__Full Title__:

*Part***II**.

**Introduction**.

**.**

*The*__Dialectic__of NatureDear

**,**

*Reader*The present blog-entry is the

**second**blog-entry in this series on the

*dialectical**‘*modeling’ of the

**-**__meta__**, as presently known to science [except that the**

*natural history of the total cosmos**‘*

**-**__meta__**model**’ narrated herein does

__yet__

**not***explicitly*address

*“*and

**Dark Energy**”*“*].

**Dark Matter**”Part

**I**. of this series is available via the following link --

http://feddialectics-miguel.blogspot.com/2014/04/part-i-prolegomena-dialectic-of-nature.html

**,**

*Regards*Miguel

**Part**

**II**.:

**Narration**--

*Dialectical**-*

**Mathematical**-__Meta__**Model****--**

*of our Cosmos*__Story__**Introduction**.

*Preliminary Considerations on*__Dialectic__al*-*--

**Cosmological**-__Meta__**Modeling**”

*Recounting the Story of the Ontological*__Self__*-*

**Revolution**__s__

**of Pre**-**Human Cosmological Nature***,*

__Dialectic__al*-***Mathematically***.*

**as well as Narratively****: Throughout this part, we employ two key**

__Please Note__**scientifico-philosophical terms.**

*ancient*Their resurrection in the

**also serves well to catalyze an urgently needed**

*present***transition, to a**

*future**‘*,

**trans**-**modern**’**--**

*dialectical science***1**. «

**», which means, e.g**

__Monad__*., “*

__qual__itative

*Unit**”*,

*“*

__qual__itative

*logical*__Individual__*”*, or

*“*

__qual__itative

__Element__*”*-- a single one of the many like-kind 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 like “kind”.**

__categore__ma**: Many of the special, technical words employed below are also hypertext links to definitions of those words [often for the first occurrence of each such word**

__Please Note Also__*only*].

*The*

*Dialectical**‘*

*Theory of Everything**’*

*‘*--

**-**__Meta__**Equation**’

*The*

*Historical**-*

*Dialectical*

*‘*

*Meta**-*

**Monadology**’

*of*__Pre__*-*(

**Human Natural Formation****),**

__s__**.**

*and Beyond*The dialectical ‘meta-equation meta-model’ of

**which we will be exploring, and iterating for escalating values of its “discrete**

*the total cosmos***ime” parameter, or ‘epoch parameter’,**

__t__**t**

**, and whose story we will be narrating throughout this series, is the following --**

_{ALL}

_{ALL}

__>-|-<__

_{t}

_{ALL}**= <**

_{ALL}

__r__**>**

^{2t}

^{ALL}-- wherein

_{ALL}**denotes the primordial ‘cosmo-ontological category’ of p**

__r__**e-nuclea**

__r__**“pa**

__r__**ticles”,**

__r__i.e., the category of “

**elementary**”

**, belongs to a general family of such historical-dialectical ‘meta-models’, whose various features can be defined as follows --**

*bosons and fermions*__and____composite__The

**F**.

**.**

*E***. solution to this**

*D**‘*

*Dialectical*

*Theory of Everything***meta**-

**equation**’ exhibits an «

**»**

*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**‘*

*Dialectical*

*Theory of Everything***meta**-

**equation**’

**in**

*particular*.

This ‘

**meta**-

**equation**’, so interpreted, constitutes a

*‘*

**dialectical**

*meta**-*, and one which also tells the

**model**’**of**

*story*

*our cosmos as natural**-*, to-date, and also one with the wherewithal to

**historical totality****rate predictions of a next future**

*gene**‘*. This categorial-progression

**cosmo**-**ontological revolution**’**“follows from” its initial category,**

*story*

_{ALL}**, by ‘connotational entailment’, once the**

__r__

**principle**__s__of*of the product of the initial, self-multiplication / ‘self-reflexion’ of category*

__dialectic__al interpretation

_{ALL}**, and, later, of the products of that product with itself, are set forth.**

