Sunday, December 29, 2013

Part 3 of 4: The Heart and Soul of Marxian Theory -- A Fundamental Inquiry into the Nature of Human Social Productive Force.


















Full Title -- 

Part 3 of 4The Heart and Soul of Marxian Theory --

A Fundamental Inquiry into the Nature of Human Social Productive Force, and of Its Marxian ConceptionAnalysis --

A Fundamental Exploration of the Concept of Social Productive Force.







Dear Readers,

This blog-entry contains my “improvement” of one more text by the
E.A.g. [Equitist Advocacy group], this one entitled The Heart and Soul of Marxian Theory.

 

I have provided my version of their text in the first two parts of this series of blog-entries here, and I am planning to then add two new sections, as the third and  fourth blog-entries in this series, setting forth some of the fruits of the latest research by the Foundation regarding the critical, immanentextention of the central Marxian concept of the "social forces of production", to the concept of the ‘‘‘human-societal [self-]force of human-societal [self-[re-]]production’’’, in part via an immanent critique of the ideology-compromised science of Darwinian biology, resulting in F.E.D.’s theory of Dialectical Meta-Darwinism’ as a positive fruition of that immanent critique.

 

Here are links to the E.A.g.’s original version --

http://equitism.org/Equitism/Equitism-entry.htm





Regards,

Miguel











We have ascertained, in the two preceding Parts, that “The Heart and Soul of Marxian Theory” is none other than the growth of the human social forces of production, as one of the two “sides” of the historical development of the human “social individual”, a topic-heading which includes, under its heading, the obstacles to that growth, and the ‘overcomings’ of those obstacles, and the effect of the growth of social productive force upon the other crucial “side” of the development of the human “social individual”, namely, upon the humansocial relations of production, and, thereby, also upon the state of human society as a whole, and upon ‘‘‘the human condition’’’ in its totality.




¿But what, indeed, must the phrase “social productive force(s)” mean, precisely, in Marxian theory, for it to rightly occupy so central a place in that theory?



Within the ‘Human Phenome’, the pre-existing concept/meme of “force” underwent a vast further development through the circa 1666-1687 work of Isaac Newton, especially as a result of the conceptual ‘[re-]foundation’ of modern science that he produced in his monumental treatise, the «Principia» [translated full title --  Mathematical Principles of Natural Philosophy].


¿To what extent, if any, is the Newtonian meme of “force” determinative with respect to the Marxian concept of “social productive force”?


Well, in Newton’s physics, positive force is the cause of motion, but not just a cause of “uniform motion” -- of mere, constant, velocity -- but of accelerated motion [or of decelerated motion, in the cases of, and for the causes of, “negative force].


That is, “stead[il]y” force[d] motion means, in the primary case, that of “positive force, an observed gain or growth in the velocity of the body of mass upon which the force is operating with every passing unit of time.



Note, here, that, explicitly, Newtonian force is about bodies of mass, moving, with changing velocity, in physical space, in response to forces that arise externally to those bodies, and that impinge upon them from outside of them:  external forces.


These terms of reference are largely not adequate to determine the Marxian concept of social productive force.


That concept is not concerned, directly, with physical, inertial mass, or with the movement of bodies of mass in physical space, or with the velocity of that kind of movement, ‘acceleratory’ or otherwise.



¿But are these two memes -- the Newtonian meme of physical force, and the Marxian meme of social productive force -- still related as two ‘idea-«species»’ of the same, single ‘idea-«genos»’?



Well, the Marxian concept of social productive force shares, with the Newtonian concept, the attribute of growing velocity.

However, in the Marxian ‘idea-«species»’ of “force”, it is the “velocity of production, not the velocity of a mass-body along a physical-space trajectory per se, that is determinative.


That is, the Marxian concept of productive force” does involve increments to the “velocity of production of goods -- of goods that may become, later on in an account of (the) social productive force(s), commodities, and later still, commodity-capitals -- chronologically later in history for a diachronic-dialectical, or historical-dialectical, account; systematically later in the order of presentation for a synchronic-dialectical, or systematic-dialectical, account.


