Full Title: Part III. B. Epoch tALL = 2: molecules emergent.
The Dialectic of Nature.
Dear Reader,
The present blog-entry is the fourth blog-entry in this series on the dialectical ‘meta-modeling’ of the natural history of the total cosmos, as presently known to science [except that the main ‘meta-model’ narrated herein does not yet directly and explicitly address either “Dark Energy” or “Dark Matter”].
The epoch of that natural history of the cosmos addressed in this blog-entry is the tALL = 2 epoch, in which the initial, cosmological -- cosmos-wide -- ‘neo-ontology’ of molecules is first ‘irruptant’.
Regards,
Miguel
Part III. B.: Depiction -- Dialectical-Mathematical Meta-Model Story of our Cosmos --
Epoch tALL = 2: molecules emergent.
Part III. B.: Narration -- Dialectical-Mathematical Meta-Model Story of our Cosmos --
Epoch tALL = 2: molecules emergent.
Recounting the Story of the Next Chapter of the Ontological Self-Revolutions of Pre-Human Cosmological Nature, Dialectical-Mathematically as well as Narratively.
Please Note: Throughout this blog-entry, we employ two key ancient scientifico-philosophical terms.
Their resurrection in the present also serves well to catalyze an urgently needed future transition,
to a ‘trans-modern’, science --
1. «Monad», which means, e.g., “qualitative Unit”, “qualitative logical Individual”, or “qualitative Element” -- a single one of the many like-kind constituents represented, collectively, by a “category”, and;
2. «Arithmos» [plural: «arithmoi»], which means a “category”, e.g. an “ensemble”, a “multitude”, a ‘“population”’, or an “assemblage” of «monads» -- i.e., of “qualitative units”, of “qualitative logical individuals”, or of “qualitative elements” -- all of which «monads» share a common quality, or a common predicate, i.e., a «categorema» in common; a like “kind”.
Please Note Also: 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 only].
The Dialectical ‘Theory of Everything’ Equation for Epoch tALL = 2 --
Irruption of the molecules-as-Monads ‘Cosmo-Ontology’ via ‘Self-Meta-Monadization’ of atoms «Monads».
The dialectical ‘meta-equation meta-model’ of the total cosmos which we will be exploring, and iterating, for escalating values of its “discrete time” parameter, or ‘epoch parameter’, denoted by tALL, and whose story we will be narrating throughout this series, is the following --
ALL>-|-<tALL = < ALLr >2tALL
-- wherein ALLr denotes the primordial ‘cosmo-ontological category’ of pre-nuclear “particles”, i.e., denotes the category of “elementary” and composite bosons and fermions, as well as of anything else actually existent in primordial Nature, but presently unknown to the human sciences.
In the present blog-entry of this series of blog-entries, we will be narrating those parts of our, and of its, ‘‘‘story of everything’’’, that inhere in the 2nd epoch, per this ‘meta-equation’, i.e., that inhere in the equation that inheres in this ‘meta-equation’ for the tALL = 2 value of its discrete-time, epoch parameter, tALL.
2. Epoch tALL = 2: molecules ontology ‘irruptant’ --
A general overview of the crucial role of specifically molecular ‘cosmo-ontology’ can be gleaned from the concluding summary of the 2013 book The Cosmic-Chemical Bond: Chemistry from the Big Bang to Planet Formation, by D. A. Williams and T. W. Harquist --
“The [MD: rather recent] discovery of molecules in interstellar space has revolutionized astronomers’ view of the Universe.”
“...It is now recognized that molecules are required to provide cooling mechanisms for gas in the processes of collapse to form proto-galaxies and proto-stars.”
[D. A. Williams and T. W. Harquist, The Cosmic-Chemical Bond: Chemistry from the Big Bang to Planet Formation, The Royal Society of Chemistry [Cambridge: 2013], p. 199, emphases added by M.D.].
2.1 Formulaic Summary for the Second Full Epoch of ‘Cosmological Meta-Evolution’. An ‘Ideographized’ /- ‘ideogramized’, “shorthand” summary of the narrative rendition below.
