There is a power within any volume that stirs up a pressure throughout it. Where two pressures interact a dynamic trochoidal surface may be envisaged, defining the dynamic boundary of the hitherto indeterminate volume. Such trochoidal surfaces when they interact may determine a curvilineal line of force and or a surface of equipotential pressure.

It is these curvilineal lines of force and surfaces of equipotential pressure by which I will define rules or proportions of pressure and proportions of force proportional to changes in accelerated motion being : change in velocity by some measure of change in displacement in some direction by some quantity of measure, by some frequency of rotation of an agreed metronome or pendulum.

In order to make a suitable scale uniformity or regularity may be employed or some more complex curvilineal uniformity based on none uniform elements. Beyond this a repeating pattern amenable to some law of synthesis may also serve to reveal any variation from that law. And so it is by dialectic resolutions of assonance and dissonance I will approach a sound expertise in diagnosing the states of behaviours around me, at all scales.

In exploring TroTorted it has become very apparent that relative frequencies are crucialntomapprehending the function of the form in any interaction. . Simple frequencies are only guides to potential form .Dynamics add functionality to the form

These next videos are to fix in my mind that materiality has a frequency distribution. I want to use the spectroscopic frequencies of elements to inform the frequency ratios in my model, beyond just the law of angular momentum analogy.

TroTorted gives some interesting surfaces for helium noth as a nucleus and as an atom .

Bunsen and Kirchoff change everything from materiality into frequency of radiation in plasma states

Firstly we see wavelength used not frequency. This is because diffraction gratings use length between slits to disperse the spectrum by diffraction . Newton called this dispersion by refraction in a prism, so many scientists are still confused by Diffraction.

Don't be confused. Newyon chopped light transversal ly into corpuscles, modern photons do the same. Grimaldi slice light lengthwise into streamers that therefore spread apart like shavings by a plane. Clearly corpuscles or photons need to be dispersed, and refraction is used to do the dispersing. In a diffraction grating the split streams interact constructively and destructively by the wavelength in the stream.

While refraction can be used to characterise dispersion, it does not explain diffraction patterns .mthe wave length interaction does.

Now stepping up a gear, frequencies interact. While physicists want to base this on a one wavelength, this is not necessary. We can see frequency interactions in rotating or vibrating systems. Sine wave lengths provide a visual analogue for what is a rotational phenomenon.

Secondly the neat mathematical process obviously is contrived to allow numbers to represent energy levels rather than using directly measurable frequencies. The history of direct measurements follows the use of length as in dispersion angle , to average angular displacement on a dial, to oscillating circuits tuned to certain frequencies of oscillation.

We convert from wavelength to frequencies by formulae because early data was measured bybWavelength. Now we can measure ire ly in frequencies.usingbradio spectroscopy, etc, but we still get taught about the wavelength of light, giving the impression that light particles move through empty space.

The transmitting medium is oscillated vorticular ly at a spectrum of frequencies , as evidenced in earthquake waves, or vibrating materials carrying shock "waves" . These shock waves or vibrations are often called phonons or solitons, to fit in with particle depictions!

They are better understood , in my opinion, as vorticular rotations spreading through the medium, with a range of frequencies.

Comparing with attains model, we do not use to believe protons are jumping up and down in energy levels, rather we can use relative frequency proportions as governing coherent topological dynamics and thus more stable structures vis a vis incoherent and quickly decaying unstable structures

https://en.m.wikipedia.org/wiki/Moseley's_law Tutin's model assumes negative charges in centre, but they saybMosely mpiriclly refutes this . But note spectral lines are measured in wavelengths not frequencies, making it harder to conceive of the alternative but not impossible . It is not usually pointed out that the Bohr model of the atom has many excited states or levels making the " atom" in this state as big as some viruses! http://web.mit.edu/8.13/www/pdf_files/moseley-1913-high-freq-spectra-elements-part2.pdf The Frequncy is associated with Bohrs model, but equally Tutin can have protons travelling at that speed!/ frequency

http://www.sengpielaudio.com/calculator-wavelength.htm Characterising elements b their spectral lines of emission and absorption usually is done using wavelengths, for reasons explained above. But using frequency data enables me to generate a trochoidally dynamic model in TriTorted , which gives a 3d topological representation using surfaces.

Because it is based on thecQuaternion frame I can modulate at most 4 " axes" for any spheroidal dynamic . I need 6 because Trotorted locks 2 in the plane and uses them to determine the radius of the sphere. It attaches one frequency to this pair. Th other pair are left hanging , but I can assign frequencies to each .

