Special Systems Theory as a Nondual Nonintegral Singular Conjunctive Meta-theory The Farthest Frontier of Integral Research Kent D. Palmer, Ph.D.2
[email protected] http://kdp.me 714-633-9508 Copyright 2010, 2016 K.D. Palmer. All Rights Reserved. Not for distribution. Rough Draft Started 7/28/2010; Version 04; 8/08/2010; nis01a05.docx This is a compendium expositions from emails to Steven Wallis and Scott Anderson. References have been generalized to improve readability. Edited 2016.04.22 http://orcid.org/0000-0002-5298-4422 http://schematheory.net Researcher ID O-4956-2015
Keywords: special systems
Robustness and other Meta-theoretic criteria Steven Wallis advances a meta-theory criteria of the robustness for the maturity and the revolutionary nature of a given theory. Here we will consider how this criterion relates to a subset of General Schemas Theory called Special Systems Theory which is nestled between the System schema and its inverse dual the Meta-system (Open-scape) schema. We will make the case that Special Systems theory has a robustness of one. Of social science theories Wallis has studied Complex Adaptive Systems Theory has the highest robustness measure. Special Systems theory is an advance on Complex Adaptive Systems theory. However, Special Systems theory has a unique history and a unique structure that allows us to go beyond the criteria of robustness to deeper characteristics that may be gleaned from this theory. In fact, we advance the provocative claim that Special Systems theory itself sets up a measure by which all other meta-theories might be judged that goes beyond the robustness measure. The concept of Robustness is based on the idea of Secondness if we are to put it in terms of the categories of C.S. Peirce. It is about the ration of elements in the theory to their connections with each other. Theories of robustness one are fully combinatory, in other words their relation of concepts to paths between concepts are such that the connections are fully maximized. This gives a robustness of one. Theories normally in their infancy have a low robustness. But as they mature they offer a higher degree of robustness until they become at maturity fully robust. In such a theory all the possible paths between the concepts are fully articulated such that the paths define the concepts and the concepts define the paths. This idea is in line with the idea of Schlick that the perfect theory would have no percepts and would have only concepts, and their relations with each other. This is what is called an Axiomatic Platform. A perfectly robust axiom set allows the relations between the elements defined by the axiom to define fully the elements themselves. Thus for Mathematical Disciplines
1
Special Systems Theory As A Nondual Nonintegral Singular Meta-Theory – Kent Palmer
axiomatic platforms are the basis for reasoning that attempts to develops proofs that are consistent, complete and well-formed based on a small set of independent axioms. When we move from mathematics to physics there is always some percepts that have to be operationalized, that also play into the conceptual system. But still Wallis believes that the best theories will still have a set of concepts and relations between concepts that fully define each concept by articulating all possible paths between the concepts or precepts within the theory. Thus the concepts within the theory are defined by the relations between them, and the relations between them are defined by the combinatory of the possible paths. This maximization often occurs with fully worked out theories, that are both practical, and revolutionary when discovered. And the track of science is toward creating fully robust theories. Our claim is that Special Systems Theory is fully robust. But beyond that it has other characteristics that go beyond robustness which is a property related to what C.S. Peirce calls seconds. Peirce himself said that besides firsts, i.e. the isolate, there are also Thirds, i.e. continuities that can exist not only in theory but in practical ensembles. Thirds are based on the idea of Hegel which is called synthesis. Peirce thought that there was a way which he called percession of seeing how the parts of a synthesis play into the whole, without taking the synthesis apart by analysis. Peirce said that this property of Thirds was the ultimate property that any phenomena can have. However, later B. Fuller defined some trans-Peircian principles which he called Synergy (Fourth) and Integrity (Fifth). Synergy is the reuse of elements for multiple purposes within the synthesis. Integrity is the tension within a Synthesis between static and flexible elements within the whole. An excellent example of Integrity is Tensegrity. In it rods and wires together working against but with each other form stable structures. I have added to these trans-Peircian principles the idea that there is a zeroth principle called either Emptiness or Void. Void is empty space itself which is a singular. Emptiness are regimes of domain walls between portions of empty space, but with different valences. This applies the concepts of higher singularities from Bose-Einstein condensates to Space. There are point singularities, line singularities called vortices and surface singularities called domain walls in space. Thus there is a difference between the unstriated space of the Void and the striated spaces of Emptiness. Also there is another principle called the Holodial, which has to do with Interpenetration, and has the characteristic of Poise (Sixth). The Seventh is also the Negenary principle which is both the beginning and end of the sequence and it is a Singularity in both cases. Since Robustness is the characteristic of the fully articulated Secondness, i.e. relata in relation to Firsts (isolata), there should be fully articulated versions of each of these principles. We won’t give them separate names we will just speak about minimal or maximal nature of a given principle. It would be too confusing to have separate names for each. Our claim is that Special Systems theory is maximal in relation to all the trans-Peircian principles not just the robustness of maximal secondness.
The Origin of Special Systems Theory Special Systems Theory arose as I was writing a book called Fragmentation of Being and the Path beyond the Void. In that book I was writing about the structure of the Western worldview as seen from the point of view of Western Mythology. In that book I was applying the concept of the Meta-levels of Being to the development of an ontomythological study of the Western worldview. In the course of this study I decided to do a commentary on Plato’s Laws to show how they exemplified the structure that I had been analyzing in mythology, and how that spilled over into early philosophy. Plato’s Laws was the first example of a Sociology book, and also the first book of Systems Theory. It described the well ordering of the City, and imaginary city called Megara that was far from the sea. I noticed that when we compared Megara with the city in the Republic/Ancient Athens, and Atlantis, i.e. a port city and a city in the midst of the sea which were at war, that these cities all had some very odd properties that were all different from each
Special Systems Theory As A Nondual Nonintegral Singular Meta-Theory – Kent Palmer
other but singular in their conception. I decided that I should start to look for those properties in Mathematics and I happened to be studying the nature of Hypercomplex imaginary numbers at that time which had a similar structure. So I started studying Hyper complex algebras more carefully and also started looking for other mathematical structures that had similar oddities. Eventually that turned into a quest to discover mathematical anomalies, and the comparison of those anomalies to each other and the structure of Plato’s cities. Eventually I discovered several similar anomalous patterns in different parts of mathematics, and at a certain point I realized that if we put them together they told us something different about each of the Systems that represented Plato’s imaginary cities. Eventually, I decided to follow the mathematics where it led, and dropped comparing them to Plato’s cities and other oddities in Plato’s works, and started creating an advanced systems theory based on two ideas. One idea is that there is an inverse dual of the System called the Meta-system, and the other idea is that between the system and the metasystem there are three partial systems/meta-systems called the Special Systems. Later I realized that if one takes the three special systems and put them together with a normal system then one gets a meta-systemic structure called the Emergent Meta-system. And then finally I worked out the next level of abstraction up from Systems Theory called Schemas theory which exemplified all possible schemas. Those possible schemas include Pattern, Form, System, Meta-system (Open-scape), Domain and World, as well as other non-experiential domains such as Facet, Monad at one end of the spectrum, and the Kosmos and Pluriverse at the other end of the spectrum. Schemas nest with each other with no gaps, and thus they all have different scopes, and Systems and Meta-systems are at the center of the range of Schemas, and Special Systems are at the center between Systems and Meta-systems in the interstice between them. There are three Special Systems:
Dissipative Ordering: Prigogine (Dissipative Structures)
Autopoietic Symbiotic: Maturana and Varella (Autopoiesis)
Reflexive Social: O’Malley, Blum, Sandywell (Reflexive Social Theory)
All of these theories address negatively entropic systems in far from equilibrium energy flow regimes. Special Systems theory is a meta-theory that connects these special purpose theories within it. It constrains those theories with mathematical analogies based on mathematical anomalies. Due to this constraint these theories must be interpreted differently due to the nature of the constraining mathematical constructs that are construed to be their context by the meta-theory. Our understanding of the sub-theories can change and get better over time, but the meta-theory constraints remain the same and guide the teleonomic development of the sub-theories. The mathematical basis for the meta-theory are among others:
Hyper Complex Algebras
N-dimensional Geometry
Non-orientable surfaces
Aliquot Numbers
Special Systems Theory As A Nondual Nonintegral Singular Meta-Theory – Kent Palmer
Pascal Triangle
Interestingly the Special Systems cannot be understood without first understanding the difference between Systems and Meta-system schemas. They are inverse duals of each other. The system represents a whole greater than the sum of its parts, while the meta-system represents a whole less than the sum of its parts. Thus a Special System represents a whole exactly equal to the sum of its parts. And this nature of the perfection of the fittingness of the parts to the whole is the hallmark of the special system. We call these systems after Koestler holons, and we speak of them as being a holarchy, and the study of the special systems we call Holonomics. They are parts that are also wholes at the same time, but all the parts fit precisely into the whole as a synthesis. Like Perfect numbers these Special Systems are very rare. And they have a property of ultra-efficaciousness, i.e. hyper-effectiveness and hyper-efficiency. This property is due to the fact that these systems lift the pressure of entropy locally ever so slightly even though that is paid for dearly by compensating global increases of entropy. But because of the negentropy there is Dissipative Order production within the Dissipative Special System along with the lines that Prigogine demonstrated was possible. But the order that is generated is not a normal order, but rather a highly constrained and anomalous order determined by the mathematics that envelops these systems and makes them possible. Autopoietic theory is the basis for understanding the second Special System up in the Holarchy. But unfortunately that Existentialist biology formulated by Maturana and Varella assumed that Autopoietic systems were unities. Unfortunately in their book they used the term “unit” (sic). But instead Autopoietic systems are not unities but conjunctions of Dissipative Ordering Special Systems and thus are symbiotic instead of unitary. Thus the metatheory driven by the mathematics causes us to have to modify Autopoietic Theory to accommodate the constraints of the mathematics. The next higher holonic conjunction is the Reflexive Social Special System and that is composed of Four Dissipative Ordering Special Systems, two pairs of the six possible combinations are embodied and the other four are virtual. These two pairs are embodied as Autopoietic Special Systems. That means there are two virtual other virtual Autopoietic Special Systems that are possibilities within the Reflexive Social Special System. To describe these Reflexive Special Systems we use a variety of theories of Reflexive Sociology that are advanced by Blum, O’Malley, and Sandywell among others. But there are other Reflexive theories we can draw from in order to give more information about how this most complex level of the holarchy operates from a phenomenological perspective. Basically all subtheories are interpreted as approximation to the constraints imposed by the mathematical anomalies that are interlocked to constrain the various theories. A theory that comes closest to describing the holarchy itself is that of Deleuze and Guattari advanced in Anti-Oedipus and Thousand Plateaus where they describe desiring machines, individuals and the socius as levels of phenomena. Desiring machines exist in a rhizome which is a chaotically structured network within the socius. We distinguish between Desiring machines and others which are Avoiding, Disseminating, and Absorbing, and we prefer to talk about practices rather than machines. Deleuze and Guattari meant something that was nondual, but the word in English is misleading, however they also meant something like Tattvas, or what was known in Sumaria as Me, i.e. parts of existence that work together functionally to produce a partial result, like the seven basic machines. These nondual machines hang off of the “body without organs” like medals on the chest of a General. Thus the individual believes he has a virtual body which has no organs that support the partial objects of the nondual machines. But as Zizek says one can reverse that and also talk of “organs without bodies” like the Cheshire Cat’s head, which is the other side of the virtual body, that makes it actual by having a bizarre quality that is un-contained. If we reinterpret Deleuze and Guattari to be consistent with the Meta-theoretical framework we are suggesting then we can use their theory as an example of a spanning theory that takes into account the relations between all three levels of the holarchy between the System and the Meta-system (or environment, ecosystem, context, media, etc.). We interpret the Meta-system in terms of
Special Systems Theory As A Nondual Nonintegral Singular Meta-Theory – Kent Palmer
Bataille’s General Economy via Plotnitsky, and consider the System to be a Restricted Economy. What the meta-theory gives us is a criteria for the kinds of characteristics we want in a theory that exemplifies one of the Special Systems, or the Meta-system, or the System. Theories that are good fits exist, and that gives us some idea what the final meta-theory/theory complex might be like when it is fully developed filled out by sub-theories that are robust as well. But the variety of theories that fit into the niches in the meta-theory is an asset and we are not looking for any one final theory, because the fact that we can fit different sub-theories in to the meta-theory is what gives the meta-theory its versatility. The final piece of the puzzle came when I started looking for physical anomalies that are like the mathematical ones. And fortunately they exist.
