I have already established that motive in a fluid not only provides acceleration in a fluid, it also transforms the boundary of a fluid element.. Thus the transfer of motive across a changing boundary has to be considered.
This is complex because a given amount of motive or type of motive is not transferred, norbisbit transferred instantaneously. .thus a rate of transfer or motive has to be considered, and a rate of deformation of the transferring boundary. The directions of these rates of change are also important and the reaction to these rates of change also need to be considered.
The instantaneous changes in the rate of change as a action reaction system also have to be updated at each instant in order to develop the combined result. To avoid all of this consideration, fluid dynamics has proceeded on the obvious steady state achieved after initial conditions have been introduced. This has usually resulted in a profile of instantaneous velocities which are evolved time wise to describe the modelled motion.
I can proceed along that path, but I won't because the notion of an active boundary is thereby lost.
An active boundary is like a bubble surface. It clearly expands under omnidirectional train. Thus a surface tension has to be introduced in any boundary change, thus shaping the motive transmission profile , and introducing tangential and Twistorque motives into the description. These are clearly dependent on the nature of the medium, and contribute to its viscosity profile, as well as the conservation of matters/ energy effects.
Transmission and diffusion rates need to be compared to gauge energy or matter conservation effects.
Using an active boundary to describe what happens at the surface of a fluid element means I can introduce vorticity into the surface layer to determine the lubricity or viscosity of the fluid element relative to its surroundings.
The internal motive distribution of a fluid element may be discountable if the surface behaviour, that is vorticity, viscosity nd undulatory behaviour defines its motive impact on its surroundings. The elasticity of the surface boundary , the so called surface tension will also be a feature, especially in defining when a fluid element is separated into parts.
At this moment it seems reasonable to define that as when the dispersion of the fluid element leads to a morphology in which the surface boundary thickness touches , that is when at least one of the dimensions is less than 2 times the surface boundary thickness, given that this thickness will thin as the fluid element is stretched, but will not be assumed to tend to zero..
The behaviour of cracks seems relevant at this point, to determine when a surface tension will break off an oscillating " bubble of motive". Such a bubble will primarily use it's motive to stabilise its form, providing less uni directional acceleration. Brownian like motion is to be expected as bubble motives break off and stabilise.
While this video may seem off topic, it represents the fulfilment of fluid dynamics. When I have apprehended it I should be able to provide the theoretical model for this set of experimental results, I hope.
You can see that we were pretty close in Oliver Heavisides time, Tesla's experiments lighting the way. Today I believe Eric Dollard and Ivor Catt are the vanguard of a resurrection of the advancement of the theory of Electromagnetism into a revision of the theory of SpaceMatter,heat and so called gravity.
I have quaintly called this Shunya field theory, more for my own purposes of distinction, and allowing a mental lab where this redacted and revised and progressive view can be formed than any assertion of the undoubted esoteric and spiritual connection with the sages of the past.
In addition I was clarifying in my mind how Quasz works, using the Quaternions Z and C to represent 3d rotational space.
The two modes,Julia and Mandelbrot, make use of the underlying for loops to iterate through the quaternion block.
For the Julia mode.C is a fixed 3d rotational space, while Z is an initialised 3d rotational space, which is initialised by the for loop variables. Once initialised the Z space is transformed by the iteration algorithm and coloured accordingly. Th C space provides a fixed additive translation to the transformation. So it is like a rotating "cloud" moving through C space as determined by the C space behaviour.
For Mandelbrot mode. The Z 3d rotational space is fixed, and the C 3d rotational space is initialised by the for loop variables. Once initialised the Z space is transformed by the iteration algorithm loop which typically holds C space constant with the initialised values. When the algorithm loop is complete then Z space returns to its fixed settings while C space is initialised at a new point. thus this is as if the C space is moving in a step sequence with the Z space.z space is now mutually relative to C space, but in a precise sequenced way.
This standard process can be considerably modified and complexities by defining the algorithm loop behaviours in a more complex way. To override the fixed C space in the Julia mode, it will be necessary to define C within the algorithm iteration. The only variables available to do this within Quasz are the coefficient parameters of the space which are initialised by the for loops, the control panel and the local variables during iteration. Thus it is necessary to clarify what variables are actually changing and how in any non standard modification of thr Quasz modes.
Additionally, the user can define initial values independently of the default app processes! In Quasz the for loop variables are not directly accessible. The local variable which initialise from the for loop variables are accessible, and the user defined variables are necessarily accessible. The algorithms therefore are defined by local variables which are fixed or varied in the 2 modes defined above..
Local variables are therefore fixed relative to for loop variables or fixed relative to algorithm iteration (local) variables or both. All variables have to be initialised and this should not be confused with the term "fixing" a variable. A variable when initialised may have the initial values fixed, or it may not. If not these values will be updated within the algorithm . For a fixed variable, time can be saved by initialising outside the iteration algorithm, but flexibility for modification is sacrificed, if it is needed. The programmer needs to think through whether he needs to use processing cycles to update a fixed variable!
