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 four abstraction layers, the forth layer is the actual holarchy society of organisations which is analogous to the "world" consisting of culture and society, and was the layer focused on in the Holarchy article. The first three layers are what the holon mechanism has to provide to enable this forth layer, and is the focus of this article.

Layer 1: Instance (|)

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

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.

• resource division
• public and private scopes

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.

• composability requires inherent organisation of executional focus within structure which MUX provides

Scale-independence

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.

Layer 2: Class & Instance (ⵜ)

Layer two extends the layer one instance-tree concept with a second tree, the class-tree which we symbolise in the model as a horizontal axis orthogonal to the vertical instance axis defined in layer one.

In the Holarchy article we summarised the class-instance by saying that classes are unique names that refer to specific packages of evolving knowledge and behaviour structure. And that they exist in the form of groups of instances throughout the holarchy, and their collective version is the totality of all instance's variations of it, and is maintained by those instances which are all structural representations of the class backed by real resource and in a state of in-flux development and operation. In this section, we look at the specific data structure and processes operating on it that implements this name-cluster concept.

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. The second 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.

We started with layer four since that's easiest to intuitively connect with being the abstraction layer that relates to real world organisation. But now we'll move the discussion to the second layer where class and instance are defined.

The vertical axis represents instance which is a top-down process, and the horizontal represents class which is a bottom-up process. The vertical instance axis is actually the first abstraction layer, and the horizontal class axis is the second abstraction layer. And actually the first abstraction layer includes a more general layer that we call layer zero'. In this article we'll just give a brief introduction to layer two, the details of layers zero, one and two are covered in the holon mechanism article.

The mechanism results in a number of important fundamental conceptual meanings which also form the most general characteristics for subsequent layers. These concepts are represented as the primary (vertical and horizontal) axis pair, which are shown in the image to the right, and are also depicted as the blue "+" in the diagram of layers above.

Layer two is takes the form of dichotomies, in fact it's a dichotomy of dichotomies. Dipoles, opposites and parent-child relationships.

Layer three uses and extends this layer two class-instance environment to create the familiar high-level organisation context of the forth layer introduced above.

The four quadrant system informs and responds to change, but is not the ultimate actualisor of it. The system does not define change itself, it only organises it ontologically to be utilised by the actual agents of change. In terms of the diagram, the change occurs in the centre as an action representing the current class and instance.

Both class and instance 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.

The first kind of scope is the usual public/private vertical dimension that we're used to with an object from OOP, these are instance scope forming the instance tree. The second kind of scope, which is complimentary in its operation to the first, are class scope making up the class tree.

Within this primary axis pair, the instance tree is the primary or original axis and the class tree is derived from it. Even though instances are instantiated from and guided by their classes, they depend entirely on the instances to represent them, because only the instance actually exist by being backed by real resource.

The top is public, the bottom is private, the left is abstract and the right is actual. Each primary direction defines a meaning that's common to a pair of quadrants. In terms of functionality this layer creates the scopes and a feedback loop dynamic, but it does not actually do anything within these scopes in terms of creating or responding to change - that's where the second abstraction layer comes into play.

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.

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 contextual conditions they're performed within. The ontology is thus a semantic network formed by established and evolving dependence and relevance.

• 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

Layer 3: Agent and arena (⤫)

The third layer of the mechanism executes in the context of the private instance scope. This is where the diagonal loops between opposite quadrants 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.

The four quadrants occupy the third abstraction layer of the model, derived from the interaction of the vertical and horizontal axes constituting layer two. The second layer defines the most general contextual features for the four quadrants - what scopes they operate within, and the meanings that the upper, lower, left and right directions have. It made possible a new subjective local perspective, and the third layer is halfway between these two perspectives, having "a foot in each side". The lower quadrants represent the inner local subjective perspective, and the upper quadrants represent the outer collective perspective.

We often refer to layer three as the "objective-subjective", because it's an objective "unconscious" process like layer two, but it occurs in the local subjective scope. We often refer to this private subjective perspective as taking place in situ.

The third layer introduces the concept of the centre, where all change that takes place in layer three takes the form of action passing through the self at the centre. Always interacting between beyond and within, and fits with the saying "as above, so below". And also all interaction is between conceptual and actual, classifying ("ontologising") or instantiating.