Thus for the hydrogen nucleus or atom I can assign3 of the 4 major frequencies . The use of octonions would allow me to assign more frequencies, but I am not very familiar with the topology of octonions.

I have yet to apply these frequency ratios to fractal generator app Quasz, which does have an octonion capability.

As Norman points out: the topological representation of a basis that spans a combinatorial form is arbitrary. Here he uses lineal combinations , uses the term lineal etc out of a convention that prescribes numbers as segments on a straight line. However the same logic applies to curvilineal lines and we could emphasis this by calling them curvilineal combinations that must span .

Now span means to tessellated a topological space. In that regard,a saciometrical interpretation is vital for utility in depicting a topological Form, but combinatorial ly we are free to write down all possible combinations.

We should note that the integers saved the day topologically in enabling a span to reach all parts of a spaciometric grid or reference frame. In a curvilineal frame they are strictly not necessary as factors or coefficients, but as exponents they are extremely useful to depict fractional or rational coefficients, and to describe the direction of curvilineal displacement, motion and acceleration.

When used in this way they also found the notion of frequency in a closed curvilineal frame, and phase. The coefficients can also be used to found the notion of amplitude, power and statistical probability.

From frequency and amplitude we can derive the notion of wave length .

A curvilineal reference frame therefore potentially enables us to deal with M sets', as Nrman defines them, that are data sets of these kinds of measurements found within spectroscopy . Without loss of generality we can depict spectroscopic information by complex curvilineal forms or topologies, and these may be our models of substrate behaviours.

We might call this weird quantum dynamics, or even String,Mbrane, or DBrane theory, but I call it trochoidally dynamic surfaces.

Where Eilliam Shanks helps out enormously is by developing an application that places these patterns in 3D. And where Quaternions help is by making that possible and making possible Terry Gintz Quasz fractal generator. He can be found at www.Mysticalfractals.com, and also at Fractalforums.com. As I pointed out Quaternions are inadequate to encode a full spectral analysis except for hydrogen but given the development of Trotorted by Will Shanks one could model up to 3 of the main frequencies in the spectrum of a material for each assumed particle / proton/ neutron in a nuclear and or atomic configuration or ensemblage. The trochoidally dynamic form thus realised may be of no use whatsoever or it may prove to be very insightful within a fluid dynamic setting.

The computational power to model the entire spectral database in this way may become extreme , but proportionality comes to the rescue at least in the simplified case .

The Beryllium nucleus I depicted is not representative of the spectral frequencies. I will shortly post a video of the hydrogen nucleus/ atom, and the hydrogen molecule using the Sticky Pudding concept that was ascribed to Thompson in a derisory manner.

Not just purely for entertainment. The point is, by selecting the bailout or cut off dimension, the iteration level, the magnification and the colour cycling frequency as well as the colour correspondence to displacement these amazing patterns are made sensible and visible.

What do they mean?

They mean that cycling or trochoidal motions can be applied to all scales connectedly . Despite seeming a continuous line that curves in the p,and, what we in fact can see is a complex trochoidal pattern of connected points.

Physically we can not resolve our measurements of space-time behaviours to these extremes, but we do see similar patterns realised in what we can observe.

The meaning of this is still under philosophical discussion by many. In my opinion as Newton opined, we do not present reality with our measures, but rather discover complex proportions that inform our lack of apprehension of the relationships between what we measure.

The expert may assign a correspondence between any of the controls mentioned above and a physical dynamic . If that leads to further predictable insights then he has found one of possibly many ways forward. If not he may at least generate aesthetically pleasing sculptures.

The Madelbrot set connects the many Julia sets which are probably of greater physical utility to scientists and technologists. How the Julia sets represent measured results is an area for deeper study, especially of Julia sets in 3 dimensions in dynamic behaviours.

The key is the Boscovich theory of force interactions as monads. This makes pressures depict able by curvilineal lines which we may call force lines in the sense of accelerative motion locii. Thus invisible"Power" become correspondents with pressures in a volume which are depict able by curvilineal lines of force. Whether, as Maxwell surmised these lines themselves trace out vorticular dynamics around themselves or as visualised above some more complex dynamics is a matter of further investigation and application of spectral measurements of frequencies .

It is my opinion that Faradays lines although elegantly simple represent a geometry that is classical rather than Fractal and therefore provide an over simplified depiction of magnetic behaviours, whereas a trochoidal description may provide an overly complex description but nevertheless a consistent one that accounts for all measurements.

