Rudy's Diamond Strategies

This complementary Blog to the Chinese Challenge Blog is presenting studies to a mathematical theory of Diamonds. Diamond theory is studying for the first time, tabular categories as an interaction of categories and saltatories.

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Monday, January 30, 2012

Complementary Calculi: Distinction and Differentiation

George Spencer-Brown and Marin Mersenne

Headaches with complementary calculi

If two formal systems have a very close familiarity as a duality or even a complementarity, and are therefore to some degree nearly indistinguishable, but you nevertheless discovered in a strange situation of an insight a decisive difference between them. 

Then it might easily be possible, as in my case, that you get nightmares of endless oscillations and manifestations of something you don’t yet have access to, and what, as far as you guess, what it could be, you anyway wouldn’t like at all.

That’s what happens with the discovery of the complementary calculus of indication, a calculus I call a Mersenne calculus of differentiation and separation, in contrast to the Spencer-Brown calculus of indication and distinction. 

I have never been a friend of this calculus of The Laws of Form, therefore to get involved with its complementary calculus is no pleasure at all.

Obviously, to get rid of the headache with the CI and its ambitious and annoying celebrations, especially in German humanities, the best is to show, or even to prove, that there is a complementary calculus to the calculus of indication, too.

With that, the sectarian propaganda of the CI boils down to a strictly one-sided and utterly blind endeavour.

In-between I have written some papers dealing with the complementarity and applications of the concepts of the CI and the MC.

There might still be too much non-deliberated obfuscation involved, at least, some clear aspects of the new calculus of differentiation, CD, and its complementarity to the calculus of indication and distinction are now elaborated as far as it takes to get a primary understanding of the new situation.

Indication and differentiation in graphematics

Moshe Klein has given a simple introduction to George Spencer-Brown's calculus of indication (CI) as a special case of a bracket grammar. 
A context-free language with the grammar:
                                              S ⟶ SS|(S)| λ
is generating the proper paranthesis for formal languages. 

What was an act of a genius becomes an adhoc decision to restrict the grammar of bracket production.

Set the restriction of bracket rules to:
                                              (()) () = () (())
and you get the basic foundation of the famous CI as introduced by George Spencer-Brown. 

Nobody insists that this is an appropriate approach but it seems that it takes its legitimacy from the formal correctness of the approach.

Now, with the same decisionism, albeit not pre-thought by a genius, I opt for an alternative restriction,
                                             (( )) = ( ).
This decision is delivering the base system for a Mersenne calculus, interpreted as a calculus of differentiation, CD. 

I stipulate that both calculi, the CI and the CD, are complementary. And both calculi have additionally their own internal duality, delivering the dual calculi, i.e. the dual-CI and the dual-CD.

It will shown that, despite of its non-motivated adhocism, both calculi are well founded in graphematical systems, and are to be seen as interpretations of independent complementary graphematical calculi.

In fact, they belong, with the identity system for semiotics to the only two non-kenogrammatic graphematical systems of the general architectonics of graphematics. 

The paper "Diamond Calculus of Formation of Forms. A calculus of dynamic complexions of distinctions as an interplay of worlds and distinctions” was mainly based on a deconstruction of the conditions of the calculus of indiction, i.e. the assumption of a “world” and “distinctions” in it. 

The present paper “Complementary Calculi: Distinction and Differentiation” opts for a graphematic turn in the understanding of calculi in general. This turn is exemplified with the George Spencer-Brown’s Calculus of Indication and the still to be discovered complementary Mersenne calculus of differentiations. 

First steps toward a graphematics had been presented with “Interplay of Elementary Graphematic Calculi. Graphematic Fourfoldness of semiotics, Indication, Differentiation and Kenogrammatics".

Graphematic calculi are not primarily related to a world or many worlds, like the CI and its diamondization. Graphematic calculi are studying the rules of the graphematic economy of kenomic inscriptions.

Graphematics was invented in the early 1970s as an interpretation of Gotthard Gunther’s keno- and morphogrammatics, inspired by Jaques Derrida’s grammatology and graphematics. 

Spencer-Brown’s calculus of indication has been extensively used to interpret human behavior in general (Niklas Luhmann). 

The proposed new complementary calculus to the indicational calculus, the Mersenne calculus, might not be applicable to human beings, but there is a great chance that it will be a success for the interaction and study of non-human beings, e.g. robots, aliens, and Others.


Friday, January 20, 2012



It is believed that with the understanding of morphograms as rules for morphic cellular automata a new approach for an understanding of the specific rationality of Chinese writing systems is achieved. With that the Blog "THE CHINESE CHALLENGE" enters into a new level of understanding Chinese rationality in a non-Western way.
(For technical reasons I publish these comments on the Blog "Rudy's Diamond Strategies" too.)

