Morphospere(s): Asymmetric Palindromes

The Trompe-l'œils of Semiospheres

Abstract

Surprisingly, there is a simple key to distinguish and to open up morphospheres in contrast to the semiosphere: symmetric versus asymmetric palindromes. Asymmetric palindromes of the morphosphere are paradox and oxymoric in the understanding of the semiosphere. 

Only in the context of human madness and its poetic explosions oxymoric palindromes could eventually occur. Paradoxes, logical and linguistic, are restricted to some crazy word games or mathematical constructions but would never leave their logocentric cage to produce something like paradoxical and asymmetric palindromes.


Morphosphere(s) are opened up by oxymoric palindromes. Morphosphere(s) are the field where asymmetric palindromes get a scientific, mathematical and programmable exposure.

Introduction

Palindromes are well known. "Anna" is one, "elle" is one, and the letter "b" is one, too. Palindromes are read symmetrically forwards and backwards. Both readings result in the same word.

All examples are working with palindromes that are, by definition, obviously, symmetric.

It seems to be very strange to postulate asymmetric palindromes.

But who said that we have to stay in the semiotic sphere, the semiosphere of semiotically founded science and literature?

A glance on morphogrammatics uncovers the funny result that the composition of "anna", "b" and "elle" to "annabelle" is a nice example of an asymmetric morphogrammatic palindrome. 

It reads 'forwards' and 'backwards' morphogrammatically as the same.

Albeit it is semiotically, i.e.alphabetically an asymmetric word, and therefore not a palindrome at all, it is a palindrome of the morphosphere.

How does it work?

Some hints are given by the excerpts of the paper  
"Morphosphere(s): Asymmetric Palindromes as Keys" 
published at:
http://memristors.memristics.com/Morphospheres/Asymmetric%20Palindromes.pdf
http://memristors.memristics.com/Morphospheres/Asymmetric%20Palindromes.html

Strategies towards morphosphere(s)

Also I’m not attracted to the concept of spheres, except, maybe, that of Johannes Kepler’s Music of Spheres, I think it would give my work about graphematics some reasonable positioning if it could be understood as a sphere and could then clearly be differentiated from other spheres, especially from the bio-, logo-, noospheres, but also from Yuri Lotman’s semiosphere.

In this setting, graphematics, as it was introduced in the early ‘70s, is the developing science of studying the morphosphere.

Graphematics contains the studies of
 polycontexturality, polycontextural logic, arithmetics, semiotics and programming,
kenogrammatics,
morphogrammatics,
on the different levels of the graphematic system of inscription.

As Lotman introduced his project of a culture-theoretic understanding of systems of sign praxis as the new thematization of the semiosphere in distinguishing it from Vernadsky’s biosphere, my  introduction of the project of morphosphere(s) follows Lotman’s programmatic text in a complementary and deconstructive move to elucidate some aspects necessary to establish the new sphere of graphematics, the morphosphere. Leaving a sphere for another new one is not done without use/abuse of past concepts and strategies, and a balance between mimicry, plagiarism and tabu breaking creativity.

Surprisingly, or maybe not so surprisingly, the topos of palindromes, that is leading Lotman’s exposition of the semiosphere, appears as a ‘multi-functional’ key for the establishing of the concept, strategy and project of morphosphere(s).

Sometimes, deep insights are extremely simple.

The key of the distinction between Lotman's semiosphere and the proposed morphosphere(s) has this simplicity, albeit there is no guarantee that this simplicity is also related to a deep insight. The simple difference between the deep-structure of the semiosphere and the deep-structure of the morphosphere is established with the difference of symmetric and asymmetric palindromes.

"The proof that mirror symmetry can radically change the functionality of the semiotic mechanism, lies in the palindrome.” (Y. Lotman)

Palindromes are by definition symmetric. This holds for all occurrences of palindromes in the bio- and the semiosphere.

Asymmetric palindromes are oxymorons.

Enantiomorph oppositions are logically and semiotically dual and are leading to tautologies, avoiding the confrontation with paradoxes, parallaxes, and other monstrosities.

Asymmetric palindromes are presenting the deep-structure of the deep-structure of the semiosphere. It unmasks it as a restricted economy of sings in the mode of linearity and binarity; elaborated as enantiomorphism.

The guide to enter the morphosphere(s) are offered therefore by oxymoric palindromes and their asymmetry.

Oxymoric palindromes are hidden to the phenomenological sight. They cannot be seen and brought to evidence. Up to now there is no insight into the existence of asymmetric palindromes in the scientific spheres of semiotics, linguistics, rhetorics and in corresponding attempts in the sciences of the biosphere, especially in microbiology and genetics.

In contrast, semio-linguistic palindromes needs to be seen. Without the visuality, or other perceptionalities, palindromes cannot be established.

"Thus, the mechanism of the Russian palindrome lies in the fact that the word is seen. This then allows it to be read in the reverse order.” (Y. Lotman)

Palindromes in the Chinese writing

It seems that the complicity of the semiospheric palindromes with Western logocentrism has been observed by Lotman. He confronts his results with the non-logical features of Chinese writing.

"A very curious thing occurs: in the Chinese language, where the word hieroglyph seems to hide its morpho-grammatical structure, reading it in the reverse order helps to reveal this hidden construction, displaying the hidden sequential choice of structural elements in a holistic and visible way.”

"From this, V. M. Alekseev drew the methodologically interesting conclusion: that the palindrome represents the best material for studying the grammar of the Chinese language.

The conclusions are clear:
(1) The palindrome represents the best possible means of illustrating the interrelationship of Chinese syllabic words, without resorting to the artificial lecture-theatre style of displacement and unity exercised by students of Chinese syntax, lacking in skill and talent.

(2) The palindrome represent the best Chinese material for the construction of a theory of Chinese (and perhaps not only Chinese) words and simple sentences. (Alekseev 1951: 102)." (Y. Lotman)

The hidden cannot be seen, it has to be elaborated, uncovered and unmasked by the work of calculation.

An oxymoric palindrome is therefore not given to phenomenological and semiospheric evidence of cognition.
 There is nothing to be seen and to be read backwards then.

Paradoxes

Kalevi Kull hints with his paper “Semiosphere and a dual ecology: Paradoxes of communication “ to the importance of paradoxes for the introduction of Lotman’s concept of semiosphere.

"In several of his lectures, Juri Lotman liked to begin his talk with a paradox. Since semiosphere is a very general notion, a description of it via paradoxes might indeed be helpful. A paradox with what it would be appropriate to start here is the famous paradox of learning — Meno’s paradox.” 

http://www.ut.ee/SOSE/sss/kull331.pdf

A new way of seeing things has to be learned and trained. This happens with the support of scriptural calculations.

