Part III. A. Epoch t = 0. Epoch t = 1: Atoms Emergent. The Dialectic of Nature.

Full Title:  Part III. A.   Epoch t_ALL = 0.   Epoch t_ALL = 1:  atoms emergent.   

The Dialectic of Nature.







Dear Reader,


The present blog-entry is the third blog-entry in this series on the dialectical ‘meta-modeling’ of the natural history of the total, known 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”].


Regards,

Miguel







Part III. A.:  Narration -- Dialectical-Mathematical Meta-Model Story of our Cosmos --
Epoch t_ALL = 0.  Epoch t_ALL = 1:  atoms emergent.  



Recounting the Story of the Opening Chapter of the Ontological Self-Revolutions of Pre-Human Cosmological Nature, Dialectical-Mathematically as well as Narratively.




Please Note:  Throughout this part, 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 t_ALL = 1 --


Irruption of the atoms as Monads ‘Cosmo-Ontology’ via ‘Self-Meta-Monadization’ of ‘Elementary Particles’ «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’, t_ALL, 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., the category of “elementary” and composite bosons and fermions [and of anything else primordially existent, but unknown, as yet, to human science], belongs to a general family of such historical-dialectical ‘meta-models’, whose various features can be defined as follows --

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 0th and the 1st epochs per this ‘meta-equation’, i.e., that inhere in the equations that inhere in this ‘meta-equation’ for the t_ALL = 0 value, and for the t_ALL = 1 value, of its discrete-time, epoch parameter, t_ALL.

0.  “Epoch” t_ALL = 0:  Point of Departure -- “ pre-nuclear, pre-atomic “particles” ” --

Bosonic and Fermionic pre-atomic “particles” form the Given, the Ground, the Premise, the Base, and the Root of this ‘Meta-Model’, and of Its Entire ‘Temporal Qualo-Fractal’ Progression.

0.1  Formulaic Summary for the “ pre-nuclear, pre-atomic “particles” ” «arché» physical-ontological category, during it epoch of sole ‘extantcy’, “epoch 0”. 

This sub-section presents the ‘Ideographized’ / ‘ideogramized’, algebraical/arithmetical, “shorthand” summary of the narrative rendition, below, for our meta-model’s “epoch t_ALL = 0”.

In the following formula, _ALLr denotes the ‘physio-ontological’ category of “ pre-nuclear,

pre-atomic “particles” ”, i.e., of  “elementary” and composite bosons and 

fermions --

If t_ALL = 0, then -- 
   




_ALL>-|-<_tALL  =  _ALL>-|-<₀  =   





< _ALLr >²⁰ = 





< _ALLr >¹   =   _ALLr¹   =   _ALLr.

“Epoch 0” ‘‘‘contains’’’ only the ontology of our «arché» cosmological category, denoted by _ALLr.

0.2  Narrative  Summary for the “ pre-nuclear, pre-atomic “particles” ” «arché» category of physical ontology, during its epoch of sole ‘extantcy’, during which no other cosmological-ontological categories are as yet instantiated, epoch 0.



Brian May, Patrick Moore, and Chris Lintott, writing in the fourth edition of their book Bang!:  The Complete History of the Universe, issued in 2012, characterize what the model narrated herein terms “epoch 0” , in terms of the “Big Bang” theory, as follows --


“Everything, space, time, matter, came into existence with a ‘Big Bang’, around 13.7 billion years ago.”

“The Universe then was a strange place -- as alien as it could possibly be.”

“There were no planets, stars, or galaxies; there was only a melee of elementary particles; these filled the Universe.” 

[May, Moore, and Linott, Bang!:  The Complete History of the Universe, Carlton Books, Ltd. [London: 2012], p. 14]




The early universe -- the “epoch 0” universe, per the ‘meta-model’ narrated in this series -- was not only quantitatively strange:  it was qualitatively strange.

Moreover, that universe was not only qualitatively strange:  it was qualitatively strange in a deep sense.  It was ontologically strange, ontologically alien to contemplate, for us.


What we mean is that the ontological content of the “epoch 0” universe was missing all of the major «monads» that we assign to most of the familiar ontological categories by which we characterize the contemporary cosmos.

Our meta-model’s universe, reconstructed for ‘epoch t_ALL = 0’, is missing essentially all of the «monads» of the atoms, molecules, ‘pre-ekaryotic living cells’, and eukaryotic living cells ‘cosmo-ontological’ categories, as well as those of all of the ‘multi-[eukaryotic-]cellular meta-biota’ [“meta-phyta” and “meta-zoa”] ‘cosmo-ontological’ categories, and beyond [not even mentioning we, ourselves -- the human-societal «monads»].

That is, that epoch was missing nearly every kind of thing that is tangible for human beings -- that is sensorially accessible for us -- in the contemporary cosmos, e.g., the “meta-phyta” and the “meta-zoa”, as well as the kinds -- the ‘cosmo-ontological’ categories -- whose «monads» are sensuously “intangible” and “invisible” to the unaided, genomic human sensorium, but that we have learned about recently in our history, via the most advanced developments of the ‘human phenome’ -- via the technological ‘extent-tions’ of our genomic sensorium; via science -- such as the “microbes”, the molecules, and the atoms.


The ‘epoch t_ALL = 0’, per our ‘meta-model’, was contained only the «monads» of the most sensually remote, most exotic, most microscopic, most recently discerned denizens of our most deeply delved data to-date:   it was missing everything but _ALLr; everything but the ‘pre-atomic’ “particle” «monads»!



