**How to Calculate**[

__Dialectically__**and purely**]

__qual__itativelyDear Readers,

I have already presented in this blog, several of the

**F**.

**.**

__E__**.**

__D__*“*, formulated using the ideographical, arithmetical/algebraic language of the

__dialectical__**meta**-**models**”**F**.

**.**

__E__**.**

__D__*“*, that of the

**First**__Dialectical__**Arithmetic**”**N**

__Q__*“*.

**dialectors**”The purpose of this post is to show, in detail, how to generate those

*“*, and others like them, from their “

**-**__dialectical__meta**models**”**Dyadic Seldon Functions**”, using the

*rules**-*– the

**system****of**

*system***– of the**

*axioms***N**

**, purely-qualitative**

__Q__**, axioms or rules that I have already presented in this thread, in an earlier blog entry here.**

__dialectical__languageFor instance, we presented excerpts from the “

**Dialectic of Nature**” natural-

**historical**-

__dialectical__*“*, through epoch

**meta**-**model**”**t =**

**3**--

__>-|-<__**t**

**=**

**3**

**=**

**<**

__n__>^(2^3)**=**

__n__

**+**

__s__**+**

__q__**/**

**s**

**n**

**+**

__a__**+**

__q__**/**

**a**

**n**

**+**

__q__**/**

**a**

**s**

**+**

__q__**/**

**a**

**s**

**n**

**+**

__m__-- wherein, using, for

**n**in

**N**,

__q__**/n <----]**to assert “

__x__

__q__**/n**is

**/**

*assigned to***/**

*interpreted as*

*used to model***” --**

__x__

__q__**/1 <----]**the physio-ontological category of sub-

__n__=**uclear “particles” [ <<**

__n__**>>], e.g.,**

*arche’***quarks**;

**gluons**;

__q__**/2 <----]**stands for the physio-ontological category of

__s__**ub-atomic “particles”, e.g.,**

__s__**protons**;

__q__**/3 <----]**

__q__**/**

**s**

**n =**physio-ontological category of processes which [expandedly re-]produce

**from**

__s__**,**

__n__**&**also produce, e.g.,

**neutrons**by combination of

**electrons**

**&**

**protons**;

__q__**/4 <----]**stands for the physio-ontological category of the production of ionized, plasma

__a__**tomic nuclei, e.g., by "cosmological nucleo-synthesis" ["original accumulation" of**

__a__**tomics];**

__a__

__q__**/5 <----]**

__q__**/**

**a**

**n =**physio-ontological category of cosmos processes which [expandedly re-]produce

__a__**from**

**,**

__n__**&**which also produce, e.g., electrically neutral [

**electron**-[sub-]orbital(s)-bearing]

**ydrogen**

__H__**toms;**

__a__

__q__**/6 <----]**

__q__**/**

**a**

**s =**physio-ontological category of cosmological processes which [expandedly re-]produce

**from**

__a__**, e.g., “**

__s__**1**st generation”

**stars**, which expandedly reproduce ionic, plasmic

**toms [e.g., ionic, plasmic, normal**

__a__**lium nuclei, or "alpha particles"] from plasma ionized**

__He__**ydrogen**

__H__**toms [e.g., from ionic normal**

__a__**ydrogen nuclei, or free**

__H__**protons**], by "stellar nucleo-synthesis";

__q__**/7 <----]**

__q__/asn**=**physio-ontological category of processes which [expandedly re-]produce

__a__**from**

__q__**/**

**s**

**n**, e.g., electrically neutral,

**electron**-rich

**toms, with**

__a__**neutron**-rich nuclei, e.g., by advanced "stellar nucleo-synthesis" ["reproductive accumulation" of

**tomics];**

__a__

__q__**/8 <----]**stands for the physio-ontological category “

__m__**olecules”, i.e., "**

__m__

__meta__*-*

**toms", each made up out of a [usually]**

__a__*geneous multiplicity of*

__hetero__**toms, e.g.,**

__a__**H**

**2O**;

**CO**

**2**;

**CH**

**4**;

**O**

**2**;

**H**

**2**;

**H**

**2S**;

**CN**, etc.

We have also presented a simplified

**systematic**-

**“meta-model” of the “content-structure” of Marx’s**

__dialectical__**, one which captures**

__Capital__*only*the circulations-process value-forms of the capitals-system, starting from the socio-ideo-ontological category of “

