# Re: Fractal Foundations of mathematics: Axioms notions and the set FS as a model

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## Newton's Principia on Fluid Mechanics

http://en.wikipedia.org/wiki/Philosophiæ_Naturalis_Principia_Mathematica

The complete English Breakfast!
http://en.wikisource.org/wiki/The_Mathematical_Principles_of_Natural_Philosophy_(1846)

http://en.wikisource.org/wiki/The_Mathematical_Principles_of_Natural_Philosophy_(1846)/BookII-IX
In which Newton puzzles over is concept of a Vortex but misses the motive of vorticty, that is curved or angular acceleration.

Thus let

Ω

be angular acceleration of a body about a centre, and m the measure of the quantity of density spread throughout its volume
And density be that ratio of its volume compared to pure water which balances a rotating pulley between the two;

Then let the measure called Twistorque(T) be defined thus

T = mΩ

by which we may define the measure Force that balances it

F=Tr

r being the radius at which the pressure is resolved into force.

Thus we may identify tha the lineal acceleration a is related thusly

F= ma =tr
a=Ωr.

What we can conclude is that for every lineal acceleration we may posit an identical rotational one acting at a distance r.

Seeing thereby the naturalness of circular action at a distance given a medium that transmits the pressure and resolves it there!

That a medium should exist in somewhat empty space is doubtless to be doubted; yet having such evidence as we do in that which is fluid let us not dither, but press on.

Now it seems that this fluid material is hard to get a handle on, but it is bounded by a container. The formulation that Newton devised takes the container out of the process if needs be, replacing it by a ratio. What this means is that we can talk generally about any space, but not differentially.

The calculus of differenials may allow us to get into these details, if needed, but in fact we have moved to the paradigm of Energy or work.

Work is defined as pressure acting on a surface of a mass and moving that mass a distance. But a pressure usually accelerates a mass so work is being done continuously to accelerate, Once acceleration stops, no mor work is being done, even theoug the mass is still moving!. This is considered to be the kinetic energy of the mass in motion, in other word it is the direct analogy to the celerity in an object.

Work like a mptive, increases the kinetic energy like celerity is increased by motive. the proportions of this relaton are generally specified in the energy identities.

energy is not new, but the particular formulation of it has undergone several revisions over time. The concept of it is a mysterious metaphysics that physicists rarely want to get into. Well , for what it is worth, einstein called this energy motive, and ecognised the inertial motive as well as the pressure motive. Tese correspond to the kinetic and potential energy of a system when its equilibrium is perturbed.

Returning to my force identites , the definition of twistorque is a angular force, but the definition of lineal force can be seen as an angukar energy or angular work. However this does not work dimensionally because the concept of work is a resolved one: a resolved force moves a mass an actual distance.. Thus angukar work or energy will meed to be defined by

W=TøR/r

where øR/r gives the resolving proportion; that is where the energy is actually drawn out of the system in rotation.

this is different. in the defining of work it is assumed that the mass remaons coherent and tha pressure is resolved into the coherent mass. However, in a fluid it is evident, upon inspection, that the energy is not distributed uniformly instantaneously, and in a rotating system, it is evident the energy is distributed radially. The consequence of this energy density vaiation is conflated into Newtons Third and fourth laws of motion for the solid, but for the liquid and gas situations, these laws hold only to a crtain point of coherence!

Thus in fluid dynamics, work done can result in the fluid losing its cohesiveness and coherency and we need laws of motion to describe that.

It ould seem clear that we need a form that a body transforms into. This form i propose is the ellipsoid. which further fractalises into smaller ellipsoids according to boundary conditions that must reflect conservation of spacematter,conservation of total work done, conservation of the centres of vorticity within a medium.

This last conservation law is the hardest to determone, but has to be there if we have a preservation of regional distributivity of the fractal regions within a substance.. If regions can be created and destroyed, this means that at the large scale work cannot be done to preserve spacematter! Thus points would coallesce and we would not see the deformation of matter having any effect on volume rate of flow!

The micro scale is fratally similar to the macroscale when we see turbulence. That is the conservation laws are being applied at nearly all scales. What determines the turbulent structure seems to be the compound of the mixture, At a certain work load the mixture begins to show where the boundaries of compounding are, and we see this in real time as a turbulent flow. This is the several subatances responding differently to the avalilabelenergy of excitation, or work, while also bein constrained by the energy that is compounding them.

Thus a straon ellipsoid shows what 2 centres of rotation would do if stressed apart. The strain between the 2 centres of rotation which were formally one defines an eeliptic form.

What if the centre is strained into 3 centres, what form is determined then?

We can clearly investigate forms associated with x numbers of centres of rotation casued by straining the substances apart, but the rule we need is one that tell us the likely number of centres that will appear under what work load, Thinking backwards we could determine from a chemical analysis what the elements are and at what energy they disociate, this would give us a count of the number of strained centres likely to develop at given workloads

We have moved into the area of statisitcs.

To describe a complex urbulent flow we mus know the work being done on the flowing material, the strain profile for that compound in the form of a Strain distribution for probable straincentres and then likely spatiometric forms for these transforming regional structures. These will be in dynamic rotational transformation at all scales, snd the micro spatiometric gorms will impat on the larger scale regional behaviours. We will observe Turbulence, but characterised by a definite pattern..

The overall result would be he resultant of a work or energy analysisi of the flow, accounting for kinetc and inertail /potential dynamicboth pressure anr reactive pressuresat all levels with the strain pattern in the medium dynamically, in timesteps describing turbulence.

Thus we want a set of identites that describee spatial relations across the regions for every time step or videoframe. Placing all these frames into a video should show turbulence characteristic of the material.

Since i think Universal Hyperbolic geometry is a natural spaciometry for fluid mechanics i will have to define celocity, acceleration force and work in these terms.
The Spheroidal ellipsoids as models of regional pressure.

The strain ellipse allows one to model strain deformation in a laminar flow. The idea is to use some useful properties of an ellipse to model both rotation and strain in a circular fluid element. The assumptions are that the circle is sheared in 2 directions by a linear velocity profile which is anti symmetric . This velocity profile is a property of fluids sheared between 2 rigid boundaries, but observed in certain viscous fluids.
In fluids with such a shearing " force" the velocity profile is visualised by small bubbles flowing in and along with the fluid. The shear " profile" is seen only in a region near the boundaries and is dependent on the viscosity. Of the liquid. The greater the viscosity the larger the region in which this flow is seen.

The profile was first discussed by Newton in terms of lubricity. It seems likely that he noticed it in spinning buckets containing water. What he noticed was the slow progression of rotational motion toward the centre of the fluid mass and the rising of the mass up the side of the rotating bucket.. His comment that the velocity of the streams of water appeared to depend on the lubricity of the fluid was taken to justify that the shear " force" was equatable to some constant times the velocity gradient.

https://en.wikisource.org/wiki/The_Mathematical_Principles_of_Natural_Philosophy_(1846)/BookII-IX

Having now found access to Newtons book 2 I can make a correction in some statements about his opinion. His opinion was that his theory in book 1 gave a better description than his theory in Book 2. By this he does not conclude that vortices are not tenable as descriptions of planetary motions, but rather they perplex the explanation, and by his premises contradict the empirical data.

It is fair to say that he gave a reasonable stab at a vorticular explanation, but several important bits of empirical data are missing from his assumptions, not the least the correct relation and propagation of pressure through resisting media.

It is also good to see that Newton proposed this standard of fluid dynamics as a hypothesis! Later he remarks that it is unquestionably a wrong hypothesis, but the best he could obtain!

Again, Newton and laminar flow are not synonymous. He expects viscosity because he uses the phrase " the want of lubricity!". Thus I feel I can now define viscosity as the want of lubricity.

This is not an inverse description, but rather a negated description: viscosity is "not lubricity", or contra lubricity. Thus Newton anticipates a fluid in which a body experiences no resistance as being perfectly lubricious. Thus no viscosity is not viscosity which is not ( not lubricity) , and not not cancels leaving lubricity.

Any proportionality is therefore entirely within the chosen descriptor. Today we use viscosity, and we may expect it to be proportional to the transfer of motion through a fluid.. The use of a velocity gradient, even in a steady flow system is therefore entirely misleading!

The analytical and observed system is a dynamic transfer of velocity through the fluid medium. Thus the medium is accelerated relative to the driving force and this is communicated to the body being moved. The velocity gradient is a visible experience of that acceleration or deceleration.

The velocity gradient therefore is not a slope in space, but a slope in sequential time. The slope in space is a kind of Hookes law of the shear force, whereas we ought to expect, and certainly of Newton, a law bases on the second derivative with respect to time!

In a steady flow, and in Eulerian reference frames we should expect to see a dynamically stable equilibrium deceleration! Or acceleration, in other words a constant acceleration. The second derivative would be a constant, which is what we see a constant change in velocity.

The fact that this change in velocity is spread throughout the medium . Instead of in a line, gives us additional information about force. The best explanation is in fact that force should be replaced by a volumetric pressure. The velocity gradient is then a consequence not of the "shear force" but rather the shearing pressure in the flow which acts multidirectionally.

Using a radiating pressure and resolving it through a surface into normal and tangential forces helps to explain fluid behaviour more empirically.

## The General Pressure Notion

The problem with force is it is non specific, even today. Newton defined a measure he called vis which was a differential form of Hooke's law. Hookes law is specific to springs, but force is a more general vector type.

