The Algorithmics of Dialectics, via a simplified Short-hand Notation. Part 05: Seldon on ‘Dialectical Categorial Progressions’ Series.

  

 

 

 

Part 05: Seldon on 

‘Dialectical Categorial Progressions’ Series.

 

 

 The Algorithmics

 

of

 

Dialectics,

 

via a simplified

 

Short-hand

Notation.

 

 

 

 

 

 

 

Dear Reader,

 

 

It is my pleasure, and my honor, as an elected member of the Foundation Encyclopedia Dialectica [F.E.D.] General Council, and as a voting member of F.E.D., to share, with you, from time to time, as they are approved for public release by the F.E.D. General Council, Seldon’s commentaries on key Encyclopedia Dialectica concepts of Seldonian Theory.

 

 

This 5th text in this new such series is posted herewith, together with supporting text-images and diagrams [Some E.D. standard edits have been applied, in the version presented below, by the editors of the F.E.D. Special Council for the Encyclopedia, to the direct transcript of our co-founder’s discourse].

 

 

 

 

 

 

 

 

 

 

 Seldon –

“We have been busy developing an algorithmic dialectical ideography, via a much-simplified short-hand, much easier to learn, and not so evocative of the intimidating and even traumatizing teaching of mathematics that so many have suffered in contemporary society, almost worldwide.”

 

“We use, for this short-hand, a dual notation, with a capital Greek letter Kappa, bolded and underscored – K – to signify a category in general, together with one or more – preferably just one – subscript(s), for example, ‘_a’, to specify the specific category being addressed, hence, for example, K_a.  The letter Kappa comes from the first letter of Aristotle’s term for his categories, “Kātegoríai”.” 

 

“In this, simplified, short-hand notation, a dialectical categorial progression can be expressed compactly, with K_a as «arché»-category, or starting-category, viz. –

 

K_a ® K_a& K_aa ® K_a& K_b ® K_a& K_b& K_ba ® K_a & K_b & K_c ®

K_a & K_b& K_c& K_ca ® K_a& K_b& K_c& K_bb ® K_a& K_b& K_c& K_d…  .”

– wherein the categorial, evolute advance is driven by copying the latest category abbreviation, and appending that copy to the right-most of the preceding series of short-hand category abbreviations, then appending the subscript of the starting category to the single subscript of the copy of the former latest category abbreviation, now becoming the new latest category abbreviation in the series.”

 

“It is then a matter of solving for the meaning, in the context of the Domain being analyzed, of that new-latest, now “bi-vocal”, dual-subscript short-hand category description, an replacing that dual subscript with a single new subscripted character, one that mnemonically abbreviates the character-string that spells the name or the phrase that defines that new-latest category, uni-vocally.”

 

“This procedure can be iterated until you reach a category-description abbreviation that you cannot solve for, or define, in terms of widely-known, extant category names.”

 

“The self-«aufheben» dialectical process is signified by category description abbreviations of the form K_xx, solved as, say, K_y, which can be interpreted as meaning that each unit of category K_y is made up out of a heterogeneous multiplicity of [some] of the [former] units of category K_x, forming ‘self-hybrid’ category K_y.”

 

“Note that many of our ‘dialectograms’ terminate their dialectic’s depictions at the ‘K_a  &   K_b &   K_ba’ stage, typically because we cannot see any solution for K_ca or K_bb, or for anything beyond it – i.e., for K_caa, K_caaa, K_caaaa, etc.”

 

“The five rules for generating such dialectical categorial progression analyses of a subject-matter Domain are as follows –

 

Rules-System.  This short-hand dialectical method, described generally, is the combined, sequential application of the following 5 rules:

§1.  First write down your short-hand category description for your starting-category for the subject matter field that you want to learn, or to present – call it, generically, K_a. 