**”, or**

__Commodities__

__q__**/1 (----]**

**, as <<**

__C__**>>, a**

*arche’***systematic**-

**which is complete, for its limited scope, as of step**

__dialectic__**s =**

**3**--

__)-|-(__**s**

**=**

**3 =**

**(**

__C__**)^**

**(**

**2^3**

**) =**

__C__**+**

__M__**+**

__q__/**M**

**C**

**+**

__K__**+**

__q__/**K**

**C**

**+**

__q__/**K**

**M**

**+**

__q__/**K**

**M**

**C**

**+**

__R__-- wherein --

__q__**/1 (----]**

**the Marxian human-social ideo-ontological category of “**

__C__=

__C__**” [ <<**

__ommodities__**>>];**

*arche’*

__q__**/2 (----]**

**stands for the Marxian human-social ideo-ontological category of “**

__M__

__M__**”;**

__onies__

__q__**/3 (----]**

__q__**/**

**M**

**C**stands for the Marxian category “

__M__

__onies Mediated__

__C__**”, or “**

__ommodities Circulations__

__M__

__M__

__C__**”;**

__C__

__q__**/4 (----]**

**stands for the Marxian human-social ideo-ontological category of “**

__K____<<__”;

**K**>>*apitals*

__q__**/5 (----]**

__q__**/**

**K**

**C**stands for the Marxian category of “

__C__

__ommodity____-<<__”;

**K**>>*apitals*

__q__**/6 (----]**

__q__**/**

**K**

**M**stands for the Marxian category of “

__M__

__oney____-__

__<<__”;

**K**>>*apitals*

__q__**/7 (----]**

__q__**/**

**K**

**M**

**C**stands for the Marxian category of “Subsumption of

__M__

__M__

__C__**by <<**

__C__**>>”, or the process of the circulations of “<<**

__K__*apitals***>>” as a whole;**

__K__*apitals*

__q__**/8 (----]**

**stands for the Marxian human-social ideo-ontological category of social “**

__R__

__R____evolutions__” contra capitalism, the

**from the global-market capitalist socio-politico-economic system to its global successor socio-politico-economic system.**

*transition*What both of these “<<

**>>-fic**

*speci**,*

**-**__dialectical__meta**models**”**&**a host of other such

*“*besides, all have in common, is the “<<

**-**__dialectical__meta**models**”**>>-ric**

*gene**–*

**dialectical****meta**-**model**”

__|-|-|__**k**

**=3 =**

**[**

__q__/1 ]^(2^3) =

__q__**/1**

**+**

__q__**/2**

**+**

__q__**/3**

**+**

__q__**/4**

**+**

__q__**/5**

**+**

__q__**/6**

**+**

__q__**/7**

**+**

__q__**/8**

-- wherein --

__q__**/1**

**[----]**the generic dialectical category of <<

**>>-**

*arche’***thesis**, or <<

**>>-<<**

*arche’***>> [ <<**

*physis***>>];**

*arche’*

__q__**/2**

**[----]**the generic dialectical category of

**1**st

**contra**-

**thesis**, or

**1**st

**meta**-<<

**>>;**

*physis*

__q__**/3**

**[----]**the generic dialectical category of

**1**st [

__full__]**uni**-

**thesis**, or

**1**st [

**]**

__full__**uni**-<<

**>>;**

*physis*

__q__**/4**

**[----]**the generic dialectical category of

**2**nd

**contra**-

**thesis**, or

**2**nd

**meta**-<<

**>>;**

*physis*

__q__**/5**

**[----]**the generic dialectical category of

**1**st

**-**

__partial__uni**thesis**, or

**1**st

**-<<**

__partial__uni**>>;**

*physis*

__q__**/6**

**[----]**the generic dialectical category of

**2**nd

**-**

__partial__uni**thesis**, or

**2**nd

**-<<**

__partial__uni**>>;**

*physis*

__q__**/7**

**[----]**the generic dialectical category of

**2**nd

**-**

__full__uni**thesis**, or

**2**nd

**-<<**

__full__uni**>>;**

*physis*

__q__**/8**

**[----]**the generic dialectical category of

**3**rd

**contra**-

**thesis**, or

**3**rd

**meta**-<<

**>>.**

*physis*[

__Note__: in

__q__**/n**,

**n**is in

**N =**

**{1, 2, 3, 4, . . .}**, whereas, in --

__|-|-|__**k**

**=**

**[**,

__q__/1 ]^(2^k)**--**

**k**is in --

**W**

**=**

**{ 0, 1, 2, 3, 4, . . .}**. ].

Therefore, we will explain the

__|-|-|__**0**,

__|-|-|__**1**,

__|-|-|__**2**, and

__|-|-|__**3**

*“*calculations, below, in detail, justifying each step in these calculations via explicit reference to the rules, or “axioms”, of the

