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One of the plane facts is that matter is variable in its intensity and that it has continuous and discrete forms .
Further we recognise energy -phase changes that is to say simply : solid liquid gas plasma. States of matter with different vibrational signatures.
It was determined by Newton et al that heat was best described or pictured mentally as a vibration in a corpuscular region corpuscles were thus conceived as flexible plasmas from the nascent biological discoveries of the time.their flexibility was merely a way of accommodating the vibrational modes conceived as heat .
We have since developed the heat model into the Energy ,Odell.nsuch a model really has its foundation in Gilbert's magnetic philosophy which recognised 2 forms of magnetism: crystalline lattice or mineral magnetism and biological magnetism, that is organic lattice type. The one was called the iron or ferro magnetism, the other Electra magnetism or amber magnetism.
These specs were later intensively studied and distinguished into models that were fundamentally mysteriously related. However the various guilds of magnet makers and electric charge makers jealously hung on tontheirbtrade secrets and further distinguished the common link, that is the fundamental material experience and phases of matter at different energy or vibrational states.
Matter and space were philosophically divided in the most natural way , but space was called empty for religious reasons. It was desired that spirit be distinct from matter, and invisible able to manifest to conscious souls, themselves spiritual.
Such a model kept the material world that technology was exploiting as a distinct environment that mankind could "play" with like a child, but spirit was the playground of the gods and those ascended humans who struggled to grasp it.
Of course the material philosophers were brought up in that Matrix of ideas ad models, but younger more ambitious material scientists saw no valid reason to limit material science in this way and technology indeed advanced to miraculous inventions gadgets and contraptions which supported that viewpoint.
Unfortunately the mathematical clan or guild retained enough obscuranting mystics to cover the material viewpoint with a pseudo mystical or religious analogue of religious theology . Bishop Berkely wrote a powerful attack on mathematical religious views pointing out that material scientist of the mechanical philosophy were in fact no more clear of superstitious nonsense or beliefs and practices than religious theologians and clergy
Accepting that point we may progress toward a common view proposed in detail by Hegel et sl and eastern mystics since way back, that spce is in fact something that is connected to a singular concept that contains all: if you like spiritual and material are two aspects of an entity with many aspects.
The Aether or Ether philosophies attempted to place that view as foundational to the material sciences, but all clans and guilds fell apart in disarray: a modern Babel of jargon and gobble de gook .
We do not have to be so inclined. A simple and useful combinatorial model underpins the technological achievements of mankind. It is rather humble in its scope and often symbolically and ritually obscure. Attempts to make it clearer usually do the opposite, academically. But those who actually make things using their whole organism develop inexpressible expertises that often seem to those not involved in the physical actions of making , well they seem like magic, even magycke of the old kind.
Regularly organic and rock crystals cry out to us ! We call them TV's and Radios!!
So we can take material science or specifically the science of material and develop an expertise that Tribology or tribologists express. This level of expertise is an art form found among the few material scientists with a broad enough range of experiences and understanding. It is eclectic and very much in its infancy .
For example, topology would help to provide a structural overlay akin to corpuscular philosophy of Newtons time. Topology fundamentally is a combinatorial art that gives forms or formats for space in its most general Aetheric model . These formats may then be used to count and measure regions and distinguish behavioural changes in material over time, circumstance and internal and external conditions.
Topology allows us to place atomic or molecular models into regions of space so we can characterise certain regions by their phase and nearby status and their visual characteristics . The stresscandvstressors in such a space become characteristics of the phase of the element or molecular material as well as contact behaviours between such characterised materials.
Clearly a chemistry and organic/ biochemistry based on these characteristic measurements and observations has proved very fruitful in organising our technological advances. But we have found some who want to isolate these behavioural and technical expertises away from common knowledge to support some particular world view or religious ideology.
While the knowledge is presented as iconic, eclectic, difficult to understand, even iconoclastic, it is in fact not. The simplicity of the energy/ vibration - phase model of matter is how it has been hidden in plain sight.