Recently the Faraday disc motor has come to my attention.
I know that both Fraday and Maxwell were fascinated by Argos experiment that generated an electric potential or EMF by rotating a disc. I believe that this is explained by atmospheric triboelectric effects today. If not, it certainly should be considered as an explanation.
I am close, through the expositions of the Electric Universe guys to formulating electromagnetic phenomena in terms of a magnetic, ponderous core substance shrouded by a more energetic or grater motive capacitor substance we call electric. Both substances are fluids with a root mean internal speed of around the speed of light. When I use the term speed it is because the vector notion is not an adequate descriptor I have come to believe. Just as we have vectors I think versors and twistors need to be used descriptively also.
It is interesting how few know that Grassmann thoroughly exposited this notion in a Vorrede to his 1844 Ausdehnungslhre, in which he reports on his realisation of the Inner and other product processes developed on his earlier paper on the Ebb and flow of tides. Though Hamilton published Uaternions in 1843, it is clear fom vis own remarks in 1854 that he recognised th primacy of the more general notions in the Ausdehnungslehre. This is not to say that many others even acknowledged Hermnn's wok beyond Peano Hamilton, and some small few others.
Historically I would like to read Hermanns assessment of Uaternions from the point of view of his Formenlehre or method of Analysing and synthesising forms. Again I havebo point out that Hermnn was revising mathematical methods back to the techniques and understanding of Apollonius in particular, but Pappus in general, who were perhaps the Neo Neopythsgreans!. This school traces its genealogical roots through the Athenian form of Platonic Academy, of which it is now apparent there were at least 2 centres, the one in Athens, and thevonebin Alexandria under Euclids direction.
The Aristotelian form of Platonism promulgates through the Lycum, and apart from being intellectually directed by Aristotle, it's real difference or me is it's modification of Pythagorean scholasticism and teaching, rejecting some key Pythagorean teachings on Arithmos.
Thus we have a form of Pythagorean teachings and a modified form of Pythagorean teachings hich both are proud to trace their genealogy back to Plato!, who was a dedicated Pythagorean all his life.
My reseàrch reveals the overwhelming " leg brain" bias , the love of symbols as script over the love of symbols as line. The difference is reflected in how some translate the Lineal algebra of Grassmann as a linear algebra. The terms are distinct. In Grassmnn's lineal algebra, the line segments are the symbols. This is in fact the case in Early Cartesian Geomeytrie. The symbols are letters that stand for lines as extensive magnitudes. However Grassmann does not allow this distinction to wander. Rather he thinks and conceives entirely in symbolic lines!.
It is noticeable how some believe it is an advantage to be able to formulate in suggestive symbols. I might point to Morgan and Bertrand Russell as extreme exponents of this view. But Grassmann was not proposing a symbolic Algrbra without referent , he was proposing a procedural algebra in which the line segment and the point were the symbols! Thus I draw a line. It is not just a line, it is a symbol of a quantity and a direction, and an orientation. Thus I can rewrite Grassmann lineal algebra entirely by using lines as symbols thus / + + |
Which is a combination of 3 lines. I can label these combinations by a label say A, to continue the discussion, and I cn distinguish A as a trilineal.
Similarly I can write . + . + . as B and call it a tri puntal.
Clearly B only makes sense notation ally if the 3 points ar not idntical. So now I have a combination notation tht represents any 3 points in space. In fact we know that this is the definition of kind of space we call a plane if we specify that every tri puntal T has to be a scalar multiple of B. for a fixed tri puntal B we fix a plane in which this condition is true. Thus B can be considered as the bais or very tri puntal in that plane.
In addition, we have to tackle the notion of a scalar multiple of a tripuntal. In fact we find that this only makes sense in a lineal space where the points are elements of a line segment that has at least direction or orientation. This is why Grassmann andvEuclid start t the synthetic level of the line as a ymbol. With a line bing generated dynamically by points! Points in motion is where the three greats ; Euclid, Newton and Grassmann start from. Thus the Tripuntal B is not actually a generator of a plane, the trilineal A providing the lines connectbthev3 points of the tripuntal B forms the basis of the plane.
Grassmann however does find a use for the Tripuntal scalar multiplication in terms of the Schwerpunkt, but apparat from its definitional completeness in his analytical and synthetic method I currently know of no other uses as yet for the point Algebra.
It will be un to explore!
I have written on how Grassmann realised the limit of his lineal symbology , and further extended his method beyond geometrical, intuitive descriptions to physical and phorometric and kinematic ones. That is he recognised, as did Newyon, that the geometry he was presented with actually derives from Mechanics nd the study ofbMotion. This it is that Grasmmanns Ausdhnungslehre, is a direct analogy of Newton's Pincipia, whether deliberately or unconsciously. However, Hermann never got to complete his grand design, due o the exigencies ofbthebtime principally, but also the Social manipulation of Gauss, who while not deliberately burying Hermannsvork, certainly promotedbhisbown ideas over it though Riemann!