intense form of this aether is a plasmoid. The energy stored in a plasmoid is proportional to the amplitude and frequency of the rotations within it. Thus the higher the frequency and the larger the amplitude the greater the energy available for work and the greater the power and thus the rate of doing work.

These gigantic magnetic structures do not need explanation of the curl or curvilinear form rather any straight line dynamic is what requires explanation

]]>

Lord Rayleigh ( John Strutt) made some influential notes about wave motion throughout his life. Bearing in mind he was born just before Quaternions were announced and Grassmann published his Ausdehnungslehre to a dismal response, and was in university at Cambridge about the time Maxwell published on Electromagnetism, using Quaternions and MacCullaghs curl potential, we can see he was right in the thick of the rests early attempts to model 3 d rotation mathematically.

It was really down to a few doughty souls to progress physics of the wave to its prominent position vis a vis the corpuscular dynamics of chemistry, which was making noteable headway in the industrial setting.

We have seen how Arago and Fresnel created a huge rift, with young , in the philosophical explanation of matter in the aether or plenum. While Newton provided a consisten theoretical model based on corpuscles , it was evident that it was not physical or empirical. At the same time the Wave theory was not physical with regard to light. Youngs experimental double slit interference patterns were not convincing enough , and it was the influence of Fresnel and Arago that enabled the results to make headway in the broader scientific, non chemistry based community. These tended to be more mathematically minded scientists who could understand the sine graph, intruded by Euler as a model of a wave.

The notion of a wave is very rarely examined. One is usually immediately programmed to consider the circular functions of Euler as a wave. Thus a disconnect with physicality is immediately taught. Scientists no longer see any real wave, but rather approximations to the ideal sine graph! However in this process the ideal sine graph is misconstrued as a wave and so it’s true meaning is lost even as it is plainly laid out before the students eyes.

Firstly let us remove the blinkers.

Euler took a circle of unit radius, that is its radius was defined as 1. Then he defined it’s semi circle or hemi arc as [tex]\pi[/tex] to about 30 decimal places. Thus he was able to draw an axis marked off in units of [tex]pi[/tex]. Thus this axis represented the rotation of a point around the circle or the motion of the centre as the circle rolled in that axial direction . In each case the circle was in dynamic motion called rotation.

Thus the sine graph represents not a wave motion , whatever that may be , but a rotation motion.

Now let us turn to wave motion. It must be observed that wave motion, vibration and periodicity are tautologically the same perceived behaviours. Any difference lies in the observers intention or purposes. Thus in the context of a sea wave the perception of a rolling body of water traversing the surface of the sea and rolling out onto the beach gives way to the undulatory motion of such waves on the personal stability of the observer. Indeed the bobbing motion of floating objects predominates over the passage of a rolling wad of water beneath !

Waves are observable on the surface of flats flowing rivers, but there the current predominates the observers senses and little mention is made of them. So what are the causes of these mounds of water in the surface of a dynamic fluid? It turned out not to be bobbing at all , but complex vortex behaviour. Both Lord Kelvin and Helmholtz regarded this as a groundbreaking phenomenon and they set out to describe a kinematics of vorticity. A first attempt.

This was a major influence on Stokes, Navier and Rayleigh, but Maxwell was conceptually in advance of these 2 great mathematical physicists. He wanted the vortices to act like gears nd springs and transmit strain. He opted to use Hamiltons Quaternions to express his ideas. Lord Kelvin was not amused. He like many scientists in his time felt this use of the imaginaries was Jabberwokky. A term coined by Lewis Carol, a prominent traditional Mathematicin, who derided this kind of Alice in wonderland mathematics in his book of the same title.

Consequently Maxwell was forced to recent, and in a remarkable turn around went from prise of Quaternions to a dire denouncing of them! This was at the behest of Lord Kelvin who was developing the ideas of vectors set out by a young American student of thermodynamics called Gibbs. It is a dark but not unfamiliar tale of underhand tactics. As a result, overnight research into Quaternions was shelved in America after a fateful conference on the issue of how physics should be taught.

