Full Title --
Part 4 of 4: The Heart and Soul of Marxian Theory --
A Fundamental Inquiry into the Nature of Human Social Productive Force, and of Its Marxian Conception.
Step-by-Step Construction of an ‘Historically-Generic’, ‘Qualo-Quantitative’ Measure of Human-Social Productive Force that is Adequate to its Concept.
This blog-entry contains part of my “improvement” of one more text
by the E.A.g. [Equitist Advocacy
group], this one entitled “The Heart and Soul of
I have already provided my version of their text, in the first two parts. I planned to then add two new sections, as a third and fourth part -- the present blog-entry forming the fourth and final part in this series of blog-entries.
The final two parts are intended to set forth some of the fruits of the latest research by the Foundation regarding the critical, immanent ‘extention’ of the central Marxian concept -- the concept of "the social forces of production" -- to the concept of the ‘‘‘human-societal [self-]force of human-societal [self-]reproduction’’’, 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 my three earlier blog-entries here, corresponding to the three earlier parts --
Here are links to the E.A.g.’s original version --
¿In terms of what [qualitative] units-of-measure are we to count the magnitude, to aggregate the ‘‘‘quantifiers’’’, of human societal productive force?
- Such increases in the rate of production of an individual kind of good might be measured as the number of discrete units of that particular good that is being finished, and "put-out", or "out-put", per unit of time -- say per the hour unit of time-measurement, i.e., in “#/hr.” as a compound metrical unit qualifier;
- Or, such increases in the rate of production of an individual kind of good might be measured as the number of units of the physical mass of a particular good that is being finished/output, say in ton units, e.g., per hour unit, i.e., in “tons/hr.” as a compound metrical unit qualifier;
- Or, such increases in the rate of production of an individual kind of good might be measured as the number of units of money, e.g., in dollar units, of the unit sales price, or in the unit margin [profit], gross or net, of that particular good, that is being output per hour unit, i.e., in “$s/hr.” as a compound metrical unit qualifier.
That is, the annual “percentage growth rate of real GDP” [i.e., of “real” [“deflated”] Gross Domestic Product] of nation-state societies is measured, in current econometric practice, by the ratio --
of count/count, of count+1 x count-1, of count+1-1, or of count0 --
#/# = # ÷ # = #+1 x #-1 = #+1-1 = #0 = %
-- the “zero degree”, or “dimensionless”, “percentage” unit of measurement.
The ratio above compares, by division, a time-period, annual value, for year t -1, placed in the denominator, to a “between periods” difference-comparison result, created by a subtraction, i.e., to a value [possibly positive, zero, or negative] measuring the gain in population, from year t -1 to year t, placed in the numerator.
The form[ula] to which we have just arrived above can be characterized as one which compares, by division, a difference-measure of most-recent time-period's population gain, [relative] to a difference-measure of the immediately-previous time-period's population gain.
In what Karl Seldon calls ‘time-offset self-space’, the ‘past-self-relative’, period-population gain-rate formula, above, Dpt-1/Dpt-2, coincides, in form, with the Newtonian, “divided differences”, “time rate of change”, population growth rate, or “population-difference divided by time-difference” formula, Dpt-1/D(t-1), or Dpt/Dt, but not, entirely, in content.
The ‘self-space’ graphical construct is often used, under other names, such as “graphical iteration”, to analyze, to present, and to “solve” especially the nonlinear , “fractal”, often “chaotic” finite difference equations, e.g., “quadratic maps” [see, for example, Heinz-Otto Peitgen, Harmut Jürgens, and Dietmar Saupe, Chaos and Fractals: New Frontiers of Science, Springer-Verlag, [NY: 1992], p. 510 et passim].
In the resulting --
Y _|_ X = zt _|_ zt-1
-- 'auto-space', or 'self-space', as distinct from the more conventional --
Y _|_ X = zt _|_ t
-- 'allo-space', or 'hetero-space', of [discretized] Newtonian dynamics, the “ordered pairs” to be graphed in this graph-space are [if we indicate ordered pairs by means of their enclosure in "angle-brackets", e.g., by '< _, _ >] --
< x, y > = < zt-1, zt >
-- and not --
< x, y > = < t, zt >.
