Heat Theory 3: the paradigm Shift
The paradigm shift has been looming, bu the final straw for me is documented in another forum thread.
I have been having discussions with Ivor Catt, and reading and comparing his Electromagneti theory with that of Maxwells.,the one thing that this kind of focus made me do was look at the alternative theory, the Magnetoelectric one.mthe Thunderbolts Project also was a powerful motivator to not blind myself to alternatives.
My own Shunya Field theory a mechanical vortex explanation underlay all my skepticism, but I knew my theory was fanciful and empirically unsatisfactory. Still I chipped away at the mindset that blocked my vision. I was not satisfied with the cobbled together theory of the standard model at all levels, but I did not know what to fundamentally replace it with. I was also much clearer on the role of " mathematics" so called.
Howard Johnsons book on magnetism had one confirmatory image of the Equipotential contours of a bar magnets force field.
Ivor Catt had evidence of a "step" electromagnetic wave moving through space creating these force field contours and extending the model of the capacitor, especially as transmission lines, but also as batteries, frequency generators and power transformers.
Faraday had set out the parallel description of matter which was relevant diamagnetic and paramagnetic versus dielectric and semiconductors or paraconductors!
The notion of fluids was utilised at every stage of the development of the classical understanding, but the Maths was in conflict!
The Royal philosophical society has many many documented empirical phenomenon on both magnetic and electric behaviours not commonly known, in which electromagnetism was posited before Maxwell as a phenomenon of light.
The list goes on, overturning years of wrong beliefs and teachings!
And finally Samuel Earnshaws crystallised what fluid mechanics could so easily have done in 1842. No stable charge fluid can exist in an inverse square law force field.
There can be no classical magneto statics or electrostatics!
In my mind I could get rid of the electric force field, perse and the magnetic force field and replace them both with a singular vorticular dynamic force field!. ExH whatever that meant in descriptive terms had to represent a vorticular laminar flow according to Catts theory of Electromagnetism. The step was important because in fluid dynamic terms it represents a laminar shear!
Thus I could see the value of moving directly to a fluid dynamic model of matter and it's behaviours with the fundamental shear behaviour representing what has up until now been resolved into an "electric" component and a "magnetic" component.
But even this was not sufficient. I knew from consideration of Newton's analysis, and Grassmanns Aalysis that this Cartesian resolution was not sufficient. The classical philosophers always applied a third resolution and that was into the curvature of a circle.
I knew also , from Archimedes, that when you apply all the resolutions, that is you combine them appropriately you end up with a vorticular loci I. Surface and volume. The complete set of techniques allowed philosophers or rather astrologers to model complex vorticular motions, surfaces or volumes in space and or in" time", by which I mean Tyme the data of the position of stars and planets.
Why would we apparently forget these things?
It is not so much that we have forgotten, but more that we have lacked the understanding! When the industrial revolution hit on our shaws all sorts of uneducated men suddenly became rich and powerful! This was nothing new! Either by war or luck brute force has dominated the cultural landscape. Only where it has sought the wisdom of the astrologers and Magii has it preserved their understandings to pass on to future generations. But mostly, as in the case of Archimedes, this fine understanding was brutishly destroyed, dismembered, burnt as of no value, dispersed as decoration nd booty of war, dismantled , desecrated and hidden in secret cves, societies and tribal memories and or myths.
The vorticular mature of Spaciometry is most straightforwardly described by Newton. Applying his principles and method, vorticular motions arise as if by magic from the chain of reasoning. The occult explanations are thereby avoided rather than disproved, and all may proceed serenely above the machintions of any Demon, should there be one
Maxwell , perceiving this deliberately brought a demon back into the picture of pristine serenity created by Newton. Why?
The devil is in the detail! And no matter how he tried Maxwell kept coming upon the devilishly clever nature of Newton's praxis!. He just could not understand how it all worked! He thought there was a problem, because Navier and Stokes could not get their equations to do anything but behave ridiculously! Helmholtz and others could seemingly only produce translational motion or rotational motion. This was in fact all they could model! Somehow they could not think differently
A little daemon was needed to upset the apple cart, and to do it Maxwell had to utilise statistics and probability.
The difference between statistics and probability is the difference between rotation and translation , or rather translation and rotation.
Translation was always going to move into unpredictability, rotation was destined, so it was thought, to repeat endlessly.. However, do not be fooled. Dynamic rotation, as Ed Lorenz showed is as unpredictable as anything else!
Maxwells daemon was thus deployed in the statistical modelling of the arbitrary behaviours of a large number of uniform particles. The reasoning behind this was immediately accepted and developed. It meant that the mass of solutions to differential equations could be statistically weighted for example. Suddenly a lot more work had to be done to model the behaviour of gasses and liquids, but the statistical map meant that a range of solutions could be chosen, organised by the statistics, combined as in normal solutions and statistical outputs obtained.
The diffusion of gases was investigated by Kelvin using this model, and found to be statistically " accurate" . Of course to those who did not understand the modelling process they were amazed that " mathematics" could now explain gas diffusion!