I.e., Marxian “society-productive force” does involve the rate of production of such goods, such “use-values”.


This rate might be measured as the number of units of a particular good that is being finished and "put out", or "out-put", per unit of time -- say per the hour unit of time-measurement.

Or, this rate might be measured as the number of units of the physical mass of a particular good that is being finished/output, e.g., per hour unit.

Or, this rate might be measured as the number of units of money of the unit sales price of a particular good that is being output per hour unit.


None of these measures of ‘“production-rate”’, or of ‘production-velocity, are the same as the classical measure of “physical velocity” -- the change in the physical-space location of the body of mass in question, in units of distance, e.g., of miles, per unit of time, say, again, per hour unit.



Nonetheless, these various ‘‘‘metrical’’’ or ‘measuremental’ definitions of various ‘‘force’’ concepts can all be grasped as qualitatively different ‘idea-«species»’ of a single ‘idea-«genos»’ concept of ‘“velocity-in-general”’, in an ‘ideo- systematics’, ‘ideo-classificatory’, systematic/synchronic ‘dialectic of force’, by which we mean, in a ‘‘‘trans-Platonian’’’, ‘‘‘modernized’’’ version of Plato’s originating form of explicit dialectics, his «arithmoi eidetikoi», or “assemblages of idea-units”, categorial-taxonomic dialectics.


The velocity of production”, or rate of production” ‘ideo-«species» of the ‘‘‘velocity-in-general’’’ category is related to classical political-economic concepts of “productivity”, and of “the productivity of labor”.

As an accelerator of the rate of production, the “social productive force must be measured as [incremental] increases in the rate of production, or in the velocity of production’ -- as increases in productivity-in-general.

Given the centrality of the wage-labor ‘‘‘factor’’’ of production in creating ‘capital-productivity’, i.e., capital-profitability, per Marx’s analysis, by way of surplus-labor, and by way of the surplus-value of that surplus-labor, social productive force must be measured, from the Marxian, analytical viewpoint, and, to a degree, from viewpoint of the personifications of capital, via sustained increases in labor value-productivity, measured specifically as the number of monetary units of the sales-price of a given capitalist’s latest batch of goods-commodities produced, divided by the number of monetary units of a given capitalist’s unit-purchase-price of labor-power -- wages, or salaries -- used up / consumed in the process of that production.

In terms of the Marxian, dialectical analysis of the actual ‘‘‘productions-process of capitals’’’, this metric can be expressed, algebraically, as (c + v + s)/v, i.e., as units of exchange-value of the product produced, divided by units of exchange-value of labor consumed in that production, with c representing the “constant capital” [raw materials, machinery wear-and-tear, etc.], dead labor”-consumption-costs of production of that goods-commodities output, with v representing the “variable capital” [wages] living labor”-consumption-cost of production of that goods-commodities output, and with s representing “surplus-value” of the “surplus-labor” embodied in that goods-commodities output, i.e., the potential gross profit on that output [setting aside the effects of the process of the formation of the general rate of profit, on that potential].

In terms of the Marxian analysis of what really matters to the personifications of capital -- the profit-productivity’ of their capital, or its ‘return on costs invested’ -- this metric becomes the net gain time-offset self-ratio, or net gain self-rate, of output in relatio(n) to input’, where gross output is measured as (c + v + s), and net output self-rate as, i.e., net output minus [earlier] input, then also divided by that same [earlier] input’, in the form of  s’/(c + v), which has the form of a net Output over Input net gain ratio, (O - I)/I, and wherein --

s’  =  (c + v + s) - c - v - r - i - t - ...

-- i.e., wherein s’ represents the net surplus-value, the output, net of input [costs of production], and also net of other deductions, that the given capitalist must pay to others, e.g., also after the deduction of rent expenses [part of the revenue supporting the [sub-]class(es) of land owners], interest expenses [part of the revenue supporting the [sub-]class(es) of financial capitalists], tax expenses [part of the revenue supporting the [sub-]class(es) of state bureaucrats], etc., etc.


