Dear Reader,
Why are the LHSs [Left-Hand-Sides] of the F.E.D. 'dialectical equations' always 'cumulum' symbols -- symbols like --
>-|-<tau
-- for Historical Dialectical 'Meta-Models', and like --
)-|-(stage
-- for Systematic Dialectical 'Meta-Models',
both being symbols for a heterogeneous, non-reductionist, non-amalgamative sum of dialectical ontological category symbols -- rather than [, in the case of Historical Dialectics,] symbols for the single new category that is the new category irrupted into existence in the "natural revolution" that characterizes each next epoch of cosmological "meta-evolution"?
In the sphere of Historical Dialectics, when we are dealing, for example, with the F.E.D. Dialectical 'Meta-Model' of the Dialectical History of the Cosmos as THE Totality, which takes the ontological category of the pre-nuclear "particles" [e.g., "quarks" and "gluons"], connoted by n, as its beginning category, or <<arche'>>, why is it correct that we obtain, for the ontological "state", or "dynate", of the cosmos by the end of epoch tau = 1 --
>-|-<1 = <n>^(2^1) = <n>^2 = n + s?
Furthermore, why is it correct that we obtain, for the ontological "state" of the cosmos by the end of epoch tau = 2 --
>-|-<2 = <n>^(2^2) ~= <n>^4 = n + s + q/sn + a
-- wherein a connotes the ontological category of the atoms [e.g., Helium], which are "meta-sub-atomic particles", each one made up out of a heterogeneous multiplicity of sub-atomic "particles", instead of just --
>-|-<2 = <n>^(2^2) ~= <n>^4 = a?
Why do previously-irrupted ontological category symbols continue to appear in these dialectical-algebraic representations, with the most-recently-irrupted ontological category symbol(s) "added" to them?
With respect to Historical Dialectical Meta-Models, we can answer that this continued double presence of the symbols of the past-irrupted -- both outside and "inside" the "eventities" most-recently irrupted, represented by the "right-most" symbol in the "cumulum" sum in each case -- is empirically, experientially correct, is a correct mathematical <<mimesis>> of experienced actuality.
The reason is this --
Just because the ontological category of sub-atomic "particles" has just irrupted into existence, as a qualitatively new kind of "cosmo-ontology", by the "flash" self-conversion into sub-atomic "particles" "onto-mass" of some of the former pre-nuclear "particles" "onto-mass", does not mean that all of the pre-nuclear "particles" ontological content of the cosmos will be instantaneously, or ever, converted into sub-atomic "particles" ontological content.
And, an epoch later, just because the ontological category of "atoms" has just irrupted into existence, as a qualitatively new kind of "cosmo-ontology", by the "flash" self-conversion into "atoms" "onto-mass" of some of the former sub-atomic "particles" "onto-mass", does not mean that all of the sub-atomic "particles" ontological content of the cosmos will be instantaneously, or ever, converted into "atoms" ontological content.
Our instrumentation-mediated senses continue to detect evidence of the presence of "matter" self-organized to no greater level of organization than the pre-nuclear level, not only immediately after the first irruption of "matter" self-organized up to the sub-atomic level, but no higher, but still to this very day, after many irruptions of matter self-organized to many even higher levels than the sub-atomic, in the ontological epochs since epoch tau = 1.
"Pre-nuclear particles" continue to be present in the cosmos "inside of" "sub-atomic particles". For example, protons are "made up out of" quarks.
"Pre-nuclear particles" continue to be present in the cosmos "outside of" "sub-atomic particles". For example, "Big Bang" born microwave background radiation photons continue to abound in the present cosmos, and free neutrinos continue to abound in the present cosmos.
Likewise, after the first irruption of <<monads>> or "units" of "matter" self-organized up to "atomic" level but no higher, still, and still to this day, <<monads>> of "matter" self-organized up to the "pre-nuclear particle" level, but no higher, and "matter" self-organized up to the "sub-atomic particle" level, but no higher, continue to be extant in our cosmos, outside of "atomic" level "matter".
