**A**

__,__*Marxian**Immanent Critique*of*Nonlinear Dynamical Systems Theory*Yields a*"*

__Dialectical__Systems Theory*"*

**as Its Positive Fruition**

Dear Readers,

There is a veritable <<

**>> for a**

*grundrisse***,**

*Marxian***of [**

*immanent critique***]**

__nonlinear__**, that has, as its positive fruition, a**

*dynamical systems theory*__,__

**Marxian****, set forth in the following text, from**

__Dialectical__Systems Theory**Part**

**I**.

**b**. of the published portion of the book

**:**

__Dialectical Ideography__**, pages**

*A Contribution to the Immanent Critique of Arithmetic***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

*is further extended, in a primer text, using the*

**,**__dialectical__**immanent critique****N**

**, or**

__q__/MQN**N**

**, arithmetic [the**

__q__/MU (----]__q__/7**7**th system of

*in the*

__dialectical__arithmetic**F**.

**.**

__E__**.**

__D__*presentation-model of the system*

**meta**-**systematic**-**dialectical**__of__

**s***, a presentation-model which is expressed in the language of*

__dialectical__arithmetic**N**

**, i.e.,**

__q__/NN**N**

**, or**

__q__/Q**N**

**, the**

__Q__(----]__q__/2**2**nd system of

*in that presentation / meta-system of*

__dialectical__arithmetic*].*

__dialectical__arithmeticsInterpreting the

**N**

**arithmetic, i.e., the**

__q__/MQN**N**arithmetic -- also known as the “

__q__/MU**Mu**” arithmetic, for short -- as a calculus for

*"*-- i.e., for algorithmic computations with

**dimensional analysis**”

**-**__quant__ifiable units**of**-**measure**“**qual***– that text gives details, and a worked example, for the Newtonian equation for a hypothetical/generic collisional two-planet mutually-gravitating system.*

**ifiers**”It shows how the

**Mu**‘metrical-qualifier(s’)’

*“*of the

**re**-**”**__qual__ification*standard*,

*purely-quantitative*version of that Newtonian equation averts the usual,

*"*[

**infinite**” model errors*"*], or

**infinity****residuals**"*“*, 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.

**meaninglessness**”For two renditions of

*"*, see pages

**singularity semantification**via metrical-qualifier**re**-**of singularity-entailing**__qual__ification**nonlinear**differential equations”**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__arithmetic*, the*

**s****R**

**, or**

__q__/BAMQN**R**system [wherein

__q__/BAMU (----]__q__/31**R**denotes the set or space of the "

**R**eal" Numbers] -- also known as the "

**Beta**-

**Mu**" system, for short -- applied to model a hypothetical/generic

*planet**-*

**, modeled as a [**

*less triple star system**]*

**meta**-**-**

*dynamical super*^1*, with its own*

**system****-**

*super*^1*and*

**system**-**level**state-variables*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**-*super*

**dynamical****^0-**

*system*in its on right, i.e., each as a

__[__

*simple**]*

**meta**-*, each with its own, separate*

**dynamical system***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 [

*] the concept of*

__dialectically__synthesizing*“*– or, more specifically, of that of

__-__**meta****dynamical**-__meta__**system**”*-- with that of*

**‘Meta-Systems’ as via-Conversion-Singularity Self-Bifurcating ‘Meta-Systems’**__Dialectical__*"*

**dynamical****super****^w**

*-*, with

**systems**”**w**in

**W**

**, into a new concept of**

__=__{0, 1, 2, 3, 4,…}*“*

__-__**meta****super****^w**

*-*, is available via –

__”__**systems**http://www.dialectics.org/dialectics/Briefs_files/_Brief1-29JUL2008_OCR.pdf

-- pages

**34**through

**35**,

__Scholium__**.**

__3.7__Regards,

Miguel

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