Holon mechanism

Work in Progress: This article is still in the developmental stage. Please do not base any work on this content, any aspect of it may undergo change or be removed at any time without notice.

The holarchy is just an academic curiosity if we can't represent it with a clearly definable "nuts and bolts" mechanism. In other words what data structure is involved at a program level? How does the code operate on it to actually represent the two holon behaviours that lead to the harmoniously evolving and diversifying society of self-organisations?

This article is dedicated to clearly answering these questions, but it does require a software development background to read it. The holarchy article is aimed at a more general audience, but it is also required reading for putting the context and terminology in place for understanding this article, so if you are not familiar with it, please start with that first.

Each of the four quadrants of the model are represented by actual scopes, state and process in a running holon. The run-time environment within which holons execute and progress must provide this basic means of execution itself - each private instance scope is essentially a virtual machine node progressing a self-organisation structure.

The holon has three abstraction layers, the third layer is the actual holarchy society of organisations which is analogous to the "world" consisting of culture and society. The first two layers are what the holon mechanism has to provide.

The first abstraction layer of the mechanism defines execution which takes the form of production rules organised in an evolving class-instance network space. This layer essentially creates the potential for the four quadrants, by creating the distinction between, and usage of, the public and private scopes and the organisation of production rules and their executional performance.

The second layer of the mechanism executes in the context of the private instance scope. This is where the diagonal loops and each of the quadrant loops are defined. This layer essentially extends the basic class-instance environment to enable the collective aspects of resource flow and knowledge evolution and the individual characteristics of developmental and operational progression in time.

Layer one

We introduced the four quadrants conceptually as coming from the individualised form of the class-instance concept being extended to also include a collectivised form of the pair.

Layer one introduces a data structure and a process operating on it that brings about just such a basic individualised form of the class and instance concept. And it permits a complimentary process that represents the collectivised extension of the concept (which is defined in layer two), thus yielding the four-quadrant basis.

For the purposes of this discussion, we start with the assumption that we have a local hierarchical namespace functionality such as an associative array. This assumption is fine in the context of information technology, but in the context philosophy we must even define the mechanism of names and symbols which is an ongoing discussion in the Four quadrant holon philosophy article.

What this foundation gives us in terms of the holarchy is the possibility to create graphs of holons that can contain arbitrary content and relationships to each other. Holons here are within a typical key:value pair space in which the keys are always class-names and values are always instances of that class. Note that we don't depend on the concepts of class and instance existing within our program environment, these concepts are provided by the four-quadrant holon mechanism extending the basic associative array functionality.

Two trees

In terms of data structure, class and instance are a pair of graphs that each relate the single set of holons together in two distinct, but complimentary, grouping strategies. We call these two structures trees, although technically only the instances are connected in the form of a one-to-many tree, the classes are connected as a "semantic network" that we call the unified ontology.

These trees are very much like what we see in traditional OOP where there is a structure of live actualised instances and an ecosystem of classes from which instances are instantiated and which determines how they operate.

The instance-tree in the holarchy system is easily understood because it's much like a runtime structure of object instances in any traditional running OO program. Instances control a set of "child siblings" as a parent context itself being a sibling performing a function in the next layer of abstraction higher.

As discussed above, the class aspect of the system as a semantic network or ontology, which is formed from all the many local instances of each class. This aspect of connectivity is not so intuitive, because in traditional OOP there is no inherent connection between instances by virtue of them being of the same class.

The class tree is created by a global process of merging all variations of the class across all the instances of it in the tree. The class tree does not define how variations can arise, just how to integrate them into a global whole if they were to arise somehow. The class tree defines the structure of classes, and as a whole defines the shared unified ontology of classes.

The merging of variations essentially means that the parent-child relationships in this tree are not black and white, but rather each relationship is itself a tree of optional relevant variations.

Instances take on the form defined by their respective classes, and the classes are the collective product of their instances. So the class-instance relationship is in the form of a co-evolving feedback loop.

The two-tree process is a way of permitting a tree to extend itself within subjectively. This leads to two separate graphs of one set of nodes, each having an inside-outside perspective of scope that together constitute the subjective world of meaning within. From here the four quadrants can be actualised by allowing mergeable process execution within the context of each scope-pair.

