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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 wrests early attempts to model 3 drotation mathematically.

It was really down to a few doughty souls to progress physics of the wave to its prominent position vis a vis yhe 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 Newyon 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 to about 30 decimal places. Thus he was able to draw an axis marked off in units of . 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 Gometry and a fractal distribution

Light unfortunately is associated with wave motion. This arises due to the Fresnel analysis of superpositional interference : constructive or destructive interference. In truth wavelength does not enter the picture, but a picture is drawn to expound the concept.

From the start of measuring the speed of light, light pulses have been used to provide an Intrinsic parameterisation.  That means within the beam or promulgation of light a natural or imposed division of " time "was  established. To precisely mark the time a spinning shutter or mirror was used. This rotational frequency was used to calibrate the time stamps

Of course frequency allows us to calculate a length once we know the speed. Determining the speed required ver precisely synchronised clocks and very precisely measured distances.

The frequency of the flashes were crucial . Several methods of measurement were tried but most relied on the synchronicity of the flashes. Thus frequency is the paramount measure of light .

Later as the popularity of the sine wave model grew it became possible to calibrate by spectroscopy the interference patterns , and this revealed a variation in wave length. Light colour or spectrum was then calibrated in terms of wavelength as opposed to the optimum frequency required to get good interference patterns..

We need to understand the role of rotation not only in calibrating light speed and wavelength, but in the nature of light propagation itself.

Huygens model of spherical intermediary light sources , induced by incoming light  is always drawn either as arrows or wave fronts. The physical fact is wave fronts are spatial. They are not ephemeral boundaries. Thus a wave front passes through a region of space by a meaurable disturbance in that region.

Until now that disturbance has been mis-characterised either as a transverse motion or a plane front! . The transverse motion has always been accompanied by a transverse motion out of phase. This has been interpreted as an electric and a magnetic signal. It may also be interpreted as a rolling spatial motion.

This rolling of space is regional but it is accompanied by many regions like it spread spherically throughout the space around a light source.. As they promulgate in contiguous contact, they behave like Rayleigh surface "waves", giving the appearance of a surface , characterised as a wave front.  This means that light also has a longitudinal  or compression like progression, but of ourselves at these speeds it is hardly meaurable, requiring Doppler techniques to properly distinguish the phenomenon. The wave front is slightly bluer at one phase and slightly redder at the opposite phase in the rotational cycle, but the eye will not detect this in the overall intensity of the progression through the medium.

Rolling wave fronts best explain diffraction and dispersion , but the necessity of a viscosity in the medium is what has hindered the consideration of these physical phenomena. The viscosity in the vacuum is misinterpreted as electro magnetic constants. . These change as the medium of transmission is changed, but the assumption is that the vacuum is perfectly  non viscous. This cannot be true as light and other electromagnetic phenomena reflect and refract and diffract at regional density boundaries, with absorption and retransmission. In the vacuum very little light is visible from the surrounding space because no retransmission takes place. The free transmission of the rolling wave front  is only interrupted as the viscosity of the medium it is absorb into transforms it into different frequencies  for re transmission.

When pictures of the sun are taken at these different frequencies the viscosity of the space involved is clearly visible, but where the viscosity is uniform, no retransmission continues to occur.

Daniel Russels page gives an understandable description of " wave" reflection.

http://www.acs.psu.edu/drussell/Demos/reflect/reflect.html

Of course it opts to call on Newton rather than actually explain.

To start with, a sine wave is not possible in a madium with no tensile attribution or property. In general no viscosity no sine wave. The only possible wave is thus longitudinal and the medium must therefore possess an elastic attribution. Again no viscosity no compression wave.

Simple compaction will transmit into a medium with no elasticity but the energy will be absorbed and dissipated by contiguous contact and the build up of affected inertial mass. The energy of the system may be constant but for the impacted medium what Newton called the measure of the quantity of motion.mv will be increased with no appreciable net velocity gain. Thus mv is a measure of the energy within a body, and the logarithm of mv² will be a type of temperature measure.

Temperature is usually a measure of heat pressure, that is the quantity of motion transmitted to a very motile fluid such as water or mercury. As it is usually measured in a small region it represents a proportion of the whole which is quite small. The method for accounting for small proportions was devised by Napier in his famous treatise on logarithms. Establishing a base for these types of logarithms requires a geometric proportion which is why mv² is used.

