# Autopoiesis and Its Efficacy—A Metacybernetic View

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Setting

#### 2.1. Contexts

#### 2.2. Parameters

- (1)
- Social relationships. These have three paired value parameters: (a) equality versus authority, where determination is sought about how inequality is handled in a given situation, how status is demonstrated and how respect is given, and what interactions are appropriate for those of unequal status; (b) individualism versus collectivism, where it is sought to determine which prevails, the interests of the individual or the interest of the group, and to what degree are interpersonal relationships valued; and (c) nurture versus challenge, where, by equality/authority, it is sought to determine which is the more important set of goals, cooperation and security or recognition and advancement, which achieves better outcomes, and which are supportive or challenging acts.
- (2)
- Epistemological. There are three paired value parameters: (a) stability seeking versus uncertainty acceptance, where determination is sought for how uncertainty is dealt with, being either avoided or accepted, whether structure is seen to be more important than flexibility, and what the status of knowledge is and how it is used in development; (b) logical argumentation versus reasonableness, where one seeks to determine how arguments are developed, which is more important—logical consistency or practical outcomes—and how disagreement is managed; and (c) causality versus complexity, where determination is sought about how causality is assigned typically, whether it is assigned to a single, most likely source, or whether it is assigned to the broader context [39].
- (3)
- Temporal. This has two paired value parameters: (a) clock time versus event time, where determination is sought on whether people conform to an external measure of time, or rather permitting the event at hand to unfold on its own time, and whether deadlines or relationships are more important; and (b) linear versus cyclic time, where determination is sought about whether people see time as a path and whether goals are necessary destinations, or if time is seen as a pattern of interlocking cycles into which they step in and out over the course of a life.

#### 2.3. Internalisation and Anticipation

## 3. The Schemas

#### 3.1. General Collective Intelligence (GCI) and Autopoiesis

- Centralisation:
- Process selection
- ○
- selected processes to be executed to satisfy fitness in achieving collective outcomes so that it is possible to maximise those outcomes.

- Decentralisation:
- Process operation
- ○
- is purely Peer-to-Peer, with no third-party involvement;
- ○
- is decentralised, where process activities have role assignations;
- ○
- is user-centric, with no third-party information;
- ○
- is massively collaborative, with no predefined limits that scale participation.

- Relative value determination
- ○
- of work, universally to enable open participation by subagencies in collective processes;
- ○
- of resources, enabling more open sharing of those resources, thus enabling collective processes.

- Metric of fitness definition for
- ○
- subagency participation, through openness, enabling subagency substitution for others able to better enhance viability in the cooperative process;
- ○
- subagency process, enabling selection of the best process in which to participate.

#### 3.2. Eigenform, Internalisation, and Anticipation

_{t}) is the result of a cognitive (or sensory–motor) operation COORD (an autopoietic imperative that, in due course, results in an ideate) on the previous instance of observation (obs

_{t}

_{−1}):

_{t}= COORD(obs

_{t}

_{−1})

_{i}) to this equation which do not exist in a strictly mathematical sense, since there are no initial conditions. However, they do represent an autopoietic couple stability in the chain of COORD operations. This refers to those values which maintain their structure (or operation, or function) when cognitive operations on them are repeatedly performed as the equation pursues its indefinite recursive chain:

_{i}=> obs

_{t}= COORD(COORD(...COORD(obs

_{t}

_{−n}= O

_{i}))...)

_{t}arises, then this indicates that a convergence has arisen to an eigenvalue for which O

_{i}is its representation. Such eigenvalues are self-defining/self-referent in their autopoietic couple stability, which, through the operator COORD, implies a complementary relationship (circularity, closure) between eigenvalues and cognitive operators, where one implies/defines the other. As Rocha [89] explains, eigenvalues represent the externally observable manifestations of the (introspectively accessible) cognitive operations (COORD). Eigenbehaviour is thus used to define the consequences of self-production deriving from autonomous cognitive systems, which, through cognitive closure, give rise to perceptual regularities.

