Monday, April 29, 2019

‘The Marxian Singularity’.





The Marxian Singularity.







Dear Readers,



In the Grundrisse manuscripts, as well as elsewhere, Karl Marx wrote about the way in which fixed capital is the ‘epitomeous’ form of capital, coming to dominate capital-mass in the epoch of the ‘“real domination”’ or “real subsumption” of the labor process by capital, the epoch that begins with a prevalence of the “relative surplus-value” form of surplus-value production, and which Seldon also identifies as the “descendence phase” of the capitalist system.  Marx also wrote there about how fixed capital lawfully tends to develop into an automatic system of machinery, as the incarnation and objectification of the very essence of “the capital-relation” itself in the shape of the physical embodiment of capital as fixed capital.

In the third volume of «Das Kapital», Marx wrote of what Seldon calls The Marxian Singularity, and which others have termed The Automation Crisis, in these words --

A development of the productive forces [M.D.:  E.g., a penultimate level of growth of industrial productivity via automation] which would diminish the absolute number of laborers, i.e., enable the entire nation to accomplish its total production in a shorter time-span would cause a revolution [and would thus also constitute an historical boundary, a productive force upper bound and limit, of the capitals-system; an end of the very possibility of the continuing the capitals-system; of the capital social-relation-of-production as predominating social relation of social reproduction -- M.D.] because it would put the bulk of the population out of the running.

[Karl Marx, Capital, volume III, The Process of Capitalist Production as a Whole, International Publishers Co., Inc. [NY:  1967], p. 263, bold italic shadowed emphasis added by M.D.].

It might be instructive, as a “thought-experiment”, to note what happens in the ‘Marxian ratios’ -- the “dimensionless” value proportions central to the Marxian “law of value”, and to the Marxian theory of the capitalist system as a whole -- in a scenario characterized by an extremity of automation.  Such a scenario would be modeled “in the limit” as “Variable capital-value”, V -- the aggregate of the values of wages or of living human labor-power commodities purchased to form part of “productive capital” -- goes to 0.

A.  Let us first apply this limit-process to the Marxian value-profit-rate ratio -- the ratio that resides at the very heart of Marx’s theory of the historical dynamics and ‘meta-dynamics’ [Seldon] of “the capital relation”, and of its lawful fate -- in its “purely”-quantitative, classical form:


lim    .      S    .       =   .  0  .       =   0
V --> 0    
          (C + V)           C


-- wherein S goes to zero together with V, because no “necessary labor” also means no “surplus-labor”, hence no “surplus-value”, S, hence no net “surplus-value”, S.  And no net “surplus-value” means no profit, hence, before long, no capitalism.

It is also interesting to see what happens in this V --> 0 limit to that form of the Marxian value-profit-rate ratio which arises by multiplying both the denominator and the numerator of the ratio as given above by 1 in the form of ((1/V)/(1/V)) -- the form in which both the “organic composition of capital” ratio, C/V, and the (net) “rate of surplus-value” ratio, (S/V), figure explicitly, as ‘sub-ratios’ --



lim    .      (S/V)     .       =   .      oo      .       =  . oo .
V --> 0    
           ((C/V) + 1)            (oo + 1)              oo


 =  ‘“indeterminate”’.



We might visualize this scenario-idealization, of ‘automation extremity’, as one in which --

*     All agental production work, which no longer figures as “living [human] labor”, is performed by AI ‘‘‘Android Robots’’’, whose costs of reproduction do not figure as V, but might, rather, be assimilated to C, or;

*     All such production work, which, again, no longer figures as “living [human] labor”, is performed by genomically re-engineered ‘meta-humans’, whose costs of reproduction therefore also no longer figure as V, or;

*      All such production work, which, again, no longer figures as “living [human] labor”, is performed by ‘hybrid meta-humans’, that combine genomically re-engineered genotypes with implants/artificial body-parts [i.e., ‘‘‘prosthetics’’’] originally developed for Android Robots, i.e., by ‘‘‘Cyborgs’’’, whose costs of reproduction thus also no longer figure as V.

-- or by combinations of the three cases described above.