The only thing Maxwells statistical approach did was unblock the frozen minds of philosophers, and expand their minds to the complexities of the things they were meditating on. The empirical data gathered, and the methods of gathering it provide the explanatory model, not the mathematics!
The work of Grassmann is key in this discussion. By showing that we should embrace the complexities by clever use of notation, and clear understanding of the combinatorial rules he demonstrated in 1844, 2 years after Earnshaws proved inverse square laws were unstable, that you could do a whole class of calculations in one go if you notated things correctly and kept the combinatorial rules clear. He demonstrated this in detail by creating singlehandedly, lineal Algebra.
Hamilton 10 years previously had created the first abstract algebraic method for conjugate functions in order to vindicate imaginary quantities and in particular imaginary Logarithms.. The Algebra at the time was mostly Cartesian , following his geometrical ideas which he claimed were drawn from the Greek fathers, and which later Scholars confused with the Stoikeioon! Descartes Greek Fathers were the Technetium or Mechanical engineers of Grrek society, the architects and engineers. Some may have come from Euclids mechanical works like optics and perspectives etc. Nevertheless the algebra was as Newton believed it should be, heuristic, just how you had to think to get the answer. The answer and it interpretation was more important.
Hamilton had to convince a naive public that heuristic algebra was a subject of great importance, because it revealed how we come to our conclusions.
The Grassmanns went a step further. They showed hoe heuristic algebra was a set of rules which we unfailingly apply to generate our answers. If we make a mistake in applying the rules we get an unexpected answer. Therefore we must know the rules explicitly so we get the expected answer.
But then we could design the rules differently! If we purposely did that what would be the expected answer?. This expected answer was completely determined by the rules. This was in short he axiomatic constructive method, Kant, Schilling and Ficht were devising as the foundation of " mathematics". The assumed primitives were geometry, algebra and arithmetic.
Hermann Grassmann , inspired by his Father's analysis took his research to the next level and showed the method of achieving a sound set of actions. To demonstrate his point he created lineal Algebra. This was not his purpose. His purpose was to vindicate the analytical and synthetically method.. His demonstration piece was always defective because he hoped collaborators would join with him in a great research to advance natural philosophy to its ultimate conclusion. He pointed out himself that he had not done the work for the circular line !!
As far as I know no one has even among the Clifford algebras. Despite the name spinors are not circular lines. It mat seem redundant to explore this aspect when we can use spinous in ways like Bezier lines to tangent out curves, but in terms of notational design, I think Hermann wanted to do that work. He had learnt so much just with straight lines what would come fron circular arc?
I believe a more natural vorticular algebra would have energeed.
Having said this hermanns work has greatly inspired computer scientists in developing programming algorithms
Thus Maxwell was able to take advantage of some of the latest mathematical praxis to formulate his mathematic description of what he felt was a complex fluid flow of a sea of vortices.
Maxwells distribution, illustrated in the link clearly makes 3 reasonable modelling assumptions, and uses one arcane mathematical identity as one of them. Few would know that a probability quantity is related to a function quantity if they both rely on the same parameters and those parameters are orthogonal!
Instead of orthogonal maxwell uses the idea of independence. This starts a debate about the precise meaning of orthogonal.
It comes to have 2 meanings a philosophical and a strict geometrical one. This becomes confusing and leads to many mistaken applications of this distribution. The Pythagorean law requires strict geometrical orthogonally, but it can be relaxed by adding additional terms. This became exploited in the contra variant and covariant notation which leads eventually to tensor forms of the distribution.
The Maths here is relatively simple ratios, but it's unfamiliar contexts, notations and grandiosity makes the average person quail!
Has the math revealed anything? No. It has modelled an idea that a quantity of distribution can be measured and displayed in a 3d graphical space. It lays out the procedure to do so. Once we have the model we can look at the images and meditate. This is what gives us insight into the behaviour of the model. However we need also to look at the real circumstance and meditate. This tels us whether the model is any use or not!
Doing both things gives us additional insight into how we can apprehend , represent and display our experiences. But in the end it only ever allows us to interpolate. We can never truly extrapolate from any mathematical model.
What did Maxwells distribution achieve? It achieved a paradigm shift in heretical thinking. Now theoreticians could approach the complex cases statistically with some quantifiable verification being the out come.mtheir ideas of vorticular flow were not just qualitative they could statistically quantify it. D' Alembets paradox for fluid mechanics was not challenged because it was just thought he math was indisputable, vn if nature defied it! The retreat to mathematical models had begun.mno one wanted to believe the evidence of their own eyes ere long.
Which was a pity, because Maxwells distribution was the ideal weapon, ith Earnshaws s theorem to disprove D'Alembert.
At any rate it could now be posited that heat pressure and a concept called mass , better density of space were important factors in a quantity newton called a quantity of motion. No one paid much attention to that, instead concentrating on Leibniz vis viva or living inherent force inside a volume of space. Unfortunately, instead of definitely supporting a fluid dynamic description, kelvin used it to support a particle description of space.
Never mind, we can correct that now.