A new advanced systems theory concerning the emergent nature of the Social, Consciousness and Life based on Mathematics and Physical Analogies is presented. This meta-theory concerns the distance between the emergent levels of these phenomena and their ultra-efficacious nature. The theory is based on the distinction between Systems and Meta-systems (organized Openscape environments).
We first realize that we can understand the difference between the System and the Meta-system in terms of the relation between a ‘Whole greater than the sum of the parts’ and a ‘Whole less than the sum of its parts’, i.e. a whole full of holes (like a sponge) that provide niches for systems in the environment. Once we understand this distinction and clarify the nature of the unusual organization of the Meta-system, then it is possible to understand that there is a third possibility which is a whole exactly equal to the sum of its parts that is only supervenient like perfect numbers.
In fact, there are three kinds of Special System corresponding to the perfect, amicable and sociable aliquot numbers. These are all equal to the sum of their parts but with different degrees of differing and deferring of what Derrida calls “differance”. All other numbers are either excessive (systemic) or deficient (metasystemic) in this regard. The Special Systems are based on various mathematical analogies and some physical analogies.
But the most important of the mathematical analogies is with the hypercomplex algebras which include the Complex Numbers, Quaternions and Octonions, with the Sedenions corresponding to the Emergent Meta-system. However other analogies are the Hopf fibrations between hyperspheres of various dimensions, nonorientable surfaces, soliton solutions, etc.
These special systems have a long history within the tradition since they can be traced back to the imaginary cities of Plato. The Emergent Meta-system is a higher order global structure that includes the System with the three Special Systems as a cycle. An example of that from our tradition is in the Monadology of Leibniz. There is an conjunctive relation between the System schema and the Special Systems that produces the Meta-system schema which appears as this cycle. The Special Systems are a meta-model for the relation between the emergent levels of Consciousness (Dissipative Ordering based on the theory of negative entropy of Prigogine), Living (Autopoietic Symbiotic based on the theory of Maturana and Varela), Social (Reflexive based on the theory of John O’Malley and Barry Sandywell).
The Idea of Universal Concrete Systems Theory Explored On Information, Entropy, Energy, and Matter as Universal Concrete Principles
David Rousseau mentions the idea of developing Universal Concrete principles in Systems Theory. I strike out on my own and try to imagine what those might be and come up with an answer different from his recently published derivation of Systems Concepts (principles) in his Systemology. The two approaches are very different. But in the process the relations between Set Theory and Category is explored and their relation to Concrete Universals of Plato and Hegel brought to the surface, as well as attempting to show how these relate to Special Systems Theory,
Elaborating Linkage Propositions with Linkage Hypotheses based on General Schemas Theory, Special Systems Theory, and Emergent Meta-systems Theory
Len Troncale has produced a draft series of Linkage Propositions to which elaborations have been added in italics based on General Schemas Theory and Special Systems Theory. Kent Palmer developed General Schemas Theory and Special Systems Theory as well as Emergent Meta-systems theory independently. See http://kentpalmer.info This elaboration shows the relation between Troncale’s Linkage Propositions and the theories of Kent Palmer expressed as Linkage Hypotheses