‘Appropriated
Ambiguities’
in
Dialectical-Algebraic
Category-Symbols.
Dear Reader,
Consider the first eight
category-symbols in the ‘Historical-Dialectic of Nature’ purely-qualitative,
ontological-categorial equation, based upon qr, denoting the ontological category of the “particles” in the “Standard Model
of Particle Physics”, as «arché»-category:
qr23 ¶|-º qr+ qa+ qar+ qm+ qmr+ qma+ qmar+ qp.
We usually
solve for the second algebraic
category-symbol, in this categorial series ‘‘‘sum’’’ of «genos»
category-symbols, whose unsolved form is qrr, as qa, denoting the cosmo-ontological category of atoms.
This means ionic atomic nuclei
that were produced via the initial, ‘Cosmological Nucleosynthesis’ – long
before any stars and their “stellar nucleosynthesis” processes yet existed –
that produced Helium atomic nuclei, Lithium atomic nuclei,
etc., after the “Big Bang” space-time-mass-energy plasma-ball expanded sufficiently, hence cooled
sufficiently, for such combinations of protons and neutrons to be sustained,
rather than immediately disintegrated by their hyper-high-energy surroundings.
But that single-meaning
interpretation is based upon our ‘“principal value”’ or
‘principal species’ convention.
More generally, as a «genos»
category-symbol, qrr connotes more than a single species; connotes its multiple species of units that are combinations of “particle” units, that are implicit within the qrr «genos»-category.
Algebraic, unsolved
category-symbol qrr stands for a new «genos»-category of units which are combinations of “particles”; or for [meta-]“particle” units, each one made up out of multiple “particle” units,
or for the self-conversions of multiple “particle” units into such single ‘meta’-“particle” units.
That generic description
certainly describes atoms, each typical, neutral atom unit being made up out of a
heterogeneous multiplicity of electron “particle” units, proton “particle” units and neutron “particle” units.
However, it also fits for the
self-transition of “non-composite particle units” into “composite particle units”, which
comes before, and transitional to, the formation of atom units.
That is, both the proton unit and
neutron unit components of atom units, are themselves “composite particle” units,
composed of the “non-composite particle” units, known as “gluon” units and “quark” units.
Electron units are “non-composite
particle
units”, so that, in these terms, atom units are hybrid meta-units, combining “composite particle units”
and/with “non-composite particle units”.
When we apply
the ‘principal species principle’, we usually choose the more widely-known
and more familiar – hence more mnemonic – species-category name to abbreviate
the «genos»-category name, as here: using qa as our
shorthand representation for the, specific, atom units category.
But it is important to
remember that qrr connotes also other species-categories within this «genos»-category – not just the atom units species-category.
A better, more
species-encompassing, if less mnemonic, decoding of the qa «genos»
category-symbol would be a definition such as ‘units each of which is a self-aggregation of [multiple, typically diverse] “particle” units’.
Similarly, with our
solution for the fourth «genos» category-symbol – the initially algebraic-unknown category-symbol qaa.
We solve it as qm, standing for the cosmo-ontological category of “molecule” units.
Again, we see
the “molecule” units category, or, e.g., the “molecular cloud” units cosmo-ontological category, as the
‘principal species-category’ of «genos»-category qaa.
However, the combinations of
atoms with atoms «genos»-category, which this category-symbol connotes, includes also other species than that of molecule units, including a
transitional species-category, situated chronologically and ‘contentally’ in
between the qrr atom-units ontology species-category and the qm molecule-units ontology
species-category.
This other species-category of the qaa «genos»-category of ‘[meta-]atom units, each one made up out of multiple atom units’, or of ‘atom units self-converted into meta-atom units’, also
describes the more complex atom units, of higher atomic number and of higher atomic
weight – beyond the cosmological nucleosynthesis products, e.g., Helium atom units and Lithium atom units – that arise via the subsequent, stellar nucleosyntheses
in the hearts of stars.
That stellar
nucleosynthesis synthesizes bigger, heavier nuclei that increasingly
“metalize” the initial compositions of subsequent generations of star units.
This “metalization” lays the
groundwork for the spinning disk nebulae units that, by self-gravitation, precipitate
out of such higher-atomic-species-enriched molecular cloud units, to become, no longer
merely single star units, double star units, etc., but star units with planet units.