If tALL = 2, then --
ALL>-|-<tALL = ALL>-|-<2 =
< ALLr >22 =
< ALLr >4 = ALLr2 x ALLr2 =
< ALLr + ALLa > x < ALLr + ALLa > =
< ALLr + ALLa > + Delta< ALLr + ALLa > =
ALLr + ALLa + ALLqar + ALLqaa.
-- as tALL = 1 → tALL = 2.
The ‘epoch 2’ equation will feature a ‘poly-qualinomial’ and “non-amalgamative sum”, containing of 22 = 4 category-symbols.
The ‘epoch 2’ equation will still include the ‘since epoch 0’ ontology of our «arché» cosmological
category, denoted by ALLr, as [possibly] still existent, as well as the ‘since epoch 1’ ontology of atoms, denoted by ALLa, as [possibly] still existent as of and throughout ‘epoch 2’.
However, our ‘epoch 2’ equation also includes a third ‘cosmo-ontological’ category-symbol, for a
predicted / ‘retrodicted’ / reconstructed [possible] new ontology, that of a new, third,
hybrid/synthesis «arithmos» of «monads», one of a qualitatively different kind of «monads»,
or of units, than the units of the first, ALLr, «arithmos» of «monads», and than the units of
the second, ALLa, «arithmos» of «monads», and such that this third [possible] «arithmos»
of «monads» is denoted, ‘‘‘algebraically’’’, byALLqar.
Moreover, our ‘epoch 2’ equation includes, in addition, a fourth ‘cosmo-ontological’ category-symbol, for another predicted / ‘retrodicted’ / reconstructed [possible] new ontology, that of a new, fourth, «arithmos», one of a qualitatively different kind of monads, or of units, than the units of
the first, ALLr, «arithmos» of «monads», and than the units of the second, ALLa, «arithmos»
of «monads», as well as than the units of the third possible -- hybrid -- «arithmos»
of «monads», denoted, ‘‘‘algebraically’’’, by ALLqar, with this fourth possible «arithmos»
of «monads» being denoted, ‘‘‘algebraically’’’, by ALLqaa.
Our task, with respect to this epoch tALL = 2 model-equation, of our overall ‘meta-model
meta-equation’, is the “solve for” the meanings of these two new terms, ALLqar and ALLqaa,
that is, to identify the two already known categories of ‘cosmos-ontology’ that came into
existence next after the irruption into existence of ALLa, and as an outgrowth of/from ALLa,
by means of -- respectively -- a hybridizing interaction of «monads» of the ALLa «arithmos»
with «monads» of the ALLr «arithmos», and of a self-«aufheben» ‘self-meta-monadization’
of «monads» of the ALLa «arithmos».
The standard “first try” method of solution for ‘dialectical-algebraic unknown’ terms of the form,
ALLqaa, is to scan our knowledge of Nature for units, or «monads», each of which can be
aptly characterized as ‘a meta-ALLa unit, each one made up out of a heterogeneous multiplicity
of ALLa units’ -- i.e., ‘a meta-“atom” unit, each one made up out of a [typically] heterogeneous
multiplicity of “atoms” ’.
To our minds, the natural formation that “fills this bill” is called the “molecule”.
Each typical “molecule” unit is made up out of two or more “atom” units.
But the simplest such ‘meta-«monad»’ -- a kind of ‘meta-«monad»’ that is composed of a
‘homogeneous multiplicity’ of ALLa “atom” «monads» -- i.e., the simplest and most
cosmologically-prevalent molecule «monad» -- especially so during the epoch of the first
‘irruptancy’ of molecular ontology in our cosmos, i.e., in tALL = 2 -- is the diatomic
Hydrogen molecule, H2, which is a ‘homogeneous minimal multiplicity’ of thus
exactly 2, mutually chemically-bonded Hydrogen atom «monads» -- two ALLa units.
The rare, most complex such ‘meta-«monads»’ so far found in interstellar space today, i.e., in
the present cosmological epoch -- molecules which are, indeed, made up out of
‘heterogeneous higher multiplicities of ALLa «monads»’ -- include methanol [CH3OH,
containing 6 atoms], ethanol [CH3CH2OH, containing 9 atoms], dimethyl ether
[CH3OCH3, containing 9 atoms], and propanal [CH3CH2CHO, containing 10 atoms],
as well as cyanodecapentayne [HC10CN, containing 13 atoms] -- discovered first in
interstellar space; only later, guided by that astronomical characterization, duplicated in
Earthly laboratories -- and, perhaps also [“the jury is still out” as of this writing],
Polycyclic Aromatic Hydrocarbons [PAHs], which may contain up to 100 atoms,
with Carbon atoms in hexagonal arrays [i.e., in graphite-like arrays], terminated by
peripheral Hydrogen atoms or by other molecular sub-structures.
