**An Easy Take on**

**F**.

**.**

__E__**.'**

__D__**s**

**1**

**st**

__Dialectical__IdeographyDear Readers,

It is all a matter of the

http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Cumulum/Cumulum.htm

**. This blog entry is my attempt at a low-detail take on the essence of the**__Preface__**F**.**.**__E__**.**__D__*"*.**first**__dialectical__**arithmetic**"**. The**__[Almost] "No Math.", "No Frills" Intro. to the__*first**Dialectical**Ideography***of the**__dialectical__ideograms**F**.**.**__E__**.**__D__*"*can be used, as follows below, to discover [to reconstruct] the**first**"__dialectical__ideography**, and [to "pre-construct"] the***past***, of various human-natural, and pre-human-natural, self-formation-processes, or systems, as well as to illuminate, in systematic fashion, the***future***"meta-anatomy" and "meta-physiology" of presently thriving systems -- the organizational processes by which they reproduce, or maintain, and expand, their processes, their organization, and their substantiality, illuminating the progress[ions] of nature / of natural systems, and/or the progress[ions] of human idea-systems.***present*It is all a matter of the

*"*of each single category, or of each "**squaring**"__with____itself__**cumulum**" of more than a single category, and of the**cumula**tive effect of all of these "anded" categorial**ities /**__qual__**ifiers / intensions / connotations on the human mind -- on that of the user, and on those of the user's audience(s).**__qual__**cumulum**, pl.**cumula**http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Cumulum/Cumulum.htm

__Step-by-Step Application of the____F__*.*__.__**E**.**D**.**Dialectical Method**at Its First [Minimal] Level of Richness__Step__**. In step**__a__**a**., the user of this ideographical method/algorithm decides what is the best starting point category -- for example, the ontological category of "**quarks**", and such, for the dialectic of nature, and that of commodities, or, more deeply, that of "the elementary form of value", for Marx's dialectical presentation of the capitals-system -- and simply "posits" that beginning:**tep**__s__**=****a**.__"__.**thesis**"__Step__**. Next, to get to step**__b__**b**., the user*"*, or "self-multiplies", or "self-interacts", or "self-operate", or "self-applies", or "self-confronts" the content/result of step**squares**"**a**., and considers the meaning of the result thereof:**tep**__s__**=****b**.__"__

**thesis**"*"times"*

__"__

**thesis**"**=**

__"__

**thesis**"*"of"*

__"__

**thesis**"**=**

__"__

**thesis**"**&**

__"__.

**anti**-**thesis**"__Step__

**. Next, to get to step**

__c__**c**., the user

*"*again, but this time

**squares**"*"*, or "[re-]

**squares**"

*self**-*, the

**reflects**"**of**

__result__*"*the step

**squaring**"**a**. result, that result being the content of step

**b**., namely, the "cumulum" content

--

__"__

**thesis**"**&**

__"__:

**anti**-**thesis**"**tep**

__s__

**=**

**c**.

(

(

(

(

__"__**thesis**"**&**__"__)**anti**-**thesis**"*"times"*(

__"__**thesis**"**&**__"__)**anti**-**thesis**"**=**(

__"__**thesis**"**&**__"__)**anti**-**thesis**"*"of"*(

__"__**thesis**"**&**__"__)**anti**-**thesis**"**=**__"__**thesis**"**&**__"__**anti**-**thesis**"**&**__"__**syn**-**thesis**"**&**__"__.**second****anti**-**thesis**"__Step__**. Next, to get to step**__d__**d**., the user would*"*again, this time**square**"*"*, or "[re-]**squaring**"*self**-*, the**reflecting**"**of**__result__*"*the step**squaring**"**b**. result, that result being the content of step**c**., namely, the "**cumulum**" content --__"__

**thesis**"**&**

__"__

**anti**-**thesis**"**&**

__"__

**syn**-**thesis**"**&**

__"__

**second****anti**-**thesis**"

-- and so on, for as many subsequent steps -- for as long -- as the succeeding result / content / "

**cumula**" of symbolized categories makes sense, to the user, for the application at hand.**. All of the rules ["axioms"] of the**__Commentary__**F**.**.**__E__**. "first dialectical ideography" rules-system ["axiom**__D____s__*-*system"], whose main rules were presented to this thread in a previous blog-entry, entry**# 4**--http://feddialectics-miguel.blogspot.com/2011/08/axioms-rules-of-fed-first-dialectical.html