At first it seems to be important to understand that the concept of paradoxes and antinomies is a limited construction depending on the Greek concept and understanding of logos and anti-logos. The study of paradoxes of all kind is having its sophisticated endeavour in the semiosphere.

The structure of perception and cognition in the semiosphere is fundamentally phenomenological. 
Despite the dialogical, holistic and intertextual attempts, the modi of perception and evidence in the semiosphere have their foundation in the egology of logocentrism.

Semiospheric studies might be deep-structural studies in contrast to semiotic studies but they remain blind to their own deep-structural decisions.

The semiosphere is not touched by grammatological and graphematical considerations and interventions.

Morphogrammatics of paradoxes

In a radical change of interests and strategies, morphospheric studies, if they still can be called studies without falling back into logocentric complicity with its concept of dialogical truth and rationality, are accepting the work of deconstruction of the very basic presumption of Western culture: its semiospheric umbrella, or as other prefer to say, its logo-phonocentric prison.

The symmetric production rule  “S ⟹ a|aSa“ is not considering the asymmetric productions that are morphogrammatically accepted as palindromes, like for example the morphogram [1,2,3,4,1,2] with [1,2,3] = [2,1,4],  
[1,2,3,4,1,2], [2,1,4,3,2,1], and tnf[2,1,4,3,2,1] = [1,2,3,4,1,2]. 

Hence, the context-dependence of the morphic production rule is restricted to symmetric productions with restricted context-dependence.

The filter-method is also not producing constructively the set of palindromes but is filtering them out of the produced trito-universe TU of morphograms.

Morphogrammatic palindrome:

fun kref ks = tnf(rev ks);
- fun ispalindrome l = (l = kref l);
val ispalindrome = fn : int list -> bool
- ispalindrome [1,1,2,2];
val it = true : bool

Symbolic palindrome: 

fun palindrome l = (l = rev l);

- palindrome [1,1,2,2];
val it = false : bool

Filtered results of length 6 from TU
 Tcontexture 6;

List.filter palindrome “Tcontexture 6";   

- length it;
val it = 180 : int


Results for the 31 morphogrammatic palindromes of length 6 from [1,1,1,1,1,1] to [1,2,3,4,5,6]:

[1,1,1,1,1,1],[1,1,1,2,2,2],[1,1,2,1,2,2],[1,1,2,2,1,1],[1,1,2,2,3,3],[1,1,2,3,1,1],[1,1,2,3,4,4],
[1,2,1,1,2,1],[1,2,1,1,3,1],[1,2,1,2,1,2],[1,2,1,3,2,3],[1,2,1,3,4,3],[1,2,2,1,1,2],[1,2,2,2,2,1],
[1,2,2,2,2,3],[1,2,2,3,3,1],[1,2,2,3,3,4],[1,2,3,1,2,3],[1,2,3,1,4,3],[1,2,3,2,3,1],[1,2,3,2,3,4],
[1,2,3,3,1,2],[1,2,3,3,2,1],[1,2,3,3,2,4],[1,2,3,3,4,1],[1,2,3,3,4,5],[1,2,3,4,1,2],[1,2,3,4,2,1],
[1,2,3,4,2,5],[1,2,3,4,5,1],  [1,2,3,4,5,6].

Palindromes(6,6) = 31

Symmetric palindromes(6,6) = 5

Symmetric morphogrammatic palindromes of length 6 taken out from TU:

val it =
  [[1,1,1,1,1,1],[1,1,2,2,1,1],[1,2,1,1,2,1],[1,2,2,2,2,1],[1,2,3,3,2,1]] : int list list
- length it;
val it = 5 : int

Example :
"Annabelle"

asymmetric palindrome [1,2,2,1,3,4,5,5,4]


"anna" : num(anna) = [1,7,7,1]

” b”                        = [2]

"elle”   :   num(elle) = [4,5,5,4]


num(annabelle) = [1,7,7,1,2,4,5,5,4]

- tnf[1,7,7,1,2,4,5,5,4];
val it = [1,2,2,1,3,4,5,5,4] : int 

list 
ispalindrome[1,2,2,1,3,4,5,5,4]?

val it = true : bool

- kref[4,5,5,4,3,1,2,2,1];
val it = [1,2,2,1,3,4,5,5,4] : int list

Again, morphograms are not defined over an alphabet but by differentiations. 

The ENstructure is calculating the differentiation of a morphogram, with N=non-equal and E=equal at the subsystem place.

- ENstructure [1,2,2,1];
val it = [[],[(1,2,N)],[(1,3,N),(2,3,E)],[(1,4,E),(2,4,N),(3,4,N)]]
  : (int * int * EN) list list

That is, the trito-normal form tnf of the numeric interpretations of the words “anna” and “elle”, num(anna) = [1,7,7,1] and num(elle) = [4,5,5,4] are equivalent: 
tnf[1,7,7,1] = [1,2,2,1] = tnf[4,5,5,4]. 

But localized in the context of the whole word they are different.

Operation on oxymoric palindromes

Quite obviously there are at a first glance not too many operations possible on asymmetric palindromes that are remaining in the domain of palindromes.
The operation of inversion is part of the definition. General permutations are destroying the definition of palindromes.

Is the ‘addition’(concatenation) of two palindromes a palindrome?

As a metaphor: 

You might lock your door with to small keys, say [1,2,3] and [1,2,3,1], but you have to unlock your door with a single key that is the morphic palindromic addition of the smaller keys. For example, with kconcat [1,2,3][1,2,3,1]; there are 5 composed keys of length 7 available.

Coalitions
 
- kconcat [1,2,3][1,2,3];

- length(kconcat [1,2,3][1,2,3]);
val it = 34 : int

Morphograms: 34.

Palindromes: 14

val it =
  [[1,2,3,1,2,3],[1,2,3,2,3,1],[1,2,3,3,1,2],[1,2,3,3,2,1],[1,2,3,4,1,2],
   [1,2,3,4,2,1],[1,2,3,1,4,3],[1,2,3,3,4,1],[1,2,3,4,5,1],[1,2,3,2,3,4],
   [1,2,3,3,2,4],[1,2,3,4,2,5],[1,2,3,3,4,5],[1,2,3,4,5,6]] : int list list
- length it;
val it = 14 : int

Symmetric palindromes: 1

val it = [[1,2,3,3,2,1]] : int list list

  Cooperations

- kmul [1,2,3][1,2,3]

- length(kmul [1,2,3][1,2,3]);
val it = 588 : int


Morphograms: 588.

