The Strain Ellipsoid and the theorem of Pappus, It's links to Maxwells orthogonal Vortices and the theory of antiontology
In fluid mechanics there is a basic question. What generates viscosity?
Viscosity and lubricious are fundamental characteristics of natter. Along with density. In the Newtonian reference frame density is a comparison of volumes under a constant pressure split by some strongly viscous body to create opposing areas of vorticity.
The development of mechanics with highl viscous materials has obscured some of these basic fundamentals. The approach using a strain Ellipsoid in contra stream flows helps to restore these insight, rotation or vorticity in opposing translational flow is a fundamental consequence of these pressures on viscous materials, and so also is strain. Rotation is therefore a consequence of viscosity in these pressure systems, pressure systems produce motion of all types, but the specific type is a function of pressure pattern and viscosity .
There is an argument, however that viscosity is anti rotational and anti translational and anti strain motion! That is viscosity is inertial. That is what I want to explore
Hooke, it must be acknowledged is one of those Newton gives credit to for the background, scientific discourse and discussion and philosophy of the natural order. The history of geometry and mechanics is intertwined because Descartes chose to call the mechanical knowledge of the Greeks and Islamic scholars " La Geometrie". These simplistic mechanical techniques, for in the main demonstrating validity of measurement, we're thought to be too mundane for academic thought, and yet again and again, this is where academic innovation has its source, it's demise and is renewal!
I find, in the labours of science taking place I Newton's troubled times many mean dreamed of greatness, some even snatched at it, but greatness was conferred upon the great by a consensus of committees of men. Hooke by his hard work never impressed enough men to gain this accolade. However, a later age such as ours might rightly review the extensivenesses of his contribution.ngreatness ultimately is no man or committee's to give. It is a legendary thing perhaps rightly ascribed as the gift of some mythological being, but that should not obscure the fundamental importance of the works of the also rans!
Gravitation While many of his contemporaries believed in the aether as a medium for transmitting attraction or repulsion between separated celestial bodies, Hooke argued for an attracting principle of gravitation in Micrographia of 1665. Hooke's 1666 Royal society lecture "On gravity" added two further principles – that all bodies move in straight lines till deflected by some force and that the attractive force is stronger for closer bodies. Dugald Stewart, in his Elements of the Philosophy of the Human Mind, quoted Hooke's own words on his system of the world. "I will explain," says Hooke, in a communication to the Royal Society in 1666, "a system of the world very different from any yet received. It is founded on the following positions. 1. That all the heavenly bodies have not only a gravitation of their parts to their own proper centre, but that they also mutually attract each other within their spheres of action. 2. That all bodies having a simple motion, will continue to move in a straight line, unless continually deflected from it by some extraneous force, causing them to describe a circle, an ellipse, or some other curve. 3. That this attraction is so much the greater as the bodies are nearer. As to the proportion in which those forces diminish by an increase of distance, I own I have not discovered it…." Hooke's 1670 Gresham lecture explained that gravitation applied to "all celestial bodies" and added the principles that the gravitating power decreases with distance and that in the absence of any such power bodies move in straight lines. Hooke published his ideas about the "System of the World" again in somewhat developed form in 1674, as an addition to "An Attempt to Prove the Motion of the Earth from Observations". Hooke clearly postulated mutual attractions between the Sun and planets, in a way that increased with nearness to the attracting body. Hooke's statements up to 1674 made no mention, however, that an inverse square law applies or might apply to these attractions. Hooke's gravitation was also not yet universal, though it approached universality more closely than previous hypotheses. Hooke also did not provide accompanying evidence or mathematical demonstration. On these two aspects, Hooke stated in 1674: "Now what these several degrees [of gravitational attraction] are I have not yet experimentally verified" (indicating that he did not yet know what law the gravitation might follow); and as to his whole proposal: "This I only hint at present", "having my self many other things in hand which I would first compleat, and therefore cannot so well attend it" (i.e. "prosecuting this Inquiry"). In November 1679, Hooke initiated a remarkable exchange of letters with Newton (of which the full text is now published). Hooke's ostensible purpose was to tell Newton that Hooke had been appointed to manage the Royal Society's correspondence. Hooke therefore wanted to hear from members about their researches, or their views about the researches of others; and as if to whet Newton's interest, he asked what Newton thought about various matters, giving a whole list, mentioning "compounding the celestial motions of the planetts of a direct motion by the tangent and an attractive motion towards the central body", and "my hypothesis of the lawes or causes of springinesse", and then a new hypothesis from Paris about planetary motions (which Hooke described at length), and then efforts to carry out or improve national surveys, the difference of latitude between London and Cambridge, and other items. Newton's reply offered "a fansy of my own" about a terrestrial experiment (not a proposal about celestial motions) which might detect the Earth's motion, by the use of a body first suspended in air and then dropped to let it fall. The main point was to indicate how Newton thought the falling body could experimentally reveal the Earth's motion by its direction of deviation from the vertical, but he went on hypothetically to consider how its motion could continue if the solid Earth had not been in the way (on a spiral path to the centre). Hooke disagreed with Newton's idea of how the body would continue to move. A short further correspondence developed, and towards the end of it Hooke, writing on 6 January 1679|80 to Newton, communicated his "supposition … that the Attraction always is in a duplicate proportion to the Distance from the Center Reciprocall, and Consequently that the Velocity will be in a subduplicate proportion to the Attraction and Consequently as Kepler Supposes Reciprocall to the Distance." (Hooke's inference about the velocity was actually incorrect) In 1686, when the first book of Newton's 'Principia' was presented to the Royal Society, Hooke claimed that Newton had had from him the "notion" of "the rule of the decrease of Gravity, being reciprocally as the squares of the distances from the Center". At the same time (according to Edmond Halley's contemporary report) Hooke agreed that "the Demonstration of the Curves generated therby" was wholly Newton's.