"Thought it might be useful to reproduce here the core "axioms" -- the main rules -- of the "rules-system", or "axiom

-- as well as the "Dyadic Seldon Function" itself, are aimed at inducing the above-rendered "m.o.", the above-rendered <<

Now, please note that the pattern of this method, or algorithm, is "

-- in that, for example, the content of step

Likewise, the content of step

This "re-

That is, step

-- as it would be per a "

-- because the

Likewise, step

-- or even just --

-- or even just --

-- but is, instead --

-- since, as Hegel said, '''the [record of the] process of arriving at the result is [part of] the result'''.

"Thought it might be useful to reproduce here the core "axioms" -- the main rules -- of the "rules-system", or "axiom

__s__*-*system" ["axiomatic system"] of the**F**.**.**__E__**.**__D__*"*.**First**"__Dialectical__Arithmetic-- as well as the "Dyadic Seldon Function" itself, are aimed at inducing the above-rendered "m.o.", the above-rendered <<

**>> -- the above-rendered "algorithmic" behavior:***modus operandi**"*, i.e.,**the****-**__re____squaring__**of the**"__previously____squared__*"*, or, the "**the re**-**self**-**reflecting of each result of previous self**-**reflection**"**-**__re__*self-*<<**>>***aufheben**-ing"*of each result of previous*"self-*<<**>>***aufheben**s**"*-- in each**ric**__gene__*"*of the**dialector**"__N____Q__**_****, when those**__dialectical__ideography**ric***gene**"*are assigned to, or interpreted as standing for, i.e., as**dialectors**"**,***connoting***ontological categories, as named as such,**__dialectical__**rically, in the steps above, by the names***gene*__"__, and**thesis**"__"__, and**anti**-**thesis**"__"__, and**syn**-**thesis**"__"__, and so on.**second****anti**-**thesis**"Now, please note that the pattern of this method, or algorithm, is "

**evolute**", not "**convolute**" --**evolute**vs.**convolute***http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Evolute/Evolute.htm*-- in that, for example, the content of step

**a**. is still present in the content of step**b**., though also present "anded"*with*something new, or something newly-**plicit/actual, formerly**__ex__**plicit/potential.**__im__Likewise, the content of step

**b**. [and therefore also the content of step**a**.] remains present in the content of step**c**., although, again, together with something(s) new. And so on, for each of the higher/later steps.This "re-

*present**-*ation" of the past is part of the*"*of that universal process which is the very**conservation**moment"**of all dialectic: the <<**__essence__**>> process of***aufheben**"*.**conservation**-**elevation/transformation**"That is, step

**b**. is**just --**__not____"__.**anti**-**thesis**"-- as it would be per a "

**convolute**" product rule, but is, instead --__"__**thesis**"**&**__"__**anti**-**thesis**"-- because the

__"__, though surpassed in step**thesis**"**b**., is still, even if "faded",**forgotten; is still present in the "accumulator" of this**__not__*"*computation"; is still extant in the human memory of the user, and in the memories of the user's audience(s) -- even if somewhat "fadedly" present from "full present-ness" in both, relative to the "present-ness" to memory of the most recently "presented" ontological category, for both.**itative**__qual__Likewise, step

**c**. is not just --__"__**syn**-**thesis**"-- or even just --

__"__**syn**-**thesis**"**&**__"__**second****anti**-**thesis**"-- or even just --

__"__**anti**-**thesis**"**&**__"__**syn**-**thesis**"**&**__"__**second****anti**-**thesis**"-- but is, instead --

__"__**thesis**"**&**__"__**anti**-**thesis**"**&**__"__**syn**-**thesis**"**&**__"__**second****anti**-**thesis**"-- since, as Hegel said, '''the [record of the] process of arriving at the result is [part of] the result'''.