Palindromes “Palin(kmul [1,2,3][1,2,3])": 44

val it =
  [[1,2,3,2,3,1,3,1,2],[1,2,3,3,1,2,2,3,1],[1,2,3,2,1,4,3,4,1],
   [1,2,3,2,1,4,5,4,1],[1,2,3,2,4,1,3,1,2],[1,2,3,2,4,1,5,1,2],
   [1,2,3,4,1,2,3,4,1],[1,2,3,4,1,2,5,4,1],[1,2,3,3,1,4,4,5,1],
   [1,2,3,4,3,1,3,5,4],[1,2,3,4,1,5,2,3,1],[1,2,3,4,1,5,3,6,1],
   [1,2,3,4,1,5,6,7,1],[1,2,3,4,5,1,2,3,4],[1,2,3,4,5,1,3,6,4],
   [1,2,3,4,5,1,6,7,4],[1,2,3,2,3,4,3,4,1],[1,2,3,2,3,4,3,4,5],
   [1,2,3,3,4,2,2,3,1],[1,2,3,3,4,2,2,3,5],[1,2,3,4,3,2,3,4,1],
   [1,2,3,4,3,2,3,4,5],[1,2,3,2,4,5,3,5,1],[1,2,3,2,4,5,6,5,1],
   [1,2,3,2,4,5,3,5,6],[1,2,3,2,4,5,6,5,7],[1,2,3,4,5,2,3,4,1],
   [1,2,3,4,5,2,6,4,1],[1,2,3,4,5,2,3,4,6],[1,2,3,4,5,2,6,4,7],
   [1,2,3,3,4,5,5,1,2],[1,2,3,3,4,5,5,6,1],[1,2,3,3,4,5,5,6,7],
   [1,2,3,4,3,5,3,1,2],[1,2,3,4,3,5,3,6,1],[1,2,3,4,3,5,3,6,7],
   [1,2,3,4,5,6,2,3,1],[1,2,3,4,5,6,3,1,2],[1,2,3,4,5,6,7,1,2],
   [1,2,3,4,5,6,3,7,1],[1,2,3,4,5,6,7,8,1],[1,2,3,4,5,6,2,3,7],
   [1,2,3,4,5,6,3,7,8],[1,2,3,4,5,6,7,8,9]] : int list list

- length it;
val it = 44 : int

Interpretations

It seems not to too surprising that coalitions (additions, concatenations) of palindromes are accepting some closure under the category “palindrome”.

More surprisingly, at least at a first glance, is the fact that the cooperation (multiplication) of palindromes of the same type are realizing palindromes again.

The coalitions and cooperation of asymmetric palindromes are resulting in asymmetric palindromes as well as in symmetric palindrome. Thus the coalition and cooperation of asymmetric palindromes has a common set of symmetric palindromes.

As a rule it appears that the cooperation of symmetric palindromes is producing a symmetric result.

This could open up some insights into the process of cooperations and coalitions in the context of morphic interpretations of phenomena in the realm of the bio- and semiosphere.

Therefore, systems theory (of what ever level or color) that is successfully applied to the bio- and semiosphere stops to have a successful application in the morphosphere.

In other words, the “Anomaliengrammatik" (Alfred Toth) of palindromes is describing anomalies of the first kind, i.e. symmetric anomalies. 

Things are getting hopeless if asymmetric anomalies occur at the desk of our scientifically trained controllers.

What’s the result of the journey?
 

It isn’t possible for a semiotician to decide what kind of object he, she or it is eying. In the eye of a semiotician, the object he/she eyes is unavoidably a “trompe-l'œil”. 

The eyed palindrome is not showing its identity, i.e. its way of coming into existence remains hidden. 

The palindrome is eyed as a textual object. It is seen through the eyes of a semiotician. 

A semiotic palindrome as an object is hiding its way of construction that would show its character as belonging to the semio- or to the morphosphere. 


This objectification of textual events is not prohibiting semioticians to us palindromes as strategies, and strategic tools.

What is studied is the cultural product, not its modi of becoming a product (construction, creation, elaboration). Obviously, semioticians will see it differently.

A semiotic palindrome as a product is always both, a semiotic construction on the base of atomistic concatenation and as the result of a retrograde recursive morphogram.

Because all symmetric palindromes are at a first glance, and without involving them into a constructive play, simultaneously members of both spheres, the semio- and the morphosphere, the semiotic view is blind for this constitutive difference.

As much as palindromes function as a key for semiotic studies, it jumps into the eyes, that the whole endeavour of semiotics is the victim of a sophisticated trompe-l'œil.

Hence, what is eyed is not what is seen. Palindromes cannot be seen. Even the seen palindrome might turn out not to be what had been seen.

The phenomena are not given to the eye of a semiotician, they have to be elaborated by methods not in the reach of the eyes.

More at:
http://memristors.memristics.com/Morphospheres/Asymmetric%20Palindromes.pdf
http://memristors.memristics.com/Morphospheres/Asymmetric%20Palindromes.html

Morphogrammatics and Computational Reflection

Applying insights from the retro-grade recursivity concept of morphogrammatics to questions of reflectionality and interactionality of programming

"Reflection may one day be as common as recursion" - Brian Smith, Reflection and semantics in Lisp

http://nl.ijs.si/~damjan/cr.html

FULL TEXT
http://memristors.memristics.com/MorphoReflection/Morphogrammatics%20of%20Reflection.html
http://memristors.memristics.com/MorphoReflection/Morphogrammatics%20of%20Reflection.pdf

Abstract
Turning back from the studies of morphogrammatics to some open questions of reflectional programming, the recountered problematics might be put into a different light and new methods of handling formal aspects of reflection and reflectionality shall be introduced. Albeit the use of light-metaphors, morphogrammatic reflection is not sketched along the paradigm of optical metaphors.

Morphograms are presenting neither propositions nor perceptions able for mirroring (representation). 


Exercises in defining morphogrammatic retro-grade recursion and reflection schemata are continued from the paper “Sketches to Morphogrammatic Programming”.
As for previous papers, this is work in progress and not a chapter of a text-book.

Standards of Reflectional Programming

Marginality of general concepts and devices

It isn’t in any sense new, and there is no need to be new, but it might be expanded to even an inflationary use, that terms like reflection, reflexivity, recursion, re-entry, self-referentiality, Self, and Identity are labels in nearly all contemporary fields of writing in science, culture, ideology, art, comedy and everywhere else.

This sign of reflexivity is not necessarily connected with a flexible awareness of others. Might they be other productions in the field of the Self-business or happening in disjunct codes, media, habits, cultures and languages.