It is a simple robust and powerful combinatorial system that was advanced by Navier Stokes and yes even Newton into the fluid dynamic model. Helmholtz and Kelvin added the Vottex model rules (inaccurately: see Claes Johnson work) but all of this was obscured by the Mathrmaticians. Helmholtz following perhaps Euler and Lagrange felt that the differential equation format was the safest way to express natural laws of motion in space-like material especially if they were fluid.
In a sense , given the prevailing attitude that aether was basically solid billiard balls at the femto metre scale( an assumption since demonstrated to be misleading especially by quantum Mechanics) his reliance on the continuous nature of differential equations by design does preserve the fluidity of the foundational corpuscular theory of Newton et al.
The use of hard billiard ballasts representing corpuscles is a mistake we can trace back to Leibniz et sl . But even then he was not insisting that matter was thus. The mathematical topology was simpler if this was assumed , and produced useful models. It also produced strange aberrational models which rightly were ignored! Now they are mystically clumped together in the quantum mechanical world viee.
The fluid mechanical expertise is very difficult to establish except in the simplest cases, but in fact computationally it has provided us with some excellent models within the boundary conditions appropriate to the study. The advent of more powerful computers and computational schemes has made it possible to model complex data increasingly accurately, by applying a whole mish mash of equations topologically to a spatial region.
The one fundamental breakthrough for physical topology is ascribed to Benoit Mandelbrot. His Fractal Geometry inspired many computer geeks to model the particular types of inductive or iterative( recursive) equations that hitherto were avoided by Mathematicians as monsters. Ad yet we know Focault and many others were studying them quietly prior to the wars with little academic support .
We can laugh, but it was mathematicians that were the Luddites when computers were first introduced!!
Today I watch a lovely flowing scene of actual waves lapping onto a shore with all the sound effect on a flat, crystalline organic matrix presenting the display of raw data as processed by billions of logic gates in some silicon(rock) chip processor with a certain vibration/ energy which has to have the heat removed by invisible gases passing over it as winds!
The fluid dynamic models expressed as differential Equations may be nonsense. But the expertise that organises itself in this way around the energy phase model really has a powerful set of models with which to develop further models and technological advances .
Why have I not mentioned Maxwell, and Einstein? Because they represent a deliberate mystification of the simple model. Faraday was not happy with how Maxwell fundamentally distorted his ideas. In fact Örsted Faraday, Ampère Volta and others held that a circular force o rather a rotational force was fundamental to our understanding of all models built on observation. Newton, unlike his successors took a circular or rotational force for granted.
This simple topological element distinguishes models that account for quantum behaviours from those that do not.
And yes the mathematics becomes confusing and complicated, but only when the circle and the trochoids based on circles are excluded.
Include trochoids in space in your models and you can model magnetic behaviours topologically in a consistent way.
The gravity of this point should not be missed, as Gravity to this day is still touted as a mysterious force, all forces are fundamentally mysterious characteristics of topologically described space. Their iscavsimple reason why conic curves describe both gravity and magnetic attraction and repulsion. The topology of space that best describes them is rotational or circular. Add to that fractal geometrical topologies and you can model fluid dynamics in appropriate small boundary conditions.
Add phase changes at different energy and thus vibrational states( frequency amplitude and trochoidal topologies) and you arrive at discrete regional distributions with phase changes marking the boundaries of regions fractally.
What we know about bonds is dependent on these fractal regional surface phase change behaviours at differing energy/ vibrational statuses
We require a new label for application of fractal geometry to real physical behaviours and forms : fractal topology ..
Even the greatest mathematicians become hostages of the theories they create when they take too seriously their creations. An excellent example of this is the so-called d’Alembert’s Paradox which results when one ascribes to a mere model - be it in the form of partial differential equations of Euler, or Navier and Stokes - an intelligence of its own, and takes the model too seriously.
In your last comment you have touched upon important philosophical questions which had widely been discussed by eminent minds of the past, at various levels, and they still remain largely unresolved. The Letters of Euler to a German Princess is one of such discussions that you will find, hopefully, interesting (in particular, letters 138-154 on electricity and letters 169-186 on magnetism).