The singular importance of these revelations is to demonstrate that Hooke had a claim to have contributed to Newton's theoris, which Newton obliquely acknowledges, but trumps the claim o the specific inverse square law formulation.. Hooke relate to Newton Kepler's law of motions which invoke reciprocal squares nd velocities, but interestingly sub duplicate relationships. Sub duplicates are inverse square laws by another name, for just as duplicate proportions are called square proportions to day so sub duplicate are inverse square.
Newton's claim to reliability in his formulation of the square law rests on an important subtlety. Newton distinguished celerity into velocit and acceleration. The cause of celerity, Newton proposed was motive.. Today we may not understand how confusing the use of the term velocity was! Velocity covered also what we call acceleration. While Galileo distinguished acceleration, it took Newton to define a measure that made use of it. This measure he named vis!
Up until Newton's Principia vis was defined by Hookes law
Let us look at the difference for it bears on fluid MecanicsIn.
Hooke discovered that a measure of force could be defined using springs. This measure was simple: measure a length! In point of fact it was a measure of a change in length either "positive" or " negative". This change in length was a decreasing velocity to an equilibrium position. What Newton observed was that it was a fluid motion to which he could apply his method of fluents. Accordingly it was clear to Newton that the vis on Hookes definition actually was proportional to a changing velocity hat is coming to an equilibrium position! Thus Hookes measure he modified by a more complex process of measurement. One had to make several measurements to determine the deceleration.
Newton performed several experiments to refine his insight due to fluents, but essentially he was refining some well established mechanical principles which happen(!) to be those enunciated by Hooke.
Because Newton had belief in his insight, he fundamentally pursued gravity with this notion of the measure vis. The Kepler notion of an ellipse therefore again produces an inverse square law, as Kepler pointed out, but Newton no longer used velocity in an unspecified way, he recognised again that a changing velocity would be accessible to his acceleration definition. He therefore reworked the common calculations from that point of view. This was more thn jut putting a where everybody else put v or even l, this was introducing a new procedure of measurement, a new level of complexity.
Physics kinematics takes this well in its stride, but what everyone ignores is the fundamental fluid dynamic basis of this approach. Hookes spring or elastic law is a fluid dynamic law, and we find it introduced as the first kind of fluid " force" equation in fluid mechanics.
There has bern a move to drop the name fluid in favour of continuum. This is due to the fact that fluid dynamics is ostensibly a mathematical treatment of Hookes law in various plastic and elastic materials. Elasticity and plasticity, are all distinguished by different constants or moduli. Essentially these constants distinguish the notion of viscosity..
Newton started to investigate fluid mechanics using the notion of lubricity. Contrast tht with elasticity and appreciate the real difference between fluid mechanics and continuum mechanics. In fluid mechanics we would properly discount viscosity. When that is done it is called a Newtonian fluid mechanic. Yet we know that velocity gradients exist , and so acceleration exists. Newton felt this acceleration would be spiral. We can see that others were not of the same opinion, and even today people believe we would fall straight down to the earths centre!
By this account and method of analysis I see that Newton takes away any elasticity or spring as a concept of a fluid constant and replaces it with a kind of spiral watch spring!, at least in the case of the planet.
