What are the “nerves” of a schema?
An inquiry into Structures of Patterns, Essences of Forms, Nuclei of Systems, and Nexuses of Meta-systems.
There is a concept in Chinese called LI. 理 Li (Neo-Confucianism) | Wikiwand
This term means both principle and pattern. The example of pattern is the exact configuration of content on the surface of a jade stone.
Notice how the content of the stone has various colors which have particular qualities that appear as dark and light veins in the substance of the jade. This is Li as specific concrete pattern. The patterns are always unique.
Li also means Principle in which case it means how the unique patterns are generated. In other words, before the pattern appears there are constraints on what sort of pattern could possibly appear in the circumstances. You will notice that the pattern that does appear could have been slightly different in many ways but overall given the circumstances in the jade formation certain types of pattern are probable and among those one gets actualized.
Patterns that do appear take time to manifest, but the Principle of generation is there prior to the actual pattern appearing and the principle is embodied by the pattern that does appear. In different circumstances different types of LI apply, and thus there are myriad Li for every type of possible pattern.
The actual development of the pattern Li based on the principle Li is brought about by Chi which is the subtle energy by which the content is moved to its final configuration through the process of development. For instance, the growth of the living tree that produces the rings in a tree due to growth patterns in different seasons over the years.
We mostly understand these ideas based on Complexity Theory and Chaos Theory, as well Dynamics of various kinds. But our view tends to be abstracted from the concreteness of the patterns and principles at work in the Chinese perspective. To us Principle and Pattern are different things. But the Chinese saw them as two aspects of the same thing.
However, it seems to me that it is useful to think of Principles as generators of instances of schemas. Principles are always concepts for us which are abstracted from particular situations given a specific perspective. But concepts are understood in terms of exemplars and prototypes as well as abstractions. Thus we can think of the principles as being concepts, abstracted from a situation given a particular perspective in a specific domain that generate exemplars and prototypes that have in their concrete realization specific patterns of content. Content is monadic, i.e. bundles of qualia in concrete configurations. Those configurations are the patterns which are myriad and specific to the circumstance of their realization. But this content tends to be seen as something that fills the form, and thus gives a pattern of content that is exposed on the surface of the form.
The form is the overall shape of the thing, for instance a bowl made of a burl of wood. The content is determined by the substance, in this case burl maple wood that goes all the way through the bowl, but the content is exposed on the surface of the bowl to give patterns determined by the grain of the wood which exhibits the growth and force patterns that played out in the development of the tree to produce the burl that gives us its unique pattern of content. In this case the cellulose wood cells are the monads, that make up the content of the form, and produce a pattern on the surface of the form of the bowl.
Li is the specific pattern in this case that is the frozen result of the dynamics of Chi that produced the pattern during the growth of the tree.
But the underlying principle LI is what is behind the growth of the Burl on trees that produced that specific pattern.
The difference between Schemas and the Chinese concept is the level of abstraction. Schemas cover all instances of a particular dimensional configuration. There is just one pattern schema that can be either one or two dimensions. And that fits into a Form schema which is of two or three dimensions. Everything which is one or two dimensions can be seen as a pattern and everything that is two or three dimensions can be seen as a form. We see two dimensional pattern and form together in a watercolor painting for instance.
The difference between Schemas and the Chinese concept of Li is that Pattern schemas are universals within specific dimensions covering all things within spacetime in that dimension as either one schema or another in a given dimension. Schemas are holonic in that they face two different schemas and they relate part to whole. They are templates of Understanding of spacetime configurations that are immediately intelligible. We look at the painting and we immediately see the patterning of colors within the outlines of the form of the branches. Every bit of color soaked into a particular spot on the paper are monadic qualia content, in the case of water color seen as mass effects.
Schemas are phenomenological in the sense that as you look out on the world — the schemas are the things you naturally see if you are brought up within the auspices of the Western worldview. Whether they are more general beyond our culture is an open question. But within our cultural tradition within the West they are well defined philosophically and historically within our tradition of aesthetic connoisseurship and artisan-ship.