The above, “infinity over infinity”, “indeterminate” result arises from the outcome that both the (C/V) ‘sub-ratio’, in the denominator, and the (S/V) ‘sub-ratio’, in the numerator, “become infinite” in the limit as V goes to 0, due to divisions by zero, in terms of such calculations as are available in standard, “purely”-quantitative “Real” arithmetic, as augmented by the “limit” operation and by the non-standard "infinity" symbol ‘oo’ --

lim    . C .       =   . C .      =  oo
V --> 0    
            V           0

-- and --

lim    . S.       =   . S.      =  oo .
V --> 0    
            V            0



B.  Let us next apply this limit-process to the Marxian value-profit-rate in its Seldonian, ‘qualo-quantitative’ or ‘quanto-qualitative” form, as that form arises through ontological and metrical ‘re-qualification’ of ‘‘‘quantifiers’’’, by ontological and metrical ‘arithmetical qualifier’ factors or coefficients, in the seventh ‘arithmetic for dialectic’ in the “slow version” of the Seldonian ‘‘‘systematic-dialectical’’’ method of presentation of the axioms-systems of the Seldonian ‘arithmetics for dialectic’, as a dialectical categorial progression of axioms-systems’ categories:  [forthcoming].




For more information regarding, and for [further] instantiations of, these Seldonian insights, please see --

and


For ‘poster-izations’ of many of these insights -- as specimens of dialectical art -- see:




¡ENJOY!



Regards,


Miguel Detonacciones,

Member, Foundation Encyclopedia Dialectica [F.E.D.],
Participant, F.E.D. Special Council for Public Liaison,
Officer, F.E.D. Office of Public Liaison.







Sunday, April 28, 2019

‘The Singular Dialectic of Nature’.







Our «Kosmos» is a Single Vast Continuing Recurrent Helicating Self-Iterating «AUFHEBEN»-Movement:  The [singular] Dialectic of Nature.







Dear Readers,



Our cosmos is a single, vast, continuing, recurrent, ‘qualo-fractally helicating’, ‘self-[re-]iterating’ «AUFHEBEN»-Movement/dialectical process -- The [singular] Dialectic of Nature.

We might want to temporally divide -- or “periodize” -- this vast singleness into a connected series of ‘‘‘dialecticS of Nature’’’, e.g. --

·         ‘The dialectic of “Dark Energy” [i.e., of space self-expansion as “pure” time/universal clock] and/versus “Dark Matter”, leading on to --

·         ‘The dialectic of “composite” and/versus “non-composite” so-called “particles”, leading on to --

·         ‘The dialectic of molecules and/versus atoms’, leading on to --

·         ‘The dialectic of “eukaryotic” living cells and/versus “prokaryotic living cells”, leading on to --

·         ‘The dialectic of social and/versus solitary meta-biota’, leading on to --

·         ‘The dialectic of human[oid]ities and/versus the rest of, ‘exo-human’/pre-human, Nature’, leading on to --

·         ‘The dialectic of ‘meta-humanities’ and/versus mere humanities . . ..

However, it is also well to keep in mind the ‘‘‘singularity’’’, the seamless singleness, ‘the «aufheben»-meta-monad-izing’ genericity, of this vast cosmological movement/‘‘‘eventity’’’ that IS our dialectical «Kosmos».







For more information regarding, and for [further] instantiations of, these Seldonian insights, please see --

and


For ‘poster-izations’ of many of these insights -- as specimens of dialectical art -- see:




¡ENJOY!



Regards,


Miguel Detonacciones,

Member, Foundation Encyclopedia Dialectica [F.E.D.],
Participant, F.E.D. Special Council for Public Liaison,
Officer, F.E.D. Office of Public Liaison.







Saturday, April 27, 2019

“The Concept of Capital” According to Marx.








The Concept of Capital According to Marx.









Dear Readers,



Marx’s Grundrisse manuscript in particular is peppered with passages such as the following [emphases added], referring to “the concept of capital” --

The exact development of the concept of capital [is] necessary, since it [is] the fundamental concept of modern economics, just as capital itself, whose abstract, reflected image [is] its concept [dessen abstraktes Gegenbild sein Begriff], [is] the foundation of bourgeois society.  The sharp formulation of the basic presuppositions of the relation must bring out all the contradictions of bourgeois production, as well as the boundary where it drives beyond itself. [p. 331].

... (3) Looked at precisely, that is, the realization process of capital -- and money becomes capital only through the realization process -- appears at the same time as its devaluation process [Entwertungs-prozess], its demonetization.  And this in two respects.  First, to the extent that capital does not increase absolute labor-time but rather decreases the relative, necessary labor time, by increasing the force of production, to that extent does it reduce the costs of its own production -- in so far as it was presupposed as a certain sum of commodities, reduces its exchange value:  one part of the capital on hand is constantly devalued owing to a decrease in the costs of production at which it can be reproduced;  not because of a decrease in the amount of labor objectified in it, but because of a decease in the amount of living labor which it is henceforth necessary to objectify in this specific product.  This constant devaluation of the existing capital does not belong here, since it already presupposes capital as completed.  It is merely to be noted here in order to indicate how later developments are already contained in the general concept of capital.  Belongs in the doctrine of the concentration and competition of capitals. [p. 402-403].

