General Schemas Theory

General Schemas Theory starts with a simple question which is . . . What is the next level of abstraction up from General Systems Theory. Strange that this question does not seem to have been asked before despite almost sixty years of Systems Science research. When we say the next level up of abstraction we mean … What is there that is like a “System” but different? In other words we call everything a “System” these days, is there anything else something might be rather than a “System”? And the answer to that is obvious, it could be a Form, or a Pattern, or some other a priori organization that is known within science when things are not called a system. But if there are other kinds of organization than a “System” then how many of these different kinds of a priori organizations are there?
General Schemas Theory attempts to encompass all possible intelligible organizations that we project on things including Systems and determine what their relations to each other are. Our program to kick off General Schemas Theory starts with the S-prime hypothesis which says exactly how many schemas there are and what their relations to each other is, as well as their relation to mathematics.
S-prime hypothesis posits . . .
Ten Schemas: Facet, Monad, Pattern, Form, System, Meta-system (OpenScape), Domain, World, Kosmos, and Pluriverse. Their relation to each other is that they are nested. And their nesting is such that they follow a rule: Two dimensions per schema and two schemas per dimension.
Once we have this hypothesis then the real work begins as we try to disprove it. As Popper says the work of Science is falsification. Therefore, you are invited to try to disprove this hypothesis. Can you find more schemas? Are there gaps in the nesting of the schemas? Are there more dimensions to a given schema than two? How do we project schemas on Spacetime? What is the nature of their intelligibility?
We are assuming that schemas are of the Mathematical and Geometrical type as defined by Umberto Eco in Kant and the Platypus. Fortunately Eco has provided a history of the schema for us already and what we are calling a schema is really just the most basic type which is the organization of spacetime via a priori synthesis as defined by Kant. Kant thought all of Space and Time were posited as a priori syntheses with space on the form of geometry and time on the form of arithmetic. Now however we know that spacetime is a phasespace and we posit that there is not just one organization of all spacetime but that there are different organizations at different scopes and that these scopes are limited by their associated dimensionalities. How it is that no one noticed this before is a huge mystery. It is so obvious that we have more than one schema by which we understand a priori the organization of things. The things themselves that are organized as a priori syntheses are called ontic, And their emergent organizations fall into different levels like:
quark
fundamental particle
atom
molecule
macro molecule
cell
multi-cell
organ
organism
society
ecology
gaia
What ever the ontic emergent levels we can see that any given ontic emergent entity can be seen to be representative of multiple ontological schemas. Thus we can see patterns, forms, systems, environments (meta-systems) etc at any of these levels as different disciplines look at the same phenomena. These various templates of intelligibility that we project upon the ontic emergent entities through the work of science are the schemas. The question is why has no one collected these possible schemas together before and tried to figure out their relations to each other. You would expected this to occur in art criticism, or architecture, or some other discipline which deals with multiple schemas. But as far as I can see it has not been done previously. It has been assumed that schematization of spacetime was homogeneous as Kant thought even though we talk about schemas by which we understand things all the time. We talk about forms, patterns, monads, as well as systems and environments (meta-systems). But what we do not talk about is the relations between these various templates of intelligibility of different scales and scopes. What General Schemas Theory does is to attempt to understand their relations to each other through their dimensional limitations. Probably they are each limited to one or two dimensions each, definitely no more than five. But let’s start with the simplest hypothesis which is that there are only two dimensions per schema and two schemas per dimension. This gives the following correspondence between schemas in their nesting and the dimensionalities:
pluriverse 9, 8
kosmos 8, 7
world 6, 7
domain 5, 6
meta-system 4, 5
system 3, 4
form 2, 3
pattern 1, 2
monad 0, 1
facet -1, 1
This assignment of dimensions to the nested schemas tells us some things immediately one of which is that anything above the ninth dimension is unschematized. And interestingly enough it is in the tenth dimension that string theory starts. M theory is 11 dimensional and F theory is 12 dimensional. All these are unscematized, in other words we do not have a template of intelligibility to immediately understand string theory, or brane theory by as immediately available to us. Also there is no schematization of the negative dimensions beyond negative one. But there is a schematization of the negative first dimension which is interesting because it is in this dimension that imaginary numbers exist as a singularity. It turns out that the ninth dimension is also unique in as much as in it the difference between inside and outside breaks down. This is shown by the fact that if you inscribe a sphere in this dimension within the inter-space between a lattice of larger spheres that the inscribed sphere breaks the bounds of the bounding spheres. In other words our ideas of boundary break down in the ninth dimension. So there is a good reason that our schemas of intelligibility cannot reach beyond the ninth dimension. Between these two limits, i.e. -1 and 9 there are ten schema, i.e. ten templates of intelligibility by which we understand a priori the organization of synthetic manifolds. And the problem of General Schemas Theory is to understand the relations of these schemas to each other as mediated by their dimensionality. This problem has been studied in my various works. See General Schemas Theory Research or Archonic.net
The key point is that all this takes place in the zeroth meta-dimension where there are n-dimensions possible. Schemas are a finite structure within this n-dimensional expanse. Schemas could have been infinite, or of large finite extent, but it turns out that they only reach up to the ninth dimension where our ideas of inside and outside boundaries break down geometrically in ninth dimensional space. If Schemas are within the zeroth meta-dimension then what is there at the higher or lower meta-dimensions. Seems no one has asked that question before that I can find. When we look for the finite structures that are embodied within the meta-dimensions then we pass out of General Schemas Theory into Emergent Worlds Theory.