Once we realize that within our tradition there are a series of schemas … monad, pattern, form, system, … that nest and between which there are no gaps and are thus are well defined phenomenologically in practice, then it is possible to see what the term Software Pattern means, which is a pattern of forms. In other words, we can read the hierarchy of schemas in two directions. Normally we consider a pattern of monads as we have been considering. But we can also read the series in the other direction as Alexander did who created the Pattern Language in the context of his Timeless way of Building that produces a quality with no name. The quality with no name is what you are aiming for in each case if you are to build something aesthetically pleasing as a living environment for human beings. Engineers are inherently crippled in this respect as they have no idea at all concerning the quality with no name. The best they can do is sense smells. But that of course is merely a way to talk indirectly about Li. Primordial natural pattern generation by humans that give configurations that fit human beings in all possible ways as living environments that are not just aesthetically pleasing but brings the best out of the experience of life in terms of affordances within the lifeworld. Patterns Languages concern the patterns of forms that produce the quality with no name at various scales based on some amorphous undefined principles rooted in our inherent knowledge of human dwelling. [Living Spaces] Alexander specifically told the software community that their use of his idea of ‘Pattern Languages’ did not capture its essence and were not what he was talking about in his books. But this reduction from what Alexander was indicating that goes beyond words to Software Pattern languages ends up being their reduction to patterns of forms which capture configurations of forms that turn up often and seem to work well in Architectural Design of Software Systems.
But what this alerts us to is the fact that we can have monads of patterns, and forms of systems, as well as patterns of forms. The reversal of the normal series of the schemas and their pairing lead to new ways of looking at things as Alexander discovered. The monad of the pattern is very much like the Chinese concept of Li. It is an irreducible pattern generator that is unique in terms of organization and quality [Grenander, Ulf, and Michael I. Miller. Pattern Theory: From Representation to Inference. Oxford: Oxford University Press, 2007.]. The form of a system is more or less the kind of a system. That is to say one particular systemic configuration that is different from other systemic configurations. We might think of them as something along the lines of Isomorphies in Len Troncale’s sense.
Forms have essences traditionally. The essence is the constraints on the attributes of the form. Attributes are parameters that characterize the content of the form. The equivalent of the essence of forms at the pattern level could be called the Li, i.e. the principle by which the pattern is generated. In the West we do not have a general term for it. But instead we use the term “structure” which is static rather than dynamic. We consider the structure of a pattern the underlying rules or algorithm that constrains the generated pattern. Example is Mendeleev’s periodic table of elements.
Within our tradition generally we can say Essences are to Forms what Structures are to Patterns of content, i.e. Monads.
At this point we get to Hegel’s fundamental critique of Formalism in Kant, which is that if forms do not comprehend their contents then the contents are in themselves, but if forms comprehend their contents then the contents are for the other. i.e. the form. And forms cannot be for themselves unless the others are for them. Self-knowledge only comes through the mediation of the other. This critique was the beginning of taking seriously the need for structuralism within our tradition. If forms do not care about their contents and are blind to them then they lack understanding of their content and therefore they are not truly forms but some degenerate type of comprehension that exemplifies ignorance of what is contained in the form. Basically, Hegel was saying that for form to be for itself it needs to comprehend the structure of the content within it. Everything needs take into account for self, for other, in self and in other for full comprehension that can call itself self-conscious knowledge. If content is in itself, but not for form, and form is in itself and not for content, then this is not real knowledge. Only if the content is for the other of form, and the form is for the other of content, only then can content be through its structure for itself, and form through its essence be for itself. In other words the essence of form mediates the structure of content and the structure of contents mediates the essence of form to each other. That is self-conscious knowledge as opposed to mere consciousness. Only completely self-conscious knowledge can be fully rational.
The same is true for Systems and Forms. We don’t have a term for the equivalent of the essence of a system or the structure of a pattern. But in physics the inner structure of the atom composed of different fundamental particles which is stable is called the nucleus, so we could use that term for the core of the system. This is of course an analogy. Systems are gestalts, i.e. backgrounds on which forms appear, that background can be conceived as the boundary of the system, that contains several forms within it that each can be figures on the ground of the system for our inspection. The dual of the System is the Meta-system, i.e. what lies beyond the boundary to the horizon of the environment. Systems also have a dual which is the process with its meta-process. The duality of system and process is constrained by the nucleus of the system/process. Once we have a name corresponding to essence (form) or structure (pattern) in this case “nucleus” of the system/process as well as the meta-system/meta-process then it is possible to apply Hegel’s criteria to the relation of forms to system.
Nucleus is to the System what Essence is to Form and Structure is to Pattern.
Therefore, forms within a system can be in themselves, for themselves, for others, or in others and the same thing is true of the system.
