Seldon: «Monads» Everywhere, hence «Arithmoi» Everywhere: A Latter-Day ‘Meta-Pythagorean’ Vision of Our «Kosmos». GLOBAL STRATEGIC HYPOTHESES.

 

 

 

 

 

 

 

 

 

 

 

 

Seldon:

 

«Monads» Everywhere,

 

hence

 

«Arithmoi» Everywhere:

 

A Latter-Day

‘Meta-Pythagorean’

Vision

of

Our «Kosmos».

 

 

 

GLOBAL STRATEGIC HYPOTHESES.

 

 

 

 

 

 

 

 

 

 

 

Dear Reader, 

The text below, by our co-founder, Karl Seldon, ‘explicitizes’ the connection -- by means of a concurrent, ‘«aufheben»-ating’ immanent-critique/‘ideic scale’ elevation/conservation of the ideology of the ancient Pythagoreans -- to the Foundation’s ‘Dialectical Theory of Everything’ .

 

 

 

Seldon –

 

“All is «Arithmos».” 

 

“The «Monads» of being arise by kinds, in multiples.”

 

“Absolutely-unique, «sui generis» units are vanishingly rare.”

 

“Everything is made of «monads», even the «monads» themselves [Except for the «arché-monads»’ «arithmos»], but these «monads» are not Democratean “atoms”.”

 

“These «monads» include units which not only differ from one another with “individual differences”, but which collectively differ qualitatively, differ in kind – i.e., which differ ontologically.  Thus, they are groupable into categories by their shared qualities, i.e., they are mentally-groupable into kind-«arithmoi» .

“«Arithmos», a word from the ancient Greek language, means ‘‘‘number’’’, but not quite in our modern sense.”

 

“A «monad» is a unit of an «arithmos»/‘‘‘number’’’, of a given kind.”

 

“Thus, “All is number’’, in a quite concrete, reasonable, and even sensuous sense – no mysticisms required.”

 

“An «Arithmos», made up out of units, all of one kind, is a ‘kind-number’, an ‘ontological number’, an «onto-arithmos».”

 

“A ‘‘‘kind’’’ [cf. Platon’s, dialectical, «arithmoi eidetikoi»] is a mental assemblage of units, all of the same, qualitative, ontological ‘“species”’ – a ‘qualitative number’.”

 

“Arithmetic”, «Arithmetikê», was, anciently, ‘‘‘the science of [such] number(s)’’’.”

 

“The Foundation’s ‘_NQ Arithmetic’ is an arithmetic/algebra for representing, and ‘non-quantitatively calculating’ with, especially the, concrete, ontological, hence “purely”-qualitative, ‘‘‘[[meta-]Natural] [meta-]numbers’’’, i.e., indefinite numerosities of kind-«monads», by means of its ‘‘‘[meta-]numerals’’’.”

 

“Each symbolic unit/«monad» of the finite-indefinite ‘‘‘number of idea-units’’’/«ideo-arithmos» named _NQ is, in its uttermost root meaning, a symbolic, ideographical, ‘‘‘[meta-Natural-]numeralic’’’ representation of a ‘qualitative finitary ordinal number’.” 

 

“That is, the generic symbol-unit/«monad» of the _NQ «arithmos», namely q_n, incorporates the generic “natural” number, n, as denoting the nth order-count/order-place/order-number.  But the symbol q_n as a whole denotes the ordinal quality of ‘nth-ness’.”

 

“Interpreted/applied for mathematical-models of categorial progressions, generic q_n denotes the nth category in [any] such, strictly-ordered, categorial progression.” 

 

“That is, in set-theoretic language, q_n denotes the set of all categories such that each one occupies the nth order-place in its native categorial progression; the nth category generally; the ‘ideic’ quality of categorial nth-ness – the intension of the extension of all nth-in-order-place categories.”  

 

“This generic ‘categorial-ordinal arithmetical language’ can therefore be used to symbolize strictly-ordered categorial progressions of myriad kinds, for myriad ontological Domains – for ‘[ideo-]physi[c]o-ontological’ Domains, for myriad “pure” ‘ideo-ontological’ Domains, and for myriad ‘‘‘mixed’’’, i.e., for ‘ideo-physio-ontological’ Domains as well.”