The inherent form of the quadrants is that they're grouped into a pair of feedback loops connecting diagonally opposite quadrants. These loops connect the internal subjective view of the agent to the external objective arena, hence naming the layer the "agent-arena relationship". They're also the variation loop and the selection loop constituting the evolutionary system. We use the word "inherent" because the information flow that defines these diagonal feedback loops between opposite quadrants are created by the first layer mechanism. The mechanism itself is beyond the scope of this article, what we cover herein is the meaning of these scopes and loops.

Before we go into any detail about the diagonals, we need to have a clear conceptual understanding of the individual quadrants. The easiest way to introduce the quadrants is to start with the already-familiar class and instance concepts on the left and the right respectively, and then divide them into an upper collectivised version of the pair and an individuated version below. The image to the right demonstrates this with the original class-instance axis horizontally in the middle.

The top quadrants represent the local holon's perception of, and contribution to, the whole tree (graph) of classes and instances, which we call "ontology" and "market" respectively. Since it's a bottom-up peer-to-peer architecture, these collective-oriented top quadrants are not the whole itself (which would have to be "centrally served"), they're a local representation of the whole from the local subjective perspective with self at the centre.

The bottom quadrants represent the local holon's internal private world. This lower pair is conceptually more fine-grained than the general (and abstract) class-and-instance concept represented by the horizontal axis. They represent the local subjective meaning of the class and instance dynamic. Classes are designed to be instances, their utility and purpose comes from how they behave within their subjective instantiated contexts. The internal class quadrant in the bottom-left is called "development" and it takes the form of conditional structure (the condition aspect of the production rule structure). The internal instance quadrant in the bottom-right is called "production" and represents the holon as a progressing activity (the action aspect of the production rules).

Each of the quadrants is delineated by the vertical and horizontal axes of the first layer discussed above. This means they each represent a pair of scopes, one from each primary axis. This gives us a clear foundation from which to derive the meaning and process for each quadrant that forms its concept of progress.

Since the processes are operating on the same state (all being aspects of the same holon), they must be complimentary and non-destructive to each other. But as we've described, the de-coupled production rule and blackboard model gives us exactly the non-destructive process-form we need here.

The quadrants in the third layer

The second abstraction layer of the holon model is all about the function and dynamics of the quadrants, it doesn't concern any user-facing aspects of the quadrants which is how they were introduced above in layer four. Here we'll discuss each quadrant again, but this time in terms of their relation to the class-instance system of layer two.

The quadrants of layer three are in the form of data structures in the context of both class and instance and in both the individual and collective forms. The meaning of each quadrant is also defined by how the quadrant behaves within its specific dual-scope context.

We discussed above with regards to the layer four quadrants that each quadrant has both in inward facing individual (self-assertive) behaviour and an outward facing collective (integrative) behaviour. This is also the case with the quadrants here in layer three, but here the quadrant's behaviours relate systemically with the layer two concepts.

In the third layer, one of the behaviours of each quadrant acts upon the diagonally opposite quadrant, which creates a dynamic of two orthogonal feedback loops. The upper quadrant's inward behaviours act upon their lower diagonal opposites, and the lower quadrant's outward behaviours act upon the upper diagonal opposites.

Following is a discussion about each quadrant outlining for each of them what their inward and outward behaviours are, and below that we'll go into more detail about the diagonal feedback loops. We've shown the loop-contributing action direction in square brackets in each heading.

Top-left (ontology) [🡖]

This quadrant is the "collectivised" version of the class concept. It's a left quadrant, which means that it concerns abstract knowledge which is not actualised in time. It's also a top quadrant putting it in the public scope, which means it's a peer-to-peer collective contribution process. This quadrant is called "culture" in Integral Theory, and it's Aristotle's "formal cause", which is often described as a "blueprint". In our model, this quadrant is called Ontology.

The outward collective behaviour of the top-left is of contributing to the unified ontology, the collective of holons connected by association into a unified semantic network. Relationships of dependence and usage volume form the skeleton of this network. The local ontology is a filter of the whole based on local experience, interest and opportunity. The local perspectives throughout the network are all mergeable in any order (idempotent) leading to a unified coherent whole (albeit abstract).

The inward individual behaviour of the top-left quadrant, i.e. the local private usage of the collective ontology, concerns presenting local agency with an actionable objective. The agentic performance of the action (such as code execution) takes place in the centre of the model in the here and now (the centre is outside holarchy scopes). After the action has been performed it is seen as an account in the bottom-right, and so in the model we say that the top-left quadrant acts upon the bottom-right.