Maxwells statistical approach to gases suited Lord Kelvins own Kinetic theory and so statistical Mrchanics was developed by Gibbs to great effect, but the mathematics of fluid mechanics and ths Elrctromagnetism based on that floundered. This was because Maxwell expressed all the main concepts in terms of Quaternions. The fledgling vector algebras were not sufficiently graped to be able to compete with this elegant description. In addition, the Curl of a vector field was developed by McCullagh a mathematician in the same tradition as Hamilton, who used Quaternions to formulate his ideas, and the relationship with Knots and the properties of vortices in space.

The second tautological concept of a wave is periodicity. Thus when we experience the unwise everyday we apprehend periodicity, but hardly intend to call it a wave! It is clearly a rotation which involves very large scales of distance and time. Nevertheless we have to cknoledge that repeated variation which immediately makes it sn logos to regular bobbing up and down as in wave motion.

Periodicity reveals to me the essential rotation that is evident in a sea wave is lo evident at a much larger scale in astronomical terms. Astronomers since Eudoxus have modelled these circular motions to give. Apparent relative motions of planets. These motions were very wavelike and hence planets were called wanderers!

We now know that our solar system wanders in the milky way galaxy on some spiralling rotating arm of the galactic structure. This wavelike motion is on a time scale of tens of thousands of years and on a displacement on sn astronomical scale .

My third example of the notion of wave motion is vibration. Typically we think of a piano string or a washing machine . We are told to think a piano string vibrates up and down. In fact it vibrates round and round! Despite precise plucking or striking the mechanical behaviour of taught wires in vibration is rotational. These rotations may be elliptical rather than circular but they are not up and down like a slow moving tension curl in a skipping rope.

While it is always possible to dampen the elliptical motion ofa vibrating string by placing constraints, this only emphasises the point. Vibrations are helical waves travelling bidirectionally in a tensile medium.

It really does not matter what scale you go to vibration or wave motion is due to rotational motion .

It is clear that rotation at any scale is almost similar. Thus we can expect the same mathematical formulae for wave motion to apply at ll scales.

Schroedinger’s wave equation is simply derived for rotating systems at ll scales. The idea that an atom is a planetary system look alike makedps this expectation almost inevitable. However we must not confuse rotation with planetary systems. A much more general graph of a rolling circle is called a trochoid.mit is complexes of these that better describe arbitrary rotation in space. We shall see that means regionality is inherent in rotational motion, as is integer relationships between regional complexes.

These regional complexes define a fractal Geometry and a fractal distribution

<From Fractalforums.com topic Light page 11>

]]>**This is a 2d Rayleigh wave. We will see how a Rayleigh wave is the general wave notion we should use in physics and how it avoids the ultraviolet catastrophe.**

**This is the math that Rayleigh used with a colleague to derive the ultraviolet catastrophic equation. Notice it does not use Rayleigh waves. **

**The Planck derivation is in the first video **

**A clearer depiction of a Rayleigh wave , evident at a surface boundary where freedom of movement I greater. **

**So we see the the many modes of wave propagation are generalised in the spherical wave with an exponential description. At any surface boundary love and Rayleigh waves are generated.**

**Assuming a sine wave node at a black body boundary is thus a mistake, Planck by assuming a spring behaviour was closer to boundary reality conditions. **

**The propagation beyond the boundary , the black body glow will therefore be a spherical wave propagation. Such a propagation necessarily occurs in discrete frequency modes which Planck called quanta without understanding why his spring model was better than Rayleigh node model. **

