**,**__Marxian__*of*

**Immanent Critique**

**Nonlinear Dynamical Systems Theory**Dear Readers,

Below is my "genericization" of a recent dialogue on

**Marxian****&**

**F**.

__.__

**E**__.__

**D**__vis-a-vis__

**Dialectics***in which I participated.*

**Nonlinear Dynamical Systems Theory**My theses are labelled "

**M.D.**" below, and the interlocutor's theses by "

**D**".

__--__

**Dialogue Excerpt****M.D.**: I strongly agree with the points regarding

*/*

**systems theory***/*

**complexity theory***that you stated below, namely --*

**cybernetics****D.**: The idea of an 'information ecosystem' is an example of idealism / dualism since it conveniently detaches the societal mental realm from the underlying, productive activities of society and its politics.

**M.D.**: Agreed, and I further note that such

*versus-*

**ideo**-*detachment is a typical symptom of capitalist ideology in general.*

**physio****D.**: Complexity theory is socially valuable and progressive in that it can enable frameworks and descriptions of natural and social systems that don't overlook those systems' intricate interconnections and vigorous dynamics.

**M.D.**: Agreed, that "complexity theory" is

*progressive [a view on the*

**partially***progressive,*

**partially**-*ideological character of "complexity theory", which, from some of your earlier theses, I understand that you also hold], and that, in particular, it has the potential to overcome that <<*

**partially**-*>> of*

**species***which wants to*

**reductionism***the reality of each given sub-system of a super*

**reduce****^w**-system to the reality of just one of the super-system levels -- e.g., to the "highest"/latest-to-emerge level -- that contains them, retaining only the description of that super-system level, or that want to

*, e.g., the reality of everything above the deepest sub-system level, including the "highest"/latest-to-emerge super-system level, to that of only the "deepest" sub-system level, retaining only the description of that deepest sub-system level as if complete and accurate to describe the whole reality, thus ignoring "complex multi-level interdependencies", to say the least!*

**reduce**An example would be an attempt to describe the total <<

*>>, at the stage in its self-development that includes the present moment of our locality, strictly in terms of pre-nuclear "particles", e.g., strictly in terms of quarks, electron, neutrinos, photons, etc., ignoring all description in terms of other/later-to-emerge levels of reality, e.g., the position that: "Everything is just quarks, floating in the void".*

**kosmos****D.**: (Conventional linear equations cannot hope to capture the complex multi-level interdependencies that are recognized and accounted for with a complexity-systems approach.)

**M.D.**: Agreed. Indeed,

*integro-differential equations tend to assert a kind of "equilibriumist*

**linear***, or, at best, a kind*

__-dynamics"__**anti***"*dynamics", limited to single, global basins of a single, monolithic fixed-point attractor, repellor, or "neutral" solution-geometry in the state-space, that are most generally vastly

**-**__pseudo____realistic as models of the dynamics of the natural systems, including of the human-social systems, that we actually observe and, to some extent, measure.__

**un**__[shared with__

**Claim****s****F**.

__.__

**E**__.]:__

**D****. The ease with which general, "closed-form", "analytical" solution of systems of**

1

1

*integro-differential equations have been obtained by modern mathematics, and the great difficulty encountered with attempts at "closed-form", "analytical" solution of systems of*

**linear***integro-differential equations*

**-**__non__**linear***, is a symptom of [*

**in general**__conscious] capitalist <<__

**un***>>, and resultant [again,*

**mentalite'**__conscious] capitalist__

**un***, embedded in modern mathematics, the result of which is to block the development of a mathematics which would be at home with, and successful in solving, general*

**ideology***integro-differential systems.*

**nonlinear****. The requirement that differentiation [and/or integration] of the differential equation solution-function**

2

2

__known, aptly modeling a given empirical phenomenon / phenomenology, produce a__

**un**

**non***-*linear,

*"*[higher in absolute value of degree] expression, to achieve fitness to the empirical data/measurements on that phenomenon/phenomenology, is a sign-post of the

**higher degree**"*"*of that empirical phenomenon/phenomenology.

__"__**dialecticality***in dynamical systems is, in general, an expression of their*

__Non__linearity*"*.

__-__**dialectical****ness**"*is this*

__So____bad____conscious enfetterment of the progress of mathematical science by [__

**un**__conscious] capitalist <<__

**un***>> and*

**mentailte'***, that the highest expressions of*

**ideology***so far attained -- typically taking the forms of*

**the**"**laws**"**of nature***--*

**systems of**__non__linear__partial__differential equations**HAVE NEVER**,

**TO THIS DAY**,

**BEEN SOLVED**, so that the vast riches of potential information, and of potential technologically applicable knowledge, that these

__solved equations__

**un***, and which could be made*

__implicitly__"contain"*"*by their general solution, has yet to be made accessible, and usable, for the progress of the social forces of

__explicit__"*"*expanded social reproduction of humankind,

**o-**__quant__**itatively"**__qual__**TO THIS VERY DAY**, except in a few particular cases, of mostly

*"*

**barely***-*

**nonlinear**" equations[-systems], which have nonetheless proven richly applicable in the advance of the human productive forces.

