Rudy's Diamond Strategies: October 2008

A monomorphy based sketch of morphogrammatic transformations

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Its all about change.

From the Book of Change (I Ching) to the challenges of a change in politics.  

How to change something?  

What are the possibilities of a change of something?

 How to be changed by changing something? 
How can change happen without something being changed? 
How can change be changed by change?
How can something change the changer of a change? 
How can something change the changer of a change without being itself neither change nor something at all? 

And what’s about the “Change we can believe in"?
  

Is it not enough into what we believed in all the time, again and again?

Isn't it time to stop believing and to start to compute our beliefs in an arithmetic we have not to believe in, like we have to do with our "natural and universal" systems of computation nobody believes in because nobody even knows that their calculations are based on beliefs.

Change we can count on.
Count we can believe in.
Belief on which we can trust and count.
Count we can change.
Trust and count we haven't to believe in.
On ins and ons we neither bet.

To study such difficult conceptual challenges it seems to be reasonable to study it with the most simple model possible. 

There is nothing more elementary and well known than natural numbers, sign systems or the stroke calculus.  

By adding a new stroke to a chain of strokes, or by adding a numeric unit to a number, or to add a sign to an existing sign sequence is the most elementary operation of change. As we know it until now.

And this simple operation is secure. It is based on our fundamental intuition, initialized by education – and its axiomatics. And this simple operation can be repeated endlessly. Never ever encountering any obstacle. There are no limits in the resources of matter, time and space. And the poor guys who have to count. At least in this world of abstraction.

But is that enough?

In a non-notational scenario children or scientists are adding to their Lego blocks new Lego blocks to build an extension, prolongation, i.e. a change towards more exiting Lego constructions. Such an extension of a pattern can happen at all loci possible for continuation. No linearity has to be supposed.

And for the metaphor we can forget the need for any atomicity of the added elements. In the same sense, the actor is changing his identity depending on what and how he or she or it is creating his constructions and how those interactions are changing simultaneously the definitions of the actors.  

In an experimental scenario children or scientists might add at each possible location of their chemical formulas new elements to produce more complex chemical patterns. Or they may organize mutations to their organisms.  

And obviously, all started in the caves and ended with Paul Lorenzen’s stroke calculus.

Nevertheless, there are different modi of change. Are there?   And why should we trust in numbers which don’t know their past and are blind to their future – by principle?  

There are no changes without new beginnings and no new beginnings without changes.

  For real-world systems based on numbers there is necessarily only endless iteration of the same or fatal crash.  

What has changed for the formal theory of change, keno- and morphogrammatics, in the last 40 years?  

For a change I will sketch some ideas about elementary features of change in formal systems surpassing, as it will turn out, the principal limitations of known formalisms. This sketch of morphogrammatics is choosing thoroughly a descriptive approach.  

Maybe there is still a way out of the cave of neolitic inscriptions and its culmination in the stroke calculus of digital speculations?

Modi of beginnings and transformations

Instead of a beginning with the statement “Given X”, the kenomic formulation might be “Having encountered Y”. That is, if having encountered Y, find an appropriate succession or predeccession of Y. Depending on the structural complexity of Y, different prolongations are opened up. Not all have to be realized.

Hence, a decision for a specific prolongation (succession) has to be drawn.   Therefore, there is no beginning pre-given.

Each situation encountered might be accepted as a beginning of an interaction. Complementary, there is no situation given which couldn’t be accepted as an end.  

Semiotics, category theory and arithmetic are playing with a single ultimate beginning and are believing in endless continuation. “One start, no end” is the slogan of the dream. Until it gets stopped by a wee crash.  

To begin with the simplest elements in a formalism is more a question of an economic or stylistic decision than a compulsory conceptual necessity. As much as we can agree to start a stroke calculus with a single elementary stroke as the first action of the calculus we can agree to accept to encounter a morphogram of whatever complexity and to start to interact with it on the level of its encountered complexity.

Atomic concatenation

The most secure mode of change is to add to an existing linear sequence of signs, numbers or marks an new one. This addition, called concatenation, is strictly independent of the pre-existing sequence and refers only to a pre-given sign repertoire, i.e. to its alphabet. Its security is demanding to accept the linear order of the atomic signs and the rule not to intervene into the pre-given sign sequence.  

Probably the most popular presentation of semiotic concatenation is given by the concept of lists and its manipulation in the programming language Lisp. Lisp was leading the advent and decline of AI (Artificial Intelligence) research.

Kenomic evolution

Kenogrammatic concatenation still relies to some degree on the linear order of its kenoms. But there is no need anymore for a pre-given alphabet and concatenation itself is only one of elementary operation of change. Further operations are chaining and different kinds of fusion.