Do I get closer to reality by this?

I think not. But I provide greater opportunity for alternative creative solutions to some technical problems which we now face on the nano scale . Remember, it was Boscovich who pointed out that there are more force behaviours than "gravity", and the way we account for them should change our view of Newtons Universe.

Einstins brave attempt to use space-time geometries after Minkowski is only the first step not the final solution. Misunderstanding Einstein does not help, even if Tesla is the mouthpiece!

At the same time mathemythics is not the solution either. We have minds for that purpose not dogmas.

I have been meditating on the problems of two solid discs rotating in parallel with the same direction of rotation and the same rate of revolution.

It exposed how mysterious rotation is to me/ us and how Einstein and other geometers sought to use its curvature to define force, in this case the notion of force is pragmatically the same as gravitational attraction, because one way or another we define our units of force by comparison with a gravitational force so called.

Weight, which is the common force used to define units for practical forces regardless of direction, because the direction is always rotatateable by a pulley or block and pulley system, assuming uniform tensions in Inelastic ropes etc, is a different notion to the inertial force that is measured as opposing acceleration . It is a resistive force that is there as an observed phenomenon but also not explained. By introducing geometrical curvature and geodesics Einstein sought to combine the inherent properties of the two forces as far as gravity is concerned.

The amount of curvature is a measure of inertial forces that frustrate any definition of acceleration that is curvilineal from matching with any expected value of a definition for a flat straight non curvilineal force. Einsteins idea was that the difference could be used as a gravitational force measure that is intrinsic to the geometry of space, and thus universal because it does not depend on mass and other physical measures, but rather it informs mass and materiality by governing it's motion properties.

We can then define our measures as if we lived in a flat space and expect that uniformity to be disturbed by a curved space. How curved that space is is set proportional to the gravitational field around massive object.

Thus the dictum curvature tells matter how to move, matter tells space how to curve!

It is an intriguing invention, but relies upon us understanding rotation and curvilineal forces. Unfortunately we do not.

The invention of Torque Gors back to the pulley, and is unsuitable for fluid dynamic situations. Usually the torque is made to disappear in equations by differential arguments, but in reality curvilineal motion is not in general a torque. From torque the notion of angular momentum(L) is derived as a mathematical moment. The moment of inertia for rotating objects is derived as a measure and so the whole system of angular measures Is built relative to the straight tangential line. Einstein tried an approach that circumnavigated this reliance on the extremely special straight line.

In his day only the Euler , Grassmann and Hamilton legacies provided the mathematics to conceive of this. The Gauss Riemann axis regarding curvature was also a contributor, but despite protestations by the Gauss school , the effective course of geometrical Interpretation in Physics is given by the former mentioned pioneers.

We need a curvilineal understanding of rotation that does not rely on the straight line but rather defines the straight line as a composition of curvilineal elements.

In any case the curvilineal force resulting from a dynamic pressure in any volume inherently explains inertia as a resistance to changing curvature or the sum of circular curvatures within a trocholdal dynamic.

Whereas straight line forces may be vectorially summed to give a change in direction and magnitude curvilineal forces may be vectorially summed to give a change in direction magnitude curvature and phase and amplitude. These other factors may be utilised in any proposed measure of inertia, and directly as resistance found within any pressure gradient of a dynamic nature.

Curvilineal notions of measure like radians often obscure the rotational aspect of a system in imagination, equating it to some straight axis. Thus turn either as a fraction or whole is often more correspond ing. But then notions of acceleration and velocity in turns do not assist in combining geometrically as well as radian arcs do, when attempting to define the combined effect of interacting rotations or turn velocities or turn accelerations.

One third measure is frequency: that is turn velocity by another name, and frequency is often converted to a third measure called wavelength that erroneously gives the impression of translational motion within rotations!

The concept of strain transmission whichbMaxwrll worked on does not require vortices to do anything but oscillate about their proposed centres. Thus what transmits is the rate at which these centres are made to displace periodically from their centres and the amount of displacement. The propagation of cracks in materials is similarly studied.

Thus light fir example is not a moving wave , but a changing rate of induction in materiality . We perceive the frequency of that change, not the wavelength! On the other hand length and frequency are li krd not by a formula, but by resonance of dominant frequency. We find that the lower frequencies require larger spaces to detect their effects, as they are "tuned" out by smaller cavities/ spaces/ antennae in the form of " wires" or rather wave guides for rotational displacements, or oscillations.

