F.E.D. Dialectics

Sunday, March 22, 2026

The Dialectic of Euclidean Geometry. Part 8.: Cases of Dialectic Series.

The Dialectic

Euclidean

Geometry.

Part 8.:

Cases of Dialectic Series.

Dear Reader,

In the ‘dialectogram’ posted above, the depicted «arché» category, or ‘premise category’, is the category whose units are the axiomatic systems of the Euclidean Geometries, color-coded ‘red-ish’.

For those geometries, based upon Euclid’s fifth axiom, or “5th postulate”, the number of lines parallel to a given line is exactly one, or, in the ‘dialectogram’s short-hand,

#(||) = 1.

The depicted ‘first contra-category’ to this «arché» category is the category whose units are the axioms-systems of the standard, classical “Non-Euclidean Geometries”, color-coded orange, and placed at a higher elevation in the ‘dialectogram’, to signify the greater ‘thought-complexity’ of this second category, and of its units.

The key characteristic of these classical “Non-Euclidean Geometries” is that the number of lines parallel to a given line is different from one, or, in the dialectogram’s short-hand, #(||) ~= 1.

Two sub-species of this species of “Non-Euclidean Geometries” are also depicted in that ‘dialectogram’.

The left-most sub-species category depiction is that for the axioms-systems units of the “Elliptic” Non-Euclidean Geometries, for which the number of lines parallel to a given line is less than one, or, in the dialectogram’s short-hand, #(||) < 1; in fact, for which #(||) = 0.

The right-most sub-species category depiction is that for the axioms-systems units of the “Hyperbolic” Non-Euclidean Geometries, for which the number of lines parallel to a given line is less than one, or, in that dialectogram’s short-hand, #(||) > 1; in fact, for which #(||) = “¥”.

The depicted third category, the ‘first uni-category’, uniting or unifying the «arché» category and its ‘first contra-category’, is the category whose units are the axioms-systems of the “Riemannian Geometries”, color-coded ‘yellow-ish’, and placed at the highest elevation in that ‘dialectogram’, to signify the greater ‘thought-complexity’ of this third category, and of its units, relative to the other categories depicted in this ‘dialectogram’, and to their units.

The “manifolds’ – the spaces of Riemannian Geometries – can combine regions of “flat”, Euclidean-like geometry, with regions of “curved”, Elliptic-like geometry and with other regions of “curved”, Hyperbolic-like geometry, as well as with other kinds of “curved” geometries!

Humanity’s presently-known best – most observationally and experimentally corroborated – mathematical model of large-scale physical space[-time]; of the large-scale universe, and of universal gravity, uses the “pseudo-Riemannian” or “semi-Riemannian” geometry, developed by Albert Einstein in his theory of universal gravitation, “The General Theory of Relativity’.

The Domain of this case of dialectic, ‘the dialectic of Euclidean versus Non-Euclidean geometries’, we name “Euclidean and Related Geometries-in-General”, or ERG for short – D = ERG.

The category-symbol that we have adopted for the «arché» category, of “Euclidean Geometries”, is ‘q_E’. The category-symbol that we used, above, for the second category, the ‘first contra-category’, of “Non-Euclidean Geometries”, is ‘q_N’, or, equivalently, is ‘q_EE’, connoting the immanent critique, or self-critique, of the “Euclidean Geometries”. The category-symbol that we used, above, for the “Riemannian Geometries”, is ‘q_R’, or, equivalently, is ‘q_N_E’, signifying the mutual critique, mutual conversion, combination or unification of category ‘q_N’ and category ‘q_E’.

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!

Saturday, March 07, 2026

Ubiquitous ‘Onto-Dynamasis’: Our Everywhere Self-Creative Cosmos.

Ubiquitous

‘Onto-Dynamasis’:

Our

Everywhere

Self-Creative

Cosmos.

Dear Reader,

This blog-entry is inspired via a YouTube presentation by Bruce Director of Promethean Action, a group of followers of the late Lyndon LaRouche, who “got religion”, but whose views are also rooted in LaRouche’s theory of “physical economy”, which was rooted, in turn, for LaRouche, originally, in Marx’s work, so that the Promethean Action group is a pro-productive-force-growth, pro-MAGA group.

LaRouche himself converted to Catholicism after his incarceration by the U.S. Federal Government.

In his 28 February 2026 presentation, entitled “A New Scientific Revolution, 150 Years of Materialism is Ending”, Bruce Director states the following regarding the “LaRouche-Riemann Method”, for “advancing man’s [sic] power in and over nature” –

“…it basically boils down to a simple, basic idea, that the universe is everywhere creative, …that the fundamental characteristic of the universe is creativity, not just human creativity, but creativity everywhere in the universe, that everything in the universe is in the process of being creative.”

With this statement, we of F.E.D. most heartily agree!

I will explain why and how it is that we agree with that statement a little further below.

Bruce Director then goes on to say that the above-quoted statement implies: “…that, if the universe is creative, that it has a Creator, and [that] there [was] an act of Creation.”

