Sunday, 7 August 2011

Phase space a.k.a. the fractal 'bubbles' out of network's froth conceptualised to .. analysis .. form an imaginary mathematical construct

Phase space a.k.a. the fractal 'bubbles' out of network's froth conceptualised to .. analysis .. from an imaginary mathematical construct to network's unleashed activity envisaged ..where all acts .. trajectories

--- separates the boundaries .. the empty space .. the physical impossibility

'Introducing chaos' by Ziauddin Sardar and Iwona Abrams, page 48.

".. suppose instead of fixed object (a building), we had a moving object - say, a pendulum. We can represent the horizontal and vertical motion of the pendulum in a two-dimensional graph."

the horizontal and vertical motion .. tracing its movement .. writing its history .. its horizontal/vertical displacement .. moving object .. hence, dynamic .. recording the object's, under study .. dynamics

the object .. the focus of study .. towards which one's attention is drawn .. whatever structure that is .. abstract or sense-defined .. the horizontal/vertical attributes, arbitrary ..constructed .. mental constructs .. anchors .. out of which .. its displacement from the horizontal/vertical .. is envisaged .. provide discernible information..

"..phase space represents the state of an object in a multi-dimensional plane. The motion of the simple pendulum could be shown on a graph where the x-axis is the angle of displacement from the vertical and the y-axis is the angular velocity."

..a succession of states .. states out of the .. arrangement of the elements, the under study system is comprised of .. elements constantly arranged as 'wholes' .. as 'more than the sum of its parts' wholes .. the presented states .. of an ever-evolving, dynamic object .. its states represented .. constantly morphing as the influence exerted ..out of all its properties ..never cease to be ..

.. angle .. skewed towards .. the system's overriding property(-ies).. system's properties acting as the dimensions of the afore-mentioned system and the moving object .. what is conceptualised out of these properties ..

combine .. combined effect .. object constantly coherent .. as it is presented as a 'whole' .. none other .. to whatever shape .. that 'whole' might be .. no matter how long .. that 'whole' element arrangement .. lasts ..

(formulas constantly present solutions .. no matter how fast the replacement of the factors in a formula .. take place )

.. angular velocity .. the change over time .. out of the conditions prevailing .. determining .. how durable the shape of an object is ..

"On this phase space diagram, the simple pendulum shows as a circle."

.. the clarity afforded ..

"Phase space turns dull statistical data into a telling picture, abstracting all the essential information from the moving parts and providing us with an easy to grasp overview of the system's behaviour over time."

.. dull statistical data .. trivial information .. information that do not lead to system comprehension .. system poorly comprehended .. undermine knowledge .. provide spurious explanations .. objects presented are not understood in their entirety .. objects incoherent .. information dis-information .. mis-information ..

.. abstracting essential information .. information depicting engaged properties .. exerted influence .. 'weighted' .. not only their presence .. but their degree of involvement ..

.. overview of the system's behaviour over time .. the particular sequence of states .. achieved .. a history of successive states .. the succession of states ..

"In phase space, the complete state of knowledge about a dynamical system at a single instant collapses to a point. That point then is the dynamical system at that instant. At the next instant, the system will have changed, and so the point moves."

a network itself .. residing upon networks

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