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
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