Of course, sub-nuclear <<monads>> and sub-atomic <<monads>> continue to be extant inside of "atomic" level "matter", because, e.g., protons are made of quarks, and gluons, and because the nuclei of atoms are made, in part, of protons.
That is, the physical, historical cosmos is "evolute", not "convolute".
In paleontological parlance, an "evolute" spiral shell is one whose past whorls are still visible together with its latest whorl, because the shell grows in a "vertical" direction, so that succeeding whorls do not hide preceding whorls from view, side-on.
A "convolute" spiral shell grows outward on a single "vertical" level, so that successor whorls do hide predecessor whorls from side-on view.
For epoch tau = 1, for --
>-|-<1 = n + s
-- per F.E.D., the n is called the "tail" or rearguard of the categorial progression, and s is called the vanguard or '[meta-]meristem' ["growing edge"].
Likewise, for tau = 2, in --
>-|-<2 = n + s + q/sn + a
-- per F.E.D.,
n + s + q/sn
is called the "tail" of the progression, and
a
is called its '[meta-]meristem', or "vanguard".
So much for the diachronic ontological-categorial progressions of Historical Dialectics, and for their having an "evolute", "tail"-versus-"meristem" sub-structure.
But what of the ~synchronic categorial progressions of Systematic Dialectics?
Why should the stages of a Systematic-Dialectical categorial-progression presentation of a theorized totality exhibit this "evolute", "tail"-versus-"meristem" sub-structure?
Hypothesis: The "evolute", "meristem"-vs.-"tail" sub-structure of the content of Systematic-Dialectical categorial progression presentations has a different, human-cognitive, causation and justification, vis-a-vis the causation / justification of the similar sub-structure in the sphere of Historical Dialectics.
More about this will follow, in my future post(s).
F.E.D. sources tapped for this exposition --
(1) Supplements to the F.E.D. Introductory Letter, Supplement B., Part II., Example 3.: a ‘‘‘Historical-Dialectical’’’ Mathematical Model of The Dialectic of Nature, pp. B-19 through B-22.
http://www.dialectics.info/dialectics/Welcome.html
http://www.dialectics.info/dialectics/Primer.html
http://www.dialectics.info/dialectics/Primer_files/4_F.E.D.%20Intro.%20Letter,%20Supplement%20B-1,%20v.2_OCR.pdf
(2) The Q, or Purely-Qualitative, Dialectical Algebra as <<Characteristica Universalis>>: A Step-by-Step Guide on How to Use It as an <<Organon>> for Discovery, Example 1., pp. 7-11.
http://www.dialectics.info/dialectics/Briefs.html
http://www.dialectics.info/dialectics/Briefs_files/_Brief1-29JUL2008_OCR.pdf
(3) A Dialectical Theory of Everything -- A Graphical Manifesto; graphics / narratives / formulas modules 21 & 121.
Regards,
Miguel
F.E.D. Definitions of special terms utilized above --
<<arche'>>
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Arche/Arche.htm
convolute
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Convolute/Convolute.htm
cumulum
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Cumulum/Cumulum.htm
diachronic
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Diachronic/Diachronic.htm
dynate
No definition for this term is as yet available in the Clarifications Archive.
epoch
No definition for this term is as yet available in the Clarifications Archive.
eventity
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Eventity/Eventity.htm
evolute
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Evolute/Evolute.htm
historical dialectics
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/HistoricalDialectics/HistoricalDialectics.htm
[meta-]meristem
No definition for this term is as yet available in the Clarifications Archive.
meta-model
No definition for this term is as yet available in the Clarifications Archive.
<<memesis>>
No definition for this term is as yet available in the Clarifications Archive.
<<monad>>
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Monad/Monad.htm
non-amalgamative sum
No definition for this term is as yet available in the Clarifications Archive.
ontological category
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Onto/Onto.htm
onto-mass
No definition for this term is as yet available in the Clarifications Archive.
<<organon>>
No definition for this term is as yet available in the Clarifications Archive.
~synchronic
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Synchronic/Synchronic.htm
systematic dialectics
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/SystematicDialectics/SystematicDialectics.htm
tail
No definition for this term is as yet available in the Clarifications Archive.
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