Many of these higher atomic
species units can even be described as combinations [‘“fusions”’] of 3 or more Helium nuclei
– e.g., Carbon atom units, atomic number 6, »combining 3 Helium nuclei, and Oxygen atom units,
atomic number 8, »combining 4 Helium nuclei.
A
better, more species-encompassing, if less mnemonic, decoding of the qm «genos»
category-symbol would be a definition such as ‘units each of which is a self-catalyzed
manifold of [multiple, typically diverse] “atom” units’, especially when crystals, metal ores and rocks, etc., are taken into account.
Likewise, for our solution for the eighth
«genos» – the initially algebraic-unknown category-symbol qmm.
We solve it as qp, standing for the Terran ontological category, and possible cosmo-ontological category, of “prokaryotic living cell units”.
Again, we see
the “prokaryotic living cell units” Terran ontological category, which
is possibly also a cosmological-ontological category, widespread throughout our cosmos, as the ‘principal species-category’
for/within/inherent in/immanent to «genos»-category qmm.
However, the ‘combinations of molecule units
and/with other molecule units’ «genos»-category, which this category-symbol connotes, includes also other species-categories than the species-category of molecule units, including a
transitional species-category, situated chronologically and ‘contentally’ in
between the qm molecule-units-ontology species-category and
the qp “prokaryotic living cell units”-ontology species-category.
This other species-category of «genos»-category qmm, for ‘[meta-]molecule
units, each unit made up out of multiple molecule units’, or of ‘[micro-]molecule units self-converted into
meta-molecule units’, also describes the more complex, ‘meso-molecular’
molecule units and “macromolecule” molecule units, of higher complexity, higher 3-D volume and higher
mass – the ‘“poly-mers”’, beyond the mere ‘‘‘mono-mers’’’, or even ‘sub-mono-mers’,
such as H2, O2, H2O, CO2, NH3 and CH4.
The “macromolecule” units include “polymer” units such as ‘“poly-saccharide”’ units, ‘“poly-peptide”’ units, or ‘“poly-amide”’ units, that
form “protein macromolecule” units, and the ‘‘‘poly-nucleotide’’’ units that form RNA and DNA units.
Other widely-familiar “macromolecule” units include
chlorophyll units, crucial to plant photosynthesis of food molecule units, and hemoglobin units, crucial to the blood-transport of Oxygen molecule units, O2, for respirative metabolism, to the eukaryotic cell units inside ‘multi-[eukaryotic-] cellular’ animal organism units.
“In biological contexts, essentially all biological macromolecules – i.e., proteins (polyamindes), nucleic acids (polynucleotides), and polysaccharides – are purely polymeric, or are composed in large part of polymeric components.”
Note also that each polymer ‘meta-unit’, is the result of a Nature-dialectical, ‘self-aufheben meta-unit-ization’ combination of a (typically very large) multiplicity of former ‘mere mer’ units.
The formation of some of
these “macromolecule” units – outside of prokaryotic cell units, and before
prokaryotic cell units came into existence, or even could come into
existence – formed a necessary prelude and de facto preparation for the
possibility of the pre-human-natural formation of living prokaryotic cell units.
A better, more species-encompassing,
if less mnemonic, decoding of the qp «genos»
category-symbol would be a definition such as ‘units each of which is a self-catalyzed
‘poly-molecular’ spontaneous natural
formation unit made up out of multiple “monomer”, “molecular”
units’.
So far, we have considered
the connotational surfeits, the expanded meanings, only of the ‘self-hybrid’,
‘auto-hybrid’ cosmological-ontological category-symbols qrr, qaa and qmm, all arising with in the third
epoch, the ordinal t = 3 epoch, of the ‘Dialectic of Nature meta-equation’, whose
LHS is qr2t, for t = 3.
What of the “merely hybrid”, ‘allo-hybrid’
cosmological-ontological categories of this t = 3
cosmo-ontological categorial progression, namely – qar, qmr, qma & qmar?
Well, let’s consider «genos»
category-symbol qar.
