Gunther’s Negation Cycles and Morphic Palindromes

Applications of morphic palindromes to the study of Gunther’s negative language

Rudolf Kaehr Dr.phil@

Copyright ThinkArt Lab ISSN 2041-4358



Gunther’s concept of technology is based on a ‘melting’ of number and notion in a polycontextural setting. A key to its study is established by the negation-cycles of polycontextural (meontic) logics that are establishing a negative language.

It is proposed that a morphogrammatic understanding of technology is uncovering a level deeper than polycontexturality and is conecting numbers and concepts not just with the will and its proaxeological actions but with ‘labor’ (Arbeit) in the sense of Marx’s Grundrisse ("Arbeit als absolute Armut”.)
Palindromic cycles are offering a deeper access for the definition of negative languages than the meontic cycles. Morphogrammatics is opening up languages of creativity and work.
(work in progress, vers. 0.1, Oct. 2013)

1.  Gunther’s Negative Language

1.1.  Cycles as palindromes

From a polycontextural point of view, complexity, i.e. polycontexturality is first. Simplicity is a late product of simplification. Domains, contextures or fields are at first considered as discontextural. There is at first no common ground or umbrella to collect the differences into one family and home of sameness or identity.

List of oppositions

hierarchy / heterarchy,
positive / negative,
polycontexturality / morphogrammatics,
negation cycles / palindromes,
hamilton / journey,
negations / U, O, K, I
combinatorics / number of palindromes
symmetry / asymmetry

Palindromicity of the names of the negations / permutation of the values of negations.

Complementarity of negation cycles and morphic palindromes.

"We begin this time with another Hamilton cycle which exhibits an easily understandable rhythm in the distribution of the negations. “
p = N1-2-3-1-3-2-1-3-1-2-3-1-3-2-1-3-1-2- 3-1-3-2 p     (p. 44)

"Each individual circle represents a 'word' in a technical dictionary of negative laguage that does not describe existing - already created - Being in a positive language; rather, each of the 3744 cycles represents a specific instruction, how something can be performed, how something can be constructed."

Kreisumfang / circumference : 8 10 12 14 16 18 20 22 24
Anzahl / number :                24 72 264 456 708 920 912 336 44

Palindromes with rhythmic repetitions.

1.1.1.  Negative languages in action

Negative language in action:
Gotthard Gunther: Philosophical speculations,

Mitterauer, Gerhard Thomas: Computer model, patents, Volitronics
Mitterauer: Therapy of decision conflicts,
Der Formalismus der Negativsprache
Therapie von Entscheidungskonflikten
2007, pp 76-80


Dirk Baecker: Sociology and LoF, Negativsprachen aus soziologischer Sicht

Alfred Toth,,
15. Die semiotische Negativsprache

Eberhard von Goldammer:
Vom Subjekt zum Projekt oder vom projekt zur subjektivität !

A funny application by Kaehr:

1.1.2.  Polycontexturality of negative languages


               &nbs ... bsp;       Arbeit     <br />     

The presupposition of those approaches was and still is the acceptance of “frozen” values that are easy to be involved in a treatement by mathematical permutations.

Neither the proemiality of the values nor their “braided” permutations as they are common in bi-category theory had been recognized.

According to the newly proposed theory of morphospheres, the permutational negative language is operating on a surface structure while the morphic palindromes are involved with the deep-structure of morphogrammatics.

The surface-structure of negative languages might be highly complex and surpassing everything a positive language is capable to thematize or invoke but it remains nevertheless on the value-level of meontics, covered by polycontexturality, and is not prepared to address the processuality of morphogrammatic structurations on the deep-level of inscription.

Obviously, terms like deep and surface structures are lend from other disciplines and are applied here as nothing more than “operative” metaphors.

The negative language proposed by Gunther and studied by his followers is covering the surface-structure of semiotic polysemy as it occurs in polycontextural systems.

1.1.3.  Auto-cyclicity of negative languages

There is a surprisingly observation too.
Because negation cycles are based on negations and morphograms are negation-invariant kenogrammatic patterns it turns out that the whole cycle is based on one morphogram, and is therefore morphogrammatically auto-cyclic.

Negation cycles are zooming into the structure of the permutation of the value-theoretical interpretation of a single morphogram.

How can the attempt be saved on a morphogrammatic level if a negation cycle is morphogrammatically auto-referential and is therfore not telling much about its own cyclicity?

Gunther has prepared an answer himself. Albeit never being used, the idea of emanation of morphogrammatic systems gives the clue.

The cycle that is uncovered is the cycle between the levels of emanative disremption: from nil differentiation to full differentiation, and back.

Other cycles are possible too. A mix of evolutive and emanative morphic cycles is covering an interesting expansion of the idea of cyclic structures on the morphogrammatic level.

