F.E.D. Dialectics: ‘Contra-Euclid’. -- Part 10: Quoting Seldon Series.

‘Contra-Euclid’.

-- Part 10: Quoting Seldon Series.

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, key excerpts from the internal writings, and from the internal sayings, of our co-founder, Karl Seldon.

This 10th release of this new such series is posted below [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].

In this 10th installment, Seldon updates and critically extends, a pervasive ancient Mediterranean view of units-in-general -- of <<monads>> -- & of their <<arithmoi>>, that blocked the ancient mind from detecting the <<aufheben>> process and content-structure, the ‘<<aufheben>>, dialectical architectonic’, of our cosmos, i.e., that, in part, blocked the ancient mind from perceiving ‘the dialectic of Nature’, both systematic and historical. Apparently, there are some ostensibly “modern” minds that still fail in their perception of this.

Seldon –

“… . Per our sources, Euclid held a view of “number” that also pervaded the ancient Mediterranean ‘human phenomes’, one that verged on the kind of radical atomism that was more extremely pursued by Democritus, Epicurus, Lucretius, etc., but that was more moderately evident in the thinking of Plato[, Socrates], Aristotle, Archimedes, Eudoxus, and many other thinkers of antiquity.”

“We tie it, ‘‘‘psychohistorically’’’, to the “antediluvian”, pre-capitalist relative development of social praxis of “the exchange-value” [Marx] in that ancient human-social world, and the more sensuous, less abstract concept of “number” -- <<arithmos>> -- that therefore then prevailed.”

“But let us first hear about Euclid’s views, as those of an exalted exemplar of that ancient mentalité –

“EUCLID defines in the Elements, VII, 2, a number [KS: <<arithmos>>] as “the multitude made up of units” [KS: i.e., as an <<arithmos>> made of <<monads>>] having previously said (Elements, VII, 1) that a unit [KS: <<monad>>] is “that by virtue of which each of existing things is called one”. As a unit is not composed of units, neither EUCLID nor ARISTOTLE regard a unit as a number, but rather [KS: regard any single unit] as “the basis [KS: <<arché>>] of counting, or as the origin [KS: <<arché>>] of number.”

-- excerpted from Numbers, by H. Hermes, et al., Graduate Texts in Mathematics 123: Readings in Mathematics, 1991, Springer-Verlag, NY, page 12, emphasis added.”

“With regard to the proposition “a unit is not composed of units”, we beg to differ.”

“We beg to differ, because the exo-human sub-cosmos, including the pre-human sub-cosmos, per our best present evidence, and ‘the human [sub-]cosmos’ as well, exhibit countless and ubiquitous examples, all ‘modelable’ by the following, contrary proposition –

Each typical unit is composed of [sub¹-]units, which, in turn, are typically themselves each composed of [sub²-]units, which are, in turn, typically each composed of [sub³-]units, which…

-- and so on, for some finite, n-fold regress of ‘subⁿ’ scales, for n denoting a “natural” number.”

“What we see -- both historically and systematically, i.e., both diachronically and »synchronically -- is the following picture –

Some monads/units of a given arithmos constitute multiple sub-arithmoi of/within that arithmos, which in their coalescence, constitute a higher kind of unit, or monad, presenting as a higher arithmos of higher monads/units, with some monads/units of that higher arithmos too constituting its own, multiple sub-arithmoi, presenting, in their coalescence, as a yet higher arithmos of yet higher monads/units, and so on.”

“Such examples include –

1. For our known cosmos, for Nature as the

totality, from the presently-known

‘MICROcosmic arché’: sub-atomic “particle” units are contained in “atom” units, which are contained in “molecule” units, which are contained in…“living cell” units, which are contained in “multicellular organism” units, which are contained in animal and plant “society” units,…;

2. Human, written language systems: phonetic

character units, or “letter” units, are oft

contained in “syllable” units, which are oft

contained in “word” units, which are oft

contained in “phrase” units, which are oft

contained in “sentence” units, which are oft

contained in “paragraph” units, oft

contained in, e.g., “chapter” units, which are

oft contained in “book” units, which are oft

contained in, e.g., “library” units;

3. Human-social formations, contemporary and

historical: [contemporary] family units are

contained in neighborhood units, which are

contained in city units, which are contained in county units, which are contained in state or province units, which are contained in nation-state units; [ancient-historical] multiple primeval hunter-gatherer-forager-scavenger band units, coalesce into multi-band, multi-family camp units, some of which later coalesce into multi-camp village units, some of which later coalesce into multi-village chiefdom units, some of which later coalesce into multi-chiefdom, “multi-tribal” city-state units, some of which later coalesce into multi-city-state empire units;

4. Monolithic Integrated Circuits: “integrated circuit” units are [meta¹-]circuits of circuits/contain multiple “mere” circuit units;

5. Modern ‘Computerware’: “Bit” units are

typically contained in “byte” units, which

are typically contained in “word” units, which are typically contained in “command” units, which are typically contained in “program” units, which are typically contained in “software system” units;

6. Television Programming: “Episode” units are

contained in “Season” units, which, in turn,

are contained in “Series” units, which, in

turn, may be contained in ‘Multi-Series’

units [e.g., the Star Trek ‘multi-series’];

7. Our known cosmos, Nature as the totality,

from a ‘MACROcosmic arché’: …“galaxy”

units are typically contained in galactic

“cluster” units, which, in turn, are typically

contained in galactic “super-cluster” units,

which, in turn, are typically contained in multi-super-cluster “filament” units, which are, in turn, contained in … “the cosmic web”.”

“In fairness to Euclid and others of this ancient <<mentalité>> about <<arithmoi>>/numbers, I should say that the ‘scaled sub-unitary regresses’ within commonly-perceptible units for ancient Mediterranean humanity, including for the original Pythagoreans, were not so obvious as they have become for at least scientifically-educated humans of today.”

“If we recall the more concrete meaning of “number” as <<arithmos>>, reflecting the more sensuous, use-value centered, pre-capitalist psychohistorical milieu/-phenomes of most of ancient Mediterranean humanity -- so remote from the far more abstract and ‘de-sensualized’ meaning of “number” for modern humanity, under the influence of a far more extensive development of capital, of money, of price, and of the permeation of social-reproductive praxis by exchange-value exchange; by the semi-conscious modern paradigm that Marx called “The Elementary Form of Value”, and made the <<arché>> of his critique of capitalist political economy -- then assertions attributed to the original Pythagoreans can be seen in a new light.”

“The assertion that “All is number” sounds hyper-mystical to us today, given our abstract notions of “number”, and also sounded so even to the also-ancient but latter-day “Neo-Pythagoreans”.

“But “All is <<arithmos>>” to the earlier ancient ear could be interpreted as the very sensuous, concrete, empirical assertion that most <<monads>> come in multitudes, each such multitude sorted, or sortable, into its own specific, qualitative “kind”; that absolutely unique, sui generis units are rare.”

“Plato even presented the fundamental ideas as ‘monadic’ and ‘arithmic’ -- as a self-broken, self-discretized, rhythmic flow [<<rhythmos>>] -- i.e., as forming qualitative <<arithmoi>>, the <<arithmoi eidetikoi>>, made up out of ‘‘‘ideo-<<monads>>’’’, for his version of <<dialektikê>>.”

For more information regarding these Seldonian insights, please see --

www.dialectics.info

For partially pictographical, ‘poster-ized’ visualizations of many of these Seldonian insights -- specimens of ‘dialectical art’ – as well as dialectically-illustrated books by the F.E.D. Press, see --