It is therefore very astounding to read a bulk of papers and books in Anglo-British language about and of the mentioned topics, sujets, challenges, debates without finding any reflection on the fact that the whole debate is encapsulated in a specific and local idiom.

I’m not speaking about African dialects or Siberian historic languages, not even about well known European languages like Eastern European languages, no I speak about the languages of the Post War Europe. 


To read a couple of books about Self, reflexivity, recursion and reflection without encountering a single German or French citation is disturbing if not catastrophic. I’m not speaking about the 3 mentioned thinker, French or German, for whom there are some rudimentary translations available at Amazon. 



Such ignorance at a time of maximal accessibility is paramount. And its aftermath catastrophic, when our Chinese friends who studied at such great institutions like Oxbridge or Goldsmiths are overrunning us with our local theories, now transformed into global truth. This movement is further advanced than we like to accept if we get forced to learn from Singapore what Jacques Derrida really has written to us. And then there are immediately our PC maniacs in duty.



But there is no Anglo-British academic text about reflexivity which would take the courage to reflect its own marginal insularity. Hence, the concepts and strategies of system and environment, presupposed for reflection, reflexion and reflexivity, are not applied to the conditions of production of those eminent pretentious textual elaborations. Such texts are not reflecting their inter-textuality.



A possible language barrier is no excuse at all for the inflexibility of reflection; it is a conscious strategy. And this becomes even more crucial if we forget the whole language debate and its different cultures by reflecting on different ways of writing.
Texts about the mentioned topics of flexible reflexivity are written in stable homogeneity realizing the narrative forms of essays, monologues or conceptual novels. 


Whatever those texts might be from a media-theoretical perspective, there is no disruption between formal and notional languages and writing. What is written is easily be spoken and lectured too. 



The whole tradition of formal-mathematical studies about identity, reflexivity, reflection, self-reference, iteration, recursion and much more is segregated as non-profound calculations missing the deepness of philosophical, sociological and psychological contemplation. Crucial techniques, methods and results don’t get any mentioning. Such redlined endeavours might be seen as good enough for reflectional computers but of no serious relevance for human cultural studies.

Mirrors and Meta-programming

"The principles of extending reflexive theories, formulated so far (Gödel, Turing, Feferman) have been limited to incremental, linear advance along the progression of (transfinite) ordinals (Giunchiglia & Smaill 89). Such advance is, however, non-reflexive: the usual extension operator does not take into account its own role in the process of extension: it only repeatedly reproduces the basis for its application.

A reflexive extension operator would not do away with the incompleteness of a reflexive theory, but it could extend it in longer leaps along the progression of ordinals. Such reflexive progressions of reflexive theories could be a better model of the kind of reflection which is peculiar to consciousness and which is usually considered to surpass the reflexivity of reflexive formal theories.” (Damjan Bojadziev)
http://nl.ijs.si/~damjan/phen.html 

Reflective computational systems allow computations to observe and modify properties of their own behavior, especially properties that are typically observed only from some external, meta-level viewpoint. 



For example, by representing its interpreter, a program could monitor its own execution to detect loops and then modify (itself or) its interpreter to avoid them.

Reflection in the Integral Object-Oriented System

"Reflection is the capability of a computational system to “reason about and act upon itself” (Maes 1987) and adjust itself to changing conditions. The computational domain of a reflective system is the structure and the computations of the system itself. Two kinds of reflection can be observed: structural and computational reflection (Ferber 1989).

• Structural Reflection: is the most obvious and still the most developed form of reflection. It concerns the infinitary status of some data structures defined by reflexive domains (Ferber 1988). The Java Reflection API (Sun 1997) is an example of a restricted kind of Structural Reflection (better called ).

• Computational or Behavioral Reflection: Is the ability for a process to describe, analyse and modify itself while running."

Further concepts about reflexion, reflexivity, self-reference, eigenform and the “I” are well disseminated in the higher circles of conceptual recreations. Of the many, two successful examples shall be mentioned. Both are stacked in the paradigm of relations, relational logic and relationalism, and are lost in all kinds of loops, “knots and braids”. Douglas D. Hofstadter and Luis H. Kauffman. The publications of this trend are certainly well known but strangely are not appearing as such in the literature about reflexivity in/of societal systems.

Post-Hofstaedterian Reflexions on reflexivity

Also “This essay is a discussion of the concept of reflexivity and its relationships with self-reference, re-entry, eigenform and the foundations of physics.” (Kauffman) and not so much a direct study about social systems it could be of some liberating effects to study what had been developed from at the other side from the early 70s onwards.



"Reflexive is a term that refers to the presence of a relationship between an entity and itself. One can be aware of one's own thoughts. An organism produces itself through its own action and its own productions. A market or a system of finance is composed of actions and individuals, and the actions of those individuals influence the market just as the global information from the market influences the actions of the individuals. Here it is the self-relations of the market through its own structure and the structure of its individuals that moves its evolution forward.”



"Does the infinite nest of boxes exist? Certainly it does not exist on this page or anywhere
in the physical world with which we are familiar. The infinite nest of boxes exists in the imagination. It is a symbolic entity.”
http://www.math.uic.edu/~kauffman/ReflexANPA 

Further entertainment about the relational approach and its loops is aviable at Rocha's:
http://informatics.indiana.edu/rocha/ps/tilsccai.pdf 

Strangely forgotten Strange loops

"In the end, we are self-perceiving, self-inventing, locked-in mirages that are little miracles of self-reference."
 
— Douglas Hofstadter, I Am a Strange Loop p.363

http://en.wikipedia.org/wiki/Gödel,_Escher,_Bach 

Finite State Machines and Morphogrammatics

Machines on Differences, and Differences of Machines

Abstract

Morphograms had been introduced into the academic world by Gotthard Gunther with his theory of “transjunctional operations’ for a cybernetic logic of self-reflection at the BCL at the 1st of April 1962.

Meanwhile new approaches emerged, especially with the understanding of morphograms not just as pre-logical patterns but also as rules (operators), realized by the concept of morphogrammatic cellular automata. 


This paper is sketching a further approach toward a better understanding of morphogrammatics: Morphic Finite State Machines, exactly, Morphic Difference Machines.

It seems that the difference-theoretical aspect of morphogrammatics gets an even more direct thematization and formalization in the context of an analogon to FSM.

Are morphic FSAs Finite State Automata at all?

This proposal tried to sketch the idea of a morphogrammatic analogon to the semiotic concept of FSAs and others. At the end of the journey of analogization it might turn out that non of the definitorial constituents of those machines could be covered by the morphogrammatic approach to abstract machines.