In practice, in accord with the kind of consciousness that is "lawfully" native to the class of the personifications of the capital-relatio[n], such personifications measure ‘the profit-productivity of their capital’ as r’/f, where r’ stands for the periodic [say, annual, or quarterly] net profit return from sale of the periodic produce / output of their production operation.

Therein, in that ‘‘‘return-on-investment’’’ rate, or ratio, the variable f stands for that part of Marx’s dialectical-analytical category of “constant capital” that was not consumed in the production of the output whose sale generated that net return[ed-value] numerator.

That is, f stands for the undepreciated” portion of the given capitalist’s “capital plant and equipment” value, called ‘“fixed capital value’’’, or '"fixed assets value"'.

Such “fixed” capital-value is “fixed” in that it has not yet been “consumed”, and thereby “converted”, into the product/output which was “circulated” for sale, and, in fact, actually sold -- or was “realized” -- to generate that return.

The algebraic variable f thus stands for the value of “capital plant and equipment” that remained fixed in that accounting period, as opposed to c, the value of the raw materials, etc. that went entirely into embodiment in the product-output, and also of the wear-and-tear depreciation / "productive consumption" of a portion of that, formerly fixed, portion of the “capital plant and equipment” value, that also went into “circulating capital”, along with the “raw materials” value, but in the form of “wear-and-tear” depreciation expense, reflecting, and compensating the capitalist for, the “productive consumption” of that capitalist’s “capital plant and equipment”, the consumption-of-itself-by-its-production-use.

The personifications of capital, in their accounts of profitability, and in their accounting systems, tend to see their fixed-capital plant and equipment as the sole source and cause of their profits-return, and to treat raw materials costs and wages costs as mere expenses, much like they treat rent expense, interest expense, tax expense, etc.

All of these metrics might be aptly described as measurements of ‘the exchange-value productivity of capital-value’, or of ‘the monetary-value productivity of capital’, or of ‘the potential-new capital-value productivity of capital-value’, or, more simply, as the value productivity of capital’. [see Marx, «Grundrisse», [Nicolaus translation, p. 630n.]:  *The productivity of capital as capital is not the productive force which increases use-values; but rather its capacity to create value; the degree to which it produces value.” [emphases added by M.M.], thus well-measured by the Marxian ratio --

(O - I)/I   =   s’/(c + v) ].


However, the acceleration of productivity could also be measured as sustained increases in the number of units, or in the number of the physical mass units, of a particular good, of its use-value, produced, say, per hour, by the entire “production entity”, or “human social organization”, that is producing that use-value: ‘new use-value productivity of prior use-value’, completely side-stepping any reference to monetary[, exchange]-value units-of-measure.

Indeed, there are many sub-«species» of metrics for the single «species» of positive “social productive force”, grasped as sustained productivity ratio growth-qua-sustained-rate-of-increase of the velocity-of-production.


We will consider the relative merits of various of these sub-«species» in the final Part of this series, Part 4, in which we plan to derive a comprehensively-adequate ‘quanto-qualitative’ metric for the Marxian concept of social productive force.



Any of these sub-«species» of concepts/metrics/definitions of “social productive force” may be applied in various human-social contexts, and at various human-social scales.

¿What context, and what scale, is the right scale for an adequate definition of the Marxian concept of “social productive force”?


To decide this question, let us test our tentative, generic concept of “social productive force” as “that which ‘sustainedly’ increases productivity” -- at which we have just arrived by our inquiry so far -- to various such human-social contexts and scales, so as to find out, by means of these “thought experiments”, which scale(s) and which such context(s) (is)(are) definitive for the Marxian concept of “social productive force”.


Let us order this inquiry by starting from the simplest, most “human-scale”, most sensuously-concrete, most localized context and scale, and then consider, consecutively, more complex, larger-scale, more sensuously-remote, less localized contexts and scales thereafter.