The metaphysics of acceleration required a cause Newton called motive. This, like celerity entered a body to hasten it. But when Boyle et al. studied fluids they found a motive disbursed throughout the material they called pressure. The concept of pressure and motive are identical, but the measure of pressure was counterbalancing: a force against the area it acted upon against a pressure and the area it acted on.

It is clear that pressure is a more specific notion than force, being MULTI directional and appreciated by its action on a surface. This in fact closely matches Newtons description of an action on a body that produces a vectored acceleration. The notion of pressure is a better more satisfying notion than force. We can accommodate the so called four forces into it.

If we have a pressure, we really do not know the cause. It could be an electric motive, or a magnetic motive a mechanical motive( including gravity and gas pressures) , a nuclear weak or a nuclear strong motive, not forgetting a thermodynamic motive, that is heat pressure(temperature) and expansive contractive motive.

Since we do not know the distinguished motive we put them all in to the equations. Effectively they are weighted pressure terms, their proportional effect either guessed or discounted. In this way we determine a weight for the action of each motive by approximation and judgement of the observed behaviour.

What are we looking at in terms of pressure? It seems to be a kind of weighted mixture of motives,which we have distinguished into 4. They act radially , but seem to have a vectored maximal for the electric and magnetic motives. Others seem to be uni vectored but environmentally determined. Others seem to have their own innate vector action, and all are susceptible to scale, except the electromagnetic(fluid dynamic) descriptions.

Is Pressure a vector?

We find it difficult to apply the notion of a vector to a multioriented magnitude. We tend to call them scalar potential fields. Theirs is a theory of conservative fields that defines this precisely, but essentially it is simple. If something is everywhere and in every direction then it is a potential scalar field. We cannot vectorise it. our notion of vector as a line label does not apply and is misleading. However, in spaciometry i have called these types of fields compass multivector networks, and written a few posts on the topic. These are the basic or fundamental seemeioon algebra, that is a Grassmann point A;gebra.

So i am going to be looking at how a Grassmann point algebra compares with a conservative field theory. These types of fields rings or groups are looked at as topological spaces in which the usual way to measure is to use the real number measuring tape and pythagoras theorem. However more unusual "metrics", rules of measuring, can be invented to help by analogous reasoning in other areas of comparison or specification.

P = α pe + β pm + γps + δpw + ζ pl + θ pt + μ pi + ς pd

Which is electric, magnetic strong weak, lever, thermal inertial and deformation pressures weighted.

Now we are accustomed to thinking in terms of gravitational pressure, but i have deliberately left this out of the general pressure notion except in the sense of a balanced lever or a mechanical "force".

The fact that things fall with acceleration is unexplained. or inexplicable out of context, but within the context of a general pressure notion "gravity" may be interpreted.

Why do we include the others? Each one creates spatial motion of acceleration, some damped. Gravity therefore obscures the effects of each of these others. It also obscure the fact that at least 3 other pressures could be used to define relative density and so mass as a product concept of relative density and volume.

I seem able to characterise pressures by their internal source and external action. Some pressure self actuate by an internal source or potential which cannot be located no matter how narrowly we search: others are activated by an external system or medium directing these internal pressures by boundaries and passing between boundaries in the most curious ways.

We have to acknowledge, as in the case of boiling water, our environment feeds into our local measurements. Gravity as it is used is a catch all because all our science has been defined against an assumed global characterisitic, and so in universal contexts we need to account for it. It is merely an accounting correction which we may be able to eliminate by more strictly defining these others

The empirical data suggests that pressure acts radially and spherically.

It is not possible to isolate a spherical action from a radial one, nor should we fall into that mistake. Therefore , using newtons resolution of his reference frame, my model must contain radial vectors and circular arc vectors or twistors acting in the surface of an expanding sphere. This is the fundamental structure from which I can resolve a tangential vector! In fact in 3d it will be a tangentially expanding circular plane which provides tangential vectors to the spherical surface relative to a given point, but also arc twistors in that circular plane. These can be resolved into tangential vectors to the circular plane in the plane

A spherical pressure thereby exhibits a fractal functional relationship in detailing its likely vector structure. However this vector structure is not realised until a test particle is placed in a pressure surface, so the description is Potential! Because it is not a vector it is called a scalar potential, but this is not explained clearly, rather it is obscured behind symbolic relationships. Probably because no one really understood what it meant rhetorically, they could just give examples in definition.

For a scalar potently to be useful it must be measurable. So a scalar potential exists in a topological space.

A simple topological space is an inelastic line. Now if I have another line that is elastic, I can compare the 2 and consequently recognise deformation. The elastic line is a topological space, but it is dynamic, which means I cannot describe its measured behaviour except relative to an Inelastic line. This means my visual sense is relying on my kinaesthetic sense to describe and distinguish an observed behaviour. If I did not make this comparison I would not be able to measure reliably, because I would be unaware of the elastic nature of my Metron.

Given this, I may now define a scalar potential for the elastic Metron. By making points on the elastic topological space I can refer to the extension of the Metron under different kinaesthetic pressures by noting the displacement of the distinguished points on to the inelastic space as a ratio. The inelastic ratio data is a scalar potential. It is a "measurement" associated with a point. Given the elastic Metron, and the correct kinaesthetic pressure I can read off a scalar definition by comparing distinguished points against the inelastic scale and noting the assigned ratio. We forget that all measurements are in fact ratios normalised.

Of course the inelastic line has its own orientation and so I have turned a potential reading into a representational vector in the elastic line. The vector is in the elastic line because I can orient this extended piece of elastic in any orientation on the surface of a sphere with the radius given by the topology of the in elastic line. It is the elastic line that has realised the vector potential of the topology.

For a pressure we realise the vector potential of a topological space by placing a surface that is translatable and orient able in it. The topological measure in the space is given by some function of the coordinate frame established appropriately in the space to provide a Metron, and in addition a Pythagoras rule for trianglesl

The Pythagoras rule is fundamental to our apprehension of how straight lines behave in space. It is not so much that it gives us a metric as it gives us a relationship between 3 points in a plane that is universally true for straight lines. The Euclidean notion of a good line goes beyond it bing straight. It defines a difficult but supporting concept that is a plane. While points can be defined by the first 2 given, a plane can be defined only by dual points and only then can a straight line of dual points be defined. Thus a straight line implies some plane and 3 dual points connected by straight lines specify it.

Of course dual points imply intersecting spherical surfaces, which is the fundamental superstructure or Hupostasis of Eudoxian and Euclidean ideas/ forms.

So now these forms or spaces can be specified by some reference frame. And some function based on this reference frame can specify a scalar potential in that space.

I have just used an example of Hookes law, let me now use an example of an inverse square law.

Specifying in polar coordinates makes this relatively simple. The scalar potential is (1/r^2 ,€) if the reference points are ( r,€). This is in the plane.

How do we now turn this circular potential into a vector field? We use newtons reference frame and resolve into vectors using newtons parallelogram rule, avoiding the mistake of giving primacy to the tangent. The tangent is a resolved vector in Newtons framework..

So now let us apply it to a spherical pressure potential.

The nature of potential is spherical so I can expect to see changes in potential radially therefore I can draw a vector radially to indicate a direction of potential change. Now I have a choice ofndrawingnanvector whose magnitude is the potential at the point or a vector which indicates the potential difference.

Placing an object in such a field of Vectors allows us to use the resolution of vectors . Thus we find that circular twistors counteract but tangent vectors do not for a spherical curved object. The material resists by Twistorque forces that cancel, leaving the tangent force( derived) to combine with the normal forces to push the shape or attract the shape. The force vectors for the potential field act as if the body was enclosing or embedding the field within its volume. Thus we have to calculate the overall effect of a pressure field on a body from all the pressure effects, not just from the surface pressure effects.

Because of the spherical potential field the pressure vectors will act on a spherical surface differently to a flat planar surface.mthe resolution of the vector fields will be different.

Now, so far I have only considered the lever effect of a pressure field. There are other pressures within a pressure field. I need to know the potential field for the electric and magnetic pressures within a general pressure field. In addition the resistive or reaction pressures themselves differentiate the electric and magnetic pressure effects. Triboelectric and tribomagnetic pressures are resultants of a general pressure field. The other contributory pressures also require their potential idles so thir effect cn be considered.

Anyone of these many component pressures acting through a body surface, and throughout its volume could compound to effect the dynamic stability of the combined system. The potential to rotate a body is therefore always present, and overwhelmingly so. The naturally resultant motion on any object under pressure would therefore be to follow an arbitrary trochoidal path. "Damping" of rotation or forcing of rotation may lead to a smaller or larger radius of curvature to the resultant motion.

The ballistic description of motion often incorrectly identifies the resultant motion of a missile as parabolic. It is in fact elliptic, because the object would return to its starting point if not impeded. A missile would have to exceed the escape velocity of the earth to get anywhere near being parabolic. However, it is the collective experience of these elliptical paths, more generally trochoidal paths, that we call gravity.

As I have hinted at, these general trochoidal paths are the resultants of a spherical potential pressure field consisting in many components.

The notion of a potential field from which we compose a vector field should not obscure the fact that these are topological models of a dynamic experience! In this the very topology is dynamic. It is exactly saying that Hookes law is dependent on the substance in which it is applied, and for how long that substance remains stable in its configuration, and in its position!

A pressure field varies dynamically. In fact from studying weather we know that we have to conceive of a system of pressure fields in dynamic relationships, and at different scales and levels all fractally entrained. The most energetic of these systems we call turbulence.

Turbulence is a matter of energy driving rotational regional motions a at all scales with fractal damping mechanisms back feeding through the complex system resulting in diffusion, dissipation and transformation.