Dissipative Special Systems are embodied in Solitons
Autopoietic Special Systems are embodied in Breathers and Cooper Pairs of Super Conductivity
Reflexive Special Systems are embodied in hypothesized Hyper Breathers and BoseEinstein Condensates
The Soliton is a wave of with special properties that does not lose energy when traveling down a trough. Solitons can bounce off walls and pass through each other without losing energy. They can go on indefinitely if not disturbed in a continuous trough of the same size and shape. Breathers are two solitons negative and positive that fall into each other. They have a stable boundary unlike a soliton which must always be moving to keep its shape. I hypothesize that there are hyper breathers that are made up of four solitons or two breathers, but have not found reference to this in the physics literature as yet. But there are other examples such as the Cooper Pairs of Superconductivity that can represent the Autopoietic system as moving pairs of particles that have no resistance between them and their environment. And there is the example of the Bose-Einstein Condensate for the Reflexive Special system. Notice that Breathers do not move but that Cooper Pairs move. Notice that Condensates move so we assume that Hyper Breathers would move, and we consider as a candidate for hyper breathers instantatons complexes and quantum tunneling. Needless to say by identifying these physical anomalies we note that the theory of Special Systems has physical consequences. What we are saying is that they have consequences of constraining and determining the behavior and structural limits of all conscious, living social entities. So just as the meta-theory constrains the sub-theories, so the meta-theory constrains the physical world in its expression as what Stuart Kauffman calls the generation of order out of nowhere. And the structure that produces this order out of nowhere is the Emergent Meta-system which is a cycle composed of a system together with the three special systems working together. The emergent meta-system is the basic structure constraining all systems that produce order out of nowhere. And it exemplifies the structure of Constructal Law of Bejan. The Discovery of Special Systems theory has been an interesting intellectual adventure. Most of the time since the theory was discovered has been spent looking for precursors. Many have been found. For instance, Leibniz Monadology shows signs of being a model of the Emergent Metasystem. But the main source in the Western Tradition is still Plato. Traces of this the signature of this system can be seen in Egyptian Mythology. Plato said he received his wisdom from Egypt. It appears all the obscure aspects of Plato’s dialogues are references to this wisdom concerning Special Systems as he understood them from Egypt. Also we can see evidence for the understanding of Special Systems in some early Alchemy, such as that of Bolos, but also others as late as Ripley. However, the best examples of precursors are non-western. For instance there is
Special Systems Theory As A Nondual Nonintegral Singular Meta-Theory – Kent Palmer
Acupuncture Theory which is a fully Autopoietic view of the human body. It works but no one knows from where its efficacy comes from. We can guess it comes from Autopoietic Systems Theory in its form as a kind of special system. Homeopathy on the other hand is a non-invasive non-lethal, some would say non-effective Western medicine that seems to be based on the Dissipative Special System. Acupuncture and Homeopathy are duals of each other, and that suggests that there may be a traditional kind of therapy based on Reflexive Special Systems but that has not been found as yet. For instance, it has been discovered that Go/Wei Chi game from China/Japan is a model of the Emergent Meta-system. And the only book found so far from a foreign culture that is a conscious description of the Emergent Meta-system is Fa Tsang’s commentary on the Awakening of Faith. But it is generally Buddhism and Taoism that gives us models of these Special Systems. In Buddhism the three jewels (Dharma, Buddha, Sangha) are embodiments of the special systems and the mudras are a model of their relations to each other. The cyclical description of nature in the Tao Te Ching is an image of the Emergent Meta-system cycle. In general nondual systems of thought tend to produce images of the special systems. Fro instance the propositions Garab Dorje as interpreted by Manjushrimitra are an example like that of Bolos of a summarizing of the essence of the Special Systems. In fact we hypothesize that DzogChen was at its root based on an insight into the nature of the Special Systems. There is a clear relation between Special Systems Theory and Nondual Philosophy of Buddhism, Taoism, and Tibetan Bon and Buddhist Dzogchen. DzogChen is a kind of more primordial way than either Taoism and Buddhism that came later, but influenced both in the Tibetan region. For more information about this theory see Reflexive Autopoietic Systems Theory, and Reflexive Autopoietic Dissipative Special Systems Theory by the author at http://works.bepress.com/kent_palmer.
Levels of Meta-theory What is meta-theory? I would say is that we are always talking about theory, theory of theory, theory of theory of theory, etc. And that brings us to the idea of the Meta-levels of Being, and it is now known there are at least five of those, so there must be five meta-levels of theory, even though I never thought about it before. So they would be:
Pure Theory
Process Theory
Hyper Theory
Wild Theory
Ultra Theory
This would probably be the striated opposite with an unstriated element which would be practice. And that would explain why practice is such a problem for theory to deal with, ala Bourdieu, and de Certeau, etc.
Special Systems Theory As A Nondual Nonintegral Singular Meta-Theory – Kent Palmer
Pure Theory is the present-at-hand (pointing) a temporal Parmenidian construct of ideas that we all know and love from the history of Sociology and other disciplines.
Process Theory, i.e. theory of theory, would be about the production of theory and is Heraclitian as being within change and also effecting change. This is ready-to-hand (grasping) theory as a tool in our hand as we deal with data, and which evolves.
Hyper Theory, i.e. theory of theory of theory, is differance in the sense of Derrida. It is the discontinuous changes in theory and it is related to the in-hand modality and bearing. It is when the tool of theory transforms spontaneously in our hands into some other theory, and this is of course where paradigm and epsiteme changes occur.
Wild Theory, i.e. theory of theory of theory of theory, is what Merleau-Ponty calls chiasmic, or reversible and which I like to call intaglio. It is related to encompassing and the out of hand. This is where theory transforms itself fundamentally into something else, becoming itself practice, that we cannot control but which in fact encompasses us. This comes when theory itself arises from the data for instance in Grounded Theory, Action Research etc.
Finally there is Ultra Theory, theory to the fifth degree, which is a singularity, in which all the rules break down that would allow us to differentiate theory from practice.
Now what I would like to point out is that if we take these as the meta-levels of theory then what we would see is that the Special Systems and Emergent Meta-systems theories span this entire spectrum which is what we would expect from an n-theory, i.e. a theory that completely spans the meta-levels of being and thus is itself an emergent event, or a face of the world.
Pure Theory is the way that the Math, and the Special Systems theory is frozen in time as a theory which has all of its concepts isomorphic with mathematical constructs.
Special Systems Theory As A Nondual Nonintegral Singular Meta-Theory – Kent Palmer
Process Theory appears when we start to apply Special Systems theory to various phenomena and realize that it fits different phenomena in different fashions, such that each phenomena reveals something about the theory, and also each phenomena has a special way of embodying the theory that is specific to it. Thus the theory is in process of developing as it is applied, and also our understanding expands as we apply it to the phenomena.
Hyper Theory appears when we take into account that the theory is really about the discontinuities between System and Meta-system, and between all the other schemas such as pattern, world, form to which the central distinction between System and Meta-system is contrast. Then there is the distinction between these two and the Special Systems. And there is the difference between the Special Systems themselves. And finally there is the difference between all these and their synthesis which is the Emergent Meta-system. There are many of these discontinuities between within the theory between different sub-theories, and we are continually moving back and forth across these boundaries. Hyper theory is about the nature of the discontinuities between the sub-theories and their relation to each other in which they fit together very precisely to produce a whole way of looking at phenomena that is different from our normal way of looking at things that seeks continuity and relation between things, rather than discontinuous breaks.
Wild Theory appears when we realize that we are what this theory is about. We are conscious, living, social creatures and that the theory is describing in some way our own essence, so that we cannot disentangle ourselves from the theory.
Ultra Theory appears when we understand that ultimately this theory, which is like a Rosetta stone for understanding human social systems and our own psychology, because it is rooted in given mathematical anomalies cannot ultimately be understood, the entire theory is anomalous, and should not really exist, because it is unlike any other theory, in the depth of its rootedness in anomalous mathematical and physical phenomena that themselves do not make a lot of sense to us because it is counter to our traditional ways of thinking about ourselves which are dualistic, and it is intrinsically nondual. Cf. http://nondual.net. Thus at some fundamental level this theory escapes all theory because it points toward the nondual as the source of all theory and practice.