§2.  Next, place, to its right, an ampersand, and a second short-hand category description, but with the subscript for your first category description re-appended, again, next to that initial subscript, with the ‘&’ sign, for ‘concrete addition’ – i.e., for “non-amalgamative” addition – placed between these, now two, shorthand category descriptions, thus forming a second short-hand category description with a double, repeat subscript added: generically K_a & K_aa. 

§3.  Next, replace that repeat-subscript of that second short-hand category description with a single, different subscript, a subscript that abbreviates and stands for a widely-know name for your meaning for the new kind of units signaled by the new, second short-hand category description – standing for each such new category’s new kind of unit, that was generated by the unifying mutual combination of some of the former units of your starting-category: generically, K_a & K_b. 

§4.  From then on, to construct each next short-hand category description, just copy your last, right-most short-hand category description, and place it immediately to the right of itself, after an ampersand, ‘&’, but then simply juxtapose the subscript for your starting category to the right of the subscript of your copy of your most recent previous short-hand category description.  

Then try to find a single character that characterizes, or abbreviates the name of, and thus can aptly replace, the resulting multiple subscripts by a lesser number of subscripts; best by a single subscript.

For example, the next step to the generic example of step 3, above, generically, is to form the series – 

K_a & K_b & K_ba.  

Then find a single-word, widely-known name for category description K_ba, and abbreviate that name by its initial letter, if non-redundant, perhaps “c”, as subscript, thus rewriting your now three-fold categorial series as –

 K_a & K_b & K_c.  

If “c” is redundant with respect to previously used subscripts, try using a letter embedded within the character-string that spells the widely-known name or phrase that defines this third category. 

Continue iterating this step, together with rule §5., below, wherever it is applicable, until a short-hand category description results whose potential meaning you do not recognize, and cannot name or define.

§5.  If this adding of the subscript of the starting short-hand category description creates a double subscript in the form of a repeat subscript, then, for consistency, replace that repeat subscript with the single subscript by which you replaced that repeat subscript previously, in your short-hand category descriptions progression so far.  Or, if this repeat subscript is appearing for the first time, replace it with a single subscript abbreviating the widely-known name or phrase which defines the category for that next higher-level, higher-scale ‘self-hybrid’ kind of units.”

 

“The following example applies this short-hand dialectical-ideographical method to the dialectic of Nature as a whole, using the category of Standard Model “particles” as starting category.”

 

“1.  “particles” (short-hand: K_r).

  2.  atoms (short-hand: K_rr or K_a).

  3.  molecules (short-hand: K_aa or K_m).

  4.  prokaryotic living cells (short-hand: K_mm or K_p).

  5.  eukaryotic living cells (short-hand: K_pp or K_e).

  6.  multicellular organisms, asocial (short-hand: K_ee or K_o).

  7.  social organisms [“social animals” & ‘social plants’] (K_oo or K_s).

  8.  human, or ‘super-social’, societies (short-hand: K_ss or K_h).”

 

“For the first eight cosmological-ontological, dialectic of Nature categories, with both ‘self-hybrid’ and “merely-hybrid” categories included, we generate, by the given rules, the following dialectical categorial progression representation –

To begin this example, apply the five rules given above, beginning with our chosen starting short-hand category description, k_r.

1.  Write  k_r, describing, in that dialectical-ideographic short-hand, the category of pre-atomic, and, later, of sub-atomic particle units, as your chosen starting short-hand category description for presently-known cosmological objects.

 

2.  Write k_r & k_rr, with k_rr describing a category each unit of which is a combination of “particles” units, i.e., “atoms” units, which combine former, unbound “particles” units known as electrons, protons, and neutrons.

 

3.  Re-write k_r & k_rr as k_r & k_a, with subscript a standing for, and ‘mnemonizing’, the category of “atoms” units. 

4.  Write – 

k_r & k_a& k_ar.  