The deformation of space matter involved in these turbulent conditions reveal the application of fractal damping, or inertia in maintaining some form of regionalised structure at each scale. We can only account for this by means of conservative actions. Conservative actions allow forces to react, dynamic situations to be in static equilibrium, inertial actions to be proposed, momenta to be maintained and opposite or contra actions in general to be expected?

How we frame our conservation laws defines our models of spacematter interactions, but in general it is reasonable to divide any magnitude into 2 contra magnitudes thus for any pressure field there is an anti pressure field. How that exhibits itself to our senses is not defined by conservation laws, but by experience.

When a spherical pressure potential acts on an area or in a volume it produces twistorque vectors as well as radial vectors. The acceleration radially is a(r)r, the acceleration vorticularly is @(r)r which indicates that the combined motion is a funcyion which is dependent on the vectors and the radial distance from the source of the pressure potential .

The resultant force for a given volume with crossesction A will be RAm+TAm where R is the radial accelerative motive. and T i the twistor accelerative motive when resolved and summed. This is for a given radial with a surface neighbourhood on the sphere with Area A, small enough to be approximated by the tangent circle at that radial.

The twistorque forces are usually not accounted for. If they are they are set to zero, implying perfectly elastic materials circilarly but perfectly rigid radially and tangentially! Since this can hardly be the general case, we should expect twistor vectors to be non zero and there to be net twistorque related to the viscosity of the medium under pressure and the wave propogation properties of the medium as a function of that viscosity as a tensile medium.

Finally the torque of the vorticular forces must be a function of the energy required to conserve matter in that action with that viscosity. The model is therefore fractally complex

PAm = RAm + TAm

The Strain Ellipsoid and the theorem of Pappus, It's links to Maxwells orthogonal Vortices and the theory of antiontology

In fluid mechanics there is a basic question. What generates viscosity?

Viscosity and lubricious are fundamental characteristics of natter. Along with density. In the Newtonian reference frame density is a comparison of volumes under a constant pressure split by some strongly viscous body to create opposing areas of vorticity.

The development of mechanics with highl viscous materials has obscured some of these basic fundamentals. The approach using a strain Ellipsoid in contra stream flows helps to restore these insight, rotation or vorticity in opposing translational flow is a fundamental consequence of these pressures on viscous materials, and so also is strain. Rotation is therefore a consequence of viscosity in these pressure systems, pressure systems produce motion of all types, but the specific type is a function of pressure pattern and viscosity .

There is an argument, however that viscosity is anti rotational and anti translational and anti strain motion! That is viscosity is inertial. That is what I want to explore

http://en.wikipedia.org/wiki/Robert_Hooke
Hooke, it must be acknowledged is one of those Newton gives credit to for the background, scientific discourse and discussion and philosophy of the natural order. The history of geometry and mechanics is intertwined because Descartes chose to call the mechanical knowledge of the Greeks and Islamic scholars " La Geometrie". These simplistic mechanical techniques, for in the main demonstrating validity of measurement, we're thought to be too mundane for academic thought, and yet again and again, this is where academic innovation has its source, it's demise and is renewal!

I find, in the labours of science taking place I Newton's troubled times many mean dreamed of greatness, some even snatched at it, but greatness was conferred upon the great by a consensus of committees of men. Hooke by his hard work never impressed enough men to gain this accolade. However, a later age such as ours might rightly review the extensivenesses of his contribution.ngreatness ultimately is no man or committee's to give. It is a legendary thing perhaps rightly ascribed as the gift of some mythological being, but that should not obscure the fundamental importance of the works of the also rans!

The singular importance of these revelations is to demonstrate that Hooke had a claim to have contributed to Newton's theoris, which Newton obliquely acknowledges, but trumps the claim o the specific inverse square law formulation.. Hooke relate to Newton Kepler's law of motions which invoke reciprocal squares nd velocities, but interestingly sub duplicate relationships. Sub duplicates are inverse square laws by another name, for just as duplicate proportions are called square proportions to day so sub duplicate are inverse square.

Newton's claim to reliability in his formulation of the square law rests on an important subtlety. Newton distinguished celerity into velocit and acceleration. The cause of celerity, Newton proposed was motive.. Today we may not understand how confusing the use of the term velocity was! Velocity covered also what we call acceleration. While Galileo distinguished acceleration, it took Newton to define a measure that made use of it. This measure he named vis!
Up until Newton's Principia vis was defined by Hookes law

Let us look at the difference for it bears on fluid MecanicsIn.

Hooke discovered that a measure of force could be defined using springs. This measure was simple: measure a length! In point of fact it was a measure of a change in length either "positive" or " negative". This change in length was a decreasing velocity to an equilibrium position. What Newton observed was that it was a fluid motion to which he could apply his method of fluents. Accordingly it was clear to Newton that the vis on Hookes definition actually was proportional to a changing velocity hat is coming to an equilibrium position! Thus Hookes measure he modified by a more complex process of measurement. One had to make several measurements to determine the deceleration.

Newton performed several experiments to refine his insight due to fluents, but essentially he was refining some well established mechanical principles which happen(!) to be those enunciated by Hooke.

Because Newton had belief in his insight, he fundamentally pursued gravity with this notion of the measure vis. The Kepler notion of an ellipse therefore again produces an inverse square law, as Kepler pointed out, but Newton no longer used velocity in an unspecified way, he recognised again that a changing velocity would be accessible to his acceleration definition. He therefore reworked the common calculations from that point of view. This was more thn jut putting a where everybody else put v or even l, this was introducing a new procedure of measurement, a new level of complexity.

Physics kinematics takes this well in its stride, but what everyone ignores is the fundamental fluid dynamic basis of this approach. Hookes spring or elastic law is a fluid dynamic law, and we find it introduced as the first kind of fluid " force" equation in fluid mechanics.

There has bern a move to drop the name fluid in favour of continuum. This is due to the fact that fluid dynamics is ostensibly a mathematical treatment of Hookes law in various plastic and elastic materials. Elasticity and plasticity, are all distinguished by different constants or moduli. Essentially these constants distinguish the notion of viscosity..

Newton started to investigate fluid mechanics using the notion of lubricity. Contrast tht with elasticity and appreciate the real difference between fluid mechanics and continuum mechanics. In fluid mechanics we would properly discount viscosity. When that is done it is called a Newtonian fluid mechanic. Yet we know that velocity gradients exist , and so acceleration exists. Newton felt this acceleration would be spiral. We can see that others were not of the same opinion, and even today people believe we would fall straight down to the earths centre!

By this account and method of analysis I see that Newton takes away any elasticity or spring as a concept of a fluid constant and replaces it with a kind of spiral watch spring!, at least in the case of the planet.

Newton already thought innovatively about Hookes law in elastic and in elastic collision scenarios, and included its oscillatory or undulatory reactions in his third and fourth laws of motion. This watch spring analogy for the motion of planets was an initial avenue of thought he did not pursue until Cotes came up with votes Euler exponential identity. This potentially explains mathematically how a coiled watch spring could explain planetary motion.

The notion of action at a distance still mystified Newton, who believed in an immaterial aether, which by religious philosophy was of god and so depending on what school of thought, could not or one could in some highly odd way, interact with SpaceMatter.

The strain ellipse is a highly evocative model recalling the analysis of spring deformation, but in general it is a given tha fluid mechanics has borrowed more from rigid mechanics than Newton foresaw, perhaps.

The notion of lubricity was a genuine attempt to enter a dissimilar realm. Viscosity is a more gradualist relaxation of elastic principles. Plasticity, the way deformations are retained by a form also takes elasticity that one step further before discontinuity or break. However the terminology itself hides the notion of lubricity which starts at contiguity, discrete boundary contacts and how they become harder or easier to overcome. Newtonian fluid mechanics is therefore contiguous mechanics not continuum mechanics.

If you study Maxwells solution for electromagnetic force you see that surrounding the vortices are little round circles. These represent ball bearings which were meant to provide a mechanical interpretation of lubricity base on contiguity.. In practice, bearings work well as models of lubricity, but fail when they come into contiguous contact if driven by the same pressure system. The solution is down to scale! If a smaller ball bearing is slipped between the two. Then lubricity is enhance. However the dynamic centre of this smaller ball bearing has to remain relatively the same. If this is not fixed then the ball oscillates up and down between the larger balls, leading to a complete snake like oscillation in the bearing s. pragmatically this results in generation of acoustic vibrations and heat.

Thus we see that lubricity is associated with vibration, particularly ln the acoustic range, but really across all vibrational ranges, and also the generation of heat and heat pressure( temperature). Although not usually noted I assume there to be also radiation of " heat" from the system as well as convection.

Contiguous mechanics, that is fluid mechanics therefore naturally involves many disciplines which through subject wars have defended their boundaries. In particular, in this rudimentary way it involves electromagnetism.

We might also usefully note that the fractal nature of fluid mechanics indeed all mathematical treatments is a serious omission. However, practitioners of fluid mechanics more than any others have to pragmatically acknowledge the influence of scale and iteration and recursion.

The reason why I do not support the notion of a continuos mechanics is because it brings with it several non fractal prejudices. Like for example starting with a uniform distribution! Starting with a continuous media etc, non of which are logically necessary and all of which can be advanced under the notions of contiguity.

I must now turn my attention to the strain ellipsoid and to rotation, which for a while in fluid mechanics enjoyed the notions of vorticity. There is a lack of apprehension about curved motion, brought about as we have seen by a misreading of the notions of both Hooke and Newton.mfor both of them curved motion existed in its own right, and could be resolved into axial displacements if need be, but in point of fact curved motion itself formed a curvilinear axis.
Axles of course are usually straight , but they do not need to be so axles are the precursors of both axes and axioms both of which can be circular!

