The Quality of Dynamic Magnitude 2
Monday, May 14, 2012 10:51:17 PM
Everything flows, nothing stands still.
Vorticularity we tend to associate with the helical cone shape, but this is the view inside the bubble. The whole system is more akin to a Bubble system of moving space which naturally pairs opposites
Newton in his method of Fluxions starts with the Euclidean rectangle in arbitrary motion. From this he derives the fundamental formula for differentiation of polynomial terms. But i get ahead of myself.
Some preparatory notions, to dispose one to the notion that there is some "order" to dynamic motion rather than as is usually assumed some "randomness". For if we start with a stationary object we may observe the object rotating at varying speed on the "spot" . Then we can consider rotating motion which rotates around the spot in wider and wider spirals at various speeds and at various rates of change of the radius of the spiral. The motion of the object is then, relative to the observer, seen to move in a path that is curved. But this curve has greater or lesser curvature depending on how big the radius of the spiral is. Thus the motion of the object is that of a right line for the circumstances. However it is a curved line (not defined) rather than a straight line(not defined), but clearly, depending on the circumstance it may be defined as one or the other.
Motion in a right line does not tie one down to a straight line, but to a line that meets the defined circumstances, and Euclid clearly defines a good line as being one commensurate, that is coplanar with a plane, "epiphaneia" .For his analytical method this was a crucial definition.
Thus the motion of a spinning object is defined according to the circumstances of its motion relative to instantaneous shapes in space.. The shapes themselves are various and arbitrary, but we start with the shapes Euclid explored. These shapes are "instantaneous" shapes in the dynamic situation, and only ppear static.
Instantanaeity is defined by the Euclidean form that fits a motion that is being tracked/tymed. The form is instantaneous in the mind of the observer, that is it is a sequent, a motion sequent , a frame in the track of the motion as a whole. How do we get a freeze frame, instantaneous motion sequent?
The freeze frame comes from a persistence in the visual signal effect, a persistence the auditory signal effect, a persistence in every sensor signal effect. This persistence, this delay, is utilised in the processing of my experience to give a smooth continuous experience, but also the change in processing orientation frames this persistence utilisation by rapidly generating a new persistence situation in the sensory meshses. The changes in these situations are recorded like frames in a movie. These frames are arbitrary and epochal.
The frames are analogised by the film paradigm, and the regularity of that medium is misleading with regard to the actual functioning of the brain. However the general principles are the same, so the "frame" now acts as a sample of the ongoing experience, and this is what i mean by an instance of an ongoing experience.
Instantanaeity is based on this notion of an instance or a sample. In this circumstance an instantaneous experience of the motion is a frame that possibly incorporates a blink of the eye. If the frame ended by one blink is compared with the frame ended by a successive blink, a shape can be fitted in between the 2 positions. That shape could be anything, but Euclid provides us with a set of relationships that enable comparisons and connected dualities.
The instantaneous form for each blink changes, and so a connection is made between instances through the Euclidean relationships.(The frame itself is considerably flexible, and not necessarily "still", but the memory system is able to pick a still moment rather like a pause button, even within a frame. However, the greater the frequency of sampling, the less variability in the frame, and the less information the memory system has to select from. Thus eventually the memory system reaches a limit of functionality where it is not able to process the old frame in the time it takes to be presented with a new frame, and in addition if the persistence in the sensor has not cleared to allow a refresh and a new sensitivity to the ongoing experience then the sensor is operationally ineffective and cannot forward a new or a distinct signal free from combinations with the old .)
The instantaneous frames we use are defined or appropriate to the motion track, and loosely typify a motion sequent.Thus the more regular the instantaneous frames the more regular the motion sequents. The frames that i may naturally utilise by my own subjective processing may be irregular and difficult to use in terms of utilising the Euclidean relationships, thus some Tool that assists in regularising the frames would possibly be of assistance, and in fact the design of such a tool may be the method required to utilise the euclidean relations,That is the action of designing the tool may be all that is neceessary to analyse the motion sufficiently to derive relevant relationships, thus making the manufacture of the tool unnecessary.
However it may be now clear that in the 3d space, the extension of Euclidean relations goes hand in hand with human faculty, functionality and ingenuity.
The right path of a moving rotating object thus always has to be defined in relation to the circumstance.
Returning to the rotating body that is in motion around a spot on some version of a spiral : this description is general but not arbitrary without specifying the arbitrary nature of the radial between the object and the "centre" of rotaion. Now the arbitrariness extends also to the centre of rotation or curvature, and the path of the motion of the rotating body is thus an arbitrary rotation about arbitrary centres of rotation of arbitrary radial magnitude. The magnitudes experienced are multiple and dependent on the frame and the shape chosen for reference and application of Euclidean relations.
The general motion is therefore complex, but the applied relative frames determine the apprehended magnitudes.
It becomes necessary therefore to agree reference frames, shapes and relative positioning with others to communicate perceived magnitudes of any motion.