**F**.**.**__E__**. holds this**__D__**of "***principle***" to be one of its several***evoluteness**historically**-*<<**>>***gene**-***ric***"*, applying, albeit for different, "<<__universal__**principles**"**>>-al", reasons, to both the***speci**"*<<**-**__physio__**onto**-**dynamasis**"**>> and the***species**"*<<**-**__ideo__**onto**-**dynamasis**"**>> of the universal pattern of ontology net-expansion.***species***ontology dynamics****& onto-dynamasis**

http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/OntoDynamasis/OntoDynamasis.htm

**,**

ontologyontology

**physio-ontology**,**&****ideo-ontology**

http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/PhysioOntology/PhysioOntology.htm**.**__Some Examples__**A**. Hegel's__<<__.**>>***Logik*

__: A__

NoteNote

*"Triadic*Seldon Function's" output develops from one category in step.**a**., to three categories in step**b**., to nine categories in step**c**., and so on, whereas the output of a*"Dyadic*Seldon Function", such as employed above, develops, as we have seen, from one category in step**a**., to two categories in step**b**., to four categories in step**c**.[, to eight categories in step**d**.], and so on, i.e., a category count, for the*Seldon Function, of three to the power zero for step zero, of three to the power one for step one, of three to the power two for step two, and so on, versus a category-count, for the*__Tri__ad-ic*Seldon Function, of two to the power zero for step zero, of two to the power one for step one, of two to the power two for step two, and so on.*__Dy__ad-ic**tep**__s__**a**.**.**__Abstract Being__**tep**__s__**b**.**"cubed"**__Abstract Being__**=**

__Abstract Being__**&**

__Abstract Nothing__**&**

__Becoming__[per

*"*-ic" Seldon function],__Triad__**=****+**

__B__**+**

__N__**.**

__q__/NB**B**. Marx's

**. Marx designates, in his Preface to the first German edition of**

__Capital__**, vol.**

__Capital__**I**. [pages

**7**to

**8**, International Publishers, New World paperback edition, fifth printing,

**1973**], two distinct <<

**>>, or starting-points, for his four volume treatise on the societal-self-reproductive system of the "capital-relation", i.e., for the epoch of capital as predominant human-social-relation-of-production:**

*arche'*". . . in bourgeois society the commodity form of the product of labour -- or the value-form of the commodity -- is the economic cell-form."

The "shallower" <<

**>> is, thus, the commodity[-capital] value-form in**

*arche'***ral, as, i.e., <<**

*gene***>>. The "deeper" <<**

*genos***>> is, thus, the "elementary or accidental form of [commodity[-capital]-]value", as, i.e., first <<**