**generic Dyadic Seldon Function**”**N**“First Dialectical Arithmetic” –- axioms which are already gathered together,

__Q__**&**commented upon, here, in an earlier blog-entry.

[

__Note__: in the title of this blog-entry, we have asserted that the

*“*to be demonstrated herein, are also

**”**__dialectical__calculations*“*calculations. That assertion is true for the

**purely**-**”**__qual__itative*“*level of

**script**”**N**dialectical arithmetic, the level proper of the direct operations / calculations, of that arithmetic. However, the

__Q__**N**arithmetic is a

__Q__**, or <<**

__dialectical__**>>,**

*aufheben**“self-subsumption”*,

*“meta-*, or

**unit**-ization”*“meta-<<*, of the

**monad**>>-ization”*“*

**purely**-**”**__quant__itative**, or <<**

*units***>>, of the**

*monads***N**arithmetic, and of the

**W**arithmetic, so that the

*purely**-*calculations of the

**”**__quant__itative**N**, and of the

**W**, arithmetics, respectively, still persist, i.e., are <<

**>>-**

*aufheben***, at the**

*conserved**“*script” level, and at the

**-**__sub__*“*script” level, of the

**-**__super__**N**dialectical arithmetic, because those levels are the

__Q__*loci of conservation*of the predecessor-system of arithmetic, that of the

**N**“

**atural” numbers, with respect to which the**

__N__**N**system of arithmetic is the immediate successor system, in the

__Q__**F**.

**.**

__E__**.**

__D__*“*. The

**meta**-**system**-**atic****of the**__dialectic____dialectical__**arithmetics**”

*purely**-*calculations, at the

**”**__quant__itative*“*script” level of the

**-**__sub__**N**arithmetic, arise only in the context of its “multiplication” operation, as defined via

__Q__**.]**

__Axiom # 9__**(**

**0)**For the

**k =**

**0**, “

**0**th self-iteration” from

__q__**/1**, we need only know, from “Standard Arithmetic”, that

**n**

**^0**

**=**

**1**for all

**n**in

**N**, e.g., that

**2^**

**(+**

**1**

**) =**

**2**, and that

**2^**

**(-**

**1**

**) =**

**1/2**, and therefore that --

**2**

**^**

**(**

**0**

**) = 2/2 = 2**

**/1**x

**1/2**

**= 2**

**^**

**(+**

**1**

**)**x

**2**

**^**

**(-**

**1**

**) = 2**

**^**

**(+**

**1**

**-**

**1**

**) = 2**

**^**

**(**

**0**

**) =**

**1**

-- and also that --

**^**

__x__**(+**

**1**

**) =**

**, e.g.,**

__x__**[**

__q__**/1**

**]**

**^**

**(+**

**1**

**) =**

__q__**/1**,

so that we calculate as follows:

__|-|-|__**0**

**=**

**[**

__q__/1 ]^(2^0)**=**

**[**

__q__/1 ]^(1)**=**

**[**

__q__/1 ]**=**

__q__**/1**

**=**

**[**

__q__/1 ]^1[

__Note__: Confining the

*“*script” level arithmetical operations for the arithmetical system of the

**-**__super__**N**to those of

__Q__**N**

__=__

**{ 1, 2, 3, 4, . . .}**, as we strictly should, rather than to those of the immediate successor system of

**N**, namely, to those of the "

**W**hole" numbers,

**W**

__=__

**{ 0, 1, 2, 3, 4, . . .}**, this calculation doesn't even arise. It is included here to illustrate the fuller scope of the Dyadic Seldon Function, for it