However, most of this latter-day abundance, and richness of diversity, of molecular species
in the interstellar medium of our galaxy, and of other galaxies, is the product, not of ALLqaa,
i.e., not of the “original accumulation” of molecular «monads», and of the epoch of the
‘“formal subsumption”’, of atomic, and of previous, ‘cosmo-ontology’, by molecular
‘cosmo-ontology’, i.e., does not belong to our model’s epoch tALL = 2.
Rather, most of the diversity of the mass-energy in our cosmos, that is organized up to the
molecular level of organization of matter-energy, but no higher, is the product of the later,
next epoch of cosmological ‘‘‘meta-evolution’’’, namely, of epoch tALL = 3, the epoch of
the ‘reproductive accumulation’ of molecular ‘cosmo-ontology’; the epoch of the ‘‘‘real
subsumption’’’ of prior, atomic, and earlier, ‘cosmo-ontology’, by molecular
‘cosmo-ontology’, as represented by new terms/category-descriptions of the tALL = 3 equation,
such as ALLqma and ALLqmar.
We can assert [‘|-.’] this solution for the meaning / “intension” / “connotation” of the algebraic
unknown term ALLqaa, formally, as follows, using ALLm to connote the category named
“molecules” --
ALLqaa |-.= ALLm.
Our partial solution, so far, to our epoch tALL = 2 dialectical-algebraic equation --
ALL>-|-<2 =
ALLr + ALLa + ALLqar + ALLqaa
-- containing two initially known, or previously solved, category-symbols --
ALLr, and ALLa
-- and two initially unknown category-symbols --
ALLqar, and ALLqaa
-- is therefore now --
ALL>-|-<2 =
ALLr + ALLa + ALLqar + ALLm
-- an equation which now contains three known category-symbols for epoch 2 --
ALLr and ALLa and ALLm
-- and one remaining “unsolved-for” / “to be solved-for”, unknown category-symbol:
ALLqar.
In the above -- thus partially “solved” -- equation, the ALLr term is still there, because some
epoch 0 pre-atomic “particles” still persist in[to] epoch 1, and because some epoch 1
interactions among pre-atomic “particles” -- e.g., some high energy collisions among
the ALLr, which produce other constituents of ALLr -- still reproduce results that remain
[within] ALLr.
The ALLqrr |-.=ALLa term is also still there, in that equation, to represent those lasting
products of ALLr with ALLr interactions that produce atoms, the category denoted by ALLa.
Our remaining task, with respect to this epoch tALL = 2 model-equation -- an equation that
inheres in our overall ‘meta-model meta-equation’ -- is the “solve for” the meaning of the
remaining new term, ALLqar, that is, to identify that already known category of
‘cosmological-ontology’ that came into existence next after the irruption-into-existence of
ALLa, and by means of a hybridizing interaction of «monads» of the ALLa «arithmos»
with «monads» of the ALLr «arithmos», and as a joint outgrowth of/from ALLa, and ALLr.
The standard “first try” method of solution for ‘dialectical-algebraic unknown’ terms of the form,
ALLqar, is to scan our knowledge of Nature for units, or «monads», each of which can be
aptly characterized as a combination, composite, or ‘‘‘complex unity’’’ of units of the
ALLqa «arithmos»/category, with units of the ALLqr «arithmos»/category -- e.g.,
a ‘‘‘synthesis’’’ of ALLqas and ALLqrs, and/or a formation that converts ALLqrs
into ALLqas, and in which that conversion of ALLqrs is catalyzed by the presence, and
involvement, of ALLqas.
To our minds, the ‘natural self-formations’ that “fill this bill” are, primarily, those intra-galactic atomic nuclei / pre-atomic “particles” co-formations known as stars, primarily in the internal stellar processes known collectively as (1) “stellar nucleosynthesis”.