Multiplexing

The two trees are created, maintained and related by a simple process called time-division multiplexing. This is a process by which a continuous flow of executional focus is quantised into arbitrary units which cyclically iterate the entire instance-tree structure.

This iteration process is a movement of executional focus from one node to another. When focus enters a node it's akin to the calling of a function (sub-routine) in a program, because it's moving "down" into a more specific context that is deeper within the structure. Conversely the leaving of focus after completion corresponds to the returning from the function back up the "call-tree" to the "caller" above. The movement downward is a process of division of focus, and the movement upward is a process of information integration, aggregation and propagation "upward", "outward" or "beyond".

As with traditional OOP, or indeed with organisational structure in general, this vertical directionality gives rise to a structured scope system where there is an outer public side and an inner private side to every node. These correspond to the outward-facing and inward-facing concepts in Koestler's holon model, to the outside and inside of a biological cell, or to the public and private property contexts of organisation.

In the holon, the kind of time being multiplexed is executional focus (or agentic attention more generally). The multiplexing movement of focus throughout the structure is a repeating pattern determined by the structure itself. This pattern exhibits a continuous bidirectional flow of function-like calling and returning. This can be considered as a way of representing organisational structure in general.

The multiplexing pattern of focus moving amongst the scopes is what creates hierarchy and its return. Objectively it's just a flat graph, but the movement of focus over time creates the subjective perspective of hierarchy seen from within private scopes. The return flow makes possible the sharing of structure amongst these perspectives.

Multiplexing in this way can be considered as the "collectivised" version of function calling. The compliment of function-calling is to return the result of action, which taken to it's collectivised version is a scale-independent merging or aggregation operation.

Multiplexing is the mechanism behind our implementation of the blackboard pattern and its decoupled approach to private scope. We now have a system where the operation is decoupled both horizontally (blackboard and production-rules) and vertically as well via the "collectivised" function calling and returning model.

The multiplex: This name refers to the concept of a actual running multiplexing instance, occupying real space, in a particular state and requiring real resource for its continuance and progress. The multiplex only has meaning from within the subjective perspective (described above).

• lead out with connection back to four quadrants

Layer two

The holon (p2p peer) behaves as both collective and individual parallel behaviours (of course in reality they're alternating due to all distinction coming from the multiplexing pattern).

The concepts of collective and individual are defined by how they relate to each other and the shared common environment they maintain together. Both are teli, each progressing in accord with their own particular idea of improvement.

The multiplexing nature of layer one is the basis of individuality, enabling private scope (and therefore also public scope) and enabling a perspective of continuous threads. All multiplex instance tree contexts are structurally within the linear space-time multiplex.

Layer two takes place within this context of non-local class knowledge, actual instance state, both in private and public contexts provided by layer one, all as a structured mosaic of independent continuous threads.

The common form of progression is the production rule, which can in turn be generalised as a feedback loop between self (self-organisation) and environment (collective p2p or collective-aspect-of-self).

The collective is enabled and supported by the individual behaviour. The bottom-up shared collective process is non-local, not in the linear space-time multiplex, but merged with all locations, and done so in a way that globally synchronises in between consecutive local moments from all local perspectives. This is subjective non-locality, subjective contexts include apparent non-locality.

The diagonals (⤫)

As is quite intuitive and can be seen in the diagram to the right, the quadrants naturally form a diagonal pair of axes. But the diagonals also represent the actual algorithmic/mechanistic connections between the quadrants too. We won't go into the details of the mechanism behind the formation of the four quadrants in this article, but the diagonals are one specific consequence of this mechanism.

There is an important conceptual reason for the diagonal connections as well which is that classes are made specifically to perform in local subjective contexts as instances, and the basis of all classes is a feedback loop that orients the performance towards the form it defines (so that the state and development gravitate around the evolving form of the concept like the Ship of Theseus). What this means is that collective class meaning is defined in relation to individual instance, knowledge is defined in relation to performance, which is the top-left to bottom-right diagonal.

On the other hand, class structure requires real resource backing, and so its collectivisation is the instance world. The instance collective structure is defined in relation to salient class structure, which is a connection between the bottom-left and top-right quadrants.