**explicitly appear in these calculations for the arithmetical system of the**

*would***W**, as also for

__Q__**successors, e.g., for those of the**

*its***Z**, of the

__Q__**Q**, of the

__Q__**R**, of the

__Q__**C**, and of the

__Q__**H**, etc., wherein

__Q__**Z**denotes the “integers”,

**Q**the “rational” numbers,

**R**the “

**eal” numbers,**

__R__**C**the “

**omplex” numbers,**

__C__**H**the

**amilton Quaternions, etc.]**

__H__**(**

**1)**For the

**k =**

**1**, “

**1**st self-iteration” from

__q__**/1**, we need know only, in addition, that, as in “Standard Arithmetic” --

__x__**^(2)**

__=__

__x__

**x**

__x__

__=__

**-“squared”**

__x__-- for a straightforward application of

**N**rule

__Q__**# 9**--

__Axiom__**: For every**

__# 9__**j**

**&**

**k**in

**N**,

**[**

__q__/k]**x**

**[**

__q__/j]**=**

**[**

__q__/j]**+**

**[**

__q__/(k**+**

**j)]**

--

**&**, thus, per that rule

**# 9**, with, in this case,

**j =**

**k =**

**1**, we calculate as follows --

__|-|-|__**1**

**=**

**[**

__q__/1 ]^(2^1)**=**

**[**

__q__/1 ]^(2) =**[**

__q__/1 ]**x**

**[**

__q__/1 ] =

__q__/1 +

__q__/(1+**1**

**) =**

__|-|-|__**0**

**x**

__|-|-|__**0**

**=**

__|-|-|__**0**

**^2 =**

__|-|-|__**1**

**=**

**[**

__q__/1 ]^(2) =

__q__/1 +**,**

__q__/2which, by rule

**#8**--

__Axiom__**: For every**

__# 8__**j**

**&**

**k**in

**N**:

If

**j**is

*to*

__itatively__**quant****equal**__un__**k**, then

__q__**/j +**

**is**

__q__/k**to**

__qual__itatively__un__equal

__q__**/x**

for every

**x**in

**N**

-- cannot be further “amalgamated”/cannot be “reduced”.

**(2)**For the

**k =**

**2**, “

**2**nd [cumulative] self-iteration” from

__q__**/1**, we have

**2**options.

We can

**(A.)**carry out the full, “

__bi__*-*nomial” self-multiplication, or “[re-]squaring”, of –-

**[**

__q__/1 ]^(2) =

__q__/1 +

__q__/2-- calculating as follows --

__|-|-|__**2**

**=**

**[**

__q__/1 ]^(2^2) =**[**

__q__/1 ]^(4) =**[[**x

__q__/1 ]^(2)]**[[**

__q__/1 ]^(2)] =**[**

__q__/1 +**x**

__q__/2]**[**

__q__/1 +

__q__/2] =

__|-|-|__**1**

**x**

__|-|-|__**1**

**=**

__|-|-|__**1**

**^2,**

then, multiplying each term in the left-hand sum onto each term in the right-hand sum, using