The input of temperature( heat pressure) into a medium results often in material property changes and usually the creation of viscosity. Once viscosity can be adduced then lastic and wave behaviours become possible and probable. Quite often a fine plasma envelops the impacting body as the inertial mass increases creating an elastic fluid reaction product that ejects past the impacting object taking a good proportion of the quantity of motion with it. The viscosity of this plasma has yet to be measured I think, but its presence is well attested.

Viscosity therefore is necessary to expound on any wave mechanical description, and if it is assumed not to exist, natural events seem bound to create the property.

Returning to the medium which permits compression waves but supposedly not transverse waves, the compression creates a viscosity / elasticity in such a medium. The chemistry of this product is usually ignored by physicists, but in fact it is quite important at the small scale. The injection of heat pressure encourages endothelial reactions which may be homeostatic, releasing the compression product in an rndothermal reaction , restoring the initial state. This is a viscous behaviour.

Newton spent a great deal of time and effort attempting to understand these chemical behaviours of materials. He wanted to know where the " stickiness" in matter came from. Unfortunately in fluids he assumed they were resistive media only and considered only lubricity, that is how easily an object passed through another. He dd not think that this was a function of stickiness or viscosity.

Thus we can expound upon compression waves in terms of a measure of elasticity. As for gases this elasticity was renowned and called pressure. Boyles Gas pressure laws helped to account for sound compression waves. Waves at ths time meant like we see in water! Newton in fact used a very elegant water vapour demonstration of waves in gases based on the humidity of a gas, which was observed to vary with pressure.

The viscosity of a gas was yet to be explained, and it was Maxwell whose velocity probability distribution , based on Boltzmanns observations, that gave Kelvin the grist for his kinetic theory of gases. The viscosity was locked away in the energy density due to the contraction of volume. It took a while for viscosity to become isolated as a general factor in wave propagation.

Light however was thought to be different. Descartes felt it was a wave propagation like all the others, but Newton felt it was a ballistic rø paganism of corpuscles. He saw or refused to see any evidence of water or harbour waves. Grimaldi on the other hand believed he had detected them in a phenomenon he called diffraction.

The problem arose because no one saw any reason to admit rotation into the general discussion on waves. Compression waves were all assumed to bunch up like water. Nobody actually investigated water to see what it was doing until waves became important.

When they were investigated, chiefly by the fluid mechanics, Helmholtz, Navier Stokes  Rayleigh it became obvious that rotation was involved. But by then Fresnel had accounted for light by means of sine" waves" nd insisted transverse motion was ll that could properly account for it. Young believed that longitudinal motion had to be involved but he was overruled.

Rayleigh demonstrated that longitudinal motion was involved but he was marginalised to the seismic community and later the radio engineers!

In fact Ray,eight demonstrated that at a surface rolling waves were the solution.

We can now return to compression waves and add in the left out rotation factors. All compression involves some element of rotation, and in fact strain methods account for the behaviours of materials using strain ellipsoids..the viscosity of the material effects the behavioural outcome, especially when viscosity is known to behave rotationally!

Finally we address the wave motion in a tensile medium.

The medium is viscous because of its tensile nature. This means compressive and rotational moments of force are resisted viscously, ie elastically. Providing the viscous modulus is not breached a medium has a restorative force behaviour. Hooke is the most famous scientist to use this to describe force, it is often overlooked that Newton derived his force measure from Hookes observation. Hooke was interested in statics, Neeton in Dynmics, thus he observed what Hooke factored out, the accelerations involved in these restorative forces.

In many senses inertia means Hookes steady spring state, that is a force equilibrium. Newton just observed that inertia is achieved over time as forces tend toward equilibrium.. Acceleration thus was the determiner of that active principle called force with celerity or velocity bring the result of force.

When Newton observed that rest and uniform motion were both equilibrium states he opened the eyes of engineers forevermore! The question of why objects continue moving when no force is applied was quickly forgotten. Newtons philosophical causes Motive and celerity were removed from consideration by simple measurement! His formulae derived from his deep thinking were good enough to build bridges with! Let the philosophers ponder the rest!

So in a tensile medium any change in the balance of equilibrium results in a restorative force that is equal and opposite. The behaviour of the system under these conditions produces oscillations that damp down. The reason for this Newton observed is complex but it is a redistribution of the quantity of motion often resulting in a rise in heat pressure.

The actual chemical and viscous behaviour was not examined until fluid Dynamics started to be computationally possible.