It is quite likely that this milestone achievement will be marked in the history of fluid dynamics as a watershed moment in our understanding of the mechanism of flight. This development is so extraordinary that it took more than three years for the publisher to take the courage to publish it and yet felt it prudent to cover its butt with the following Editorial Foreword:
The special character of this article requires some comments by the editors on the purpose of its publication. Though, its mathematical content does not meet the degree of mathematical rigor usually expected by articles in this journal, the implications of the argument and the accompanying novel numerical computations are of such far reaching importance for technical fluid dynamics, particularly for the computation of certain features in turbulent flow, that it deserves serious consideration. The main purpose of this publication is therefore to stimulate critical discussion among the experts in this area about the relevance and justification of the view taken in this article and its possible consequences for modeling and computation of turbulent flow.
It is worthwhile noting also intellectual integrity and human dignity of Prof. Johnson who decided to not accept to receive the Ludwig Prandtl Medal for reasons outlined in his Letter to the General Assembly of ECCOMAS .
Heartfelt congratulations, Prof. Johnson!
Not!!!
A fluid dynamic paradigm removes this modelling paradigm.
A magnetic plasma vorticularly pulsating is a better model . Using hydraulic gearing principles we can model magnetic behaviour, even with a non compressible fluid! Some fluids clearly must be compressible or expandable but the fundamental fluid would be non compressible, like the solid or irreducible atomic particle.
Replacing solidity by in compressibility allows fluids to be contiguous without preventing resisted motion through it. Instantaneous solidity replaces the concept of solid material,nalongside the measure called viscosity.
Magnetism can be modelled by these kinds of fluid interactions xx
Gilbert reduced magnets to tiny magnetic "monopoles " we are told. But in fact he reduced a full magnet to tiny magnetic domains, before magnetic domains were revealed by metallurgical science. His contention was that these domains somehow moved , collecting at either end of a bar magnet or in regions of a Lodestone crystal lattice.
The most advanced research calls these regions Skyrmions. They are small thin layered domains that move through materials especially at junctions of differing materials. Thus metals that are doped with other " magnetic" materials are rich in these vorticular Skyrmion regions.
The implications are huge. As you can see on the sun huge areas of the surfaces are structured by domains that have the same " potential". That means these tiny Skyrmions domains can tessellate into vast regions in 3 dimensional space ,dynamically flowing in great arcs toward the opposite potential. However this is not attraction or repulsion it is dynamic rotation. The opposing rotations of space create the effect of repulsion or attraction.
Magnetic domains are coherent regions of magnetic structure. That structure is often simplified to a north south axis, but in fact we ought to better model it as a rotational planar motion! This planar rotation is itself rotating. The radii of these rotations regionalise magnetic structures and behaviours.
Tesla did not claim to know what he was experimenting with beyond a fundamental rotating power of space. Ric Dollard has taken his research further and demonstrated Tesla's results at the root of his revelations and conceptions.
Today aerie is writing an in depth theoretical work on Alternating or cycling current based on his research and ideas from the greats like Tesla, Steunmetz and others
My contention is simple : allow for a force that is trochoidal in natural expression and everything can be modelled more simply.
This demonstration indicates that gravitational attraction is an electrodynamic/electromagnetic rotational or magnetic current effect.
The rotating force is emphasised by this demonstration the longitudinal forceis emphasised right at the end.
Gravity is magnetic, that is rotational , it just seems centripetal .but centripetal is Newtond resolution of a rotational force! He was not confused we are! Xxx
Of course Newton is wrongly used in this account, and yet not entirely misleading. Newtondecomposed rotation inti non linear centrifugal and centripetal force action. His model is way cooler than most understand or care to explain, but essentially he assumes rotational forces as givens!
Most assume he reduced everything to lineal forces and impulses, but he explains that rotational motion is more easily modelled by centripetal and centrifugal forces relating to the Geometrical form of the circle. In this format the circular force is instantaneously or rather at each instant in time represented by a tangent line to the point at that instant. This then allows the principal axes of any circle to non linearly resolve the centripetal force and the centrifugal force always perpendicular to each other .
