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