In the tensile material long chains of material are linked by electro Thermo magneto dynamics. As the material is deformed these chains are stressed or compressed . They behave viscously, that is like springs. The rounding of the material produces rotational forces in the material that restore the material. Thus it is rotational forces that generate the restorative forces as tangential components to the rounding.

Imposing a potential energy initial condition in a tensile medium results in the restoration of the medium through rotational oscillations. Applying the potential as an impulse results in a rolling wave transport in the tensile medium. The rolling wave carries the potential impulse and the restorative ftces in a time dependent way. It is how quickly and how strongly the restorative forces act that determines the speed of the wave. Interestingly this speed is determined by mc² = T the restorative force! However m here is an inertial mass constant , but a mass related factor even if dimensionally different,

This rolling wave is time dependent, but the front of the wave is carrying the potential element which is generating the restorative force that acts at the rear. The rotation is thus a swivel backwards and forwards.. The amplitude or spatial motion of the tensile medium determines the action of the rotating swivel . It will lift the medium against gravity on the leading edge and assist the material with gravity on the trailing edge.

When we now look at reflection we see that the leading edge encounters a different viscosity medium. This absorbs the potential as a rotation and begins to return the tensile medium by its restorative forces.in so doing it counteracts the potential imparting force by its own equilibrium restoring forces. If these act fast enough it can return the medium to the rest position before the peak potential arrives and then send back a reflected wave that interferes with the on coming potential..

If the medium is not very fast as in the second case the return wave pulse can be returned as the rear restoring force interacts. The 2 forces combine to send back a strong signal without interference or polarisation by phase. If the medium behaves inelastically  the wave may just be damped at the end as if it was free.

The important point is that this wave motion requires a rotating or swivelling bend to propsgate.  Propagation does not occur without this time dependent rotation in a viscous medium.
http://www.researchgate.net/post/What_is_bulk_sound_speed

This time dependent rotation of the material is hidden within the bulk characteristics of a medium.mby that I mean the usual ideas for measures do not admit the rotation that is present , but rather use trig ratios to measure bending strain. This bending strain is dynamic and so really should be thought of as a rotation. In particular to propagate a rolling wave form usually called a transverse wave , the trailing edge must accelerate the tensile restoring http://www.researchgate.net/post/What_is_bulk_sound_speedforce: thus the whip hand effect transmits the pulse as opposed to just raising the tensile medium.

Finally, all these modes of behaviour in media characterise the transmission of a fluid motive we now call energy. What all these behaviours demonstrate is how energy is first transformed into various kinds of force based on rotational forces.

http://www.roymech.co.uk/Related/Fluids/Fluids_Characteristics.html#Compressibility

<a href="http://www.youtube.com/v/If6J-jWnb7c&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/If6J-jWnb7c&rel=1&fs=1&hd=1</a>

Note emissivity is a measure of " electric" field strength(? Whatever that is!) and mu is the permeability of magnetic rotation in space.

The rotation of magnetism is fundamental to our theories of light and matter, and yet we consistently ignore this spaciometric fundamental of motion in space.

Here is a treatment using Riemannian concepts, and where Riemann is Grassmann will not be far behind!
http://gregegan.customer.netspace.net.au/ORTHOGONAL/04/EMExtra.html

The X-ray light source was used to split the electron. The electron is not a fundamental particle anymore. It never was.

<a href="https://www.youtube.com/v/dvzT1Pz6W4Y&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/dvzT1Pz6W4Y&rel=1&fs=1&hd=1</a>

Ok, so now I get the Galilean principle. It took a while and it required the freedom of Grassmann Schwerpunkt or weightpoint concept to understand where I was not understanding!

Newton distinguishes his quantities as mathematical not physical. Most physicists not being philosophers will not catch the difference.the word Mathematical is a translation of the Greek which was eluded into the Latin. It is simply a qualification for a Pythagorean scholar or adept. Thus if I rephrase Newton as saying his quantities are astrological not physical, you may understand why his Principia is better translated as the Astrological principles.

There is a story that Newton picked up a astrological tract from a penny arcade and found the figures therein incomprehensible! This was his first introduction, the story goes, to Euclids " geometrical" philosophy, which to be fair is in the Stoikeia, but he probably was reading an Islamic Atistotelian version!

What the Galilean principle states, in the mouth of Galileos characters in the dialogue is that a uniformly moving and isolated box imparts its motion to everything within it. Thus an observer within cannot tell any difference in the physical laws of phenomena! This last induction or rather adduction was added principally by Einstein nd Lorentz. However it is well founded in Galileos thought experiments based on his astrological observations of Jupiter!

