Wednesday, July 17, 2013

Part II. The Psychohistorical-Dialectical Equation of Human-Social Formations ‘Meta-Evolution’. Narration.

Full Title The Psychohistorical-Dialectical Equation of Human-Social Formations Meta-Evolution’.  Part II.

Dear Readers,

The present blog-entry is the second blog-entry in this series on the psychohistorical-dialectical modeling of human history, focusing on the "social formations" [cf. Marx] aspect of that history.



Part II.:  Narration -- Dialectical-Mathematical-Model Story of Human Social Formation -- 
Categorial Progression Reconstruction of Past-to-Present Human Social Formations.  

Preliminary Considerations on Psychohistorical-Dialectical Modeling.

Please Note:  Throughout this part, we employ two key ancient scientifico-philosophical terms.  Their resurrection serves well to catalyze the transition to a ‘trans-modern’, dialectical science --

1.   « Monad », which means, e.g., “qualitative Unit, qualitative logical Individual, or qualitative Element -- one of the constituents represented, collectively, by a category, and;

2.   « Arithmos » [plural:  «arithmoi»], which means a category, e.g. anensemble, a multitude, a ‘“population”’, or  an assemblage of «monads» -- i.e., of qualitative units, of qualitative logical individuals, or of qualitative elements  -- all of which «monads» share a common quality, or a common predicate, i.e., a «categorema» in common; a “kind”.

Please Note Also:  Many of the special, technical words employed below are also hypertext links to definitions of those words [usually for the first occurrence of each such word only].

Equation #4:  The [Psycho]Historical-Dialectical Meta-Monadology of Human-Social Formation(s).

The F.E.D. solution to this equation exhibits an « aufheben » progression which features the     Qualo-Peanic , ‘ meta-fractal ’, ‘metamonad»-ic’ archéonic consecuum process / structure which characterizes dialectics in general, and the dialectics of the  F.E.D. psychohistorical equations in particular

This equation, so interpreted, constitutes a dialectical [meta-]model, and one which also tells [an aspect of ] the psychohistorical story of Terran humanity itself, to-date.

This dialectical [meta-]model is, in part, one of a physical dialectic, or ‘«physis» dialectic’  [although the Ancient mind might have called it ‘‘‘the [his]story of the «anti-physis»’’’] — indeed, models an aspect of The Dialectic of Nature within its ‘human-social’ epoch.  

It is the ‘dialectic of human-social formation(s)’, in terms of the «monads», and of the «arithmoi», of human settlement / governance structures. 

However, it is also one of ‘«psyche»-ic dialectic, of cognitive dialectic, or of ideo-dialectic, because of the “memes”, and the gains in collective human cognitive capabilities, required to attain, and to sustain [to socially reproduce, for periods of centuries and more], these rising levels of human «species» self-organization; of ‘“complexity/consciousness”’ [cf. Chardin]. 

As noted earlier, F.E.D. has stated that they view these successive human ‘‘‘social formations’’’ [cf. Marx], as partly physical, ‘meta-geological formations’ of the Earth’s surface, i.e., as ‘archaeological / meta-geomorphological sedimentary layerings’ — ‘[human-]natur[e-]al’, ‘megalithic meta-encrustations of the Earth’s crust’.

The ‘meta-dynamics’ of the ‘meta-evolution’ of these [this] ‘[meta-]dynamical [meta-]system[s]’ of such human-social formation(s) constitute(s) an «autokinesis», and an « auto-onto-dynamasis » at the level of ‘human-social ontology’ -- a creation of new kinds [of human-social productions, and of human-social relations of such productions]. 

The systems-progression, or ‘diachronic meta-system’, of these successive “social formations” is grasped as a self-«aufheben» self-progression’ of Qualo-Peanic, meta-fractal, ‘meta-«monad»-ic’, archeonic consecuum process / structure, when we grasp each of its successive «arithmoi» of human social formation «monads» [e.g., the global assemblages / «arithmoi» of living village units, or of living chiefdom units, or of living city-state units, etc., as of some epoch in Terran human history when any one or more of them are extant] as a collective human subject[-ivity]’, or as a collective human agent[-ivity]’.

This systems-self-progression is therefore one that qualifies as a[n] ‘[psycho]historical-dialectical process per F.E.D.’s definition, and -- psychohistorical given this ‘subject[-ivity]’. 