Secondary processes that also fit this ALLqar description include: (2) processes of
pre-atomic “particle(s)” capture and absorption by atomic nuclei, including those associated
with novae and super-novae end-stage stellar self-explosions, (3) processes of spontaneous
radioactive decay of atomic nuclei, typically emitting pre-atomic “particles” in that process,
and (4) those processes of “spallation”, in which bombardment of atomic nuclei by, e.g.,
“cosmic ray” pre-atomic “particles”, converts some of the [e.g., more abundant] species of
atomic nuclei into some of the [e.g., rarer] atomic nuclei species.
Processes (3) in the list above are described, by Harry Y. McSween, Jr., and Gary R. Russ, in their 2010 book Cosmochemistry, as follows --
“In addition to the processes of stellar nucleosynthesis, there are two other ways in which isotopes are produced.”
“One is radioactive decay.”
“Many of the nuclides produced by explosive nucleosynthesis [M.D.: Our ‘(2)’ in the list above] are unstable and decay to stable nuclei with timescales ranging from a fraction of a second to billions of years.”
“Those with very short half-lives decayed completely into their daughter isotopes before any evidence of their existence was recorded in objects from our solar system. However, radioactive nuclei from stellar nucleosynthesis that have half-lives of > 100,000 years left a record in solar system materials.”
“The ultimate fate of all radioactive nuclides is to decay to their stable daughter nuclides.”
“Thus, the only real distinction between isotopes produced by stellar nucleosynthesis and those produced by radioactive nuclides produced by stellar nucleosynthesis [M.D.: in particular, by “explosive” stellar nucleosynthesis, e.g., in stellar supernovae star death] is the time scale of their decay.”
[Harry Y. McSween, Jr. and Gary R. Huss, Cosmochemistry, Cambridge University Press [NY: 2010], p. 80, emphases added by M.D.]
Processes (4) in the list above are described, in the same text, as follows --
“Irradiation of matter by high energy particles, primarily protons and [alpha-]particles [M.D.: i.e., Helium nuclei], can change one isotope into another.”
“These high-energy particles are typically called cosmic rays, and they can originate either in the Sun or in a variety of environments elsewhere in the galaxy.”
“Spallation reactions are those in which a nucleus is split by an incoming cosmic ray into two or more smaller nuclides. Much of the lithium, beryllium, and boron in the galaxy is produced by cosmic-ray-induced spallation on abundant species such as 12C, 16O, 20Ne, 24Mg, and 28Si.”
“Spallation reactions often release neutrons, which can be captured by other nuclides. In the outer meter or so of asteroids and other solid objects, these secondary neutrons from spallation reactions in the surface layer can produce measurable changes in the isotopic compositions of the constituent elements.”
[Harry Y. McSween, Jr. and Gary R. Huss, Cosmochemistry, Cambridge University Press [NY: 2010], pp. 80-81, emphases added by M.D.]
We therefore denote the univocal category for all four of these ALLqar processes by ALLs.
We can assert [‘|-.’] this solution for the meaning / “intension” / “connotation” of the algebraic
unknown term ALLqar, formally, as follows, using ALLs to connote the category of
“nucleosynthetic” processes --
ALLqar |-.= ALLs.
Our full solution to our epoch tALL = 2 dialectical-algebraic equation, whose unsolved form [for its latter two terms] is --
ALL>-|-<2 =
ALLr + ALLa + ALLqar + ALLqaa
-- containing two, initially known, or previously solved, category-symbols -- ALLr, and ALLa -- and two initially unknown category-symbols, ALLqar, and ALLqaa, is therefore now --
ALL>-|-<2 =
ALLr + ALLa + ALLs + ALLm
-- an equation which now contains only known category-symbols -- exactly four known
category-symbols, for epoch 2: ALLr and ALLa and ALLs and ALLm.
1.2 Narrative Summary for ‘epoch tALL = 2’.
Suppose that we extend, ‘‘‘universalize’’’, or ‘«gene»-realize’ Marx’s ‘«speci»-al’ application
of his terms “formal subsumption” versus [followed by] “real subsumption” -- and of his
term “original accumulation”, versus [followed by] ‘‘‘reproductive accumulation’’’ -- from
the historically- «speci»-fic contexts of subsumption by capital / by “the capital relation”, and
of capital accumulation, to the processes of the historical dialectic of nature in general.