Without a pre-given alphabet the risk has to be taken to develop change out of the encountered kenogram sequence only. With that the abstractness of the semiotic concatenation is surpassed. There is not only no alphabet given, but the kenoms involved are semiotically indistinguishable. The operation of concatenation is defined by an interaction with the encountered kenogram sequence. Its range is determined by the occurring kenoms of the sequence which remains itself still untouched by the process of concatenation.

Hence, kenogrammatic concatenation is not defined in an abstract way but retro-grade to the encountered kenomic pattern.

Lack of a pre-given alphabet
Because of the lack of an alphabet as a source for signs from the outside, i.e. from a lower level of the tectonics of the formal system, evolution of morphograms have to be constructed as extensions out of their inner structure. This is a kind of an evolution of morphograms based on the mononomorphies of the morphogram. 

Self-generated alphabets
The wording that there is “no" alphabet means, there is no alphabet pre-given as the start of a kenogrammatic calculus. But what is not pre-given is not denied to exist in a different way. Hence, a positive wording concerning the alphabet of kenogrammatics might be turned into this: Encountered a morphopgram, a kenomic abstraction is collecting the kenoms involved into the morphogram. A successor operation then can rely on those kenograms to precede to the next morphogram, in an iterative or an accretive way. Therefore, albeit there is no alphabet pre-given, kenogrammatic operations are producing situatively their own alphabet, i.e. set of kenoms, to proceed their operations. Again, it is reasonable to speak about a parallelism or diamond movement of operators and operands of kenomic operations. The kenomic alphabet has to be elicited. There is no need for a kenomic alphabet without the intended interactions with morphograms.  

Despite the big difference between semiotic and kenogrammatic concatenation there are still some important similarities. Both share a kind of a linear order of their objects, signs and kenoms. And their units of iteration and concatenation are of similar structure. Semiotics depends on atomic signs, kenogrammatics on the other hand, on monadic kenoms.   

The successor operation in kenogrammatics was up to now defined mainly as the iterative or accretive repetition of the kenoms in a kenogrammatic sequence. This approach is still supposing a kind of atomicity, i.e. of atomic separability of kenoms to be repeated. With this presumption, interesting results have been achieved.

Morphic evolution

The morphogrammatic approach to change is changing the presumption of a linear order of kenoms as it is supposed in the term “keno-sequence” and is emphasizing the tabular pattern structure of morphograms (morphe=pattern, Gestalt). As a consequence, changes in the sense of an evolution out of the pattern itself can happen at all loci of the pattern.   

Hence, their is no need for a reduction to a successional prolongation. It can happen at all loci involved. Therefore, the encountered morphogram which is involved into a morphogrammatic concatenation operation is loosing its neutrality and gets itself involved into a change.

This might be called an interventional evolution.  

Kenogrammatic concatenation is played by a retro-grade self-referentiality, which has a diamond structure. To success, simultaneously, a retro-grade action happens. But the actand itself isn’t touched by this intriguing retro-grade interaction. It remains stable and is solely offering kenograms for further prolongations of the morphogram.  

Such a change of the actand itself happens with the morphic evolution. The actand of change gets itself changed in the process of change.  This is realized with operation of reconfiguration (reconfigurative evolution, coalitions, composition).

Monomorphic concatenation

Morphograms are changed by the monomorphic concatenation according to their monomorphies. Monomorphies are patterns of kenoms and parts of the whole of the pattern-structure of the morphogram. 

A new feature out of the morphic evolution is the change of the actor (operator) of the interaction. Such an immanent evolution of morphograms is not changing the structure of the morphogram involved into the process of evolution. The structure of the original morphogram stays untouched. Despite the retro-grade movement of the kenomic successor operation to build successions the beginning morphogram is not involved in any change of the successor procedure.  

The triviality of this observation gets a new turn with the tabular notational successor operation which is changing its beginning morphogram too. That is, to add something to a morphogrammatic structure might change the structure itself.

Hence, two events happens, a) the succession of the morphogram and b) the ‘self'-transformation of the morphogram.  Therefore, an interaction with morphograms might emerge into a monomorphic evolution of the involved morphograms. Further interactions between morphograms are, e.g. concatenation, chaining and fusion. That is, the progression or succession is not depending on any external objects, kenoms, to be added from the outside to the kenomic pattern but is fully defined by the structure of the morphogram involved into the interaction. 

With that, a kind of a symmetry between the composition of morphograms and their decomposition into monomorphies is established.

Actional concatenation

A change of the actor in the process of interaction happens as a transformation of the actor “concatenation” into other evolutionary operators. It turns out that “concatenation” is only one interaction of a family of different interactions, like “chaining” and “fusion”. 