Within the world of the actual functioning holon developing and operating in its local context, the control loops are both connected to their opposite collective state, and this state is backed by a collectivisation process. The second abstraction layer of the holon takes the form of diagonal feedback loops. each composed of two loops connected together inputs to the outputs of their partner. The upper end is a collective loop and the lower end is an individual control loop.

The functionality of the quadrants takes the form of a pair of feedback loops connecting the diagonally opposite partners.

These two diagonal loops constitute dynamics of second abstraction layer of the model that refine the four quadrants behaviours and connect them all together into a harmonious whole.

How the diagonals are inherent in the mechanism

The diagonal axes are also an inherent aspect of the mechanism we've described above that gives rise to the class-and-instance concept.

By default, the layer one dynamic that bought about the class-and-instance (the multiplexing and its complimentary aggregation process) are also present in the inner subjective scope too (because the scope is extending this dynamic). In the inner scope, we have one diagonal extending the class concept with the objective dynamic, and the other diagonal extending the instance concept with it. In this section, we'll first look at how the diagonals come about in this mechanism, and then go into the details of what they mean conceptually.

The diagonals come from the fact that there are only two ways of combining the horizontal and vertical axes. Conversely we can say that with each quadrant interacting only with its opposite partner, the two original dipoles can be embodied.

The diagram to the right shows the two different ways of combining the original pair of axes. The ends of each axis have been assigned a letter so we can keep track of which are present in the combined results. Each way of combining the axes leads to a new axis connecting a combined pair of ends as shown by the green arrows. These green arrows can then overlaid on the original pair oriented orthogonally to each other, revealing that the green arrows connect the quadrants diagonally.

Executional focus appears in each of these four scope-compositions in order to create the first layer class-and-instance mechanism. Each of these sessions of focus can be extended with a second-level process which yields the two diagonal loops.

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This diagonal axis that consists of the top-left and bottom-right quadrants is the evolutionary loop, and the axis orthogonal to it consisting of bottom-left and top-right is the economic loop.

The evolutionary loop is a feedback loop involving knowledge embodiment and use, and its metrics and selection. The information being aggregated here in this layer two extension is agent centric (knowledge performer), which extends the layer one aggregate that is purely related to the knowledge being performed, not to the performer of it. In other words, the class of behaviour is extended with its instances and their performance.

The economic loop is a feedback loop between producer and consumer. Producer is like the "service provider", defining the terms of engagement and selection. Consumer is the source of demand that animates the flow of resource. The information being aggregated in this layer two extension is the commitment-backed supply and demand. In this diagonal axis, it's the first layer instance context that gets extended by the layer two aggregate information. This loop is the layer two view of the "calling" and "returning" cycle set up by the multiplexing in the first layer.

Intersection of identity and structure

• past and future, knowledge and economy, class and instance

The purple dot in the centre of the diagram is the aforementioned starting point for our description, the focus. The diagonal axes intersect in the centre forming the focus. In this way, the present moment is the intersection of the future and past axes, and the synthesis of the four quadrants of focus.

These perspectives all come together at the conceptual centre of the holon as the subjective self in the here and now. By every holon behaving in both these ways at every scale, a unified holistic evolving indeterminate harmony emerges.

This central point of focus is the intersection of the two diagonal axes, and is shown in the diagram as the purple dot in the centre. Each quadrant's effect on the local shared scope is in accord with its specific conceptual meaning. The process by which the quadrants "come together" in focus, is that each of the four receive independent attentional focus (the attentional energy the holon controls is divided internally into four).

Relevance

• relevance and dependency form the back-bone of the holarchy, form the structure
• relevance and dependency are similar, just that the latter necessary while the former is optional
• relevance is evolutionary

Focus is in the present, but interacts with the past and the future. When in focus, each axis connects their own two quadrants by a matching process.

The past axis is all about agency, the agency that's needed for production in the bottom-right, and the reputable candidates to perform it in the top-left. These comes together in the centre as the relevant candidates.

The supply and demand nature of the future axis match in the middle to yield a potential flow of exchange and production. Potential means that there is nothing missing in terms of local resource, actualisation is a matter of commitment to a process that can achieve it.

This matching process can be performed by the cheapest agency, but can also be guided by any agency present that might choose to intervene. The focus of a holon is within the present moment which is the synthesis of the four quadrant aspects. The matching process at the intersection of the axes is the mechanics of the cognitive architecture. This abstract centre point is the elusive Self in the here and now from the subjective perspective of the holon.