In all of this discussion we have not held to any measure, but when we do so it is invariably a measure based against a straight line length a gravitational force and a curvilineal pendulum motion acting under a gravitational force . Einstein attempted to release our notions from the straight line length by means of arcane mathematics, because no one wanted to hear about Aethers in America, as Tesla found out. But Aether was foundational to Maxwells concept of strain, as Powers were fundamental to Faradays conception of lines of force, and those Powers were influenced by Ideas of Örsted,Ampère, Boscovich more than any others.

We observe how tops and vortices interact with each other in solids and fluids ( liquids gases Plasmas) . These should guide us regarding the behaviours Biscovich described as general force behaviours both attractive and repulsive in nature.

There are many cases to consider when setting out a curvilineal vector sum or composition. For if a force acts jointly with another for but an instant what are we to make of such an impulse? Or what governs a curvilineal force to act mutually along the length of a curvilineal path? Frequency or turn velocity or acceleration certainly influence which curvature influences in the short term and locally .

And the size of the acceleration as well as the curvature can stretch or crimp the action of another Force . The radian velocity or acceleration , defined against the unit radius or against the circle radius obscures the curvature when converted to angle measure, so that as radius I erases the radian count should Increase almost independent of angle or degree measure! And so when a frequency is fixed at one radius, it naturally is conserved at other radii by increasing or decreasing the turn velocity, requiring acceleration to maintain a rigid disc structure , and thereby naturally resisting or attracting any alteration in the radius of curvature .

Conservation of angular velocity therefore has a place in my considerations prior to conservation of angular momentum.

When two curvilineal forces combine there is much to consider .

The hydrogen nucleus . The atom is not visibly different and the frequency of the electron is absorbed

Hydrogen gas is synthesised by two hydrogen atoms being paired not forced to I teract within each others boundary., in this way I hope to make a visual distinction between hydrogen gas and the Helium nucleus.

The vibrations in the gas molecule reflect the frequencies in the emission spectral lines

The Bohr and Quantum models compared. Khan goes into details about the model. Clever as it is the contrivance is obvious . That is why he says several times that the model is not reality. Why probability ? Few understand how probability is linked to the unit radius circle, and how DeMoivre took that relationship to set out his theory of probability.

Thus, the complexity within the sine ratio is able to establish a scale of recurrence/occurrence. This cyclical measure provides an estimate of complex motions in periodic / cyclical patterns. Rather than deal with the omplex surfaces of the frequency motions in Trochoids a probability measur of certainty is assigned to a region of space that the trochoidal surfaces will occupy.

The whole idea of a shape to an atom is ontrived, but a model can be built to account for the data of sorts as best we can. There are many models, not all the same and some ontradictory. The expert has to select which model is best for the task in hand while trying to uphold a fantasy of the atom

Looking more deeply into the spectroscopic data and the atomic data, the atomic mass informs me of a error I have made in modelling the atomic data by curvilineal forces. I have used the proton data, but of course need to include the neutron data for more accurate volumetric disposition. Of the curvilineal forces. In which case Trotorted can only model the helium atom, atomic mass 3 and 4 approximately.

My first video model would be of helium not beryllium and as it stands it contains only low frequency data not reported in the literature. The next 2 videos are in fact the hydrogen atom in its 2 isotopic expressions , not as I thought as the hydrogen gas.

You may gather from my increasing understanding of the measured data how speculative any model really is, and I make no claim as to the reality of the outcome of my exploration or the utility, but note that magnetic moment data is included in the fundamental spectroscopic data and that alone justifies my continued enquiry and curiosity.

I might addd that the confusion of units, the use of wavelengths as opposed to frequencies are indications of a need for some simpler synthesis of the models to which I hold out the hope for dynamic trochoidal surfaces.

You may see how the atomic mass and the atomic number are notated similarly http://physics.nist.gov/PhysRefData/Handbook/periodictable.htm Something that an expert would overlook , admitting to the very small confusion possible to the student! As expertise goes, these little idiosyncrasies preserve historical data and maintain an elitist ethos which is entirely academic in its origins. To dumb this down is to make the mistake of confusing a model with reality. Reality is ultimately mysterious and remains so, models however complex should not be mysterious.

http://www.citycollegiate.com/atomic_structureXIg.htm According to this neat summary the neutron has about 3 electron masses on a proton, but the comparative ratios show an increase of 5. We can accommodate the difference in rounding errors and as a consequence should rely on the mass difference average It is understood that a neutron decays into a proton and I electron generally., so the variability in the mass may also be accounted for by binding energies, so called.

