Attractor

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An attractor is the set of states a System tends to be in given what it is or how it can maintain its boundaries. An attractor defines a stable system; a system’s possible attractors can be more abstractly represented in an Attractor Landscape.

In mathematical terms,

[a]n attractor is a set of states (points in the phase space) … towards which neighboring states in a given basin of attraction asymptotically approach in the course of dynamic evolution. An attractor is defined as the smallest unit which cannot be itself decomposed into two or more attractors with distinct basins of attraction. This restriction is necessary since a Dynamical System may have multiple attractors, each with its own basin of attraction.Weisstein

This means that an attractor’s states are never actualised themselves, but the system tends to be in states as close as possible to them. Keeping this in mind, we can adopt the slightly looser formulation of a system being in an attractor state as actually meaning “in a state very nearby”, i.e. in the region around the attractor itself.

The system’s “movement” towards its attractor states can be described as a gradient flow in the state space’s vector field, i.e. as a continuous succession of states which takes the “shortest way” or “steepest descent” to an attractor.

The evolution function describing these gradient flows is the Lyapunov function:

The way something moves through this space depends on its Lyapunov function. This is a mathematical quantity that describes how a system is likely to behave under specific conditions. It returns the probability of being in any particular state as a function of that state (or, put differently, as a function of the system’s position in the state space …). If we know the Lyapunov function for each state of the system, we can write down its flow from one state to the next – and so characterise the existence of the whole system in terms of that flow.Friston (2017)

The gradient flows can be decomposed into fluctuation and oscillation, the system-specific composition of which determines the type of attractor the flows correspond to and the kind of system they describe:Friston (2019). Notice how this classification and description resonates with Dave Snowden’s Cynefin Framework.

We are interested in systems that are, have been, or could be stable, so the last category is of special importance to us.

References

An Attractor Defines a Stable System

Since the “states that will actually be observed in [a] System are the Attractors”Abraham & Shaw (1992), 13 , we can identify any system as we observe it with its attractors.

Attractor Landscape

An attractor landscape is an abstraction of the State Space of a System.

Complex System

A complex system is a Dynamical System that has the following attributes:[^derived] - It consists of a large network of individual components.

Concepts Are Attractors

Because Concepts are compressed models, and Models are Systems themselves, Concepts are also systems.

Dynamical System

A dynamical system is a System that changes over time.

Move up and Down in the Hierarchy of Systems

The world is a hierarchy of systems.

Revolutions Try to Force Systems into Imaginary Attractors

All political revolutionaries imagine a future constellation of their society and, if and when they succeed in disrupting the old system, use Power to implement the new one.

Scale Free Abstraction

We want a Sensemaking Framework that helps maximise scope, detail, and cognitive efficiency of Sensemaking.

State Space

A state space (or, which is roughly equivalent, phase space) is the set of all possible states of a Dynamical System; each state of the system corresponds to a unique point in the state space.

Strategy Is a Pattern of Actions

On an abstract level, Strategy is a set of System activities, structured in a process.

The World Is a Hierarchy of Systems

When thinking about ontology, i.