Peter Fargas
Independent Research & Prototypisation
https://informatik-handwerk.de
Leipzig, Germany
Release date: November 2013
Last update:
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Approach To Statical Space Representation Language

☰ Content

The development of paradigmatically different type of description systems has always been accompanied by educational efforts. One approach which often gets lost, mastered by Mandelbrot, is to document the process of decoupling from available thought models and attemp to write down the appoaching, sensing and discovary of previously unseen teritories.

I marked a couple of spots with ? - in case you like to puzzle a bit around or confirm yourself some of the more interesting turningpoints. Enjoy.

Original Concept

New ways of interaction bring new ways of expressing the self and I theoretized, that if programs are confied by the ways we create them, so must their model be, the programming language itself. Thus the development of a new programming language paradigm is coupled to the development of construction and inspection tools which manipulate it's instantiations. A similar area, is that of a novel hardware platform – how the interpretation of a program influences the language itself, is very clearly seen on the concept of quantum computation. Way out of my reach, I shall stay on the classical hardware platform.

Currently available computational models

To list the most common, from both, theoretical and practical camps: turing machines, language theory, process algebraic approach, various graph-theoretic variations, functional & declarative language implementations at it's micro or macro, generic purpose or visual space description or other variants.

Most documentation describes very well the specimen itself and properties –papers on common/distinct properties exist equally– but it is an ommitted step to disclose details on how or why the set of primitives was discovered/chosen. The notion of extensions is sometimes mentioned and studied deeper, those areas establish the connection between how properties of original definition translate onto the extended system. Back to the primitives – their nature is stated informally and the disection of the space they populate is rather the area of meta-mathematics.

The Configuration of Interaction

My attempt to program a generic description&simulation device has revealed a rather trivial but seldom seen subdivision or maybe spectrum of representations: the space of maximal structural possibilities — axiomatizable space of languages/descriptions having the finest/richest expression capabilities –leading to– the used and known languages. In a different explanation network with different resoluton, this spectrum can be expressed as: spaces suitable for cognition; spaces wich are theoretically and later practically automatizable up to spaces of maximal compression with respect to available primitives.

A short trip into this spectrum reveals there are multiple, possibly intertwined, dimensions. One is that of scale and it might be rather clumsily expressed, but an interesting way of viewing micro-macro scale is that of macro is composable from micro by adding of functionality whereas micro is constructable from macro by fixation. The process of system contruction is thus never quite one-way straightforward and I don't doubt many more such ying-yangs can be pondered upon. A thought paradigm on a similar base is that of information compression, where the compression function defines what is expressable by short and what by long descriptions.

Another dimension is that of element availability, some local or global configurations might not be allowed and in many systems there are good separable parts which are present exactly once. In some spaces even, each element may be present exactly once only.

...more dimensions... thoughts got lost or were not there in the first place...

As correctly felt, much of the representation is determined by the so-called "point of view". Details or whole spatial configuration types might and get cut-off out of various reasons, circular descriptions might get their symmetry broken at some point, implicite representations instead of explicite. Very much in system analysis and programming – done in head; on paper; presentations for various audiences; inspections like correctness testing which reduce space to yes/no, performance tests which enhance the space with metrics; edit tools like file-manager, text-editor or database-config which allow to view and modify certain aspect of the system, in separation or as part of a composite.

Without getting deeper into classification of this area, let us leave this as an unificatory viewpoint on working with programs – something which is taken for granted and seldom thought about. I do find it helpful to expand the mind's view to the whole area before starting. As suggested by the previous paragraphs, I shall limit myself to digital space and programming in particular.