The 'New Old'. [Excerpt from a Recent Foundation-Internal Dialogue with Karl Seldon].

Dear Reader,

I usually refrain from posting, here, blog-entries that do not EXplicitly address the dynamics, and the 'meta-dynamics', of the global capitalist economic formation.

However, this time, so seminal is the excerpt, below, on dialectics in general, and, hence, IMplicitly also, on the foundations of the dialectical-mathematical modeling of the [psycho]historical dialectic of the capitalist system, that I have decided to make an exception to my general policy in this specific, exceptional case.

I have reproduced, below, an excerpt from the edited transcript of a recent, computer-assisted Foundation-internal dialogue with our co-founder, Karl H. Seldon [denoted by "KHS" in the excerpt below], which the F.E.D. Public Liaison Office has just cleared for public disclosure.

This is another one of Seldon’s highly-concentrated summaries of his ground-breaking discoveries in his advancement of Marxian dialectics.

Enjoy!

Regards,

Miguel

“... KHS:  What I discovered is that, once demystified, the concept of «karma» of the Ancient Orient, and the [e.g., Platonian] concept of «autokinesis» [i.e., of “self-movement”] of the Ancient Occident, contain the seeds of the keys to the possibility of a new, better comprehension, and to a truly present, up-to-date mathematical modeling, of our «kosmos».

“Nonlinearity” -- such as that exhibited by, and blocking the "closed-form" solution of, the differential equation formulations of the most advanced knowledge of the primary “laws” of Nature achieved by Modern humanity to-date -- is ‘karmicity’ and ‘auto-kinesicity’.

That is, this “nonlinearity” is ‘‘‘self-reflexivity’’’ and ‘self-refluxivity’. 

Dialectic is ‘self-reflexive’, ‘self-refluxive’ ‘self-«aufheben»-icity’, arising out of the ‘self-duality’, or ‘dialectical self-/internal/immanent "contradiction"’, of ‘Nature-al’ ‘‘‘eventities’’’.

This “nonlinearity” [and its inherent prone-ness to “singularity”]* is the manifestation of dialectic within a dialectic-unknowing, ‘‘‘dianoic’’’ [cf. Plato], «verstand»-imprisoned [cf. Hegel], modern mathematics.

‘Deeply-connectedly’, logical and set-theoretical “paradox” [Bertrand Russell’s diagnosis:  these paradoxes are due to “reflexiveness”] is the form in which dialectic has inescapably manifested itself within a dialectics-denying, ideologically and polemically ‘‘‘dianoic’’’ “mathematical [‘mathematicized’] logic” and set theory.

The «kosmos» has constituted itself, in the past, and continues to constitute itself -- right now -- in the present, and into the future, as and via a process of ‘self-reflexive self-refluxion’, described, in the simplest form, via the simplest system of the ‘mathematics of dialectics’ available to us, by the following formula --

-- wherein, by the term ‘“sub-nuclear [“non-composite”] particles”’, we mean the ‘cosmo-ontological category’ that includes “non-composite” bosons, and fermions, i.e., for the fermions, the [“non-composite”] quarks, and all leptons [which, given their “Pauli Exclusion” behavior, and their lack of “strong interaction” behavior, are not expected to “compose” -- are not expected to form “composite” “particles” -- and have not been observed as doing so], and wherein also the other symbolic-elements of the formula above are defined as follows --

[For enhanced legibility, see the enlarged version of the above image at the bottom of this blog-entry.]

For descriptively richer, more complex, more concrete renditions of the dialectic «modus operandi» of ‘Nature as a Dialectical Totality’, I also discovered a progression of axioms-systems of ever more powerful ‘mathematics of dialectics’, which I later found could be organized -- presented in taxonomic, ‘classificatory’, pedagogically-optimal order -- and represented compactly, by the following formula, a ‘dialectical meta-equation meta-model’, formulated in the ideographical language of the first system of “mathematics of dialectics” that I discovered in 1996 --

-- which instantiates the Marxian, dialectical “method of presentation” -- that Marx wrote about in his «Grundrisse», and used in organizing and writing his world-historical, world-changing «magnum opus» -- so instantiating by way of generating, in systematic, pedagogical order, a progressive-cumulative presentation of those axioms-systems of mathematics of increasing mathematical modeling power, a ‘dialectic of the mathematics of dialectics’, if you will.

This ‘dialectic of the axioms-systems of explicitly dialectical mathematics’ starts from ³_hN__{#_}, which connotes the specification of the axioms-system of the Peano “Natural Numbers” using only the language of “first-order” symbolic logic, a specification long known, albeit “non-constructively” so, to harbor “non-standard models” of “Natural Numbers” arithmetic, hence also of its algebra.

That ³_hN__{#_} axioms-system of mathematics exhibits a ‘dialecticity’, or ‘«aufheben»-icity’, that is limited to a simplest, most abstract, “purely”-quantitative, or “purely”-ordinal, ‘pre-vestige’ thereof, as exhibited in the ‘‘‘ultra-simple’’’ Peano “successor function”, s, itself -- as in  s(n)  =  n + 1.

In that definition, the argument, or operand, of the s function, or operator, namely n, which can denote any individual “Natural” number, is, ‘unifiedly’, transformed in three ways.

It is (1) changed / “negated” [given that n + 1   ~=  n], (2) “elevated” in “pure”-quantitative magnitude, or in 'ordinal order-value' [in that n + 1   >  n], and also, at the “same time”, (3) “conserved” [in that n is “contained in” n + 1], i.e., in a single word, is ‘«aufheben»-ated’. ...”

“*[In simplest, most abstract form, we can illustrate differential equation ‘nonlinearity / singularity’, as it arises within the undergirding system of arithmetic of the so-called “Real” Numbers, R, as follows --

dx₂(t)/dt    =   x₂(t)( x₂(t) )    =   x₂(t)²

-- an ‘“open-form = closed-form”’-formatted solution of which is the following solution-function, given x₂(0)  =  1 --

x₂(t)  =   t⁰ + t¹ + t² + t³ + t⁴ + . . .    =      

+(1 - t)^-1   =    

+1/(1 - t)⁺¹   =    

1/(1 - t)

-- so that a “singularity” arises at time t = 1 -- 

x₂(1)   =    

1/(1 - 1)  =    

1/0 

-- the problem being that the value / “number” (1/0) does not exist within -- and is "meaningless" within -- the system of the so-called “Real” Numbers, R, so that, here, suddenly, at the instant named t = 1, the solution of even this ‘‘‘simplest’’’ of nonlinear differential equations leaps beyond the language-limitations of the numbers-system within which it was formulated, in an apparently "absolute" kind of apparently "infinitely"-sudden, "infinite"-in-magnitude dis-continuity.

What we have here is a rudimentary mathematical model of a 'non-quantitative' '''revolution''', led up to by a "purely"-quantitative "dynamical evolution" of this '''simplest''' of nonlinear "total--differential", or "ordinary"-differential, equations!   

We will release presentations of the non-“infinite”, ‘meta-finite meta-number’ value -- a value which is not quantitatively different from, but which is qualitatively different from, i.e., which is 'ideo-ontologically' different from -- any value available within the R universe of number(s), and which, beginning in the seventh axioms-system of explicitly dialectical mathematics that arises in the dialectical progression whose formula we gave above, meaningfully resolves, or ‘semantifies’, such singularities. 

We plan to do so soon, and in another venue. 

We have been, for the most part, holding back this dialectical discovery for many years.  

However, our 'psychohistorical-dialectical' calculations have indicated that the time for its public release will soon be "right"]. ...”