I will use this proportion to determine a relative amplitude/ radius of the trochoidal dynamics.

## Comments

Where two pressures interact a dynamic trochoidal surface may be envisaged, defining the dynamic boundary of the hitherto indeterminate volume.

Such trochoidal surfaces when they interact may determine a curvilineal line of force and or a surface of equipotential pressure.

It is these curvilineal lines of force and surfaces of equipotential pressure by which I will define rules or proportions of pressure and proportions of force proportional to changes in accelerated motion being : change in velocity by some measure of change in displacement in some direction by some quantity of measure, by some frequency of rotation of an agreed metronome or pendulum.

In order to make a suitable scale uniformity or regularity may be employed or some more complex curvilineal uniformity based on none uniform elements.

Beyond this a repeating pattern amenable to some law of synthesis may also serve to reveal any variation from that law.

And so it is by dialectic resolutions of assonance and dissonance I will approach a sound expertise in diagnosing the states of behaviours around me, at all scales.

Simple frequencies are only guides to potential form .Dynamics add functionality to the form

These next videos are to fix in my mind that materiality has a frequency distribution.

I want to use the spectroscopic frequencies of elements to inform the frequency ratios in my model, beyond just the law of angular momentum analogy.

TroTorted gives some interesting surfaces for helium noth as a nucleus and as an atom .

Bunsen and Kirchoff change everything from materiality into frequency of radiation in plasma states

So now contrast with the Tutin model of the atom

Firstly we see wavelength used not frequency. This is because diffraction gratings use length between slits to disperse the spectrum by diffraction . Newton called this dispersion by refraction in a prism, so many scientists are still confused by Diffraction.

Don't be confused. Newyon chopped light transversal ly into corpuscles, modern photons do the same. Grimaldi slice light lengthwise into streamers that therefore spread apart like shavings by a plane. Clearly corpuscles or photons need to be dispersed, and refraction is used to do the dispersing. In a diffraction grating the split streams interact constructively and destructively by the wavelength in the stream.

While refraction can be used to characterise dispersion, it does not explain diffraction patterns .mthe wave length interaction does.

Now stepping up a gear, frequencies interact. While physicists want to base this on a one wavelength, this is not necessary. We can see frequency interactions in rotating or vibrating systems. Sine wave lengths provide a visual analogue for what is a rotational phenomenon.

Secondly the neat mathematical process obviously is contrived to allow numbers to represent energy levels rather than using directly measurable frequencies. The history of direct measurements follows the use of length as in dispersion angle , to average angular displacement on a dial, to oscillating circuits tuned to certain frequencies of oscillation.

We convert from wavelength to frequencies by formulae because early data was measured bybWavelength. Now we can measure ire ly in frequencies.usingbradio spectroscopy, etc, but we still get taught about the wavelength of light, giving the impression that light particles move through empty space.

The transmitting medium is oscillated vorticular ly at a spectrum of frequencies , as evidenced in earthquake waves, or vibrating materials carrying shock "waves" . These shock waves or vibrations are often called phonons or solitons, to fit in with particle depictions!

They are better understood , in my opinion, as vorticular rotations spreading through the medium, with a range of frequencies.

Comparing with attains model, we do not use to believe protons are jumping up and down in energy levels, rather we can use relative frequency proportions as governing coherent topological dynamics and thus more stable structures vis a vis incoherent and quickly decaying unstable structures

Tutin's model assumes negative charges in centre, but they saybMosely mpiriclly refutes this . But note spectral lines are measured in wavelengths not frequencies, making it harder to conceive of the alternative but not impossible .

It is not usually pointed out that the Bohr model of the atom has many excited states or levels making the " atom" in this state as big as some viruses!

http://web.mit.edu/8.13/www/pdf_files/moseley-1913-high-freq-spectra-elements-part2.pdf

The Frequncy is associated with Bohrs model, but equally Tutin can have protons travelling at that speed!/ frequency

http://www.cv.nrao.edu/course/astr534/Recombination.html

Characterising elements b their spectral lines of emission and absorption usually is done using wavelengths, for reasons explained above. But using frequency data enables me to generate a trochoidally dynamic model in TriTorted , which gives a 3d topological representation using surfaces.

Because it is based on thecQuaternion frame I can modulate at most 4 " axes" for any spheroidal dynamic . I need 6 because Trotorted locks 2 in the plane and uses them to determine the radius of the sphere. It attaches one frequency to this pair. Th other pair are left hanging , but I can assign frequencies to each .