*arche'***>> thereof.**

*species*Both <<

**'>> are embedded, as such, in the "content-structure" of Marx's actual text of**

*arche***, vol.**

__Capital__**I**. We will exemplify both, below.

"Shallower"-<<

**>> version.**

*arche'***tep**

__s__**a**.

**.**

__Commodities__**tep**

__s__**b**.

**"squared"**

__Commodities__**=**

**"self-refl**

__Commodities__**xed"**

__e__**=**

**+**

__Commodities__**.**

__Monies__**tep**

__s__**c**.

**(**+

__Commodities__**"squared"**

__Monies__)**=**

**+**

__Commodities__**+**

__Monies__

__Monies__

__Mediated__

__Commodities__**+**

__Circulations__**.**

__Capitals__"Deeper"-<<

**>> version.**

*arche'***tep**

__s__**a**.

__Value____-__.

**Form A****tep**

__s__**b**.

__Value____-__"squared"

**Form A****=**

__Value____-__"self-refl

**Form A****xed"**

__e__**=**

__Value____-__+

**Form A**

__Value____-__.

**Form B****tep**

__s__**c**.

(

__Value____-__+**Form A**__Value____-__) "squared"**Form B****=**

__Value____-__+

**Form A**

__Value____-__

**Form B****+**

__Value____-__+

**Form C**

__The Money Form [of [Capital____-__.

**]Value]**Note that, indeed,

__Value____-__, the "Total or Expanded Form of [Commodity[-Capital]-]Value" is, indeed, a

**Form B***"*<<

**meta**-**>>**

*monad**-*of the <<

**ization**"**>>, or**

*monads***, of**

*units*

__Value____-__, the "Elementary or Accidental [, or Isolated] Form of [Commodity[-Capital]-]Value", and that --

**Form A**

__Value____-__, "The General Form of Value", is, indeed, a "hybrid", or "complex unity", of --

**Form C**

__Value____-__

**Form B**-- with--

__Value____-__.

**Form A****C**.

**F**.

**.**

__E__**.'s**

__D__**of the axioms-**

*Method of Presentation***system**

__s__*-*

**progression**of their system

**of**

__s__**arithmetic --**

__dialectical__*"*

**The**

*Meta**-*

**Systematic**

__Dialectic__

*of the*

__Dialectical__**".**

*Arithmetics Themselves***tep**

__s__**a**.

**.**

__Unqualified Quantifiers System__**tep**

__s__**b**.

**"squared"**

__Unqualified Quantifiers System__**=**

**"self-refl**

__Unqualified Quantifiers System__**xed"**

__e__**=**

__Unqualified Quantifiers System__**+**

**.**

__Unquantifiable__*Ontical*Qualifiers System**tep**

__s__**c**.

**(**,

__Unqualified Quantifiers System__**+**

__Unquantifiable__*Ontical*Qualifiers System**)**, "squared"

**=**

__Unqualified Quantifiers System__**+**

__Unquantifiable__*Ontical*Qualifiers System**+**

**+**

__Quantifiable__*Ontical*Qualifiers System**.**

__Unquantifiable__*Metrical*Qualifiers System**D**.

**of Nature as Totality, per**

*Historical*__Dialectic__**F**.

**.**

__E__**. 's book**

__D__

__A Dialectical__*[excerpt, with "shallower"-<<*

__"__**Theory of Everything**"**>>].**

*arche'***tep**

__s__**a**.

**.**

__atoms__**tep**

__s__**b**.

**"squared"**

__atoms__**=**

**"self-refl**

__atoms__**xed"**

__u__**=**

**+**

__atoms__**.**

__molecules__**tep**

__s__**c**.

**(**+

__atoms__**"squared"**

__molecules__)**=**

**+**

__atoms__**+**

__molecules__

__cosmological__

__atoms__

__to__

__molecules__

__conversion____-__+

**processes**

__prokaryotic____"__

__living____"__

**.**

__cells__**E**.

**of**

*Historical*__Dialectic__**as**

*Nature***, excerpt for just the**

*Totality***of**

__dialectic____"__.

**humanitys**"**tep**

__s__**a**.

__"__.

**humanitys**"**tep**

__s__**b**.

__"__"squared"

**humanitys**"**=**

__"__"self-refl

**humanitys**"**xed"**

__u__**=**

__"__+

**humanitys**"__"__.

**meta**-**humanitys**"**tep**

__s__**c**.

(

__"__+**humanitys**"__"__) "squared"**meta**-**humanitys**"**=**__"__+

**humanitys**"__"__

**meta**-**humanitys**"**+**

__cosmological____"__

**humanitys**"-

__with____-__

__"__

**meta**-**humanitys**"__-__

**+**

__hybrids/alliances__**. . .**.

"Sub-

__dialectic__*"*of practices, or "praxes", implicitly ensuing

*/ "inside" the*

__within____"__category.

**meta**-**humanitys**"sub-

**tep**

__s__**a**.

__human____-__.

**genome biological self**-**re**-**engineering**sub-

**tep**

__s__**b**.

__human____-__"squared"

**genome biological self**-**re**-**engineering****=**

__human____-__"self-refl

**genome biological self**-**re**-**engineering****xed"**

__u__**=**

__human____-__+

**genome biological self**-**re**-**engineering**

__non____-__.

**biological android robotics**sub-

**tep**

__s__**c**.

**(**

__human____-__+

**genome biological self**-**re**-**engineering**

__non____-__

**biological android robotics****)**"squared"

**=**

__human____-__+

**genome biological self**-**re**-**engineering**

__non____-__+

**biological android robotics****+**

__cyborg prothetics / bionics__**. . .**.

**F**.

*Historical*__Dialectic__**, per**

*of the*__Dialectic__Itself**F**.