Using such a model electro magnetic behaviours can be described,
For example: a curved plasma beam in a magnetic flux or a curved magnetic flux in an earth sourced magnetic flux. Wherever we establish a magnetic flux it is always best described as curved or rotating.
The early researchers were not able to resist distinguishing Electra based phenomena from magnetic, despit Gilbert's clear steer in that direction
The issue was one of effects and materials. The stretching of induction into conduction championed by Maxwell, but well accepted by his peers confused basic researchers who could not then see the extensive surface effects on different materials as related.
Certain materials promote regions or domains of magnetic behaviour. In some materials these regions are larger than others, more coherent than others and more mobile than others.
When Ampere proposed his model of electro dynamics it was very simply a fractal topology if the present and obvious circuit. These fractally atomic circuits were not the source of electro magnetism, that was God! They were a complex model sufficiently complex to model observed behaviour. Later these were wrongly identified as electrons , and then as electrons spinning around atomic nuclei, and then as electrons paired with protons to form atomic structures with magnetic dipoles!
The identification of Skyrmions as "magnetic" vortex structures, that is magnetic flux vortices is a more accurate representation of Ampères electro dynamic circuits at the fractal scale. Both Biot,Savit and others did nothing more than organise the magnetic flux in rotational mode around a wire in a circuit .
Ampère recognised the limitation of that idea. It said magnetism is a primitive force and that's it! He said the circuit itself is the source of a primitive force by virtue of a dynamic circular or rotating force around it. This then inductively allowed him to reduce the force fractally to any level,mand to maintain a dynamic at all levels .
This did not provide an ultimate cause( beyond God) but it avoided the straight line literalism of his peers who gave no room for circular or trochoidal forces as primitives..
I do not see why this could not happen. In fact we have something in Nature which is not exactly what I have envisioned above but pretty damn close: Egg --> Caterpillar --> Chrysalis --> Butterfly --> Egg life cycle.
The whole Nature I envision as a living and breathing thing. Life is an eternal phenomenon that manifests itself everywhere in one or another form, on each and every level of fractal universe. It simply cannot disappear in one form on certain level without reappearing on some other level in a different form.
Thanks Barau. I have come down on the side of one proto paradigm: fluid dynamics/mechanics. But my fluid is what is otherwise perceived as space .
Lord Kelvin and Helmholtz really hoped vortices would explain molecular and atomic behaviours. Maxwell did not think so: his electromagnetic theory is based on strain! He wanted a fluid dynamic model of strain based on vortices, or their mechanical equivalents.
Mechanisms were crucial for mathematical modelling . Helmholtz and Kelvin could not advance their concept mathematically because it was too hard! Navier and Stokes could not advance their model because it was too hard. It took claes Johnson and the advance in computing to numerically solve these differential equations, and to show up flaws in the Kelvin Vortex Kinematics.
What this means is that we can now describe molecular behaviour, atomic structural behaviours by fluid dynamic methods, numerically calculated.
The essential abstraction is the rotating vortex. At all scales it is fractally reproducible.it is therefore able to model trochoidal kinematics in space at all scales.
To me this is fundamental to modelling magnetic behaviours and I include Electra magnetic behaviours in the overall descriptive label "magnetic ".
What distinguishes the 2 is crystalline substrate structure. Ferro versus organo crystalline structure. The ferro crystal organises into domains. But surprisingly few know these domains have fluid boundaries! The Guild of Magnet makers knows all about this, but scientifically they have to link up with the dominant electron model of matter.
Recent research into Skyrmions is revealing the vortex nature of ferro magnetic flux at these domain boundaries, and material boundaries.
The organo crystalline structure tend to be more viscous and the magnetic Skyrmions do not move the boundaries so much, this means induction does not become conduction and the magnetic Skyrmions form tessellated regions that punch up from the surface into the surrounding space" this atmosphere is perceived as electrostatic.
The full details and any improvements or corrections to the model I am still pondering.
It is important theoretically to constrain the skyrmionsvto planar rotations . If we flip a plane rotation over we get a contra rotation . We also have expanding and contracting Skyrmions to add.