Hybrid subscript ar suggests those known cosmological objects that convert some particle units, i.e., “Hydrogen ion” units, that is, proton particle units, into atom units, i.e., into Helium atomic nuclei units, by means of “stellar nucleosynthesis”.  Of course, stars also involve r in that they continually generate and emit photons, neutrinos, and charged particles.  Thus, you can replace subscript ar with s, for a category beginning with “first-generation stars” units.  Later generation star units also start with proton-electron plasma cores, but their core-surrounding outer layer consists of Helium units, but also, increasingly, of atomic species units higher than Helium, due to accumulating “metallization” from generations of “stellar nucleosynthesis”.  [Stars are macro-scopic objects.  There are also microscopic, proto-molecules that k_ar also describes, that catalyze and accelerate star formation].  The k_ar category is best grasped as a genus category, with potentially many distinct species categories included in it.  Replacing k_arwith just k_s may leave non-explicit key species that figure significantly in later categories.  Your category ‘descriptors’ series now extends to –

 k_r & k_a& k_s.

 

5.  Write –   

k_r & k_a & k_s& k_sr.  

As k_sr is also k_arr, since you replaced ar with s in the last step, and as you previously replaced subscript rr with subscript a, you can now rewrite k_sr as k_aa, and, using rule 5., you can interpret k_aa as describing a category each of whose units is a unifying combination of multiple “atom” units, i.e., whose units are “molecule” units, k_m.  The short-hand “genus”-category described by k_aa also describes other species of combinations of atoms, such as crystals and metals, but we see molecules as the principal species of the k_aa genus.  Your series now describes our cosmos when it contained only four kinds of units: k_r & k_a & k_s & k_m.

6.  Write – 

k_r & k_a & k_s & k_m & k_mr.  

As k_mr suggests combinations of molecule units with particle units, assign this short-hand category description as fitting mainly and initially for the impacts of particle units fluxes on the molecule units forming in interstellar “molecular clouds”, and the results of such [inter]actions, e.g., involving ultraviolet photon particles: molecule units’ photo-disintegrations.  Your series now describes our universe when it contained only objects fitting the following 5 category descriptions – k_r & k_a & k_s & k_m & k_mr.  We leave the 5^th short-hand category description in 2-subscript form, since a single name for that category is not extant or widely familiar. The 2-subscript form is thus more mnemonic.

 

7.  Write –

 k_r & k_a & k_s & k_m & k_mr & k_mrr.  

We previously replaced, in step 2, above, subscript rr with subscript a.  So, applying rule 5., replace k_mrr with  k_ma. The latter genus-category short-hand describes, as one of its species, the, still ongoing, conversions/combinations of chemically-unbonded atom units into new, chemically-bonded, molecule units, inside interstellar molecular cloud units, as catalyzed or promoted by the molecule units already formed inside those “molecular cloud” units.  Recall that “molecular cloud” units must have had to start out as, i.e. – ‘molecule-less’ – ‘atomic cloud’ units.  So the later, mostly-molecular clouds still contain, and are also episodically replenished, e.g., by stars’ mass expulsions, and by molecules’ photo-dissociations, with fresh, chemically-un-bonded atoms.  Conversions of atom units into molecule units are thus ongoing within interstellar cloud units.  But genus-category description k_ma also describes the composition of a sub-species of the planet units species, for planets whose composition lacks particle-emitting heavy and radioactive atom units, such as Thorium, so that unbound “particle” units, subscript r, are not also part of their make-up.  It may be that many “ice giant” planets, such as Neptune and Uranus, are of this class.  So it may be best to leave this category’s short-hand description in 2-subscript form.  Your purely-qualitative cosmos model now sums up our cosmos when it contained only objects/units of one of the following six categories/kinds – 

k_r & k_a & k_s & k_m & k_mr & k_ma.

 

8.  Write – 

 k_r & k_a & k_s & k_m & k_mr & k_ma & k_mar.  