Knowledge is not just dead information, it needs to be embodied behaviourally. It applies to a group within which it's established in collective usage. The variational aspect of the evolutionary principle is essentially about sharing aggregated performance information associated with the conditions, i.e. the objective and circumstance requiring the activity. This is how the ontology represents usable collective knowledge from classes established in usage.

All instances of like classes form into knowledge-sharing groups. In this way, every class in the ontology is a community and a map of all the instances of that class. The knowledge is naturally shareable and understandable, because the group of all instances of one class are essentially a special-interest group - they all have interest in the same specialist knowledge associated with that specific class.

The purpose of knowledge is to be used. To use it requires it to be embodied by a holon, in the form of classes that are "installed" (connected into paths of potential focus in the bottom-left quadrant) into the local environment where they can activate it (in the bottom-right quadrant) in response to appropriate local conditions as they arise (from the top-right quadrant). Knowledge is not just opinion, it's determined by how effectively it's used. For the ontology to assure utility, it must include this performance aspect with the knowledge, condition and the performers of it.

The ontology is structured by class names, and contains information about how those classes perform as children filling roles in various classes of organisation. The result is an ontology of behaviours associated with actual ability to perform them. These are the abilities that back objectives making them actualisable (by instantiation making them potential and then imminent).

The ontology evolves in diversity and complexity as the instances develop themselves (bottom-left) and share their usage knowledge (bottom-right). It's a collective form of progress which is evolutionary in nature, not a self-assertive control loop.

Bottom-right (operation) [🡔]

We call this the operation or production quadrant which takes the form of a self-assertive control-loop maintaining the private self-representation since it's a bottom quadrant. Since it's on the right, it's actualised in-time involving the consumption of concrete resource. This is Integral Theory's "behavioural" quadrant and Aristotle's "efficient cause" which is the agent that brings something into being.

The inward individual behaviour of the bottom-right quadrant concerns maintaining the local instance of the organisation operating in the local environment. Organising the actual work and resource planning of the local operation and production, including accounting and reporting.

The outward facing collective behaviour concerns fitting the local self-representation to the real state it represents, and allows it to act as an interface to it. It's "ontologising" the accounts of activity (the activity stream). This process includes the integration of selected information to the public collective ontology. This ontologising process is why we say that the bottom-right quadrant acts upon the top-left closing one of the feedback loops.

This quadrant involves the actual achievement of the holon's objectives (that were created in the bottom-left). Production is a control-loop that reduces the difference between the current resource state and the expected/desired state.

An actual agent has filled a role in the local context and performed behaviours towards achieving the various objectives. The holon has gained "experience" by putting its knowledge to use in service of the holons own private developing objectives in the bottom-left. In this aspect of the organisation, we're in the private scope of production using private property.

This quadrant is oriented towards the past, because it's about the accounting of an activity after it's been performed. The final account on completion is signed and immutable and contributes to the ontology (top-left) which has the current condition at it's root. The information contributed to the ontology is the performance, the account compared to the initial expectation, in the context of the condition (parent) that it's responding to. In this way the local knowledge is contributed to where it's relevant.

The operation/production quadrant represents the actual state of production of the holon, such as materials, access, stock, accounts etc including the state of completeness if applicable. This quadrant represents the actual performance of behaviour informationally which we call "accounts" (of the actions that occurred in response to the conditions). Performance of behaviour is carried out in accord with the top-left "ontology" quadrant, and final performance with respect to expectations is presented to the ontology for integration.

Top-right (market) [🡗]

This quadrant is at the top so it's a collective contribution in public scope, and being on the right it's within the context of actualised linear time. We call this quadrant "market", because its purpose is to harmoniously allocate limited resource amongst a potentially unlimited demand for resource by means of balanced exchange. This is Integral Theory's "society" quadrant, and Aristotle's "material cause".

It seems at first glance that connecting the meanings of "market", "society" and "material cause" across these systems is contrived to fit our designs. But remember that we're in the agent-centric organisational context of a holon, where communication between holons is purely organisational and in terms of balanced exchange and the flow of resource and value.