Thus, the Newtonian-dynamical “differences” ratio, generically Dy/Dx = Dzt/Dt, or, in the cases of our specific examples, Dpt/Dt or DrGDPt/Dt -- all precursors to the Newtonian dynamical “differential”, or “instantaneous rate of change with respect to time”, that results from “taking the limit” as Dx ---> 0 --
lim(Dx ---> 0)(DY(x)/Dx) = dz(t)/dt
-- become, instead, generically --
Dy/Dx = Dzt/Dzt-1
-- or, in the specific cases of our examples --
Dy/Dx = Dpt/Dpt-1
-- or --
Dy/Dx = DrGDPt/DrGDPt-1.
A generic rendering of this systematic dialectic of dynamics-measuring formulas -- a presentational dialectic that we have just traversed for the specific case of our developing dynamics-metric for social reproductive force -- is portrayed in the following image --
It tracks only the growth rate of human-Genomic living biomass.
But it will not do to capture the ‘Meta-Darwinian fitness’ of an ‘artifactful’, ‘Phenome-centered’ species like humanity!
D(Pt-1 + Gt-1) =
DSt-1 > 0
((Pt-2 + Gt-2) - (Pt-1 + Gt-1))
-- i.e., whenever --
D(Pt-1 + Gt-1) > D(Pt-2 + Gt-2))
-- or whenever --
DSt-1 > DSt-2.
In the image below, the ‘sgn((Pt-2 + Gt-2) - (Pt-1 + Gt-1))’ factor in the numerator serves to rectify the sign of the whole expression, when either the sign of only the
((Pt-2 + Gt-2) - (Pt-1 + Gt-1)) denominator "goes minus", or when the signs of both the ((Pt + Gt) - (Pt-1 + Gt-1)) numerator-factor, & that denominator, both “go minus” together.
In either case, the value of this ‘self-force’ is not ‘0’, not the "purely" quantitative 'empty zero' value, but, rather, takes on the 'quanto-qualitative' ‘‘‘value’’’ ‘non-existent’, connoted by the 'full-zero' symbol, ‘.’.
Therefore, the factor (Pt × Gt)/(Pt × Gt) in the image of the productive-force formula below is included, so that the formula will generate the 'quanto-qualitative' [e]valu[e][ation] ‘non-existent’, ‘.’, in any time-period for which the Gt quantifier by itself goes to the "purely" quantitative 'empty zero' value, 0, or in any time-period for which the Pt quantifier by itself goes to the "purely" quantitative 'empty zero' value, 0, or in which both the Pt quantifer and the Gt quantifier, together, go to the "purely" quantitative 'empty zero' value, 0.
The value of this (PtGt)/(PtGt) factor is 1, producing no impact at all on the overall value of the metric, as long as both the Pt quantifier and Gt quantifier are greater than 0.
But if either the quantifier Pt or the quantifier Gt, or both, go the quantifier value ‘0’, which Seldon calls ‘empty zero’, then we have a ‘‘‘division-by-zero singularity’’’, although, in this case, it is ‘empty zero’ itself that is being divided by ‘empty zero’ itself, not, as more typically for singularities, some non-0 quantifier value that is being divided by the 'empty zero' the quantifier, 0.
The value of the ‘quantifier’ part of the whole metric thus becomes (0/0), which is an "indeterminate value", an inherently non-specific value -- an "unsolvable" numerical value syntax/symbol, an arithmetical symbol which cannot be "solved" as any specific value, or as any specific '''solution subset''' of values -- within the set of the so-called "Real" numbers", R.
Taking into account also the ‘qualifier’ part of the whole metric, i.e., the ‘metrical qualifiers’ that represent the “grams” metrical unit, denoted by ‘gm.’, we have ‘full zero’, as the overall result, whenever PtGt = 0, for the entire metric expression [note, herein, by the term 'metrical', we mean 'measuremental'; we do not necessarily mean only the so-called "metric system" of dimensional units, i.e., we do not restrict the dimensional unit qualifiers so referenced to, e.g., ‘sec.’, ‘gm.’, ‘cm.’, etc.] --
(0)[gm.]/(0)[gm.] |- = . /. |- = .
-- wherein we have used the ideogramic relation symbol ‘|- =’ to stand for the phrase 'is equal to by definition' and 'is equal to by axiomatic assertion'.