__Axiom__

__# 9__**4**times,

**=**

**[ [**x

__q__/1

__q__/1] +**[**x

__q__/1

__q__/2] ] +**[ [**x

__q__/2

__q__/1] +**[**x

__q__/2

__q__/2] ] =**[**

__q__/1 +

__q__/(1+**1**

**)] +**

**[**

__q__/2 +

__q__/(1+**2**

**)] +**

**[**

__q__/1 +

__q__/(2+**1**

**)] +**

**[**

__q__/2 +

__q__/(2+**2**

**)] =**

**[**

__q__/1 +

__q__/2] +**[**

__q__/2 +

__q__/3] +**[**

__q__/1 +

__q__/3] +**[**

__q__/2 +**,**

__q__/4]then, applying rule

**# 10**--

__Axiom__**: For every**

__# 10__**j**

**&**

**k**in

**N**,

__q__**/k +**

__q__/j =

__q__/j +

__q__/k[

*commutative*

*“law”*of addition for

**N**“dialectical meta-numbers”]

__Q__**--**six times,

**&**rule

**# 11**--

__Axiom__**: For every**

__# 11__**i**,

**j**,

**&**

**k**in

**N**,

**[**

__q__/i +

__q__/j] +

__q__/k =

__q__**/i +**

**[**

__q__/j +**[**

__q__/k]*associative “law”*of addition for

**N**“meta-numbers”]

__Q__-- four times,

**=**

**[**

__q__/1 +

__q__/1] +**[**

__q__/2 +

__q__/2 +

__q__/2] +**[**

__q__/3 +

__q__/3] +**,**

__q__/4then, applying rule

**# 7**--

__Axiom__**: For every**

__# 7__**n**in

**N**,

__q__**/n +**

__q__/n =

__q__/n[

*idempotency “law”*of addition for the

**N**; the

__Q__*“*quantifiability rule”]

__un__-- three times,

**=**

**[**

__q__/1] +**[**

__q__/2 +

__q__/2] +**[**

__q__/3] +**,**

__q__/4then, applying rule

**# 7**one more time,

**=**

**[**

__q__/1] +**[**

__q__/2] +**[**

__q__/3] +

__q__/4 =

__|-|-|__**2**

**=**

**[**

__q__/1 ]^(4) =

__q__/1 +

__q__/2 +

__q__/3 +**,**

__q__/4which, by rule

**# 8**, i.e., by

__Axiom__**, cannot be “reduced”.**

__# 8__Alternatively, we can

**(B.)**carry out an

**calculation for**

*abbreviated*

__|-|-|__**2**, by applying the

**F**.

**.**

__E__**.**

__D__*“*, which is, in general, a rule of

**meristemal principle**”

__non__*-*for

**distributive multiplication****N**“dialectical meta-numbers” –-

__Q__**. If**

__Meristemal Principle__**i, j, . . ., k**are all in

**N**,

**&**were just listed in “progressive order”, i.e., if

**i < j < . . . < k**, and if

**a, b, . . ., c**are all in

**N**,

**&**were just listed in “progressive order”, then the calculation of product of

**2**generic

*“*can be abbreviated as follows --

**poly**-**qualinomials**”**[**

__q__/i +

__q__/j +**. . . +**

**x**

__q__/k ]**[**

__q__/a +

__q__/b +**. . . +**

__q__/c ] =**[**

__q__/a +

__q__/b +**. . . +**

__q__/c ] +**[**x

__q__/k

__q__/a] +**[**x

__q__/k

__q__/b] +**. . . +**

**[**x

__q__/k

__q__/c]-- i.e., after <<

**>>-**

*aufheben***the "multiplicand"/"operand"**

*conserving**“*--

**poly**-**”**__qual__inomial

**[**

__q__/a +

__q__/b +**. . . +**

**,**

__q__/c ]-- it is necessary only to apply the “

**meristemal**”, or “

**most advanced**”/“

**most progressed**” ontological categorogram of the "multiplier"/"operator" categories-sum, "cumulum", or

*“*, here

**poly**-**qualinomial**”

__q__**/k**, to each of the terms contained in that "multiplicand"/"operand"

*“*, then calculating as follows --

**poly**-**qualinomial**”

__|-|-|__**2**

**=**

**[**

__q__/1 ]^(2^2) =**[**

__q__/1 ]^(4) =**[[**

__q__/1 ]^(2)]**x**

**[[**

__q__/1 ]^(2)] =**[**

__q__/1 +

__q__/2]**x**

**[**

__q__/1 +

__q__/2] =

__|-|-|__**1**

**x**

__|-|-|__**1**

**=**

__|-|-|__**1**

**^2 =**

**[**

__q__/1 +

__q__/2] +**[**x

__q__/2

__q__/1] +**[**x

__q__/2

__q__/2] =**[**

__q__/1 +

__q__/2] +**[**

__q__/1 +

__q__/3] +**[**

__q__/2 +**,**

__q__/4]then, applying rule

**# 10**–-

__Axiom__**: For every**

__# 10__**j**

**&**

**k**in

**N**,

__q__**/k +**

__q__/j =

__q__/j +

__q__/k[

*commutative*

*“law”*of addition for

**N**“meta-numbers”]

__Q__**-- 5**times,

**&**rule

**# 11**--

__Axiom__**: For every**

__# 11__**i**,

**j**,

**&**

**k**in

**N**,

**[**

__q__/i +

__q__/j] +

__q__/k =

__q__/i +**[**

__q__/j +

__q__/k][

*associative “law”*of addition for

**N**“meta-numbers”]

__Q__--

**4**times,

**=**

**[**

__q__/1 +

__q__/1] +**[**

__q__/2 +

__q__/2] +

__q__/3 +**,**

__q__/4then, applying rule

**# 7**--

__Axiom__**: For every**

__# 7__**n**in

**N**,

__q__**/n +**

__q__/n =

__q__/n[

*idempotency “law”*of addition for the