_{t}are agency anterior autopoietic functions, then, after Rosen, agency is only living if it can anticipate. In this case, COORD is necessarily not only a function of the past and present, but also of the future, in order to entail anticipation. However, this anticipatory nature of COORD is not considered; while it involves obs

_{t}

_{−n}in recursive mode, one might suppose that it should also involve, say, obs

_{t}

_{+η}(for η = 1, 2, 3, …, Ƞ).

_{t}, R is the recursive function COORD, and A are a set of parameters that are representative of the context, and where, for any given scenario, A is to be selected. To know the function R, the values of the parameters A and the initial conditions …, y(−2), y(−1), y(0) at time t = 0, and the successive states y(t + 1), y(t + 2), y(t + 3), …, must be determined for the time interval ∆t = 1.

- Weak anticipation occurs when the ideate is an informational model of the active context, and this arises from exo-anticipation, that is, agency anticipation about the external active context that creates expectations for eigenbehaviour and hence the potential options for future agency behaviour.
- Strong anticipation arises from behavioural endo-anticipation, where the ideate becomes embedded in the agency structure which can then determine eigenbehaviour and the potential for future agency behaviour.

#### 3.3. Extreme Physical Information and Autopoietic Rationality

**y**|A). Knowing p(

**y**|A) can therefore provide some indication of the quality of contextual observations that deliver the ideate. In the end, EPI is concerned with identifying the maximum attainable change in Fisher information. This is subject to the constraints that are determined from a problem context. If one has confidence in the constraints, then there will be equal confidence in the solution for p(x). Now, the value I for observation y is defined to obey Fisher Information, as

**y**|A)))]

^{2}>

**y**|A), called the “likelihood function” in statistics. It defines the probability of each possible observation in the presence of an ideal parameter value A. Interest now lies in estimating the probability law since this defines the unknown effect under study.

**y**|A) is known, so is I, and differently shaped laws p(

**y**|A) give rise to different values for I. Equation (6) holds for the particular law p(

**y**|A) giving rise to the data. If the wrong law is assumed, the answers will be wrong since the wrong prior knowledge is being used. The law holds regardless of any error that might occur in the relative connection between the observation and the context. Such an error occurs if, for example, the observer is being tricked, and the data observed really do not arise out of the scenario under study, or, alternatively, if the prior knowledge to be used does not arise out of that scenario. In the latter case, just different (and correct) prior knowledge must be used. The need is to avoid errors in prior knowledge (which might include mean and variance).

**y**|A), it becomes apparent that I is a measure of the width of p(

**y**|A). For example, if p(

**y**|A) is a normal law, its use in Equation (5) gives I as simply 1 divided by the variance. The variance is roughly the squared width of p(

**y**|A). Hence, the wider the law p(

**y**|A) is, the smaller is the information value. The wider/broader the probability p(

**y**|A) on the fluctuation is, the more “random” the values of x are, and so the less accurate is the estimate for the parameter A from an observation y. In this case, there would be an expectation that I would take a small value indicating stability reduction, so that Φ is not a good representation of context. This is precisely what Equation (8) gives in this situation. As such, Fisher information I measures the information about an unknown parameter in the context representing a typical data value y as an indicator of the information possibilities that might be extracted by observing a context. As such, it is capable of inferring hidden structure.

^{2}in estimating the state of the observed system from its data goes as 1/I. This is called the Cramer–Rao inequality. A small value of e

^{2}indicates a low level of disorder. Thus, in summary, if the context is in itself a complex coherency, and if it is well represented by the ideate, then the ideate must also be coherent in itself with a large value I, and the ideate is well ordered as a reflection of the characteristics represented in the relationships of the context. This is the same that occurs in autopoietic couple stability in Eigenform theory, and so the two are equivalent.

