Feeds:
Posts
Comments

Archive for the ‘Systems’ Category

2. Definition of Self-Organisation

The essence of self-organisation is that system structure (at least in part) appears without explicit pressure or constraints from outside the system. In other words, the constraints on form are internal to the system and result from the interactions between the components, whilst being independant of the physical nature of those components. The organisation can evolve either in time or space, can maintain a stable form or can show transient phenomena. General resource flows into or out of the system are permitted, but are not critical to the concept.

The field of self-organisation seeks to discover the general rules under which such structure appears, the forms which it can take, and methods of predicting the changes to the structure that will result from changes to the underlying system. The results are expected to be applicable to any system exhibiting the same network characteristics.

3. What is a system ?

A system is a collection of interacting parts functioning as a whole. It is distinguishable from its surroundings with recognisable boundaries. The function depends upon the arrangement of the parts and will change in some way if parts are added, removed or rearranged. The system has properties that are emergent, that is they are not contained within any of the parts, they exist at a higher level of description.

4. What is a system property ?

If we connect a series of parts in a loop, then that loop does not exist as a property of the parts themselves. The parts can have any structure or form and yet the loop persists. If the loop shows an additional dynamic behaviour (maybe it oscillates) then this is an example of an emergent system property.

5. What is emergence ?

The appearance of a property or feature not previously seen. Generally, higher level properties are regarded as emergent – a car is an emergent property of the interconnected parts. That property disappears if the parts are disassembled and just placed in a heap.

6. What is organisation ?

The arrangement of parts in such a way as to be non-random. The restriction of the options available to a system in such a way as to confine it to a small volume of its state space.

7. What is state or phase space ?

The total arrangements (or combinations) available to the system. For a single coin toss this would be just two states (either heads or tails), but the possible states grow rapidly with complexity. If we take as an example 100 coins, then these can be arranged in over 1,000,000,000,000,000,000,000,000,000,000 different ways. We can view each coin as a separate parameter or dimension of the system, so one arrangement would be equivalent to specifying 100 binary digits (each one indicating a 1 for heads or 0 for tails for a specific coin). Generalising, any system has one dimension of state space for each variable that can change, mutation will change one or more variables and move the system a small distance in state space. State space is frequently called phase space, the two terms are interchangeable.

8. What is self-organisation ?

The evolution of a system into an organised form in the absence of external constraints. A move from a large region of state space to a persistent smaller one, under the control of the system itself.

9. Can things self-organise ?

Yes, any system that takes a form that is not imposed from outside (by walls, machines or forces) can be said to self-organise. The term is usually employed however in a more restricted sense by excluding physical laws (reductionist explanations), and suggesting that the properties that emerge are not explicable from a purely reductionist viewpoint.

10. Isn’t this just the same as selection ?

No, selection is a choice between competing options such that one arrangement is preferred over another with reference to some external criteria – this represents a choice between two stable systems in state space. In self-organisation there is only one system which internally restricts the area of state space it occupies. In essence the system moves to an attractor that covers only a small area of state space, a dynamic pattern of expression that can persist even in the face of mutation and opposing selective forces. Alternative stable options are each self-organised attractors and selection may choose between them based upon their emergent properties.

11. What is an attractor ?

A preferred position for the system, such that if the system is started from another state it will evolve until it arrives at the attractor, and will then stay there in the absence of other factors. An attractor can be a point (e.g. the centre of a bowl containing a ball), a regular path (e.g. a planetary orbit), a complex series of states (e.g. the metabolism of a cell) or an infinite sequence (called a strange attractor). All specify a restricted volume of state space. The area of state space that leads to an attractor is called its basin of attraction.

12. How do attractors and self-organisation relate ?

Any system that moves to a fixed structure can be said to be drawn to an attractor. A complex system can have many attractors and these can alter with changes to the system interconnections (mutations). Studying self-organisation is equivalent to investigating the attractors of the system, their form and dynamics.

13. What is criticality ?

A point at which system properties change suddenly, e.g. where a matrix goes from non-percolating to percolating or vice versa. This is often regarded as a phase change.

[link]

Read Full Post »

A nice idea. Could use the same idea for Systems teaching.

Read Full Post »