The tendency to create the world market is directly given in the concept of capital itself. [p. 408].

( ... Conceptually, competition is nothing other than the inner nature of capital, its essential character, appearing in and realized as the reciprocal interaction of many capitals with one another, the inner tendency as external necessity.)  Capital exists and can only exist as many capitals, and its self-determination therefore appears as their reciprocal interaction with one another). [p. 413-414].

It belongs to the concept of capital that the increased productive force of labor is posited rather     as the increase of a force [Kraft] outside itself, and as labors own debilitation [Entkräftung].  The hand tool      makes the worker independent -- posits him as proprietor.  Machinery -- as fixed capital -- posits him as          dependent, posits him as appropriated.  This effect of machinery holds only in so far as it is cast into the role of fixed capital, and this it is only because the worker relates to it as wage-worker, and [Ed.:  as] the active individual generally, as mere worker. [p. 702].


Some of these assertions -- particularly those like the fourth quote above -- may ring with tones reminiscent of Platonian idealism, as if an “immaterial” «eidos» controls the manifestations of physical and sensuous phenomena, from “behind”, “within”, and/or “above” them, from some “transcendental” realm of eternal, immutable, intangible, Parmenidean «eide».

But we hold that Marx’s “concept of capital” is neither a Platonian «eidos» nor a Hegelian-mystical, reified, subject-object inverted «Begriff».

Yes, Marx was coming to the study of the world-market capitalist system, and to the immanent critique of the ideology-compromised science of classical political economy, from the background of his earlier immanent critique of Hegelian/capitalist philosophical ideology. 

But the positive fruition of that immanent critique of Hegelian/capitalist ideology was what Seldon calls a ‘psychohistorical-materialist dialectical theory’ of human concepts in general, and of “the concept of capital” in particular, via a view which dialectically synthesized the scientifically-serviceable portions of the ideologies of French mechanical materialism [abstract ‘matter-ism’], and German classical idealism [denial of objective materiality].

Per that view, a “concept” such as Marx’s “concept of capital” must be a scientific one, embracing and unifying the totality of the empirical appearances of its object -- including even the obscure, little-known, or seldom-experienced of such appearances.  Such a Marxian, dialectical “concept” is no arbitrary construct.  To be “correct”, it must comprehensively explain, in a unifying way, all of the known empirical manifestations of the reality that it conceptualizes.  Regarding the case in point, human beings actively construct, produce, and reproduce the capital social-relation of societal self-reproduction, even if not with full consciousness or intent,  and they are beings which have the genomic potentiality to form ideas, potential “concepts”, e.g., about their own praxis in so constructing, producing, and reproducing.  The “correct” concept of capital, at least for a given historical moment, is that unique conceptualization of the capitalist experience of humanity that comprehends the totality of that experience. 

Such a “concept” can only be arrived at via relentless scientific criticism of the vast variety of deficient ideas of the global capitals-system that initially arise, and that continue to arise, some reflecting the “inverted” experience, and the ‘concrete mystification’, that the capital-praxis entails, and some reflecting deliberate attempted mystifications by the intellectual prostitutes and con-men of the capitalist ruling classes.

The formation of this “concept” of Marxian, dialectical “concepts” may be facilitated by recourse to an example from the “natural” sciences:  the example of the “concept” of “gravity”.

Newton’s breakthrough theory of “gravitational force” has been, and continues to be, enormously serviceable in calculations and predictions of the gravitational dynamics of massive bodies.

However, there are “appearances” of “gravitational force” which contradict the Newtonian expectations and calculations.

Such is the “appearance” of the shift of the perihelion of the planet Mercury in its orbitings of our Sun, that is unexplained by Newton’s model of gravity.  Einstein’s General Relativity theory of gravity was able to explain almost all of that discrepancy.

Another such is the measurable gravitational bending of the trajectories of light-rays as they pass in sufficient proximity to sufficiently-massive objects, such as stars.  Again, Einstein’s General Relativity ‘non-force’ theory of the gravitational field predicts accurately such bending.  Newton’s theory of gravity-force does not.

So, it might seem, Einstein’s General Theory of Relativity constructs the valid scientific “concept of gravity”, whereas Newton’s concept of gravitational force is deficient.

