#concept19 mentions

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.


Affordances Contribute to Attractors

An attractor defines a stable system (S1).

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.

Cultural Evolution Is Multilevel Meme Variation, Selection and Replication

Cultural Evolution is the change of information capable of affecting individuals' behavior over time.

Dynamical System

A dynamical system is a System that changes over time.


Evolution is descent with modification, that is change in the heritable characteristics of populations of individuals over successive generations.

Living System

A living system is a Complex System that actively and autonomously upholds its System Boundary by exchanging energy and information with its Environment, thus “importing” order and staying in a Non-equilibrium Steady State.

Move up and Down in the System Hierarchy

The world is a hierarchy of systems.

Move up and Down the Ladder of Abstraction

Since we want to Move up and down in the system hierarchy, a useful Strategy is to build epistemic connections between very abstract and very concrete Models, that is an easy-to-climb ladder of abstraction.

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

Scale-free abstractions are a specific type of Shorthand Abstractions: highly general concepts taken from our best current thinking about evolution, cognition, and the world as a hierarchy of systems.

Selection Is Bayesian Search

As a corollary to the systems view of Evolution, on the level of the system of nature, selection of lower-level systems can be seen as Bayesian search – as an algorithm that metaphorically fills niches and builds bridges of complexity into the void by “looking for” Attractors of nature as a System.

Self Organisation

Self-organisation is > a process where some form of overall order arises from local interactions between parts of an initially disordered System.

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 (put simply, what the world consists of), we can start with the basic fact that there is difference in the world – that “something can be distinguished from everything else”.

There Never Were Socialist States

There never were socialist states.