If a system does not comprehend its forms then the forms are in themselves, and the system is in itself. This state is called extension or what reigns is pure substitutability. But that means that the forms are blind to the system and the system is blind to the forms it contains. But this is a degenerate condition which lacks complete knowledge of both the forms and the system. Forms need to be understood by the system that contains them, just as systems need to comprehend the systems that contain them. Thus, the forms of the system need to be for the other (system), and the system also needs to be for the other (forms). And they do this through the essence and the nucleus. The nucleus of the system needs to comprehend the essences of the forms within them, and the essences of the form need to comprehend the nucleus of the system that contains them. If both sides do this then they are both for themselves by being for others. I.e. the System that has a nucleus that comprehends the essences of the forms in contains is for itself, i.e. self-conscious at the system level. And on the other hand, the Form needs to have an essence that comprehends the nucleus of the system that contains it in order to be for itself, i.e. self-conscious at the form level.
Notice that essence of form is a holon because it needs to comprehend the structure of its content looking down and the nucleus of its system, if it is in a system, looking up in the hierarchy of schematic containment. And it is this holonic nature of the essence that makes them like concrete universals, i.e. exhibiting internal relations between the contents it contains and the system that contains it as mediated by form through this essence.
With regard to the System level, which is a whole, then we get the internal relations between the parts of the system which is the way that the nucleus of the system manifests. Internal relations appear as negative information within the closure of the system.
But wholeness is not specific just to the System Schema as Hegel thought. Wholeness applies to every schema with regard to its closure and therefore negative information can appear at any schematic level, not just the system level as Hegel thought.
When we say that an essence is a constraint on attributes of a form, that constraint is negative information, i.e. a counterfactual. Similarly, when we talk about structure as a constraint on the characteristics of a pattern, that constraint is negative information, i.e. also a counterfactual. The same is true of the nucleus of the system that constraints the features of a system, the constraint is negative information and thus counterfactual. Counterfactuals appear at the level of hyper-intensional logics.
Essences to a certain extent are intensional in as much as they are like templates with slots for attributes that have variation, in which different elements that mean the same thing can be substituted, for instance red and green are both colors. Based on these intentional attributes and their substitutions we generate possible worlds. And thus possible worlds theory is the outgrowth of the problem of intensionality, i.e. that extensional substitution does not explain everything.
Counterfactuals are things that are not the case. We can define impossible worlds at the hyperintensional level that are totally based on counterfacturals. Worlds are schemas so in general there are counterfactual impossible schemas that need to be defined hyperintensionally. Belief is one of those hyperintensions. In hyperintensions we are substituting noesis rather than equivalent noema and thus getting differences.
Once we have seen that we need a concept related to a system that is equivalent but different from essence, i.e. unique to the emergent level of the system because it deals with features not attributes, that is to say the idea of the NUCLEUS of the System. Then we can recast the whole question in terms of these various types of schematic “essences” by asking what is the relation of structures of patterns, to essences of form, to nuclei of systems. The best example of a formal structural system that contains all these three schematic levels is Architecture of Systems Problem Solving by George Klir.
Klir bases his theory at the level of pattern and talks about configurations of variables, and he uses these configurations of variables to describe the level of forms and system. Thus in a sense he reduces form and system to pattern, the lowest common denominator. This makes his Systems Theory primarily structural. What if we don’t want to do this reduction but instead want each schematic level to stand by itself as well as to interrelate with the others in a nested fashion. Then we would have to complicate the picture given by Klir by introducing essences and nuclei of the system. Klir more of less assumes that variables can stand for any of these levels which is true but still this is a reductionistic account.
Structures organize all the possible characteristics within patterns. Essences organize all the possible combinations of attributes within forms. Nuclei organize all possible features of Systems. But organizing the characteristics, Structures allow all possible patterns of a certain sort to be generated. By organizing the attributes, Essences allow all possible forms to be generated. By organizing the features, nuclei allow all possible systems of a specific type to be generated.
This pretty well means that Principle, in the sense of Li can be thought of as the meta-structure of structure. And by analogy there may be a set of principles related to forms, that are quintessences, or meta-essences. And also there may be principles that are meta-nuclei of systems. These second order structures, essences or nuclei only have a name with respect to form which is quintessence, that is traditionally related to ether as opposed to the four normal Greek elements of earth, air, fire, water. In other words, it is though as a sublimation. Essentially these are meta-constraints on constraints which are rules that constrain rules that constrain characteristics, attributes or features. This sublimation at the higher degree of the structure, essence or feature has the right to be called a principle in all cases. Interestingly there is no general term for what is called here structure, essence and nucleus. But we can call them a “Nerve”. [Nerve (category theory) | Wikiwand] So a principle governs a nerve which in turn governs the wholeness of the schema. This essentially gives us then the equivalent of the Chinese Li in our Western thought structures except for the fact that the Chinese work up from the concrete case to the abstraction rather than starting from the abstraction and working down.