1.  Micro-scale.  An individual instrument, e.g., an individual, hand-held tool, wielded by an individual worker, or an individual machine, in its productive use, by a human worker, or by a group of human workers, or by a factory-scale “automatic system of machinery” [cf. Marx, «Grundrisse», pp. 692-700], etc., may induce a sustained increment to the 'velocity of production' of a given product / good / commodity[-capital], relative to the 'velocity of production' obtainable from their predecessor instrumentalities.  This case represents a growth in the “productive force” of that individual instrument. 

Likewise, an individual worker, or a team of workers, by incremental training, producing, in them, incremental production skills, may induce a sustained increment to the 'velocity of production' of a given product / good /- commodity[-capital], relative to the 'velocity of production' obtainable from another worker, or from another team of workers, less trained, e.g., from their previous self or selves, before that worker/that team of workers had '''consumed''' the incremental training in question.  This case represents a growth in the “productive force” of that individual worker, or of that team of workers as a whole.

Moreover, combinations of these two cases -- of both upgraded instrumentalities and upgraded worker(s’) skill(s) -- of increases in the “technical composition” of labor-power [cf. Marx] -- often necessarily occurring together, and in a coordinated fashion -- may also induce a sustained increment to the 'velocity of production' of a given product / good / commodity[-capital] -- often, synergistically, an even bigger such sustained increment than can either kind of upgrade alone -- relative to the 'velocity of production' obtainable prior to or without such a combination of upgrades.  This case represents a growth in the “productive force” of the ‘‘‘complex unity’’’ of individual workers, or of their ‘‘‘work-force’’’ as a whole, and of their instrumentalities, combined.


2.  Meso-scale A.  Upgrades to the “technology” of an individual factory or plant as a whole, i.e., upgrades to production capabilities embodied in its physical plant, or to the skills of its workforce, or to both, in concert, may -- e.g., in the context of a multi-factory, or multi-plant, firm -- induce a sustained increment to the “velocity of production output” of that entire factory or plant.  This case represents a growth in the “productive force” of an entire, geographically localized “production complex”. 


3.  Meso-scale B.  Upgrades to the “technology”/“technical composition of labor” of all or many of the individual factories or plants of a multi-factory, or multi-plant, firm -- may induce a sustained increment to the 'velocity of production output' of that entire firm.  This case represents a growth in the “social productive force” of the contribution, to the ‘‘‘total social product’’’, of an entire “individual capital” entity. 


4.  Meso-scale C.  Upgrades to the “social productive force” of most or many of the individual firms of a geographically-contiguous area, e.g., of an individual urbanism or municipality, possibly due to the local development, and/or to a local implementation, of a general advance in, or transition of, production technology, such as the initial advent of steam-powered industrial production in certain areas of England, or the initial advent of electrical machinery, may synergistically induce a ‘‘‘super-additive’’’ aggregate of sustained increments to the 'velocity of production output' of many local products.  This case represents a growth in “social productive force” via the contribution, to the ‘‘‘total social product’’’, of, e.g., an entire city or municipality, possibly facilitated by an epochal advance in “universal labor”, and resulting technologies.


5.  Macro-scale A.  Upgrades to the “social productive force” of many of the individual cities of a geographically-contiguous, multi-urban area, e.g., of a 'sub-state region', or sub-provincial “region”, may synergistically induce a ‘‘‘super-additive’’’ aggregate of sustained increments to the “velocity of production output” of many products, throughout this "region".  This case represents a growth in the “social productive force” of the contribution, to the ‘‘‘total social product’’’, of, e.g., an entire sub-provincial “region”.  Recent examples:  “Silicon valley”; the city-state of Hong Kong and the nearby portion of its adjacent coastal province [Guangdong] of mainland China. 


6.  Macro-scale B.  Upgrades to the “social productive force” of most, or even all, of an entire, ‘sub-national’ “province”, or 'partial-state',  may synergistically induce a ‘‘‘super-additive’’’ aggregate of sustained increments to the 'velocity of production output' of the total [provincial] social product of this entire province.  This case represents a growth in the “social productive force” of the contribution, to the ‘‘‘total social product’’’, of, e.g., an entire provincial polity.  Recent examples:  eventually, the United States of America nation-state’s "State" of California; eventually, the Chinese nation-state's province of Guangdong as a whole. 


