Foundations of Systems Architecture Design 12: Interlocking of Schemas

On the Structural Underpinning of the Schematic Hierarchy via Special Systems Theory by way of the Doubled OCD Tableau Interlock between the Adjacent Schemas and Isomorphy to Undefined Geometrical Terms and Philosophical Principles based on Pascal’s
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  1 Foundations of Systems Architecture Design Interlocking of Schemas On the Structural Underpinning of the Schematic Hierarchy via Special Systems Theory By way of the Doubled OCD Tableau Interlock between the Adjacent Schemas and Isomorphy to Undefined Geometrical Terms and Philosophial Priniples ased on Pasal’s Triangle   Kent Palmer Ph.D. 714-633-9508 Copyright 2018 KD Palmer 1  All Rights Reserved. Not for Distribution. FoundationsSystemsArchitecturalDesign_12_20180426kdp04a 2018.04.22-23; Draft Version 03; unedited Corrected 2018.04.24-25-26   Researcher ID O-4956-2015 Key Words: Systems, Architecture, Design, Special Systems, Systems Engineering, Software Engineering, Software Ontology, Formal Systems, Schemas Theory, Dagger Theory, Projective Geometry, Essence, Internal Relations, Nondual Difference, Orthogonal Centering Dialectic Abstract: Exploring Interlock between adjacent schemas  Interlock between adjacent schemas via their nerves and the Emergent Meta-systems based on the Orthogonal Centering Dialectic (OCD) tableaus is the kind of result that can only be obtained through speculative reasoning. In this paper we explore further this discovery in relation to the System and Meta-   1 See also   2 system schemas. In the previous paper we explored it in relation to the Form and Pattern Schemas. However, we place this in the context of the entire hierarchy of the Schemas as augmented by the doubled OCD Tableaus and their interlocking at of each adjacent pair of Schemas. Our exploration in these working papers have taken us seemingly far afield. But in the end, we find that the OCD, about which we are both obsessive and compulsive, is a stable unexpected structure discovered in these far flung regions which on the map of science says ‘ unknown seas, monsters lurk here ’ . But this comes at the price of treating the Schemas as nihilistic duals, and their essences as derived nihilistic duals. And when we take two OCD tableaus and put them together because each schema has a nerve, then we find that there is not only the inner relations of each schema but also around that an EMS Quadralectic that seems to service it proving the motive power for creative exploration of the Design Landscape and the honing of the design. Between the two derived nihilistic opposites that interlock, with their separate essences surrounding by an EMS quadralectic, there is the revelation of internal difference as the micogenesis between the essences. What we discover is that the internal differences appear positively as the undefined terms of geometry (point, line, surface, etc.). Thus not only to the doubled tableaus interlock they also produce an isomorphic relation to the undefined terms of geometry. But another point needs to be made which is that each Schema has both essence (set-like) and co-essence (mass-like) and it interlocks with the adjacent schema above and below. So, for instance, we see this in the Pattern Language of Christopher Alexander in which we get the ‘ Pattern of Form ’  rather than the ‘ Form that is patterned ’ . When there is this reversal the co-essence becomes dominant. In general, the essence relates to the adjacent schema above and the co-essence relates to the adjacent schema below. When we reverse the order of adjacency then we get the Pattern of Form, or the Form of Systems, or the System of Meta-systems in which the co-essence is dominant over the essence in the way we look at the schematic hierarchy and the essential relations between adjacent schemas in the hierarchy. Interlocked OCD tableaus appear between each pair of Adjacent Schemas. But also when we fold the schemas hierarchy and relate each schema to its bookend opposite schema we also get interlock between these bookended schemas, like world-pattern, or formal-domain or system-meta-system that leads to holonomics. This suggests that the same thing occurs between dissipative ordering special system and reflexive social special systems. And it suggests that this kind of interlock is between the autopoietic special system and itself rather than some different schema. This interlock formation of the OCD tableaus gives us a structural model that underlies the schematic hierarchy and gives us a way to understand the transformation from one emergent level of the schematic hierarchy to another. The fact that this structural model exists is further evidence for the schematic hypothesis S-prime. There is a single structure which is the OCD tableau that connects each Schematic Level to the next through a doubling of the tableau structure and then we see how these two tableau structures interlock with each other through the mathematics of Hyper Complex Algebras that are related to the Special Systems. Although the Special Systems only appear in the fourth dimension between System and Meta-system schemas, it appears that through the OCD tableaus the Special Systems provide the structural linkage between emergent schematic levels. Thus, there is one structural basis for the entire Schematic Hierarchy within the S-prime hypothesis. This was unexpected as a result of our speculative reasoning, but its mathematical precision once conceived is quite compelling. Of special interest is how each essence as octonion structure is surrounded by an EMS sedenion structure. This gives a specific meaning to the Quadralectic (with 2 4  basis), and then by relating to two essences of the adjacent schemas with their EMS process surrounding it to each other we get a basis for the arising of the Pentalectic based  3 on the 32-nion (so called Patheon). The 32-nion is at the level of the Pascal Triangle of 2 5  which we have noted in other studies are related to the Five Hsing in Acupuncture and Alphabets for instance appearing as a natural level of complexity that shows up in “The Signs in the Cave”.  