Monday, August 08, 2011

What is a "Dialectical Meta-Model"? What is "Meta-Evolution"?

Dear Readers,

The "17-symbol Dialectical Theory of Everything" Equation-Model of the Dialectic of Nature, which this blog reports upon, is a Cosmological Model, a Model of "Natural History" as the Total History of "Nature", "Cosmos", or "Universe", taken as the maximal Dialectical Totality, starting from the original cosmological population of pre-nuclear "particles", and summarizing that History in terms of the highest level "ontological categories" that describe the "kinds of being" so far ever extent [even if now "extinct", and also including those still extant], as well as those "kinds of being", predicted, by that Dialectical Equation-Model, to be next to "irrupt" in the Universe.

These ontological categories quite naturally extend to, and include, human-social categories.

Natural History, or the total history of Nature as "The Totality", includes the evolutions and "meta-evolutions" of the human[oid] <<species>> of Nature, and, therefore, includes human history, human society, human economic history, the history of human ideologies, etc.

That is, the work on which I am reporting echoes Marx in rejecting ideologies such as the Christian / Kantian / Lukacsian ideology of an absolute diremption, or radical dualism, of <<Natur>> vs. <<Geist>>.


I referred above to the "Dialectical Theory of Everything Model".

The work upon which I am reporting uses the term 'Meta-Model' instead.

I believe that the reason for this is that, by "Model", that work means, e.g., an ideogramic symbolic metaphor -- such as a nonlinear total-differential equation, or such as a system of such equations -- that expresses the "law of motion" historically-specific to a given epoch of natural history, and that describes mainly the quantitative "evolution" within a fixed set of qualities, or ontologies -- e.g., as represented by a fixed set of metrics, state-variables and control parameters -- that characterizes and defines that epoch.

Such a "model" is valid only up to the "resonance singularity", and/or up to the "depletion singularity", that bounds its given epoch on its later time-side, and that opens that epoch's successor epoch, with a "meta-evolution" that "irrupts" new, hitherto unprecedented qualities -- new, unprecedented ontology; new, unprecedented kinds of being.

Such "singularities" represent "self-revolutions" of and in Nature, such as the "irruption" of molecules in a universe previously organized only up to the level of atoms, or the "irruption" of prokaryotic living cells in a universe previously organized only up to molecules.

Such "singularities" typically involve "finite time infinite values", e.g., an infinite magnitude in the value of a key equational metric -- state-variable / control parameter -- arising suddenly at a finite value of the time parameter, t, and brought about by a zero value in a key denominator for that t value, i.e., by a zero division.

This makes "purely quantitative" models" break down -- become "infinitely wrong" quantitatively, i.e., suffer "infinity residuals" [a model's "residual" is the discrepancy between the actual, measured data and that model's prediction ["pre-construction"], for an [originally] future state of the reality that the model is meant to mime, or, for empirically-inferred data on past states of that reality, the model's "re-construction" thereof, calculated, for purely-quantitative models, by subtracting the model-generated value from the measured actual data value. The actual, finite value measured, minus the model's singularity-"value" of "infinity", equals "negative infinity", yielding a model-vs.-reality discrepancy that is thus "infinite" in magnitude] -- at and after that critical t value.

The work on which I am reporting has shown how to correct the "infinite model errors" produced by such "singularities", and to obtain an accurate evaluation of such equation-models at such critical t values, by "re-qualifying" those equations, using "meta-numerals" -- "metrical ["dimensional"] qualifiers", and/or "ontological qualifiers" -- "arithmetical qualifiers" that are available from the seventh, on, of the systems of arithmetic that arise in that work's dialectical meta-model of the dialectical, categorial progression of the systems of dialectical arithmetics themselves.

Thus, "models", in that work's view, echoing Marx's view, are bounded, limited in their validity, on both temporal sides, by ontological "singularity", or "natural self-revolution", boundaries.

"Models", e.g., partial-differential "evolution equations", describe mainly the purely quantitative "evolution" -- e.g., the self-expanding self-reproduction -- of a given set of ontological categories/"kinds of being" populations, a set which is qualitatively, ontologically fixed between such "self-revolutions", and fixed in the terms of reference of the "model specifications" of such "models".

A "Meta-Model", in this view, is a symbolic, e.g., ideogramic, metaphor, such as a "dialectical equation", which is "historically generic" and "quanto-qualitative", or "quanto-ontological", in that it describes a succession of "meta-evolutions" as well as of "evolutions", i.e., a progression of epochs, and of their historically-specific/-limited dynamical laws of "evolution", as well as describing the "self-revolutions in Nature", the "resonant" and "depletion" "singularities" that form the "meta-evolutionary" transitions from one such epoch to its successor epoch, all of this in a single symbolic, "quanto-qualitative", or even "purely-qualitative" / "purely-ontological" "dialectical-mathematical" expression.

Of such latter kind is their "17-Symbol Dialectical Theory of Everything Meta-Model".

Regards,

Miguel




F.E.D. definitions for special terms applied above --


dialectical equations, dialectical equation-models
no definition is as yet available in the Clarifications Archive

[The] Dialectic of Nature
no definition is as yet available in the Clarifications Archive, but see pp. B-20 to B-22 in --
http://www.dialectics.org/dialectics/Primer_files/4_F.E.D.%20Intro.%20Letter,%20Supplement%20B-1,%20v.2_OCR.pdf

historically-generic
no definition is as yet available in the Clarifications Archive

historically-specific
no definition is as yet available in the Clarifications Archive

meta-evolution, meta-evolutionary
no definition is as yet available in the Clarifications Archive

meta-model
no definition is as yet available in the Clarifications Archive

ontological category
http://www.point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Onto/Onto.htm

<<physis>>
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Physis/Physis.htm

prokaryotic living cells
no definition is as yet available in the Clarifications Archive, but see pp. c-1 through c-2 in --
http://www.dialectics.org/dialectics/Glossary_files/D.I.,Post,Phono-Neograms,%5BC%5D.w3_OCR.pdf

pre-nuclear "particles"
no definition is as yet available in the Clarifications Archive

quanto-ontological
no definition is as yet available in the Clarifications Archive

quanto-qualitative, qualo-quantitative
no definition is as yet available in the Clarifications Archive

radical dualism
no definition is as yet available in the Clarifications Archive

self-revolutions in Nature
no definition is as yet available in the Clarifications Archive

[dialectical] totality
no definition is as yet available in the Clarifications Archive

zero-division singularities of nonlinear differential equations, ontological singularity, resonant singularities, depletion singularities
no definition is as yet available in the Clarifications Archive, but see pp. A-9 through A-17 in --
http://www.dialectics.org/dialectics/Primer_files/3_F.E.D.%20Intro.%20Letter,%20Supplement%20A-1_OCR.pdf

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