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.
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