Before I move on though it is worth noting that hooks law when set as time differential gives velocity and acceleration , providing the parameters are dynamic, but in all 3 cases the differential of force gives force! Thus by this observation force is an extension, force is a velocity and force is an acceleration! We can clearly go on ad infinitum, again highlighting the highly fractal and recursive nature of Newton's formulation of the inertial system of reactive equilibria both static and dynamic.
The principle of anti ontology really says that for every ontology or ontological argument there is an anti ontology or anti ontological argument. Another way of saying this is Shunya is divisible Ito 2 fundamental complementary sets B and B' for any set B entirely contained in Shunya.

Anti ontology also deals with the predicate in propositional logics. Thus for every predicate there is a not predicate.,
This is self reflexive so that for be there is a not to be

The experiencing of me also has an anti ontological not experiencing of me.

When we seek to get behind the propositions to the referrents I find I have no choice.all possibilities must exist. I do not operate on a non existent basis. Thus I ontologically accept the existence of all things. Then my propositional faculties serve to filter this non deniable status abd allow me to use bits of it to symbolically refer to all or other bits. Now, the acceptance of this role for symbols give me the opportunity to select referrents, to misdirect and to conceal, to make explicit and to reveal. It further gives me the opportunity to analogies, and to model..

Now I can propose A and not A a predicate and a not predicate. And I can assign special roles to predicates like to be or in greek " ontos". Finally it allows me to obscure the whole basis of this discussion by adding adjectival presuppositions like " possible" . The possibilities are infinite!
On a Theory of Space
We may start with Space as the archetypal Shunya, whether i wan to divide it into multipolar vorticular fields of force equilibria, or motion field equilbria of a vorticular nature or not( where a pole in fact refers to that unreal entity called also a centre or a point of centrality, rather than a distinguished straight line relationship between two such centres!)

The concepts of materiality of space start with a conjugation into a boundary between my inner experience and my outer experience. Such a boundary is immaterial but serves to define a material experience in an otherwise indistinguishable continuum. It allows me to differentiate continuaa, and to perceive a notion related to continuaa which is extension.

Extension as Descartes eventually came to use it is a subtle concept enabling perceptible things to be in their positions in space according to my perception and distinguishing of them, and indeed my naming of them by a process of comparison. It is my ability to establish or define an immaterial boundary that gives extension its subtlety. Wherever i define a boundary to some perceeption of some quality or essence or experience of magnitude, that discretization of my continuaa allows extension to populate space with entities that are bounded and thus quantifiable.

The discretization of extensive experiences and the boundaries that entail this discretization enable contiguity, continuity, and discretenes to be identifiable concepts. Armed with these i may proceed to a more complex concept which at the last i may call materiality, but which is a convenience to mask the complexity and indeed tautology of experiences, extensivenessesm magnitudesm and quantities that now are laid out before me as Ideas or Forms in the Socratic and Platonic sense.

/the distinction of materiality, ill defined as it is , leads swiftly to another equally ill defined conception of immateriality, which latterly has come to be called synonymously "Spirit" or Essence. Proceeding by the man made "rules" of "logic" or grammar, such a description may not be allowed to mix in any way. Thus in Descartes time and beyond, much time was wasted in defending this "silly " rule and in maintaining gods independence from his creation, if you so will.

However, different cultures did not pin their very lives to such arcane rules, but allowed all things to be mixed as willed according to a Yin Yang polar continuum structure which neve achieved absoluteness, as in western Philosophical/theosophical debate. Thus allowing a more calm approach to the foibles of Natural "Law" behaviours.

The Euclidean approach to Philosophy of Socrates and {lato, The Newtonian Principles of Astrological metaphysics and his co commitant Philosophy of quantity as expressed in the Methid of Fluents, plus his Praxis of Natural Philosophy, all combined to produce a guideline for wesern industrial revolutionary Thinkers and inventors which gave them extraordinary technical abilities but misalligned them to Natural Law. It requires Ed Lorenz Aperiodic behavioural Theories to bring Western Metaphysical theory into line with the Easern Yin Yang theoretical Structures.

In the meantime, materiality and Spirituality have been divorced where they ought not to be in the west, whereas in the east They are one and the same in the polar description of existential experience.

Where Newton mislead the west is in dismissing fluids from consideration in his definition of the quantity of matter. This decision which i now call a mistake, was forced upon him by the medieval beliefs of the church at the time, but was not the case in enlightened Arabia. Where Alchemical 'Lore" was open.
Consequently, though electric and magnetic phenomenon were discussed as fluididc behaviours, they were divorced from matter in Newtons philosophy of Quantity and the quantities of motion.
Newton did discuss fluid mechanics, but only as some adjunct to his corpuscular definition of matter, which is extremely ill formed, but accepted everywhere as axiomatic.

We can address the matter today in some detail and with some confidence of improving the descriptions of matter.

The first metaphysical principle must be(by your leave):

the only goal of this endeavour is to construct a model that faithfully represents what is empirical and observable.

To what use that model may be put discoursively or in rhetorical discourse is not my concern, but misrepresentations of the model are my business to correct.

Should someone construct a similar model, identicality must be determined by comparison to empirical data. If both faithfully represent empirical data as it is known then both models(or all models which fulfill this condition) are deemed identical.The inner workings are of little account to the effocacy of the model, but individual users of the models may express a preference.

Now supposing the inner workings to be the model of the workings of space is not allowed, unless and until observable and empirical data of such inner workings may be presentable.

Thus Hypothesis, based on the models is not allowed, but hypothesis based on phenomenom and empirical data is ,
Recasting of te models, no matter how inconvenient is always allowed, with the aim of obsoleting the former model by the latter.

The duty then of the model maker is to defend the model against misrepresentation, but not necessarily to promote the new model beyond postulation to such as think they may be authorities. Should they reject the new wine, saying the old is better, this should come as no surprise, but whatever advantage the new model gives its creator should be exploited in the presence of the young, that they may be given access to the better way.

Should the old guard seek to destroy such advances and opportunities the creator of the new, improved model is advised to seek employment and living elsewhere, where his " magic " may be a[[reciated. In any case, the lesson of history is that empires are required to change the status quo, or many satisfied customers of your service. Secrets are manytimes necessary to intrigue.

The proposed model of space is simple and observable:
Space will consist in extensive magnitudes that are motile and perceivable as motile, bounded, extensive rigid and fluid. Each of these attributes will be tautologically dependent on the other as far as the processes of the perceiver are concerned, and the perceiver is aware of a fractal relationship of levels and scales and conjugations between itself and that which is not itself, the whole being termed in synthesis and in discourse as Shunya.

Accordingly, when Newton excludes fluids from his model of matter he set himself upon a different course to the one which is proposed here!
Keeping it simple
By conjugation Shunya is percieved as "me" and everything not "me". Me is a primitive undefined concept at present, but its meaning is subject to the reader.
Shunya is now going to be conjugated in an alternative way that cuts across and convolutes with the initial conjugation, but which is wholly dependent on it, that is "I" conjugate Shunya again into rigid and fluid.
I and me are identified as having the same referrent in these 2 cojugations.
Now i may through the Logos, Kairos, Sunthemata Sumbola Processes begin to develop and assign attributes and characterisitics by these convoluted conjugation processes.

My second conjugation thereby acquires the notion of extension, boundarisation, relative motions, centres of rotationasl motion, relative kinematic disitinctions, Relative intensities, and relative sensory representations, etc..

Conjugating rigid and fluid again with these additional distinctions i develop a fractal, scale free attribution of propeties and behaviours etc, a ontiguous and causal attribution of motion transformation, etc, and a sensory mesh distinction and representation of continual transformations. At the last i may adopt and adapt "Panta Rhei", the conception that everything flows.

This concept is important in my subsequent and dependent conjugation processes as i establish my scale metrons to quantify all thes qualitive experiences of magnitude. Later, i will deploy magnitude to cover the internal "m3" and so substantially change its apparent and undefined meaning for the reader.

The purpose of my study is as Newton put it , to by reason and experiment exposit the behaviours and workings of my experiential continuum, and the best model to do this with is with a fluid model.

The almost ideal introductory fluid is Water, because the notions of fluid dynamics can be developed in this medium. In particular, its phase transformations admirably indicate that Everything flows "forwards" as well as "Backwards"

Now , observing water i can make 2 conjugations : one is that water flows as a "body" which i will define as a voluminous stream.
The second is that water flows as an oscillator or undulator, which i will define as a consequence of coupled boundary conditions.

Now conjugating just to the notion of water or fluid motion i have to state fluid motion is an adjugation of bodily motion in a "stream" AND undulatory motion within a bounded condition.

This simple statement is the fundamental synthesisi of Fluid motion

fluid motion is an adjugation of bodily motion in a "stream" AND undulatory motion within a bounded condition.

One cannot fully describe fluid motoions without the 2 "components" being presented, whatever additional properties of fluids are attributed.

i may now complexify the analysis of fluid flow Phenomenon using the Newtonian Method of Fluents and the Principles of Astrology(Mathematica!)
By concentrating on flow elements called streamlines i can track differential bodily fluid flows. BUT, and this is where the simple synthesis principle above highlights a shortfall in experimental practice, i have to also add the boundary conditions of each streamline to describe its undulatory characterisitics!

