Stigmergy as a universal coordination mechanism I: Definition and components

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Abstract

The concept of stigmergy has been used to analyze self-organizing activities in an ever-widening range of domains, including social insects, robotics, web communities and human society. Yet, it is still poorly understood and as such its full power remains underappreciated. The present paper clarifies the issue by defining stigmergy as a mechanism of indirect coordination in which the trace left by an action in a medium stimulates subsequent actions. It then analyses the fundamental concepts used in the definition: action, agent, medium, trace and coordination. It clarifies how stigmergy enables complex, coordinated activity without any need for planning, control, communication, simultaneous presence, or even mutual awareness. The resulting self-organization is driven by a combination of positive and negative feedbacks, amplifying beneficial developments while suppressing errors. Thus, stigmergy is applicable to a very broad variety of cases, from chemical reactions to bodily coordination and Internet-supported collaboration in Wikipedia.

Section snippets

Past, present and future of the “stigmergy” concept

The concept of stigmergy was proposed by the French entomologist Pierre-Paul Grassé (Grassé, 1959) to describe a mechanism of coordination used by insects. The principle is that work performed by an agent leaves a trace in the environment that stimulates the performance of subsequent work—by the same or other agents. This mediation via the environment ensures that tasks are executed in the right order, without any need for planning, control, or direct interaction between the agents. The notion

From etymology to definition

The term “stigmergy” was derived by Grassé from the Greek roots, stigma, which means “mark or puncture” (typically referring to the tattoo used to mark slaves) and ergon which can mean “work, action, or the product of work”. Grassé motivated this derivation by interpreting stigma as a goad, prod or spur, i.e. a stinging movement (“piqure” in the original French text) that incites activity. Ergon is then the result of previous work responsible for this stimulus or incitement. Thus, (Grassé, 1959

Basic components of stigmergy

Let us analyze the different terms in this definition and from thereon the conceptual components necessary to build a stigmergic process.

Most primitive is the concept of action, which I interpret as a causal process that produces a change in the state of the world. Normally, we assume that an action is performed by an agent, which is typically seen as an autonomous, goal-directed system. However, the concept of agent does not appear to be necessary for a definition of stigmergy: the mechanism

Coordination

According to the Oxford Dictionary, coordination can be defined as:

the organization of the different elements of a complex body or activity so as to enable them to work together effectively.

In the case of stigmergy, the “elements” are the different actions or agents. “Effectively” means that they achieve an intended effect or goal. “Working together” means that the actions are harmonious or synergetic, the one helping rather than hindering the other. “Organization” can be defined as structure

The benefits of stigmergy

How does stigmergy solve the problem of coordination? In the examples above, the different agents would regularly check the situation at the work site and as soon as they encounter the right conditions, they would start their work. For example, once the plumbers observe that the roof and windows are in place, they would start plumbing. Simultaneously but independently, the electricians would do their job. The plasterers would begin as soon as both the plumbing and the electricity are finished.

Self-organization through negative feedback

This last point deserves an elaboration. Our assumption is that agents are individually goal-directed. Cybernetics has shown how goal-directedness emerges from negative feedback: perceived deviations from the goal are compensated by counteractions (Heylighen and Joslyn, 2003, Rosenblueth et al., 1943). This most basic mode of steering is also called error-controlled regulation: whatever the origin of the deviation or “error”, once it is sensed, its effect is suppressed by a compensatory action.

Self-organization through positive feedback

Stigmergy exhibits another fundamental “signature” of self-organization (Heylighen, 2001, Theraulaz and Bonabeau, 1999): positive feedback. Error-controlled regulation assumes negative feedback: the reduction of deviations away from the goal. However, goal-directed action can also make use of positive feedback: the amplification of movements toward the goal. In the cybernetic perspective, changes in the situation not controlled by the agent are interpreted as perturbations, since they move the

Conclusion

Our theoretical analysis of stigmergy has illustrated how wide-ranging and fundamental this mechanism is. Virtually all evolved processes that require coordination between actions seem to rely at some level on stigmergy, in the sense that subsequent actions are stimulated by the trace left by previous actions in some observable and manipulable medium. The trace functions like a registry and map, indicating which actions have been performed and which still need to be performed. It is shared by

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