The outward facing behaviour of this quadrant describes a free market based resource allocation system used and supported by a network of autonomous participants. These entities have the autonomy to choose what goods or services to produce or consume, at what price, and from whom. The resource-flow effectively represents the total of all committed intentions (expressed in all the bottom-left quadrants throughout the network). This quadrant represents the interface between the public and private sides of the holon. Its organised by linear time in the future and so from the user perspective it takes the form of a schedule. The schedule is an organisational "container" in which roles and resources are "booked" by instances that fill the roles.

The inward facing behaviour is about presenting the public market conditions to the internal private side determining which behaviours are salient. The bottom-left development quadrant will then formulate a specific response using a salient behaviour, hence we say that the top-right quadrant acts upon the bottom-left quadrant initiating a feedback loop with it.

A holon requires real resource in order to function. In other words, the self-organisation structure represented by the bottom-left quadrant needs resource organised by the top-right quadrant to represent it.

This quadrant allows the holon to participate in the wider market, contributing to the collective society of organisations.

Bottom-left (development) [🡕]

This is a bottom quadrant so, like the bottom-right, it takes the form of a self-assertive control-loop in private scope within the holon. It's on the left so it concerns abstract knowledge that is not actualised in time. Unlike the bottom-right control-loop, this quadrant concerns knowledge rather than resource. We call this the "development" quadrant, and is called the "intentional" quadrant in Integral Theory (we often refer to it by that name as well). It's Aristotle's "final cause" or telos, the objective or purpose for which something is done or exists. For example, the telos of a knife would be to cut.

The inward facing behaviour of this quadrant is the holon's self-assertive control loop. In the quadrant, the holon is navigating in potential space, developing its internal knowledge, objectives and meaning. This is the structural aspect of the private self-representation with its embodied patterns of behaviour.

The outward facing behaviour is the holons expressed intention. The expression is its public position and is the source of evolutionary selection. As a behaviour intention involves committing to resource schedules ("booking") in the top-right quadrant, and so we say that the bottom-left quadrant acts upon the top-right completing the feedback loop with it.

The objectives are defined by the condition-side of the internal production rule structure. A specific condition arising makes a subset of actions and variants salient, to be refined, selected and acted upon later in the right-hand production/operation quadrant.

The development quadrant represents the holon's objectives in the form of a structure of embodied behaviours. This structure represents the embodied and salient aspect of the holon class behaviours from the ontology (top-left), backed by resource from the market (top-right) and attained by production (bottom-right).

The diagonals

As can be seen in the diagram to the right, the quadrants naturally form a diagonal pair of axes. As was discussed above, each of the quadrants acts upon its diagonal opposite which gives rise to both of these diagonal axes taking the form of a feedback loop. The quadrants meanings derive from the dual scopes they occupy from level one, and are refined with these feedback loops.

Aside: In Integral Theory the adjacent quadrants are considered to have a tighter relationship to each other than the diagonal opposites, due to their sharing of a direction. But in our model we attribute the most direct connection to the diagonals due to them taking the form of a feedback loop with their opposite partner. The tightest relationships of all are the vertical and horizontal opposites in layer one and two.

These two diagonal loops constitute the dynamics of third abstraction layer of the model that refine the four quadrants behaviours and connect them all together into a harmonious whole. The diagonals are the form of the interface ("application") presented by level three for use and extension by level four. Just as the class-and-instance mechanism was the interface that level two provided for level three's use and extension.

The bottom two quadrants represent the familiar self-oriented organisational context. These each connect to their opposite outward partner, the bottom-left connects to the top-right forming the selection/arena loop, and the bottom-right connects to the top-left forming the variational/agent loop. The former extends the instance-tree to include the evolutionary concept of selection to become a "multiplex of intention" (the arena). The latter extends the class-tree to become an ontology of variations of knowledge in use (agent behaviour).

Each loop is a distinct way the collective forms from the individual behaviour, and conversely how the individual is guided by the collective. Each loop is a co-evolutionary progression process.

Both loops are derived from and extend the primary feedback loop dynamic form into a new concept involving knowledge derived from the local internal scope. One diagonal extending the instance-tree and the other the class-tree.

In each loop-extension there is a rating (evaluation, feedback) of the associated tree involved. The selection loop involves a subjective rating in accord with local intentions and preferences, and the variational loop involves the objective rating of local productive performance and use. Both loops involve local rating and non-local collective merging of the rating information. In both loops, local decision-making is guided by the non-local aggregate information.

