Saturday, September 10, 2011

F.E.D. Dialectical Systems Theory

A Marxian, Immanent Critique of Nonlinear Dynamical Systems Theory Yields a "Dialectical Systems Theory" as Its Positive Fruition



Dear Readers,

There is a veritable <<grundrisse>> for a Marxian, immanent critique of [nonlinear] dynamical systems theory, that has, as its positive fruition, a Marxian, Dialectical Systems Theory, set forth in the following text, from Part I.b. of the published portion of the book Dialectical IdeographyA Contribution to the Immanent Critique of Arithmetic, pages I-63 through I-73 --


http://www.dialectics.org/dialectics/Dialectic_Ideography_files/5_Dialectics-Part1b-WhyDI_OCR.pdf


-- which includes the following salient sub-sections --


Nonlinear Dynamical Systems Theory and Dialectics.

State-Space Trajectories, Control-Space Paths, and Bifurcations.

State-Space, Control-Space [Parameter-Space], and State/Control-Metaspace.

Self-Bifurcation.

The Ontological Conversion ‘Meta-Dynamic’.

Self-Bifurcating Meta-Systems and the Nonlinearity Barrier.

The Fetishism of “The “Laws” of Nature”.

The Fetishism of Abstract Time.

The Fetishism of Abstract Quantity.

Summary:  Model of Conjectured Conceptual Meta-Evolution to Meta-Dynamics Using Rhetorical Meta-Dynamics.


-- all in the section entitled --


Dialectical Meta-Systems as via-Conversion-Singularity Self-Bifurcating Meta-Systems.



The positive fruition of that dialectical, immanent critique is further extended, in a primer text, using the Nq/MQN, or Nq/MU (----] q/7, arithmetic [the 7th system of dialectical arithmetic in the F.E.D. meta-systematic-dialectical presentation-model of the systems of dialectical arithmetic, a presentation-model which is expressed in the language of Nq/NN, i.e., Nq/Q, or NQ (----] q/2, the 2nd system of dialectical arithmetic in that presentation / meta-system of dialectical arithmetics].

Interpreting the Nq/MQN arithmetic, i.e., the Nq/MU arithmetic -- also known as the “Mu” arithmetic, for short -- as a calculus for "dimensional analysis -- i.e., for algorithmic computations with quantifiable units-of-measurequalifiers– that text gives details, and a worked example, for the Newtonian equation for a hypothetical/generic collisional two-planet mutually-gravitating system.

It shows how the Mu ‘metrical-qualifier(s’)’ re-qualification of the standard, purely-quantitative version of that Newtonian equation averts the usual, "infinite” model errors ["infinity residuals"], or meaninglessness, of the equation from the moment of collision forward -- a spurious infiniteness, or a spurious meaninglessness, that is due to the “singularity” -- to the zero-division -- that arises at that moment -- to a meaningful and physically-correct value for that moment, “semantifying” the supposedly “intractable” singularity in natural way.

For two renditions of "singularity semantification via metrical-qualifier re-qualification of singularity-entailing nonlinear differential equations”, see pages A-5 through A-21 of that text via the following link –

http://www.dialectics.org/dialectics/Primer_files/3_F.E.D.%20Intro.%20Letter,%20Supplement%20A-1_OCR.pdf

-- and also see the pictorial [as well as formulaic] rendering of a worked example, using one of the more advanced systems of the F.E.D. dialectical arithmetics, the Rq/BAMQN, or Rq/BAMU (----] q/31 system [wherein R denotes the set or space of the "Real" Numbers] -- also known as the "Beta-Mu" system, for short -- applied to model a hypothetical/generic planet-less triple star system, modeled as a [meta-]dynamical super^1-system, with its own super^1-system-level state-variables and control-parameters, but also “containing” / "subsuming" its three stars as its primary constituents, each one of these stars being co-modeled as a relatively-separate [meta-]dynamical super^0-system in its on right, i.e., each as a simple [meta-]dynamical system, each with its own, separate state-variables and control-parameters.


That partially-pictorial presentation is accessible via the following link --

http://www.dialectics.org/dialectics/Applications_files/F.E.D.,Dialectical%20Pictography,Part%20III.,Meta-Systematic%20Dialectics,05MAR2008_OCR.pdf

-- pages 27 through 34.



A 2-page summary, integrating [dialectically synthesizing] the concept of meta-dynamical meta-system – or, more specifically, of that of Dialectical ‘Meta-Systems’ as via-Conversion-Singularity Self-Bifurcating ‘Meta-Systems’ -- with that of "dynamical super^w-systems, with w in W = {0, 1, 2, 3, 4,…}, into a new concept of meta-super^w-systems, is available via –

http://www.dialectics.org/dialectics/Briefs_files/_Brief1-29JUL2008_OCR.pdf

-- pages 34 through 35, Scholium 3.7.




Regards,

Miguel

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