__r__This

*‘*

__dialectic__al

__meta__*-*is, in part, one of a

**model**’*‘*, or ‘«

__phys__ical**’**__dialectic__**»**

__physis__**’ — indeed, models**

*dialectic**‘*«

**The**__Dialectic__of the Universal**», from which, at length, human consciousness is formed.**

__Physis__This

*‘*

__dialectic__al

__meta__*-*describes the ‘

**model**’**of the successive and progressive neo-ontological formation(s)’**

*dialectic***, in terms of the «**

*of cosmological Nature***», and of the «**

*monads***», of the «**

*arithmoi***»**

__phys__*-*.

**ical cosmos**However, this

*‘*

__dialectic__al

__meta__*-*is also one of ‘«

**model**’**»**

*psyche**-*

**ic**

*dialectic**’*, of

*‘*

**cognitive**

*dialectic**’*, or of

*‘*, because its rising levels of ‘“complexity/consciousness”’ [cf. Chardin], implicit in the ‘«

**ideo**-**dialectic**’**»**

__phys__

*io**-*that it describes, eventually arrive at -- and, predictively, surpass -- present-day, Terran human[oid] self-awareness.

**ontological categor**’__ies__The ‘meta-dynamics’ of the ‘meta-evolution’ of the ‘meta-dynamical meta-systems’ of such natural formation(s) constitute(s) an «

**», and an «**

*autokinesis*

*auto**-*» at the level of Nature’s ontology -- a creation of

**onto**-__dynamasis__**of being, from out of the interactions, and self-interactions, of the preceding kinds.**

*new kinds*The system

*progression, or ‘diachronic meta-system’, of these successive “natural formation*

__s__-*, is grasped as a*

__s__”*‘*«

**-**__self__**»**

*aufheben*

__self__*-*progression’ of

*‘*,

**Qualo**-**Peanic**’*‘*, ‘meta-«

**meta**-**fractal**’**»-ic’,**

*monad**‘*processes / structures, when we grasp each of its successive pre-human[oid] «

**archeonic consecuum**’**» of natural formation «**

*arithmoi***» [e.g., the global**

*monads***/ «**

*assemblages***» of living**

*arithmoi*

__atom__*s***, or of**

*unit*__s__

__molecules__**, or of living**

*unit*__s__**pre-eukaryotic cell**

*s***, etc., as of some epoch in cosmos-history when any one or more of them are extant] as a**

*unit*__s__*‘pre-consciousness*,

*,*

__unified__

*collective natural**[-ivity],*

__subject__**, and**

__verb__

__object__*’*, or as a

*‘pre-consciousness*,

*collective**natural*[-ivity]’.

__agent__This

*natural system*__s__*is therefore one that qualifies as a[n] ‘*

**-**__self__**progression**

*historical**-*per

**dialectical****process**’**F**.

**.**

*E***.’s definition.**

*D*The reader is referred to

**Supplement**

**B**(Part

**III**, pages

**B**-

**20**through

**B**-

**22**) of the

**F**.

**.**

*E***.**

*D***for the classical**

__Introductory Letter__

_{N}**Q_**‘formulaic’ rendition of the

*‘*

**dialectical***re-rendered narratively in this series --*

**-**__meta__**model**’link: http://www.dialectics.info/dialectics/Primer_files/4_F.E.D.%20Intro.%20Letter,%20Supplement%20B-1,%20v.2_OCR.pdf.

**. The cosmological story that the narrative, in the ensuing blog-entries, recounts, is “unembellished” -- it invokes no more of the details of this cosmological natural history than is given explicitly in the**

__Parsimony__**F**.

**.**

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

*D*__‘__. The forthcoming narrative of this series of blog entries instantiates a

**Helicity**’*“helical*narrative”, and is also close to being a “model-generated” narrative, emphasizing the recurring, self-similar aspects of the story encoded in the meta-equation, and of the ‘temporal

*qualo**-*

**fractal***’*that the meta-equation generates, repeating the form of the narrative account as much as possible for each epoch / whorl of the helical course of the self-development of cosmological nature.

Nonetheless, the

**,**

*cumulative***precedented,**

__un__

__non__*-*cyclical aspects of this “greatest story”, and the overall progressive gain in ontological complexity / richness / “determinateness” from epoch to epoch, also demand their due in the course of the apt description of the connotations of the meta-equation, whose equations differ qualitatively, ontologically, in each of its successive epoch / whorl, thus refuting any ideological claim of an ‘ontologically-statical’, or merely “flat-cyclical”, merely circular natural-historical motion.

