Finite Cross-sections of Infinite Systems

Finite cross-section of infinite systems; complex iterations in a conceptual vocabulary…

Generating relatively consistent philosophical models or qualitative dynamical frameworks of a holistic systems-theoretical concept can be a subtle affair. It is taken as given, foundational or axiomatic that all activity, relationship and existence is essentially internal to the system under development (that is – there is literally no outside any system considered literally holistically). It is also taken as necessary and axiomatic that the only plausible (or at least sensible) way in which any holographically-organised, distributed and decentralised systems architecture or organisational principle can exist in any such system of thought (also – of cognition or being) is by being everywhere simultaneously. The base axiom of this system is also the ontological primitive, a literally infinitely (yes, discontinuous, incomprehensible and actually infinite) multithreaded and omnipresent self-replicating process; itself the self-replication and variously-scaled iteration and acceleration or compound self-aggregation and self-gravitating harmonically entangled matrix and strange loop of its very own self-referential process and representation. A process of iterating self-replication that is effectively replicating itself and through a very special loophole managing to present itself at all places (and times) simultaneously.

Consider a spiral curve on a two-dimensional plane and as defined for convenience upon a dual perpendicular axis of X and Y. This might represent an accelerating system, context and frame of reference within a constraining, defining coordinate system. The coordinate system itself, the frame of reference and all aspiration to metrics or (to some extent to) intelligibility is being dragged along with this frame and rotating graph-or-measurement system. Now, consider that the curve on this plane is itself extended into a third (Y) dimension such that the path of the first curve is also the axis upon which this curve is drawn out into a third dimension. This is not a simple similarity or a correlation, it is a self-similar identity; it is the same curve and representation of process, drawing itself into hyper-dimensionality. The process and self-accelerating frame of reference is being dragged out into a perpendicular dimension by exactly the same curve and indication of accelerating process and tranformation. Any metric or measurement of the curve is not the axes of any notional external reference but of its own implicit internal extensivity.

This is the subtle discontinuity at work in this particular holistic systems framework. One thing that can be everywhere simultaneously in a massively distributed and discontinuously decentralised sense is a process. If this process is itself a self-replicating system above and beyond (or at least pre-emptively of) any material expression or conceptual constraint in the various useful taxonomies of scale or category that we may assign to it, it is unique in a sense of being both axiom and systems-primitive simultaneously.

At any point on this curve it is under amplification composed of (self-)similar curves or fractal, harmonic and self-replicating processes, we might say themselves indicating the general dynamic process of “temporal groups” indicating qualitative, arbitrarily-selected assemblages or taxonomies of scale and convenience. This is not simple, nor could it ever be as the primary (qualitative assertion and) mapping here is of the function and recursive flow of systems and sub-systems within self-gravitating, self-accelerating frameworks of complexity and recursive self-reference.

Some things which are missing (and notwithstanding that there will always be things which are missing and indicating foundational incompleteness, nevertheless): a method of both stabilisation and homeostasis; a clearer development of the concept of process and self-similarity at all scales; and, a plausible extension into non-abstract, “real world” systems and phenomena in ways such as to indicate relevance beyond pure mind games and sophisticated wordplay or conceptual trickery. These three suggested requirements should perhaps not be so surprising in the context of necessarily exquisite uncertainty and near-paradoxical complexity of recursion under consideration to actually reveal themselves as possessing the same identity; that holistic theories must always of necessity take into account their own existence and that through (self-)explanation they reveal that this may be the only way in which their depth can, enigmatically, ever be held in an apparently finite cognitive space such as that we appear to possess. Finite cross-sections of infinite systems are very rapidly and reflexively drawn up into curlicued complexities beyond reckoning but this does not mean we can not understand those partial views and find utility for them.

If, after Paul Verlaine, we might consider that l’application c’est le plupart de l’intelligence, then how to apply this concept in our “real”, shared and consensus world of concrete consequences and this living, embodied experience ?

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