 

“Starting from a chosen, specific-Domain «arché»-category, or starting-category/‘categorial premise’, which is always assigned to generic _NQ category-symbol q₁, the generic _NQ arithmetic/algebra can be used/specified so as to help elicit, from Domain-expert user(‘)s(’) mind(s), the entire progression of categories, synchronic, systematic or diachronic, historical – reflecting the progression of the kinds of units of the actual reality of that Domain – which if achieved by a given user, constitutes the, user-comprehended, ontological content-analysis of that Domain.”

 

 

 

 

 

 

 

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!

 

 

 

 

 

 

 

«Aufheben» Meta-Unit-ization and Identity Consolidation. GLOBAL STRATEGIC HYPOTHESES.

 

 

 

 

 

«Aufheben»

Meta-Unit-ization

and

Identity

Consolidation.

 

 

 

 

 

 

 

GLOBAL STRATEGIC HYPOTHESES.

 

 

 

 

 

 

 

 

 

 

 

Dear Reader,

 

Is the ‘identity consolidation’ that goes along with the ‘universal architectonic’ processes of «aufheben» ‘meta-unit-ization’ just a human, subjective perception, without any objective reality?

 

¿For example,

 

in q_a ® q_a2 = q_a <+> q_aa |-º q_a <+> q_m, 

is the shift from the separately-identified identities for individual atoms to multiple atom units merged into the singular identity of a molecule ‘meta-unit’ – is that just a human perception, or, given that both atoms and molecules are too small in scale to be perceptible by our senses, just a subjective, human-mental conception?

 

¿Or, is there some objective truth to such ‘identity consolidations’, independent of human perceptions and conceptions?

 

We hold that there is objective as well as human-subjective merit to the concept of ‘actual identity consolidation’.

 

 

We so hold because the objects in question actually behave more as single, ‘hol’ units, rather than as mere clusters of multiple, separate ‘hol’ units.

 

However, in the ‘‘‘complex unity’’’, the ‘meta-unity’, of such ‘meta-units’,  the individual existences of their mere units are still present, «aufheben»-conserved, if in a behaviorally-constrained, subsumed fashion.

 

 

Their «aufheben»-conserved presence, especially under certain conditions, will still obtrude into more obvious manifestation.

 

Consider, for example, the, albeit relatively weak, Van der Waals forces of molecules, e.g., the distance-dependent electrostatical attractions between neutral atoms contained in molecules, which result from chemical-bonds-related differential electron densities in the contained atoms.

 

Thus, what is obtruding in this example, is not only the atom units «aufheben»-conserved within the molecule units, but also the sub-atomic “particle” units, e.g., the electrons, «aufheben»-conserved within those atom units.

 

 

 

 

 

 

 

 

 

 

 

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!

 

 

 

 

 

 

 

Surprising Examples of Quanto-Qualitative Information Conveyance. GLOBAL STRATEGIC HYPOTHESES.

 

Surprising

Examples

of

Quanto-Qualitative

Information

Conveyance.

 

 

 

 

 

 

 

GLOBAL STRATEGIC HYPOTHESES.

 

 

 

 

 

 

 

 

 

 

 

Dear Reader,

The use of symbolic arithmetical qualifiers was born, as far as we know, in North African late Antiquity.

 

It was born in a papyrus multi-scroll treatise, composed in ancient Alexandria, Egypt, then a pinnacular city-state for mathematical, proto-scientific and engineering theory and practice – perhaps THE pinnacular such city of the ancient world – circa 250 C.E.

 

This Greek scroll was titled, per its English translation, “The Arithmetica”, and was written by Diophantus of Alexandria.

 

 

This scroll was a prevenient and protoic work of syncopated [word-abbreviating], quasi-ideographical-symbolic arithmetic and algebra, which, after the long Dark Ages, was partially recovered, translated and printed, then exercising a strong influence toward the rebirth of mathematics in general, and of algebra in particular, to the North of Alexandria, in Renaissance Europe.