In fact, morphoSFA have neither an initial nor a final state. They are not really feed by words of a regular language. They don’t begin and also don't stop. Their transitions are independent of the vocabulary, hence they are also not transitions in the sense of the definition.

They are differentiations, paradoxically differing and defering the positions of the structuration that are defining the differences as constellations or “states” of the machine.

The opposite characterization to the classical concept might give a better insight into the definition and behavior of morphogrammatic machines.

Instead of a defined start, like for FSA, morphic machines don’t have a start. What we know about the behavior of the machine is depending from the point of view of an observer.

An observation might take place and a beginning might be postulated. 
Any description of the behavior of the machine has to distinguish at least two possibilities of description: An internal (algebraic) and an external (co-algebraic) position of an observation.

An external observation might be closer connected with the point of view of classical automata theory and their concepts and apparatus. From there, the analogy and deconstruction might take place.


An internal description has to be aware of the non-conventual feature of the morphic automata.
This approach might be supported by the well known ‘experimental’ intervention with automata and the co-algebraic structures involved.

Some lessons could be learned from the construction and application of other morphogrammatic systems and ‘machines’.

It seems, that the morphic approach to cellular automata is still a novelty and worth to be studied.

Is there any use for morphic automata?

The usefulness of classical machine models like FSA, DFA, Mealy and Moore and Turing Machines, and many others, for computation, linguistics, modal logics and AI is well known, established, proven and documented. A further elaboration shall consider omega-languages and Büchi-automata in comparison to MorphoAutomata.

It is also well known that such automata concepts had been crucial for the development of modern theoretical linguistics. Noam Chomsky’s hierarchies are still governing the field.

On the other hand, it is not well known and only vaguely understood that the difference-theoretical approach to semiotics and linguistics of Ferdinand de Saussure might uncover structures and processes, i.e. structurations, that are closer to the functioning of language than the Leibniz-Chomsky paradigm, founded by the concept of abstract calculi, based on atomic signs, concatenation/substitution and linearity, could be.

Obviously, de Saussure's approach doesn’t fit into the Leibniz-Chomsky paradigm of computation.

Dealing with differences, and differences only, in a system of differences, where the loci of the differences in a complexion are themselves distinguished by differences in the system of differences, determines the ‘value’ of the difference, might get a fundamentally new and interesting conceptualization, ‘formalization’ and programming  towards a determination of the “values” of differences by morphogrammatics and morphic machines.

De Saussure wasn’t well recognized by the academic linguists, especially by the German school, and was then later successfully denied by the international Chomsky movement of linguistics.

"In language there are only differences. Even more important: a difference generally implies positive terms between which the difference is set up; but in language there are only differences without positive terms.” F. de Saussure

Jaques Derrida discovered the deep difference-theoretical endeavour of de Saussure's semiotics (sémiologie), not just for a theory of language but for an understanding of thinking at all. This post-philosophical approach got some recognition and determined the international movements of deconstructionism and deconstructivism.

Unfortunately, despite the radical insight into a pre-logical structure of de Saussure’s understanding of differences and system, différance, any attempts to connect this movement with more formal and operative achievements had not only been denied but harshly criticized, and institutionally killed.

Today, it could be a chance to begin to study this promising approach again. Might be with the help of morphogrammatics and morphogrammatic automata as formal and inspirational models.
At least, this could be one answer to the question:

What are difference-based automata for?

Morphic automata, desinged and understood as closed automata without input nor output in the strict sense are also giving some operational help to understand Humberto Maturana’s concept of autopoiesis. Despite the fact that morphic automata are just in their very beginning, morphic automata should nevertheless be contrasted with the classical, first- and second order cybernetic approaches, to a theory of living systems.

The Chinese Challenge

The Chinese Challenge

old address:

http://www.thinkartlab.com/CCR/rudys-chinese-challenge.html


new address:

http://the-chinese-challenge.blogspot.com/

NEW APPROACHES

NEW APPROACHES TO THE PROJECT OF UNDERSTANDING THE SPECIFIC RATIONALITY OF THE CHINESE WRITING SYSTEM

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.

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.

http://www.thinkartlab.com/pkl/media/Chinese%20Grammar/What%20Chinese%20Grammar.pdf

 http://www.thinkartlab.com/pkl/media/Chinese%20Grammar/What%20Chinese%20Grammar.html

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. 

http://www.thinkartlab.com/Memristics/Power%20of%20Four/Power%20of%20Four.html

http://www.thinkartlab.com/Memristics/Power%20of%20Four/Power%20of%20Four.PDF

Short Overview of Morphic Cellular Automata

http://memristors.memristics.com/CA-Overview/Short%20Overview%20of%20Cellular%20Automata.html

http://memristors.memristics.com/CA-Overview/Short%20Overview%20of%20Cellular%20Automata.html

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. 

http://memristors.memristics.com/Graphematics/Graphematics%20of%20Cellular%20Automata.html

http://memristors.memristics.com/Graphematics/Graphematics%20of%20Cellular%20Automata.PDF

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Luhmann’s secret diamonds

New entries for the Zettelkasten

FULL TEXT
http://www.thinkartlab.com/pkl/media/Luhmanns Diamonds/Luhmanns Diamonds.pdf
http://www.thinkartlab.com/pkl/media/Luhmanns Diamonds/Luhmanns Diamonds.html

Abstract

A kind of a similarity between Luhmann’s concepts of sign, system, difference and re-entry and the main figures of diamond theory is observed.

1.2. Interpretation

It seems to be more fruitful today to thematize and formalize Luhmann’s distinctions with the help of diamond theory instead of the Calculus of Indication of George Spencer Brown.

A key notion in Niklas Zettelkasten, obviously, is self-reference.
The other crucial notion is the self-referential concept of difference.

With that all kind of connections to logical, methodological and epistemological considerations are provoked. A strange connection to Spencer-Brown was inaugurated, mainly by the influence of Heinz von Foerster. The re-entry figure became a machina creativa, albeit nobody had a training in formal languages at all.

Difference and relation; différance
But Luhmann’s work is about social theories and not about logic. Neither is Luhmann’s theory of social systems a semiotic or semiological theory. This point ios not yet well understood. Semiotics, but the french “sémiologie” too, are based on relations, triadic for semiotics and dyadic for semiology. But Luhmann’s concept of a self-referential and “therefore”, paradoxical concept of difference isn’t based on relations but on difference (Unterscheidung). Relations are presupposing difference, and are thus secondary to the paradox concept of difference. Relations are logical and not paradoxical.