Thus a complex flow should be analysed by some tool or method that quantifies both these aspects. bodily stream motion And undulatory stream boundary motion.

I am going to point out that the streamlines sysnthesise "extensively", that is within a given volume you combine all the streams for the volume description. but the boundary conditions on each stream synthesise 'intensively" that is by a process of constructive and destructive combination the internal flow characteristics of an internal "test" volume are described.

The combined , superposed results of both processes hopefully model closely the actual flow phenomenon on which they are based.

I also want to draw attention to in passing, that the boundary conditions of the streamline are sufficient , and in effect the complexities of motion internal to the stream line do nt need to be known in detail.

Issues of what may be happening in a streamline at one scale are addressed by using an iterative model , a fractal modeling concept that changes the scale of measurement in a related , almost self similar way.

Also in passing, The use of this fluid dynamic model in modelling Electromagnetic phenomenon must transfer fully, so that electromagnetism is not a "wave" Phenomenon but a Streamline AND a wave Phenomenon. The ignoring of the bodily motion of space in Electromagnetism is the cause of its present difficulties. Historically this was due , in part to the collapse in confidence in an " aether" medium.

While an Aether medium may lack certain experimental evidence, it nevertheless does not negate its role in the modeling process, which does not require the reader to decide on what is real or not, merely on whether the model fulfill its analytical and synthetical purpose of accurately expositing the phenomenon. In addition, if an analogical mechanism is found to function similarly to the observed phenomenon, this validates the modelling method, but dues not make any comment on "reality". What is "Real" at the end of the day is a personal subjective decision.
Before Dirac, none considered Instantaneous Action definitionally. Instantaneous action was always a ratio with time, and to avoid infinite values the units of time were changed, uniformity was posited and empirical measurements were used rather than theoretical. Good deal of common sense was exercised to keep mathematical formalisms from introducing non pragmatic solutions.

That all changed when new philosophers, spoon fed on the belief that mathematics can speak to the attentive about reality in a way no other reasoning can, started to believe their equations and identities and formulations were reality, not mere models of human experience of reality.
When one is brought up to suppose a uniform development of theoretical ideas, that the average is good enough . it becomes difficult to deal with actual data from sensitive measuring tools. Statistical methods were developed and applied for dealimg with large volumes of data. consequently no simple direct relationships and formulae could be derived withtheoretical hypothesis.
Eventually theoretical considerations became overwhelmed by the massive uncertainty in interpreting the data. The solution was to go probabilistic with the statisitical data. Now np one could be certain about anything!
The rise of computing machines able to cope with masses of data and apply the new probabilisitic methods restored some control to a nervous and jittery scientific community. But the answer was not to go probabilistic, but to go fractal, and to go into Aperiodic behaviours, notably called "chaos". And the one trick that was missed, explpoted by Dirac was to use the envelope around space filling curves to define the value of whar is inside the envelope. The boundary condition became essential to describe behaviours within a boundary.

The issues that come together to support the modern structure of mathematical physics are wide ranging, but not always apt. De Moivre himself developed probability to a high degree in competition with Strenger, nd based on refinements of Cardsnos work in combinatorial sequences and structures. De Moivre saw a connection with the sines because producing accurate Sine tables was the major work of the times, both for commercial navigation and astronomical navigation.

Few realise that all the work on polynomials and probabilities ultimately have one root, the unit circle. De Moivre had a considerable advantage due to his mentor and the development of the Cotes De Moivre Theorems, which evenso Cotes appreciated the importance of more than he.

Thus ultimately probability is defined on closed conditions, and to extend it to open conditions is an artifice of infinity!

De Moivre was Netom's turntable. Thus , like Newton he was Archimedean. He did not accept unending quantities. Thus he expected and utilised approximations , finite quantifications. His argument was simple, but based on Euclids algorithm., shoudl a process be perisos, that is approximate, exhaustion of the process is acceptable if handled correctly. Certain elements of the procedure can be left off. These parts do not vanish, but combinatorially they are too small to make much difference, so they are simply not combined.

We can then consider the perisos result as the approximate unit for " measurement.. This unit Is used in all subsequent synthesis, and the shortfall is rounded away. It is the failure to remember that the model is approximate that generates spurious small scale effects!

The calculus of continuous and infinite processes can also generate spurious effects. It is precisely when a " model" is mistaken for reality when this has it's most devastating effect.

The rhetorical paraphernalia, or terminology , is often mistaken for procedural combinatorics.mthus he mnemonic value of the notation is mistaken as an evaluation procedure, many such mnemonics are not evaluateable. Instead, some jiggery pokery is done, and an identification is made that is evaluative, and that is used instead of the terminology. Dirac's function is a simple example of this.
Drac's delta function.

The algebraisation of astrological combinatorics does not arise , as we are told from generalisation, or going from the particular to the general. It arises from rhetorical style, in which spaciometric forms/ideas and relations are described terminologically, symbolically or translatably into another language, as in a code. Any method is already general, and not a particular instance. When I apply a method of combining forms in space that method is as general as it will ever actually get!

Now the habit of applying numerical mnemonics to these methods is not in fact a habit of giving a particular instance. It is simply reiterating the general relationship using a set of sequenced symbols. This set of sequences whether" numerical" or " alphabetic" provides inversion, to be sure, but it give illustration to the already general method of combination, and disguises, encodes this method in a format that may or may not represent it. To call its representation a particular is misleading, unless such a reference be fully put as a " particular encoding" using a " particular" encoding sequence.

Further, should one" decode "the sequence, there is no meaningful information contained I thin it, because it is not an encoding of information but an application of a method that is already general.

These combinatorial methods or procedures are called algorithms, and of themselves encode no information. They are instructions in the sense of mnemonics of actual behaviours the recipient is expected to do. As uch, they are rhetorical, and may be rewritten in any rhetorical style as art, sculpture, dance, speech etc. in biological systems of procedures they may be "written" as pure sequences of actions, resulting from mechanical/ helical/ electromagnetical interactions.

Thus the use of these rhetorical forms is a programming instructional language which we have now developed extensively into omputer programming languages with the miraculous effect of creating interactive technologies from the elements of our experiential continuum.

Let me no longer confuse " mathematics" as being anything other than an ancient omputer programming language by which detailed process instructions are conveyed to an operator to perform.

The general method of quantification exposited explicitly by Newton, but implicitly utilised by all natural philosophers especially astrological and mechanical, is to use Spaciometry to represent experiences. Dynamic spatial events are represented by dynamic spatial models, and based upon the dynamic, metronomical response we often call counting. Static spatial events are based on static spaciometries, but the real observable precursor is that these are dynamic equilibria!

Thus nothing is truly, essentially static, all is dynamic and a consequence of an interplay, an interaction of pressures and forces inducing and directing dynamically all motion.

Newton's Principia acknowledges this, because Newton wrote it in the light of his methods of fluents, a dynamical Spaciometry. Many indeed try to locate a Geometry as a prior Art, but in fact Newton only gives Mechanics as a prior art. Geometry, as Justus Grassmann, Schilling, and others found, was an entirely made up subject, drawing on mechanical principles and attempting to adhere them, unsuccessfully to Euclid's Stoikeioon. It bears repeating: Euclids Stoikeioon is not a work of geometry, but an introductory course in Platonic philosophy and the " Theory of Ideas/Forms" that Plato and Socrates put forward as a metaphysical foundation to all their philosophising.

So, as Herakleitos opined, Patna rhei, and motion, music, rhythm and dance poetry rhyme,etc are the essential rhetorical styles needed to acquire the wisdom of the Musai. Why mathematics should assume this role is a perverse set of historical circumstances which shall not detain me here( read my blog posts).

Using Spaciometry, dynamic Spaciometry in this way enables one at once to record spatial dynamics graphically. But Leibniz wanted to record it using any kind of symbol, that s algebraically. It was Hermann Grassmann who provided the Rosetta stone to translate between graphical Spaciometry nd algebraic Spaciometry. Not many people would now thank him! However it truly is one of the most remarkable nalytical methods to date.
Plano recognised this as a young man, and translated Die Ausdehnungslehre1844 into his own, redacted form in Italian. This lead to an unexpected development. While Prussian society under Gauss retarded Grassmann, the educational reforms similarly hampered any progress with his work. The Prussian empire had a major task on its hands to equip its infrastructure with the new insights and technologies and homegrown ingenuity! The Grassmann's felt this was a major priority.
It was only some years later that Robert, hermann's brother, prevailed on him to revamp and republish through his own ( Roberts) printing company. As editor Robert infused the new version with his own ideas! (1862). It took Hermann by surprise and elicited some dismay, but it did popularise his ideas and lead to a renaissance of interest in his 1844 self published work.
Although the 2 are named similarly, they represent different ideals. Robert wanted to promote his father's work through his work and that of the family name. Hermann wrote out of sheer genius and passion, and tore up the ground! Consequently Robert knew it was too far out of line to be accepted, and sought to tone it down to a more acceptable mathematical form.

I can recommend reading the 1844 version in German. All translations of it are not faithful to Herrmann, but rather are more swayed by Robert. Hermann's ideas/forms as Peano realised, are truly radical, and are the basis of Peano space filling curves , n dimensional spaces etc.

The early group and ring theoretical ideas of Justus Grassmann are carried through, but corrected by Herrmann. It is this group theoretical structuring, ring theoretical and field theoretical structure which takes the place of early combinatorial theory in Hermann's works.