From this one can get a sense of what is meant by the meta-levels of Being from my other works. But I thought there might be an interested in how the Wallis criteria might applied to meta-n-theory as a construct, and how Special Systems and Emergent Meta-systems theory along with General Schemas Theory which it is part of are exemplified at each of the meta-n-levels of Theory itself. Because this theory spans all the levels of meta-n-theory it is itself an emergent event and a face of the world. And as such I believe it is a unique meta-theory depth beyond all
Special Systems Theory As A Nondual Nonintegral Singular Meta-Theory – Kent Palmer
other meta-theories which will only go so far up the ladder of meta-n-levels of theory. And the reason for thinking that this is true is that there are not many variations of these sorts of anomalies in math, but in fact math is very constrained in that it holy has a certain kind of anomaly that seems to ramify out though the mathematical edifice in different forms, so that the anomaly in math that the special systems are modeled on is itself anomalous. And if this is true then this is the one, singular integral theory. It is the integral theory forced on us by what math offers us as an alternative, which is really only one alternative because it appears that all the related anomalies within math are various embodiments of the same hidden meta-anomaly that keeps showing up in many different guises in different kinds of mathematics. Because Special Systems is merely an attempt to piece together all these different manifestations of the same mathematical metaanomaly, and turn it into a systems theory so it can be applied to nature, and ourselves as natural exemplars of this anomaly, it is really the only possible theory that accords with the mathematics. Normally mathematics can be applied and used in multiple ways. But the mathematical anomalies because they fit together to exemplify different aspects of the meta-anomaly, that means that Special Systems theory is highly constrained and specific in its odd signature. And that makes it preeminently testable. So it could be that the reason that Social Theory is not testable in general is because without the mathematics it is not constrained enough to be specific enough to be testable. The irony is that if we test Special systems theory and it is wrong there are not many other places to go because the only thing that can be wrong his how we interpreted it into a systems theory. The math is not going to change and there are no other meta-anomalies out there that I know of that are alternatives. So it could be that there is only one chance for testability which is embodied in special systems theory because it is the only meta-theory that goes up all the meta-levels of theory. And it is the only theory that exemplifies the meta-anomaly closely. And thus it is the only theory with enough precision to be tested. And if this is true and we test it and it fails, then it may mean that the universe is ultimately not comprehensible. Or it might mean that like Relativity Theory and Quantum Mechanics there is necessarily a core of meta-theory that we cannot understand, and maybe never will understand. But until we test it somehow we will not know the answer to that question. This is what has fascinated me since I accidentally discovered the theory sometime in the early 90s. It is actually Plato's theory, I merely rediscovered it in his work, by paying attention to all the crazy and odd things he said about his cities and thinking he had written the first book of Social Systems Theory, and trying to understand what he might be telling us about Social Systems. When I found that what he seemed to be saying had analogues in Mathematics, and that the loss of properties in the mathematics created systems properties in reality, then the game was afoot as they say. Since then it has been a wild ride. But I think that if we could figure out a way to test this theory, then the wildest part of the ride might be just beginning. I have exhausted my resources and I cannot for the life of me figure out how to test it by myself. So I have been looking for someone who understood theory testing enough to figure out how to test this theory. Then I ran into Wallis, someone who had the agenda of testing theories and meta-theories. I hoped he find this theory interesting enough to apply his theory testing ideas test Special Systems Theory. I am just stumped. I guess I am just not enough of an experimentalist. Too much of a theorist. Anyway it is an exciting possibility to think that some test might be done that is convincing for enough people to take the theory seriously, enough to begin working on its implications for understanding our society, and our psychology, and our biology. Somehow I thought that was what Sociology was supposed to do, but somehow I think it went off track. But I have just kept working on my own trying to solve the problems posed at LSE when I was there as to what a good theory that was ripe for refutation should be like, and I have endeavored to produce one.
Special Systems Theory As A Nondual Nonintegral Singular Meta-Theory – Kent Palmer
Application of the Criteria for Testing Theories to the Special System Meta-theory Wallis identifies some characteristics of the testing of Theories within the context of Meta-theory. Here we explore how the Special Systems measure up to these criteria. Objective Observation Special Systems are everywhere that there are living, conscious, social creatures. But these are just a special case of a more general type of system that exists also in nature as a set of anomalies. So what we need to do is understand how the physical anomalies are like the social, psychological and biological structures and make them possible. These higher level structures are exploring possibilities that come into being within the region of the Special systems, i.e. where the weight of entropy is slightly lifted locally. We should be able to see the same structures in the higher systems that we see in the physical systems, because the biological, psychological, and social systems are also physical. Evidence Special Systems are everywhere we look on earth, where ever there is living, conscious, social life. But we have always looked at these systems as being some how different from nature because we did not until recently recognize that there were anomalies in nature that were like these higher systems. Somehow we need to correlate the higher systems with what we know about the anomalies in nature to show that they higher systems are operating on the same principles as the physical anomalies. Then we need to show that the social, psychological and biological special systems display the mathematical ordering of the special systems. This is the key. If they display this ordering which has its own special anomalous signature then we know we have a strong theory that is exemplified in the phenomena. But how to bring out that specific ordering in experiments is an open question. Experiment If we can find the same mathematical structures in the higher phenomena that embody the special systems then we should be able to formulate hypotheses that certain patterns will be repeated if we do experiments that will elicit that response from the systems. But one has to be careful because autopoietic systems are like black boxes to observation. That is central to the theory. Also the cognitive and physical processing parts of these theories are intertwined and cannot be separated. There is no mind body split in autopoietic systems according to Maturana and Varella. Metatheory Testing Basically this means that we search for theories that agree with the math. We prefer the math over our ideas of what should be. We follow the math where ever it leads, and then we find phenomena that also follows the math. And we test all other theories by this criteria. Up til now people would just make up theories that they thought might be right, like Aristotle did. But scientific theories follow the math and relate that rigorously to the experimental results regardless of how we ourselves think it should be. By doing that we discover odd things like relativity theory and quantum mechanics, i.e. things in nature that really should not exist but actually do exist regardless of whether we understand them or not. Theory Bounding
Special Systems Theory As A Nondual Nonintegral Singular Meta-Theory – Kent Palmer
First we identify that Systems have a dual, i.e. meta-systems, then we identify the difference in these two. Our culture is blind to the second one normally. But once we have a clear idea of the difference between them, then we see how that difference is made by the recognition of the special systems that are nested between them. This meta-theory is all about its bounds. the bounds between system and meta-system, and the bound between them and special systems. And the difference between the special systems. Recognizing all these differences between the bounds of the different types of system is the key to understanding the theory which is itself complex because it is an interaction between multiple different theories with different scopes that fit together as a complex meta-mechanism that delineates the properties of consciousness, life and the social. Induction I have used induction to try to substantiate the theories once discovered by trying to find precursors to the theories in other cultures and within the Western tradition. I have not been too lucky in the Western tradition, but in other traditions there is all kinds of evidence that they were known about and used as the basis of traditional sciences like Acupuncture, Homeopathy, Alchemy, etc. By induction over a lot of cases we build up a sense of what the theory can give us when we see the different forms it has take over the ages in different cultures. For instance the game of Go/Wei Chi is a prefect model of the Emergent Meta-system. Each case where there is a cultural artifact that has the same structural signature tells us something else about the theory. Repetition There are certain parts of the theory that makes it like Relativity Theory and Quantum Mechanics so that straight forward positivistic approaches to experimentation do not work. We need to be circumspect when we design our experiments like we are when we explore the relation between QM and Newtonian phenomena or when we try to understand Bells Theorem. The phenomena is too complex for simple repetition except to the extent that each living, social, conscious being is a repetition of the special systems being embodied, but these systems are very complex in themselves and stimulus response type experiments will not work. Experiments have to be indirect and sophisticated. There in lies my problem.
Critical Analysis Here the Special Systems help us to understand phenomena that we would not have understood otherwise. Once we understand the theory it opens up all kinds of vistas to us in its application to various phenomena.
Categorization
These special systems give us a basis for producing categorizations. But they are not categorizations in themselves. Categorization comes from the applying of the theory to different phenomena. Categorizations that do not follow the structural principles of Special Systems cannot stand. That means most of our social and psychological categorizations are probably wrong because they do not take the structure of special systems into account.
General Norms of Validation
Special Systems Theory As A Nondual Nonintegral Singular Meta-Theory – Kent Palmer
The mathematics makes the theory coherent. The facts we know need to be re-construed in relation to the theory, or rethought if they don't fit because our made up categorizations do not fit the way that the theory works. It is an odd theory like QM or Relativity, it is non-intuitive so it conflicts with most normal theories. Accepting it means one need a paradigm or episteme shift. The fact that something like Acupuncture works but we do no know how means that there is a pragmatic test possible for this meta-theory.
Maturity
The theory is very mature and stable, and there are many precursors that have been found. What is lacking is experimental evidence for the theory. But I would argue that it is ripe for experimental validation by our trying to refute it. But what we would be refuting is how the mathematics has been interpreted in its being turned into a systems theory and whether that systems theory has empirical exemplars that can be experimented on to see the structures that the theory predicts. Verification and Testing The west followed Aristotle's brand of science, which was the science of the common, not the science of the anomaly. Plato's science was the science of the anomaly. And he got that it seems from Ancient Egypt where a very similar theory is built into their structure of the Gods. Plato tells us he got his wisdom form Egypt. Basically were ever Plato seems to be talking nonsense is where he is referring to the special systems. this only really becomes clear when we look at his cities as systems and consider their odd properties. To Aristotle these odd properties don't count because they are not universal properties but instead they are embodiments of anomalies. but it turns out that there are anomalies in mathematics and physics, and what Special Systems theory does is recognize a pattern in those anomalies and tries to relate them structurally to each other in a systems theory that exemplifies their odd properties and structures. Verification takes place by setting up isomorphisms between the systems theory, the mathematics and the physical anomalies, and the precursors. Testing needs to look for anomalous situations in psychology, social phenomena and living systems that exemplify these odd structures. What is needed is a prototypical test that shows that these structures have a reality of their own in the various types of phenomena that they structure. I have been trying to do that by finding efficacious therapy methods and applying the theory to explain why they work. Turns out that the therapies that I have chosen do have striking similarity to the structure of the theory. But showing that experimentally is a hard problem. Perhaps the way to go is to predict a new phenomena by the theory and then go find that. The problem is that these systems are ubiquitous, and we are they, and so it is hard for us to find anything, that is living, social or conscious that do not conform to their structure, yet that structure is an anomaly in the universe as a whole. Applying trans-Peircian Categories to the Special Systems Meta-theory Here I try to expand upon and to enhance Wallis’ of Robustness of theory based on Special Systems Theory. This is an extension to Steve Wallis’ theory about how to test theories. This is based on material in my recent dissertation about Emergent Design. Theories are designed. So it might be worthwhile to consider the nature of the Design of Emergent Artifacts such as Theories and Meta-theories as a means of achieving robustness and other even higher properties. Wallis uses concatenation as a measure, i.e. the measure is that there is the same number of
Special Systems Theory As A Nondual Nonintegral Singular Meta-Theory – Kent Palmer
relations between things as there are things in the theory. In a way Special Systems takes this idea of robustness to the next higher level of sophistication. So a triangular theory, that has three concepts and three relations between any two concepts is fully concatenated and thus fully robust. And Wallis gives examples of physical theories that are like that. Special Systems Theory would suggest another deeper measure. Special Systems are entities where the thing is exactly equal to its parts with no excess nor lack
Systems are seen as having excess of parts over their whole.