7.  Macro-scale C.  Upgrades to the “social productive force” of most, or even all, of an entire “nation-state” may synergistically induce a ‘‘‘super-additive’’’ aggregate of sustained increments to the 'velocity of production output' of the total [national] social product of this entire nation.  This case represents a growth in the “social productive force” of the contribution, to the ‘‘‘world social product’’’, to the “global social product”, to the “planetary social product”, of human society as a whole, i.e., of the “human race”, of the entire, global, planetary «species» of humanity as a totality, from/by a single, individual nation-state.  Recent examples:  China, India, Brazil. 


8.  Macro-scale D.  Upgrades to the “social productive force” of most, or even all, of an entire, multi-national, geographically-contiguous sub-continental “Region” may synergistically induce a ‘‘‘super-additive’’’ aggregate of sustained increments to the 'velocity of production output' of the total [Regional] social product of this entire multi-national, sub-continental “Region”.  This case represents a growth in the “social productive force” of the contribution, to the ‘‘‘world social product’’’, to the “global social product”, to the “planetary social product”, of human society as a whole, i.e., of the “human race”, of the entire, global, planetary «species» of humanity as a totality, from/by a single, individual multi-national, sub-continental “Region”.  Recent examples:  Asia. 


9.  Macro-scale E.  Upgrades to the “social productive force” of most, or even all, of an entire continent may synergistically induce a ‘‘‘super-additive’’’ aggregate of sustained increments to the 'velocity of production output' of the total [Continental] social product of such an entire multi-national zone.  This case represents a growth in the “social productive force” of the contribution, to the ‘‘‘world social product’’’, to the “global social product”, to the “planetary social product”, of human society as a whole, i.e., of the “human race”, of the entire, global, planetary «species» of humanity as a totality, from/by a single, individual Continent.  Recent examples:  North America, Australia, Eurasia. 


10.  Macro-scale F.  Upgrades to the “social productive force” of most, or even of all, of our planet, e.g., based upon the implementation, globally, of nuclear fusion power generation, and of plasma technologies in general, may, in the future, synergistically induce a ‘‘‘super-additive’’’ aggregate of sustained increments to the 'velocity of production output' of the total [planetary] social product of planet Terra.  This case represents a growth in the “social productive force” of the ‘‘‘world social product’’’, of the “global social product”, of the “planetary social product”, of human society as a whole, i.e., of the “human race”, of the entire, global, planetary «species» of humanity as a totality:  Global Renaissance. 



Speciality & Uniqueness of the Social Productive Force Concept vis-a-vis Force Concepts Generally.

We have raised our perspective regarding the Marxian concept of the ‘“growth of the social force(s” of production”’, from just one of growth in productivity with respect to particular kinds of use-values, to one that, in its totality, grasps this concept as that of the sustainedly rising self-productivity’ of humanity; of ‘human socio-mass’; as that of the rising ‘rate of human-social reproduction’ in its totality, i.e., in the aggregate, and in the ‘‘‘dynamical system’’’, of all of the contemporaneous human societies on this planet -- as that of the rising rate of social reproduction of the Terran human species entire. 

The human productive forces, we hold, must be conceived, not as an ordinary, Newtonian external force”, as if acting upon human society “from without”, but, on the contrary, as an internal forceof human society, and also as a human societal self-force, a self-reflexive force.

By the latter, we mean a force generated by, and from within, and from out of human society itself, but also a force “bending back upon” its source; “bending back” upon itself -- acting back upon, or acting within, and thereby changing, the very human society from out of which it arises, and thereby also changing itself as well. 

Marxian “productive force” is self-reproductive self-force, the societal self-reproductive force of human society itself, the force of the self-accelerating self-expansion ofhuman socio-mass. 