Newton already thought innovatively about Hookes law in elastic and in elastic collision scenarios, and included its oscillatory or undulatory reactions in his third and fourth laws of motion. This watch spring analogy for the motion of planets was an initial avenue of thought he did not pursue until Cotes came up with votes Euler exponential identity. This potentially explains mathematically how a coiled watch spring could explain planetary motion.
The notion of action at a distance still mystified Newton, who believed in an immaterial aether, which by religious philosophy was of god and so depending on what school of thought, could not or one could in some highly odd way, interact with SpaceMatter.
The strain ellipse is a highly evocative model recalling the analysis of spring deformation, but in general it is a given tha fluid mechanics has borrowed more from rigid mechanics than Newton foresaw, perhaps.
The notion of lubricity was a genuine attempt to enter a dissimilar realm. Viscosity is a more gradualist relaxation of elastic principles. Plasticity, the way deformations are retained by a form also takes elasticity that one step further before discontinuity or break. However the terminology itself hides the notion of lubricity which starts at contiguity, discrete boundary contacts and how they become harder or easier to overcome. Newtonian fluid mechanics is therefore contiguous mechanics not continuum mechanics.
If you study Maxwells solution for electromagnetic force you see that surrounding the vortices are little round circles. These represent ball bearings which were meant to provide a mechanical interpretation of lubricity base on contiguity.. In practice, bearings work well as models of lubricity, but fail when they come into contiguous contact if driven by the same pressure system. The solution is down to scale! If a smaller ball bearing is slipped between the two. Then lubricity is enhance. However the dynamic centre of this smaller ball bearing has to remain relatively the same. If this is not fixed then the ball oscillates up and down between the larger balls, leading to a complete snake like oscillation in the bearing s. pragmatically this results in generation of acoustic vibrations and heat.
Thus we see that lubricity is associated with vibration, particularly ln the acoustic range, but really across all vibrational ranges, and also the generation of heat and heat pressure( temperature). Although not usually noted I assume there to be also radiation of " heat" from the system as well as convection.
Contiguous mechanics, that is fluid mechanics therefore naturally involves many disciplines which through subject wars have defended their boundaries. In particular, in this rudimentary way it involves electromagnetism.
We might also usefully note that the fractal nature of fluid mechanics indeed all mathematical treatments is a serious omission. However, practitioners of fluid mechanics more than any others have to pragmatically acknowledge the influence of scale and iteration and recursion.
The reason why I do not support the notion of a continuos mechanics is because it brings with it several non fractal prejudices. Like for example starting with a uniform distribution! Starting with a continuous media etc, non of which are logically necessary and all of which can be advanced under the notions of contiguity.
I must now turn my attention to the strain ellipsoid and to rotation, which for a while in fluid mechanics enjoyed the notions of vorticity. There is a lack of apprehension about curved motion, brought about as we have seen by a misreading of the notions of both Hooke and Newton.mfor both of them curved motion existed in its own right, and could be resolved into axial displacements if need be, but in point of fact curved motion itself formed a curvilinear axis.
Axles of course are usually straight , but they do not need to be so axles are the precursors of both axes and axioms both of which can be circular!
Before I move on though it is worth noting that hooks law when set as time differential gives velocity and acceleration , providing the parameters are dynamic, but in all 3 cases the differential of force gives force! Thus by this observation force is an extension, force is a velocity and force is an acceleration! We can clearly go on ad infinitum, again highlighting the highly fractal and recursive nature of Newton's formulation of the inertial system of reactive equilibria both static and dynamic.
The principle of anti ontology really says that for every ontology or ontological argument there is an anti ontology or anti ontological argument. Another way of saying this is Shunya is divisible Ito 2 fundamental complementary sets B and B' for any set B entirely contained in Shunya.
Anti ontology also deals with the predicate in propositional logics. Thus for every predicate there is a not predicate.,
This is self reflexive so that for be there is a not to be
The experiencing of me also has an anti ontological not experiencing of me.
When we seek to get behind the propositions to the referrents I find I have no choice.all possibilities must exist. I do not operate on a non existent basis. Thus I ontologically accept the existence of all things. Then my propositional faculties serve to filter this non deniable status abd allow me to use bits of it to symbolically refer to all or other bits. Now, the acceptance of this role for symbols give me the opportunity to select referrents, to misdirect and to conceal, to make explicit and to reveal. It further gives me the opportunity to analogies, and to model..
Now I can propose A and not A a predicate and a not predicate. And I can assign special roles to predicates like to be or in greek " ontos". Finally it allows me to obscure the whole basis of this discussion by adding adjectival presuppositions like " possible" . The possibilities are infinite!