ForYourInformation: Hmm... Someone who connects advanced human cognition with masturbation -- I'm not sure whether this bespeaks some deep Tantric insight, or just crude, gutter reductionism.
The full Seldon formula for dialectic, that can go as far beyond just the first three terms of the triadic dialectic as needed for a given dialectical model, is --
a^(3^S) where the S is a whole number that counts the step of the dialectical categories-progression.
This formula means that the exponent of category a, 3, is itself raised to the further exponent, S.
So, starting from S = 0, for the 0th Step of the argument/progression --
a^3^0 = a^1 = a
-- and you just get back category a, the starting point of the whole progression of categories.
When you move on to S =1, for the 1st Step of the argument/progression, you get the formula that you asked about --
a^3^1 = a^3 = a x a x a = a of (a of a) = a(a(a)) = ~(~(a)) =
aaa = a x ( a + b) = aa + ab = a + b + ab = a + b + C(a, b)
-- you can see that the "negation operator" -- the "negator", '~' -- for the category a, in the negation of the negation of category a --
-- is the category a ITSELF: ~ = category a itself, FOR / RELATIVE TO category a.
When you move on to S = 2, the 2nd Step of the argument/progression, your get --
a^(3^2) = a^9
-- which generates a "sum" of 9 qualitatively distinct categories: a triad OF TRIADS. And so on, to higher Steps in the argument/progression, if needed to model the reality at hand.
~a = a x a = aa = a + b
-- stands for the dialectical "SELF-Negation" of category a.
Dialectical self-negation is NOT the same as formal logical, propositional negation.
Dialectical self-negation is NOT just a "Not".
Dialectical self-negation is a SELF-<<Aufheben>> operation -- to use the German word, <<aufheben>>, the word that, for example, Hegel, Marx, and Engels used when writing about dialectic -- such that category a concurrently (1) transforms, (2) conserves, and (3) elevates category a itself, IN CATEGORY a's OWN WAY [also called "determinate negation", or "concrete negation", which transforms a "something" into a "something else", as opposed to formal, "abstract negation", which turns a "something" into a "nothing"].
For example, in the dialectic of pre-human Nature, when atoms expandedly reproduce their populations at various loci within the self-evolving cosmos -- within the galactic interstellar medium of each typical galaxy -- and also "self-concentrate" in terms of physical-space proximity, e.g., in the early "atomic clouds" from which new stars are self-born, atoms begin to form molecules, initially a new, unprecedented, never-before existing kind/category of physical being.
A molecule is a 'meta-atom', in that each molecule is made up out of a [typically] heterogeneous multiplicity of atoms -- H2O, CO2, CN, CH4, NH4, etc., etc.
Atoms themselves, growing quantitatively, i.e. growing in numbers, e.g., from ongoing stellar nucleosynthesis/novae/other stellar mass ejection, and concentrating, self-densifying, in local physical space volumes, themselves cause the qualitative change of the irruption of the first molecules.
Thus, this natural-historical process constitutes a dialectical SELF-negation of atoms, which produces more atoms but also the qualitatively different, new, more advanced kinds of things that are molecules --
atoms ---> atoms + molecules.
This is a "self-<<aufheben>> self-negation" of atoms, because molecules are (1) a [self-]TRANSFORMATION of atoms, that are qualitatively different from atoms; (2) a [self-]CONSERVATION of atoms, because the atoms are still there, INSIDE each molecule, and; (3) a [self-]ELEVATION of atoms, because molecules represent a new, higher [more inclusive] PLANE OF EXISTENCE, relative to the [lower, less-inclusive] PLANE OF EXISTENCE occupied / constituted by atoms / primordial interstellar atomic clouds:
atoms^3 = atoms x atoms x atoms = ~(~(atoms)) =
atoms + molecules + Combinations/Hybrids of atoms with molecules
-- e.g., C(atoms, molecules) = "galactic, interstellar MOLECULAR[/atomic] CLOUDS".