The collective can be thought of as a "service provider" (albeit a non-local peer-to-peer one) that evolves with the clients needs, and the individual (as the client) is guided by and uses the service. The ontology is a service utilised by an agent in production (producer), and the market is a service utilised by a consumer.

Naming the diagonal loops

The naming of the loops has been difficult and has changed a lot (only the names, not the functionality). They generally correspond to class and instance, but it would be confusing to use those names since they're terms used in layer one and two, something that sums up the meaning of their use to become the evolutionary system and involving the subjective perspective is required.

Both agent/arena and selection/variation sum up these extended meanings well, so we'll stick to using both pairs of names for now.

Selection takes place in the arena in the form of resource exchange amongst instances in situ. The two right-hand quadrants also represent this in-situ instantiation aspect, but the quadrants are basic static scopes inheriting their meanings from layer two, here this in situ aspect is extended with the diagonal feedback loop to become a dynamic progression of continuous development and operation.

Variations are created by instances performing class behaviours in situ, these behaviours and their variations extend the basic layer two functionality-container aspect of the class (left-hand quadrants) with the diagonal feedback loop to become the collective ontology co-evolving with in situ performance of behaviour.

So we can see that the diagonals clearly relate to class and instance, but they're a new layer three version of the concept based on feedback loops in the subjective perspective where all change occurs with respect to self at the centre.

Phases and sub-phases

Both diagonal feedback loops are formed due to the action of each quadrant upon its opposite, each loop has two "sides" with opposite directionality connecting to each other, we call these the phases of the loop. Each loop has two phases.

We call then phases because all actual change that occurs in a holon occurs via these informational exchanges between and the diagonal opposite quadrants. Each quanta of agentic focus is divided into four sub-quanta which are passed to each quadrant and used to update the aspect of the ontology it's concerned with.

When the opposite quadrant receives it's sub-quanta it extends that same aspect of the ontology further. In fact all four phase also logically follow each other in a specific sequence, all extending the ontology withinwards extending the logical prior. We'll discuss the sequence after going into more detail about the diagonal and their specific phases and sub-phases.

An action upon the opposite is essentially a message of change information being passed from one quadrant to its opposite partner, which implies that each quadrant plays the role of both sender and recipient in order to form a continuous feedback loop.

The self at the centre is common to all change within this subjective context, which means that each phase can be divided in half having one half facing towards self and the other end facing away from self, we call these the sub-phases of a loop. The quadrants relate to sub-phases as well, each has a sub-phase of its diagonal loop coming in from the centre, and one going out to the centre.

The sub-phases are important, because they constitute the most concrete functionality of the quadrant and loop they're associated with, and they also underlie the meaning of the two roles that each quadrant has.

Self at the centre

Dividing the phases into sub-phases permits the perspective of self at the centre. Information that would flow unseen and uninterrupted between opposite quadrants can be apprehended, understood and guided from the supervisory position of the centre.

The meaning and purpose (and language) of all information that passes between quadrants in the loops passes through the central POV, and is understandable by it. Indeed all information is created, maintained and guided by it. The central perspective is abstract identity around which all change flows exactly like the concept described by the Ship of Theseus.

Note that this is a different concept to self-centered which means biasing one's attention and energy towards ones own interests in an unbalanced or excessive way. The holarchy's inherent dynamic tends towards balanced exchange between individual and collective.

All information passing the centre is ontological in form, it's all meaning that is presented for the central perspective, and understandable by it. This is the perspective that higher agency perceives the context from and from where it can both apprehend meaning and act creatively on the local context. In other words, since the central perspective is always ontologically meaningful, it serves as a consistent "hook" for agency to assess or creatively intervene in the scope.

The centre is a point of possible intervention and extension by agency. Information which is, by default, directed to the opposite quadrant goes via the centre where it can be adjusted before arrival. The centre is just like a hook in traditional program code that permits extension.

The centre also represents the abstract source of agentic focus and a potential connection for higher agency, and ultimately represents the connection to the most general agency of all which is the source of actual consciousness.

Arena (selection, instance) loop (⤢)

The diagonal consisting of the bottom-left and top-right quadrant (⤢) forms the arena loop (mosaic, multiplex) and is associated with the self-assertive behaviour, the instance tree and the selection aspect of evolution.

This diagonal extends the first layer instance tree represented by the primary vertical axis and is oriented towards the future. It also extends the right-hand quadrants that represent the basic in situ aspect of scope, to become the in-flux dynamic of the resource flow.