We find David Hilbert, Klein, Cayley all exploring and writing on the same theme. In Britain, An Whitehead and Russell were influenced heavily, I'd not converts.the impact of the Grassmann analyses have been far reaching and profound and rival the impact of their contemporary Gauss. What I have come to realise is that the two camps were writing for opposite ends of the Audience: gauss for Academia, Grassmann for primary efucation. In that regard only Hermann's work could have made the crossover.

## Newton's Third Law and the Pre Socratic Philosophers

http://onlinebooks.library.upenn.edu/webbin/serial?id=philtransactions
Some research tools for Faraday in order to compare his work and Ed Leedskanlins.

http://www.livius.org/gi-gr/greeks/philosophers.html
http://www.thebigview.com/greeks/index.html

The third law of motion captures all that is essential in a philosophical analysis of mans interaction with space as mused and philosophised by numerous Greek philosophers and those that learned from them . In particular Herakleitos defined what later came to be called physics and mechanics in his concepts of Phusis and Rhea. These were taken to be primordial substances by the time of the Pythagorean schools, and the perpetual motion of reality was in this way enshrined in later Greek philosophical analyses and syntheses as a consequence of oppositional motions and states.

This concept of contra motions and states guided all natural( ie " of the goddess Natura or Phusis and Harmonia, muses of ancient Greek mythology), that is to complete the though, all Natural Philosophy including Epicurean and other schools of thought.

Newton defines Action loosely in the opening chapter of the Principia in a general discussion of his method , approach, sources and innovative definitions. It is clear that Newton was an assiduous experimentalist of an exacting nature, seeking principles that harmonise seemingly disparate areas of mechanics , and doing so sets out his method of metaphysical philosophy by which he structured his Astrological Principles, usually translated as Mathematical Principles.

Thus he lays out for consideration many philosophical principles that an Astrologer might employ to come to a version of God's Truth in so far as it may be known by man. Underpinning this is the ad infinitum philosophies of Zeno and Parmenides as the later Greek philosophers absorbed them into an iterative process of analysis and synthesis. This Newton experienced as a dynamic fluidity which he called The Method Of Fluents. The third law of motion therefore has a great universal sweep from the minuscule, some say infinitesimal or Quantum, through the everyday, to the celestial grandeur, some say infinite or cosmological.

This sweeping movement through scale is at once acknowledged and ignored! It took Mandelbrot to point out that scale has to be factored in recursively into every formulation. The tendency was and still is to find exact and exacting solutions to clearly interdependent formulations. This tendency swept so called chaos monsters under the carpet. Ed Lorenz showed that we can not do that anymore. This fractal, iterative and recursive( almost self similar ) tautology was refused by certain Western schools of philosophy, but embraced by eastern philosophies. The point here is that it is embraced by Newton, and presented in a form palatable to western religious Credos.

Of course Newton's principa was a worldwide success, bought by all philosophers of merit in the West and in the East, and understood according to the local philosophical schools of thought. Thus many Eastern philosophies after Newton had a take or point of view on what he had to say to Astrologers. Many recognised the source of his ideas, something his own peers were unable or unwilling to do.

The final aspect of the third law, as investigated by De Moivre was the probabilistic and or statistical nature of its application to complex mechanical situations. It was Maxwell who laid this aspect out in the now standard form s for statistical Mechnics.

With this considerable metaphysical and theoretical and statistical framework it became possible to tackle the issue of action at a distance enshrined at the centre of these principles, but not at all. Understood by Newton. The third law covers action at a distance but Newton was never willing to say how! Frankly he did not know how magnetism did what it did. I have explained that Newton placed magnetism tentatively at the heart of his celestial motive model. He was not being revolutionary. His was the respected conclusion of Gilbert. Boyle also wrote speculatively about this action between the celestial bodies. However Boyle and other Alchemists including Newton were constrained in exploring this openly due to British Laws against Alchemy and religious Law against Occultism.

Both Boyle and Newton through his Principles helped to get this law repealed so that the floodgates opened all the research into magnetism which included an associated effect called by Gilbert Electra magnetism , could flood out. However it was Faraday that stimulated a greater interest in what he calls electric Tension, on the back of many magical curios from European researchers and astrologers who had to make a living by patronage, very much likeable researchers and Academics before them.

Across Europe the interest in magnetism and electric magnetism grew and spread into the Americas, but it was Faraday who took a leading role in this development publishing thousands of experiments in the Royal society publications that went all around the world by the British Empire postal system, and stimulated interest and involvement, bringing to light what previously was done in this subject by others, published in their scientific societies but left to languish as occult knowledge!

This greater openness and transparency and eagerness to share led to the Newtonian Frameworks being applied to this growing subject just as Newton suggested it should. It was a revelation to see that Newtons force laws when applied to electric forces took the same kind of universal form as he had suggested for the magnetic forces between planets, commonly called Gravity because no magnets of suitable size or power could be envisaged, and magnets only attracted "Irom" it was thought. Plus Newton was not prepared to publicly back a magnetic gravity without empirical and experimental demonstration. As I said, he did not know enough to be able to do this, plus collision between corpuscles was the hot favourite in his time. La Sage spent a lifetime advancing that proposition and nearly demonstrating it, but the opinion now is that he failed to account for all empirical data. Newton, in order to preserve his work and theoris from reputational Harm had to box very cleverly. There were no end of theories that have been proposed and lost to antiquity, or fallen out of fashion, or thought to be obsolete. This would have been an unacceptable outcome for Newton, after all he had devoted his life to his theoretical pursuits. It would be inconceivable to stand before God nd admit to getting it wrong! That as a devout Christian of Protestant persuasions he could never knowingly do! We measure his devotion by what he gave up while at Cambridge, and apart from wine women and song, he gve up countless hours of sleep to pursue the correct account of all observations far into the night.

Faradays electric tension, and then Leydens Electric Current in a wire were all new groundbreaking insights into matter and it's substantive behaviours. Those who read Newton would know that his definition of Matter in the principles was now untenable. However no one thought to revise his definitions until Einstein! This was because the third law was so useful no one wanted or deigned to harm it, instead they just copied it, fitting it to situations as they saw fit, ignorant of the whole connectedness of Newton's principles for Astrologers. In fact, even after a century of applying them, many still wanted to gain fame by proving them wrong. This lead to a vigorous defence of long established and valued principles that tended to squash any innovation.

The corpuscular theory of matter had been rewritten by JJ Thompson to introduce particles distinguished by Charge. It was revised again by Rutherford and Bohr. Einstein did not agree with some of the implications behind the revisions because none of them were willing to address the logical problem of the concept of mass. The concept of mass was so enshrined in every formula that it was taken for granted. Many false arguments ensued because everyone thought they new what mass was. Nobody returned to Newton to revise the definition of mass according to the new corpuscukar theory because it was thought to be the same in aggregate. Einstein demonstrated that that was possibly a wrong assumption in a wacky theory he had . In epoch of this revision of the corpuscular theory experimenters were finding that mass was possibly due to magnetism! Experimental measurement were showing an increase in mass with an increased strength of magnetic field. Before this could be developed Einstein wrote his papers in 1905 and everyone abandoned their theories and began to verify Einstein's by the experimental method. Einsteins reputation began to grow, but he was still not uncritically accepted, because his synthesis of others research by logical deduction was counter intuitive. Those who later came to support his theories did so by force of experimental data.

When the second world war broke out scientists were marshaled into corps to fight the enemy. One curious result to do with radioactive elements drove the research from that point on. Hahn had found that there was a missing energy in accounting for radioactive decay. When the accounting was done it seemed to equal Einsteins rest energy theory! This put Einstein in Lead position and forced everyone to review the definition of mass.But also the propaganda machine could use him to cover their secret work while appearing transparent. His prestige was used to influence policy while distrusting his allegiance to the secret goal of atomic weaponry. The establishment used anything and anyone to further their aims. This included using his name to justify a radicle revision of the cu;ture of scientific collaboration. During the war the aether and the spacetime descriptions separated vitriolically, an attitude still rife today.

In late 1938, while on the winter walk on which they solved the meaning of Hahn's experimental results and introduced the idea that would be called atomic fission, Lise Meitner and Otto Robert Frisch made direct use of Einstein's equation to help them understand the quantitative energetics of the reaction which overcame the "surface tension-like" forces holding the nucleus together, and allowed the fission fragments to separate to a configuration from which their charges could force them into an energetic "fission"

http://en.wikipedia.org/wiki/Annus_Mirabilis_papers.

After the very public demonstration of huge energies released from nuclear fission after the atomic bombings of Hiroshima and Nagasaki in 1945, the equation E = mc2 became directly linked in the public eye with the power and peril of nuclear weapons. The equation was featured as early as page 2 of the Smyth Report, the official 1945 release by the US government on the development of the atomic bomb, and by 1946 the equation was linked closely enough with Einstein's work that the cover of Time magazine prominently featured a picture of Einstein next to an image of a mushroom cloud emblazoned with the equation.[65] Einstein himself had only a minor role in the Manhattan Project: he had cosigned a letter to the U.S. President in 1939 urging funding for research into atomic energy, warning that an atomic bomb was theoretically possible. The letter persuaded Roosevelt to devote a significant portion of the wartime budget to atomic research. Without a security clearance, Einstein's only scientific contribution was an analysis of an isotope separation method in theoretical terms. It was inconsequential, on account of Einstein not being given sufficient information (for security reasons) to fully work on the problem.[66]

http://en.wikipedia.org/wiki/Mass-energy_equivalence

The above Wikipedia article does a good job of highlighting the distinctions between mass and matter, but only because it ignores the clear historical meaning given by Newton to Mass in his formulation. However it clearly illustrates ow scientists subtly rework the meaning of terms to preserve valued formulae. This is mostly done by peer review so as to maintain the financial advantages of the status quo. It is then ruthlessly defended!