Accelerated ‘self-growth’ of ‘human socio-mass’ is the cause of this force, and is also its effect. 

Human socio-mass is the input, and is also the output, and is also the ‘‘‘processor’’’ of that self-same human socio-mass whose sustained self-accelerated ‘self-growth’ expresses, manifests, or materializes, that human society’s societal self-reproductive self-force.

A partly pictographic rendering of the first three ‘epoch-specific’, ‘‘‘historically specific’’’ forms of this force is presented below --




As a ‘‘‘rate of reproduction’’’, a ‘reproductive rate’, this metric also qualifies as kind of a ‘‘‘fitness’’’ metric.

However, this metric does not measure Darwinian “fitness”, or any kind of “fitness”, of human individuals, conceived as isolated from human society, or conceived in [e.g., “gladiatorial”] isolation. 

It measures the collective, holistic ‘‘‘fitness’’’ of a human society as a whole, as a global ‘‘‘dynamical system’’’; of the human “population” as a whole, or of the planetary human species as a totality, only within which can individual human lives subsist and develop.

And it does not measure the collective Darwinian “fitness” of the human Genome alone. 

It also measures the human species self-reproductive fitness of the human Phenome.

Indeed, it measures the co-evolving, conjoint fitness of the integratedhuman Phenome/human Genomecomplex unity, or ‘‘‘dialectical synthesis’’’. 

The contributions to human species reproductive success of the human Phenome versus those of the “human Genome” can only be disentangled with great difficulty, if at all. 

By the latter term, ‘human Phenome’, we mean human “culture” -- that now vast cumulum of exo-somatically transmitted, non-gene, non-chromosomal, non-Genomic “memes”.

We mean the “memes pool” of heritable acquired human characteristics, of learnings, of the fruits of “universal labor” [Marx], that have their core in spoken human language, and, later, in written human language, but also encompassing the ideas of the human mind, and of the human heart, including humanity’s entire range of Mythological, Religious , Philosophical, and Scientific ideas, that are by now at least as crucial as is the human Genome to the sustained ‘‘‘reproductive success’’’, survival, and prosperity of the human species. 

We reference this combined fitness -- of the ‘human Phenome/human Genome’ complex unity entire -- via the phrase ‘the Meta-Darwinian fitness of the human species’.



¿If this is what any metric of Marxian “productive force” must measure, then how may we measure it so?

The challenge is this:  Our ‘productive force’/‘Meta-Darwinian fitness’ metric needs two components -- one quantifying the contribution of ‘the human Phenome’, the other quantifying the contribution of “the human Genome”.  And both of these components need to be measured with a common unit of measure, i.e., via a common “dimension”.


The solution of this conundrum, the detailed, step-by-step framing of an ‘historically-generic’, across-epochs comparable, [qualo-]quantitative metric for ‘human-societal self-productivity’, for the self-reproduction rate of ‘human socio-mass’ -- for ‘the human societal self-reproductive self-force’, and, thus, also, for quantifying the Meta-Darwinian fitness’ of the human species -- is the focus of our next and final segment of this series.







Next -- 

Part 4 of 4:  Step-by-Step Construction of anHistorically-Generic’, ‘Qualo-QuantitativeMetric for Human-Social Productive Force that is Adequate to its Concept.






Saturday, December 28, 2013

F.E.D. Vignette #21, Enhanced Version of 'On the Opposition of N__ and N_Q__', has been Posted to the www.dialectics.org website.

Full Title:  F.E.D. Vignette #21, 'On the Dialectical Opposition between the 'First Standard Arithmetic', N_, and the Seldonian 'First Dialectical Arithmetic', NQ_', has just been Posted to the www.dialectics.org website.



Dear Readers,


Aoristos Dyosphainthos's newest essay, F.E.D. Vignette #21, entitled  --

On the Dialectical Opposition between the 'First Standard Arithmetic', N_, and the Seldonian 'First Dialectical Arithmetic', NQ_.

