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### First Interview with F.E.D. Co-Founder & '''Mathematics of Dialectics''' Discoverer Karl Seldon. ## Wednesday, August 24, 2011

### Part 15 -- Some Help with "Getting a Handle" on F.E.D. Dialectics: The Dialectic of the Seldonian Dialectical Arithmetics Themselves.

CONTINUED FROM MY IMMEDIATELY-PREVIOUS BLOG ENTRY

[Note:  This topic will also be continued further in my next blog entry].

space --

NB   =   { b/1, b/2, b/3, b/4, . . .}  =  { b1, b2, b3, b4, ...}.

It seems to me that many of the systems of dialectical arithmetic in this "meta-system-atic" systems-progression are strictly presentational / pedagogical / illustrative in character, in terms of presenting, step-by-step, all of the discrete steps necessary to the construction of the dialectical arithmetics that are more useful in scientific [meta-]modeling applications.

The more useful dialectical arithmetics tend to be either the R-based, or "Real" Numbers based, "quanto-qualitative" "full uni-thesis", or "grand synthesis", dialectical-arithmetical systems, which use R [---) q/1 as their <<arche'>>, rather than N, such as the --

q/3 (---] RU_

-- or the  --

q/7 (---] Rq/MU

-- or the --

q/15 (---] Rq/AMU

systems, in the R-parallel portion of that systems-progression "explicitized" above, or such as the pure-qualitative systems of dialectical arithmetic, e.g., the N-based --

q/24 (---] Nq/BA

[example(s) in use -- http://www.dialectics.org/dialectics...AY2008_OCR.pdf -- slide 7],

-- or the --

q/56 (---] Nq/GBA

[example(s) in use -- http://www.dialectics.org/dialectics...AY2008_OCR.pdf -- slide 35]

-- or the --

q/120 (---] Nq/DGBA

[example(s) in use -- http://www.dialectics.org/dialectics...AY2008_OCR.pdf -- slides 10 through 11

-- systems of dialectical arithmetic, which can explicitly model trans-Platonian, human-phenomic <<arithmoi eidetikoi>> dialectical systematizations, with, e.g., two explicit levels of "ideo-taxonomy" [Nq/BA], three explicit levels of "ideo-taxonomy" [Nq/GBA], or four explicit levels of "ideo-taxonomy" [Nq/DGBA], etc., wherein "A" stands for the first Greek [capital] letter, "Alpha", "B" for the second Greek [capital] letter, "Beta", "G" for the third Greek [capital] letter, "Gamma", and "D" for the fourth Greek [capital] letter "Delta", in [Greek] alphabetical order.

TO BE CONTINUED . . .

Regards,

Miguel

### -- for all n, k, j, and i, in an(t), mkj(t), andukji, plus all t, f, g, h, l, o, p, q, r, s, t, u, v, w, x, y, z, all inN

-- each unit, or <<monad>>, of which has the form of a "non-reductive, non-amalgamative fraction", with a system qualifier,
an [quantified by an(t), to count the number / population of this <<species>> of system that is extant as time, t, advances] as "numerator", and a non-amalgamative sum of mnk(t)-quantified and state-variable-qualified metrical qualifiers as the "denominator", thus expressing a generic, explicitly "quanto-qualified" solution-function for the state-space trajectory and/or for the control-parameter-space path -- in short, for potentially the entire course of [self-induced-cum-other-induced]development -- in what F.E.D. terms "unified, state-/control meta-space" -- of a generic dynamical system, but with, as yet, no linguistic capacity for any explicit co-exhibition of the dynamics [ and meta-dynamics"] of any included sub^n-systems, the linguistic capability for the latter arising only beginning with the

q/31 (---] Nq/BAMQN   =   Nq/BAMU   =   "Beta-[Alpha-]Mu_" arithmetic.

[Example(s) of this dialectical arithmetic in use --

38];

+

q/16 (---] Nq/AA   =   Nq/B   =   NB_   =

the fourth "contra-system" -- actually "contra" to all fifteen of the first five triads + of N-based arithmetical systems -- the N-based arithmetical system of the "purely-qualitative", "unquantifiable system qualifiers", either in the sense of a still-implicitly two-level "dynamical super^1-system", or of a still-implicitly two-level, e.g., <<genos>>/<<species>>, "ideo-systematics", "ideo-classification", or "ideo-taxonomy", i.e., a trans-Platonian <<arithmoi eidetikoi>>;

### CONTINUED FROM MY IMMEDIATELY-PREVIOUS BLOG ENTRY

[Note:  This topic will also be continued further in my next blog entry].