Newton's third law has underpinned all of this scientific analysis, but the present gatekeepers have a definite motive to keep newton out of the financial picture/

My point here is that we should not seek validation by such scientific cabals, rather by applying Newton's Principles like Ed Leedskalnin and many others we should make our own devices and technologies for our own personal benefit and those who wish to participate with us in a collaborative effort. The internet makes this an incresingly viable thing to do, and the genii must not be allowed to be put back in the bag!

Newton's Principia Mathematica are a Astrological and Celestial Mechanics that encompasses all we want to know about Electromagnatism and Quantum Mechanics, as well as rock moving mechanics!
The Twistorque Vector.

The notion of vector has been hijacked by Gibbs and appended to the work of the Grassmanns. Store ken certainly are not the Gibbsian notion of Vector. The Hamiltonian notion of vector referred to a particular constraint combination in a Quaternion combinatorial table. Thus, this combination was related in the lineal case to a line , a straight line, but only as a symbolic label. The use of combinations as symbolic or formulaic labels is a consequence of process algebra, not an algebraic consequence or even a mathematical one. The process algebra describes a combinatorial sequence process, which encodes a lineal model. Thus the line symbolises a process, and the combination of lines symbolise a combination sequence of proceesses that result in an encoding of a line said to be the resultant process symbol.

This symbolism is usually associated with straight lines, but in fact it is applicable to any set of lines. Thus combining a circular line and a straight line or even circular lines is consistent. The resultant is also a line which partakes of the 2 processes in sequence.

Newton in establishing the parallelogram law, prior to Hermann Grassmann laid out a general principle: the combined effect is the diagonal point in a parallelogram. The parallelogram however does not have to be restricted to straight lines.
The movement of a path where the sides of the parallelogram are curvilinear therefor may be plotted in equal time intervals. Such "time" intervals are a matter of record intervals rather than any admission of some quality that exists as time, for such a quality may as well be illusory as it serves only to mark equal sequencing responses performed iteratively.

Of particular interest is the combination of circular arcs and radial motions, whereupon it becomes quite clear that the resultant radial motion requires that the circular motion and the radial motion be independent of each other. Where they are not then a spiral motion is the resultant.

The resultant motion of 2 radial lines is equivalent but not identical to a radial motion obtained by a combination of a circular arc and a diminished radial one which endures extension. From this Newton derived the notion of a centrifugal extending "force". The counteracting "force" he called a centripetal one, and this is in fact the curvature force. Thus Newton could resolve any line into appropriate lines curved or otherwise appropriate to the tools for measurement.

The curved line I have named as symbolic of Twistorque, an idea different from a torque couple which resolves a curve into a tangent and a radial centripetal force. Twistorque requires no tangential resolution and develops an attendant centripetal force not as a resultant but as a product of its motion. This product is otherwise known as "charge".

Charge, as a centrifugal force is a product of a curvature which is greater than the tangential line associated with a standard circular arc. Curvature and charge are thereby linked as proportional concepts , and a theory of charge based on curvature is thus proposed.

In this way I hope to simplify the clear image of a vortex in its relation to Electromagnetic phenomena.

The circle is for Newton a special form of a spiral or vortex. The spiral path can instantaneously be resolved into a centripetal or centrifugal motion and a tangent to a circle. This has been the definition of a spiral or vortex since Archimedes. Thus for Newton these 3 motions are associated with instantaneous accelerations or fluents and his Lemmae in no way imply that curvature is the same as straight line. By trapping the curve between the tangent and the secant he merely posits that the ratio of measurements on these 2 straight lines can flow to a duality / equality with the measurement of the curving line. The measured quantity is defined by the Metron used to measure. This curious relationship is at the heart of the calculus and the fractal, for it says that continuity lies in the chosen Metron. The join of the Metron as a monad thus becomes crucial as the notion of smoothness. For a circular curve or any conical curve, for a spline or any trochoidal or roulette , involuted or convolute the notion of smoothness of join is tautologically inherent and is identical with tangential definitions of curvature.

What is lost to the physicist of today is the substantial theoretical basis for the notion of smoothness based on the Greek Spaciometry of Euclid, Appolonius, Rystarchus, Archimedes etc. these works are NOT the Stoikeioon, nor based on the Stoikeioon. Thy are the scientific combinatorial Gematria of the Greek Astrologers derived from extensive research into the wisdom of Astrologers from all conquered civilisations or commercial alliances. This collection of works and knowledge is usually called Mechanics to distinguish it from another set of related ideas which came to be called Geometry, but which in fact are a redaction and collation of earlier texts based on the format of the Stoikeioon and called the axiomatic approach to geometry.
This really did not take this form until the Prussian philosophers took the mechanical texts to pieces and tried to collate them with the theory of Ideas/form which is the introductory philosophical textbook for philosophers in the Platonic Academy. Thus the Prussian philosophers from Kant, Schlessing , Fichte , Riemann backed by Gauss, and most notably the Grassmanns who worked from the primary level of education upward, in conjunction with these others who worked from the Acadmic level downwards under the Humboldt reforms, developed a redacted form of geometrical and Mechanical theory which they felt was more pedagogic ally consistent and logical.

The influence of these Prussian philosophers who drew on the European heritage of philosophical , theological and scientific or natural philosophical thinking was immense in the New world of the united States of America. Just as many Americans were refugees from cultural persecution and religious stricture in Europe, so many scientists and philosophers escaped from the intellectual and high cultural bullying that was endemic in plagiarist European society. The united States became home for all free thinkers and inventors who were persecuted or stifled by the European set up.

The industrial and mechanical and theoretical work in Europe drove the industrial revolution around the world. The Ameicans, as persecuted Europeans persecuted indigenous people's in the Americas in order to express their sought freedoms as a Manifest Destiny. This pseudo religious credo justified whole scale slaughter and land appropriation and subjugation of indigenous peoples for white European cultural goals and agendas. The vast wealth of these lands were targeted for plunder and private wealth. This would have all been taken back to enrich the European states had not the Americans revolted and declared independence.

Historically there is much to blame the American settlers in their handling of indigenous peoples, but the European Axis cannot and must not be ignored. Many Indians and Africans were slaughtered and enslaved for European greed for profits. The rabbit hole goes deeper than it is usually propagandised.

Today in Europe the American conspiracists are usually lampooned. But this is a European propaganda tactic to avoid taking responsibility for many atrocities perpetrated around the world on indigenous peoples by European interests. Much of the hostility in the world s driven by these European interests still acting to fulfil their greed driven profit goals. The word conspiracy is a fit word, because every boardroom or governing body at any level, from a simple youth group to a multinational banking agency" conspires" to achieve their aims. Conspire is to sit not in a circle, but in a spiral to debate and act. As a circle is a degenerative spiral as Archimedes showed, most conspirators sit around round or rectangular tables to do their conspiring. Often conspiring is done openly, but for a few highly sensitive issues these meetings are held in private. This is called being transparent!

Conspiring is a natural, biological organisational way of decision making in a system, whether biological, cybernetic or electronic. We are all conspirators in one way or another. There are and always have been private or secret groups of conspirators acting at every level of every society, it is a natural organisational function of an action dependent system.

The spiral or vortex thus underpins all dynamic social, cultural, philosophical and mechanical situations and systems, and Newton based his Calculus or method of fluents on the vector resolution of spirals into radials and tangents and circles. The resolving of a spiral require these 4 elements as essentials from which in the plane we usually choose 2 or 3 to focus on. This can make th4 th one appear to be a ghostly or weak influence, but in fact this is down to poor pedagogy. Newton used and presented all four. Later Philosophers decided to down play certain elements of the 4. Lagrange however demonstrated that 4 is the Minimum set of parameters for describing Mechanical systems fully through constraints and dependent and independent relationships. Hermann Grassmann showed that there could be any number of parameters involved and demonstrated a lineal Algebraic exemplary Model, a specific example of his more general analytical method. Hamilton by a different but related process set out similar principles.

Underlying all their work was Newtond Mechanical resolution of the Spiral into the 4 elements, of which 3 are used in the notion of Charge.

## Newtons Electrodynamical Principia Astrologica

Gravity as the back EMF in an electromagnetic field.

Randy Powell and prior to him Marko Rodin, claim that there is a force or energy or spirit or all three and more combined that principally emanates from a specific point in the centre of an ABHA torus coil or a so called Rodin coil. This they call an aetheron field. I would identify this with a spinning electromagnetic field emanating as a helical jet. But more interestingly they claim the sequencing indictes a backdraft which they identify or at least Randy does, with so called gravity. This backdraft I identify as a back electro motive field .

The question is would this hang together under the current Maxwellian electromagnetic laws, and would it give the signature very very small measurements associated with a gravitational force field in our solar system?

Secondly, would back EMF align itself vectorially orthogonally to both the electric and magnetic fields?

If it does it restores my original conception of the Shunya field as 3 orthogonal motions on any given region, but in this case one would be rotational and therefore magnetic by definition, one lineal and therefore electric by definition and the other possibly lineal but tangential making it an instantaneously varying electric motion which would be rotational but not overtly magnetic because the force would appear as minuscule! This is what we may call gravity.

When looked at in this way, it becomes clear that Newtons Principia are not in fact laws of gravity, they are in fact laws of electrodynamical motion. The refusal to accept Newtons centrifugal force or magnetic analogy as clues for further research, and his definition of the quantity of matter as inadequate by default, as Newton clearly states it, is the reason why we have obscured this obvious and natural link between the force field laws.