Among these still-

*solved*

**un***are the*

**-**__non__linear integro**differential equations-systems***,*

**Newtonian***for a system of*

**gravitational equations****3**or more mutually-gravitating bodies [the very founding instance of the mathematical "laws of nature"]; the

*for electrically neutral "rheid" -- gas and liquid -- "hydrodynamics", whose general solution might enable greater in-advance-time predictability of, and reveal the "Achilles heels" of, hurricanes, tornadoes, and even tsunamis, so that, with a*

**Navier**-**Stokes Equations**__proportionately [__

**dis**__linearly] small, affordable human input of energy, these storms could be stopped in their tracks [or, in capitalist hands, would reveal how to generate hurricanes, tornadoes, and tsunamis as__

**non***of class war/other contracted social reproduction];*

**weapons***, whose general solution might enable greater in-advance-time predictability of, and even reveal the "Achilles heels" of, earthquakes and volcanic irruptions [or, in capitalist hands, would reveal how to generate earthquakes as*

**the equations of rock visco**-**plasticity and brittle**-**fracture mechanics***of class war/other contracted social reproduction];*

**weapons***; the*

**the**-__non__**constant**-**throttle rocket equations***and the*

**Klimontovich Equation***, for electrically-charged "rheid" "hydrodynamics", e.g., for the plasma phase of matter-energy, whose general solution might immediately reveal successful designs for Boron-Helium, radioactivity-free, electron-releasing-only*

**Maxwell**-**Boltzmann**-**Vlasov Equation****fusion reactors**, making abundant energy affordable for all of humanity, and; the

**10**, simultaneous

__non__linear*[or the single*

**partial**-**differential equations***] of the*

**tensor equation***.*

**Einstein General**-**Relativity Equations for the Universal Gravity Field**All that is standardly available toward solution of these "laws of nature" equations, today, are "numerical simulations" of the

*solved equations, which generate only a single state-space/physical-space "track", for a single starting-state, in a potentially infinite domain of*

__un____solved other such "starting states", and their still-uncharted "special solutions", consuming vast amounts, even of massively-parallel super-computer__

**un**__, and memory__

*time*__, in this process of deriving limited, approximate special solutions, that are typically also insensitive to essential characteristics of the general solutions, such as singularities.__

*space*The "natural law" equations that

**are**__-- and, that, therefore, have long-since been__

**linear***-- are telling in themselves: like the*

**solved**

**linear***of "Quantum Mechanics", which can*

**Schroedinger Equation***"predict" spatio-temporal*

**only***, they are*

**probability distributions***"*-- something that the capitalist <<

**missing something**"*>>, with its*

**mentalite'***/*

**atomistic***bias,*

**reductionistic****misses!**

*chronically**, e.g., cubically-nonlinear versions, of the Schroedinger Equation, along with a vast expanse of other,*

__Non__linear versions*usually "*partial differential equations, describing

__-__**barely**__linear"__**non****1**-dimensional "nonlinear waves", many of which

*analytically, in "closed form", e.g., using a*

__have__been solved*"*known as the the

**transcendental function**"*"*, have revealed mathematical models of a phenomenon that had been observed, at the "meso-scale" of our ordinary experience, but that is now known to exist also at "micro-scales" accessible to our experience only as mediated via advanced scientific instrumentation: that of

**hyperbolic secant function**"*"*now called

__non__linear**waves**"*"*, or "particle"-like

**"**__solit__ary waves*"*-- typically "one-hump" waves of "infinite period", i.e., which consist of a single wave-"mound" of heightened amplitude, without even any second "mound", "until"

**"**__solit__ons**t**"

**=**"

**+oo**, a "time" which never arrives.

The air-masses of Earth's atmosphere -- "low-[surface-]pressure areas/air masses" ["cyclones"] and "high-[surface-]pressure areas/air masses" [inverted cyclones, or "anti-cyclones"] -- "toroidal vortices" all, may be physical correlates of

*not-so-barely-*,

__non__linear*-dimensional "solitons", or "*

**3***-*

**3****D**

*-- solitary, vortex/anti-vortex paired, or otherwise -- that a general solution function for the*