Combinations of actors are involved into the actional abstractions responsible for the behavioral equality of different morphograms.  In an actor terminology we can say that change in the sense of morphogrammatics is changing all parts of interactivity, the actor and the actands and thus interaction as the operation. 

Discontexturality

But with such a fulfillment of a change in the conceptual triadicity a new feature emerges.  Until now I stipulated only one encountered morphogram.

Interactions happened with the morphogram which had been answered by a kind of a self-evolutionary process.   But what happens if two morphograms encounter? The same game might go on. In this case it doesn’t make much a difference to the singular situation of self-evolution. We continue triadicity and silently suppose that there is no discontextural difference between morphograms. How can different morphograms interact if they are of different contextures, thus not only disjunct in their elements and operators but discontextural in their conceptionality?   With the introduction of a multitude of contextures, i.e. with polycontexturality, interactions between morphogrammatic systems are enabled which are surpassing the limits of operational triadicity by disseminating it.  

To mention proudly, “the sum is more than its parts”, is supposing that a summation is possible and that the terms are commensurable. This innocent constellation might turn out as a fundamental limitation of the desire for change.

Metaphors and heuristics

Morphograms are considered as groups of monomorphies. A group, of whatever kind of objects or agents, might be in a situation where it has to change its constellation by growing or by self-differentiation. Also the group might encounter another group and strategies of co-operations, fusions or incorporation are occuring as necessary.  

What are the structural possibilities for such a group to change? 

The group may decide to not to grow, i.e. not to enlarge its domain with new positions but better to differentiate into a more complex structure or to reduce its complexity (complication) to a lower degree of differentiation.

 The group is emanating between higher or lower complication and keeping its complexity stable.  

This shall be called an emanative change of the group.

Emanative developments are preserving the structural complexity of the actional system. Hence, it easily reaches its limits. 

A new strategy is called for. The group might extend its complexity by divesting parts of it. Every part might be divested and helping the group to evolve. Such evolvement by divestment is not outsourcing its agencies but is repeating and adding its existing agencies of the group to the group as a whole.  

This is a relatively secure procedure but nevertheless it is augmenting the structural capacity of the group (organization, company, organism, chemism, etc.). Because such a divestment is purely structural it is not a simple repetive addition of existing faculties but an augmentation of the structural complexity of the whole.   

This shall be called iterative transformation (change, disremption, prolongation, augmentation, etc.). 

The group might decide to augment its complexity with a structural risk. The risk for the new to be taken by the group is transforming the complexity of the group by accepting to evolve into an unknown domain (contexture), creating a structurally new position.

Again, the degree of the risk is ruled by the structure of the group. The new, added to the group, is only new in respect to the existing constellation of the group. Hence, there is nothing hazardous involved into this risk of extending the complexity into new dimensions. What’s new is new solely in respect to the historically developed structuration of the group (organization).   

This shall be called accretive transformation (metamorphosis, change). 

Hence, iteration and accretion are the two modi of change which are augmenting the complexity of the group (whole).  

Gotthard Gunther calls this two complementary modi of transformation, evolutive change.   

Both, evolution and emanation together, are designing the framework of structural change of organizations (groups, wholes, etc.), i.e. the morphogenesis of structuration. This kind of double structuration shall be called disremption. 

Disremption is understood as the keno- and morphogrammatic opposite to the semiotic operation of concatenation.

Hence, a group inscribed as a morphogram is embedded into a complementarity of evolutive (iteration/accretion) and emanative (differentiation/reduction) transformations.   

Because the whole is build by its parts, those strategies of evolution and emanation, are applicable to the single parts as well as to the whole as such.   Such an understanding of the structuration of change is not depending on any identities, objects, agents, processes, information, etc in the known sense.   

Therefore, this strategy and theory of change (structuration) is called morphogrammatics.  

Morphogrammatics is independent of any system and complexity theory.

Its material resource are kenograms, i.e. the place-holders for the parts of morphograms (groups, constellations) created in the process of structuration. The parts of morphograms are called the monomorphies of the morphogram.   

Morphogrammatics of change sounds extremely simple.

There are no strange attractors, chaos theory, maturation and adaption, autopoiesis and homeostasis, etc. involved at all. Neither any logical systems, multiple-valued, modal, paraconsistent, etc. nor terms like paradox, circularity, antinomy, etc. nor information processing, computability, diagonalization, etc. and so on.  

But there is a morphogrammatics of logic and arithmetics, mono- and polycontextural.

With this turn, logic – and formal systems in general as our leading rational operativity – are appearing as maximally reductionist theories of change, i.e. as stable theories and formalisms of zero structural change.

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