The reader is referred to Supplement B (Part III, page B-23) of the F.E.D. Introductory Letter for the classical NQ_ ‘formulaic’ rendition of the dialectical meta-model re-rendered narratively below [link:,%20Supplement%20B-1,%20v.2_OCR.pdf ].

Parsimony. The human, psychohistorical story that the narrative, in the ensuing sections, recounts, is “unembellished” -- it invokes no more of the human drama of this human history than is given explicitly in the  F.E.D. standard solutions for the categorial terms that it narrates.

Helicity.  Moreover, the narration below instantiates a “helical narrative”, and is close to a “model-generated” narrative, emphasizing the recurring, self-similar aspects of the story of the equation, and of the ‘temporal qualo-fractal that the equation generates, repeating the form of the narrative account as much as possible for each epoch / whorl.

Nonetheless, the cumulative, unprecedented, non-cyclical aspects of the story, and the overall progressive gain in ontological complexity / richness / “determinateness” from epoch to epoch, also demand telling in the course of the apt description of the connotations of the equation, differing in each of its successive epochs / whorls, and thus refuting any ideology claiming ‘ontologically-statical’, or merely “flat-cyclical”, merely circular psychohistorical motion.  

This helical qualo-fractal ‘content-structure’ should not be mistaken as one which fits into any helical graph-trajectory, confined to a single three-dimensional mathematical space with purely-quantitative axes, whether of the R, or the Q, or the Z, or the W, or even the N variety. 

This kind of helix transcends such confinement.

Each whorl of such a standard-number-spaces-transcendent helix, though qualo-fractally’, generically similar to each of its predecessor whorls [if any], and to each of its successor whorls [if any], is also qualitatively, ontologically different from each of them, as are they from it.

No doubt metrics can often be defined, that quantify generic common features of a whole succession of such whorls, and which, for each such generic feature, map back into a helical trajectory in, e.g., an R3, purely-quantitative mathematical space.   

But each such mapping, by itself, will fail to capture the ontologically-dynamical, quantity-transcending qualo-fractalhelix in its totality.

Heuristicity.  HYPOTHESIS:  The algebra of an arithmetical language that is limited to the expression of “unquantifiable” ordinal “qualifiers”, interpreted as representing ontological categories, cannot be other than an “algorithmic heuristic” algebra, and that is what we have in the NQ_ algebra as a tool of cognition.

The algorithmic layer of this “algorithmic heuristic”, the layer of the “minimally-interpreted” -- “ordinal qualifier”-interpreted -- generic NQ_ arithmetic, exhibits only a doubly-relentless generic qualitative ordinality, denoted by q, species told by a subsumed N numeral, n, in qn --

{ q1, q2, q3, . . . }   =    

{ the quality of first-ness, the quality of second-ness, the quality of third-ness, . . . }

-- relentless, both, first, at its subscript level, and, second, at its superscript level.  That relentless ‘subscriptal’ ordinality is presented horizontally, in the rightward direction, below, and that relentless ‘superscriptal’ ordinality is presented vertically, in the downward direction, below --

q11  =   q1;  

q12  =   q1 + q2; 

q13  =   q1 + q2 + q3;  

q14  =  q1 + q2 + q3 + q4;  . . ., etc.  The logic, the followership, so far, is strictly ordinal. 

However, when the generic ordinal qualifier for “the quality of first-ness”, q1, is “interpreted’ or “assigned” -- identified with -- the specific «arché» or ultimate ancestor ontological category of a specific categorial-progression meta-genealogy -- in this case, with the earliest known “socio-ontological category” of human social formation, the foraging band, b -- then the symbol q1, and its followers,  may take on new meaning, new “intension”, new connotations. 

And, thereby, a new level of followership -- of their special ‘‘‘logic’’’ -- emerges, beyond that of the mere “qualitative ordinality” of the generic, algorithmic arithmetic, a special ‘‘‘logic’’’ which is a heuristic, intuitive, connotative logic -- a logic of connotative entailment.

For an NQ_ model to “work”, the meanings of the category-representing terms of its categorial progression must follow from one another, and from their own subscripted, interpreted epithets, specifically, connotatively, semantically, not just generically, algorithmically, syntactically.