We also associate the Nondual result of the OCD with the Quaternion, and relate the upper adjacent schema, i.e. Form, to the Real and the lower adjacent schema, i.e. Pattern, to the Imaginary Complexnion, and see the internal difference as related to the Dissipative relation between these two hyper complex algebras. The entire OCD field can be related to the hyper complex algebras which are the basis of Special Systems Theory 2 . Hyper Complex Algebras 3  and their special properties and ultra-efficaciousness provides the structural underpinning of Schemas Theory and the emergent transformation from schema to schema up and down the hierarchy of the Schemas through the interlocking of essences in doubled OCD tableaus. This I believe is an important though highly improbable result to our speculations in this series of working papers. Speculative Philosophy such as that of Hegel attempts to go beyond the information given, go beyond the safe grounds of reasoning, to approach very hard or wicked problems in a way that is so far out of the box that we have forgotten that there ever was a box (paradigm), to box in our thoughts. Many times this involves following the flow of the exploration of horizons and going beyond those horizons out into the wild territory of thought as we have attempted to do here. The key is that sometimes if we are lucky we find stable structures beyond the pale that then we can use to bootstrap a new theory, paradigm, episteme, or ontological regime. In this case we discover the OCD and then we reapply it to the problem of the relations between Schemas and we find that there is a stable structure based in the Special Systems that provides the structural underpinning of the schemas. This we consider a demonstration of the power of speculative philosophy. Without this kind of exploration of the wilds of thought, this structural basis for schemas would never have been found and we would have not discovered the interrelation between Quadralectics and Pentalectics and the structural underpinning of the schemas based on their Nerves, i.e. essences that are connected by doubled OCD tableaus. Figure 1. Dagger Theory relations between Four Series 2  3   Kantor, I L, and A S. Solodovnikov. Hypercomplex Numbers: An Elementary Introduction to Algebras  . New York: Springer-Verlag, 1989.  4 This whole line of exploration started when it was realized that schemas should have essences and their essences were all different. There were no names for these different types of essence and so we coined names. Then we started exploring the difference between internal relations of Hegel 4  and internal difference  of Deleuze 5 . Out of that came the realization of the formation of the dynamic OCD unfolding into phases. Then, we saw these phases in Epic and in recent institutions defined by the Constitution of the USA. These analogies then led to understanding the OCD as a method for approximating nondualities and non-nihilistic distinctions based on orthogonal nihilistic opposites. Given an external difference we throw out nihilistic (artificial, extreme duals that are ultimately the same) in orthogonal directions. Then we attempt to determine the internal difference that is at the center of the orthogonal (srcinal and derived) nihilistic duals. Once the center with its internal difference has been determined then between that center and the external difference there exists a middle way which is a nondual alternative. This allows us to approximate the non-nihilistic distinction between the nihilistic alternatives. Nihilism and Nonduality are thus closely intertwined. But there appears to be a methodology for approximating it which was known in antiquity and is still alive and in use today in our institutions. Then we applied this to understanding of the OCD tableaus to the Schemas as nihilistic duals. And that also means that there are orthogonal nihilistic duals that are derived which are the essences of the adjacent schemas. But this also led to the realization that each Essence had the EMS of the other OCD tableau wrapped around it, because the two tableaus of different schemas interlock . The realization of this interlocking brings several different strands of our speculative research together into an overall synthesis that allows us to explain the structural underpinning of the Schematic hierarchy. But also, part of this is the realization that each schema has both essence and co-essence related to set and mass. Schemas are nondual between set and mass ways of approaching things as they also each span dimensions giving a different face to each dimension according to the S-prime rule there are two dimensions per schema and two schemas per dimension. We have already found the mathematical basis of schemas theory in the generalized Projective Geometry 6 . And we have also realized that the opposite of the schemas is Conformal Field Theory which gives us a model of how to scale the dimensions and also to orient and apply the schemas within a dimension 7 . These were definitely advances in Schemas theory. But the interlocking of essences via the doubled OCD tableaus is probably a more important insight because it supports our theory 8  of design methodology based on Quradralectics and Pentalectics explicitly showing how they are related to the schemas and their  Nerves 9 . Nerve is the generalized term for essence across the entire hierarchy of schemas. 4   Harris, Errol E. Formal, Transcendental, and Dialectical Thinking: Logic and Reality  . New York: State University of New York Press, 1987. 5   Deleuze, Gilles, and Paul Patton. Difference and Repetition  . New York: Columbia University Press, 1994.   6  7  8  9   5 Figure 2. System Schema template Figure 3. System and Process in concept and percept Now we consider the next adjacent schema pair up in the Hierarchy of the Schemas which is the relation of Form and System. Form becomes the figure in the gestalt of the System. But unlike Pattern or Form the tradition has not named or identified the essence of the System. We call it a nucleus  on the analogy of the nucleus of the Atom. The nucleus dictates the essence of each atom, and determines its qualities associated with the number of neutrons and positrons in the nucleus. Outside the nucleus is a cloud of electrons. It turns out that the theory of atoms of Democritus was correct and the field of atomic structures was worked out by Mendeleev which was one of the greatest structural insights in Science only rivaled by that which revealed the quarks as the structural basis for understanding fundamental particles. Structure reduces variety to something that can generate that variety.  Structure in relation to Patterning is related to
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