Special Systems are wholes exactly equal to the sum of its parts.
Meta-systems are seen as having lack of parts in relation to their whole.
Most numbers in terms of their divisors are either more or less than their own wholes determined by adding the parts. Perfect numbers have exactly the same number of parts as their whole. These are very rare. I think only about 47 are known to exist. Amicable numbers are numbers whose parts at up to each other’s whole. Sociable numbers are those that add up to each other in a cyclic ring. There are many more Amicable numbers than sociable numbers and more sociable numbers that the rare perfect numbers. The criteria of robustness is essentially geometric and relates to regular shapes. A theory that maximizes its connections that are mathematically possible is robust. As we move up into higher dimensions however there is synergy as B. Fuller pointed out. For instance there is the pentahedron of four dimensional space which has a lattice 1-5-10-10-5-1. Out of five points and ten lines it creates ten triangles and five tetrahedrons. I think we might call this hyperconcatenation and the robustness is one because all the possible relations between five things have been realized in the pentahedron. However, the pentahedron has other qualities besides its robustness. It has synergy, i.e. the reuse of its elements to produce more structure than is in the elements themselves or is possible in three dimensional space. Notice that the pentahedron is merely five points connected in every way possible in a plane, but this can be taken into three and four dimensional space to produce a regular solid. But also the pentahedron has what is called by B. Fuller Integrity. Integrity is the inner tension of pieces that hold each other together yet apart. Tensegrity is the key example of integrity. The pentahedron has within it two mobius strips that are not fused into a kleinian bottle. These two mobius strip lines define each other and establish the integrity of the pentahedron in fourspace. So robustness is a only the first of a series of measures that we would like to see. It is a measure of maximal connectedness of concepts given the number of possible connections by which they can be co-defined. But beyond that there is synergy, and integrity. Because Wallis has concentrated on relations, that means one has not yet considered what Peirce called Thirdness. Thirdness is the next property beyond relation, before synergy and integrity. It is the measure of synthesis or mediation within the whole formed by the parts. Peirce defines Precission (with two ss) as the way that we look at the parts without analytically taking them apart as functioning within a synthesis. We would also like the theory to have beyond robustness, also a synthetic quality of continuity which can be recognized by precission. I develop these ideas in my dissertation. Now Perfect numbers are holoidal, that is they are models of interpenetration, which is the next higher quality up from Fuller's integrity. Perfect, sociable and amicable numbers are perfect holons where the parts are exactly equal to the whole. Special Systems are models of these holons
Special Systems Theory As A Nondual Nonintegral Singular Meta-Theory – Kent Palmer
as they operate in different contexts. So special systems not only have a robustness of ONE. But also evidence synergy, Integrity and Holoidal interpenetration of holons. However, one must be careful how we measure robustness. Wallis is measuring robustness with respect to a whole theory. But Special Systems theory is a meta-theory if not higher. That means it is about how theories fit together. Wallis says that Complex Adaptive Systems Theory has the highest Robustness. Special Systems Theory is a refinement of Complex Adaptive Systems Theory, which connects it to even more mathematics than it is now connected to. Mathematics has asymmetries within it, and anomalies within it, and Special Systems theory makes use of these anomalies to suggest ways that different theories need to fit together in order to work with ultra-efficacy. I would agree that robustness is related to efficiency. So we cannot count robustness across the whole theory complex, because part of the theory is that there are discontinuities between different sub-theories and we should not count that against a meta-theory. Each subtheory should have a high robustness, but the metatheory, because it is a meta-system needs to have lacks that allow the various sub-theories to be fitted together. Special systems theory says that there is a distinction between a System and a Meta-system (its categorical dual). However one defines a system and then represent it categorically, this relation appears in the reversal of arrows which makes a system non-self dual. No system can be self-dual because it has emergent properties that go beyond its parts. That means it has Godelian statements that describe those emergent properties that cannot be located for sure either inside or outside the system. If we locate them inside then it is a system, but if we locate the Godelian statements that describe the emergent properties outside then it is a meta-system. So because the system and the meta-system are described by category theory arrows that are reversible, we can assume that the robustness is one. This is because in category theory representations all that appears are the arrows of transformation, and not the elements. Elements are fully concatenated and reduced to their relationships. When it comes to Special Systems they are based on mathematical anomalies. But those anomalies are all minimal in the sense that they represent the minimal number of possible relations that the elements can possibility have. What makes them anomalous is that there is some sort of fusion or separation and independence going on that we do not normally see in numbers, or sets, etc. So in the case of hyper-complex numbers the Complex number, Quaternions, Octonions, Sedenions are minimal given he properties that they represent mathematically that translate into systems properties. In other words due to the relationship of discontinuity and continuity in the Hypercomplex numbers there is a greater efficiency of structural relation than we would normally expect. So these structures are hyper-robust in some sense. For instance, in complex numbers there is at base just two juxtaposed real numbers. But then a symmetry breaking occurs, and one become imaginary and the other remains real. What make the one imaginary is the fact that it is possible to have a relation 1 -> i -> -1 -> -i that is nonintuitive between the real and imaginary elements. That is an imaginary cyclical relationship that we see used in for instance electrical theory. The fact that these counter-intuitive hyper-relations exist is itself an anomaly for robustness as a measure, and leads to considering higher principles such as synergy, integrity, and interpenetration. So what I am saying is that Special Systems Theory, Emergent Meta-systems Theory and Schemas Theory that define the difference between Systems and Meta-systems and other schemas all together have a very high robustness factor approaching one and also have other qualities that go beyond robustness such as synergy, integrity and holoidal poise. That is why Special Systems theory has a high probability of being revolutionary and a mature theory that is an enhancement
Special Systems Theory As A Nondual Nonintegral Singular Meta-Theory – Kent Palmer
to Complex Adaptive Systems Theory that already had a high robustness from based on the Wallis measure analysis. A lot of work has gone in to making sure the systems theory only has concepts that fit to the mathematical anomalies being used as the basis of the theory. Those mathematical anomalies have a better fittingness than is normally possible, and so the robustness factor has to be very high for the meta-theory. Now the individual concrete theories that fill in the niches in the meta-theory are examples and they could individually have higher robustness as they develop. For instance I do not know the robustness of Prigogine's theory, or Matruana and Varella's theory, or that of O'Malley and Sandywell. Their robustness might be lower, but these theories are only used to connect the Special Systems to phenomena, and they can be evolved over time to have greater robustness. What I am talking about is the robustness of the meta-theory which is precisely modeled to fit the mathematics and physics of the anomalies. I can claim very high robustness, as well as other properties Wallis is not measuring yet that go beyond robustness. I think robustness is a good measure, but it is just a start. And one thing about Special Systems theory is that it helps to show what future theories should be like because of its mathematical and physical basis. If we just had mathematical anomalies then we might think that a theory based on anomalies might not have physical and real world consequences. But because we have corresponding physical anomalies we can be sure that some part of nature mimics these mathematical anomalies. What I am saying is that consciousness, life, and the social are also parts of nature that are anomalies in the universe going against the norm of entropy, that mimic those mathematical anomalies too. Special Systems Proposition I have been thinking about the propositional Analysis idea, and it seems to me that there is a question I have not seen Wallis address, which is that the same theory can be represented propositionally differently so that the robustness value would be different. Thus, I wonder Wallis has given any thought to the way that the propositions are generated such that they give a true value for robustness. This leads me to think that Wallis’ formulation of robustness is perhaps naive, in the sense that it assumes that there is just one representation for a theory and if we create that representation then we can measure the robustness of that representation. Probably a more sophisticated idea is that just like mathematical objects theories have multiple representations, some of which are minimal or near minimal, and I think that one would want to measure minimal representations, and not just one but several and average them or something to determine a global robustness value of the theory. Another point that I mentioned in my previous message that Wallis might have missed is that I changed the definition of robustness slightly to say it is the minimal set of connections between conceptual nodes that is possible. Sometimes mathematical objects are structured with asymmetrical properties such that there are more nodes than relation, or more relations than nodes, and so a simple division of nodes by relations may not be the minimal structure. This is only true in the simplest cases, which would apply to many theories because those theories are not structured by the mathematics but arbitrarily based on the intuition of their authors. Also following the critique I offered it should be possible to formulate propositions such that they highlight synthesis, synergy, integrity and poise as well.
Special Systems Theory As A Nondual Nonintegral Singular Meta-Theory – Kent Palmer
It turns out that one of my areas of interest is Domain Specific Languages in Model Based Engineering, and I have created a bunch of design languages, called ISEM, and in fact have created a language that encapsulates my theory of Quadralectics that was developed in my dissertation. So I have that language, and Wallis’ criteria of robustness is one of the criteria I use to create the languages that describe Quadralectics, and so I think there could be some pollution of the data because the criteria that Wallis assumes to be independent is in fact dependent, with regard to my languages. Those ISEM domain specific languages could be tested as well. They take the Special systems as the basis of their organization but they apply them to a specific field, i.e. the process of design. However, I think the challenge of producing a language that presents the key propositions of special systems theory would be a worthwhile exercise. When I get a chance I will try to do that. However, my claim of Robustness of One is based on the fact that I have been careful in my theory to reflect the mathematical structures as directly as possible, and it is well known that these mathematical objects are minimal and their simplicity and minimality is one of their surprising features. There is what I called the meta-anomaly, which is the fact that as we come down from large numbers it seems that the amount of room to maneuver in mathematical objects becomes less and less until certain features of the objects fuse, and when that happens it produces things like the hyper-complex numbers that are more efficient than one would expect, in terms of their structure and that produces special properties not available in other bigger objects. That is why robustness has to be redefined to take into account the mathematically possible connections, rather than merely dividing concepts by relations, or vice versa. For instance, the pentahedron in four dimensional space has a lattice 1-5-10-10-5-1 which is self dual and you read as 5 points, ten lines, ten surfaces, five tetrahedrons. there are many more surfaces and tetrahedrons than you would expect, and than would be possible in three dimensional space. But ten lines are all that are possible between any five points. So if we divide relations by concepts we get two. In other words it is more robust than we would normally expect because it is reaching into the fourth dimension and taking advantage of the fact there is more room there to create relationships and that is what gives rise to synergy in that figure. When we talk about integrity then we would switch to see how the pentahedron contains two mobius strips that do not fuse into a Kleinian bottle, and so there are two paths that are mobius strips though the pentahedron, and these are in tension with each other because they are held by the figure so that they do not fuse into a klienian bottle. Thus the pentahedron has integrity. And finally in terms of poise we could look at the fact that the pentahedron has the same group A5 as the icosahedron/dodecahedron in three dimensional space, and thus it has a specific relation to its context in three dimensional space that is related appears as Poise, i.e. the characteristic that points to the interpenetration of the two realms having the same underlying structure. Of course, the pentahedron is also its own synthetic whole and so it has parts that we can look at via Precission as C.S. Peirce suggests, i.e. without taking it apart analytically. The parts taken by themselves do not suggest the super-synthetic whole that exists in four dimensional space which has five tetrahedrons intertwined within it. The continuity of the whole structure is what needs to be appreciated when we move up from Robustness to the next higher principle which sees the wholeness of the object where every part articulates some aspect of the whole and thus can genuinely be called following Koestler holons. So my claim of robustness for Special Systems Theory is a priori, in the sense that if one has a theory such as the theory of the Five Hsing which is the heart of acupuncture theory, which is precisely built on the structure of the pentahedron, then because these are Platonic Solids, they
Special Systems Theory As A Nondual Nonintegral Singular Meta-Theory – Kent Palmer
are by definition as Robust as one can get, in fact in this case more robust than is possible to achieve normally due to synergy. But if we redefine robustness of ONE to be whatever is the mathematically possible simplest connection between elements and relations for a given theory, then by definition any theory that follows the mathematics precisely must have a Robustness of One. And Special Systems Theory is specifically built in this way, It follows the mathematics precisely where ever it may lead and strives for isomorphism with the mathematics. By definition, whatever is extraneous to the mathematics is extraneous to the theory. The odd thing is that by doing this we get closer to the phenomena of interest (social, conscious, living) than we might be able to do otherwise. There are actual physical phenomena that have the same structures that are equally anomalous physically as the mathematical structure are anomalous from a mathematical viewpoint. This is the wonder of the theory. Einstein mentioned the unusual efficacy of theory as being one of the greatest mysteries of the universe. Here is a first cut at a list of Meta-Theoretical Propositions that describe Special Systems Theory: o
There exist schemas as the next higher level of abstraction from Systems Theory.