In terms of self-organisation (self-as-organisation, or body-schema), this diagonal represents the on-the-organisation perspective. In other words, the perspective of directing the organisation in terms of "real world objectives"- i.e objectives that are in terms of the collective resource flux.

The bottom-left quadrant represents the self-organisational structure, which is a structure of recurring behaviours. The top-right quadrant represents the schedule of committed resource that backs these behaviours enabling their performance.

This diagonal axis extends the first layer instance tree from a purely attentional flow to a more refined concept that includes the aggregate of local market knowledge coming from subjective value judgements and decision-making.

This axis represents the holons presenting itself in its self-assertive form in the public market. In other words, its public state as an autonomous self-organisation in the public market. This self-assertive expression of intent or economic commitment, is the form that the aforementioned subjective rating takes. This is the subjective evaluation of instance, and expression of that evaluation through attentional and resource support (selection). The directed support is how objectives are determined, the selection loop is results driven (declarative) and focused on the future.

This axis represents the holon as a sub-class group from above interacting together as an organised structure of loops from past in the bottom-left to future (schedule) in the top-right. This is the mosaic of class-mixin instances referred to earlier.

This loop represents the selection aspect of evolution, and the foundation of selection is the flow of attention, which is the salience landscape, the distribution of weights that determine the flow of focus throughout the instance structure. Salience is distributed internally (bottom-left) as the tentative virtual branches extending from what's represented in the resource flow (top-right).

From the user (self-organisation) perspective this diagonal represents the market interface. The organisational structure can publicly present supply and demand schedules of various resources. The holon presents various consumer and producer interfaces and states publicly. This is how commitments are made that permit actual production, and all together make up the whole resource-flow.

The arena loop is an organisational structure spanning internal behaviours as well as resource schedules. Salience is distributed across the structure, and directing this distribution over time is self-development. Organisational structure and its salience are the common form of the bottom-left and top-right quadrants.

The loop is a bidirectional instance-tree process of interaction between internal virtual instantiation (exploring a concept) and the public market of actual resources and value. The private virtual content is essentially a "replaying" and "remixing" mosaic of instances from the public arena.

The public content (the the flow of resource as a whole) which is the total of all the internal virtual instances in the whole network that have become backed by real resource (through persistent salience). In other words, a context starts as a purely abstract concept that can be explored and gain more focus and resource, becoming booked into public resource schedules.

The top-down side of the arena loop is the flow of focus and resource that determines which instances and conditions are active (selected). The feedback flowing from the bottom up is intention, or subjective valuation of the context.

Arena phases

The two phases that constitute this loop both concern the in-flux resource aspect. One phase is top-down coming from the collective to the individual and is also classifying ("ontologising" from concrete to conceptual), this is the external condition being integrated into local ontological meaning. The other phase is bottom-up and from instantiating local ontological meaning into concrete resource terms, which we call intention or selection.

Arena sub-phases

The intention phase going from bottom-left to top-right consists of two sub-phases, bottom-left to centre and centre to top-right. The former concerns the internal process of prioritising paths forward (selecting options to instantiate), and the latter to matching selected paths with the market as an economic participant.

The condition phase going from top-right to bottom-left consists of two sub-phases, top-right to centre and centre to bottom-left. The former concerns the externally oriented process of classifying the collective conditions (ontologising) for local use which updates the salience landscape and resource allocation. The latter is internally oriented and concerns the development of the self-representation (self-organisation structure, body schema, self-development).

Agent (variation, class) loop (⤡)

The diagonal consisting of the top-left and bottom-right quadrants (⤡) forms the agent loop and is associated with the integrative behaviour, the class tree and energy in the present. It extends the second layer class tree which is inherently ontological in nature due to representing the dependency and relevance relationships between classes (classification process).

This diagonal is formed as a feedback loop between the top-left and bottom-right quadrants (⤡). The actions are being performed top-down, and the account of the resulting activities compared to initial expectations is aggregated from the bottom upwards.

In terms of organisation, this diagonal represents the perspective of in-the-organisation, i.e. the perspective of focused day-to-day operation or production within the self-organisational system.

The purpose of this feedback loop is to form a collective ontology of behaviours co-evolving with all their diverse individual usages and variations.

The top-left represents the ontology of behaviour patterns, and the bottom-right represents the actual performance, or usage of them in the local private production context. Both ends of the variational loop concern the execution aspect of the system in terms of utility and performance.