**N**; the

__Q__*“*quantifiability rule”]

__un__--

**2**times, we obtain:

__|-|-|__**2**

**=**

**[**

__q__/1 ]^(4) =

__q__/1 +

__q__/2 +

__q__/3 +**,**

__q__/4which, again, by rule

**#8**–-

__Axiom__**-- cannot be “reduced”.**

__# 8__**(3)**For the

**k =**

**3**, “

**3**rd [cumulative] self-iteration” from

__q__**/1**, we have a straightforward application of the

**F**.

**.**

__E__**.**

__D__

__non__*-*“

**distributive****meristemal principle**” shorthand rule, once we have applied our learnings from the

**1**st

**&**

**2**nd “self-iterations” from

__q__**/1**, namely, from

__|-|-|__**1**and

__|-|-|__**2**–-

__|-|-|__**3**

**=**

**[**

__q__/1 ]^(2^3) =**[**

__q__/1 ]^(8) =**[[**x

__q__/1 ]^(4)]**[[**

__q__/1 ]^(4)] =

__|-|-|__**2**

**x**

__|-|-|__**2**

**=**

__|-|-|__**2**

**^2 =**

**[**

__q__/1 +

__q__/2 +

__q__/3 +**x**

__q__/4]**[**

__q__/1 +

__q__/2 +

__q__/3 +**,**

__q__/4]then, applying the

*“*rule of

**meristemal**”*“*multiplication, for the above

**poly**-**”**__qual__inomial*“*,

**-**__tetra__**qualinomials**”**=**

**[**

__q__/1 +

__q__/2 +

__q__/3 +

__q__/4] +**[**

__q__/4**x**

__q__/1] +**[**

__q__/4**x**

__q__/2] +**[**

__q__/4**x**

__q__/3] +**[**

__q__/4**x**

__q__/4 ] =**[**

__q__/1 +

__q__/2 +

__q__/3 +

__q__/4] +**[**

__q__/1 +

__q__/5] +**[**

__q__/2 +

__q__/6] +**[**

__q__/3 +

__q__/7] +**[**

__q__/4 +**,**

__q__/8]then, applying rule

**# 10**–

__Axiom__**: For every**

__# 10__**j**

**&**

**k**in

**N**,

__q__**/k +**

__q__/j =

__q__/j +

__q__/k[

*commutative*

*“law”*of addition for

**N**“meta-numbers”]

__Q__**--**multiple times,

**&**applying rule

**# 11**--

__Axiom__**: For every**

__# 11__**i**,

**j**,

**&**

**k**in

**N**,

**[**

__q__/i +

__q__/j] +

__q__/k =

__q__**/i +**

__[q__/j +

__q__/k][

*associative “law”*of addition for

**N**“meta-numbers”]

__Q__-- also multiple times,

**=**

**[**

__q__/1 +

__q__/1] +**[**

__q__/2 +

__q__/2] +**[**

__q__/3 +

__q__/3] +**[**

__q__/4 +

__q__/4] +

__q__**/5 +**

__q__/6 +

__q__/7 +**,**

__q__/8then, applying rule

**# 7**–-

__Axiom__**: For every**

__# 7__**n**in

**N**,

__q__**/n +**

__q__/n =

__q__/n[

*idempotency “law”*of addition for the

**N**; the

__Q__*“*quantifiability rule”]

__un__--

**4**times, we obtain:

__|-|-|__**3**

**=**

**[**

__q__/1 ]^(8) =

__q__**/1 +**

__q__/2 +

__q__/3 +

__q__/4 +

__q__/5 +

__q__/6 +

__q__/7 +**,**

__q__/8which, again, by rule

**#8**, i.e., by

__Axiom__

**, cannot be “reduced”.**

__#8__The further Seldon Function “self-iterations” from

__q__**/1**follow by “recursive induction”, e.g. --

**(4)**For the

**k =**

**4**, “

**4**th [cumulative] self-iteration” from the

__q__**/1**<<

**>>, we obtain --**

*arche’*

__|-|-|__**4**

**=**

**[**

__q__/1 ]^(2^4) =**[**

__q__/1 ]^(16) =**[[**

__q__/1 ]^(8)]**x**

**[[**

__q__/1 ]^(8)] =

__|-|-|__**3**

**x**

__|-|-|__**3**

**=**

__|-|-|__**3**

**^2**

**=**

**[**

__q__/1**+**

__q__/2**+**

__q__/3**+**

__q__/4**+**

__q__/5**+**

__q__/6**+**

__q__/7**+**

__q__/8]^2**=**

**[**

__q__/1 ]^(16) =**[**

__q__/1 +

__q__/2 +

__q__/3 +

__q__/4 +

__q__/5 +

__q__/6 +

__q__/7 +

__q__/8 +

__q__/9 +

__q__/10 +

__q__/11 +

__q__/12 +

__q__/13 +

__q__/14 +

__q__/15 +**.**

__q__/16]Of course, such further cumulative self-iteration steps are immediately

**only to the extent that the new “physio-ontology” categories, or new “ideo-ontology” categories, thus generated, have been largely or wholly**

*meaningful**“*, or

**solved**”*“*, for the universe[-of-discourse] being delineated by such a

**semantified**”*“*meta-model”.

__dialectical__The number of

**steps –- and, especially, the number of**

*meaningful***terms --**

*ontological categorogram***generated, can be quite large.**

*meaningfully*For example, the [

**12**-symbol version of the]

*“*

**Theory of****Everything**”**“meta-model” of**

__Dialectical__Equation**--**

*the cosmos as a totality*

__>-|-<__**t**

**=**

**<**

__n__>**^(2^t)**

-- has been mostly

*“*, i.e.,

**solved**”*“*, or

**semantified**”**self-iterated, by the**

*meaningfully***F**.