-- for all n, k, j, and i, in an, mkj, and q/nkji, plus o, p, q, r, s, t, u, v, w, x, y, and z, all in N;

+
q/15 (---] Nq/AMQN   =   Nq/AMU   =   "Alpha-Mu_" arithmetic   =
the third full "uni-system" dialectical arithmetic of the N-based "qualo-quantitative", or "quanto-qualitative", "system quanto-qualifiers, or qualo-quantifiers"; i.e., for the space of quantifiable system-qualifiers with quantifiable metrical qualifiers, also with state-variable qualification and/or control-parameter qualification;

space --

Nq/AMQN   =   Nq/AMU   =

### CONTINUED FROM MY IMMEDIATELY-PREVIOUS BLOG ENTRY

[Note:  This topic will also be continued further in my next blog entry].

space --

Nq/AMQ   =

{
a1/( ((m11/(q/n111 +...+ q/n11o)) +...+ ((m1s/(q/n1s1 +...+ q/n1sw)) ),

a2/( ((m21/(q/n211 +...+ q/n21p)) +...+ ((m2t/(q/n2t1 +...+ q/n2tx)) ),

a3/( ((m31/(q/n311 +...+ q/n31q)) +...+ ((m3u/(q/n3u1 +...+ q/n3uy)) ),

a4/( ((m41/(q/n411 +...+ q/n41r)) +...+ ((m4v/(q/n4v1 +...+ q/n4vz)) ), ... }

### CONTINUED FROM MY IMMEDIATELY-PREVIOUS BLOG ENTRY

[Note:  This topic will also be continued further in my next blog entry].

space --

Nq/AMN  =

{
(a1xa1)/( m11xm11 + ... + m1wxm1w ),

(a2xa2)/( m21xm21 + ... + m2xxm2x ),

(a3xa3)/( m31xm31 + ... + m3yxm3y ),

(a4xa4)/( m41xm41 + ... + m4zxm4z ), ... }

-- for all an, mkj, and all n, k, and j, plus w, x, y, and z, all in N;

+

q/14 (---] Nq/AMQ    =
the eighth partial "uni-system" of the N-based "purely-qualitative", "unquantifiable system qualifiers" arithmetic; i.e., for the space of unquantifiable complex/compound "dimensional" or "unit-of-measure", multi-metrical -- multi-state-variable and multi-control-parameter -- qualifiers;

### CONTINUED FROM MY IMMEDIATELY-PREVIOUS BLOG ENTRY

[Note:  This topic will also be continued further in my next blog entry].

space --

Nq/AM   =

{
a1/(m11 + ... + m1w),

a2/(m21 + ... + m2x),

a3/(m31 + ... + m3y),

a4/(m41 + ... + m4z), ... }

-- for all n, k, j, in an and mkj, plus w, x, y, and z, all in N;

+

q/13 (---] Nq/AMN   =
the seventh partial "uni-system"; the N-based arithmetical system of the "qualo-quantitative", or "quanto-qualitative", dialectical "meta-numbers" as a system of "quantifiable, typically multi-metrical -- multi-state-variable, multi-control-parameter -- system qualifiers";

space --

Nq/AMN  =

{
(a1xa1)/( m11xm11 + ... + m1wxm1w ),

### CONTINUED FROM MY IMMEDIATELY-PREVIOUS BLOG ENTRY.

[Note:  This topic will also be continued further in my next blog entry].

space --

Nq/AQN   =   Nq/AU   =

{
(a1xa1)/( (u11xu11) + ... + (u1wxu1w) ),

(a2xa2)/( (u21xu21) + ... + (u2xxu2x) ),

(a3xa3)/( (u31xu31) + ... + (u3yxu3y) ),

(a4xa4)/( (u41xu41) + ... + (u4zxu4z) ), ... }

-- for all an, ukj, n, k, and j , plus w, x, y, and z, all in N;

+

q/12 (---] Nq/AM   =

the sixth partial "uni-system" dialectical arithmetic of the N-based arithmetical systems -- the N-based arithmetical system of the "purely-qualitative", "unquantifiable, typically multi-metrical -- multi-state-variable, multi-control-parameter -- system qualifiers";

### CONTINUED FROM MY IMMEDIATELY-PREVIOUS BLOG ENTRY

[Note:  This topic will also be continued further in my next blog entry].

+

q/10 (---] Nq/AQ  =
the fourth partial "uni-system" of the N-based "purely-qualitative", "unquantifiable", typically multi-predicate, multi-quality, or multi-determination system qualifiers";

space --

Nq/AQ   =

{
a1/(q/n11 + ... + q/n1w),

a2/(q/n21 + ... + q/n2x),

a3/(q/n31 + ... + q/n3y),

a4/(q/n41 + ... + q/n4z), ... }

-- for all nkj, and all k and j, plus w, x, y, and z, all in N;

+

q/11 (---] Nq/AQN   =   Nq/AU   =  "Alpha-U_" arithmetic   =

the fifth partial "uni-system" dialectical arithmetic of the N-based "qualo-quantitative", or "quanto-qualitative", "populations with multiple internal populations of units, or of <<monads>>, system quanto-qualifiers, or qualo-quantifiers" --

space --