o
There exist ten schemas that include Facet, Monad, Pattern, Form, System, Meta-system, Domain, World, Kosmos, and Pluriverse (Hypothesis S-prime)
o
Schemas follow the law that there are two dimensions per schema and two schemas per dimension. (Hypothesis S-prime)
o
Moving up the series of schemas which have nested scopes is done by repetition, and moving down the series is done by representation.
o
There is mimesis between representations and repetitions at the same schematic level.
o
Part of this mimesis is that between Systems and Meta-systems schematic levels there exist three special system thresholds of organization that are partial systems and partial metasystems.
o
Systems are the inverse dual of meta-systems and vice-versa. In other words inverting the arrows of a category theory representation of a system does not render it self-dual.
o
Systems are wholes greater than the sum of their parts, i.e. manifest emergence.
o
Meta-systems are wholes less than the sum of their parts, i.e. manifest de-emergence.
o
Special Systems are anomalous wholes exactly equal to the sum of their parts, and thus holons.
o
Holons are organized by conjunction.
o
The minimal holon is the Dissipative Ordering Special System.
o
This holon has the property of negentropy. Cf Prigogine's theory of dissipative structures.
o
This minimal holon is organized such that it has analogy to several specific mathematical and physical anomalies.
o
This minimal holon is homeomorphic to one half of a amicable number.
Special Systems Theory As A Nondual Nonintegral Singular Meta-Theory – Kent Palmer
o
This minimal holon is homeomorphic to the non-orientable surface of a mobius strip.
o
This minimal holon is homeomorphic to the imaginary algebras complex number (x+i). This means there is a symmetry breaking that produces this structure as an asymmetry that transforms (x+x). In that symmetry breaking the identity of the complex conjugates are lost.
o
This minimal holon is homeomorphic to other mathematical anomalies with similar structures in different parts of mathematics.
o
This minimal holon is homeomorphic to the soliton wavicle (lave) as seen in physics also called a monopole.
o
This minimal holon is analogous to two mirrors facing each other and their reflective pattern with regard to light.
o
The analogy for this level of organization is consciousness in a cell or organism with regard to the spread of knowledge as persistent potential organization.
o
Two minimal holons form the next higher level of organization of holons called the Autopoietic Symbiotic Special System.
o
Two holons are conjuncted together to form the next level of organization, but that level does not change the independence of the holons on their minimal level of negentropic organization. Holons when conjuncted are not a synthesis, but nor are they an arbitrary collection. There is a specific kind of organization that is neither a synthesis or a random assortment of elements which is holonomic.
o
The holon pair has properties similar to those proposed by Maturana and Varella in their Autopoietic Theory, but with the caveat that this system is not a unity, but a symbiotic pair in all cases. The holon pair has viability, closure, boundary, difference between organization and structure, etc.
o
An Autopoietic Symbiotic Special System is related to several specific mathematical and physical anomalies.
o
This minimal holon is homeomorphic to one half of a perfect number.
o
This minimal holon is homeomorphic to the non-orientable surface of a Kleinian bottle.
o
This minimal holon is homeomorphic to the quaternion imaginary hyper-complex algebras which have numbers of the form (x+i+j+k). In in it the commutative property is lost.
o
This minimal holon is homeomorphic to other mathematical anomalies with similar structures in different parts of mathematics.
o
This minimal holon is homeomorphic to the solotonic breather as seen in physics.
o
This minimal holon is analogous to three mirrors facing each other and their reflective pattern with regard to light.
o
The analogy for this level of organization is viable life in a cell or organism.
Special Systems Theory As A Nondual Nonintegral Singular Meta-Theory – Kent Palmer
o
An Autopoietic Special System is simultaneously composed of two negentropic holons and their conjuncted combination which yields a higher level of organization without disturbing the independence of the lower level organization. These Dissipative Ordering holons are symbiotic with each other, i.e. mutually interdependent.
o
The next higher level of organization of holons is the Reflexive Social Special System. It is composed simultaneously of four holons of the dissipative ordering type and two meta-holons of the autopoietic symbiotic type combined again by conjunction.
o
This level of holon has the main property of a complete circuit of reflexivity as described by the reflexive theorists such as John O'Malley, Barry Sandywell and others. In other words what is achieved at this level is a minimal reflexive system or circuit that is simultaneously social, i.e. it spills out beyond the organism or cell involving multiple organisms or cells.
o
Because this is a complete reflexive circuit it becomes virtualized. In other words there are six possible paths between the holons, but of these six possible paths two paths are taken up by the embodied autopoietic meta-holons, and thus there are four possible paths that are virtual for connection between the holons, these virtual paths form the reflexive circuit, which can serve as a control circuit within the social relationship between the two meta-holons.
o
We will call this next level of organization the meta2-holon. It is merely conjunctive and does not disturb the lower level dissipative ordering or autopoietic symbiotic organizations, except in as much as new social properties appear at the higher level of organization.
o
An Reflexive Social Special System is related to several specific mathematical and physical anomalies.
o
This minimal holon is homeomorphic to one half of a sociable number.
o
This minimal holon is homeomorphic to the non-orientable surface of a hyper-Kleinian bottle. The hyper kleinian bottle intersects another kleinian bottle along its circuit of selfintersection.
o
This minimal holon is homeomorphic to the octonion imaginary hyper-complex algebras which have numbers of the form (x+i+j+k+I+J+K+E). In in it the associative property is lost. The loss of that associative property makes the social important. Who sits next to whom at the dining party matters.
o
This minimal holon is homeomorphic to other mathematical anomalies with similar structures in different parts of mathematics.
o
This minimal holon is homeomorphic to the solotonic super-breather as which has not been found in physics yet but is hypothesized to exist.
o
This minimal holon is analogous to four mirrors facing each other and their reflective pattern with regard to light.
o
The analogy for this level of organization is viable society.
o
The next level of organization beyond the Reflexive Social is the Emergent Meta-system.
Special Systems Theory As A Nondual Nonintegral Singular Meta-Theory – Kent Palmer
o
There are four possibilities at this level: Emergent System, De-emergent System, Emergent Meta-System, and De-Emergent Meta-system. Emergent Systems and De-Emergent Metasystems are the norm. There is however a transformation in which a system de-emerges and that produces an Emergent Meta-system.
o
Systems may self-nest. Meta-systems may self-nest.
o
Systems and Meta-systems mutually nest with each other like Russian dolls. The systems are identified by boundaries, and the meta-systems are the space between the levels of the systems.
o
There are no gaps between the interspersed nested system and meta-system hierarchies.
o
There are no gaps between the nesting of schemas in general of all scopes.
o
However, Meta-systems are organized as horizons rather than boundaries.
o
Meta-systems are organized based on complementarity rather than unity and totality.
o
Systems are unified and totalized. Meta-systems are de-unified and de-totalized.
o
The analogy for the relation between Systems and Meta-systems is the relation between Euclidean Geometry and the complementary pair of Hyperbolic and Elliptical Non-Euclidean Geometries
o
The analogy for the relation between Systems and Meta-systems is the relation between Normal Cartesian Algebra and the complementary pair of Jordan and Lie eccentric Algebras.
o
The analogy for the transition from the System to the Meta-system is the fifth axiom of the parallel which cannot be proven to exist within the four axioms of absolute geometry and thus generates the non-euclidean geometries as a symmetry breaking. This fact make it impossible to prove that the absolute geometry axioms are complete and whole in themselves.
o
Statements like the fifth axiom are Godelian, in that they cannot be proved to be inside nor outside the system that they describe.
o
The difference between a system and a meta-system is that the godelian statements that describe the emergent properties of the system are excluded in the meta-system, and thus the system de-emerges and turns into a meta-system.
o
However, there is the anomalous case in which the meta-system has its own emergent properties and unique organization that is the dual of the organization of the system, not merely the system taken apart by analysis.
o
An Emergent Meta-system is composed of a normal System conjuncted with the three Special Systems.
o
This conjunction forms a cycle that is the relaxation of properties that follows the symmetry breakings at each level of the unfolding of the Special System.
o
This cycle begins with seeds in a pod, them produces monads in a swarm, then produces views in a constellation, and then produces candidates in a slate, which in turn produce seeds
Special Systems Theory As A Nondual Nonintegral Singular Meta-Theory – Kent Palmer
in a pod. o
Each moment of the cycle is an organization of conjuncted elements. Seed, Monad, View, and Candidate describe the elements, and Pod, Swarm, Constellation, and Slate describe the conjucted elements that together form the holon, meta-holon, or meta^2-holon structures at each moment of the cycle.
o
The structure mathematically moves from real, to imaginary, to quaternion, to octonion, to sedenion which transforms back to real.
o
This is possible because each higher hypercomplex algebra has islands of the lower level hyper-complex algebras within it.
o
The move from the octonion to the sednion loses the division property, and thus things become fused or indivisible.
o
There is an operator that takes us from each states in the EMS cycle to the next. These are in order Creation, Mutual Action, Schematization, and Annihilation operators.
o
In the EMS cycle elements are produced out of nothing, ex nihilio, in order to give what Stuart Kauffman calls order from nowhere.
o
The analogy for the EMS cycle is multiple games of Go/Wu Chi.
o
The theory that comes closest to it in the Western tradition is Leibniz theory of Monads.
o
The key and unexpected point that appears in the EMS is that unexpected imaginary orthogonal realms appear out of nowhere from singularities successively. But these successive orthogonal realms have a limit in that they lose all their special properties when they transition from the octonion to the sedenion.
o
The successive production of anomalous properties in the lower algebras is somehow related to the fact that there is less space in he lower numbers for articulation, and thus elements fuse producing anomalous structures at low dimension that do not exist at higher dimensions. This can be seen in the difference between three and four dimensional space from all higher dimensions in terms of the number and nature of the platonic solids. Special properties of these solids express the special properties of the spaces within which the solids and hyper solids exist.
o
The Quaternion is the key rotational structure in the fourth dimension. Therefore the fourth dimension's special properties are another representation of the characteristics of the special systems.
o
The pentahedron is the minimal solid in four dimensional space. Minimal solids of n-spaces are defined by the unfolding of Pascal's triangle.
o
The pentahedron controls the virtual cycle of the reflexive special system as it is injected within the autopoietic system as its internal environment.
o
The pentahedron is isomorphic to the Five Hsing in Autopoietic Theory.