If we do so, we can then comprehend the ‘meta-model’ epoch in which the «monads»
that constitute the molecules ‘cosmo-ontological category’ --
ALLqaa |-.= ALLm
-- first irrupt into existence, namely, ‘epoch tALL = 2’, as the cosmological epoch of the
‘‘‘REAL subsumption’’’ of all ‘cosmo-ontology’ ‘irruptant’ prior to the irruption of
ALLa [namely, ALLr], by the superseding ‘cosmo-ontology’of atoms, ALLa.
We can also comprehend epoch 2 as that of the merely “FORMAL subsumption” of all
epoch-2-extant ‘cosmo-ontology’, ‘irruptant’ prior to the irruption of ALLm [namely, ALLr
and ALLa], by ALLm, where ALLm is one of the two ‘newly-irruptant’ ‘cosmo-ontologies’
of epoch 2.
Epoch 2 is not yet the epoch of the ‘‘‘REAL subsumption’’’ of ALLr , and of ALLa, by ALLm.
That distinction awaits epoch tALL = 3.
As of ‘meta-model’ epoch 2, the superseding ‘cosmo-ontology’ of molecules, ALLm, has just
come into existence, from out of the densest hearts the cosmological nucleation zones of its
immediate-predecessor ‘self-hybrid’ ‘cosmo-ontology’, ALLa.
However, as of the end of ‘meta-model epoch tALL = 2’, the molecules ontology has not yet
had time to interact with any of, and thus to [partially] [REAL-ly] subsume, the remaining
pre-atomic “particles” ontology of the cosmos, or the remaining atoms ontology of the
cosmos.
But the interaction, hence the ‘‘‘REAL subsumption’’’, of ALLr, by ALLa -- connoted by the
third category-symbol of this categorial progression, the hybrid category-symbol / [dialectical]
synthesis category-symbol ALLqar -- does ensue, per this ‘meta-model’, during its epoch
tALL = 2.
‘Meta-model epoch tALL = 2’ is also the epoch of the ‘‘‘original accumulation’’’, or of the
‘‘‘primitive accumulation’’’, of the molecules ‘cosmo-ontology’, ALLm, in which some of the
«monads» of the atoms ‘cosmo-ontology’, ALLa, initially, and by processes which may be
‘transitory’and unsustainable, convert themselves into [meta-]«monads» of the molecules
‘cosmo-ontology’, ALLm.
The ‘‘‘reproductive accumulation’’’ of molecules ‘cosmo-ontology’, ALLm -- by means of
new processes which represent pathways for the continual, ongoing, sustained conversion of
ALLa into ALLm, catalyzed by the presence, and by the involvement, of the ALLm already,
earlier created, as well as by ALLm created later, by these new processes themselves -- only
arrives with the arrival of ‘meta-model epoch tALL = 3’.
It arrives in the form of its / this meta-model’s fifth, sixth, and seventh category-symbols --
ALLqmr, ALLqma, and ALLqmar, respectively -- which connote the conversion of
the products of the interactions, OF ALLr, ALLa and ALLqar ontology, catalyzed to do so
BY the presence of, and by the involvement of, i.e., with the help of, ALLm ontology, INTO
ALLm ontology, especially, initially, via the ontology that resides on the borderline between
ALLm and ALLa, namely “Di-atomic” Hydrogen molecules, denoted by H2.
It thus arrives in the form of the ALLr / ALLa / ALLqar-mediated autocatalysis of ALLm.
These later processes, connoted by our meta-model’s ‘cosmo-ontological category-symbols’,
ALLqmr, ALLqma, and ALLqmar, include processes that cosmologists describe as the
formation of galactic, interstellar “molecular clouds”, within which later-generation stars are born, and, with sufficient “metallization” via stellar nucleosynthesis, etc., and with sufficient ‘‘‘molecular coolants’’’ formation, within which also planets -- indeed, within which combined, stellar/planetary systems -- are born.