Notice that these powers of the sublimation could go up several levels. These specifically are articulated in the design field in my second dissertation. See General Schemas Theory Research. There is essentially a Cartesian cross of the Philosophical Principles and the Meta-levels of Being. But we can simplify this with regard to nerves by marking the level of their powers: Nerve^p. A lot of times in Science the Nerve^3 level are called Laws, as in laws of nature. Laws are necessary, and in this sense the constraints are constrained by necessity.
Our point here is that All schemas have nerves, and that the nerves have powers. Nerve^1 is the nerve itself which organizes the content of the schema giving it structure, essence or a nucleus in the cases of pattern, form, and system. Nerve^2 are nerve related constraints of constraints called principles, and Nerve^3 are constraints on constraints of constraints called Laws. All schemas have the equivalent of nerves, and the meta-levels of constraints up to the definition of contingency and necessity. A good source for this kind of model is Monod Chance and Necessity. Monod constricts a teleonomic system by interleaving layers of constraint and necessity which is how he thinks evolution works. But between contingency and necessity there is also conditionality which means that things are not random nor determined but conditional based on circumstances.
So let us extend this idea to the level of Meta-system (OpenScape). This schema is what exists from the boundary of the system to the horizon in the landscape in which the system exists. It is detotalized and disunified and a general economy rather than a restricted economy in the sense of Bataille. It is based on compementarities and is formally defined by the Universal Turing machine as opposed to the normal Turing machine. It can be described by rules just like the system, but the rules have to do with the allotment of resources and signaling using protocols between systems within the meta-system and also to the meta-system by the contained systems. Meta-systems a lot resources to Systems within their arena. Meta-systems are composed of source, horizon origin and arena. Systems and anti-systems appear from sources within the arena at origin points and they move through and interact with each other and their environment within the arena until they exit through anti-origins (sinks) and return to the source. Object Oriented programming systems are an example. The source is the object template. This object template gets instantiated and then is executed interacting with other objects within the system, until the various instances are killed off. The objects interact by calling each others methods with parameters which then allow the objects to change their state of internal data based on the interactions and call other objects. All the objects in the same application together are called a system. Our question is what is the nerve of the meta-system or open-scape. There is no name for it. In general meta-systems are invisible to us within our tradition. The only way we can see them is producing the inverse dual of the system realizing that the system is not self-dual. What is the non-self-dual dual of the System. We call it the Meta-system or OpenScape.
But the Meta-system schema’s nerve has no name, but we can call the nerve of this schema a “NEXUS” in the Meta-system or OpenScape. This is because the nexus of a meta-system is normally a constraint on complementary opposites that characterize the field of the arena within the meta-system. We will call what the nexus controls by its constraints field properties. In meta-systems these field properties are complementary like between electricity and magnetism. Once we have the name of the nexus that constrains the field properties then we can consider the relation of the meta-system to the systems that it contains in terms of Hegel’s critique. If the systems are in themselves and not for the other then we are merely conscious but not self-conscious of them. Thus we need to make the systems for the other of the meta-system and the meta-system for the other of the system. And if they are for each other then the system and the meta-system are for themselves rather than just in themselves. You can only be for yourself through the other, being either the contained or the container.