We usually take,
as the ‘principal species-category’ of this «genos»-category,
that cosmo-ontological category whose units are first-generation, initial-generation stars, solving, e.g., as follows: qar |-º qi.
First generation stars, we
hold, are generally supersized stars, formed, by self-gravitational
self-condensation/-‘self-densification’, not from
not-yet-existent “molecular clouds”, but from minimally-metalized
and virtually molecule-less ‘atomic clouds’, made mostly from hot
atomic Hydrogen and atomic Helium atom units.
These earliest stars have a
Helium-atoms-dominated outer layer, surrounding a hyper-hot stellar core of ‘plasma-ized’
Hydrogen atoms, i.e., a core of dissociated protons and electrons – a proton-electron
plasma – thereby sustaining thermonuclear fusion reactions that produce “di-protons”,
which become Helium atom units, during these star units’ stay on the stellar “main sequence”.
Thus, these initial stars fit the category-description ‘qar’; they combine a [Helium] atoms surround with a “particles” [protons and electrons] core, converting proton “particles” into Helium atoms by stellar nucleosynthesis fusion process.
That’s a “macroscopic”
meaning for category-descriptor ‘qar’.
But there is also a, ‘co-chronological’,
“microscopic” meaning connoted by
‘qar’ as
well.
Recent research indicates
that HeH+ “molecules” are both the first “molecules” to arise
in our cosmos, and are also “molecules” that act as an accelerant for first-generation
star formation.
But is HeH+ really a “molecule” at all?
The crux for this question is
the nature of the
H+ “ion”.
The H+ “ion” is actually not an atom at
all. It is a “naked” proton “particle” – naked of any electron “particles” at all.
Thus each HeH+ unit is a close association of a proton “particle” unit, H+, with a Helium
atom unit, with an
atomic nucleus
containing two protons and two neutrons, and with two electrons – electrons that
make this closeness of association of an He atom unit with a proton particle unit possible – electrons that resonate around
that Helium atomic nucleus, and that also share themselves
with the H+
proton particle unit.
Therefore, the HeH+ units, ‘mis-nomered’ as “molecule” units, actually fit the qar category-symbol’s
category-description, as a microscopic correspondence with the macroscopic
meaning of qar, and
do not fit the category-description qaa |-º qm.
In
summary, we have seen that these, NQ arithmetic for dialectics symbolic ambiguities can be appropriated so
as to enrich the interpreted meaning and model-fitness of those
category-symbols that exhibit such connotational multivalence ambiguities.
These
connotational multivalences, that register implicit multiple-species
sub-categories hidden within NQ dialectical-algebraic ontological «genos»
category-symbols, can also be grasped as a call for the ‘explicitization’
of the «genos»/multiple-species
categorial relationships.
Immanently
to the NQ dialectical
algebra, this means a call for progression, from the N Q_ [---) q2 category of axioms-systems
of dialectical arithmetic, to at least the –
Nq_BA [---) q24
–
24th step in that long-form dialectical progression of categories of
arithmetics for modeling dialectics, wherein generic dialectical, “purely”-qualitative
‘meta-number meta-numerals’ of the form –
_____b______
(a1 +…+ aW)
–
arise, conforming, in ‘content-structure’, to that of classical Platonian «arithmos eidetikos» dialectic, with their b’s
standing for a generic single «genos»
category, and with their (a1 +…+ aW)’s standing
for the, “non-amalgamative”, «asumbletoi» “sum” of all of their species categories,
that inhere in, and that are abstractly encompassed by, those «genos» categories, the b’s.
For more
information regarding these
Seldonian insights, and to read and/or download, free
of charge, PDFs and/or JPGs of Foundation books, other texts, and images, please see:
www.dialectics.info
For partially pictographical, ‘poster-ized’ visualizations of many of these Seldonian insights -- specimens of ‘dialectical art’ – as well as dialectically-illustrated books
published by
the F.E.D. Press, see –
https://www.etsy.com/shop/DialecticsMATH
¡ENJOY!
Regards,
Miguel
Detonacciones,
Voting Member, Foundation Encyclopedia Dialectica [F.E.D.];
Elected Member, F.E.D. General Council;
Participant, F.E.D. Special Council for Public Liaison;
Officer, F.E.D. Office of Public Liaison.
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