Later in their book, they characterize the “Big Bang” theory’s version of the demise of “epoch 0” -- i.e., the rise of “epoch 1”, per the reckoning of our ‘meta-model’ -- in the following terms --


“For the next 300,000 years following the cataclysmic period of inflation [which the authors

elsewhere in the book describe as taking place “between 10^-35 and 10^-32 seconds after the Big Bang” -- M.D.] there were no major developments. ...”

“From our point of view, the biggest difference between this Universe and the Universe we see today is that in those very early times it was completely opaque.”

“... no photon could travel very far before hitting and being absorbed by an electron ...”

“However, when the Universe cooled to a mere 3000 degrees, around 300,000 years after the Big Bang, a sudden change took place.”

“Before this critical moment, the electrons -- the lightest, and therefore fastest of the constituent of ordinary atomic matter -- had been moving too fast to be captured by the heavier atomic nuclei, but at a temperature of 3000 degrees they could no longer avoid capture.”

“The first neutral atoms were formed.”

“... A large expanse of space between each newly formed atom therefore opened up, and photons were suddenly free to travel for great distances.  In other words, matter and radiation where separated, and 300,000 years after the Big Bang the Universe became transparent.”

[May, Moore, and Linott, Bang!:  The Complete History of the Universe, Carlton Books, Ltd. [London: 2012], pp. 27-28]


Thus, per the prevailing Big Bang model, the duration of our _ALLr-only epoch, i.e., of the

“discrete time” unit duration, from the start of t_ALL = 0 to the start of t_ALL = 1, lasted,

in terms of “continuous time”, for 300,000 years -- for the very first 300,000 years of

time itself, as such!







0.3  Extended Commentary.  In a strict sense, ‘epoch t_ALL = 0’ is not an epoch

proper for this ‘meta-model’ at all, if we are to confine its language to that undergirded by the _NQ_  dialectical arithmetic, based upon/subsuming the “Natural” Numbers --

N  =  {1, 2, 3, . . .}

-- because zero is not a “Natural” Number in our tradition:  0    ~in    N.

However, including an ‘epoch 0’ in our narrative has the advantage of once again calling attention to the ‘fundamentality’ of the choice of the «arché» category, as ‘‘‘foundation’’’, ‘‘‘premise’’’, ‘‘‘ground’’’ -- for the rest of this ‘dialectical meta-model’, and for all such ‘dialectical meta-models’ -- and as ‘‘‘ever-present origin’’’ -- always present ‘‘‘inside’’’, and at the base of, all of its subsequent epochs.

Including an ‘epoch 0’ in our narrative also has the advantage of calling attention to the issues surrounding our choice of the «arché» in the case of this specific ‘dialectical meta-model’, in the context of the alternative «arché» choice-options that we considered, and, in some cases, also explored in depth, and even continue to pursue.

The _ALLr «arché» arises as a “lumping together” of the first and second categories -- that is, of

the «arché»-«physis» category, with the first meta-«physis» category -- of our standard version
of our ‘Dialectic of Nature Meta-Model’.

The «arché»» category for our standard version of our ‘Dialectic of Nature Meta-Model’ is

denoted by _ALLn, connoting the category of the ‘pre-nuclear/sub-nuclear’ “particles”, i.e.,

of the so-called “elementary” bosons and fermions only -- implicitly ‘‘‘containing’’’ the  
photons, gluons, Ws, Zs, and [perhaps] the Higgs bosons, and [perhaps] the gravitons, as
the “elementary” bosons, plus the quarks -- “up”, “down”, “charm”, “strange”, “top”, and
“bottom” --  and the [“elementary”] leptons -- electrons, electron neutrinos, muons, muon neutrinos, tauons, and tauon neutrinos -- as the “elementary” fermions, as well as the  
“anti-particles” of all of these “elementary” bosons and fermions -- ~30 “elementary
particle” species in all, if we count the “anti-matter” “elementary particles”, when they 
exist as other than their correlated “matter” “elementary particles”, separately.


It also connotes anything else that was primordially existent, but that is, as yet, unknown to human science.

The second category, the first meta-«physis» category, for that standard version of our  


‘Dialectic of Nature Meta-Model’ is denoted by _ALLs, connoting the category of the  

‘pre-atomic / sub-atomic’ “particles”, i.e., of the so-called “composite”, ‘‘‘hadronic’’’  

bosons and fermions -- implicitly ‘‘‘containing’’’ the mesons, for the “composite” bosons,

and the baryons -- ‘meta-quark/ meta-gluon’ protons, ‘meta-quark/ meta-gluon’ neutrons,

and the hyperons -- for the “composite” fermions.  The leptonic “elementary” fermions,

exhibiting the “Pauli Exclusion” behavior, and not exhibiting the “strong interaction”

behavior, are thus not seen to form composite “particles”.

The ‘meta-model’ that we are narrating in this series, which unifies the _ALLn and the _ALLs categories into the single new «arché» category, _ALLr -- of the “ pre-atomic “particles” ” -- was

chosen for presentation in this series, because it abbreviates the narrative considerably, and is perhaps more intuitive for readers not so conversant with the detailed “particles” ontological taxonomy of contemporary “particle physics”. 

With _ALLn as «arché» category, the category of the human arises as the 256th category in

the models’ categorial progression.

With _ALLr as «arché» category, the categories of the human arrives after only half of that

extent, as the 128th category in that categorial progression.

We have already noted that the “dialectical theory of everything” embodied and encoded in these ‘Dialectic of Nature Meta-Models’, falls short of covering and addressing “everything” as presently known to Terran humanity -- all known ontological categories -- in that it does not explicitly address the still largely unknown entities presently referenced as “Dark Energy” and “Dark Matter”.