However, Einstein’s model of gravity goes into division-by-zero-“singularity” failure-mode when attempting to explain the appearances/phenomena of the “total gravitational collapse” of sufficiently massive objects, e.g., of stars.  Scientists who cling to General relativity Theory at this point of its breakdown, start mysticizing about physical actual infinities, e.g., of mass-density and of infinitesimal volume, supposedly existing at the core of such collapsed stars -- “black holes”.  

The F.E.D. hypothesis is that “black holes” contain a thoroughly finite form of mass-energy substance, beyond the “degenerate” matter of “white dwarf” stars, and beyond even the ‘‘‘neutronium’’’ of “neutron stars”, which we call ‘holonium’. 

If the Einstein General Relativity equations are mapped into the Seldonian seventh, or ‘Mu’, dialectical calculus, and thus ‘re-qualified’ by arithmetical ontological qualifier ‘meta-numeral’ factors/coefficients, and also by metrical qualifier ‘meta-numeral’ factors/coefficients, then their infinite collapse division-by-zero “singularity” yields, instead of any aphysical value of infinity, the Mu ‘meta-numerical’ value of full zero, which signifies that the -- quite finite -- outcome of such “gravitational collapse”, involves an ontological category of “mass-energy” which cannot be described in the mathematical language of Einstein’s General Relativity theory, e.g., given the restricted “ontological commitments”, and relatively abstract ‘descriptivity’ of that language.

Moreover, Einstein’s General Relativity theory fails to jibe with Quantum Mechanics, which is a huge problem for which both General Relativity Theory and the ideology of Quantum Mechanics are likely both to blame, even though the gravitational interactions of quantum mechanical “particles”, due to their minimal masses, are “negligible” in magnitude.

Thus, still, despite many centuries of effort, it appears that humanity has yet to arrive at the “concept of gravity” in the Marxian, scientific, dialectical meaning of the term “concept”, or “category”.

Moreover, we see that the Marxian “concept of capital” -- even given its unprecedentedly advanced character -- is in need of improvement, especially in the light of certain phenomena of capitalism that Marx did not live long enough to experience.







For more information regarding, and for [further] instantiations of, these Seldonian insights, please see --

and


For ‘poster-izations’ of many of these insights -- as specimens of dialectical art -- see:




¡ENJOY!



Regards,


Miguel Detonacciones,

Member, Foundation Encyclopedia Dialectica [F.E.D.],
Participant, F.E.D. Special Council for Public Liaison,
Officer, F.E.D. Office of Public Liaison.






Tuesday, April 09, 2019

Part 12: Seldon’s Message Series -- ‘Actual Metafinity’ versus Fanciful Infinity: ‘Metafinite’, ‘‘‘Meta-Dynamical’’’ Change and Mathematical “Singularity”.







Part 12:  Seldon’s Message Series --

Actual Metafinity versus Fanciful Infinity: 

Metafinite, ‘‘‘Meta-Dynamical’’’ Change and Mathematical Singularity.







Dear Readers,



It is my pleasure, and my honor, as an officer of the Foundation Encyclopedia Dialectica [F.E.D.] Office of Public Liaison, to share with you, from time to time, as they are approved for public release by the F.E.D. General Council, key excerpts from the internal writings, and from the internal sayings, of our co-founder, Karl Seldon.

The twelfth such release in this new series is entered below [Some E.D. standard edits have been applied, in the version presented below, to the direct transcript of our co-founder’s discourse].

This instalment addresses the Seldonian view of the relation between the bandying about of fanciful and even mystical infinities in descendence-phase pure mathematics and even in mathematical physics, vis-a-vis the Seldonian concept of metafinity.



For more information regarding, and for [further] instantiations of, these Marxian and Seldonian insights, please see --

and


For ‘poster-ized’ visualizations of many of these Marxian and Seldonian insights -- specimens of dialectical art -- see:




ENJOY!




Regards,


Miguel Detonacciones,

Member, Foundation Encyclopedia Dialectica [F.E.D.],
Participant, F.E.D. Special Council for Public Liaison,
Officer, F.E.D. Office of Public Liaison.