With regard to that, latter statement, we cannot, in the discipline of science, be sure that anyone can empirically, reproducibly, or logically demonstrate its truth – can either prove or dis-prove it. We therefore remain scientifically agnostic about it.

Bruce Director also states his conviction that human ideas cause physical changes in the universe, especially in the human “physical economy”, with which Marx, in his theory of “universal labor”, and with which we – in the perspective that we call ‘psychohistorical materialism’ – also heartily agree, but Bruce’s ‘Idea-ism’ asserts that such ideas are also “immaterial”.

We hold that such ideas are, indeed, ‘psychē-ic’, born from the human psyche, but without knowing, as yet, given the current degree of advancement in the cognitive and neurological sciences, whether or not they are “immaterial”.

¿Why and how do we so heartily agree with Bruce and the Prometheans, that our cosmos, “Nature” – including ‘human Nature’, the human part of “Nature” – is “everywhere creative”?

This is why and how: Per our fundamental ‘meta-model’ of nature, of ‘‘‘the Dialectic of Nature’’’, our cosmos is, not only quantitatively self-expanding and [pro]creative, but is qualitatively – ONTOLOGICALLY – self-creative, its predecessor ontology ceaselessly interacting and self-interacting, continually ‘[self-]«aufheben»-ating’, and thereby giving birth to ever new successor ontology; to ever new kinds of beings, to [humans’] ever new ontological categories of «monads», that ‘cumulate’ together with [most of] that [«aufheben»-]conserved predecessor ontology.

If one wishes to model from the deepest starting category that is well-known to contemporary science – i.e., excluding, e.g., the ontological categories of “Dark Energy” and “Dark Matter” – then one can begin with the ontological category of pre-atomic “particle” units/«monads», r.

The self-interaction of the category of such “particle”, r(r), or r², conserves many such “particles” in existence, but also gives rise to their [self-]combinations, known as the r self-«aufheben» successor ontological category of atoms –

r² |-= r + a.

Next, the ‘duo-ontological cumulum’

(r + a)

itself begins to self-interact, yielding a doubled, ‘tetra-ontological cumulum’ –

(r + a) ® (r + a)² |-=

(r + a + q_ar + m)

– wherein m stands for the ontological category of molecule units, and q_ar for the ontological category of units which combine pre-atomic “particle” units and/with atom units, e.g., [initially first-generation] stars as units –

(r + a + s + m)

– for a four-fold ontological-categorial ‘cumulum’, which then, next, begins its own self-interaction –

(r + a + s + m)¹ ®

(r + a + s + m)²

– and so on, up to the most advanced ontological-categorial ‘cumulum’ of which we humans so far widely know, the cosmological ‘cumulum’ that includes us, i.e., that includes ‘human meta-societies’, and that has already begun its own self-«aufheben» self-interaction/[self-]combinations, whose new ontologies, whose new ‘merely-hybrid’ as well as ‘self-hybrid’ units/«monads» – whose new kinds of being – are not yet fully known to us:

(r + a + s + m +…+ h)² |-=

(r + a + s + m +…+ h +???)¹.

One can abbreviate this ‘meta-model’ progression of, ‘purely-ontological’, “purely”-qualitative, ‘purely-categorial’ and epochal ‘mere models’ as follows.

Understand the, underscored, symbol å to stand for a purely-ontological-categorial ‘“sum”’ – and therefore for a ‘non-amalgamative sum’ – of ontological category-symbols, without specifying, i.e., by abstracting from, the details of the “operands”, of the category-symbols so ‘‘‘summed’’’.

Then the categorial progression detailed above might be ‘abbreviatively’ summarized as the recurrent iteration of –

å ® å²

– and the above symbolization could well serve as a kind of ‘‘‘logo’’’, or generic image of cosmological ‘onto-dynamasis’; of ‘the Dialectic of Nature’, and even of ontological-categorial-progression [historical-]dialectic in general: of the, ‘«aufheben»-ic’, ‘‘‘self-creativity’’’ of our cosmos as a whole!

The following link links to Bruce Director’s presentation:

https://www.youtube.com/watch?v=gos4G5ZXTGo

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!

Thursday, March 05, 2026

Part 9.: Karl Seldon on Karl Marx Series. Marx’s ‘Historically-Generic’ ‘‘‘Economics of TIME’’’ and a Concrete Metric for Human Freedom.

Marx’s

‘Historically-

Generic’

‘‘‘Economics

TIME’’’

and a

Concrete Metric

for

Human Freedom.

Part 9.:

Karl Seldon on Karl Marx Series.

GLOBAL STRATEGIC HYPOTHESES.

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, Karl Seldon’s commentaries on the world-historic breakthrough work of Karl Marx.

This 9th text in this by now long-running 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 –

“In the notes to himself on his developing immanent critique of ‘scientific ideology’ of capitalist political economy, in the manuscript now known as the Grundrisse, Marx expounded upon many of the “historically-specific” features of the modern socio-economic formation, founded upon “the capital-relation” as the predominant “social relation of [societal self-re]production” in the modern epoch.”

