Categorial Hybridization
and
Dear Reader,
In the NQ arithmetic for modeling dialectics, in the dialectical categorial progressions that are generated by the various Seldon Functions, when the ordinally first generic NQ ‘meta-number’, q1, is interpreted for, or assigned to, the seed category of a specific, user-defined ontic Domain, ‘allo-combinations’ of categories arise, from a value of independent variable of that generic function of 1, h = 1 and beyond –
for Ds > 1 for systematic dialectical categorial
progressions, and for Dt > 1 for
historical dialectical categorial progressions.
The first ‘allo-combination’
category, or ‘uni-category’, occurs as the third category of the categorial
progression for Ds = 1 or Dt = 1.
The ordinally first category of a given Domain is the ‘seed category’, or ‘«arché»-category’,
of that
Domain as a whole.
The second category in this progression/non-amalgamative
[Platon: «asumbletoi»] sum of categories is the ‘first
contra-category’ of the Domain. It typically represents a ‘auto-combination’
or ‘self-hybridization’ of the ‘«arché»-category’, and of the units
or «monads»
for which this category stands.
The third category is a[n] [allo-]combination, a
Hegelian-like ‘complex unity’, of the second
category with the first category. That is, the third
is a hybridization of the
preceding two.
We call it the ‘first uni-category’ of the Domain.
If we assign q1 to a category
whose name begins with the letter ‘A’, i.e., forming the category-symbol qA, then the triadic
Seldon Function, with its independent variable of value 1, yields the following categories-series, if qAA well-describes
a Domain category whose name begins with the letter “B”:
qA31 = qA + qAA + qAAA = qA + qB + qBA.
If an ‘allo-combination’ category, synthesizing and unifying category qB with category qA, well-describes another
category of the Domain, whose name begins with the letter “C”, then the
series notated above becomes –
qA31 = qA + qB + qC
– and category qC is then the
‘unifying category’, or ‘dialectical synthesis category’ for opposing categories
qA and/versus qB. The hybridization
of category qA and/with category qB shows the way
to the unifying ‘dialectical synthesis category’, reconciling the opposing
categories qA and qB. But note also
that the first two opposing categories, qA and qB, still persist, ‘‘‘evolutely’’’, as possibilities,
together with their unifier, their unity, denoted here by category-symbol qC.
In the NQ arithmetic for modeling dialectics, categorial dialectical
synthesis is modeled by categorial [allo-]hybridization.
For example, if we take qr, denoting the ontological category of pre-atomic “particles” as the ‘«arché»-category’ for the Domain of the ‘‘‘[Dialectic of ] Nature’’’ entire, then
we solve its t = 1 epoch as:
qr31 = qr + qrr + qrrr = qr + qa + qar.
We see qrr as denoting [self-]combinations
of pre-atomic “particles”,
e.g., of electrons,
protons
and neutrons,
and thus as describing atoms, e.g., the proto-galactic
pre-molecular-clouds ‘atomic clouds’, thus more succinctly denoted by qa.
But what ‘‘‘Dialectic of
Nature’’’ Domain-meaning does the terse descriptiveness of the
algebraic category-symbol qar best suggest?
The key combination of atoms
and/with “particles”
that we see is that of first-generation stars, with a plasma core of nearly pure ionized Hydrogen “atoms”
– i.e., proton-particles
– intermingled with “free” electron-particles,
also in their cores, together with surrounding, gradually thickening shells of
Helium atoms – both neutral and ionic – shells or layers that slowly accumulate
as products of core ‘proton-fusion’ [“di-proton”] nucleosynthesis.
We can thus, more succinctly, notate qar as qs, and our
‘‘‘Dialectic of Nature’’’ ‘first 3ad’ of ‘cosmo-ontological’ categories becomes –
qr31 = qr + qrr + qrrr = qr + qa + qs
– wherein qs stands for the category of those stellar
combinations of atoms with particles that also constitute ‘conversion formations’ for the initial, and thence ongoing, ‘reproductive [self-]conversions’ of particles into atoms, the ‘reproductive accumulation’ of atoms, after their “original accumulation”, the qrr ‘original conversion’, of particles into
atoms – mainly into Helium atoms
– in the brief preceding period of cosmos-wide
“Big Bang Nucleosynthesis”.
For another example, consider, systematically, taxonomically, the Domain of atoms, and the three main kinds of atoms in terms of their affinities in forming molecules. There are, first, the electron-Donor atoms, qD, which cede one or more of
their electrons to the second kind of atoms,
the electron-Acceptor atoms, qA.
In this, systematic context, qDD stands for the self-critique of category qD asserted as if the only category of this Domain,
calling for the systematic next category, the next
qualitatively-distinct, more complex, second
category of this Domain, qA.
Then, the next qualitatively-distinct, more complex, third category
of this Domain is denoted by qAD, which we solve as fitting for the ‘electron-Sharor’
kind of atoms, qS.
An example of the ‘electron-Sharor’
kind of atoms are the Carbon atoms.
An example of the electron-Acceptor kind of atoms are the “oxidizing”
atoms known as “Oxygen” atoms.
An example of the electron-Donor
kind of atoms are the “reducing” atoms
known as “Hydrogen” atoms.
Thus we have, for our first [and only?] triad
of categories for this Domain –
qD31 = qD + qDD + qDDD = qD + qA + qS.
Another systematic-dialectic
example is that for the categorial triad/sum
of the Fathers, Mothers and Children categories of the Domain of human procreation, where we solve the two self-critiques of the F category – denoted by qFF and qFFF, respectively – critiquing qF asserted as if it were the sole category of this Domain, as follows –
qF31 = qF + qFF + qFFF = qF + qM + qMF
=
qF + qM + qC.
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:
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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