...leaving aside any extended commentary upon the contra-factual, ‘contra-actual’ axiomatics of Cantorian, “mathematical-Platonist” mysticism, and its deductively rigorous phantasies, for now, this is to register a few remarks regarding the mathematical “infinitism” that invades even the ostensive realism of mathematical physics.”
“The more-realistic, nonlinear partial [integro-]differential equations that abound in modern mathematical physics are prone to predict -- precisely because of their nonlinearity -- bouts of divisions by zero in real finite-time, divisions by zero which can be interpreted as representing infinite values for key physical metrics and variables:  so-called singularities.”
“Such conjunctures in the modeled time/history of a physical phenomenon or system are rightly regarded as mathematically meaningless by many of the more realistic physicists, and as marking physical conjunctures for which the equations, and the “laws” that they formulate, “break down”.” 
“There are, of course, some “mush-minded” mystoids among “physicists”, who want us to believe that, e.g., the gravitational collapse singularity of the Einstein General Relativity system of “simultaneous” nonlinear partial differential equations means that there is some kind of ‘“actual, physical infinity”’ at the core of every “black hole”, as well as at the “Big Bang” natural-historical «arché»/core of our cosmos as a whole itself.”
“However, in a metaphoric manner, there is something meaningful about such a zero-division “singularity” in an otherwise physically accurate, highly-predictively-valid equation or equations-system.  Instantaneous ‘‘‘infinite quantitative’’’ change, from the very instant in which a denominator-resident dynamical factor-variable takes on the value 0 in such an equation or equations-system, and/or in its/their solution-function(s) [in the few cases in which such functions are known in “closed form” for nonlinear equations], might signify, and might be the only way to signify, a finite but qualitative change, e.g., an ontological change, within a mathematical language which is capable only of “purely” quantitative expression(s).”
“This kind of change is what we call metafinite change’, whereby the also meta-dynamical’ character of an also dynamical system becomes manifest.”
“And, indeed, we find that, quite typically, zero-division singularities in the equations of physics and of engineering occur at critical points in the cumulative course of at first apparently only quantitative change, at which qualitative change, in the form of the self-expansion of the ontology of the phenomenon or system that the equations model, bursts forth.  And this irruption of additional ontology typically also coincides with the meta-dynamical’ transition from a predecessor dynamical system to its qualitatively, ontologically different -- ‘‘‘evolutely’’’ expanded -- successor system, that may also «aufheben»- ‘‘‘contain’’’ and incorporate its predecessor system.”
“Division-by-zero singularities typically mark, not [impossible] actual, physical infinities, but transitions from a predecessor system to its successor system:  revolutions in natural history.”
“Beginning with the seventh system of dialectical mathematics in the “slow”, “training-wheels” version of our solution to our ‘meta-equation’ for the systems-progression of the axioms-systems of dialectical mathematics, the “purely”-quantitative equations of mathematical physics become ‘[re-]qualified’, by fully-arithmetical, fully-ideographical, fully-algorithmic ‘mathematical qualifiers’.  These comprise ‘metrical qualifiers’, that arithmeticize, e.g., the more primitive, “syncopated”, “dimensional analysis” expressions like ‘sec.’, ‘gm.’, & ‘cm.’, as well as ‘ontological qualifier’ mathematical ideograms. ...  We say ‘re-qualified’, because these ideographical ‘mathematical qualifiers’ bear a psychohistorical resemblance to, and resonance with, the ‘Monad’ arithmetical qualifier ‘‘‘numeral’’’ of the psychohistorically pivotal ancient proto-algebraic work of Diophantus of Alexandria, entitled The Arithmetica, which launched modern, algebraic mathematics, while still evincing salient ‘psychoartefacts’ of the ancient Mediterranean mathematical «mentalité».’
“Per a key axiom of that seventh dialectical-mathematical axioms-system, and beyond, the multiplication, by ‘empty zero’, 0, of a ‘‘‘[re-]qualified’’’, ‘quanto-qualitative’ mathematical expression, whether that expression be ‘metrically-qualified’ only, ‘ontologically-qualified’ only, or metrically and ontologically ‘co-qualified’, yields a new kind of arithmetical value and ‘meta-numeral’, which we call ‘full zero’.”
“Occurrences of that, ‘full zero’, value, signify, in that axioms-system, and beyond, that a new successor system has emerged, starting from the moment of a sustained such singularity, such that the mathematical language of the old, finite equation(s), that may have “miraculously” well-described and predicted the finite development of the predecessor dynamical system, up to that very moment of division-by-zero singularity, is no longer adequate to describe the ‘new finite-y’ of the successor dynamical system, that has «aufheben»-irrupted from out of the very heart of the predecessor dynamical system, as an expression of the very nature of that predecessor system itself; as an ultimate, immanent, ‘‘‘evolute’’’ self-transcendence of that predecessor system, via the irruption of a new ‘qualo-fractal’ scale of -- still finite, but ontologically-expanded -- ‘cosmo-ontology’. ...