**How do we go from springs to probability?**

**The answer is interesting and illuminating.**

**De Moivre originated probability theory. De Moivre, sir Roger Coates and Newton were a powerful research team exploring Newton’s ideas and concepts. Newton was a master of infinite series and of the math of the geometry of the unit circle. Consequently he was able to accept and use the negative quantities of Brahmagupta and the other Indian mathematicians along with the Algebraic concepts of Bombelli regarding the square root of -1. .he was a student of Isaac Barrow and learnt Pythagorean geometry through his influence. He consequently formed and solved many multinomial equations and set out a basis for polynomial theory. His understanding of difference equations and expressions in calculating the trigonometric and natural and Briggs Logarithmic tables was unexcelled by his peers, . He took on De Moivre as a personal disciple and later sir Roger Coates. Both Coates and De Moivre collaborated on the theory of roots of unity in other words the discretisation of the unit circle. . Coates went on to propose the Coates Euler theorem in its logarithmic form decades before Euler proposed it in his exponential form.. of course he died before he could explain it to Newton as a generalisation of Newton’s force laws . Later Boscovich completed this line of research , really establishing the force relations as Fourier type expressions’ which are based on rotational dynamics. **

**However DeMoivre took the unit circle ideas in the direction of establishing probability theory which he.did , barely establishing preeminence over another developer. **

** ◦ These ideas of probability or expected outcomes were applied by Boltzmann to physical phenomena where populations of agents could reasonably be expected. Needless to say it was not popular with his peers who wanted exact or precise solutions. However Gauss showed how by using these ideas he could precisely predict the orbit of a comet which was only sporadically glimpsed and often immaculately measured. . By applying Boltzmann normal distribution curve to these varying data he was able to determine a bell shaped distribution which gave the probability of a range of measurements. , meanwhile Fourier was demonstrating how trigonometric functions could interpolate any polynomial and indeed any curve shape. Thus a population of sine or cosi e functions could describe a set of experimental data . Lord Kelvin promoted this view as the way forward in physics especially for the growing molecular description of material behaviour, At the same time Maxwell was using the Gauss Boltzmann normal distribution probabilities to characterise gases and the velocity of their Dalton molecular structure. All at that time accepted the aether continuum and so vortices in a continuum as proved by Helmholtz became the favoured corpuscular model for the atom. . There were no electrons until JJ Thompson demonstrated a ratio Metternich mass and so called EMF which could just as well be explained as magnetic induction force given a dynamic magnetic vortex.**

**So Rayleigh in relating radiation energy to frequency assumed a purely sinusoids wave. . Such a wave as a standing wave can have any frequency that fits the cavity. . In his reasoning the frequency obscured the wavelength. We can see that only half wavelengths can be counted, but not all frequencies will have half wave lengths that will fit a cavity. These were assumed to be destructively cancelled. . So right there we have discretised frequencies. However by averaging they obscured this discrete condition. **

**Planck on the other hand was considering populations of springs . He therefore had little choice than to start with a generalised Fourier description with its discrete frequencies. . Using the Maxwell Gauss Boltzmann De Moivre ideas an accepted energy probability curve was found, . He could not average away the discrete frequencirs. Instead he had to use the standard series sums to simplify and this gave a different form to the description. It also tied in his results with the different series used to depict the wavelength lines in rhe spectral analysis of emission spectra. **

**We see that classical exact formulations were not up to the job, but classical probability theory and Fourier analysis were. **

**Ironically Rayleigh himself pointed to flaws in the wave mechanics of his day relying too heavily on the simple sine wave. He expressed his wave mechanics in the complex Fourier form, and so predicted Rayleigh waves.Love then predicted love waves. But Planck by focusing on the modes of spring oscillations unwittingly uncovere the physical explanation of these modes of oscillation and the quanta required to isolate them.**

**Quanta are interesting. Because we do not understand the arithmoi we fail to grasp that quanta or units have to be carefully distinguished. So quanta in relativity are units of space times time. In rotational dynamics they are u its of h times frequency. In Newton’s principles quanta are units of density times volume and J J Thompson discovered a quantum that is units of mass times deposition time, called the EMF. Both electric and magnetic induction are used to establish this quantum which is why we call such waves electromagnetic.**

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