**.**

__E__**. dialectical-encyclopedists, to**

__D__**t =**

**9**, or for

**512**terms, whose physical ontology has been at least generically characterized, and, in some cases, identified with specific cosmological processes, already fully extant and recognized by Standard Science, or known to be at least partially extant, in the Terran-humanity-known

**, if not identified with previously unrecognized, but already recorded, cosmological processes, and to**

*cosmos***t =**

**10**, or for

**1,024**terms, for the predicted ontology of that epoch of

**immediately subsequent to the present [local] epoch, again, as presently known to Terran humanity.**

*the*__Dialectic__of NatureSo far, we have been demonstrating the

*“*for the successive “self-iterations” of the Dyadic Seldon Function, for

**”**__qual__itative calculations**, or**

__gene__ric*“*interpreted”,

**minimally**-*“*assigned”, “

**minimally**-**dialectograms**”,

__q__**/1**,

__q__**/2**,

__q__**/3**, etc.

The algorithms for these

*“*for

**”**__qual__itative calculations

__speci__fically*-*interpreted,

__speci__fically*-*assigned “

**dialectograms**” are less abstract, and more directly intuitive, than those for

__gene__rically*-*interpreted,

__gene__rically*-*assigned “

**dialectograms**”.

For example, if we have, as our <<

**>>-**

*arche’***thesis**, or <<

**>>-<<**

*arche’***>>, for a given**

*physis***that we are modeling,**

__dialectical__progression

__q__**/X**, or

**, where “X” is a mnemonic abbreviation for the name of the ontological category for which**

__X__**, or**

__X__

__q__**/X**, stands, e.g., such that “X” is the first letter of that name, and if

__q__**/XX**has been solved by “

**”, or by**

__Y__

__q__**/**

**Y**, e.g., because “Y” is the first letter of the name of the ontological category identified as fitting

__q__**/XX**, [e.g., because “Y” is the first letter of the name of the ontological category identified as fitting

__q__**/XX**, i.e., if “Y” abbreviates the name of the

**/<<**

*category***>> of**

*arithmos***/<<**

*units***>> which has, as its own**

*monads***/<<**

*units***>>,**

*monads**“*, or

**-**__meta__**units**”*“*<<

**-**__meta__**>>”, of the**

*monads***, or <<**

*units***>>, of the**

*monads***/<<**

*category***>> denoted by**

*arithmos***or**

__X__

__q__**/X**], then –-

**(0) s =**

**0**,

__)-|-(__**0 =**

**(**

__X__)^(2^0) =

__X__**^1 =**

**;**

__X__**(1) s =**

**1**,

__)-|-(__**1 =**

**(**

__X__)^(2^1) =

__X__^2 =

__X__**+**

__q__/XX

__=__

__X__+

__Y__**(2) s =**

**2**,

__)-|-(__**2 =**

**(**

__X__)^(2^2) =

__X__**^4 =**

**(**

__X__)^(2^2) =

(

(

__X__+

__Y__**)^2 =**

**(**

__X__+

__Y__**)**

**x**

**(**

__X__+

__Y__**) =**

**(**

__X__+

__Y__**) +**

__Y__**x**

__X__**+**

__Y__**x**

__Y__**=**

(

(

__X__+

__Y__**) +**

__q__/YX +

__q__**/YY**

__=__

__X__+

__Y__**+**

__q__**/YX +**

__Z__-- if

__q__**/YY**has been solved by “

**”, or**

__Z__

__q__**/Z**, [e.g., because “Z” is the

**1**st letter of the name of the ontological category identified as fitting

__q__**/YY**, i.e., if “Z” abbreviates the name of the

**/ <<**

*category***>> of**

*arithmos***/<<**

*units***>> which has, as its own**

*monads***/<<**

*units***>>,**

*monads**“*, or

**-**__meta__**units**”*“*<<

**-**__meta__**>>”, of the**

*monads***, or <<**

*units***>>, of the**

*monads***/<<**

*category***>> denoted by**

*arithmos***or**

__Y__

__q__**/Y**].

In the above equation, the term “

__q__**/YX**” stands for a

**ontological category, for a category wherein category**

*new***is**

__Y__*“*, or

**ontologically**”__hybridized__*“*, with category

**”**__dialectically____synthesized__**, forming a**

__X__*“*of

**complex unity**”**and**

__Y__**, or stands for a category of ontological process wherein category “**

__X__**” expandedly-reproduces itself / its**

__Y__*“*, or <<

**population**”**>>, of <<**

*arithmos***>>, or**

*monads***, by**

*units*__converting__<<