Foundation researchers are also at work on a still highly speculative hypothesis, one that, if not falsified by empirical data, could ground a new standard version of our ‘Dialectic of Nature Meta-Model’.

This hypothesis, instead of “lumping together” the «arché» category and first meta-«physis» category of the present standard version ‘Dialectic of Nature Meta-Model’, in effect ‘de-lumps’ the _ALLn as «arché» category, by seeking a category for a deeper, earlier-irrupted physical ontology, explicitly addressing “Dark Energy”, denoted _ALLx, as the new «arché», plus a new, next-irrupted physical ontology, described algebraically as  _ALLq_xx, basing an also pre-_ALLn, first meta-«physis» category, explicitly addressing non-baryonic “Dark Matter”,  _ALLc.



This hypothesis thus amends our ‘Dialectic of Nature Meta-Model meta-equation’ to the following for its epoch 2 equation --







_ALL>-|-<₂  =  < _ALLx >²²  =   





< _ALLx >⁴  =

  


< _ALLx² >²  =  < _ALLx² >  x < _ALLx² >   = 

  

< _ALLx  +_ALLq_xx >  x < _ALLx  +_ALLq_xx >  =


  
< _ALLx  +_ALLc >  x < _ALLx  +_ALLc >  =



_ALLx   + _ALLc      + _ALLq_cx     + _ALLq_cc  |-.=



_ALLx   + _ALLc      + _ALLq_cx     + _ALLn






-- with _ALLq_cx representing the category of the interactions between “Dark Matter”

and “Dark Energy”, and such that _ALLn, the present first, «arché» category of our present

standard ‘Dialectic  of Nature Meta-Model’, now arises, instead, in this new, candidate
‘meta-model’, as the fourth, or second ‘meta-«physis»’ category, namely, as --



_ALLq_xx[xx]   |-.=   _ALLq_cc   |-.=   _ALLn.






This means that, if the generic primary interpretation of these solutions for the meanings


of the terms/category-descriptions _ALLq_xx, and _ALLq_cc, as expressed in the  


‘solution sub-equations’ _ALLq_xx |-.= _ALLc, and _ALLq_cc |-.= _ALLn,


holds in the specific case of the ‘taxonomy level 1’, “everything” universe[-of-discourse],


for the _ALLc «monads» and the _ALLn «monads» of this new candidate universal


‘meta-model’ -- as it does, we have found, for so many other domains, which are

sub-domains of this ‘_ALL’ domain, and as it also holds for all of the other, later-arising


‘self-hybrid’ categories of, e.g., the 



< _ALLr >^2tALL 



‘meta-model’ version -- then we have two entailed sub-hypotheses regarding the composition


of the _ALLc “Dark Matter” «monads», and of the _ALLn -- no-longer-“elementary”



“standard elementary particles” «monads».  They are that the «monads» of the “Dark Matter”

_ALLc  «arithmos»/category are ‘meta-«monads»’ of the «monads» of the “Dark Energy”  

_ALLx  «arithmos»/category. 




The «monads» of the “Ordinary Matter” _ALLn «arithmos»/category are  

‘meta-«monads»’ of the «monads» of the “Dark Matter” _ALLc «arithmos»/category, and are

therefore also describable as ‘meta-meta-«monads»’ of the «monads» of the “Dark Energy”  

_ALLx  «arithmos»/category. 





That is, the two entailed sub-hypotheses hold that (1)  the 0 < v < c capable ‘contracton’

«monads» of the “Dark Matter” _ALLc «arithmos»/category are in some sense made of the

‘‘‘tachyonic’’’, v > c capable ‘expandon’ «monads» of the “Dark Energy” _ALLx

«arithmos»/category, and (2) the “tardyons” of the “Ordinary Matter” _ALLn


«arithmos»/category  are in some sense made of the light-speed-capable ‘contractons’


of the “Dark Matter” _ALLc «arithmos»/category.  




This also means that, in this ‘deeper «arché»’ version of the ‘Dialectic of Nature Meta-Model’,
 if it works out empirically, we will still, as in the present standard ‘meta-model’, have  


composite  sub-atomic “particles”, such as protons, _ALLs, arising as _ALLq_nn,

and atoms, _ALLa arising as _ALLq_ss, and molecules, _ALLm, arising as _ALLq_aa,


and  pre-eukaryotic living cells,  _ALLp, arising as _ALLq_mm, and so on, as before.




But, in addition, our ‘meta-model’ will be enriched with additional terms/category-descriptions, relative to our current ‘standard meta-model’, covering the possible interactions among “Dark 

Energy”, _ALLx, “Dark Matter”, _ALLc, and “Ordinary, Visible Matter” categories, starting


from _ALLn, denoting the category of the “standard elementary particles”, and onward


from there. 




For example, for epoch 3, the new candidate ‘meta-equation’ yields the equation -- 

  




_ALL>-|-<₃  =  < _ALLx >²³  =   





< _ALLx >⁸  = 




_ALLx  + _ALLc    + _ALLq_cx   + _ALLn   +



_ALLq_nx    + _ALLq_nc    + _ALLq_ncx   + _ALLs



-- including 3 additional categories/terms --  


_ALLq_nx,  _ALLq_nc, and _ALLq_ncx 


-- inserted with respect to our present standard ‘meta-model’, in-between _ALLn and _ALLs,

and addressing, respectively, possible interaction-products of “standard elementary particle” «monads» with (1) “Dark Energy” «monads», with (2) “Dark Matter” «monads», and


with (3) possible “hybrid” «monads», _ALLq_cx, the “hybrid”products of the interaction


of “Dark Matter” «monads» with “Dark Energy” «monads».




