Dear Readers,

I usually refrain from posting, here, blog-entries that do not

__address the dynamics, and the 'meta-dynamics', of the global capitalist economic formation.__**EX****plicitl****y**
However, this time, so seminal is the excerpt, below, on dialectics in general, and, hence,

__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.__**IM****plicitly**
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__**. Public Liaison Office has just cleared for public disclosure.**__D__
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 «**» of the Ancient Orient, and the [e.g., Platonian] concept of «***karma***» [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 «***autokinesis***».***kosmos**“*-- 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

**Nonlinearity**”*‘*and

**karmicity**’*‘*.

**auto**-**kinesicity**’
That is, this “nonlinearity” is ‘‘‘self-refl

**xivity’’’ and ‘self-refl**__e__**xivity’.**__u__
Dialectic is ‘self-refl

**xive’, ‘self-refl**__e__**xive’ ‘self-«**__u__**»-icity’, arising out of the ‘self-duality’, or ‘dialectical self-/internal/immanent "contradiction"’, of ‘Nature-al’ ‘‘‘eventities’’’.***aufheben*
This “nonlinearity” [and its inherent prone-ness to
“singularity”]

*****is the manifestation of dialectic within a dialectic-**knowing, ‘‘‘dianoic’’’ [cf. Plato], «**__un__**»-imprisoned [cf. Hegel], modern mathematics.***verstand*
‘Deeply-connectedly’, logical and set-theoretical “paradox”
[Bertrand Russell’s diagnosis: these paradoxes are due to

*“*] is the form in which dialectic has inescapably manifested itself within a dialectics-denying, ideologically and polemically ‘‘‘dianoic’’’ “mathematical [‘mathematicized’] logic” and set theory.**reflexiveness**”
The «

**» has constituted itself, in the past, and continues to constitute itself --***kosmos***--***right now***the present, and**__in__**the future, as and via a process of ‘self-refl***in*__to__**xive self-refl**__e__**xion’, described, in the simplest form, via the simplest system of the ‘mathematics of dialectics’ available to us, by the following formula --**__u__
-- wherein, by the term ‘“sub-

**uclear [“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 --**__n__
[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 «

**» 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**

*modus operandi***1996**--

-- which instantiates the Marxian, dialectical “method of
presentation” -- that Marx wrote about in his

__«__, and used in organizing and writing his world-historical, world-changing**»***Grundrisse***«****» -- 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.***magnum opus*
This ‘dialectic of the axioms-systems of explicitly
dialectical mathematics’ starts from

^{3}_{h}__N___**, which connotes the specification of the axioms-system of the Peano “**_{#}_{_}**atural Numbers” using only the language of “first-order” symbolic logic, a specification long known, albeit “non-constructively” so, to harbor “non-standard models” of “**__N__**atural Numbers” arithmetic, hence also of its algebra.**__N__
That

In that definition, the

It is

^{3}_{h}__N___**axioms-system of mathematics exhibits a ‘dialecticity’, or ‘«**_{#}_{_}**»-icity’, that is limited to a simplest, most abstract, “purely”-quantitative, or “purely”-ordinal, ‘pre-vestige’ thereof, as exhibited in the ‘‘‘ultra-simple’’’ Peano “***aufheben***uccessor function”,**__s__**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 “**atural”**__N__**umber, is, ‘unifiedly’, transformed in three ways.**__n__It is

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

*****[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 “**R**eal” Numbers,**R**, as follows --**dx**

_{2}(t)/dt

**=**

**x**

_{2}(t)( x_{2}(t) )

**=**

**x**

_{2}(t)^{2}
-- an ‘“

**open-form****=****closed-form**”’-**formatted**solution of which is the following solution-function, given**x**_{2}**(0)****=****1**--**x**

_{2}**(t)**

**=**

**t**

^{0}**+**

**t**

^{1}**+**

**t**

^{2}**+**

**t**

^{3}**+**

**t**

^{4}**+ . . .**

**=**

**+**

**(1**

**-**

**t**

**)**

^{-}

^{1}

**=**

**+**

**1/(1**

**-**

**t)**

^{+}

^{1}

**=**

**1/(1**

**-**

**t)**

-- so that a
“singularity” arises at time

**t****=****1**--**x**

_{2}**(1)**

**=**

**1/(1**

**-**

**1)**

**=**

**1/0**

**(1/0)**does not exist within -- and is "meaningless" within -- the system of the so-called “

__eal” Numbers,__

**R****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

*'*quantitative'

__-__**non***'''*, led up to by a "purely"-quantitative

**revolution**'''*"dynamical*of this '''simplest''' of nonlinear "total--differential", or "ordinary"-differential, equations!

**evolution**"We will release presentations of the

__non__*-*“infinite”, ‘meta-

**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**

__finite__**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"]. ...”

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