 

A prominent feature of the Arithmetica manuscript was the use of a proto-symbol standing for the ultimate unit of any «arithmos», or assemblage/«ensemble» of concrete qualitative – qualit(y)(ies)-bearing – units, the «Monad», hence its syncopated, proto-symbolic representation in that manuscript, M^o.

 

 

But the European development of arithmetic, algebra, and beyond opted for abstract quantities, and ideographical symbolizations of “pure”, unqualified quantities only, reflecting, we think, the mostly unwitting psychohistorical impact of the parallel development, to a more massive scale than ever before in human history, of the money-mediated exchange of commodities, and of mercantile and manufacturing capital.

 

For long centuries, arithmetic and algebra exhibited an ‘Elision of the Arithmetical Qualifiers’, until the discovery of the possible workability of, and then the widespread adoption of, i, symbol for the +Ö(-1), later furthered by the less-widespread adoption of other arithmetical qualifiers, such as the Grassmann qualitative units, not to mention those of the Quaternions and Octonions.

 

Nonetheless, a ‘Re-Emergence of the Arithmetical Qualifiers’ was underway, and the development of the Seldonian axioms-systems of arithmetics/algebras for modeling dialectics is one of the little-known latter-day culminations of that re-emergence.

 

But, apart from this more macro psychohistorical trend, de facto arithmetical qualifiers, typically not fully understood as such, have continued to pop-up in practical and engineering applications of arithmetics and algebras.

 

Most all of us have encountered the quantification of ‘metrological quasi-arithmetical unit qualifers’, e.g., of the units-of-measure symbols – albeit still “syncopated”, much like the proto-ideograms of the ancient Arithmetica manuscript, still after all of these centuries! – 

e.g., 8 hrs., 10 lbs., 20 cm., 72 °F., 20$s, etc. 

At last, these syncopations become fully arithmetical – and fully ideographical – in the longform Seldon Dialectical Progression, starting in its seventh arithmetic-system, that is, in the _Rq_MQR º _Rq_MU º _Rm axioms-system.

 

In that, Seldonian, system, the R-inherent quantifiers quantify the M-inherent metrological-unit qualifiers, and, together, those two, as one, ‘quanto-qualify’ the ontological-qualifer units of U.

 

But, far apart from these Seldonian developments, surprising examples of arithmetical ‘quanto-qualities’ have emerged.

 

Consider the following standard expression in the film-making world: 1920 ´ 1080p, which, for example, AIs often write as “1920 ´ 1080p”, thus giving special emphasis to the “p” via its italicization.

 

That “p” is an arithmetical qualifier in its own right, because it is not a quantity, an arithmetical quantifier.  It stands for the word “pixel”, which is a concrete, qualitative unit, a unit of digital depiction.

 

The arithmetical quantifier, (1920 ´ 1080), will tell us explicitly, when the stated multiplication is carried out, the number of pixels in a given “frame” of the digital film file: (2,073,600)p.  This expression would tell us the “video resolution” of the film.  But something useful would be lost thereby. 

 

The carrying-out of even this, “purely-quantitative”, multiplication operation would cause a loss of qualitative information.  

 

This is because the unmultiplied expression, 1920 ´ 1080, tells us the shape of the frame, by telling us the width versus the height, the “aspect ratio”, of each frame in that, standard, digital film file.

 

Here quantitative information, expressed in a certain way, also conveys qualitative information.

 

Evidently, then, ‘quanto-qualitative’ mathematics is not always a matter of the strict separation of ‘arithmetical quantifiers’ from ‘arithmetical qualifiers’, asserted by the expression –

 

(arithmetical quantifiers) “´” [arithmetical qualifiers], e.g.,

 

 (1920 ´ 1080) Ä [p]

 

– where, herein, ‘Ä’ symbolizes a generalized concept of the “multiplication” operation, that covers multiplication of quantifiers by quantifiers, qualifiers by quantifiers, and qualifiers by qualifiers.

 

 

 

 

 

 

 

 

 

 

 

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!