This new research hypothesis seeks to anchor the entire ‘Dialectic of Nature Meta-Model’, in what, per this hypothesis, represents the primary ‘intra-duality’, or ‘self-duality’, of our cosmos -- in the older language of dialectics, the primary internal, immanent, or self-“contradiction” [a relationship that we signify via the relation-sign ‘#’] of this cosmos as totality, as expressed this meta-model’s first pair of terms, its first “antithesis sum” --




_ALL>-|-<₁  =  < _ALLx >²¹  =   





< _ALLx >²  = 

 

< _ALLx¹ >  x < _ALLx¹ >   =   



 _ALLx   + _ALLq_xx  |-.=    _ALLx   + _ALLc.










The “first antithesis” expressed by the ‘oppositional sum’ of the first two terms of this tentative new version of the ‘Dialectic of Nature Meta-Model’ might be formulated as --  

‘Dark Energy  #  Dark Matter’.

However, the Foundation researchers prefer to formulate that “first antithesis” in terms of the mutually opposing cosmological tendencies of -- 

‘Dark Anti-Gravity  #  Dark Gravity’

-- or --

‘Unknown-Source Anti-Gravity  #  Unknown-Source Dark Gravity’

-- or, better still, in terms of the mutually counter-acting tendencies of --  


‘space-time pro-expansivity  vs.  space-time anti-expansivity’.  

-- or --

‘space-time expansivity  vs.  space-time contractivity’.  

They see the ‘space-time expansivity’ “side”, or ‘‘‘dual’’’, of this dialectical internal duality, or ‘self-duality’, of the whole cosmos, as manifesting first in the history of our cosmos, making it

appropriate to choose _ALLx as their new, candidate «arché» category of their sought new,

“Dark Energy”/“Dark Matter” comprehending, deeper-«arché» ‘Dialectic of Nature Meta-Model’. 

They also see the cosmological-expansive _ALLx  “Dark Energy” ‘anti-gravitic’ ‘‘‘force’’’ as

manifesting in three major manners, so far, in the history of our cosmos, to present human
knowledge --

(1) as the initial “Big Bang” expansion; (2) as the theorized early post-“Big Bang” episode of
 faster-than-light-speed “cosmological inflation” expansion of the ‘space-time-mass-energy’
of the total cosmos, and; (3) as the currently-observed, slower-than-light-speed acceleration
in the rate of expansion of the “space-time” of our cosmos.

They see the cosmological-contractive _ALLc  “Dark Matter”  ‘‘‘gravitic’’’ force as manifesting,

so far in the history of our cosmos, to present human knowledge, in the formation of galactic

‘superⁿ-clusters’; super²-clusters or “super-super-clusters”, super¹-clusters,

“mere” [super⁰-]clusters, and galaxies themselves -- also enabling the formation of stars

and of stellar-systems, including of stellar/planetary systems, etc., within galaxies.

They see the faster-than-light-speed expansion-capability of the _ALLx  “Dark Energy” ‘‘‘force’’’

as a possible key clue to the classification and identification of that ” ‘anti-gravitic’ ‘‘‘force’’’, as

well as to the classification and identification of cosmologically-contractive _ALLc  “Dark Matter”.

It suggests to them that a form of ‘‘‘materiality’’’ that is capable of faster-than-light-speed
celerity will also be an extremely “ghostly” -- or “subtle” and “intangible” -- form of ‘‘‘materiality’’’, one that will lack almost all of the basic interaction capabilities and

behaviors associated with “Ordinary Matter”, _ALLn and beyond. 



That is, such a ‘‘‘materiality’’’ will lack electromagnetic interaction capability,
 making it “Dark”, as well as lacking capability for the “strong” and the “weak”
interactions, retaining only the ‘‘‘gravitic’’’ ‘interactivity’, in the form of an  
‘anti-graviticity’.

It further suggests to them that the ‘‘‘materiality’’’ of cosmologically-contractive _ALLc  “Dark 

Matter” will be less “ghostly”, less “subtle” and “intangible”, relative to the ‘‘‘materiality’’’ of _ALLx  “Dark Energy”, but still very “ghostly”, or “subtle” / “intangible” relative to the tangible ‘‘‘materiality’’’ of _ALLn “Ordinary Matter”.

In particular, they suspect that the «monads» of _ALLc  “Dark Matter” will be, like photonic

‘‘‘materiality’’’*, capable of traveling at light speed, c, but no greater [thus distinguishing


it from _ALLx  “Dark Energy”], and, unlike 0 rest mass photon «monads», have  


> 0 rest mass, and will be capable of traveling at speeds less than c as well, also unlike  

0 rest mass photon «monads», which are observed to travel only at exactly the speed of light.

 

*[For this reason, they group photons -- those ‘luxonic bosons’ -- together with
‘contractons’, as two species of a common «genos», which they sometimes call
‘alacritons’, signifying the «genos» of light-speed-capable «monads»].

As a consequence of these celerity characteristics, we further suspect that the > 0 rest mass

«monads» of _ALLc  “Dark Matter” will lack electromagnetic interaction capability, as well as

lacking capability for the “strong” interaction, retaining only the “weak” interaction, and the ‘‘‘gravitic’’’ interaction, similar to the 0 rest mass photon «monads», which are the ‘‘‘bosonic’’’ carriers of the electromagnetic interaction, and which lack capability for the “strong” and the “weak” interactions, but which also retain ‘‘‘gravitic’’’ ‘interactivity’.