1.1.4.  Philosophical interpretation: Wille vs. Arbeitskraft

Arbeit, Handlung, Wille, Denken

Labor is not just action.

Gunther writes:

"Wir haben hier einen enorm wichtigen Punkt einer Handlungstheorie berührt, in der Begriff und Zahl verschmolzen werden und in dieser Verschmelzung zur Inkarnation des Willens in der Technik führen.

"Die Technik ist die einzige historische Gestalt, in der das Wollen sich eine allgemein verbindliche Gestalt geben kann.”

                &nb ... \    /<br />             Technik

The unknown form A a a A

The German politician Joachim Paul aka Nick Haflinger from the Pirate Party writes:

"Ja, ich liebe Marx, und zwar Groucho Marx und seine Brüder.”

I’m not a Groucho fan. I love Karl Marx.

Groucho Marx is, as people believe, well known.

Unfortunately, Karl Marx is more or less not known to the students and politicians. Especially in the USA dominated world. What is known are the bourgeois cliches about Marx and, obviously, about Marxism.

Joachim Paul also knows Gotthard Gunther quite well.

This paper will open up some insights and perspectives of thinking beyond classical cliches with the help of nearly unknow sentence, if it still is a sentence at all, I discovered in the early 1970s in the Grundrisse of Karl Marx on page 203.

The non-apophantic text of Marx reads:

Arbeit als absolute Armut, Armut nicht als Mangel sondern Ermöglichung jeglichen Reichtums. Karl Marx

This inscription alone offers a kind of a clue to the understanding of Marx as a non-Marxist thinker. It pushes him beyond any Hegelian attempts of understanding society. Like all the bourgeois socologists and economists up to such guys like Peter Krugman.

Gotthard Gunther tried it with his negative language.

Marx was obviously shocked and mesmerized by his inscription too. Therefore, he has given the potential reader some paraphrasing explanations.

It might all be different. But also the paraphrases are un-neccessary at all, the didactic help wasn’t recognized and accepted by his followers.

Today, Google gives only a very few hits to the ’magic’ sentence.

The paraphrase goes on to explain:

Die Arbeit nicht als Gegenstand, sondern als Tätigkeit, nicht als selbst Wert, sondern als lebendige Quelle des Wertes. Der allgemeine Reichtum, gegenüber dem Kapital, worin er gegenständlich, als Wirklichkeit existiert, als allgemeine Möglichkeit desselben, die sich in der Aktion als solche bewährt.

K. Marx: Grundrisse der Kritik der politischen Õkonomie. Frankfurt/Wien 1939, S.203

But Marx has also given a much more interesting hint for the very understanding of his ‘non-sentence’:

"Es widerspricht sich also in keiner Weise, oder vielmehr der in jeder Weise sich widersprechende Satz, daß die Arbeit einerseits die absolute Armut als Gegenstand, andererseits die allgemeine Möglichkeit des Reichtums als Subjekt und als Tätigkeit ist, bedingen sich wechselseitig ..." Marx 1953, S. 203

Again, in a more Hegelian turn, Marx puts it into other words.

Die Arbeit als die absolute Armut: die Armut, nicht als Mangel, sondern als völliges Ausschließen des gegenständlichen Reichtums. Oder auch als der existierende Nicht-Wert und daher rein gegenständliche Gebrauchswert, ohne Vermittlung existierend, kann diese Gegenständlichkeit nur eine nicht von der Person getrennte: nur eine mit ihrer unmittelbaren Leiblichkeit zusammenfallende sein. (Marx 1953, S. 203.)

As we see, one page from Marx’ s Grundrisse says it all.

Unfortunately, with all those explanations, reflections and didactical paraphrases by Marx, the magic is veiled and obscured in favor of a possible academic reader.

The magic of the inscription is forgotten in the delirium of explanations.

The magic is extremely simple: “Arbeit als absolute Armut”, a non-sentence, is of the form “AaaA".

The quadrantation of the phonological apophansis.

For non-linguists I remark, a real sentence is of the basic form: “A is B".

The AaaA script has no onto-logical copula “is”. There is no “being” involved, and no ‘meaning’ to capitalize Marx’s formula.

The sentence is in a strict sense not translatable, thus it isn’t a sentence in linguistic terms. In any translation of the content (surface structure), the form it shows evades.

The form could be called a little chiasm. In contrast to the big chiasms of the whole Marxian economy: ABBA, ABAB, etcetera.

I have to admit that nearly nobody followed my enthusiasm when I presented my insights in a seminar I organized just for that discovery at the Free University WestBerlin in the early 1970s.

My thesis was and still is, that such a non-sentence is understandable only with the help of Gunther's kenogrammatics and Jacques Derrida’s grammatology.


"Since the classic theory of rationality is indissolubly linked with the concept of value, first of all one has to show that the whole "value issue" covers the body of logic like a thin coat of paint.