The Jovian system is a carriage without walls, an isolated system, apparently, in which the moons circle the planet  as it wanders! As Galileo says, " All is explained in a diagram".

It is clear, but an assumption nonetheless, that the diagram implies that Jupiter is a " solar" system. In the terms of his day that was a Copernican system. Thus in showing Jupiter has moons that circle it , and the earth has a moon that circles it, he removed the main objection to the idea that the sun has planets that circle it! This is a fractal system if ever there was one!

But then the objection becomes, how can these moons follow after their planets ? The answer then was the basis of the theory of gravity. Each moving centre imparts by Newtonisn accelerative vis a motion to those bodies circling it , so that the sum of their motions may be called the motive vis in the Newtonian vis economy. This is none other than a restatement of the Galilean principle, as illustrated by his diagram. In addition, Newton idesteps causal philosophy by separating out absolute vis as causal.mthus he was free to develop the accelerative motive vis relationship as a quantitative measure relationship.

Leaving that to one side, we must note that the Galilean principle is used to deduce an action st a distance principle called gravity. It may also be used to deduce a centrifugal principle called levity, and finally it was adduced by Einstein principally to say the laws of physics hold in a reference frame that is moving uniformly.

Now a reference frame is not taught as a physical obstruct, but rather as a geometrical ubjectively construct which may move with the observer. It is formal, geometrical and relative. It should have no affect on physics whatever! So what is missing in the mathematical geometrical understanding of a reference frame?

Principally it was the motion of a luminiferous aether! At the time most philosophers took for granted that an aether pervaded all space including the vacuum . However it depended on your religion as to whether it did nothing , or rather was allowed to be anything physical. It was hoped that science might determine these things, by certain scientists, philosophers shall we say. However certain theologians were opposed to this idea of empirical evidence.

Nevertheless the Galilean principle relies on the centre imparting motion to the circling bodies. So far the only accepted and epicurean idea was that of gravity. Newton was at pains to point out that the word was not defined! But it was convenient for the church , philosophers and others to define it tautologically.nthis led logically to the idea of action bring caused at a distance by no coupling medium! This was abhorrent to Newton.

Later Faraday and Arago  demonstrated a magnetic field of force affected iron in space around a lodestone or a current shrouded wire, and Örsted and Ampère demonstrated that this force was a circular force! Even today scientists can't accept that empirical fact, but back in Ampères day it was met with incredulity by Lagrange, Laplace , Binot, Savot, and even Maxwell! Coulomb in particular was convinced that the "Newtonian" gravitational mathematical model was all that was required. By then most had rejected Newtons subtle modifications to his Galilean reference frame and baldly stated that force acted only in straight lines!

Ampère was convinced that electrodynamics revealed for the first time a fundamental circular force and set out the laws for it. However after convincingly demonstrating his hypothesis he returned to his studies, troubling the status quo no further. Consequenyly his ideas were not advanced into the public consciousness. Ironically the force he so meticulously deduced the mathematical law for is known in France as Laplaces force!

Thus by the time we come to Einstein a spatial field of influence concept , mostly based on Faradays description and philosophising was ripe for the picking. The Galilean principle could now be recast generally as a field effect with gravity and electrodynamic fields as empirical examples.

Because aether became a political word during the world wars it meant that physics was in a crisis. Einsteins concepts of a Galilean principle evidenced by the empirical fields, plus his photoelectric paper allowed American scientists in particular to recast physics in terms of fields, and the Geometry in terms of spacetime. This seemed to be a new conception in the 1920's but in fact it was an out working of the Galilean principle. Because it seemed new many dictatorial versions came out, and press releases dumbed down the subtleties.


Einstein never gave up the aether concept as a physical medium. The mathmatical version of it was his concept of spacetime . But how could a system in our universe be isolated from its observers? This was a conundrum brought about by the misunderstanding of the Galilean principle. The Jovian system is not isolated inside a box, but it clearly has its own local reference frame. It's local reference frame means that observers have a relativistic choice: they can and do describe the moons of Jupiter treatise to Jupiter, or they can describe the moons and Jupiter relative to their local system. The two descriptions are independent, mutually exclusive and in that precise relativistic sense " isolated" from one another. But they are combined in the same super system or higher reference frame, which can be understood as a 3rd all encompassing frame.