1.  Epoch t_ALL = 1:  atomic nuclei ontology ‘irruptant’ --

Primarily Hydrogen and Helium Nuclei -- Hydrogen Ions [Naked Protons] and Helium Ions /- Plasmas -- and, Later, Neutral Gaseous Hydrogen and Helium Atoms, with Electron Shells /- Probability Clouds -- Emerge into Existence for the First Time, via the Fusion Process called “Primordial Nucleosynthesis”, or “Cosmological [non-stellar] Nucleosynthesis” -- the “Original Accumulation” of atoms.

1.1  Formulaic Summary for the First Full Epoch of ‘Cosmological Meta-Evolution’.  ‘Ideographized’ /- ‘ideogramized’, “shorthand” summary of the narrative rendition below.

If t_ALL = 1, then -- 

  




_ALL>-|-<_tALL  = _ALL>-|-<1  =   





< _ALLr >²¹   = 

< _ALLr >²  =  _ALLr¹  x _ALLr¹   =    






_ALLr   x  _ALLr  =




_ALLr   +  Delta<_ALLr >   =   _ALLr   + _ALLq_rr.

-- as t_ALL = 0 →  t_ALL = 1.





‘Epoch 1’ still includes the ontology of our «arché» cosmological category, denoted by _ALLr, as

[possibly] still existent, but also includes a second ‘cosmo-ontological’ category, for a predicted / ‘retrodicted’ / reconstructed new ontology, that of a new, second «arithmos», one of qualitatively different kinds of monads, or of units, than the units of the first, _ALLr, «arithmos» of «monads», this second possible «arithmos» being denoted, ‘‘‘algebraically’’’, by _ALLq_rr.

Our task, with respect to this epoch t_ALL = 1 model-equation of our overall ‘meta-model  

meta-equation’, is the “solve for” the meaning of this new term, _ALLq_rr, that is, to find that


already known category of ‘cosmos-ontology’ that came into existence next after _ALLr, as an


outgrowth of/from _ALLr, by means of a self-«aufheben» ‘self-meta-monadization’ of the


«monads» of the _ALLr «arithmos».




That is, the standard “first try” method of solution for the ‘dialectical-algebraic unknown’ term, _ALLq_rr, is to scan our knowledge of Nature for units, or «monads», each of which can be aptly characterized as ‘a meta-_ALLr unit, each one made up out of a heterogeneous multiplicity of  

_ALLr units’ -- i.e., ‘a meta-“particle” unit, each one made up out of a heterogeneous multiplicity of

“particles” ’.



To our minds, the natural formation that “fills this bill” is called the “atom”.



Each typical “atom” unit is made up out of one or more proton, neutron, and electron sub-units, each of which is a “ pre-nuclear, pre-atomic “particle” ”.


The simplest such ‘meta-«monads»’ -- ‘heterogeneous multiplicities of _ALLr  «monads»’ 

‘meta-«monads»’ -- i.e., the simplest atom «monad», is the normal, neutral Hydrogen atom, 1H, which is a ‘heterogeneous minimal multiplicity’ of thus exactly 2, indeed heterogeneous -- mutually qualitatively different -- _ALLr units:  one electron «monad», and one proton «monad».


The most complex such ‘meta-«monads»’ -- ‘heterogeneous multiplicities of _ALLr  «monads»’  

‘meta-«monads»’ -- i.e., the most complex atom «monad», that arises spontaneously, and “primordially”, in pre-human Nature, and that persists for substantial durations -- that is, apart from those atoms that arise only via the advanced technological activities within human Nature -- is the  

Plutonium Isotope 244Pu,  which is a ‘heterogeneous multiplicity’ of 338_ALLr units: 



94 electron «monads», and 94 proton «monads», and 150 neutron «monads».




We can assert [ ‘|-.’ ] this solution for the meaning / “intension” / “connotation” of the algebraic unknown term _ALLq_rr, formally, as follows, using _ALLa to connote the category named
“atoms” --

_ALLq_rr     |-.=    _ALLa.

Our solution to the epoch 1 dialectical-algebraic equation --


_ALL>-|-<1  =   _ALLr   +  _ALLq_rr



-- containing one known category-symbol, _ALLr, and one unknown category-symbol, _ALLq_rr,
is therefore --


_ALL>-|-<1  =   _ALLr   +  _ALLa



-- an equation which contains only known category-symbols -- exactly two known
category-symbols for epoch 1:  _ALLr   and _ALLa.




In the above -- thus “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 _ALLq_rr |-.=_ALLa term is there, in that equation, to represent those lasting products of

_ALLr with _ALLr interactions that produce atoms, _ALLa.






1.2  Narrative  Summary for ‘epoch t_ALL = 1’.

The ‘meta-model’ epoch in which the «monads» that constitute the atoms ‘cosmo-ontological

category’ -- _ALLq_rr   |-.=  _ALLa  --  first irrupt into existence , namely, ‘epoch t_ALL = 1’ -- if

we extend, ‘‘‘universalize’’’, or ‘«gene»-ralize’  Marx’s ‘«speci»-al’ application of his terms “formal subsumption” versus [followed by] “real subsumption”, and 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 -- is the cosmological epoch of the merely ‘‘‘formal subsumption’’’ of all previous

‘cosmo-ontology’ [namely, _ALLr], by the superceding ‘cosmo-ontology’ of atoms, _ALLa, the

newly-irruptant a ‘cosmo-ontology’, and is not yet that of the ‘‘‘real subsumption’’’ of _ALLr

by  _ALLa. 