Special Systems Theory As A Nondual Nonintegral Singular Meta-Theory – Kent Palmer
o
There are four virtual elements to the injected reflexive structure. We will call these receptivities. We will use as their analogy the four elements in the western tradition, called Earth, Air, Fire, Water.
o
Earth Air Fire Water are combinations of Hot/Cold (Yang) and Wet/Dry (Yin) and thus these are merely permutatons of causal relations between Yang and Yin elements.
o
Thus there are twenty possible interactions between the control hypercycle of the Five Hsing and the receptivities or the four elements.
o
These twenty possible interactons appear as the sources in which reversibility and substitution is taken out of the relations between yin and yang at the level 2^6 =64. This is the level of complexity where the I Ching is formulated and also the level at which DNA is structured in terms of its codons. 64 is a special number where the two dimensional can be transformed into the three dimensional without losing information. This is what determines that there are 20 amino acids referenced by the DNA code. This code is error correcting and robustly error resistant.
o
This code appears in the relation between the five hsing and the four receptivies, or controlled virtual elements within the autopoietic system. This appears in the relation of the pentahedron to the icosa-dodecahedron, i.e. between the isomorphisim between the orderings in three and four dimensional space.
o
Icosahedron/Dodecahedron has a lattice of 1-12-30-20-1.
o
This means that the Icosahedron/Dodecahedron three dimensional structure converts the interaction of the hypercycle of the pentahedron, in relation to the four virtual elements that are receptivities from the reflexive special system into action in three dimensional space via the A5 group.
o
The A5 group is what prevents us from solving higher polynomial equations greater than degree five. And this is what prevents us from modeling what is occurring within the autopoietic system mathematically.
o
A5 is probably one of the most important anomalies in mathematics as it severely limits the effectivity of mathematical analysis to lower order polynomials. Higher order polynomials cannot be solved simply due to the asymmetrical structure of A5.
o
This means that it is precisely the same mathematical anomaly that makes the inner workings of the autopoietic system closed, that makes it possible to translate the hypercycle controls into three dimensional action in space. Thus closure of practice to theoretical inspection is entailed in this anomalous structure giving rise to the problems considered by Bourdieu and de Certeau regarding the relations between practical and theoretical reason which was first formulated by Kant in his critiques of Pure and Practical reason.
o
The key idea here is that there are a series of mathematical anomalies that chain together to have a determining consequences in reality and that this series is represented by the Special System and the Emergent Meta-system and is translated into Geometry of the third and fourth dimensions.
Special Systems Theory As A Nondual Nonintegral Singular Meta-Theory – Kent Palmer
o
Each part of Special Systems Theory relates to these mathematical anomalies and their systemic and meta-systemic relations to each other that allows us to translate their consequences from the purely mathematical realm into constraints in physical existence that determine also higher emergent levels such as consciousness, life and the social.
o
Special Systems Theory, Emergent Meta-systems Theory, and more generally Schemas Theory has no elements that are not homeomorphic with mathematical counterparts. Thus the theory has the robustness that appears in the mathematics, i.e. in the possible relations between elements that exist in the math. But it means it also has the qualities of synthesis, synergy, integrity and poise that go beyond robustness at higher emergent philosophical levels. This means due to the ultra-efficiency of mathematical relations seen in the special systems that it has greater robustness than one would normally expect in a theory, that is an arbitrary relation between concepts and relations. And in fact it means that this theory can be used as a criteria for analyzing all other theories because it stands at the limit of robustness, synthesis, synergy, integrity, and poise. However, the caveat is that it describes systems that are not normal emergent syntheses, but rather something between synthesis and analysis and we call that holons and its study holonomics. The special systems define the nature of the holarchy as completely conjunctive in its organization, and therefore anomalous in as much as it is describing swarms, schools, fleets, and other ways of looking at things that is nondual between set and mass approaches to description of the organization of elements. In looking at these elements we can be both precise and also have precission. We can be precise because we are dealing with isolatable holons, but we can be precissive because they exist inseparable from the swarm that they are in. We can call this organization a para-synthesis. It is neither emergent nor supervenient but something else, it is conjunctive.
o
Special Systems are an embodiment of the Nondual and Non-integral.
o
The integral is merely an intensification of dualism. It takes a sum over the AQAL. The opposite of integral is derivative., i.e. identifying a tangent point.
o
Special Systems is neither a summation over arbitrary levels of quadratic categories, nor an accumulation of tangential non-integral points of view.
o
Rather, Special Systems are holonomic, they look at the order of the holons in the holarchy and how they are mathematically defined in relation to each other, and how that mathematical definition spills over into physical relations that are anomalous and give rise to special phenomena like consciousness, life and the social.
Thoughts on Robustness of Theories and Meta-theories The act of writing down propositions in my last message actually led to some interesting insights about the theory for me. And it made me think about the multiple representations that are possible about the theory. First of all this is a meta-theory, and so it does not have many causal predictions, because those would be in the sub-theories, the meta-theory is about constraints. So it seems that is a major problem in trying to formulate a theory which is robust about causality. Thinking about Wallis’ meaning of robustness I realized that he meant robustness in causal relationships, not merely having sets of relationships that are balanced with the conceptual nodes. So in a sense my theory does not qualify because it is about not causal relationships but is about
Special Systems Theory As A Nondual Nonintegral Singular Meta-Theory – Kent Palmer
constraints on causal relationships. In fact to be more precise, it is about how the constraint on entropy is lifted in certain rare situations where negentropy exists, and what are the levels of ramification of possible orders in that region. Sub-theories specify the actual relationships that do in fact obtain. The theory is about the degrees of freedom that are available in neg-entropy and its higher dimensions. It is not about how those degrees of freedom are used in any particular case, that is why it is a general theory of life, consciousness, and the social. It basically says that once negative entropy obtains, here is the mechanism by which organizations are elaborated, but it does not say what specific organizations evolve. What is interesting about the theory is that many of the characteristics of consciousness, life and the social are embedded in the mathematical framework that determines the constraints, and are not particular to life, consciousness and the social themselves. So there are physical phenomena that have similar anomalous structures to these higher phenomena, because they depend on the same mathematical anomalies that manifest as the constraints for consciousness, life and the social. So, in a sense there might be a different criteria for meta-theories than there are for causal theories such as Wallis is aiming to determine the robustness through. They probably have their own type of robustness with regard to how they specify the constraints. This is what I was thinking about not the robustness of causal predictions, because I don't have any causal predictions. I don't really think causal predictions are that important in the realm of consciousness, life and the social. If we can get some that is great, but I expect them to be rare. The best we can probably do is deal with probabilities and covariances as we see in most social science, and whether these are really causal is always a question. To me prediction is not very high on my list of things I would want to do with respect to social phenomena. Rather what I want to do is understand where the discontinuities are in the dynamics of the phenomena, and that is what the special systems theory provides a guide to, and what makes it valuable. As to robustness itself. I realized that the reason I think my theory has a robustness of one with respect to the constraints that it specifies is that it is made out of triangles like the ones that Wallis says are part of the great theories that Wallis mentions, where there are three concepts with three relations, giving a robustness of one in the simplest case. I still think the fact that a tetrahedron would not have a robustness of one is a problem for Wallis’ theory. Robustness should not be a simple division of relations by concepts, but should follow the mathematical possibilities for each dimension. B. Fuller said that the minimal system is a tetrahedron, which I take to be true, as that is the minimal system in three dimensional space in which we are embedded and so if that minimal system does not have robustness of one then there is a fundamental problem with the measure. In two dimensions the triangle is the minimal structure. So what we are saying is that science has mostly come up with robust theories that are two dimensional. We have not really come up with many three dimensional robust theories, that approximate the tetrahedron in three dimensionality space. Anyway, be that as it may, what I realized is that it just so happens that Special Systems theory is made up of triangles of concepts and relations, and one can represent the theory as a cascade of these. So for instance there is the System//Special System/Meta-system triangle. The twist is that in each case these triangles that are part of the cascade of triangles have a special form. They have a form in which there are two duals and a nondual. So for instance Systems and Metasystems are duals, one is a whole greater than the sum of its parts (gestalt) and the other is a whole less than the sum of its parts. The nondual between these is a whole exactly equal to the sum of its parts. This is equivalent to the saying in Buddhism that form is emptiness and emptiness is form. The nondual is a form that embodies the nonduality of emptiness in each case. Therefore, to get to this special type of triangle one must reason thusly: As Badiou says there
Special Systems Theory As A Nondual Nonintegral Singular Meta-Theory – Kent Palmer