As I have surmised throughout this blog, the definition of mass and therefore matter was obscured and obscuring, and was wrongly left unrevised in science because prejudicial lay alchemy was thought to be the work of the devil by religious leaders who like the king craved the ubstance of gold and silver.

We have a chance now to properly define matter in terms of the Shunya field theory, and I invite anyone to criticise and extend my ideas in line with empirical, tautological data.
http://www.thunderbolts.info/wp/2011/10/17/essential-guide-to-the-eu-chapter-2/
Sir Robert Boyle is also not to be forgotten in his pioneering efforts on developing the Electrodynamical universe theory and in working to free alchemical enquiry into it in the British Dominions.
Weight for Newton became his model of force.

Weight is an old old idea, like money as a medium of exchange. One must understand the sensory codings in our experiential continuum. To keep it simple we usually designate the 5 senses, one for each digit on one hand. We model this into internal experiences and external experiences, interiorceptors and exteriorceptors. Being the supposed sensors that pick up these sources or causes of experience. Thus we use a cause and effect ,scientific model. But we are already at a level of complexity where most people would say who cares!

We further collate these sensory meshes,now recognising their inherent complexity, into systems designated visual auditory, gustatory/ olfactory and kinaesthetic/ proprioceptive.. Using this system the magic of encoding can be roughly exposited.

The notion of weight is a kinaesthetic / proprioceptive one derived by the musculoskeletal skeletal sensory mesh interacting in syncopy with the other meshes. We pit our strength against one another, against objects, against the elemental forces of nature, and we carry only what we can bear. Some bear more than others, and the weight they bear easily is a measure of their prowess.

The mechanical lever became a way of comparing these weights. By the lever equal weights could be compared by balance and by balance unequal weights could be compared, and considered in a rationed way. Thus the kinaesthetic mesh grounded our notion of strength and value, and this Newton took as his basic tool to establish a mechanical tool to quantify vis. The Latin word was taken to tautologically define a notion of mechanics, but it was Newton who gave an empirical standard definition of it . Vis and weight derive from the same root etymologically, but by different language routes. The process of giving a precise definition was one which Newton following Wallis, who in turn followed Euclid, used to great effect.

Thus we can readily see he Newtons explorations in Alchemy furnished him with a great understanding of density and all it's qualities.

Having a defined concept of vis and a tool to measure it made Newtons conception and theoretical structuring that much more understandable and impactful on space. Straight away newto could see that weight/ vis was proportional to bulk and the quality of matter. It therefore became necessary to have a standard quality of matter and this was taken to be water, barley grains or some other universal matter that was commonplace. The water standard actually came in quite late in the game, with grain crops and even precious metals or standard alloys being common place prior to that.

The quality of matter was crucial and eventually led to the establishment of so called density lists to define the notion of quality. From the grain models it became clear that a corpuscular model had to be devised, in which the recently observed corpuscles in the plant and blood samples viewed under primitive microscopes could be taken into account. This left the notion of quality dependent on the density of the corpuscles. In fact density and quality were interchangeable at this level. To separate out the notions of quality and density a fixed volume was established. It soon became clear that the count of grains in this fixed volume was the crucial ratio. Tautologically this was established by using the balancing tool! So density was not an independent notion, but rather a tautological complement to weight. The different practices and intentional goals for the balancing procedures was thought to be sufficiently distinct to ensure a valid process. In addition, quality was not just assessed on volume and density ratios alone, other sensory meshes were now brought into the interaction, so colour, texture and tast often selected the desired quality to undergo the balance procedures.

Newton was therefore stating as a matter of definition what was already commercially accepted: the quality/ density of a commodity conjuncted with its bulk was sufficient to indicate the amount of weight that would have to be shifted, and thus how many men, horses and carts would be needed to move it.

So now, with these standards and some other mechanical definitions Newton turned to Galileo and proceeded to make sense of his findings. Galileo showed how commodities of different weight fell to the ground with the same speed or velocity. This at once indicated that a different principle was in play not related to the bulk or quality/ density of the commodity. This principle was called motive by Newton and it produced this constant acceleration. The puzzle was how could different weights balance under this new principle? Well the clue was in the measurement tool. The constant acceleration, even constant speed did not change the ratios of the measuring tool. Because it was assumed to be a constant the ratios scaled equally if conjuncted with the commodity. It was Newtons suspicion that isolating a commodity revealed its true interaction, whereas comparing commodities revealed a constant relationship. This was the basis of his experimental .

The recursive and iterative nature of these Newtonian formulations are obscured by convention. Thus the choice of definition to smooth out tautologies or to label separate sub routines or procedures which are complementary to the formulaic notation are often downplayed to glorify some simplistic version of the actual complexity.

Newton, by his tool of balancing weights was able to put to practical use the law of levers, which Archimedes himself derived from the Euclidean extreme and mean proportionalities. These proportionalities were a theoretical way to record and measure circular interactions by the ideal/ formal means of the Platonic Mechanics. Such a mechanics linked directly into the Astrological mechanisms seen in the heavens and cast by shadows here on earth. The Platonic ideals formed a universal mechanics and were fully explored by students of Astrology for all time since. Newton's formulation therefore fits into a long established tradition, but distinguishes itself by its clear fractal structure.

The concept of a sphere of influence around a magnet and a charged rod are immediately demonstrated by the behaviours of reactive particles, which fall into a shape that delineates the action and reaction to this "Field" of influence. But over familiarity prevents us from seeing the field of influence we interact with most often and mostly kinaesthetically. This is the Weight field!

The Spaciometry of such a field, being so ubiquitous should give us pause when thinking of the electromagnetic fields. Such neat lines are in fact an anomaly. Most magnetic lines are involved in complex loops and trochoids which we do not care to think about for fear of hurting our brains!

From weight being synonymous with volume and density, Newton moved to the notion that weight was proportional to volume and density. Weight he realised had to include this motive or vis which accelerated all commodities in the same way. The volume and density were not significant in the acceleration because the acceleration appeared to be constant, but they were significant in the weight or force of a commodity. Conjuncting all three and holding any two parameters constant gave Newton his force model, and experimentation confirmed it locally weight is a conjunction of 3 measures, and is itself thereby a measure. Thus Newton was able to construct a model of conjuncted measures that itself was a measure and it measured a quantity he came to call vis or F for Fis or Force. The behaviour of the model depended on what was kept constant and what was allowed to vary. Mass ass a mechanical constant derives from Newtons formulations. Lagrange on the other hand developed a mechanical approach in which all the parameters, as he called them could vary , and it was the constraints on these variations that defined the mechanics. This notion was further developed by Hamilton and is the basis of modern mechanics today. The constants and the constraints are the defining quantities of our mechanical universe under a Hamiltonian Lagrangian, Grassmannian Mechanic, for it is these Three who set mechanics on its modern footing. To these we may add Mandelbrot for his notion of fractal geometry which clarifies the underpinning of all so called geometries and mechanics in line with the Grassmannian view.

F= V*d*a.

As straightforward as this looks it is in fact a recursive formula, highly iterative and dependent on the method of fluents to out into true effect.

F= V*(N/v)*a is a version dependent on Avogadros number N.

We can go on to expand a to (u1 – U2)/ t, the difference of two constant velocities.

We can go on to define t as the comparison of 2 pendula swinging, on and on we can go in a great tautological circularity to ultimately add nothing of utility to the model, but perhaps a sense of wisdom at the interaction of ourselves and our sensory meshes with space.

We are clearly taught a fiction under the cover of Newtonian Mathematical principles, and that is gravity is due to matter. Newton in no way implies this falsehood, which contravenes the evidence of Galileo which demonstrated that gravitational acceleration is independent of mass. The question of what is this constant motive was not answerable in Newtons day because it involved the use of what were called occult practices to determine. Nowadays we have forgotten even what the question was?

The cause of this constant acceleration is the electromagnetic field, that is a field that consists in 2 attributes, an electric field and a magnetic field.

Newton was able to show that the centripetal force of this electromagnetic field acceleration was proportional to the mass of materials of all descriptions around it. The quantity of matter, as he defined it was a measure of the electromagnetic field strength around a central region. Apart from metaphorising a magnetic "field" as the cause Newton had no clue what or how this operated

However this explanation will not suffice. And for this reason i point the reader to the Shunya Field Theory whose 2 attributes are a mechanical vorticular condensing field and a vorticular rarefaction field both of which are fractal in structure and exhibited at every scale. The dynamic uniformity we measure as acceleration is an artefact of this vorticular stucture and is only locally constant. In the "great rarefaction" of the vorticular fields perturbations should be measrable, but Ed Lorenz effects unpredictably switch these vortices into other "modes". Our Models can only approximate the collective dynamic.

http://hypertextbook.com/facts/2004/MichaelRobbins.shtml
Einsteins Equation E=mc2 means that electromagnetic energy is "measured" by the quantity of matter. It, like Newtons quantity of matter is a mesure of the quantity of Electromagnetic energy by conjuncting the quantity of matter with the square of the constant speed of electromagnetic motion. That this motion is an undulatory wave motion is signigicant, because it means this energy is not measured by particle velocity but by field disturbance. that radiates from the central mass or in toward the central mass or quantity of matter.Yhis radiating field disturbanceimplies the central quantity of matter is in some form of disturbing or perturbing motion relatice to the field of electromagnetism. The probable nature of this disturbance i have surmised in my post. revisiting space.
July 2012
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