As we have previously interpreted subscript ar as subscript s, consistency with that earlier interpretation would lead us to replace subscript mar with the two-place subscript ms, describing the combinations, or interactions, between molecule units and “first-generation” star units.  This subscript can be interpreted as describing the conversion, into new, advancing, more-complex species of molecules, fostered or catalyzed by some of the molecules already produced in intra-galactic, interstellar “molecular/atomic clouds”, of the atoms of advancing, more-complex atomic species, created by, and initially inside, slowly ‘self-metallizing’ star units.  Includes supernova explosion’s particles’-impacts, producing high proton-count atoms, then available to bond with lighter atoms in molecular clouds. 

In short, subscript ms suggests the further ‘molecularization’ of the stars-produced, higher species – “metallic” species –  of atoms; of atomic species beyond Helium.  Subscript ms can also suggest the catalytic actions of certain kinds of molecule units on the formation of later-generation star units, e.g., now accompanied by planet units, made possible by, more “metallic”, atomic and molecular species.  The mar subscript also describes planets, especially “rocky” planets that have “particles”-emitting heavy, radioactive atoms, such as Thorium, in their cores.  More specifically, the short-hand category description, k_ms, can be grasped as describing the actions, by molecules, in the molecular clouds that precipitate “proplyds” [proto-planetary discs], that accelerate the transformation of those proplyds into stars [e.g., with orbiting planets] as the accumulating “metallization” of successive generation stars, and therefore also of the “molecular clouds” that they supply with higher atomic-number atoms, proceeds. 

However, the full short-hand category description, k_mar, describes more than this.  It describes cooler stars, and even cooler portions of some hotter stars, cool enough for molecules to form and persist inside such stars.  It describes the composition of galaxies, and even of galactic clusters, galactic super-clusters, and super-cluster filaments, in their pre-biological stages.  In their, hypothesized, later, biologic stages, they become k_pmar, k_epmar, and so on. Better, then, that we keep this step’s new category description in its full, more general, 3-subscript form.  Your purely-qualitative cosmos content inventory now describes the universe when it contained only objects/units fitting the following seven short-hand category descriptions –

k_r & k_a & k_s & k_m & k_mr & k_ma & k_mar.

9.  Write – 

k_r & k_a & k_s & k_m & k_mr & k_ma & k_mar & k_marr.  

As we have, previously, using rule 5., replaced subscript rr with subscript a, subscript marr is therefore replaceable by subscript maa.  As we have previously replaced subscript aa, using rule 5., with subscript m, subscript maa is thus replaceable by subscript mm.  Subscript mm, per rule 5., suggests a new category composed of a yet new type of units, beyond the molecule units’ category – units each of which is, typically, a unifying combination of myriad molecule units.  Thus, subscript mm can describe trans-molecular, prokaryotic cell units, e.g., bacterial cell units.  Such units are presently known to exist, so far, only “locally”, on our own home planet – on planet Earth.  If we hypothesize that such cell units will be found, in the future of human deep space observation and exploration, to be plentiful across our home galaxy, and across the cosmos, in galaxy after galaxy, then we are conjecturing the category of prokaryote units to be a cosmological category in its own right, not just a Terran category.  Your “purely”- qualitative cosmos history description now fits for the universe when it contained only objects that fit the following 8 short-hand category descriptions:

k_r & k_a & k_ar & k_m & k_mr & k_ma & k_mar & k_p.

 

Further iterations, using rules 4. and 5., can reach to a total sequence of 128 ‘anded’ short-hand category descriptions, up to a final, 128^th short-hand category description, that for “humanitys”, or of ‘human super-societies’ as its units, with its short-hand category description as k_h.” 

 

“One might, of course, choose to speculate about what – possibly future-born – category might be signified, and, indeed, ‘pre-constructed’ symbolically, or “predicted”, by category description abbreviation k_hh.”

 

 

 

 

 

 

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

and

https://independent.academia.edu/KarlSeldon

 

 

 

 

 

 

 

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.

 

 

 

 

 

 

YOU are invited to post your comments on this blog-entry below!