That is, when, in the seventh Seldonian dialectical arithmetic/algebra, a ‘‘‘quantifier’’’ value of ‘empty zero’, 0, multiplies the ‘metrical qualifier’ in one of its ‘qualo-quantitative’ arithmetical /- algebraic expressions, the result is axiomatically, but also intuitively, held to be what Seldon calls ‘full zero’, which we denote by ‘.’ -- a symbol which stands for a new kind of arithmetical value, one which first takes full shape in this Seldonian seventh system of dialectical arithmetic.
This ‘full zero’ value, in the axioms-system of that seventh Seldonian dialectical arithmetic, stands for ‘no longer exists’, i.e., for the qualitative, ontological ‘‘‘non-existence’’’ of the entity measured by the metric formula when that metric formula takes on this ‘.’ value, signifying, in the metric formula of the image above, as in the logic of our argument, above, that human-social productive force can exist only while both Pt and Gt maintain above 0 values, i.e., while --
Pt > 0 < Gt.
The meaning of the value named "full zero". The 'meta-number' denoted by ‘.’ does not signify contra-empirical states of affairs, such as '''actual infinity''', or '''absolute nothingness'''.
When a metric, or an equation, takes on the value ‘.’, this does not signify "abstract negation".
On the contrary, the value ‘.’ represents that state of affairs in which a given mathematical model has breached the limits of its descriptive capacity.
This state of affairs, denoted ‘.’, in a dynamical system, is analogous to Godel incompleteness in an axiomatic system of arithmetic, wherein the statement of an "unprovable theorem" of that system "deformalizes" into a system-specific ["diophantine"] equation whose specific solution cannot be expressed in terms of the '''arithmetical vocabulary''', or '''numerical vocabulary''', that is available in that axiomatic system of arithmetic.
The value ‘.’, represents a situation in which, as predicted by the given dynamical equation or model, an older, concrete, specific, determinate state of affairs -- a state which CAN be described within the limitations of the "language" of that model -- gives way to, or turns itself into, a new, concrete, specific, determinate state of affairs -- a state which can NO LONGER be described within the limitations of the "language" of that model -- one which CANNOT be expressed given the '''ontological commitments''' of the model specification, its '''vocabulary''' and '''terms of reference''', BECAUSE some of the old ontology presupposed in that model specification has ceased to exist, has descended into non-existence, and/or in which some new, e.g., unprecedented ontology, not referenced in that model specification, has arisen into existence, e.g., for the first time.
[For the 'social reproductive force' metric presented herein, examples might include, for some future time-period, t*, a period 'characterizeable' as one of 'metafinite singularity' for the given human-social unit, the disappearance of the entire human-Phenomic social infrastructure as such, as signified by Pt* = 0, coupled with the emergence, for the first time, from out of the most concentrated core of the given human civilization, of the unprecedented 'new ontology' of a '''meta-human''' population of '"artificially-intelligent''', e.g., of '''android''', robots, interconnected with a disappearance, within that social unit, of the living human population, as signified by Gt* = 0.
Alternatively, examples might include a future total assimilation of the entire living, Genomic human population of a given social unit, as signified by Gt* = 0, and of its entire, Phenomic social infrastructure, as signified by Pt* = 0, into/by a '''meta-human''' population of '''cyborgs''', combining both human-Genomic features, including a technologically-reengineered, formerly-human, Genome, as signified by Gt* = 0, and robotic features, so that --
Pt ---> t* ---> 0 <--- Gt ---> t*].
The sign ‘.’ thus signifies the outcome of a "determinate negation" of a former state of affairs, not of an "abstract negation" [e.g., the transition of that concrete state of affairs into "absolute nothingness"], but of a "determinate negation" which cannot be described "determinately" -- concretely and specifically -- within the "mathematical language" limitations of the model specification, and which thus can only be described, within the limitations of that model specification, generically, by the generic ‘.’ value, because the specific "determinations" of the new state of affairs -- the result of the "determinate [self-]negation" of the former state of affairs -- are beyond the expressive capabilities of the model which produced this ‘.’ value as its prediction for a time beyond it descriptive reach; a model which generated this ‘.’ value as a sign of its limited expressive/descriptive capabilities reaching, and breaching, their limits.
For more about this seventh of the Seldonian dialectical arithmetics, the “Mu” arithmetic, R