Derrida has given strong deconstruction of the semiological and semiotic sign concept and its relational foundations in logocentrism. With his radicalized interpretation of de Saussure’s semiology, he transformed the concept of difference to the paradoxical non-concept of différance. The difference of the difference, the différance, is not in a relationship to relations.

Similar, Gotthard Gunther’s non-concept of proemial relationship.

Hence, Luhmann’s insistence on self-reference might well be reformulated in different ways. One, which I proposed for many years, is interpreting self-reference and its circularity in the framework of a polycontextural understanding of chiasms, i.e., technically, as proemial relationships.

Now, after this chiastic theory got some maturity, albeit not much recognition, it is time to introduce the diamond approach to difference and circularity of system and environment . Diamond strategies are a further radicalization of the earlier approach of polycontextural chiasm.

Also Luhmann’s work is not well known in the Anglo-Saxon world, it isn’t a wrong feeling to observe that also the themes and topics, and their highly reflected treatment by Luhmann, has no real existence in the world-leading sociological literature of the super-power theoreticians.

2. Supplementing the Zettelkasten

It doesn’t seem too risky to risk an interpretation of Luhmann’s theoretizations out-side or beyond second-order cybernetic figures and metaphors.
In other words, is there a strict necessity to understand Luhmann’s adventure in terms of his entries of his own Zettelkasten?
Is it possible to ‘re-construct’ his constructivism and re-enter into it without its terminology and jargon of difference, distinctions, re-entry and self-referentiality?
Luhmann’s theory is self-referential, thus it could refer to itself in different terminological modi, and still keeping its adventures strategies and networks of constructing a de/constructive theory of social systems alive.

Hence, I will take the risk to supplement the Zettelkasten by smuggeling some non-contents of diamond boxes into this, now electronic, Zettelkasten.

By re-reading the passage with its introduction of the difference of system and environment, I think that I’m observing, or as I prefere to say, hallucinating some features not yet been recognized and mentioned, neither explicitly by Luhmann nor by his followers.

Self-referentiality without referentiality?

The rhetoric figures of Luhmann’s texts are not necessarily determined by the frameworks of the used technical weaponry. The cage of the jargon is not necessarily incarcerating the dynamics of the gesture.

Technically, I try to understand Luhmann’s theory of social systems from the viewpoint of polycontextural and diamond systems. Hence, I try to avoid to go into the litany of second-order cybernetics, systems theory and Spencer-Brown’s Calculus of Indication and its extensions.
Even more technically, my interpretation of Luhmann’s gestures with the introduction of his rhetoric figures is due to a morphogrammatic subversion, abandoning any jargon and terminological content, as crucial as it might be, and conceiving the dynamics of the pattern, only.

After this new diamond approach is introduced, experienced and further developed, a renewed lecture of Luhmann’s work as involved with the above mentioned second-order trends, might happen again.

The term “diamond” refers to itself, only. There is no reference to exposed marketing labels necessary.

2.2. Uncovering Luhmann’s diamonds

Statement
"When a communication constitutes a previous communication as a communication, it simultaneously distinguishes it from all those other things in the world that are not communication. In this sense, all operations of autopoietic systems always constitute the difference between the system and its environment

How can this happen? If an operation of an autopoietic systems is producing by its action, i.e. operation, both, the intended operation and at the same time, the operation of distinguishing the system of the first operation from its environment, then it “constitute[s] the dfference between the system and its environment”. How is an autopoietic operation simultaneously operating in its domain (system) and producing an environment of the domain? Or in other words, how is an operation operating that it is able to operate and thereby by such operation constituting (operating) its own environment?

The first answer, which might be given by Luhmann is the hint to Spencer Brown’s Calculus of Indication: “Draw a distinction!” With this distinction, the ‘world’ is ‘divided’, i.e. ‘distinguished’ into two parts, the inside and the outside of the ‘world’ or ‘space’.
But what is given by the CI? Two ‘equations'.
In this formulation, no world appears. The world or space is presuposed and realized by a sheet of paper or another medium of inscription. This might be interpreted cognitively by a user of the CI. And this interpretation will become a meta-theoretical environment of the calculus. But nevertheless no part of the calculus in question.

Again, "When a communication constitutes a previous communication as a communication, it simultaneously distinguishes it from all those other thing in the world that are not communication.”

Interpretation
"When a communication constitutes a previous communication as a communication"
This is involving several procedures:
1. "communication constitutes a previous communication", this might be naturally understood as a composition of two communications.
2. "as a communication” means, that the composition has to be realized as a composition of communications and nothing else. But this condition is exactly what is called the ‘matching conditions for compositions'.
4. With this formulation we get a clue to understand what could be meant by the consequence: “it simultaneously distinguishes it from all those other thing in the world that are not communication."
This consequence of the composition of communications is following consecutively the ‘assumption' of the operation of composition albeit it states its simultaneity.

Diamondization
Luhmann’s communicational statement, the ‘axiom’ of communication, interpreted as a categorical composition of communications offers a natural introduction of the otherness of communication, i.e. the simultaneous environment of communication by the saltatorical hetero-morphisms.
It needs two communications to realize communication and its environment as the singular otherness of communication. This asymmetry is directly covered by the saltatories od diamond theory, which are complementary to the categories of communication.

Because of the operativity of the diamond interpretation of Luhmann’s conception of communication, communication might now be studied operatively on all levels of complexity and complication necessary, together with their interplay.

This diamond interpretation is not reducible to the indicational calculus and its use for autopoietic and communicational systems.

Again, what are the conditions for communication? Communications have to be “anschlussfähig”, i.e. they have to fulfil the conditions of connectivity.
In category and diamond theory, such conditions are exactly the matching conditions of composition.

Now, there are two possibilities opened up.
One insists that the conditions of the possibility of something are not identical with such a conditional something.
The other position could take a highly formalistic turn towards self-referentiality and postulate that there is no logical difference between the conditions of something and such a something.
Without doubt, the latter position leads quite directly to logical paradoxes. But who cares?
Why should we use logic? And which logic anyway?
It also could be mentioned that the comparison itself is too much restricted by logic and alternativity.

The first position sounds harmless if we take the statement in a hierarchical way, i.e. if we postulate a sequential order between the conditions and the entity. But why should we accept this decision as the only working possibility?
The diamond approach, obviously is postulating a simultaneity of both thematizations, the conditions of the possibility and the characteristics of the entity.

It might be a question of taste which of both positions has to be considered as more crazy: the ultra-formalistic or the diamond approach.

