Let me clarify the difference between a System and its inverse dual the Meta-system or Openscape.
Originally I had this idea when I read an article in the International Systems Science Journal of George Klir where he published my article on Design Methods. In that same issue one of George Klir’s students had undertaken a Category Theory analysis of Architecture of Systems Problem Solving. At that time all I knew of Category Theory was that if you revered the arrows then you get the dual of a given category. So I tried going through the thought process of reversing the arrows in the Categorical Description and I discovered that it was not self-dual. And that meant that there had to be some dual of the Formal Structural System as Klir defined it. I started searching for that dual.
Eventually I came upon the work of Bataille Accursed Share that distinguished a General Economy from Restricted Economies and the work of Plotnitsky in Complementarities where he talks about the relation of the General Economy to the work of Bohr and Derrida. This distinction between General and Restricted Economy is foundational to much of Continental Thought such as that of Baudrillard who wrote Critique of the Economy of the Sign for instance. But also the work of Derrida, Deleuze, Zizek etc.
But what I wanted to do was formalize the duality. Eventually I discovered that the formalization was the difference between the Universal Turing Machine and the Normal Turing Machine.
The difference is between what is inside the boundary of the system and what is outside the boundary of the system, how ever that boundary is drawn. This is assuming that a system boundary is a gestalt and thus what is outside that boundary is a proto-gestalt.
The key point is that systems and meta-systems have completely different organizations from each other. Their essences are completely different. Yet they are inverse duals of each other.
Thus in a meta-system you get the making available of resources in niches that hold systems. You get protocols enforced by which systems signal each other and also signal the meta-system.
Unlike other Schemas () metasystems do not have a single name in our culture. We have a blindspot toward metasystems in our culture. Thus we call it context, situation, environment, ecosystem, medium, etc. And generally it is the non-system. In my usage of the many meanings of “meta” the meaning meant here is “beyond” the meta-system is beyond the system. That means outside its boundary to the horizon. Eventually I found that the concept of Scape corresponds to the Meta-system as I conceived it as the inverse dual of the system. Inverse means reverse the arrows. Dual means that it is not self-dual but is different from the system, in the way a co-algebra is different from an algebra. But in our language Scape is always accompanied by another term like landscape, or seascape or mindscape, so in order to make it general I called the Meta-system an OpenScape. It is everything from the boundary of the system to the horizon of the landscape in which the system exists in a panormama around the system in all directions.
Meta-systems are completely different from Systems of Systems. A SoS is merely a reiteration of the system schema at a higher level of organization. Thus we have Supersystems, Systems, SubSystems. And interleaved between these is the meta-systems for each system, i.e. the environment within the Supersystem in which the system lives. Some definitions of SoS include features like meta-systems, but there is not a clear conceptualization of the difference between Meta-system in my sense and Supersystems in the sense that SoS is normally taken.
Normally, the mistake we make is to think that what ever is outside the boundary of the system is a homogeneous plenum and has no structure. Rather what ever the system needs within its niche to function which are fed to it as standing reserves of resources, and also what maintains multiple systems together and allows them to interact is the Meta-system of a given system at a given level of abstraction or construction.
A key point if you are looking for the System and Non-system in other cultures is the fact that Being only exists in Indo-european languages. Other languages have various existential but no Being. So we assume that Being is universal but it is not, rather it is an anomaly. The word system goes back to the greek. Kant was the one who said that we needed it as a hypothesis to do science. So it is Kant who raised System as a concept to the level we assign it today. However, in the Western tradition it is Form that is the central schema historically. Recently the pattern or structure schema has also become important as a way to view nature as we seen in Mendeleev’s table and the table of quarks. So there are at least three schemas that are very significant for us today, which are combined by Klir as Formal Structural Systems.
To get to the schemas all one needs to do is ask what is the next higher level of abstraction higher than the system. This would be the level that would contain all the non-systems. The point is that there are many non-systems not just one. Non-systems are all the other schemas that have been developed in our tradition. My Sprime hypothesis maintains that there are ten of them: Facet, Monad, Pattern, Form, System, Meta-system, Domain, World, Kosmos, Pluriverse. And there is a rule that says that there is two schemas per dimension and two dimensions per schema. This rule connects the schemas to a central concept in mathematics. Lately I have found the mathematical foundation of schemas in Pascal’s Triangle what Leibniz called Analysis Situs.
Thus I propose that beyond Systems Science and Systems Engineering there is a wider realm called Schemas Science and Schemas Engineering. And the fact that we do not recognize that puts blinders on us because in practice we are using all these schemas which have been developed in our tradition. A good place to see lots of these schemas called out is Philosophical Grammar by Wittgenstein. The definition of schema as I use it is given in Kant and the Platypus by Umberto Eco where they are called Mathematical and Geometrical Schemas.
