Part 06:
Seldon’s Slogans Series.
My Views on Slogan 5.
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, key Encyclopedia Dialectica themes of Seldonian Theory.
The 5th text in 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].
Seldon’s Slogans, #5 --
“Ontodynamis models Ontodynamasis.”
M.D.: My views on this Seldonian slogan are the following:
This slogan is more about the mathematical modeling of dialectical ‘onto-dynamasis’ than about the concrete, physical process of ‘onto-dynamasis’ in itself.
‘Onto-dynamasis’ is Seldon’s term for the dynamical character of real ontological change, and, especially, of ontological gain; ontology [net-]expansion.
‘Onto-dynamasis’ is about the ways in which a single kind of old – already extant – ontology ‘«aufheben»-ates’ itself, by ‘meta-«monad»-izing its «monads», or about the ways in which multiple, disparate ‘onto-types’ mutually ‘«aufheben»-ate’ and hybridize/dialectically-synthesize, in either case to irrupt new kinds of being, new ‘onto-types’; new ontology.
‘Onto-Dynamis’ has its etymology from the ancient Mediterranean civilizations, especially from the ancient ‘‘‘G[r]eeks’’’, and their theory of arithmetic, and, in particular, in the historic culmination of that ‘‘‘psychohistorical’’’ era’s «mentalité» in the famous circa 250 C.E. proto-algebraic treatise by Diophantus of Alexandria, entitled «Arithmetikê».
In his introduction to that work, Diophantus wrote as follows: “All numbers are made up of some multitude of units [i.e., of «monads»]….Among them are –
squares, which are formed when any number is multiplied by itself; the number itself is called the side of a square….”
“Now each of these numbers, which have been given abbreviated names, is recognized as an element in arithmetical science; the square [of the unknown quantity] is called dynamis, and its sign is D with the index U, that is DU; ….The number which has none of these characteristics, but merely has in it an undetermined [unknown] multitude of units [«monads»], is called arithmos, and its sign is V. There is also another sign, denoting the invariable element in determinate numbers, the unit [‘«Monad»’], and its sign is M with the index O, that is Mo.”
[Victor J, Katz, A History of Mathematics: An Introduction, 2nd ed., Addison-Wesley, NY, 1998, p. 174].
Seldon’s neologism, built on Diophantus’s use of dynamis as above – namely ‘onto-dynamis’ – refers to the “squaring” of the ‘«arché»-ontic category’s symbol, in stage 1, h = 1, of the generic dialectical function that we call ‘The Dyadic Seldon Function’, and, also per that function, the subsequent re-squaring of each new, expanded ontological-possibilities-cumulum of category-symbols that follow from the squaring of each [non-amalgamative] sum of ontological category-symbols that follow from the squaring of that first squaring.
In many ancient Greek philosophies, the words «dynamis» and «dynameis» had broader meanings than Diophantus made explicit in his definitions, quoted above. They meant “powers” in the sense of “dynamic qualities” and of “opposed powers”, also called «pathe», and, later, also potentialities as distinct from actualizations.
In mathematics today, we refer to the exponents of, e.g., variable quantities, as powers, e.g., the “power” 2 as in x2, the “power” 3, as in x3, the power 4, as in x4, etc. Diophantus’s usage of «dynamis» appears to be restricted to what we would today call the “power” of two, the “quadratic” power, the “second degree”.
We believe that Diophantus’s use of the term «dynamis» – “power” – as his name for squaring influenced later algebraists’ usage of “power” to refer to exponents other than 2, as well as to the power 2.
Seldon calls ‘dialectical ontological categories’ and their symbols by the name ‘ontos’, for short, so that ‘onto-dynamis’ describes and names ‘the squarings of ontological category-symbols’.
So the historical-dialectical ‘Dyadic Seldon Function’ –
2жt = á a ñ2t
– represents the ‘self-iterated’ squaring and re-squaring of the «arché»-onto – the «arché» ontic-category symbol – a, and to the squarings of all of the subsequent ontic category-symbols that arise, from that initial squaring, by their [re-]squaring.
Hence “Ontodynamis models Ontodynamasis.”.
For more information regarding these Seldonian insights, including free-of-charge downloads of F.E.D. books and other texts, please see --
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.
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