Cosmologists call the earlier process, connoted by ALLqaa -- the process of what we call
the ‘‘‘original accumulation’’’, or ‘‘‘primitive accumulation’’’, of the first molecular
«monads» -- by names like ‘“primordial cosmochemistry”’, or ‘“primordial
astrochemistry”’, or ‘“primordial galactic chemical evolution”’, as distinct from the later,
‘‘‘reproductive accumulation’’’ forms, in which existing-molecules catalyzed the
synthesis of new molecules, connoted by ALLqmr, ALLqma, and ALLqmar.
The detailed vicissitudes of the irruption of molecules ‘cosmo-ontology’ from out of the
‘‘‘intra-action’’’ of atoms ‘cosmo-ontology’, connoted by ALLqaa, and of the atoms-catalyzed
formation of higher species of atoms [“stellar nucleosynthesis”, etc.] from pre-atomic “particles”
[e.g., from bare protons -- “ionized Hydrogen”], connoted by ALLqar, are addressed by our
epoch 2 ‘dialectical equation’ model, only “connotationally”, or “intensionally”, and summarily --
ALL>-|-<2 =
ALLr + ALLa + ALLs + ALLm
-- and only with deep implicitude, i.e., only at their highest level of gene-rality, and only
purely-qualitatively.
The NQ_ dialectical-ideographical language can also be used to more fully ‘explicitize’
those details, by the formulation of sub-models, tracking the qualitative “dynamics” and
‘meta-dynamics’ “internal” to those categories, i.e., of the sub-categories of / “within”
categories like ALLr and ALLa and ALLs and ALLm, sometimes also plus nested
sub-sub-models, tracking the sub-sub-categories, and so on.
The detailed quantitative determinations of these “dynamics” and ‘meta-dynamics’ are not captured by models that use the language of ‘the Seldonian First Dialectical Arithmetic/Algebra’ --
NqNN = NQ_ [---> q1.
To ‘explicitize’ the population quantity “dynamics” of the successive cosmological ontological category’ ‘qualo-quantitative [meta-]dynamics’ “as a function of time” would require at least ‘the Seldonian Second Dialectical Arithmetic/Algebra’ --
Nq_QN = NU_ [---> q3.
To go further into mathematical-linguistic descriptive richness capability, to explicitly describe the state-variable and control-parameter ‘qualo-quantitative’ ‘Real[-numbers]’ “dynamics” and ‘‘‘meta-dynamics’’’ of the successive cosmological ontological categories, “as a function of ‘Real[-number] time’, would require at least ‘the Seldonian Sixth Dialectical Arithmetic/Algebra’ over the “Real Numbers Field” --
Rq_MQN = Rq_MU = RMu_ [---> q7
-- and would be better served by formulation in later “Real Numbers Field”-subsuming versions of the Seldonian dialectical ideographies / axioms-systems, such as the 15th axioms-system, in which explicit [meta-]dynamical systems can be directly expressed, or such as the 31st axioms-system, in which such systems with explicit sub-systems can be directly expressed, or such as the 63rd axioms-system, in which such systems with explicit sub-systems, each with explicit sub-sub-systems of their own, can be directly expressed, etc. -- i.e., respectively, per the following categories, representing the axioms-systems of the ‘meta-systematic dialectical’ progression of the Seldonian dialectical arithmetics/algebras ‘ideo-ontology’--
Rq_AMQN = Rq_AMU = R, AlphaMu_ [---> q15
-- and --
Rq_BAMQN = Rq_BAMU = R, BetaMu_ [---> q31
-- and --
Rq_GBAMQN = Rq_GBAMU = R, GammaMu_ [---> q63
-- all of which represent solutions for individual category-symbols, or axioms-system-symbols, generated by the ‘meta-model meta-equation’ for the dialectic of the Seldonian dialectical arithmetics itself --
#_)-|-(s# = < #_N_ >2t#_
-- wherein the «arché» axioms-system of arithmetic category, #_N_, connotes the first-order [only] axioms-system of the “Natural” Numbers.
TO BE CONTINUED.
NEXT --
The Dialectic of Nature.
Part III. C.
Epoch t = 3:
pre-eukaryotic living cells emergent.
Hypothetical 'Dialectic of Nature' epoch 9 dialectical/aufheben equation, with "Dark Energy" and "Dark Matter" included:
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