**y**|A) and subject to the Equation (12) connecting I and J. The extremum is attained through a variation of the shape of p(

**y**|A). Equation (12) is the extremum principle used to find solution probability laws p(

**y**|A), and is the overall principle of “Extreme Physical Information”. The naming comes from considering that the information change I − J is lost information, denoted by K.

- (1)
- Knowledge of a fixed upper-bound level J to the information. All quantities are to obey a principle of minimum loss of information: I − J = minimum. The p(x) that obeys this minimisation principle is guaranteed to give an I that is the desired maximum value. Having said this, practically, the value of J assumed is no longer of interest.
- (2)
- Knowledge of constraints that are obeyed by the unknown law p(x) (as mentioned above). These are:
- a.
- Normalisation (its integral over all x equals 1) indicating the total probability of obtaining x = 0 or Δx or 2Δx or …. (last possible value) is unity: in other words, one such value of x must occur during a measurement of x.
- b.
- In trying to solve for p(x), one has to first go through the algebraic steps of inputting everything known about p(x), such as its moments, required in order to undertake a solution procedure for p(
**y**|A). By “moment” is meant the average value over x as a continuous integral over its range (where 1st moment is mean, 2nd moment is variance, 3rd moment is skewness). Observing fundamental effects or constraints to create inputs occurs through repeated measurements, this requiring an averaging <x>. - c.
- Possible knowledge of correlation of x with other outside variables with (say) known statistics p(z), z denoting a different system. By “outside” is meant some possible other system phenomenon affecting or constraining the x values that is “outside our considerations.” Mathematically, this means that not enough constraints have been imposed through either: (a) that there is some other, additional set that likewise constrain the solution p(
**y**|A), or (b) the wrong set of constraints might have been used in the first place. The constraints bound the problem specification, and change these and the problem changes.

**y**|A), given A, is always independent of the size of J, only depending on the existence of J, which, in turn, follows from the philosophy of Immanuel Kant. Moreover, knowledge type 2a is not difficult to implement. However, knowledge type 2b is a potential source of error. In physics, use of the least possible number of such constraints gives the best results for the analytical solution p(

**y**|A). In essence, the observer has to “know” what constraints are essential to the underlying effect p(

**y**|P). By comparison, societal or economic systems have generally more complex causes than physical ones, so it makes sense to use more constraints in analysing these by EPI.

## 4. Consequences for Metacybernetic Theory and Overview

#### 4.1. Efficacy in Metacybernetics

- Anterior autopoiesis acquires its notion of context from the anterior (operative) system, creates or recognises and updates the context map, and then, through internalisation, manifests a cognitive map (or cognitive map update) in the posterior system (the metasystem) as an ideate Φ (or ideate adjustment) that is assimilated and/or accommodated. In the case of adjustment and with accommodation, regulative structures are modified, as may be strategic structures. In the case of autopoietic stability and with accommodation, the cognitive map is the result of a causal effect that impacts on strategic–regulative self-organisation and delivers eigenvalues.
- Posterior autopoiesis acquires its notion of the ideate from the posterior system (the metasystem), creates or recognises or updates the cognitive map, and then, through anticipation, it compares the cognitive map to the context map in the anterior system, where necessary seeking an update from behavioural intelligence (another type of causal-agent projected into active context) for the context map. This enables the operative structure to be adjusted, this modifying the potential from which behaviour results. In the case of stability and with strong anticipation, the context map is the result of a causal effect that impacts on operative self-organisation, thereby delivering eigenbehaviour.

_{a}and/or κ

_{p}). This efficacy is a result of the network of autopoietic (operative intelligence) processes working together effectively and coherently, while autopoietic couple assembly is regulated by the posterior system to this couple. Where this intelligence network is not coherent, it delivers a causal effect that is incoherent, i.e., the causal-agent observation is not well-ordered in its relation with the causal effect. In this case, the first-order causal-agent autopoiesis can be cited as a cause for disorder/instability. Noting that there are two possible trajectories for autopoiesis, in the case of anterior autopoiesis, the ideate will, for instance, represent the context incorrectly—for instance, by biasing a set of parameters and/or parametric relationships. In the case of posterior autopoiesis, the ideate will not be well-represented as a context map from which structure and behaviour are sufficiently well-linked.