The ontology in its basic form is created in the second layer, based on volume of usage. Then in the third layer it's extended to include the performance metrics corresponding to the specific performances of behaviours including their conditional context. This process expresses the principle that knowledge is not black and white, it's embodiment is proven and assessed through actual performance.

In this subjective inner context, the information being aggregated is the performance of the knowledge in-use internally. This aggregate knowledge forms a class-wide community map of instances (performances representing the class) and also underpins performing-instance's "reputation" or potential effecting it's likelihood of being matched in the market again in the future.

This loop is a bidirectional class-tree process of interaction between internal usage and execution of a behaviour and the institutional map of knowledge relating to the behaviour. This loop is responsible for the variational aspect of evolution.

The top-down side of the agent loop is the institutional knowledge and guidance (map) flowing inward from the collective class to enable action. The bottom-up feedback side is the objective performance (of the embodied knowledge) and usage statistics of local production in aggregate form flowing outward.

Agent phases

The two phases that constitute this agent or variation loop both concern the performance of behaviour. One phase is top-down coming from the collective to the individual and is also going from conceptual to concrete form, this is the current behaviour pattern being provided by the established collective for specific local use and being performed internally, we usually call this phase action. The other phase is bottom-up merging the concrete actuality of the performed behaviour with the collective ontological knowledge which we call metrics or variation.

Agent sub-phases

The action phase going from top-left to bottom-right consists of two sub-phases, top-left to centre and centre to bottom-right. The former concerns the externally oriented process of instantiating the current behaviour pattern for local performance. The latter is internally oriented and concerns the actual operation of the behaviour in the local context.

The metric phase going from bottom-right to top-left consists of two sub-phases, bottom-right to centre and centre to top-left. The former concerns the internal process of generating an auditable and immutable account of the performance, and the latter to integrating the local knowledge gained with the collective ontology of behaviours, variations and metrics.

The four phases

Each loop is constituted of two phases, and active side and a feedback side, and we call them "phases" due to their repeating cyclic nature. But the name is also used because all four of the phases ontologically follow each other, each refining the ontological meaning of the logically prior phase.

The condition is the ontological form of the current state of the local environment. This eventually a response will be selected which refines the ontological context of the condition with an objective - usually matching the condition in such a way as to mitigate it. Over time actions will be performed towards the objective refining the ontological meaning with the further details of costs and expectations, and finally the immutable accounts of the actions performed will refine the ontological context further.

The immutable account is the actuality of the past, and all such accounts are collectively the source of changing conditions. This forms a complete logically causal loop form to the quadrant as a whole.

The fact that each phase extends the same ontological context as the prior phase means that they occur in the same scope as each other both locally (instance scope) and non-locally (ontological-scope), which means that the process is entirely local and hence can involve a single quanta of agentic or executional focus.

The concept of message-passing between opposite quadrants is just a useful metaphor to understand the process, but it's not literal since they all share the same executional scope which is between (in local contact with) the four quadrant-scopes.

The four phases are the essence of all the forms of holonic development. The integrative behaviour progress towards greater integrity and resilience and the self-assertive behaviour progresses towards greater autonomy and potential. The ontology evolves to greater utility and diversity, the economy of resource flows forward, the holon develops as an organisation and progresses in its undertakings.

Scaling to a network

Everything we've talked about so far is in the context of what we call the "simple local holarchy", which is that we're considering the entire holarchy to be a single local data structure. But in reality many holons will be separate entities in a network connected by arbitrarily slow transport media including "sneaker net" or "carrier pidgin".

Instance trees are the framework of resource allocation, and this forms the skeleton of communication permitting the class tree to synchronise. In a sparse network, we don't know how long aggregation of class information may take at any level of the instance tree.

The kind of information being aggregated is class metrics which are always idempotent, meaning that multicast and best-effort paradigms are able to be used for this process. In other words class-synchronisation is "p2p friendly".

How the diagonals are inherent in the mechanism

• the diagonals have a mechanistic ("physical") origin as well, layer one sets up a dual dipole dynamic involving the scopes of the calling/returning dynamic and the meaningful points the agentic focus can appear in

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.

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.

Related projects

• holons.io - hierarchical payments
• Coasys - an alternative holarchy built on holochain
• We Collective - a holonic organisational social network

See also

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