This plays out in an interesting way in relation to the system and meta-systems because either may be either emergent or de-emergent. Emergent Systems are wholes greater than the sum of their parts and they overflow supervenience, isomorphic relations between superstructure and base. De-emergent systems are taken apart by analysis and thus do not have their emergent properties that they would have if properly assembled. This is like the difference between a car taken apart or put together by the mechanic. But interestingly usually the meta-system is considered de-emergent, in other words it is the field or proto-gestalt within which the parts are arranged in relation to each other when taken apart, i.e. the floor of the garage on which the parts are strewn. To the mechanic this is a field in which the parts have dispositions to go back together to make the car work. To an ordinary person they are just junk thrown out on the floor with no implications with respect to each other. But there is a possibility of an Emergent Meta-system, i.e. a meta-systemic field with its own emergent properties. And this is produced by a combination of the special systems (that appear in the interstice between system and meta-system) along with the normal system which gives an Emergent Meta-system. We can characterize the difference between emergence and de-emergence in terms of the realization of inner relations between parts. Thus we can characterize the difference between in itself and for itself of Hegel, along with for others and in others as the means to distinguish emergence from de-emergence, or what we have known up till now as the blindness to content or the blindness of the content. So when the systems are in themselves and the meta-system is in itself then it is merely supervenitent. But if the system contents become for the other of the meta-system, and the meta-system becomes for the other of the system, then they escape supervenience. The system then becomes a whole greater than the sum of its parts, and the addition is what the system knows about its contents beyond the mere containment of them. We can use the term “knows” because the schemas are templates of intelligibility of spacetime configurations. Schemas are a kind of knowledge of things organized in spacetime. In other words the system schema, it knows and responds to the essence of its forms. And the same thing can be said of the meta-system except it is always a whole less than the sum of its parts. That means that what it knows of and responds to the nucleus of its constituent systems that is always less than the sum of its parts. But if the meta-system is emergent then it knows more despite having holes in the meta-system, i.e. niches for systems, and this appears as its own counter organization that complements the system. Now special systems are supervenient. And that means they have a special knowledge that balances for itself and for others, with in itself and in others, and this is called in-and-for-itself. Special Systems are in and for themselves. This makes them examples of Concrete Universals or in another terminology Holons.
See . . .
In general we can say that it is important to identify the equivalent of the “essence of the form” for all the schemas. We have identified these as the ‘structure of the pattern’, the ‘nucleus of the system’, and the ‘nexus of the meta-system’. And once we have these various nerves defined then we have the ability to think about the knowledge that each of them has about the other, in other words does the contained know about the container and does the container know about the contained in each case. They know about each other by their response to the nerve of each. And these nerves can reach deep through their various levels of sublimation.
Patterns know about the content of its monads via the nerve of the monads that it contains.
Form knows about the content of its patterns of monads via the structure of the patterns of the monads.
System knows about the content of its forms of patterns via the essence of the forms of the patterned monads.
Meta-system knows about the content of its systems of its forms via nuclei of the systems of and the essences of the forms and the structures of the patterns of monads it contains.
Likewise Pattern knows about its form container through understanding and responding to the essence of the form that contains it.
Form knows about its system container through understanding and responding to the nucleus of the system that contains it.
System knows about its meta-system container through understanding and responding to the nexus of the meta-system that contains it.
Meta-system knows about its Domain container through understanding and responding to the nerve of the Domain that contains it.
In each case the relation between the nerves of the schemas make explicit the implicit internal relations between the elements at each schematic level to the other schematic level. These internal relations appear as negative information at each level within the whole of the schema. In this way we address the criticism of Kant and all purely formal systems by Hegel. Every schema has an internal set of constraints that govern its functioning. These internal constraints may function at different levels of sublimation. As we go up these levels they become less correlations and more like causes, less like principles and more like laws. Therefore, when we ask what is a principle or what is a pattern there is a wider framework given by Schemas Theory in which these questions can be answered. We do not just have to answer these questions a vacuum where principle and pattern stand in opposition to each other without considering anything else. Rather, it is much better to consider this question in a context where it can have an answer that is not arbitrary or just conventional. We live in a philosophical and scientific community that tends to be purely formal since B. Russell attempted to kill the idea of Bradley of Internal Relations taken from Hegel. But Hegel’s critique still stands as valid in relation to all kinds of formalists. But how does this apply when we recognize more types of schemas than merely form? We have to identify the nerve of every schema. We have identified nerves for Pattern (Structure), Form (Essence), System (Nucleus) and Meta-system (Nexus). Then we see that the understanding of one schema in relation to another means to come to terms with its nerve, i.e. to recognize it and respond to it coming to know it. Unless you understand the structure generating the patterns then you will never be able to account for it as a container form. And pattern unless it understands the essence of the form will never be able to respond to it properly within its context. So the connection of nerves of each schema to each other is their proper knowledge of the other, and it is only through knowledge of the other that it can have complete knowledge of itself. So basically a given schema is only in itself unless it comprehends and reacts to the nerves of its adjacent schemas, both those it contains and those it is contained by, its containers. But this is the same as having internal relations at each schematic level where each level is treated as a whole itself that is only really known through the other adjacent levels but not purely on its own as a formalism of a given schematic level.