#### 4.2. Overview and Discussion

- The first state of internalisation occurs through anterior autopoiesis, which involves an autopoietically constructed model of an observed and recognised active context that the agency assimilates internally as an ideate, and which delivers only implicit cognition and recognition, both of which are information processes.
- The second state of internalisation increases complexification, incorporating the assimilated model into the agency posterior system structure through accommodation, this leading to explicit cognition and recognition, enabling conscious awareness with rationality.

- The first state of anticipation is a consequence of assimilation, and corresponds to exo-anticipation, where agency anticipates the external active context through expectations about the need for future behaviour.
- The second state of anticipation is a consequence of accommodation, and corresponds to endo-anticipation, when the ideate becomes embedded in the agency structure, which then determines its eigenbehaviour (as operative structure) and creates potential for future behaviour.

## 5. Conclusions

_{a}, and that for the anticipation causal effect is that of posterior autopoiesis represented by κ

_{p.}Since, according to GCI, the subagencies that are involved in each trajectory are autonomous and organisationally distributed, there is no reason to suppose that κ

_{a}= κ

_{p}, and likely they will normally be different. The Dubois Eigenform equations that represent these two causal-agent processes, when solvable, indicate autopoietic stability. During internalisation, stability results in eigenvalues, and during anticipation, stability results in eigenbehaviour. It should be realised that eigenbehaviour is nothing other than the operative structure that enables the potential for behaviour. Thus, the teeth of a lion or the neck of a giraffe are operative structures that directly influence behaviours.

## Author Contributions

## Funding

## Conflicts of Interest

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**Table 1.**Relationship between the Bitbol and Luisi and Bielecki stages of living system development.

Consciousness Stage | Bitbol and Luisi Hierarchy | Bielecki Hierarchy | Stage Relationship |
---|---|---|---|

1 | Null pre-conscious. Devoid of internalisation. | Reflexive. Living system can only create behaviours that directly support existence and remove threats. | Null preconscious occurs prior to reflexive since, in the former, threats cannot be recognised. |

2 | Limited consciousness. Integration of environmental factors. | Associative. Able to undertake simple analysis of direct cause-and-effect relationships. | Limited consciousness occurs at a stage prior to associative, the former being devoid of analytic ability. |

3 | Enduring modifications in self-production. Stable dynamic support provided able to deliver strongly anticipative behaviour. | Conscious. Can model complex cause-and-effect chains, with a conditional option permitting future events variants, and an ability for complex strategies of activity. | Enduring modifications in self-production is approximated by the consciousness stage since cause–effect chains deliver strategy that implies anticipation. |

4 | More complex changes that influence behaviour. Involves observation of the exterior, but without awareness of an external independent world. | Self-consciousness. Epistemic perspective can change, with awareness of the existence of conscious goals perhaps devoid of proven reliable criteria. | More complex changes are prior to self-consciousness since the proof requires awareness and access to the outside independent world. |

5 | Collective consciousness that recognises social aspects. Knowledge develops by ascribing properties to intersubjective invariants. Intersubjectively shared predictive common rules become a collective consciousness obeying internal closure | The hypothetical omniscient stage, with proven criteria and proof of the reliability to use it. | Collective consciousness is likely equivalent to omniscient if one considers that proof is a social phenomenon. |

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Yolles, M.; Frieden, B.R.
Autopoiesis and Its Efficacy—A Metacybernetic View. *Systems* **2021**, *9*, 75.
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Yolles M, Frieden BR.
Autopoiesis and Its Efficacy—A Metacybernetic View. *Systems*. 2021; 9(4):75.
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2021. "Autopoiesis and Its Efficacy—A Metacybernetic View" *Systems* 9, no. 4: 75.
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