**"**__non__linear waves

**highly**-__non__linear*would model.*

**Navier**-**Stokes Equations**This opens the possibility -- not yet actualized, to my knowledge -- of a new,

__Non__linear Quantum*"*, which models quantized "particles" as [

**Mechanics**"*,*

**solitary***]*

__non__linear*in a universal, unitary field, and which replaces the*

**waves***"*

__causal"__

**a***functions of a*

**linear***[*

**random***distribution-spanning] variable of*

**probability**-*"Quantum Mechanics", with*

**Linear**__but__

**causal***of a*

__non__linear functions__variable, whose physical-time-variation, and physical-space-variation, exhibits an "entangle-able", "chaotic" attractor, or "strange" attractor, subject to bifurcation "quantum leaps", from one such "attractor" to another -- with an asymptotically__

**determinate***periodic -- pattern with respect to each such attractor, which asymptotically mimic the patterns of the probability distributions of*

**a***quantum mechanics after long-duration "inter*

**linear***-*interaction-entanglement.

__linear-__**non****wavicle**"__: A key task of Marxians is to continue/extend Marx's__

**Claim**__,__

**dialectical***of the capitalist ideological science of "political economy" / "economics", and its positive scientific advances/fruitions, not only within itself, and not only into the spheres of the other capitalist-ideological social sciences, but also into the spheres of the capitalist-ideological natural sciences, and of capitalist-ideological mathematics itself, as well.*

**immanent critique**The

*exemplified, but not explicitly defined, in the writings of Marx and Engels, coupled with the capability to understand the causes of, and to see beyond,*

__dialectical__logic**<<**

*capitalist**>> and*

**mentalite'***, coupled with the ability to not assume for all eternity, but to see beyond, the present social formation, that of global/descendant capitalism -- all of which is beyond the capability of, or is "taboo" to,*

**ideology**__consciously capitalist-ideology-permeated scientists, or consciously pro-capitalist scientists, or consciously capitalist-apologist scientists, affords Marxians a unique potential to perform "universal labor" [Marx] which contributes advances to the social, natural, and mathematical sciences -- advances that, in themselves, already constitute contributions to capital-relation-dissolving, capitalism-dissolving further growth of the human-social forces of human-societal [expanded self-re-]production, in the form of scientific / technological advances: "the most solid form of social wealth" [Marx, <<__

**un**__>>].__

**Grundrisse****D.**: - . . . (The 'balance of nature' model is obviously flawed and ideological, as noted, since it imposes a concept of a set equilibrium that does not actually exist in nature.)

**M.D.**: I strongly agree.

"Attractor" solution-geometries for

__differential equations consist of single "fixed points" in state-space, approached asymptotically by the state-space trajectories of the systems modeled by that state-space with ever-diminishing, exponentially-diminishing "state-space velocities" ["temporal__

**linear**__celeration, to zero "at"__

**de**

**t**"

**=**"

**+oo**].

Those "fixed point" attractors represent

__"equilibria" -- points which, e.g., if ever reached in finite time, would represent states of the absolute death of all change for these systems; single states from which these systems can never again escape; single states that these systems must "stay" in "for all eternity": unreaslistic, state-space "__

**absolute****black holes**".

Such

__differential equation models are hopelessly unfit to actuality.__

**linear**Even "black holes" do not represent the absolute abolition of all change which

*"dynamics" demands.*

**linear**Even "black holes" are predicted to "self-evaporate" over a sufficiently long duration.

**D.**: The 'selfish gene' theory, or biological determinism generally, lends itself to ideology as well since it hyper-balkanizes humanity's common interests and props up the institution of private property as handed down through biological lineages.

**M.D.**: I strongly agree.

*"*,

**Biological determinisms**"*"socio-biologies"*, and other such ideologies involve a capitalist-ideology-characteristic move of

*, or "back-to-[prior-]nature-ism" in terms of "scientific" explanation.*

**ontological reductionism**They represent a

*that the new ontology that emerged with the*

**denial***of the earlier-emerged ontology of*

**-**__dialectical__self**transformation***social meta-zoa -- of pre-social, pre-language multicellular animals -- is actual, and they represent a*

**a***of those new qualities, new properties, new behaviors, and new "laws" that emerged with social animals and with their proto-language-based animal societies, and with human[oid](s)-led "meta-societies" that came next; a*

**reduction**

**reduction***to those of the qualities, properties, behaviors, and "laws" characteristic of those*

**back**__social meta-zoa, attempting to conceptually collapse the very actuality of those emergences.__

**a**This is particularly relevant to this dialogue, I think, because, as I perceive them, some of our other interlocutors' formulations exhibit these sub-Marxian characteristics, lacking

*, and abiding in the*

**historical specificity***realm of explaining the cognitive problems of humanity in strictly biological-*

**historically**-**generic***terms, ignoring entirely the historical succession of qualitatively-different human-social ideologies, founded in the historically self-developing*

**genomic***, and associated with the qualitatively different*

**human****phenome***predominating in each successive human-social formation, culminating in the capital-centered global formation of today, and in the ideologies*

**social relations of production**

*historically**-*

**thereto.**

*specific*Regards,

Miguel

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