Thus for the hydrogen nucleus or atom I can assign3 of the 4 major frequencies .

The use of octonions would allow me to assign more frequencies, but I am not very familiar with the topology of octonions.

I have yet to apply these frequency ratios to fractal generator app Quasz, which does have an octonion capability.

As Norman points out: the topological representation of a basis that spans a combinatorial form is arbitrary. Here he uses lineal combinations , uses the term lineal etc out of a convention that prescribes numbers as segments on a straight line. However the same logic applies to curvilineal lines and we could emphasis this by calling them curvilineal combinations that must span .

Now span means to tessellated a topological space. In that regard,a saciometrical interpretation is vital for utility in depicting a topological

Form, but combinatorial ly we are free to write down all possible combinations.

We should note that the integers saved the day topologically in enabling a span to reach all parts of a spaciometric grid or reference frame. In a curvilineal frame they are strictly not necessary as factors or coefficients, but as exponents they are extremely useful to depict fractional or rational coefficients, and to describe the direction of curvilineal displacement, motion and acceleration.

When used in this way they also found the notion of frequency in a closed curvilineal frame, and phase.

The coefficients can also be used to found the notion of amplitude, power and statistical probability.

From frequency and amplitude we can derive the notion of wave length .

A curvilineal reference frame therefore potentially enables us to deal with M sets', as Nrman defines them, that are data sets of these kinds of measurements found within spectroscopy . Without loss of generality we can depict spectroscopic information by complex curvilineal forms or topologies, and these may be our models of substrate behaviours.

We might call this weird quantum dynamics, or even String,Mbrane, or DBrane theory, but I call it trochoidally dynamic surfaces.

Where Eilliam Shanks helps out enormously is by developing an application that places these patterns in 3D. And where Quaternions help is by making that possible and making possible Terry Gintz Quasz fractal generator. He can be found at www.Mysticalfractals.com, and also at Fractalforums.com.

As I pointed out Quaternions are inadequate to encode a full spectral analysis except for hydrogen but given the development of Trotorted by Will Shanks one could model up to 3 of the main frequencies in the spectrum of a material for each assumed particle / proton/ neutron in a nuclear and or atomic configuration or ensemblage. The trochoidally dynamic form thus realised may be of no use whatsoever or it may prove to be very insightful within a fluid dynamic setting.

The computational power to model the entire spectral database in this way may become extreme , but proportionality comes to the rescue at least in the simplified case .

The Beryllium nucleus I depicted is not representative of the spectral frequencies.

I will shortly post a video of the hydrogen nucleus/ atom, and the hydrogen molecule using the Sticky Pudding concept that was ascribed to Thompson in a derisory manner.

Not just purely for entertainment.

The point is, by selecting the bailout or cut off dimension, the iteration level, the magnification and the colour cycling frequency as well as the colour correspondence to displacement these amazing patterns are made sensible and visible.

What do they mean?

They mean that cycling or trochoidal motions can be applied to all scales connectedly . Despite seeming a continuous line that curves in the p,and, what we in fact can see is a complex trochoidal pattern of connected points.

Physically we can not resolve our measurements of space-time behaviours to these extremes, but we do see similar patterns realised in what we can observe.

The meaning of this is still under philosophical discussion by many. In my opinion as Newton opined, we do not present reality with our measures, but rather discover complex proportions that inform our lack of apprehension of the relationships between what we measure.

The expert may assign a correspondence between any of the controls mentioned above and a physical dynamic . If that leads to further predictable insights then he has found one of possibly many ways forward. If not he may at least generate aesthetically pleasing sculptures.

The Madelbrot set connects the many Julia sets which are probably of greater physical utility to scientists and technologists. How the Julia sets represent measured results is an area for deeper study, especially of Julia sets in 3 dimensions in dynamic behaviours.

The key is the Boscovich theory of force interactions as monads. This makes pressures depict able by curvilineal lines which we may call force lines in the sense of accelerative motion locii. Thus invisible"Power" become correspondents with pressures in a volume which are depict able by curvilineal lines of force. Whether, as Maxwell surmised these lines themselves trace out vorticular dynamics around themselves or as visualised above some more complex dynamics is a matter of further investigation and application of spectral measurements of frequencies .

It is my opinion that Faradays lines although elegantly simple represent a geometry that is classical rather than Fractal and therefore provide an over simplified depiction of magnetic behaviours, whereas a trochoidal description may provide an overly complex description but nevertheless a consistent one that accounts for all measurements.