Magnetic behaviours can then be modelled as gear like actions, and gear chain structures in which the gears are composed of vortices and vorticular wave action.
Your idea and example is modelable by fluid dynamics.
You said: This is a paradigm appealing to many, myself included. Electrical engineer Arend Lammertink is another one.
Here is how he puts it (Questioning Quantum Mechanics): You also said: My firm belief is that successful modelling of the phenomenon of life cannot be accomplished without employing in some way fractal regression. Contemporary science will never solve the riddle of life because it is looking for something that does not exist - elementary particle(s).
Imagine a physicist who saw the Mandelbrot set, drilled through few layers of it and, dazzled and fascinated by its beauty, decided to find the "elementary particles" which comprise the "Mandelbrot universe". He would be sorely disappointed for he would never find any elementary particles. But if he was lucky enough to guess that what he needs to search for is the algorithm and not elementary particles, he might have ultimately succeeded.
I was fortunate enough to participate in the search for the Mandelbulb!
That was a phenomena that reawakened my mathematical delusion!
I had from about 12 dedicated myself to becoming a famous mathematician. Unfortunately when I got to university I found out that I had been duped about Mathematics!
I found Hilberts book on mathematical foundations and dedicated myself to revising the subjects foundations. Thus my 3 years of mathematical exposure were not wasted by a sense of having been brought to university under false pretenses!
However it was not until years later that I was mature enough to begin to tackle the issue.
My researches can be found by googling jehovajah Fractalforums or jehovajah Shunya.
The other thing I learned at university was how to code a computer in any language !
Back in those days Fortran, Algol60 were the teaching paradigms . C and Basic were just around the corner as was MsDos .
So when I eventually concluded Maths was not salvageable and we needed to recognise that it was not only dead but actually poisonous I came across Sir William Rowan Hamilton and his reconstruction through his paper on "Pure Time". I did a detailed analysis of the first part of that paper, and met quaternions and Doug Sweetster !
In one of our discussions he mentioned Grassmann. I already knew about Clifford, so was astonished to find Clifford was a Grassmann acolyte!
To cut a long story short I googled Grassmann found not only Hestenes but also Norman Wildbergers information.
I found Hestenes work too Academic, but Norman was and is a breath of fresh air!
He briefly revived my hopes of refounding Mathermatics!
However, I was intrigued by Grassmann. So much so that I decided to read his book in German and translate it myself!
You will find many of my translations on Fractalforums under my username Jehovajah,
I am slowly working through Justus Grassmanns seminal ideas .
At one time I had the urgency of a pioneer! But now I am a mere hobbyist.
The books themselves were written by Hobbyists!
Despite my appeals for discussion and multiple translation contributions my threads attract few participants but great interest! It is enough that a few try to assimilate my poor attempts at commenting on the work of the Grassmanns .
The threads are open and anyone can contribute. If you feel inclined I would welcome some stimulating company there also.
Life has a way of setting its own priorities. These works are fundamentally important to shifting paradigms but sadly no longer my top priority. I will probably translate them until I die because both Hermann and Justus speak to me across the centuries, but many take the easy route and use the excellent translations by Kannenberg
I find these translations disconnect me from Hermann and keep me in the modern delusion , whereas Hermann takes me out of the modern delusion into the early 19th century one!!
That maybe better for all if we returned to that delusional state as critiqued by the Grassmanns
Probably it is no accident that great mathematicians of the past - like Descartes, Newton, Leibniz, Euler, Gauss and Bernoullis - all were natural philosophers. In fact, all mathematical results were discovered not mathematically but by employing induction and analogy through the process called plausible reasoning.
As G. Polya shows conclusively in his two-volume book Mathematics and Plausible Reasoning (Volume I: Induction and Analogy in Mathematics and Volume II: Patterns of Plausible Inference), the discovery of the truth behind any theorem is always non-mathematical in its nature, i. e. mathematical truths are guessed first and only then proved with mathematical rigor.
I would go even further and assert that mathematics itself, with all its diverse branches, is discovered non-mathematically.