The solution of an interpreted NQ_ equation’s “poly-qualinomial”, or ontological categorial progression, is a determination of a meaning, of an intension, of a connotation, for each «arché»-subsequent term in that heterogeneous sum of category-symbol-terms, a meaning that intuitively follows from the given meaning of the «arché» / first term, and that also intuitively follows from the meaning of every already so solved-for, predecessor term of the term now being solved-for, all the way back to that «arché», or originating, meaning-given term, in accord with the canons of interpretation codified in the procedure-narrative of the F.E.D. solution-method, the organonic algebraic method for solving Seldon Function equations.

That is, in this case, if generic q1 is identified with specific b, with the “socio-ontology” of the prehistoric, “hunting and gathering”, scavenging and foraging bands of proto-humans, then, for a user of the NQ_ cognitive tool who is also versed and immersed in knowledge about -- in the reconstructed phenomena / phenomenology of -- prehistoric human social formation(s), a meaning, a solution, for the next specific term, for the term that corresponds to the generic q2, for the term Db  =  qbb, must suggest itself, if the model is to “work”.

This means that, when such a user “self-inquires” in the form of “self-asking” the question --

¿What known, past human social formation corresponds to the algorithm-generated description / definition:  “The term qbb designates a “band of bands”, an «arithmoi» of “meta1-band” social formation units, such that each such unit is made up out of a heterogeneous multiplicity of bandunits as its sub-units?

-- that a user-known prehistoric formation -- in this case, “camps, qbb  =   c -- must come to mind as the answer to that question; as the solution for that term.

For an NQ_ model to “work”, such apt, symbol-connotation-evoked “comings-to-mind” must continue, from epoch t = 1, all the way out to epoch t = max., i.e., the maximal ordinal epoch needed to reconstruct all of the incremental ontology “begat” by the «arché» in question in history so far -- in this case, in the history of human social formation to-date, i.e., to epoch t = 7.

This criterion of model success applies most unequivocally to the solution / “semantification” of the “self-hybrid” or ‘”auto-hybrid” terms -- the terms of the form Dx  =  qxx.

For the “merely hybrid”, or “allo-hybrid” terms, of form qyx..., it has been found that some of them may be rightly “solved” to be impossibles”, i.e., to be “inoperative terms”, so named by analogy with the unused terms often encountered in specific applications of the generic Lagrange Equations.   

Thomas K. Simpson describes, as follows, the process by which James Clerk Maxwell derived the dynamical equations of the electromagnetic field, using the Lagrange Equations.   

Maxwell did so by honing down the full possible ensemble of terms of the latter to those that were actual for electromagnetic field dynamics:

...Maxwell approaches the construction of his own electromagnetic theory with a clear initial vision of the shape it must take.  He does not begin with a collection of basic empirical results and seek a merely complete and convenient set of equations which will save the appearances."  

"Maxwell knows at the outset that his theory must take the form of the equations of motion of a moving material system; these, as we have seen, are Lagrange’s equations of motion, which in Maxwell’s view simply explicate mathematically our a priori concept of matter in motion."  

"A priori, Maxwell’s equations are merely a special case of Lagrange’s equations."  

"Therefore, Maxwell’s program for a “dynamical” approach to electromagnetism must be this:  beginning with Lagrange’s equations of motion, identify the generalized coordinates and velocities which characterize an electromagnetic system, and then determine by experiment which of the possible coefficients are actually operative in this particular science, and what relationships exist among the coefficients and the coordinates."  

"Lagrange’s equations, thus related to electromagnetism and sifted of inoperative terms, will be the basic equations of electromagnetism."  

"At the same time, they will characterize in broad strokes a particular form of connected system.

[Thomas K. Simpson, Maxwell’s Mathematical Rhetoric: Rethinking the Treatise on Electricity and Magnetism, Green Lion Press [Santa Fe:  2010], pages 272-273, emphasis added].

Of course, this solution-method, as a heuristic method, and as a “semantic” method, will, even more so than the methods of mathematical logic, of formal-logical followership, involve differences of opinion about solutions.   

It would be naive to expect otherwise.   

And «vive les differences»!   

Civil dialogue about such differences evokes new insights, and new and fruitful hypotheses.   

The NQ_ “algorithmic heuristic” method can conduce to greater clarity in such dialogues.

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