Why not just ombine them in each others local frame? The reason is conceptual. Each frame has its own frame points that move with the observer. Thus these frame points overlap but are not the same! The concept of a weightpoint captures this aspect that any arbitrary point is the sum of an infinite set of specific frame points. As one frame moves the point identifying an object in another frame changes. If however that object is within that frame, the point identifying it will not change as it moves!

The moving jovian system shows this quite well, with the moons  moving with Jupiter. A more everyday example , nowadays is sitting in a moving car. Thus the concept of a reference frame in the Grasmann system is physical, not mathematical. For Einstein a reference frame means all of the measurement structures with all of the physics!

Now space has a physical constraint on the speed of light. This is a bulk property of space. The permeability snd emissivity officiants in maxwells equations are bulk space property ratios. Yes they are fudge factors o make the equations ok, but that is how we model physical behaviours by mathematical quantities. We never say more about a physicl system by obscuring the behaviour behind quantitative symbols! What we do is reveal precisely how we process these symbolic relationships in our algebra.

The fact of light being a bulk property constrained phenomena is seen every time we see a refraction! A pride for example so constrains light that it appears to,split it into rinse colours. In fact what is happening is relativistic, the speed of light is slower in glass than in air  but as soon as the light hits air it " speeds up" . This strange phenomenon we call refraction, but it is an everyday example of the Galilean principle. But the prism is not moving! Light however is moving within the prism. For someone within the prism the speed of light would be constrained to a value true for them . They would be unaware that light could travel at a faster speed in a different medium.

Now suppose the prism to be moving, that will not alter the speed of light within the prism! It is now a local centrally constrained bulk property! What will alter is the phase properties of the light within the prism. This is the Doppler effect, but it principally acts at the boundaries between the media. The amount of incident light energy will vary with the motion of the prism altering intensity within the prism, the exiting light energy will be lower the longer the path through the medium, not due to absorption and reradiation soldly( which cannot be discounted) but Also simply due to the motion of the prism, as it transfers fom one bulk property constraint to another. The speeding up stretches what is coming out ,if you will, lowering the frequency .

Another way to apprehend this is that the frequency of oscillation of the bulk deformation is altered by passage through a different medium, so what comes out has a different frequency at a different speed!

The prism is meant to put Galileos principle inside a glass box. What comes out is inevitably altered by the surrounding bulk space properties. Add into those observations the oncepts of gravity and electrodynamics and you have one hell of a can of worms that needs sorting!

I think we can do it best using the Grassmann method of Analysis very carefully, without relying on it to tell us truth, rather to use it to model empirical behaviours and see if the model predicts empirical observations.

Norman has continued his introductory lectures on relativistic geometry and linear algebra, precisely as I engaged in further research into the Galilean fractals model of the universe expressing his principle of the same relative motions in relatively moving systems.( uniformly).

It strikes me now that the fractal and recursive nature of these ideas are inescapable except by ignoring them and concentration on a local frame! Thus our intuition is adequate for the frame and scale we choose to accept, but unfamiliar with the relativistic variations necessary to advance beyond that frame. In this regard relativity theiry is fundamentally crucial, even if shot through with many less empirical opinions!.

The relation to light, electro and particularly magneto dynamics is a fractal revelation. The computation schemes required to visualise the behaviours of forces and energies , masses and systems now exist in fractal generators. The consequence of this is that simpler rules can now be used to solve these system equations, because computers can do it more quickly making elegance and efficiency of secondary importance.

Of course mathematicians were afraid of this from the outset of computing algorithms, but they need not have feared. It requires the insight of mathematical and computational training to improve the efficiency and applicability of these algorithms.

Meanwhile the surface layering algorithms add some physical property extension possibilities only dreamed of by earlier mathematicians nd philosophers. We can now add " mass" to equations of relativistic frame transformations in the form of regional surfaces and colours.!

I have long realised that the surface plot aspect of the fractal generator was a topic I needed to understand, but now it seems I have the underpinning framework and analogies to do so in a way that is meaningful and exciting to me.

It is these surface plots which give " life" to the dry bones of the reference frame transformations, and connect directly to my sensory experience of dynamic spatial environments.

In addition, the quantum level is no longer a strange world, rather it is an uncendored world which as the information passes up my sensory mesh becomes filtered and srnsored into one unique view, one reality out of the many at the base of my sensory network.

I will explain that concept more as time goes on.