Schemas as I use the term are a priori ontological structures projected on Spacetime. They are not ontic structures such as quarks, fundamental particles, atoms, molecules, cells, organisms, social groups, ecologies, gaia. Rather they are templates of understanding that give intelligiblity to organizations of entities that we just naturally project on our experience and see in nature.
So connecting these schemas to the idea of non-system the hypothesis is that there are many different types of non-system. But only one of these types is the Categorical Dual of the system, and that is the OpenScape called Meta-system in this case.
Just like Being is not universal, there is no evidence that Schemas are universal beyond the Western Worldview. Other cultures probably have other schematizations. This is an open area for anthropological research. Chinese for instance does not have a traditional word for System according to an informant who I talked to recently. This means that seeing everything in terms of systems is a form of European ethnocentrism.
But in order to understand schemas and their application to System Architectural Design we need other important terms as well such as the Philosophical Principles of C.S. Peirce and B. Fuller. The Foundaitonal Mathematical Categories, and the View/Order Epistemological Hierarchies. In other words, Schemas are not enough to understand in a fundamental way the nature of Design Synthesis. They are merely the content, i.e. the material of the Design. All Designs make use of the Schemas for the artificial content of the Design Synthesis. And this is why they are important. When we design we do not just design Systems, we design Forms, and Patterns our of Monads with facets in the context of Domains, Worlds and the Kosmos in which we live.
The other important thing about Schemas is that they are higher dimensional. This means that our designs are higher dimensional conceptualizations. Schemas are a natural way for us to organize higher dimensional elements and think about them. What ever is beyond the ninth dimension is unschematized, for instance string theory that exists in the tenth dimension. We cannot understand string theory directly and in a natural way, it is not immediately intelligible to us because we have no schemas to apply to it. We only have the mathematics that describes it.
It is said that short term memory is 7+/-2 elements. But we say independent elements. And that means we can hold in our short term memory up to nine dimensional conceptual structures that we understand directly through schematization. The fact that Design deals with higher dimensional object configurations shows why it is so difficult. But also why Flat Binary relations between entities such as we get in UML/SysML is inadequate for capturing designs. We at least need multi-way relations in order to even come close to capturing designs in ways that are coherent with our schematization of higher dimensional configurations of design entities.
This is some of the key points in Schemas Theory. For more information see the tutorial or some of the papers I have written over the years about it.
Let me end by saying that Schemas Theory was invented in order to understand the nature of the Special Systems that exist only between the System and the Meta-system. If you do not have a clear idea of the duality of system and meta-system then the special systems are invisible. The special systems are a holonomic theory of what exists in the niche in the meta-system between it and the system. There are special structures that are mathematically defined that have ultra-efficacy that exist between the system and the meta-system.
Part of Schemas Theory is the suggestion that Systems Science should become Mathematically based and that it should adopt Category Theory as its fundamental language as Kenneth Lloyd has also suggested. The whole key to Schemas Theory and Special Systems Theory is its connection to mathematics, and following where the mathematics leads, which is many times counterintuitive. Category Theory tells us that every category has a dual if we reverse the arrows, and sometimes those inversions of arrows lead to structures we do not expect, as when Algebra gave rise to Co-Algebra. Similarly, System give rise to its non-self-dual Co-system, which is the Meta-system or OpenScape.
We have a Western Philosophical and Scientific Tradition that over time have developed many different schemas by which things in the world can be understood. Why would we not make use of all of these Schemas, why would we limit ourselves to the System Schema and ignore all the others given to us in our rich tradition. Systems Science deserves to exist because this schema has been underrepresented in Academia. There are very few departments of Systems Science in universities. But this does not mean we should ignore all the other schemas, especially when from a pragmatic point of view we are constantly dealing with them in our practice. When we build complex artifacts we deal with all the schemas. And the reason is that they help us to comprehend higher dimensional organizations of things in configuration. Without them we could not design very complex artifacts.
Also the problem we have with defining what a system is stems from the fact that we do not know what the other schemas are, and once we know what the other schemas are that delimits the essence of the system. The constant reiteration of the problem of the definition of the system is a symptom of our ignorance of the greater context of the other schemas, of the many non-systems that exist but we are ignoring to our own peril.
For instance, As I said in an article long ago. When the terrorists attack our infrastructure they are attacking our meta-systems. Since we have no theory of meta-systems we are blind to those attacks. If nothing else we need to develop a theory of meta-systems to counter the existential threat of terrorism. And once we admit that there are other schemas besides systems, and that they all have interesting complementary relations to each other at the next higher theoretical level that Schemas Theory represents then suddenly a new horizon opens up which allows us to see that what we thought was Systems Engineering is really Schemas Engineering, which uses all the Schemas to design artifacts of high complexity that offer us new affordances in our lifeworld, thus transforming our world in ways that we would not have imagined possible not long ago. As long as we do not recognize schemas we are blind to the transformations that are overtaking us and that we are participating in creating. We basically have no foundation for our practice without schemas theory.
I talk about this relation of schemas theory to practice in detail in my dissertation on Emergent Design ().