-- has just been posted to the Vignettes Page of the www.dialectics.org website:

http://www.dialectics.org/dialectics/Welcome.html

http://www.dialectics.org/dialectics/Vignettes.html


This essay, especially in its final section, contains substantial material relating to the Marxian, immanent critique of capitalist political economy, and to the ongoing extension of that immanent critique to encompass other 'ideology-compromised sciences' of the capitalist epoch.


Enjoy!!!



HAPPY NEW YEAR !!!,



Regards,


Miguel

Saturday, December 07, 2013

The 'New Old'. [Excerpt from a Recent Foundation-Internal Dialogue with Karl Seldon].

Dear Readers,

I usually refrain from posting, here, blog-entries that do not EXplicitly address the dynamics, and the 'meta-dynamics', of the global capitalist economic formation.

However, this time, so seminal is the excerpt, below, on dialectics in general, and, hence, IMplicitly also, on the foundations of the dialectical-mathematical modeling of the [psycho]historical dialectic of the capitalist system, that I have decided to make an exception to my general policy in this specific, exceptional case.

I have reproduced, below, an excerpt from the edited transcript of a recent, computer-assisted Foundation-internal dialogue with our co-founder, Karl H. Seldon [denoted by "KHS" in the excerpt below], which the F.E.D. Public Liaison Office has just cleared for public disclosure.

This is another one of Seldon’s highly-concentrated summaries of his ground-breaking discoveries in his advancement of Marxian dialectics.


Enjoy!





Regards,

Miguel










“... KHS:  What I discovered is that, once demystified, the concept of «karma» of the Ancient Orient, and the [e.g., Platonian] concept of «autokinesis» [i.e., of “self-movement”] of the Ancient Occident, contain the seeds of the keys to the possibility of a new, better comprehension, and to a truly present, up-to-date mathematical modeling, of our «kosmos».

Nonlinearity -- such as that exhibited by, and blocking the "closed-form" solution of, the differential equation formulations of the most advanced knowledge of the primary “laws” of Nature achieved by Modern humanity to-date -- is karmicity and auto-kinesicity.

That is, this “nonlinearity” is ‘‘‘self-reflexivity’’’ and ‘self-refluxivity’. 

Dialectic is ‘self-reflexive’, ‘self-refluxive’ ‘self-«aufheben»-icity’, arising out of the ‘self-duality’, or ‘dialectical self-/internal/immanent "contradiction"’, of ‘Nature-al’ ‘‘‘eventities’’’.

This “nonlinearity” [and its inherent prone-ness to “singularity”]* is the manifestation of dialectic within a dialectic-unknowing, ‘‘‘dianoic’’’ [cf. Plato], «verstand»-imprisoned [cf. Hegel], modern mathematics.

‘Deeply-connectedly’, logical and set-theoretical “paradox” [Bertrand Russell’s diagnosis:  these paradoxes are due to reflexiveness] is the form in which dialectic has inescapably manifested itself within a dialectics-denying, ideologically and polemically ‘‘‘dianoic’’’ “mathematical [‘mathematicized’] logic” and set theory.

The «kosmos» has constituted itself, in the past, and continues to constitute itself -- right now -- in the present, and into the future, as and via a process of ‘self-reflexive self-refluxion’, described, in the simplest form, via the simplest system of the ‘mathematics of dialectics’ available to us, by the following formula --



-- wherein, by the term ‘“sub-nuclear [“non-composite”] particles”’, we mean the ‘cosmo-ontological category’ that includes “non-composite” bosons, and fermions, i.e., for the fermions, the [“non-composite”] quarks, and all leptons [which, given their “Pauli Exclusion” behavior, and their lack of “strong interaction” behavior, are not expected to “compose” -- are not expected to form “composite” “particles” -- and have not been observed as doing so], and wherein also the other symbolic-elements of the formula above are defined as follows --

[For enhanced legibility, see the enlarged version of the above image at the bottom of this blog-entry.]