The superceding ‘cosmo-ontology’ of atoms, _ALLa, has just come into existence, from out of the
densest core of its predecessor ‘cosmo-ontology’, _ALLr.


However, as of the end of ‘meta-model epoch t_ALL = 1’, the atoms ontology has not yet had time
to interact with, and thus to [partially] [real-ly] subsume, the remaining pre-atomic “particles” ontology of the cosmos.


That 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 _ALLq_ar -- only begins with the beginning of

‘meta-model epoch t_ALL = 2’.



‘Meta-model epoch t_ALL = 1’ is also the epoch of the ‘‘‘original accumulation’’’, or of the  

‘‘‘primitive accumulation’’’, of the atoms ‘cosmo-ontology’, _ALLa, in which some of the

«monads» of the pre-atomic “particles” ‘cosmo-ontology’, _ALLr, initially, ‘transitorially’ and  

unsustainably, convert themselves into [meta-]«monads» of the atoms ‘cosmo-ontology’, _ALLa.



The ‘‘‘reproductive accumulation’’’ of atoms ontology, _ALLa -- by means of a continual,

ongoing, sustained conversion of _ALLr into _ALLa, catalyzed by the _ALLa already, earlier

created, inside the hearts of those ‘‘‘natural formations’’’ that cosmologists call
 “first generation stars” which “burn” protons [i.e., which “burn” plasma “Hydrogen ions”,
or “Hydrogen nuclei”], by nuclear fusion, into Helium nuclei/atoms and, later, “burn”  
Helium nuclei/atoms, etc., into the atom «monads» of the higher atomic ‘«speci»es’,
e.g., Carbon atoms, Oxygen atoms, Nitrogen atoms, etc. -- only arrives with the arrival
of ‘meta-model epoch t_ALL = 2’.


It arrives in the form of its / this meta-model’s third category-symbol, _ALLq_ar, which connotes

 the conversion OF _ALLr ontology, catalyzed to do so BY, or with the help of, _ALLa ontology,

INTO _ALLa ontology, especially via the ontology that resides on the borderline between _ALLa

and _ALLr, namely ‘electron-less’ Hydrogen atoms’ ions / nuclei, denoted by H+; thus,

the _ALLr mediated autocatalysis of _ALLa.




This later process, connoted by our meta-model’s ‘cosmo-ontological category-symbol’,  


_ALLq_ar, is the process that cosmologists call “stellar nucleosynthesis”, with _ALLq_ar

connoting especially the “first generation”, ‘_ALLr-converting’, or ‘_ALLr-burning’,


i.e., ‘‘‘proton-burning’’’, almost pure-Hydrogen[-ion plasma],


minimally-“metallized” stars.



Cosmologists call the earlier process, connoted by _ALLq_rr  -- the process of the ‘‘‘original 

accumulation’’’, or ‘‘‘primitive accumulation’’’, of the first atoms «monads» -- by the names “cosmological nucleosynthesis”, or “primordial nucleosynthesis”, or “big bang nucleosynthesis”,
as distinct from what they call the later, ‘‘‘reproductive accumulation’’’ form of

“nucleosysthesis” -- of the “synthesis” of atomic “nuclei” -- namely, “stellar nucleosynthesis”, connoted by _ALLq_ar.



Steve Weinberg sets forth, succinctly, the present scientific evidentiary and theoretical necessity for the ‘retrodiction’ of an era of pre-stellar, “cosmological nucleosynthesis”, in the 1993 second edition of his book The First Three Minutes:  A Modern View of the Origin of the Universe, as follows --


 “Today it is generally believed that nucleosynthesis occurs both cosmologically and in stars; the helium and perhaps a few other light nuclei were synthesized in the early universe, while the stars are responsible for everything else.”

“The “big bang” theory of nucleosynthesis [M.D.:  the original version of that theory, by George Gamow, et al., which held that most of nucleosynthesis occurred universe-wide, in the “early universe”, rather than later, in stars], by trying to do too much, had lost the plausibility that it really deserved as a theory of helium synthesis.”

[Steven Weinberg, The First Three Minutes, second edition, BasicBooks, [NY:  1993], p. 130].



Donald Goldsmith, in his year 2000 book The Runaway Universe:  The Race to Find the Future of the Cosmos, provides further detail on the content of the contemporary theory of “cosmological nucleosynthesis”, in the following passage -- 


“The first few minutes of big-bang nucleosynthesis began with ordinary matter mostly in the form of protons (hydrogen nuclei), which underwent wholesale fusion into helium niclei throughout the universe.”

“As a result, when the era of big-bang nucleosynthesis came to an end, a few minutes after the big bang, about 25 percent of the total mass of ordinary matter had taken the form of helium-4 nuclei, each of which contains two protons and two neutrons.”

“Almost all of the remaining 75 percent of ordinary matter continued to reside in the form of protons.”

“The first few minutes after the big bang did not provide time to produce significant amounts of any nuclei heavier than helium through additional nuclear fusion.”

[Donald Goldsmith, The Runaway Universe, Perseus Books, [Cambridge, MA.:  2000], pp. 73-74].