This will be elaborated in a special paper.

Here are some papers mentioned that had been on the way to this new understanding of the dynamics and pragmatics of Chinese characters.

An intermediary paper to this understanding was published as "What Chinese Grammar".

What Chinese Grammar?
Interchangeability and morphogrammatics of interpretations 

To put it bluntly: Ancient Chinese characters (signs, hieroglyphs, characters) are
conceived in a transclassic setting as morphograms

This insight is achieved with the approach of a polcontextural transformation of the categorical concept of bifunctoriality and understood as the interchangeability of locus of a character and the character itself.
Furthermore the interchangeability of Western grammatical categories to characterize Chinese characters and sentences is applied.

This is proposed with the help of a positive reading of Rolf Elberfeld studies (2003, 2007) and a negative differentiation to other approaches which are not reflecting their complicity with Western grammar.

The Amazing Power of Four
Gotthard Gunther’s space-travel algorithm and Leon Chua’s Fourth electronic Element supported by Robert Rosen’s speculations about anticipative systems

Speculations about trans-functorial and morphic metamorphosis of space - time and worlds on one side, and flux and charge of electronics on the other side, leading to the memristor and memristive systems of nanoelectronics.

Achievements and attempts to surpass classical paradigms of science by Gotthard Gunther and Leon O. Chua are portrayed and other attempts of Robert Rosen’s anticipatory systems are sketched and Martin Heidegger’s late philosophy of the Fourfold are mentioned. 

Short Overview of Morphic Cellular Automata

Graphematic System of Cellular Automata
Short characterization of cellular automata by the 9 graphematic levels of inscription

As a further specification of the “overview of morphic cellular automata”, described before, a graphematic classification of the inscriptional systems shall be introduced and applied to different types of cellular automata. 

Tuesday, January 17, 2012

Towards Abstract Memristic Machines

A new paper about the

Memristic machines are time-tensed machines of the nanosphere. Their definition and their rules are not covered by ordinary logic, arithmetics and semiotics, basic for a theory of abstract automata. The difference to classical concepts of machines to tensed, i.e. memristive machines is elaborated. As an attempt to develop memristive machines, basic constructs from morphogrammatics are applied.  
Properties of retro-gradeness (antidromicity), self-referentiality, simultaneity and locality (positionality) of operations as they occur in kenogramamtic and morphogrammatic basic operations, like the successor operations, ‘addition’ and ‘multiplication’ have to be realized on all levels of operativity in memristive systems.  
Hence, the tiny memristive properties of time- and history-dependence for kenomic successors are presented for all further operations, like “addition" (coalition), "multiplication”, “reflection”, etc. Morphogrammatics will be further developed in Part II of the paper.

A new framework for design and analysis for memristive systems, i.e. memristics, shall be sketched as a complex methodology of Morphogrammatics, Diamond Category Theory, Diagrammatics and Nanotechnology.

Graphematics of Conflicts

Since my studies of memristics in the framework of trans-classical logic, I developed a new concept of cellular automata, and discovered an interesting application of morphogrammatic-based cellular automata for an interpretation of the pragmatical aspects of Chinese characters.
With this post, I would like to introduce an application of novel distinctions to a theory of conflict management. And an application to a theory of propaganda analysis is proposed.

"Inconsistency robustness is information system performance in the face of continually pervasive inconsistencies–- a shift from the previously dominant paradigms of inconsistency denial and inconsistency elimination attempting to sweep them under the rug.” (Carl Hewitt)

The role of contradictions and gaps in the analysis of propaganda and databases

Some preliminary thoughts and notes about conflict-theory and the strategies of propaganda in politics and science are developed in the framework of graphematics.

This is not yet taking into account the complementary diamond aspects of conflicts.

Orwell’s characterization of propaganda: Newspeak, Doublethink and Memory-loss as a defence of truth are modeled by the features of graphematic calculi as new operative tools of propaganda analysis and deconstruction.

Traditionally, a theory of propaganda is covered by the techniques of rhetorics of speech-acts. Graphematics proposes elements of a deconstruction of propaganda beyond the level of rhetorics.

On one side we have the propaganda analysis of George Orwell based on a defence of truth, on the other side the self-reflections of the propagandist Joseph Goebbels about the rationality of propaganda as being neutral to the categories of truth and false. 

An application of graphematic distinctions to the definition of conflicts in databases is taken as a contrast to explain and demonstrate the functioning of graphematic approaches to conflicts and contradictions, like Boolean, Mersennian, Brownian and Stirlingian.