Re-entry and in-sourcing
``To cope with these consequences of a re-entry of the internal/external difference in itself, the system needs and constructs time.” (Luhmann)

Again, in-sourcing:
"The idea of in-sourcing the matching conditions into the definition of diamonds seems to be in correspondence with the two main postulates of "Chinese Ontology", i.e., the permanent change of things and the finiteness or closeness of situations. That is, diamonds should be designed as structural explications of the happenstance of compositions and not as a succession of events (morphisms)."

The figure of re-entry tries to correspond to the device to include “the internal/external difference in itself”. This happens in “consequences” and needs/constructs time.
Hence, the idea of a simultaneous realization of the difference of system and its environment gets lost in the infinit delirium of self-reference.

In-sourcing the matching conditions of composition is a finite and simultaneous constellation of categories and saltatories. It is the interplay of both, categories and saltatories of a diamond constellation, which is realizing the figure of re-entry in a finit and differential manner.
Both strategies, the re-entry and the in-sourcing, seems to correspond to a similar gesture.

FULL TEXT
http://www.thinkartlab.com/pkl/media/Luhmanns Diamonds/Luhmanns Diamonds.pdf
http://www.thinkartlab.com/pkl/media/Luhmanns Diamonds/Luhmanns Diamonds.html

The Chinese Challenge-华文?谁怕谁!

推广华语理事会推出崭新的活动《华文?谁怕谁!》，让华族新加坡人和永久居民，通过有趣的问答游戏，感受中华文化的博大精深，深化对华文华语的认识，并进一步提升华语掌握能力。

The Chinese Challenge

"The Promote Mandarin Council has launched an exciting new initiative, The Chinese Challenge, to encourage Singaporeans and Permanent Residents to enjoy and improve their Mandarin and deepen their knowledge of Chinese culture through experiencing the finest in Chinese culture and language."

http://www.thechinesechallenge.sg/

"If we can raise the level of Chinese language and appreciation of Chinese culture, it could have an indirect impact on our economy in the future,' he said."

http://www.straitstimes.com/

The Chinese Challenge

中国挑战

The Chinese Challenge: Hallucinations for Other Futures

What can we learn from China that China is not teaching us?

It is the paradigm of writing on which main cultures are depending. Their kind of rationality, their efficiency of technology, the way they organize society and communication, arts and sciences, all are not to separate from their paradigm of writing. How people are involved in writing and scriptural practice is enabling their possibility of thinking and living. Main cultures always depend on their paradigm of writing. Writing in general is the most abstract mechanism and technology of cultural, political and technological formations.

中 国对西方的挑战不是经济的、也不是政治的或者军事的；苏醒的技术中国和经济中国这个事件并不构成对西方的所谓的"大挑战"，真正的挑战是重新发现她的文字 系统，并设计出新的理性形式系统，就像创造新的数学和新的编程语言一样；是面对一个崛起的中国我们是否做好了充分的准备。

The Chinese Challenge to the West is not economical, political or military. It is not the event of a re-awakening economic and technological China which is the Grand Challenge to the West but the possible re-discovery of the operationality of its writing system for the design of new rational
formal systems, like new mathematics and new programming languages

http://www.thinkartlab.com/CCR/2006_08_01_rudys-chinese-challenge_archive.htm

Text in Chinese

http://www.thinkartlab.com/pkl/media/The Chinese Challenge-CN.pdf

Video Chinese&English

http://www.youtube.com/watch?v=jCNcFmPl-9E

Xanadu's textems

Diamond theoretical reflections on hypertextuality

FULL TEXT
http://www.thinkartlab.com/pkl/lola/Xanadu-textemes/Xanadu-textemes.pdf


Abstract
Xanadu is still not yet realized. Nevertheless, it is appropriate, not only to understand its principles and its radical difference to established Web hypertext and multimedia, but to try to think and design even more advanced concepts of non-traditional interactions. One interesting extension of identity-oriented thematizations is opened up by polycontextural, kenogrammatic and diamond approaches to text theory; proposed recently as textems or textemes. Textemes are based on the interplay of anchored semiotic diamonds and are delivering necessary environments for transclusions. Transclusions and transjunctions are modeled additionally in a polycontextural setting. The characteristics of ‘electronic’ text in contrast to ‘physical’ paper texts are emphasized.

1.1. Hyper-textuality

Since some decades, everybody knows Xanadu and nearly nobody ever has seen it working.

Most people think of it as a special kind of a hypertext project with two-way links and connected with projects like Hypercard. Hence, the focus is on the machinery of links.

Personally I had a similar perception and therefore wasn’t specially interested in it.
But there is a very crucial distinction at place which makes a profound difference to all kind of linking systems. It is Nelson’s insistence on the difference of ‘physical’ and ‘electronic’ documents. At the first glance this seems to be obvious and trivial too, but it isn’t at all.

There is a lot of postmodern writing about the virtuality and simulacrum of electronic media. Nevertheless I couldn’t find any conceptually and technically useful elaborations.

With such a change, from the ‘physical to the ‘electronic’ , in the ontological and epistemological status of documents and texts, the whole topic of links (transclusions, deep links, content links, etc.) appears as a ‘natural’ consequence of the new understanding of text ('electronic’., digital’, ‘virtual').

1.1.1 Ted Nelson’s Xanadu

"To Project Xanadu, that means enacting two types of connection: profuse and unbreakable *deep links* to embody the arbitrary connections that may be made by many authors throughout the world (content links); and *a system of visible, principled re-use*, showing the origins and context of quotations, excerpts and anthologized materials, and content transiting between versions (transclusions).

This may be simplified to: connections between things which are *different*, and connections between things which are *the same*. They must be implemented differently and orthogonally, in order that linked materials may be transcluded and vice versa. This double structure of abstracted literary connection -- *content links* and *transclusion* -- constitute xanalogical structure."

Transclusion
"Transclusion is what quotation, copying and cross-referencing merely attempt: they are ways that people have had to *imitate* transclusion, which is the true abstract relationship that paper cannot show. Transclusions are not copies and they are not instances, but *the same thing knowably and visibly in more than once place*. This is a simple point which is remarkably difficult to get across. While copies and cross-reference are workarounds in place of transclusion, aliases and caches are *forms* of transclusion."

Text is not simply text
"Nelson always meant hypermedia when he said hypertext, it's one of the things that people get wrong about Nelson. They think that they've invented hypermedia and he only invented hypertext. He meant 'text' in the sense of corpus, not text in the sense of characters. I know this for a fact because we've talked about it many times (van Dam 1999, interview)."

Hypertextuality in the sense of the Web and its WEB-0.X-mythology, is restricted to a unidirectional exchange of signs as data without environments. Web links are not only uni-directional by definition but they have only two logical states: broken/unbroken.