“But therein, beyond capitalism’s epochal, “historical specificity”, Marx also describes something about economics that represents its ‘historical genericity’, a ‘historically generic’ feature which all historical human economic formations must share, as follows:

“… . The less time the society requires to produce wheat, cattle etc., the more time it wins for other production, material or mental. Just as in the case of an individual, the multiplicity of its development, its enjoyment and its activity depends on economization of time. Economy of time, to this all economy ultimately reduces itself. …”.”*

“Marx further notes, later in the Grundrisse, that –

“*...In relation to the whole of society, the creation of disposable time is then also the creation of time for the production of science, art, etc.”.”**

“Years later, in Marx’s manuscript that Frederick Engels edited to produce the third volume of «Das Kapital», Marx wrote out a significant expansion on the above, much earlier-written, ‘‘‘economics of [human societies’ use and allocation of human life-]time’’’, this time centering on the time-use interconnections between the “realm of freedom” and/versus the “realm of necessity” in the context of their ‘historical genericity’:

“…it depends on the labor productivity how much use-value shall be produced in a definite time, hence also in a definite surplus labor-time.”

“The actual wealth of society, and the possibility of constantly expanding its reproduction process, therefore do not depend upon the duration of surplus-labor, but upon its productivity [K.S.: I.e., upon its “productive force” – Marx] and the more or less copious conditions of production under which it is performed.”

“In fact, the realm of freedom actually begins only where labor which is determined by necessity and mundane considerations ceases; thus in the very nature of things it lies beyond the sphere of actual material production.”

“Just as the savage must wrestle with Nature to satisfy his wants, to maintain and reproduce his life, so must civilized man, and he must do so in all social formations and under all possible modes of production”.

“With his development this realm of physical necessity expands as a result of his wants [K.S.: also expanding]; but, at the same time, the forces of production which satisfy these wants also increase.”

“Freedom in this field can only consist in socialized man, the associated producers, rationally regulating their interchange with Nature, bringing it under their common control, instead of being ruled by it as by the blind forces of Nature; and achieving this with the least expenditure of energy and under conditions most favorable to, and worthy of, their human nature. But it nonetheless still remains a realm of necessity.”

“Beyond it begins that development of human energy which is an end in itself, the true realm of freedom, which, however, can blossom forth only with this realm of necessity as its basis. The shortening of the working-day is its basic prerequisite.”.”***

“The passage above suggests, to us, a concrete, ‘historically-generic’ metric for the quantitative measurement of the, too often nebulous, loosely-bandied-about, and often ideological concept of human freedom. This metric is a measure of the social [re]productive force of the human species, but it is also a measure of what, we predict, will become the real “rate of profit”, of the real form of profit, for actualized humanity. Social reproductive force and rate of profit will reconverge, we hold, for trans-capitalist humanity.”

“That simple metric, capturing ‘the quantitative shadow of the qualitative’, is the percentage ratio of the size of the realm of freedom to/divided-by the size of the realm of necessity, both measured in time units – in human life-hours: (f/n).”

“This (f/n) ratio can be measured at the level of a single human life. Or, it can be measured for an escalating series of scales of aggregated groups of human lives, up to and including applying it to the whole of society – of a given social formation.”

“As applied to a whole society, it could produce a per capita ((f/N)/(n/N)) ratio, where N is the count of human lives, the population count, for that society, f the aggregate “free time” and n the aggregate “necessary time”.”

“For the whole historical series of class-divided societies, in which the majority of the populations were slaves, or serfs, or, still today, work-time-paid, wagéd or salaried workers, this would produce a bad average.”

“A tiny portion of the population would have (f/n) ratios approaching (f/0); almost nothing but “free time”, perhaps better described as [“freely”-]‘disposable time’, d. That population would be the ruling class population.”

“Most of the rest of the social population would have (f/n) ratios approaching (0/n); almost no “free time”, no ‘disposable time’, d; with almost all of their life-time as ‘necessary time’, perhaps better described as ‘pre-allocated time’.”

“Only in Marx’s [and our] predicted higher successor system to the capitalist system, should we expect the typical social-individual’s ‘freedom metric’ to look like this –

(f/n)

– or –

(d/p).”

“The increasing production and reproduction of daily, freely-disposable human life-time is the true form of profit and of wealth for an actualized humanity.”

*[Karl Marx, Grundrisse: Foundations of the Critique of Political Economy (Rough Draft), Translated and edited by Martin Nicolaus, Penguin Books, Middlesex, England, UK, 1973, pp. 172 to 173, emphases added by K.S.].

**[Ibid., p.401n, emphasis as in source text.].

***[Karl Marx, Capital: A Critique of Political Economy, vol. III, New World, NY, NY, USA, 1967, p. 820, paragraphs-partitioning and emphases added by K.S.; British spellings converted to American spellings.].