For descriptively richer, more complex, more concrete renditions of the dialectic «modus operandi» of ‘Nature as a Dialectical Totality’, I also discovered a progression of axioms-systems of ever more powerful ‘mathematics of dialectics’, which I later found could be organized -- presented in taxonomic, ‘classificatory’, pedagogically-optimal order -- and represented compactly, by the following formula, a ‘dialectical meta-equation meta-model’, formulated in the ideographical language of the first system of “mathematics of dialectics” that I discovered in 1996 --


-- which instantiates the Marxian, dialectical “method of presentation” -- that Marx wrote about in his «Grundrisse», and used in organizing and writing his world-historical, world-changing «magnum opus» -- so instantiating by way of generating, in systematic, pedagogical order, a progressive-cumulative presentation of those axioms-systems of mathematics of increasing mathematical modeling power, a ‘dialectic of the mathematics of dialectics’, if you will.

This ‘dialectic of the axioms-systems of explicitly dialectical mathematics’ starts from 3hN_#_, which connotes the specification of the axioms-system of the Peano “Natural Numbers” using only the language of “first-order” symbolic logic, a specification long known, albeit “non-constructively” so, to harbor “non-standard models” of “Natural Numbers” arithmetic, hence also of its algebra.

That 3hN_#_ axioms-system of mathematics exhibits a ‘dialecticity’, or ‘«aufheben»-icity’, that is limited to a simplest, most abstract, “purely”-quantitative, or “purely”-ordinal, ‘pre-vestige’ thereof, as exhibited in the ‘‘‘ultra-simple’’’ Peano “successor function”, s, itself -- as in  s(n)  =  n + 1.

In that definition, the argument, or operand, of the s function, or operator, namely n, which can denote any individual “Natural” number, is, ‘unifiedly’, transformed in three ways.

It is (1) changed / negated[given that n + 1   ~=  n], (2) elevated in “pure”-quantitative magnitude, or in 'ordinal order-value' [in that n + 1   >  n], and also, at the “same time”, (3) conserved[in that n is “contained in” n + 1], i.e., in a single word, is ‘«aufheben»-ated’. ...”







*[In simplest, most abstract form, we can illustrate differential equation ‘nonlinearity / singularity’, as it arises within the undergirding system of arithmetic of the so-called “Real” Numbers, R, as follows --

dx2(t)/dt    =   x2(t)( x2(t) )    =   x2(t)2

-- an ‘“open-form = closed-form”’-formatted solution of which is the following solution-function, given x2(0)  =  1 --

x2(t)  =   t0 + t1 + t2 + t3 + t4 + . . .    =      

+(1 - t)-1   =    

+1/(1 - t)+1   =    

1/(1 - t)

-- so that a “singularity” arises at time t = 1 -- 

x2(1)   =    

1/(1 - 1)  =    

1/0 

-- the problem being that the value / “number” (1/0) does not exist within -- and is "meaningless" within -- the system of the so-called Real Numbers, R, so that, here, suddenly, at the instant named t = 1, the solution of even this ‘‘‘simplest’’’ of nonlinear differential equations leaps beyond the language-limitations of the numbers-system within which it was formulated, in an apparently "absolute" kind of apparently "infinitely"-sudden, "infinite"-in-magnitude dis-continuity.

What we have here is a rudimentary mathematical model of a 'non-quantitative' '''revolution''', led up to by a "purely"-quantitative "dynamical evolution" of this '''simplest''' of nonlinear "total--differential", or "ordinary"-differential, equations!   

We will release presentations of the non-“infinite”, ‘meta-finite meta-number’ value -- a value which is not quantitatively different from, but which is qualitatively different from, i.e., which is 'ideo-ontologically' different from -- any value available within the R universe of number(s), and which, beginning in the seventh axioms-system of explicitly dialectical mathematics that arises in the dialectical progression whose formula we gave above, meaningfully resolves, or ‘semantifies’, such singularities. 

We plan to do so soon, and in another venue. 

We have been, for the most part, holding back this dialectical discovery for many years.  

However, our 'psychohistorical-dialectical' calculations have indicated that the time for its public release will soon be "right"]. ...