This helical

*‘*‘content-structure’ should not be mistaken as one which can be fitted to any helical graph-trajectory, confined to a single three-dimensional mathematical space with purely-quantitative axe

**qualo**-**fractal**’*, whether of the*

__s__**R**, or of the

**Q**, or of the

**Z**, or of the

**W**, or even of 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

**Heuristicity**’*“*quantifiable” ordinal “qualifiers”, interpreted as representing ontological categories, cannot be other than an

__un__*“*” algebra, and that is what we have in the

**algorithmic heuristic**

_{N}**Q_**algebra as a tool of cognition.

The algorithmic layer of this

*“*, the layer of the “minimally-interpreted” -- “ordinal qualifier”-interpreted -- generic

**algorithmic heuristic**”

_{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.**

_{4}The

**, 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 primordial universal ontological category” of human social formation, the foraging “

**meta**-**genealogy**”**p**

__r__**e-nuclear**

**particle**

__s__*”*, connoted herein by

_{ALL}**-- then the symbol**

__r__

__q__**, and its**

_{1}*“*, may take on new meaning, new

**followers**”“intension”, new connotations.

And, thereby, a new level of

*“*-- of their special

**followership**”*‘‘‘*-- emerges, beyond that of the mere “qualitative ordinality” of the

**logic**’’’*, algorithmic arithmetic; a special*

**gene**ric*‘‘‘*which is a heuristic, intuitive, connotative logic -- a logic of

**logic**’’’*“*.

**connotative entailment**”For an

_{N}**Q_**‘meta-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 a**

*solution***t**-specific, interpreted

_{N }**Q_**equation’s “poly-qualinomial”, or ontological

categorial progression/cumulum, 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 meta-equations.

**organonic algebraic method**”That is, in this case, if

*generic*

__q__**is identified with**

_{1}*specific*

_{ALL}**, with the “physio-ontology” of**

__r__the of “

**elementary**”

**, then, for a user of the**

*bosons and fermions*__and____composite__

_{ }

_{N}**Q_**cognitive tool who is also versed and immersed in knowledge about -- in the

reconstructed phenomena / phenomenology of -- pre-human, cosmological natural formation(s), a meaning, a

**, for the next**

*solution**term, for the term that corresponds to the*

**speci**fic

**gene**ric

__q__**, for the term**

_{2}

__delta__

__r__

__=__

__q__**, must suggest itself, if the model is to “work”.**

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

*“*What known, past pre-human natural formation corresponds to the algorithm-generated description / definition: “The term

**¿**

__q__**designates a “pa**

_{rr}**ticle**

__r__**pa**

*of***ticle**

__r__

*s**”*, an «

**» of “**

*arithmoi***meta**

**-particle**

^{1}

__s__*”*natural formation

**, such that each such**

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

*unit**“*

*particle**”*as its

**units**

__sub__*-*

**units**”**?**-- that a

*user-known*pre-human cosmological natural-historic formation -- in this case, “

**a**

*toms**”*--

__q__

_{rr}

__=__

**a**

-- must come to mind as the answer to that question; as the

**for that category-describing 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 cosmological natural history so far -- in this case, in the natural history of natural formation to-date, i.e., to this meta-model’s cosmological 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

__delta__

__x__

__=__

__q__**.**

_{xx}
For
the “merely hybrid”, or “allo-hybrid” terms, of form

__q___{yx}**...**, it has been found that some of them may be rightly “solved” to be*“*possibles”, i.e., to be__im__*“*operative terms”, so named by analogy with the__in__**often encountered in***unused terms**applications of the***speci**fic*Lagrange Equations.***gene**ricThomas 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 solution

**followership**”**.**

*s*It would be naive to expect otherwise.

And «

**»!**

*vive les difference*__s__Civil dialogue about such differences evokes new insights, and new and fruitful hypotheses.

The

_{N}**Q_**

*“*method can conduce to greater clarity in such

**algorithmic heuristic**”dialogues.

## No comments:

## Post a Comment