__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.

Regards,

Miguel

**Part II**.:

**Narration**--

__Dialectical__*-*

*Mathematical**-*

**Model****--**

*of Human Social Formation*__Story__

**Categorial Progression Reconstruction of**

__Past__*-*

**-**__to____Present__**Human Social Formation**.

__s__*.*

**Preliminary Considerations on Psychohistorical**-**Dialectical Modeling****: Throughout this part, we employ two key ancient scientifico-philosophical terms. Their resurrection serves well to catalyze the transition to a ‘trans-modern’,**

__Please Note__**--**

__dialectical__science**1**. «

**», which means, e.g**

__Monad__*., “*

__qual__itative

__Unit__*”*,

*“*

__qual__itative

*logical*__Individual__*”*, or

*“*

__qual__itative

__Element__*”*-- one of the constituents represented,

**, by a**

*collectively**“*, and;

**category**”**2**. «

**» [plural: «**

*Arithmos***»], which means a**

*arithmo*__i__*“*, e.g

**”**__category__*.*an

*“*, a

**ensemble**”*“*, a

**multitude**”*‘“*, or an

**population**”’*“*of «

**assemblage**”**» -- i.e., of**

*monads**“*

__qual__itative

*units**”*, of

*“*

__qual__itative

*logical individuals**”*, or of

*“*

__qual__itative

*elements**”*-- all of which «

**» share a common**

*monads***, or a common**

__qual__ity**, i.e., a «**

*predicate***» in common; a “kind”.**

__categore__ma**: 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**

__Please Note Also__*only*].

The

**F**.**.**__E__**. solution to this equation exhibits an «**__D__**»***aufheben***which features the***progression**‘*, ‘**Qualo-Peanic**’*’, ‘meta-«***meta**-**fractal****»-ic’***monad**‘*process / structure which characterizes**archéonic consecuum**’**in**__dialectics__*general*, and the**of the**__dialectics__**F**.**.**__E__**.**__D__**in***psychohistorical equations**particular*.
This equation, so interpreted, constitutes a

*‘*[__dialectical__*meta**-*]*model**’*, and one which also tells [an aspect of ] the*psychohistorical***of Terran humanity itself, to-date.***story*
This

*‘*[__dialectical__*meta**-*]*model**’*is, in part, one of a*‘*, or ‘«__phys__ical**‘**__dialectic__**»**__physis__**’ [although the Ancient mind might have called it ‘‘‘the [his]story of the «**__dialectic____anti__*-*»’’’] — indeed, models an aspect of**physis***‘*within its ‘human-social’ epoch.**The**’__Dialectic__of Nature
It is the ‘

**of human-social formation(s)’, in terms of the «**__dialectic__**», and of the «***monads***», of human settlement / governance structures.***arithmoi*
However, it is also one of ‘«

**»***psyche**-***ic**__dialectic__*’*, of*‘***cognitive**__dialectic__*’*, or of*‘*, 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 «**-**__ideo__**’**__dialectic__**» self-organization; of ‘“complexity/consciousness”’ [cf. Chardin].**__species__
As noted earlier,

**F**.**.**__E__**. 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’.**__D__
The ‘meta-dynamics’ of the ‘meta-evolution’ of these
[this] ‘[meta-]dynamical [meta-]system[s]’ of such human-social
formation(s) constitute(s) an «

**», and an «***autokinesis**auto**-*» at the level of ‘human-social ontology’ -- a creation of**onto**-__dynamasis__**[of human-social productions, and of human-social relations of such productions].***new*__kinds__
The systems-progression, or ‘diachronic meta-system’, of
these successive “social formations” is grasped as a

*‘*«__self__-**»***aufheben**progression’ of*__self__-*‘*,**Qualo**-**Peanic**’*‘*, ‘meta-«**meta**-**fractal**’**»-ic’,***monad**‘*process / structure, when we grasp each of its successive «**archeonic consecuum**’**» of human social formation «***arithmoi***» [e.g., the global***monads***/ «***assemblages***» of living***arithmoi*__village__**, or of living***units*__chiefdom__**, or of living***units***city-state****, etc., as of some epoch in Terran human history when any one or more of them are extant] as a***units**‘collective human*[-ivity]’, or as a__subject__*‘collective human*[-ivity]’.__agent__
This systems-

*self-*progression is therefore one that qualifies as a[n] ‘[**]***psycho**historical**-*per__dialectical__**process**’**F**.**.**__E__**.’s definition, and --**__D__**historical given this ‘***psycho***[-ivity]’.**__subject__
The reader is referred to

**Supplement B**(Part**III**, page**B**-**23**) of the**F**.**.**__E__**.**__D__**for the classical**__Introductory Letter___{N}**Q****_**‘formulaic’ rendition of the*‘*re-rendered narratively below [link: http://www.dialectics.org/dialectics/Primer_files/4_F.E.D.%20Intro.%20Letter,%20Supplement%20B-1,%20v.2_OCR.pdf ].__dialectical__**meta**-**model**’**. 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**

__Parsimony__**F**.

**.**

__E__**. standard solutions for the categorial terms that it narrates.**

__D____‘__. 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

**Helicity**’

*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

*‘*‘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**qualo**-**fractal**’**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-