**>>, or**

*monads***, of category**

*units***into those of category**

__X__**.**

__Y__For example,

__q__**/MC**stands for the socio-ontological category of the “socio-ontological hybridization”, or “

**”, or “real subsumption”, of the “**

__dialectical____synthesis__**” socio-ontological category**

__Commodities__**&**/by the “

**” socio-ontological category, in the**

__Monies__

__Capital__*-*

__dialectic__**Equation**, connoting the socio-ontological process-category of “

**”.**

__Monies Mediated Commodities Circulations__Likewise,

__q__**/KC**stands for the socio-ontological category of “

**”, the result of the “socio-ontological hybridization”, or “**

__Commodity-Capital__**”, or “real subsumption”, of the “**

__dialectical____synthesis__**” socio-ontological category**

__Commodities__**&**/by the “

**” socio-ontological category, in the**

__Kapitals__

__Capital__*-*

__dialectic__**Equation**.

Likewise,

__q__**/KM**

**stands for the socio-ontological category of “**

**”, the result of the “socio-ontological hybridization”, or “**

__Money-Capital__**”, or “real subsumption”, of the “**

__dialectical____synthesis__**” socio-ontological category**

__Monies__**&**/by the “

**” socio-ontological category, in the**

__Kapitals__

__Capital__*-*

__dialectic__**Equation**.

Likewise,

__q__**/KMC**stands for the socio-ontological process-category of “

**”, which connotes, in**

__Monies-and-Commodities-Mediated Kapitals-Circulations__

*historical**-*context, the result of the “socio-ontological hybridization”, or “

__dialectical__**”, or “real subsumption”, of the “**

__dialectical____synthesis__**” [**

__Monies Mediated Commodities Circulations__

__q__**/MC**or

__M__

__M__

__C__**] socio-ontological category**

__C__**&**/by the “

**” socio-ontological category, in the**

__Kapitals__

__Capital__*-*

__dialectic__**Equation**; the “appropriation” of

__M__

__M__

__C__**by**

__C__**, or, in**

__K__

*systematic**-*context, the “

__dialectical__

__de__*-*abstraction” of

**from**

__K__

__q__**/MC**, or the “

__re__*-*concretization”/”

__re__*-*determination” of

__q__**/MC**with/by

__q__**/K**, yielding

__q__**/KMC**.

Similarly,

__q__**/as**stands for the

*"*<<

**-**__uni__**>>" of**

*physis*

__a__**&**

**, the physio-ontological category of cosmological processes which [expandedly re-]produce, or reproductively accumulate,**

__s__**,**

__a__**toms, by transforming/consuming/depleting**

__a__**,**

__s__**ub-atomic “particles”**

__s__**, or <<**

*populations***>>, e.g.,**

*arithmoi***protons**, converting them, together with

**electrons**and

**neutrons**, into

**toms**

__a__**, or <<**

*populations***>>, e.g.,**

*arithmoi***lium**

__He__**toms [e.g., of stellar-plasma/ionized**

__a__**lium**

__He__**toms:**

__a__**lium nuclei or "alpha particles"].**

__He__What can we identify as cosmological

**, or <<**

*units***>>, known to conduct such cosmological processes?**

*monads*Such are the

**, or <<**

*units***>>, known as “first generation”**

*monads***stars**, in which the

**, or <<**

*units***>>, of**

*monads***toms [e.g.,**

__a__**lium**

__He__**toms],**

__a__**&**the

**, or <<**

*units***>>, of**

*monads***ub-atomic “particles” [e.g.,**

__s__**protons**], inter-mingle, and whose very “life-process” is the

*“*o-

__qual__**itatively”-expanding self-reproduction of**

__quant__**toms [e.g., of plasma/ionized**

__a__**lium nuclei] by these**

__He__**stars**’ conversion of their interiorized “

**ub-atomic particles” called**

__s__**protons**[e.g., of

**protons**as stellar-plasma/ionized

**ydrogen**

__H__**toms: “**

__a__**Hydrogen nuclei**”], plus

**electrons**, and

**neutrons**, into their interiorized

**toms of “higher**

__a__**tomic <<**

__a__**>>” [e.g., into**

*species***lium**

__He__**toms, i.e., of stellar-plasma/ionized**

__a__**lium**

__He__**toms:**

__a__**lium nuclei or "alpha particles"].**

__He__Regards,

Miguel

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