must be a pre-numerical state which he calls the Multiple. Then he says that there is an event by which the ultra-one arises. Once one has the ultra-one you can count and you can differentiate one from plurality. The prime case of plurality is two, the only even prime number. Plurality and the Multiple are opposites. Duality and Oneness are opposites. When we specify nonduality we say Not One! Not Two! In other words the nondual is neither One nor Two, but something else. It is non-countable. Once one has exhausted the permutations of the countable, then you realize that there is something else that is non-countable that is outside those permutations. By the way the Integral is merely a re-imposition of duality at the level of the collective, and a crossing of duality with itself, and thus is an intensification of duality. That is why I say the theory is both non-dual and non-integral. Now what we are saying is that in every conceptual triangle within special systems theory there are the two duals, and the third position which is outside that which is nondual that is represented by some aspect of the theory. The third position is not nondual. But it splits itself into another triangle. We see this in the hypercomplex algebras themselves. First there is the dual of x+x, and then there is a symmetry breaking to create the complex number which is x+i. The singularity of negative one via the square root operation yields the orthogonality of the complex plane and we get the circulation that goes 1 -> i -> -1 -> -i. But at the quaternion level you get i turning into i, j, k another a little triangle. Then at the octonion level the i, j, k replicates itself as I, J, K and then gives the opposite of x which is E. So you see that there is a proliferation of little triangles. Tensor math which was discovered by C.S. Peirce as nonions, is the permutation of the relations between i, j, k into nine elements, and that forms an axiomatic platform. Out of this tringle at the quaternion level we get the property of triality, i.e. three way complementarity at the octonion level which is the ultimate in robustness. Three way complementarities are rare. So what I realized is that if one looks at my theory, then one has a whole series of these triangles that are made up of dualities and a nondual element. So for instance there is the System//Special System//Meta-system, and then the Special Systems splits into Dissipative Ordering//Autopoietic Symbiotic//Reflexive Social. All of the analogies have the same form, that is their anomalous structure that makes them recognizable in mathematics. So the fact that the theory itself, to the extent it is true to itself, is made up of triangles, means that it has robustness of one at each level of abstraction. But this robustness has to do with the constraints not causality. And what is happening is that the constraints are such that they produce at low numbers a fusion of elements that has unexpected properties. For instance, the Quaternion imaginaries are related to each other by triality relations in a cycle, but we cannot see into them. They are identical except for their place in the cycle, and their order of generation. This impossibility of seeing into them, but the fact that they are related to each other like Aczel's non-well-founded sets, except that they follow the rule that something can be a member of itself, only through something else, gives a model of interpenetration which is the embodiment of the nondual. Things within the region of negative entropy at the second level where the quaternion rules and we get entry into four dimensional space, are such that they at a fundamental level have to interpenetrate. This is a condition for their existence in this negentroic region where the highest degree of mathematical fusion occurs. In physics we get the cooper pairs of super-conductivity, a phenomena that just should not exist, but was discovered, and took twenty years to explain once it
Special Systems Theory As A Nondual Nonintegral Singular Meta-Theory – Kent Palmer
was discovered as an anomaly in physics. So I guess this is why I would claim a robustness of ONE for my theory. It is all triangles of concepts and relations, that emanate in a cascade, but represent the relation of nonduality to duality in each case until it gets to triality which is three way complementarity, which is perfect robustness as an operation that exemplifies interpenetration. I think one needs to distinguish robustness at the meta-theory level from robustness at the theory level. If you are studying the robustness of causal theories as is Wallis, then what I am offering is a robust meta-theory about constraints. It is embodied by a cascade of robust triangles of concepts and relations. where two elements bifurcate at each level, just like the progression into chaos. The equivalent to Chaos occurs at the Sedenion level where the division property is lost and things fuse because they cannot be distinguished any more unambiguously. This is a fact I had not consciously realized about the theory previously. And now that I know it I need to go back and make sure my theoretical constructs do not violate this principle in the way that I constructed the theory. For all the relations I have reviewed so far this principle holds. So through this interaction with Wallis’ testing criteria I have come to understand my theory better, and that is a good thing. Once I work out the cascades of triangles then that should be a shorter form of the theory which conforms to Wallis’ concept of robustness, but with the caveat that it is about constraints rather than causal relations. We can thank Wallis for his work that has helped me refine my understanding of Special Systems Theory. I have not run into anyone else's work that has contributed so directly to the understanding of the theory as Wallis’ theory concerning the causal testing of theories. So that makes me think Wallis is on to something in pursuit of robust testable theories in the social sciences. But I guess the question my work raises is how do we test a meta-theory. Since it does not make causal predictions, but only sets constraints. I guess we would look for violations of those constraints. That is probably much harder to test than predictions about causality. Probably each meta-level of theory is harder to test because it is much more subtle than the lower metalevels of theory. The testing probably must be much more circumspect at each meta-level of theory. Complexity and Freedom Whatever depth my analysis has just comes from following the math where ever it leads, we only need to be as complicated as the math itself is. But if we are less complicated then we are just glossing and are not really understanding. I am not a mathematician and I don't understand a lot of the math, but what I do understand I try to find analogs for in systems theory so that the mathematics can be understood. For instance, it was Onar Aam that came up with the analog of facing mirrors for the hypercomplex algebra. We have all been in situations where there are facing mirrors, so we can understand that intuitively even if we do not completely understand the imaginary numbers. But by following the mathematics that makes the theory so it has a robustness of ONE, and also have higher principles such as Synthesis, Synergy, Integrity and Poise. if we just face the complexity of the Math itself and try to be true to that complexity how ever much that is, then just as in physics we have a very solid theory as a result. The difference is that in physics it is always a question of which math to use to understand a phenomena and to organize our thinking about it. But in the case of special systems there is only one meta-anomaly that shows up many places in mathematics and what we are doing is taking those representation of the meta-anomaly and piecing them together to get a picture of how they relate to each other
Special Systems Theory As A Nondual Nonintegral Singular Meta-Theory – Kent Palmer
and thus define different aspects of special systems theory. Because there is only one metaanomaly that I know of, then we are extremely limited in our choices of what math to apply to all living conscious social phenomena. It has its own inherent complexity which is not trivial but is not staggering either. We only need to come to terms with that, and that determines the depth of the theory. And it also sets up a criteria by which we can judge all other theories that claim to be about the living social conscious phenomena. Mandelbrot set is very complex but we have great pattern recognition facilities built in so we even though it is an infinite fractal object based on the intensities and their lines of flight on the complex plane we can comprehend it and its amazing patterns quite easily as we burrow down into its endlessness due to the fact that it is a repeating patter, with variations. Quaternions and Octonions are also fractal structures as has been shown. I think Onar Aam was the first I know to create Octonion fractal images at my suggestion in the research group we had with Ben Goertzel and Tony Smith. These are weird shapes but also comprehensible in our pattern recognition way of dealing with complexity. So I don't think complexity is that much of a problem due to the development of Complex Systems Theory and Fractals and other ways of dealing with complexity that are being developed. But even though the complex plane gives us the Mandelbrot set, the imaginary numbers really just mean that there is an orthogonality that can be accessed anywhere along the real number line, but which unfolds from the number -1 as a singularity. All the other hyper complex numbers are the same, they are separate orthogonalities that appear from various singularities that produce via the square root of the singularity an orthogonality. What is in that space is complex. For instance what is in the Quaternion space is the fourth dimension. The weird properties of the fourth geometrical dimension probably come from its coincidence with the Quaternion orthogonalities via the break out of hyper imaginaries. But even though what is in the space is complex, like hyper-mandelbrots, i.e. Quaterbots, we can understand it through our pattern recognition capacities. The idea of orthogonality merely comes from the ideas of True, and Right taken together. One is an aspect of Being and the other is a nondual at the core of Being.
So all the complexity goes back to things that are simple but anomalous in their structure verses what we expect. We don't expect orthogonal spaces to unfold from singularities. And we don't expect that conjunction will allow order. The symmetry breaking between x+x to x+i is quite surprising. But once one knows this happens as we are taught in higher math classes then we come to expect it. First of all the unpredictability of Complex systems is a way that Freedom and manifold possibilities are made accessible to living, conscious social systems that is not available to many physical systems that are deterministic. Second of all the precision of QM is in its characterization of probabilities, not determinacies. And one thing that QM shows us is that low probability events are possible and can be actualized like Quantum tunneling. So it seems to me that we are built in such a way that Special Systems can be understood by us, in as much as the actual generating structure say of hypercomplex numbers is fairly simple, but their ramifications though complex result in fractal patterns that we can recognize and deal with by our prodigious pattern recognition capabilities. The fact that neg-entropic systems have a different basis for ordering is the surprise. But the fact that they are not completely determined is in fact what generates the space in which evolution can take place. At the level of consciousness it allows for many different conscious states, and myriad forms of "enlightenment" and endarkenment. At the social level it leads to all the worlds and worldviews and languages that we are driving to extinction as we drive other species to extinction, but which in their staggering variety shows the
Special Systems Theory As A Nondual Nonintegral Singular Meta-Theory – Kent Palmer
proliferation of realized possibilities. So I think the fittingness of our capacity to understand the mathematical anomalies is quite striking. I am not a mathematician and I can after study understand a lot of it. It is like anything if one applies one’s self to it one will eventually get an inkling. Of course, it helps to have very intelligent people explain it to others, as Onar Aam and Ben Geortzel did for me with respect to Special Systems Theory when I first developed it. They offered a lot of great suggestions as to how to improve the theory. But by reading all the math books on the subject, which i not that many I made good progress even before I met them. Once one has absorbed a few analogies and get the gist of it then it is not that difficult to reason about the set of hyper complex systems. I think the fundamental problem is the making of the commitment to understand the mathematics, rather than following ones own inclinations in thought. The problem we have seen over and over in physics is that theories that come from our own inclinations tend to be wrong, Aristotle's theories of physics for instance which clouded the issue for almost two thousand years. The only difference is that with special systems there is only one meta-anomaly and so what we are trying to get a grip on is the way that this meta-anomaly manifests in different types of mathematics and how these representations fit together to forge the special systems theory characteristics. In other words in special systems theory we are severely constrained by the math as to the structure of the theory, rather than trying to figure out which parts of math to apply to a given phenomenon. It is as if mathematics itself has an optima and that social conscious living things tend toward the realization around this optima.