**.**

__E__**. --**

__D__**tep**

__s__**a**.

__Systematic__**.**

__Dialectic__**tep**

__s__**b**.

__Systematic__**"squared"**

__Dialectic__**=**

__Systematic__**"self-refl**

__Dialectic__**xed"**

__u__**=**

__Systematic__**+**

__Dialectic__**.**

__Historical Dialectic__**tep**

__s__**c**.

(

**+**__Systematic Dialectic__**) "squared"**__Historical Dialectic__**=**

__Systematic__**+**

__Dialectic__

__Historical__**+**

__Dialectic__

__Meta____-__

__System__

__atic__**+**

__Dialectic__

__Psycho__

__historical__**.**

__Dialectic__**.**

G

G

**F**.

**.**

__E__**.'s**

__D__

__Meta__

__-__**Systematic**

__Dialectic__*"*for their method-of-presentation of the

**meta**-**model**"*"*of the

**ideo**-**ontology**"

*contemporary**"*of the axiomatic system

**meta**-**system**"**of the "Standard" arithmetics.**

__s__**tep**

__s__**a**.

**.**

__Natural Numbers System__[the "second-order logic", +, axiomatic system of the

**N**__=__**{1**,**2**,**3**,**...}**"**atural" Numbers' Arithmetic].**__N__**tep**

__s__**b**.

**"squared"**

__Natural Numbers System__**=**

**"self-refl**

__Natural Numbers System__**xed"**

__e__**=**

**+**

__Natural Numbers System__

__The System of the____"__,

**Aught**"**Numbers**

**(---)**

__N__**+**

**.**

__A__[the "second-order logic",

**+**, axiomatic system of the "

**ughts",**

__A__**A**

__=__**{ 0**s

**}**

__=__**{1**

**-**

**1**

**, 2**

**-**

**2**

**, 3**

**-**

**3**

**, ...}**].

**tep**

__s__**c**.

**(**+

__Natural Numbers System__

__The System of the____"__

**Aught**"**Numbers****)**"squared"

**=**

**+**

__Natural Numbers System__

__The System of the____"__+

**Aught**"**Numbers**

__The System for Converting/Reconciling__

__Natural Numbers Arithmetic__

__to/with__**+**

__"Aught" Arithmetic__

__The System of the____"__,

**Minus**"**Numbers****(---)**

__N__**+**

**+**

__A__**+**

__q__/AN

__M__

__=__

__W__**+**

__M__-- wherein --

**q/**

**A**

**N**

__=__

**{0...01**,

**0...02**,

**0...03**,

**...}**

-- and --

**M**

__=__

**{ ...**,

**-**

**3**,

**-**

**2**,

**-**

**1**

**}**

-- and --

**W**

__=__

**{0...0**,

**0...01**,

**0...02**,

**0...03**,

**...}**

-- the "

**hole" Numbers.**__W__**tep**

__s__**d**.

**(**+

__N__**+**

__A__**+**

__q__/AN**"squared"**

__M__)**=**

__N__**+**

**+**

__A__**+**

__q__/AN**+**

__M__

__System for Converting/Reconciling Natural Numbers Arithmetic to/with Minus Arithmetic__**+**

__System for Converting/Reconciling Aught Number(s) Arithmetic to/with Minus Arithmetic__**+**

**...**

__System for Converting/Reconciling the__

__q__**/**

**A**

**N**...

__System of Arithmetic to/with Minus Arithmetic__**+**

__System of Fractional Arithmetic__**(---)**

__N__**+**

**+**

__A__**+**

__q__/AN**+**

__M__**+**

__q__/MN**+**

__q__/MA**+**

__q__/MAN

__F__

__=__

__Z__**+**

__F__-- wherein --

**q/**

**M**

**N**

__=__**{+0...01**,

**+0...02**,

**+0...03**,

**...}**

-- and --

**q/**

**M**

**A**

__=__**{ ±0**s

**}**...

**...**

__=__**{ ±(1**

**-**

**1**

**)**,

**±(2**

**-**

**2**

**)**,

**±(3**

**-**

**3**

**)**,

**...}**

-- and --

**q/**

**M**

**A**

**N**

__=__

**{ ±0...0**,

**+0...01**,

**+0...02**,

**+0...03**,

**...}**

-- and --

**F**

__=__

**{.....**

**-**

**0...0**

**3**

**/1**

**....**

**-**

**0...0**

**2**

**/1**

**....**

**-**

**0...0**

**1**

**/1**

**....±0...0/1....+ 0...01/1....+0...02/1....+0...03/1.....}**

-- [more aptly, for every

**n**and

**m**in

**N**,

**F**

__=__**{ m/n }**

__=__**{ ./. }**, but leads to the "dense" number-set notated above by step

**e**., in which the arithmetic of "ratio-nal" numbers, or comprehensive

**uotient numbers -- the**

__Q__**arithmetic -- emerges]**

__Q__-- and --

**Z**

__=__

**{...**,

**-**

**0...0**

**3**,

**-**

**0...0**

**2**,

**-**

**0...0**

**1**,

**±0...0**,

**+0...01**,

**+0...02**,

**+0...03**,

**...}**.

Regards,

Miguel