Alan Guth, one of the originators of the theory of “cosmological inflation” -- that is, the theory of a momentaneous period of faster-than-light-speed self-expansion of the space-time of the early cosmos, just after the “big bang” -- provides the following more detailed recounting of the ‘retrodictions’ of the then-prevailing mathematical models of the “big bang” early universe, in his 1997 book The Inflationary Universe:  The Quest for a New Theory of Cosmic Origins --


“The description of [M.D.:  cosmological] nucleosynthesis can be started at 0.1 seconds after the big bang, when the temperature [M.D.:  the average temperature of the entire cosmos] was 31.5 billion degrees Kelvin.” 

“This temperature is so high that neither atoms nor even nuclei would have been stable -- the random motion of the intense heat would have torn them apart, setting free the electrons, protons, and neutrons to stream through space as free particles. (The protons and neutrons themselves are

stable at these temperatures, although at temperatures higher than about 10^13o Kelvin they too would be broken into their constituents, called quarks.)”

“For every neutron there were 1.61 protons.”

“The [M.D.: mass-]density of protons and neutrons was very modest, only about one and a half times that of water.”

“However, although the protons and neutrons are important to us (we are made of them! [M.D.:  as well as of electrons, and, in a sense, of photons also, and of the quarks and gluons within our protons and neutrons]), they were only a slight seasoning in a very dense cosmic soup that was thickened by other ingredients.”

“The extreme heat produced a blaze of black body radiation so intense that its energy dwarfed that of the protons and neutrons.  According to relativity, the energy density of radiation is equivalent to a mass density, which was 5 million times larger than the mass density of protons and neutrons.  Quantum theory implies that the energy of electromagnetic radiation is not spread out smoothly in space, but instead is concentrated in bundles [M.D.:  I.e., manifests in the form of a ‘«speci»-al’ kind of pre-atomic «monads»] called photons, which are essentially particles of light. ... we can talk about photons in the same way that we talk about protons or electrons.”

“At this time there were about 1.7 billion photons for every neutron.”

“the cosmic inventory also included electrons and their antiparticles, called positrons, both of which were produced in large numbers by the energetic collisions of other particles.”

“Collisions also produced a thick soup of neutrinos and antineutrinos.”

“For every eight photons there were six electrons, six positrons, nine neutrinos, and nine antineutrinos.”

“There was also one electron for every proton, so that the mix was electrically neutral.”

...

“Nucleosynthesis started at one second in the sense that the proton to neutron ratio began to deviate from its thermal equilibrium value -- a fact that is crucial in determining the abundances of the chemical elements [M.D.:  I.e., the proportions of the ‘«speci»es’ of  atomic «monads»] that are later produced.” 

“The actual formation of nuclei, however, did not begin until much later.”

“By about 1.5 seconds the universe had cooled enough so that helium-4 nuclei could have held together if they were formed, but helium-4 is not at the beginning of the chain.”

“The chain starts with the production of deuterium [M.D.:  a variant, or “isotope”, of the normal Hydrogen nucleus -- i.e., of a single proton -- that consists of a proton and a neutron ‘nuclearly-bonded’ together by the “strong nuclear force”, and sometimes called “heavy Hydrogen” -- the simplest atomic nucleus that is more than a single proton].”

“Since deuterium is an extremely fragile nucleus, this “deuterium bottleneck” delayed [M.D.:  cosmological] nucleosynthesis until about three and a half minutes after the big bang.”

[Alan H. Guth, The Inflationary Universe, Helix Books, [NY:  1997], pp. 90-92; 94].




Malcolm Longhair, in his 1996 book Our Evolving Universe, summarized both the content of the then-current theory of “cosmological nucleosynthesis”-followed-by-“stellar nucleosynthesis”,

regarding the self-organization of mass-energy to the atomic level of organization/ontology, _ALLa

[but no higher], and the scientific rationale -- both theoretical and evidentiary -- for the adoption of this theory --

“Let us study the evolution of the various constituents of the Universe ... .”

“The computations begin at such high temperatures and densities that all the particles which can exist at these temperatures are maintained in their equilibrium abundances.”

“Protons, neutrons and radiation are present, as well as other particles which must be present because the system is in thermal equilibrium -- these particles include neutrinos, muons, electrons and their antiparticles.”

“Of particular importance is the fact that the protons and neutrons are maintained in their equilibrium abundances by weak interactions involving electron neutrinos...”

“As the Universe cools, the time-scales of these weak interactions increase rapidly and, when the Universe is about one second old, they become greater than the age of the universe.  The neutrinos are therefore no longer able to maintain the equilibrium abundances of neutrons and protons at later times and the neutron-to-proton ratio is more or less frozen at the value it had when the neutrinos decoupled.”

“This epoch, when the neutrinos decoupled from the protons and neutrons, results in a neutrino barrier ... .  If we were able to observe the Universe in neutrinos, we would never be able to observe neutrinos from epochs earlier than this barrier ... .”

“The electrons and their antiparticles, the positrons, are also maintained in their equilibrium abundances by the process of electron-positron pair production in collisions of high energy [M.D.:  gamma-]rays of the thermal background radiation but, when the average energy of the [M.D.:  gamma-]rays falls below the rest energy of the electron, the electrons and positrons annihilate [M.D.: as before, but this time without any replenishment by further new creation of electron-positron pairs via colliding gamma-ray photons' mutual annihilations [photons being "their own antiparticles"], so that the primordial electron and positron populations dwindle] and the energy released slightly heats up the thermal background radiation ... .”

“All that are left now are protons and neutrons [M.D. and, of course, photons], which can combine to form the simplest compound nucleus, deuterium (2H), which consists of a proton and neutron -- this simple nucleus is often referred to as a deuteron.”