The general motion is not spiral but combined spirals/helixes, and on a small enough scale would mimic Brownian Motion. However Brownian motion when enlarged still looks like brownian motion until one arrives at the molecular level. At this level the motion of a particle of commensurate size would be that of combined spirals/helixes. However the usual fleck used to define Brownian motion is many molecular sizes bigger, and its behaviour is more inertial and momentum driven than a single molecule would be. Thus the motion will be inertially driven, latent in responsiveness and thus tardier in the paths it takes. Brownian motion will show this behaviour when the ratio between the fleck and the surrounding molecules in motion is large to small, unequal.
Thus we may see that underlying the supposedly random motion scenario is in fact a combination of spiral/helical motions, the effect of proportions and ratios of inertia modify the motion behaviour.
Again, the notion of the right motion has to be defined by the circumstances.
The general motion therefore can satisfactorily be described by rotational motion with arbitrary centres of rotation and arbitrary radial magnitudes.
The question arises , however, whether Euclid's analysis,( the Stoikeioon represent Euclidean analysis of Space or "Raum") is the best we can come up with, or rather is it well suited to the purposs to which we want to put it?
In Gauss's time the harping critics reached a culmination and threw Euclid out on a strawman argument! That is they created a false image of the Stoikeioon , undermined it an supplanted it with their own supposedly superior or more general notions. However, the Stoikeioon is not the geometry that they thought to overturn. That geometry is as much a fiction of Euclid 's Stoikeioon as was the false representation that was created. Even today, if you mention Euclid a mathematician will characterise his ANALYTICAL method as being flat geometry.
Euclid's analytical method is alive and kicking, it is just purported to be dead! Analysis, Mechanics, Combinatoric as well as abstract Geometries and algebras all spring from and owe there nature to The Stoikeioon, and its developments by Greek and indian scientists, although i accept the argument of the uniqueness of vedic mathematics, and its indigenous origins, yet it is still influenced by Hellenism and the greek occupation of Northern india. Through Alexander's expansionist vision and concession of local hegemony, the greek empire enjoyed access to knowledges of all its conquered and affiliated peoples, and the sharing of ideas and methods was encouraged as much in this time as in the days of Arab Empire. However the Arab Empire's insistence on one state language into which all knowledge and wisdom should be translated is the crucial difference. The Arab Empire became a publishing empire which made known all the secrets of the nations!
So we find that In Persia in particular the Arab empire sponsored mathematicians who calculated the stars positions to calculate the directions toward Mecca. In doing this they used and developed greek mathematical ideas many prior to Euclid's collation of them in the Stoikeioon. Thus Euclid already had access to methods of measuring and caldulating dynamic magnitudes. Also, these methods applied to curved topos, or locations in space, surfaces or regions. It is from these analytical methods and solutions to real, spatial and dynamic problems that Euclid Drew his Stoikeioon!
Stoikeioon means orders teaching material suitable for learning from first principles! The word translated Elements means,apart from its theistic allusions, the fundamental notions of understanding, the ground from which we start and build. Thus to call this just geometry is to nisname and misdirect. This is a fundamental analytical method to be applied to the real dynamic magnitudes in ones experience. So of course it applies to dynamic circumstances!
Leaving aside Gauss, Bolyai and Lobachevski, and all the so called debate about postulate 5, and focusing on Grassmann, i find that his analysis and the Analytical method he derives and modifies draws heavily on this realisation that Euclidean Stoikeioon is not about geometry but about analysing dynamism in space. Along with this growing realisation was the awareness that new discoveries impacted on this understanding of Euclid and its applicability. For Grassmann it was not that postulate could be varied and give a different kind of geometry, which as i say Euclid and those before him Already knew and applied, but that the observer and measurer had to be figurd into the magnitudes.
Not only do magnitudes vary, they also "apparently" vary. Parallax for example was a well known issue with magnitude measurement and especially dynamic magnitudes. So to parallax Phorias needed to be added, perspectives were a nother classical adjustment to apprehension of magnitude. These all meant that measurement could not be known to be accurate without ruling each of these observer relative difficulties out.
However it was Grassmann's genius to realise that far from being an annoying problem, they actually were key to understanding how we mentally process magnitudinal data, and radically what the "true " nature of reality might be! Thus today, whenever one watches 3D movies one is experiencing what Grassmann realised might be the nature of our experience of reality: magnitudes disposed in space in such a way as to manifest to us a 3d reality!
We still use the early research into binocular vision and the results of phorometry in our modern entertainment systems, but profoundly we have moved Grasssmann's "idea" into a technology that recreates on command the manifestations he thought existed in space by God's command and disposition! We now command with disc , disc reader and light projections and screens what Grassmann believed were inherent codifications of reality in space, and in this way we demonstrate not only the principles but also the application of personal, observer relativity and personal experiential continuum experiences. Das Sein which arises out of the Denkprocess, or Denkakt of an individual is well attested to by the CYBERSPACE experience.
It is clearly not a simple process to delineate all that the Quality of Dynamic Magnitudes entail, for as Herakleitos observed "all flows,not one thing remains!"