The most relevant types of activity through which energy can potentially flow become prominent from matching the past with the future. Over time this process guides the allocation of energy over the complex landscapes of intention and production to yield the evolutionary collective aspects of ontology and economy.

To merge or maybe not

All activity that takes place in the system is in the form of potentials being reduced by action. The potentials are all in the form of two class names, one as parent and the other as child. This connection once completed generates reputational data which enables the continuously improving local control loops and evolution of the collective.

Both sides of the match are an axis, but are essentially a class-name, so it's really class names themselves that comes with the special non-local extension. Primarily as the extension of instance into the name-connected graph, then in their connection with other names in the parent-child relationship the non-local aspect extends further to the future and past forms of non-local information.

Scale-independence

• subjective non-locality
• decoupled operation (horizontally and vertically)
• continuous-able - scale-independence is not only about size and depth, it's also discrete/continuous agnostic

Multiplexing is a scale-independent process, which means that the same dividing process applies to arbitrary depth (and may be part of larger structure beyond), forming a hierarchy of threads from what is ultimately just a single thread. The width or depth of any local group of threads is all arbitrary in the sense that the multiplexing mechanism itself is content agnostic.

The cycle of top-down and bottom-up movement is used to create the class-tree. Since the process is responsible for dividing the executional focus throughout the whole instance tree cyclically, it also has the option of using a portion of that focus unconditionally for maintaining the class-tree.

Classes are not associated with any specific time or location, which is why the class-tree is called abstract and non-local.

The two trees define the different scopes of operation within the holarchy system. The class-tree defines non-local scope which groups all instances of the same class together regardless of their whereabouts in the holarchy.

The non-local connection of an instance to its class-group does not occur instantaneously, it only appears so from the local POV since it happens between successive quanta of focus at that level. The instance-tree defines public scope (public is not necessarily actually public, it simply means not encapsulated) and private scope which correspond to a specific locations and times.

The general structure of the ontology is defined by what is established in usage. Which path variations are chosen locally becomes a non-local landscape of variation tied to the contexts they appear in. The ontology is thus a semantic network formed by established and evolving dependence and relevance.

Revisiting first-class citizenry

• the origin is private-scope and the concept of encapsulation
• this means the child is responsible for its own actions, and for apprehending the conditions
• encapsulation makes the system decoupled vertically, the essence of scale-independence
• this is the self-assertive behaviour, the support of true autonomy by the collective, and the source of sovereignty and liberty

Mechanism conclusion

First we introduced the four quadrant system generally as a model and what it means from a real-world organisational perspective. We finished that discussion by tying the system in to it's overall alignment to scale-independent harmonious organisation.

Then we introduced a specific mechanism that represents this four-quadrant model. This mechanism is simple and symmetrical, and is entirely mechanical in the sense that all its interactions depend entirely on its own structure and state.

The first abstraction layer is just a pair of tree structures changing in accord with a process that operates in accord with the structure of those trees, yielding a self-organising tree-pair. The behaviour of each tree is simple and deterministic, but yet they're complimentary, and together they open up a second abstraction layer in which the class-instance concept is manifest and usable.

This second abstraction layer is the same dynamic again, but this time in the local private context of subjective value. This local scope takes the form of the two diagonals, the economic and evolutionary loops. Even though this second layer functionality involves high-level concepts, it's still entirely mechanical, extending the first layers dynamics recursively within with the same dynamic again.

This is an amazing conclusion which is hard to believe. It's showing us that there's a class-instance concept inherently hidden within the simple process of multiplexing (combined with its complimentary aggregation process), which is itself amazing. But it goes further saying that when used within the context of itself, this same dynamic reveals the high-level feedback dynamics of evolution and economy. The multiplexing dynamic when connected back onto itself inherently manifests holarchy, the self-organising holarchy of self-organisations.

The primary axes

• todo: this section is too complex, some needs to go to mechanism

First we'll go into a bit more detail about the primary (vertical and horizontal) axes that compose the first abstraction layer, depicted as the blue "+" in the layers diagram above. Each end of an axis represents an aspect of behaviour which is common to two quadrants.