 “When radiation temperature is as high as 3 000 000 000 K, however, the deuterons do not survive as they are dissociated by the [M.D.:  gamma-]rays of the background radiation and a very low abundance of deuterium is expected ... .”

“As the Universe continues to expand and cool down, however, more and more of the deuterium survives.”

“The deuterons then interact with protons and neutrons and other deuterons to form heavier elements.”



[M.D.:  Informally, in a Seldonian algebraic shorthand for a taxonomy level 2 ‘sub-model’ of these reactions, or interactions, that lead to Deuterium and beyond, for the domain, or universe-of-discourse, of atoms alone, with protons [Hydrogen ions] and neutrons as the «arché» «monads» of the «arché» «arithmos», i.e., as the «arché» ontological categories for domain 2a, these processes can be connoted, with the ‘pre-subscipt’ ‘₂’ indicating the taxonomy level 2  

‘‘‘location’’’ of these processes, and the ‘pre-superscripts’ indicating the atomic weight of the different kinds of atoms produced, and ‘|+|’ indicating the co-presence of an indefinite number/population of «monads» of the category indicated, the qualitative, categorial details of these processes/interactions/reactions could be expressed as --



₂1H  |+| ₂n   =   ₂p  |+| ₂n   =   ₂q_p |+| ₂q_n,   --->
   

< ₂q_p |+| ₂q_n > of < ₂q_p |+| ₂q_n >   =    < ₂q_p |+| ₂q_n >²   =


₂q_p |+| ₂q_n  |+| ₂q_pp |+| ₂q_pn |+| ₂q_nn  =  

₂p  |+| ₂n  |+| ₂2D  |+| ₂2D  |+|  .    =   ₂p  |+| ₂n  |+| ₂2D,   --->  


< ₂p |+| ₂n |+| ₂2D > of < ₂p  |+| ₂n  |+| ₂2D >    =

< ₂p  |+| ₂n  |+| ₂2D >2    =
 

₂p  |+| ₂n  |+| ₂2D  |+| ₂q_Dp  |+|  ₂q_Dn  |+| ₂q_DD  =

₂p  |+| ₂n  |+| ₂2D  |+| ₂3He  |+| ₂3T  |+| ₂3He   |+| ₂3T  =


₂n  |+| ₂1H  |+| ₂2H  |+| ₂3H  |+| ₂3He,   ---> 


<₂n  |+| ₂1H  |+| ₂2H  |+| ₂3H  |+| ₂3He ₂ >2    =
 

₂n  |+| ₂1H  |+| ₂2H  |+| ₂3H  |+| ₂3He ₂  |+| ₂4He ₂ |+| . . .

. . .

-- wherein ‘.’ denotes a non-existent or unknown stable/enduring reaction product category.  In the expression above, both  

₂p  and  ₂1H  represent the category of the proton or the “ionized normal Hydrogen atom”, or “normal Hydrogen  

nucleus”, both ₂2D  and ₂2H represent the category of Deuterium, and both ₂3T and ₂3H  represent the category

of Tritium [the Hydrogen isotope with two neutrons in its nucleus, thus with atomic weight 3].



“By the time the temperature has dropped to 300 000 000 K, all the nuclear reactions are over.”


“...most of the neutrons have been combined with protons to form the most stable helium isotope,  

4He, but there are also traces of other light elements such as deuterium, the lighter isotope of

helium, 3He, and a little Lithium, 7Li.”


“It is striking that no heavier elements such as Carbon and Oxygen are created.”

 “The reason for this is that there are no stable species with five and eight nucleons -- beryllium-8, for example, is a totally unstable nucleus.”



“The spectacular result of these calculations is that the elements which are formed by this process of primordial nucleosynthesis are precisely those which have proved impossible to account for by nucleosynthesis in stars.”

“... wherever we look in the Universe, helium always seems to be present with an abundance of 25% by mass, quite independent of the abundance of the heavier elements.”

“The remarkable result of these calculations of primordial nucleosynthesis is that, for any reasonable value of average density of ordinary matter in the Universe now, about 23 to 24% of helium by mass is created by nuclear reactions in the first few minutes of the Big Bang.”

“While stars can produce a small amount of helium, we do not know of any way of creating as much as 25% of helium by nucleosynthesis in stars.”

“Equally, it is very difficult to understand how deuterium could be created by nucleosynthesis inside stars.  It is such a fragile element that it is destroyed in stellar interiors rather rather than being created.”

“Primordial nucleosynthesis in the Big Bang solves these dilemmas.”

[Malcolm S. Longhair, Our Evolving Universe, Cambridge University Press, [NY:  1996], pp. 140-141].




The detailed vicissitudes described in the quotes above are only captured, by our epoch 1 ‘dialectical equation’, “connotationally”, or “intensionally”, and summarily, via the high-level category-symbols

for ‘pre-atoms’, _ALLr, and for their «aufheben» ‘self-meta-«monad»-ization’, _ALLq_rr, yielding  

atoms, _ALLa --




_ALL>-|-<1  =  




 _ALLr    + _ALLq_rr  =  _ALLr    + _ALLa




-- 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 ‘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 _ALLq_rr, or  

_ALLa, 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’ --   


Nq_NN = 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 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_ [---> q<sub>15


-- and --</sub>



Rq__BAMQN = Rq__BAMU = R, BetaMu_ [---> q<sub>31



-- and --</sub>



Rq__GBAMQN = Rq__GBAMU = R, GammaMu_ [---> q<sub>63




-- 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 --</sub>



#_)-|-(_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. B. 
   

Epoch t = 2:   Molecules Emergent.