Do I get closer to reality by this?

I think not. But I provide greater opportunity for alternative creative solutions to some technical problems which we now face on the nano scale .

Remember, it was Boscovich who pointed out that there are more force behaviours than "gravity", and the way we account for them should change our view of Newtons Universe.

Einstins brave attempt to use space-time geometries after Minkowski is only the first step not the final solution. Misunderstanding Einstein does not help, even if Tesla is the mouthpiece!

At the same time mathemythics is not the solution either. We have minds for that purpose not dogmas.

It exposed how mysterious rotation is to me/ us and how Einstein and other geometers sought to use its curvature to define force, in this case the notion of force is pragmatically the same as gravitational attraction, because one way or another we define our units of force by comparison with a gravitational force so called.

Weight, which is the common force used to define units for practical forces regardless of direction, because the direction is always rotatateable by a pulley or block and pulley system, assuming uniform tensions in Inelastic ropes etc, is a different notion to the inertial force that is measured as opposing acceleration . It is a resistive force that is there as an observed phenomenon but also not explained. By introducing geometrical curvature and geodesics Einstein sought to combine the inherent properties of the two forces as far as gravity is concerned.

The amount of curvature is a measure of inertial forces that frustrate any definition of acceleration that is curvilineal from matching with any expected value of a definition for a flat straight non curvilineal force. Einsteins idea was that the difference could be used as a gravitational force measure that is intrinsic to the geometry of space, and thus universal because it does not depend on mass and other physical measures, but rather it informs mass and materiality by governing it's motion properties.

We can then define our measures as if we lived in a flat space and expect that uniformity to be disturbed by a curved space. How curved that space is is set proportional to the gravitational field around massive object.

Thus the dictum curvature tells matter how to move, matter tells space how to curve!

It is an intriguing invention, but relies upon us understanding rotation and curvilineal forces. Unfortunately we do not.

The invention of Torque Gors back to the pulley, and is unsuitable for fluid dynamic situations. Usually the torque is made to disappear in equations by differential arguments, but in reality curvilineal motion is not in general a torque. From torque the notion of angular momentum(L) is derived as a mathematical moment. The moment of inertia for rotating objects is derived as a measure and so the whole system of angular measures Is built relative to the straight tangential line. Einstein tried an approach that circumnavigated this reliance on the extremely special straight line.

In his day only the Euler , Grassmann and Hamilton legacies provided the mathematics to conceive of this. The Gauss Riemann axis regarding curvature was also a contributor, but despite protestations by the Gauss school , the effective course of geometrical Interpretation in Physics is given by the former mentioned pioneers.

We need a curvilineal understanding of rotation that does not rely on the straight line but rather defines the straight line as a composition of curvilineal elements.

In any case the curvilineal force resulting from a dynamic pressure in any volume inherently explains inertia as a resistance to changing curvature or the sum of circular curvatures within a trocholdal dynamic.

Whereas straight line forces may be vectorially summed to give a change in direction and magnitude curvilineal forces may be vectorially summed to give a change in direction magnitude curvature and phase and amplitude. These other factors may be utilised in any proposed measure of inertia, and directly as resistance found within any pressure gradient of a dynamic nature.

Curvilineal notions of measure like radians often obscure the rotational aspect of a system in imagination, equating it to some straight axis. Thus turn either as a fraction or whole is often more correspond ing. But then notions of acceleration and velocity in turns do not assist in combining geometrically as well as radian arcs do, when attempting to define the combined effect of interacting rotations or turn velocities or turn accelerations.

One third measure is frequency: that is turn velocity by another name, and frequency is often converted to a third measure called wavelength that erroneously gives the impression of translational motion within rotations!

The concept of strain transmission whichbMaxwrll worked on does not require vortices to do anything but oscillate about their proposed centres. Thus what transmits is the rate at which these centres are made to displace periodically from their centres and the amount of displacement. The propagation of cracks in materials is similarly studied.

Thus light fir example is not a moving wave , but a changing rate of induction in materiality . We perceive the frequency of that change, not the wavelength!

On the other hand length and frequency are li krd not by a formula, but by resonance of dominant frequency. We find that the lower frequencies require larger spaces to detect their effects, as they are "tuned" out by smaller cavities/ spaces/ antennae in the form of " wires" or rather wave guides for rotational displacements, or oscillations.