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Cut down version: All concepts that make up the holon model are dichotomies, so in any scope of concern in the model, there's always a clear conceptual division into complimentary pairs.

There is an inherent geometric correspondence of a complimentary pair as being an axis with a centre and a negative and a positive end. For a complimentary pair to actually be represented in some system, it would also need to "contain" structured state of some kind (but we're agnostic to the specific form of the state at this level of generality).

There may be infinite possibilities of form and state that the content structure might take, but they all have these basic geometric qualities in common independently from their content.

When two axes (dimensions) share a common centre but are otherwise independent from each other, we call them orthogonal (geometrically perpendicular) to each other and forming a plane.

An orthogonal pair that both operate on themselves as state can be two aspects of the same state. This is the case with our orthogonal pair of axes in the holon. The two axes each represent orthogonal concepts that each progress themselves as state in their own way.

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All concepts that make up the holon model are dichotomies, so in any scope of concern in the model, there's always a clear conceptual division into complimentary pairs.

There is an inherent geometric correspondence of a complimentary pair as being an axis with a centre and a negative and a positive end. For a complimentary pair to actually be represented in some system, it would also need to "contain" structured state of some kind (but we're agnostic to the specific form of the state at this level of generality).

There may be infinite possibilities of form and state that the content structure might take, but they all have these basic geometric qualities in common independently from their content. When two axes (dimensions) share a common centre but are otherwise independent from each other, we call them orthogonal (geometrically perpendicular) to each other and forming a plane.

An orthogonal pair that both operate on themselves as state can be two aspects of the same state. This is the case with our orthogonal pair of axes in the holon. The two axes each represent orthogonal concepts that each progress themselves as state in their own way.

Both concepts take the form of a scope (namespace) concept with the positive end representing being not within the scope, and the negative side being within it. It's this way around specifically, because outward is multiplying the scale of the scope making it larger and inward is dividing it making it smaller.

We'll talk about a specific mechanism behind this below, but for now we'll just start by saying that the first method of scope is the usual public/private vertical dimension that we're used to with an object from OOP. And that the second method of scope (which is complimentary in its operation to the first) is about time, one end represents that which is in the linear timeline, and the other end is that which occupies the cyclic energy aspect. The top is public, the bottom is private, the left is abstract and the right is actual.

The operations that bring about the primary axes are the first abstraction layer of the model. Both subsequent layers feature these conceptual directions at the most general level of their ontologies. Each primary direction defines behaviour that is common to a pair of quadrants. The behaviours are composable (production rule blackboard) permitting each quadrant to embody the behaviours of both of its adjacent directional influences.

Top (public)

Top represents the integrative behaviour of the holon that contributes "unconsciously" to the collective. The collective unconscious (ontology, culture) and the material state of resource flow (society), it's the scope outside the holon's subjective perspective that maintains the network as a whole.

The top pair of quadrants both progress the public scope, the left in the form of evolutionary progress of knowledge and the right as the flow of resource exchange progressing over linear time.

In terms of time the top represents the future, what's possible, potential and imminent.

Bottom (private)

The bottom represents the self-assertive behaviour of individual autonomy, which in our system means taking the form of a control loop. This is the perspective from within the holon's private subjective scope. The subjective scope is production rule oriented, and represents the self-development and production aspects of the holon. In terms of time, the bottom represents the past that has been created through operation and development.

Private scope consists of a list of sibling names which are all things that "reside" within that same scope, such as information and other agents. The contents of the private scope are "local" to each other.

The bottom quadrant pair both operate as a control loop which continuously brings the local scope to a better state. Both lower quadrants progress the state self, the left subjectively developing the self and the right progressing the objective material state.

Left

The left represents the abstract world which we call class, but it's also Koestler's fixed rules and represents structure, knowledge and possibility. In terms of time, the left represents, the cyclic nature of abstract behavioural patterns (spectrum that's orthogonal to linear time).

Right

The right represents the concrete actualised world inside of time which we call "instance". This is Koestler's flexible strategies and represents day-to-day organisation, exchange and operation. In terms of time, the right represents the visible world of actual resource flowing within linear time.

See also

• Holarchy
• four quadrant holon model needs to be merged and redirected to here
• Philosophy of the holarchy