What is great about this situation is that we can measure our understanding against the criteria of the mathematical representations of the meta-anomaly. In other words whatever ideas we have that are not founded on the meta-anomaly representations but just our opinion are suspect, and anything founded on the direct transformation of the representations of the meta-anomaly are rooted in the ground of the mathematics and have foundational stature. So we can measure our own thought against the criteria of the mathematical structures. So for instance, Scott Anderson’s time line theory, to the extent that it represents the underlying mathematics it has a chance of being correct, and to the extent it represents his own opinions and personal inclinations to deviate from the structures of the underlying mathematical structure then it is open to question. It also means that no one owns the theory. Wilber owns his theory because he just made it up as a set of categories which like Aristotle's attempt to cover everything known. Unlike Aristotle's categories Wilber's are not that well thought out. But still he just made up the dualities that he thought might work, and it just so happens that he built structure that intensify duality and are thus nihilistic, even though he passes them off as being "enlightened" in some sense because they are "integral" i.e. they cover all the possibilities that Wilber can conceive. (There is more in the world than is imagined by your philosophy, Horatio, is an apt line to apply to Wilber's endeavor). But unlike Wilber's theory no one owns the Special Systems, except maybe the Egyptian Priests and others like Fa Tsang, as well as other Buddhists and Taoists, who created images of them in other cultures, or Plato within our tradition who tried to pass Egyptian wisdom on to the West but failed ultimately. But the special systems carry with them their own criteria for understanding them. And thus one can measure one’s own understanding against those criteria. One might say that the Meta-anomaly owns itself as a basis for a systems theory. My special systems theory is an approximation, that represents the limitations of my understanding of the meta-anomaly and how it can be translated out of mathematics proper into a systems theory, using the resources of other existing theories that already approximate the various sub-theories within the Meta-theory as a whole. But what fascinates me is that man’s facilities seem particularly adapted to understand special systems theory. That is why we have acupuncture, because even though people did not
Special Systems Theory As A Nondual Nonintegral Singular Meta-Theory – Kent Palmer
understand the mathematics underlying it, they understood the way that things worked according to the Tao, which was shaped by the meta-anomaly in mathematics as it manifests in the life of social conscious creatures such as ourselves. The fact that acupuncture works, but cannot be understood in terms of Western causal models is a fundamental example of how when we approximate the special systems theory closely we get efficacious results that we would not normally expect to be possible. Special Systems Theory as Nondual and Nonintegral Special Systems Theory is holonomic. And also it is a picture of the nondual. But that also means that it is a nonintegral theory as well. Nondual means Not One! Not Two! Not Many! i.e. it not only does away with plurality but also monism. It describes a vantage that is not part of the combinatorics and positionality of any conceptual or physically realizable system. But because Integral Theory as described by Wilber is based on the idea of “All Quadrants and All Levels” is the sine quo non of so called “Integral” Theories. Here the word Integral means the same thing as Integration in Calculus, i.e. the summation of all we know about in a comprehensive framework. Of course, the audacity that we can know that much is pretty amazing. But more fundamentally we must realize that Wilber’s Quadrant is an intensification of dualism which is precisely the opposite of the nondual, as exemplified by the Special Systems. Wilber takes the subject object duality, and repeats it at a collective level defining the intersubjective and the interobjective as other quadrants beyond the subject and object. In essence he takes the idea of dualism and repeats it at another level of collective phenomena rather than individuated phenomena. Thus the Integral framework is an intensification of dualism rather than something that moves toward the nondual. It also introduces hierarchy rather than the rhizome of Deleuze and Guattari and is thus arboristic rather than decentralized and nomadic. Special Systems are decentralized and nomadic and do not fare well in totalitarian regimes of either monism or dualism, or hyper-dualism. Thus Special Systems are not just embodiments of the Nondual they are also Nonintegral as well, and the Nonintegral is the opposite of the intensification of dualism given the name Integral by Wilber and his followers. The Quadrants are based on the number of persons in language. But it turns out that these are not universal as seen in "Person and number in pronouns: a feature-geometric analysis" by Heidi Harley, University of Arizona and Elizabeth Ritter, University of Calgary says "The geometry in 6 (a figure) also captures the intuition that so-called 3rd person is in fact not a true personal form. As Benveniste emphasizes, ‘the ordinary definition of the personal pronouns as containing the three terms, I, you and he simply destroys the notion of “person”’ (1971:219). This intuition is encoded in our geometry because the Participant node represents only 1st and 2nd person. When the Participant node is absent, the underspecified Referring Expression node receives a so-called 3rd person interpretation." "However, without external stipulation and assuming the geometric analysis, we might expect to find languages that are exceptions to Greenberg’s universal because they fail to activate the Participant node altogether, or they fail to activate the Addressee node dependent upon it. In other words, there might be a language that lacks 1st and 2nd person pronouns altogether, or has a single pronoun or set of pronouns for all discourse participants. We conjecture that a language with no 1st or 2nd person pronouns is a language with no personal pronouns. In fact, this has been suggested of Japanese, Thai and other Southeast Asian languages, which use titles, kinship terms, names, etc. in place of pronouns.40 If this is indeed the case, then these languages make no use of person features. We would expect that such languages would also lack verb agreement for person (as well as number and gender). This is certainly true of Japanese and Thai." "In short, Greenberg’s claim that all languages have pronoun systems with at least three persons
Special Systems Theory As A Nondual Nonintegral Singular Meta-Theory – Kent Palmer
and two numbers is subject to exceptions, and the exceptions attested are in fact expected, given the geometry proposed here. What we predict not to exist are languages that use the same pronoun (or in a language with cases, the same set of pronouns) for both 1st and 3rd or both 2nd or 3rd persons. In fact, none of the languages we looked at has such a pronoun or set of pronouns in its inventory."
I think persons in language is a very complex subject. Three persons just are not enough. I liked Clint Fuhs idea of a fourth person. Even though supposedly it is not grammatical according to the article. It is of course gender, as I have written previously. Women/Men are not kinds of a kind but modifications of a kind. Steven G. Smith was wrong about women/men being a kind of a kind, at least from a category theory perspective. So one can see that beyond the second person things get all mixed up. One can only count or distinguish between count and mass after individual differences are seen.
Fifth (fluctuation?) [bystander???]
Fourth (modification) = Gender [narrator???]
Third (natural transformation) = Other (class, kinds) [character]
Individual
differences
(makes
possible
number)
-------------------------------------------------------------------------------
Second (functor) = Addressee [reader]
First (arrow) = Speaker [author]
Zeroth (element) = empty person of children's talk in acquisition
Negative One = anti-person = enemy (war)
Negative Two = non-person = slave
--------------------------------------------------------------------------------
Negative Three = non-human = animal
Negative Four = inanimate
Negative Fifth = The Blob. Solaris the planet etc. Monstrous non-individuated
All this is just made up to show how complicated the question is. But the point is that four quadrants do not cut it. The problem for me and my own work on perspectives is by this model a modification is related to a narrator. That is hard to understand. Will have to think about this for a while. But I like the idea of five positive and negative stages of person centered around the zero person.
Special Systems Theory As A Nondual Nonintegral Singular Meta-Theory – Kent Palmer
There are a lot of interesting relations here. For instance there is the general addressee, but there is also the addressee who is also the anti-person, i.e. the enemy. And we see that especially in the Iliad where two fighters meet. They discuss their respective genealogies, and then they fight and one dies. It is the killing of the genealogy that is important, and the person is merely a representative of the genealogy. But addressing the enemy in war is a huge area of human endeavor, where the enemy is the addressee, not one of us. For instance the conversations with Patroclus are of the later sort where as an Addressee he is part of the We with Achilles so much so that Achilles lends him his amour. Of course, Braises is Achilles war gift, part of the booty, that Agamemnon snatches when his war prize is taken from him by Apollo. She is a non-person. When Achilles goes berserk then he becomes non-human, like a force of nature killing indiscriminately. When Achilles kills Hector and refuses to give up his body after dragging it around the city, he treats the body as something inanimate. And only becomes human again after the exchange with Hector's father when he gives the body back so it can be buried with full honors rending also the body human again, In the Iliad the river seems to act as if it were the inhuman blob, the force of nature that has no care for humanities finitude. Achilles is likened to the river when he goes berserk as I remember. So all the negative persons are just as important as the positive ones if not more important. I don't think this hierarchy is completely correct, it is not completely consistent in the negative range. There is the mixture of non-X and anti-X which is not really the same as different levels. But the whole way we talk about persons is a little crazy because we talk of ourselves as first persons, while actually we are probably second or third. The Addressee is probably really the first person, because they are near at hand and fully present. The third person can also be present. We actually infer our own existence from them so we are at least third in reality. This is why Dasein is first and foremost embedded in the Mitsein primordially. So calling First Person "First" is a prejudice of our culture that is egocentric. Once one starts renumbering the persons then thing really get messed up. So we won't do that. What is really odd is how the all the other persons get mixed up in the third person, as Other in languages. I think we might want to appeal to Badiou here and his idea of the Multiple. Really Other is Multiple, and there is a struggle for the ultra-one to appear so there can be differentiated different persons. Probably the Addressee is the first of the persons to arise. Then probably the Otherness is differentiated into a plurality. And very last of all the speaker becomes differentiated. Then in Western culture we set up the speaker as subject, as ego, as individuated and individualism arises, and the speaker becomes FIRST person, and as first person he starts counting out from himself when he creates grammar. It is no accident that Foucault uses a Grammar as the basis of his discussion of the Classical (Cartesian) period where dualism is installed. Grammar establishes the duality as fundamental that Descartes posits. Later we realize that the Other of third person has all sorts of odd persons in it as well as count verses mass and other differentiations like classes. What all this says for Wilber is that his reinforced duality, by making the subject/object dualism operative at the collective level as well as the individual level, assumes that the Multiple has been broken by the appearance of the ultra-one. It assumes that the grammar is in place to give numbers to the persons from the subjective point of view. It assumes Indo-European bias. It raises the status of the inanimate objects by putting them on the same plane as the third person. The duality between the third person as intersubjective and the inanimate as interobjective is artificial in the extreme, and only is there as a way to deal with objectivity of things, contrasting them with groups of people who can be Other. But linguistically, and even psychologically, inanimate things hardly figure on our scale of things we deal with in the world, even though to our culture they have been raised on high by industrialization and commodification. We can never take the
Special Systems Theory As A Nondual Nonintegral Singular Meta-Theory – Kent Palmer
eccentric and extreme Western worldview as a norm. It has intrinsic duality of Subject and Object, which philosophy has been trying to overcome since Descartes, and Heidegger was the first one to figure out how it might be done with his Dasein concept of the pre-subject, prior to the arising of the subject/object dichotomy. But if we look at the linguistic evidence objects are normally way down on the totem pole of persons, and so we have raised something that normally would be marginal and at the bottom of the hierarchy of interest to the top, and we have centered the ego at the first person, because we invented grammar from our own perspective and gave the numbers to the persons, but in many cultures the individual comes last not first. I am still trying to figure out how the narrator fits into the hierarchy of persons. It could very well be that it is not a hierarchy and that representing it as if it were a number line is the first mistake. This is especially obvious when one starts seeing contrasts between anti-X and non-X. This is just a clarification and some caveats about the model of persons I have proposed to counter the idea that there are only the three persons of grammar. And I give Clint Fuhs credit for this insight by referring to the fourth person, although what he called the fourth person is probably wrong. For my theory the fourth person is the narrator. The point of all this is that Quadrants are not exhaustive nor universal and thus covering all the quadrants that intensify duality, are not completely integral. Because the special systems are based in large part on Hyper Complex Algebras, and these algebras are related directly to the fourth dimension, it is clear that Nonduality is embodied by four-dimensional structures. Thus any Nonintegral Nondual theory should be built on structures related to the structure of the fourth dimension. Just to be clear the persons beyond two and negative two get mixed up in the third person. That is what the lines in the diagram of “persons” mean and that is what the geometry of persons in universal grammar article suggests.