Scrape the paint off and you will discover an unsuspected system of structural forms and relations suggesting methods of thinking which surpass immeasurably all classic theories. This was the purpose of my paper "Time, Timeless Logic and Self-Referential Systems." The trans-classic order which we discover beyond the classic theory of logic was called "kenogrammatic structure."


"Je parlerai, donc, d’une lettre.
De la première, s’il faut en croire l’alphabet et la plupart des spéculations qui s’y sont aventurées.
Je parlerai donc de la lettre a, de cette lettre première qu’il a pu paraître nécessaire d’introduire, ici ou là, dans l’écriture du mot différence; et cela dans le cours d’une écriture sur l’écriture, d’une écriture dans l’écriture aussi dont les différents trajets se trouvent donc tous passer, en certains points très déterminés, par une sorte de grosse faute d’orthographe, par ce manquement à l’orthodoxie réglant une écriture, à la loi réglant l’écrit et le contenant en sa bienséance.

Politics: Beyond left and right:

"Déconstruire, c'est dépasser toutes les oppositions conceptuelles rigides (masculin/féminin, nature/culture, sujet/objet, sensible/intelligible, passé/présent, etc.) et ne pas traiter les concepts comme s'ils étaient différents les uns des autres.”

Gunther didn’t follow his own advice much further, after he successfully “scraped the paint of”, and went on, mainly, with his meontic theory of negative languages. He left, officially, the whole body and burden of kenogrammatics to my enjoyment and responsability.

This paper is dedicated to the enterprise to connect the kenogrammatic approach with the meontic approach of negative languages, concerning negation cycles, and their interpretation for a theory of action (Wille, Handlungstheorie).  by K Lichtblau

1.2.  Palindromes as Cycles

Cycles as palindromes.
Are negation cycles even balanced classic palindromes?
Not all negation cycles are palindromic.

Self-cycles in palindromes   palindromic negation cycle
[1,1,1,2,1,2,1,2,2,2]           [1,2,1,2,1,2]

Kaehr/Thomas (1976), negation systems.

Permutation group

- ispalindrome(tnf[1,3,1,3]);
val it = true : bool
- ispalindrome[1,2,1,2,1,2];
val it = true : bool
- ispalindrome(tnf[2,3,2,3,2,3]);
val it = true : bool

p ≡ N1. p.

- ispalindrome[1,2,3,2,3,2,1,2,1,2,3,2,3,2,1,2,1,2,3,2,3,2,1,2];
val it = false : bool

1.3.  Morphic Palindromes

typeset structure

Representation of morphograms:
The single morphogram [1,2,3,4] has 4! = 24 representation on a symbolic level of permutations.

There are just 7 palindromes of length 4 on the level of morphograms.


1.4.  Iterability of morphic palindromes

typeset structure

    <br />              2 - c ... ;                 

RowBox[{              &n ...  {220.75, 227.75}, ImageMargins -> {{0., 0.}, {0., 12.75}}, ImageRegion -> {{0., 1.}, {0., 1.}}]}]


         Iterability scheme for [1, 2, 3]     ...  [4, 2, 5] <br /> [3, 4, 5] <br /> [4, 5, 6]     [1, 2, 3] <br /> [1, 4, 3]   

Example : Tcontexture 6 Tcontexture 6 ; -length it ; val it = 203 : int

List.filter ispalindrome (Tcontexture 6);
val it =
1. [[1,1,1,1,1,1],[1,1,1,2,2,2],                                                                                :2
2.[1,1,2,1,2,2],[1,1,2,2,1,1],[1,1,2,3,4,4],[1,1,2,2,3,3],[1,1,2,3,1,1],                         :5
3.[1,2,1,2,1,2],[1,2,1,1,2,1],[1,2,1,3,2,3],[1,2,1,1,3,1],[1,2,1,3,4,3],[1,2,1,3,4,3],      :6
4.[1,2,2,1,1,2],[1,2,2,2,2,1],[1,2,2,3,3,1],[1,2,2,2,2,3],[1,2,2,3,3,4],                         :5
5.[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],  :14

Tcontexture (6) opens up 5 fields of palindromes of length 6. Number   of   fields for palindr ... rams from Tcontexture 6 : <br /> Underoverscript[∑, k = 1, arg3] Sn (k, 3) = 1 + 3 + 1 = 5.

1.5.  Palindromes as e/v-Structures

To avoid interpretational misunderstandings with morphic palindromes written as morphic lists the e/v-abstraction is opening up a new field of palindromic research.

fun ENpalindrome n = map ENstructureEN(List.filter ispalindrome(Tcontexture n));

- ENpalindrome 6;

val it =
   [[],[N],[N,N],[N,N,N],[N,N,N,N],[N,N,N,N,N]]] : EN list list list