It would by great to enjoy a more dynamic bi-directional Web connectivity in the sense of transclusions (Ted Nelson). But Xanadu links are postulated as UNBREAKABLE. Does it matter if they are one- or two-way links if they are not qualified to perish? http://www.xanadu.com/xuTheModel/

What’s an ‘electronic’ text?

It isn’t easy to characterize properly ‘electronic’ or ‘digital’ texts and documents in the sense of Nelson’s intentions.

One hint is given by the distinction of “same” and “different” instead of ‘equal’ and ‘unequal’.

” ... connections between things which are *different*, and connections between things which are *the same*."

A further hint to the different epistemological character of ‘electronic’ texts is given by the necessity of ‘orthogonal’ structures.
"They must be implemented differently and orthogonally, in order that linked materials may be transcluded and vice versa.”

Furthermore, ‘electronic’ texts are charactericed by a complementarity of polar distinctions, i.e. by a double structure of ‘content links’ and ‘transclusions’.
"This double structure of abstracted literary connection -- *content links* and *transclusion* -- constitute xanalogical structure."

Some more distinctions might help to grasp the specific character of ‘electronic’ texts.

1. The mainstream understanding of text is still dominated by the sentence-model. A text is a composition of sentences (phrases, statements, etc.). A sentence is ideally a well-formed statement with a clear meaning.

2. Hypertext in the mainstream understanding is a text of a text. As a meta-level, a markup language is constructed to link textual elements of the primary text.

"In a classical node-link hypertext, a graph can be constructed on the set of nodes where each edge is identified with a link and structure discussions typically take place with respect to this graph.” (Neumuller, p.89)

”The Web link is in essence little more than a goto or a jump instruction to the Web browser to retrieve and display a new document.” (ibd., p. 149)

3. And to give the whole thing some meaning, a markup language of a markup language of the ordinary text is introduced. This is the concept of text in an ontology-based Semantic Web.

4. Nelson’s Docuverse, "deep electronic literature”, virtual documents

”...transclusions are hard to formalize in graph theory: are they nodes themselves? If they are, they would transform trees into directed graphs. I have included them in this section, as they seem to mark a breakpoint of graph theory.” (ibd., p.90)

The same at different places, without ‘physical’ representation by copy-and-paste.

"Transclusions are not copies and they are not instances, but ‘the same thing knowably and visibly in more than one place’.” (Nelson)

Key Concepts
• Parallel Documents
• The Big three : Transpointing, Transclusion and Transcopyright.
• Transpublishing.

Hence a further aspect of the epistemology of ‘electronic’ texts is the fact that they have to be placed, that they have to take place in a textual space. There is no such thing in classical text theory as a textual place or locus. This shouldn’t be confused with the triviality that in classical text theory all kinds of topologies, hodologies and super-graphs might be used to explain, model and formalize classical texts as complex objects.

FULL TEXT
http://www.thinkartlab.com/pkl/lola/Xanadu-textemes/Xanadu-textemes.pdf

Diamond Text Theory

From signs to textems

FULL TEXT
http://www.thinkartlab.com/pkl/media/Textems/Textems.pdf
http://www.thinkartlab.com/pkl/media/Textems/Textems.html


"From signs to textems” is sketching the basic constituents for an intertextual theory of texts, based on the diamond concepts of bi-signs and textems.
Applications to inter/intra/trans- and hypertextuality (Xanadu) are sketched.

Some remarks about the relationship between semiotics and Gunther’s place-valued logic in the 70s are added.

1.2 Inter/intra/trans- and hyper-textuality

1.2.1 Signs and environments

Text theory seems to be fundamental for any media and cultural theory.


But classical, modern and post-modern studies of intertextuality in general is restricted mainly to a semantic or pragmatic level, concerning the intertextuality of meaning as an interaction of different texts, discourses and stratagemes in translation, interpretation or reconstruction of what happened anyway.



Poetic, evocative, propagandistic and prophetic modi, transformed by post-scientific writing, are taboo to the enlightened elite.



The basic semiotic system of whatever color is presupposed by such highly propagandistic and delirious and post-technological SiFI-fantasy and are not by themselves involved into the interaction of intertextuality in general.


It is understood that there is no semiotic theory of sign systems which is reflecting inner and outer environments of basic signs as a constitutive part of the definition of signs.



The literate reader of postmodern education will know very well that he will fail to answer a single question about how his or hers pragmatistic, interactive, discourse driven, multimedial, deconstructivist, quantum-inspired dialogism (and much more) is working. 



The laconism to write of/on signs and their paradoxical subversions is not generating jobs.



Therefore, a first step to a general theory of interactional semiotics on the base of the new concept of textems, i.e. bi-sign systems or anchored diamonds, consisting of the semiotic intra-kernel and the semiotic internal/external environments, and its interplay, is proposed.

1.4.4 Conceptual graph for two bi-signs building a textem

A textem consist of two diamondized anchord signs, i.e. bi-signs, inter-playing together by their mediated external environments.

Hence, a textem is an interplay of two bi-signs.
A bi-sign is a diamondized anchord sign, i.e. a sign with intrinsic environments and its anchors. 



This is a kind of botton up introduction. Because we know signs and have not yet experienced textems, this way of building up textems is legitimate.

But nevertheless, it works only because we know how to construct textems out of signs which are not able to offer any of the principles of textems, which are needed to realize such a construction, like their chiastic interplay between the environments of signs, the environments of signs and the anchoring of signs.



As we no well enough, signs lack environments, there is no chance to construct out of signs inn sign-theoretical sense a semiotic environment of the sign conception.

And obviously, there is no such mechanism as a chiasm in the sense of proemiality for signs. Hence, neither environments, internal and external, nor interactions between signs based on their environments are conceivable.



Therefore, as a consequence, there is no such thing as a reduction mechanism for textems, which is reducing without loss, textems to signs.

On the other hand, after the intuition of textems is introduced, formalized and implemented, reductions are naturally available.
 


Hence:

A textem is reducible to its interacting bi-signs by excluding its chiastic interactivity. 
A semiotic diamond is a bi-sign, de-rooted from its anchor.

A single bi-sign is disconnected from its neighbor bi-sign, hence it is a bi-sign without interaction but realizing an anchored semiotic diamond with its isolated, and hence restricted, environment. 

A sign is a semiotic diamond, depraved from its environment.


FULL TEXT
http://www.thinkartlab.com/pkl/media/Textems/Textems.pdf
http://www.thinkartlab.com/pkl/media/Textems/Textems.html