In all of this discussion we have not held to any measure, but when we do so it is invariably a measure based against a straight line length a gravitational force and a curvilineal pendulum motion acting under a gravitational force . Einstein attempted to release our notions from the straight line length by means of arcane mathematics, because no one wanted to hear about Aethers in America, as Tesla found out. But Aether was foundational to Maxwells concept of strain, as Powers were fundamental to Faradays conception of lines of force, and those Powers were influenced by Ideas of Örsted,Ampère, Boscovich more than any others.

We observe how tops and vortices interact with each other in solids and fluids ( liquids gases Plasmas) . These should guide us regarding the behaviours Biscovich described as general force behaviours both attractive and repulsive in nature.

Or what governs a curvilineal force to act mutually along the length of a curvilineal path?

Frequency or turn velocity or acceleration certainly influence which curvature influences in the short term and locally .

And the size of the acceleration as well as the curvature can stretch or crimp the action of another Force .

The radian velocity or acceleration , defined against the unit radius or against the circle radius obscures the curvature when converted to angle measure, so that as radius I erases the radian count should Increase almost independent of angle or degree measure!

And so when a frequency is fixed at one radius, it naturally is conserved at other radii by increasing or decreasing the turn velocity, requiring acceleration to maintain a rigid disc structure , and thereby naturally resisting or attracting any alteration in the radius of curvature .

Conservation of angular velocity therefore has a place in my considerations prior to conservation of angular momentum.

When two curvilineal forces combine there is much to consider .

The hydrogen nucleus . The atom is not visibly different and the frequency of the electron is absorbed

Hydrogen gas is synthesised by two hydrogen atoms being paired not forced to I teract within each others boundary., in this way I hope to make a visual distinction between hydrogen gas and the Helium nucleus.

The vibrations in the gas molecule reflect the frequencies in the emission spectral lines

The Bohr and Quantum models compared. Khan goes into details about the model. Clever as it is the contrivance is obvious . That is why he says several times that the model is not reality.

Why probability ?

Few understand how probability is linked to the unit radius circle, and how DeMoivre took that relationship to set out his theory of probability.

Thus, the complexity within the sine ratio is able to establish a scale of recurrence/occurrence. This cyclical measure provides an estimate of complex motions in periodic / cyclical patterns. Rather than deal with the omplex surfaces of the frequency motions in Trochoids a probability measur of certainty is assigned to a region of space that the trochoidal surfaces will occupy.

The whole idea of a shape to an atom is ontrived, but a model can be built to account for the data of sorts as best we can. There are many models, not all the same and some ontradictory. The expert has to select which model is best for the task in hand while trying to uphold a fantasy of the atom

Helium spectral lines

Looking more deeply into the spectroscopic data and the atomic data, the atomic mass informs me of a error I have made in modelling the atomic data by curvilineal forces. I have used the proton data, but of course need to include the neutron data for more accurate volumetric disposition. Of the curvilineal forces. In which case Trotorted can only model the helium atom, atomic mass 3 and 4 approximately.

My first video model would be of helium not beryllium and as it stands it contains only low frequency data not reported in the literature.

The next 2 videos are in fact the hydrogen atom in its 2 isotopic expressions , not as I thought as the hydrogen gas.

You may gather from my increasing understanding of the measured data how speculative any model really is, and I make no claim as to the reality of the outcome of my exploration or the utility, but note that magnetic moment data is included in the fundamental spectroscopic data and that alone justifies my continued enquiry and curiosity.

I might addd that the confusion of units, the use of wavelengths as opposed to frequencies are indications of a need for some simpler synthesis of the models to which I hold out the hope for dynamic trochoidal surfaces.

http://physics.nist.gov/PhysRefData/Handbook/Tables/heliumtable1.htm

You may see how the atomic mass and the atomic number are notated similarly

http://physics.nist.gov/PhysRefData/Handbook/periodictable.htm

Something that an expert would overlook , admitting to the very small confusion possible to the student! As expertise goes, these little idiosyncrasies preserve historical data and maintain an elitist ethos which is entirely academic in its origins. To dumb this down is to make the mistake of confusing a model with reality.

Reality is ultimately mysterious and remains so, models however complex should not be mysterious.

According to this neat summary the neutron has about 3 electron masses on a proton, but the comparative ratios show an increase of 5.

We can accommodate the difference in rounding errors and as a consequence should rely on the mass difference average

It is understood that a neutron decays into a proton and I electron generally., so the variability in the mass may also be accounted for by binding energies, so called.

I will use this proportion to determine a relative amplitude/ radius of the trochoidal dynamics.