**helix, though***transcendent**‘*generically**qualo**-**fractally**’,**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.***similar*
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

**R****, purely-quantitative mathematical space.**^{3}
But each such
mapping, by itself, will fail to capture the ontologically-dynamical,
quantity-transcending

*‘*helix in its totality.**qualo**-**fractal**’__‘__. 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

**Heuristicity**’

__N__

__Q__**algebra as a tool of cognition.**

_____
The algorithmic layer of this “algorithmic heuristic”, the layer
of the “minimally-interpreted” -- “ordinal qualifier”-interpreted -- generic

__N____Q__**arithmetic, exhibits only a doubly-relentless**_____*generic*qualitative ordinality, denoted by**,**__q__*species*told by a subsumed**N**numeral,**n**, in__q__**--**_{n}**{**

__q__**,**

_{1}

__q__**,**

_{2}

__q__**,**

_{3}**. . .**

**}**

__=__

**{**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 --

__q__

_{1}

^{1}=

__q__**;**

_{1}

__q__

_{1}

^{2}=

__q__

_{1}+

__q__**;**

_{2}

__q__

_{1}

^{3}=

__q__

_{1}+

__q__

_{2}+

__q__**;**

_{3}

__q__

_{1}

^{4}=

__q__

_{1}+

__q__

_{2}+

__q__

_{3}+

__q__**; . . ., etc. The**

_{4}**, the**

*logic**“*, so far, is strictly

**followership**”**.**

*ordinal*
However, when the

*generic*ordinal qualifier for “the quality of*first**-*”,**ness**__q__**, is “interpreted’ or “assigned” -- identified with -- the**_{1}*specific*«**» or***arché**“*ontological category of a**ultimate ancestor**”*specific*categorial-progression*“*-- in this case, with the earliest known “socio-ontological category” of human social formation, the foraging**meta**-**genealogy**”*“*__b__*and**”*,**-- then the symbol**__b____q__**, and its**_{1}*“*, may take on new meaning, new “intension”, new connotations.**followers**”
And, thereby, a new level of

*“*-- of their special**followership**”*‘‘‘*-- emerges, beyond that of the mere “qualitative ordinality” of the**logic**’’’*generic*, algorithmic arithmetic, a special*‘‘‘*which is a heuristic, intuitive, connotative logic -- a logic of**logic**’’’*“*.**”**__connotative____entailment__
For an

__N____Q__**model to “work”, the meanings of the category-representing terms of its categorial progression must**_____**, and from their own subscripted, interpreted epithets, specifically, connotatively, semantically,***follow from one another***just generically, algorithmically, syntactically.**__not__
The

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

*generic*__q__**is identified with**_{1}*specific***, with the “socio-ontology” of the prehistoric, “hunting and gathering”, scavenging and foraging**__b__**of proto-humans, then, for a user of the***bands*__N____Q__**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**_____**, for the next**__solution__*specific*term, for the term that corresponds to the*generic*__q__**, for the term**_{2}__D____b____=____q__**, must suggest itself, if the model is to “work”.**_{bb}
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

**¿**

__q__**designates a “**

_{bb}**and**

__b__

*of***ands”, an «**

__b__**» of “**

*arithmoi*

__meta__**-**

^{1}**and” social formation**

__b__**, such that each such**

*units***is made up out of a heterogeneous multiplicity of**

*unit**“*

__b__*and**”*as its

**units**

__sub__*-*

**units**”**?**
-- that a

*user-known*prehistoric formation -- in this case, “__c__*amps**”*,__q___{bb}__=__**-- must come to mind as the answer to that question; as the**__c__**for that term.**__solution__
For an

__N____Q__**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**imal ordinal epoch needed to reconstruct all of the incremental ontology “begat” by the «**__max__**» in question in history so far -- in this case, in the history of human social formation to-date, i.e., to epoch***arché***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

__D____x____=____q__**.**_{xx}
For
the “merely hybrid”, or “allo-hybrid” terms, of form

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

__q__**..., it has been found that some of them may be rightly “solved” to be**_{yx}*“*possibles”, i.e., to be “inoperative terms”, so named by analogy with the__im__**often encountered in***unused terms**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

**ensemble of terms of the latter to those that were***possible***for electromagnetic field dynamics:**__actual__**“**...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

**coordinates and velocities which characterize an electromagnetic system, and then determine by experiment which of the***generalized***coefficients are***possible**actually***in this***operative***science, and what relationships exist among the coefficients and the coordinates."***particular*
"Lagrange’s equations, thus related to
electromagnetism and

**, will be the basic equations of electromagnetism."***sifted of*__inoperative____terms__
"At the
same time, they will characterize in broad strokes a

**form of connected system.***particular***”**
[Thomas K. Simpson,

**:**__Maxwell’s Mathematical Rhetoric__**, Green Lion Press [Santa Fe:***Rethinking the*__Treatise on Electricity and Magnetism__**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

*“*, involve differences of opinion about solutions.**followership**”
It would be naive to expect otherwise.

And «

**»!***vive les differences*
Civil
dialogue about such differences evokes new insights, and new and fruitful
hypotheses.

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