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to appear in T. Lewis & L. Marsh (Eds.), Human Stigmergy: Theoretical Developments
and New Applications. Springer.
1
Stigmergy as a Universal Coordination Mechanism:
components, varieties and applications
Francis Heylighen
Evolution, Complexity and Cognition group
Vrije Universiteit Brussel
Abstract: The concept of stigmergy has been used to analyze self-organizing
activities in an ever-widening range of domains, including social insects, robotics,
social media, 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 a subsequent action. It then analyses the
fundamental concepts used in the definition: action, agent, medium, trace and
coordination. Stigmergy enables complex, coordinated activity without any need
for planning, control, communication, simultaneous presence, or even mutual
awareness. This makes the concept applicable to a very broad variety of cases,
from chemical reactions to individual cognition and Internet-supported
collaboration in Wikipedia. The paper classifies different varieties of stigmergy
according to general aspects (number of agents, scope, persistence, sematectonic
vs. marker-based, and quantitative vs. qualitative), while emphasizing the
fundamental continuity between these cases. This continuity can be understood
from a non-linear dynamics that lets more complex forms of coordination evolve
out of simpler ones. The paper concludes with two specifically human
applications, cognition and cooperation, suggesting that without stigmergy these
phenomena may never even have evolved.
Past, present and future of the “stigmergy” concept
The concept of stigmergy was introduced 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 of stigmergy
allowed Grassé to solve the “coordination paradox” (Theraulaz & Bonabeau, 1999), i.e.
the question of how insects of very limited intelligence, without apparent communication,
manage to collaboratively tackle complex projects, such as building a nest.
to appear in T. Lewis & L. Marsh (Eds.), Human Stigmergy: Theoretical Developments
and New Applications. Springer.
2
The insight came from Grassé’s observation of how termites repair their nest. He
noted that initially termites wander around more or less randomly, carrying mud and
depositing it here or there. However, the deposits that are created in this haphazard way
then stimulate the insects to add more mud in the same place. Thus, the small heaps
quickly grow into columns that eventually come together to form an intricate cathedral of
interlocking arches. The only communication between the termites is indirect: the
partially executed work of the ones provides information to the others about where to
make their own contribution.
Another classic example of stigmergy can be found in the pheromone trails left by
ants that come back from a food source (Sumpter & Beekman, 2003). The pheromone
stimulates other ants to follow the same path. When they find food, they too will
reinforce the pheromone trail while following the trail back to the nest. This mechanism
leads to the emergence of an efficient network of trails connecting the nest via the
shortest routes to all the major food sources.
Up to about 1990, the notion of stigmergy appears to have remained limited to a
small circle of researchers studying the behavior of social insects. However, one of these
insect specialists, Jean-Louis Deneubourg, was also a member of the “Brussels School”
of complex systems, headed by the late Nobel Prize in chemistry, Ilya Prigogine. In this
interdisciplinary environment, it became clear that stigmergy was a prime example of
spontaneous ordering or self-organization (Camazine et al., 2003; Deneubourg, 1977),
and as such potentially applicable to complex systems other than insect societies.
With the advent of the agent-based paradigm in computer simulation, insect
societies were conceptualized as swarms of simple agents that are able to perform
complex tasks using various forms of self-organization, and especially stigmergy
(Deneubourg, Theraulaz, & Beckers, 1992). The general ability to tackle complex
problems exhibited by such self-organizing multi-agent collectives became known as
swarm intelligence (Bonabeau, Dorigo, & Theraulaz, 1999; Kennedy, 2006). One class of
stigmergic mechanisms in particular, so-called ant algorithms, turned out to be
surprisingly powerful in tackling a variety of computational problems, including the
notorious traveling salesman problem (Dorigo, Bonabeau, & Theraulaz, 2000) and the
optimization of packet routing along communication networks (Kassabalidis et al., 2001).
A similar stigmergic mechanism was recently recognized in molecular biology
(Tabony, 2006) to explain the self-organization of the microtubules that support many
functions in the cell. These microscopic tubes change shape and move by absorbing
tubulin proteins at one end, and releasing them at the other end. The “trail” of tubulin left
at the shrinking end attracts the growing ends of other microtubules, resulting in the
formation of a coherent “wave” of microtubules moving in the same direction.
Stigmergy was applied not only to software agents, but to their hardware
analogues: autonomous robots. Groups of very primitive robots proved able to tackle
non-trivial tasks, such as clustering items in different groupings, in a way similar to ants
(Beckers, Holland, & Deneubourg, 1994; Deneubourg et al., 1991; O. Holland &
Melhuish, 1999). These robotic implementations inspired the application of stigmergic
to appear in T. Lewis & L. Marsh (Eds.), Human Stigmergy: Theoretical Developments
and New Applications. Springer.
3
models to problems of coordination and control in manufacturing (Valckenaers, Van
Brussel, Kollingbaum, & Bochmann, 2006). After this expansion of the stigmergy
concept from social insects to the domains of artificial life, artificial intelligence and
behavior-based robotics, a perhaps obvious next step was computer-supported
collaboration between human agents, in particular via the world-wide web (Dron, Boyne,
& Mitchell, 2001; Heylighen, 1999; Elliott, 2007; Bolici, Howison, & Crowston, 2009).
A prototypical example is Wikipedia, the free web encyclopedia which has grown
to become the largest one in existence thanks to the fact that every reader is stimulated to
improve and expand the writings of previous contributors (Heylighen, 2007). A similar
dynamics of contributions building further on previous contributions characterizes open-
source software development (Bolici et al., 2009; Robles, Merelo, & Gonzalez-Barahona,
2005). But it quickly became clear that human collaboration does not need computer
support to profit from stigmergy (Parunak, 2006; Elliott, 2007). Probably the best-known
example of stigmergic self-organization is the “invisible hand” of the market: the actions
of buying and selling leave a trace by affecting the price of the transacted commodities.
This price in turn stimulates further transactions. Via the related conceptions of
distributed cognition and the extended mind, stigmergy has now also started to make its
mark on theories of cognition and epistemology (Marsh & Onof, 2008; Ricci, Omicini,
Viroli, Gardelli, & Oliva, 2006; Susi & Ziemke, 2001).
It is clear that since 1990, the concept of stigmergy has undergone a rapid
diffusion across an ever-growing number of application domains. While the number of
publications that mention the term “stigmergy” appears to have remained roughly
constant at about 1 per year in between 1960 and 1990, the following years witnessed an
impressive exponential growth in that number: from 3 in 1991 to about 500 in 2006 (as
measured via a search on scholar.google.com). The growth then slowed down, reaching
about 700 in 2013. However, to me it seems likely that this is still merely the first stage
of an on-going development. The as yet underinvestigated application of stigmergy to
human affairs opens the way to a virtually limitless expansion across the various
scientific, technological and social disciplines that study society, cognition, and behavior.
I contend in this paper that the potential for theoretical explanation and practical
application of the stigmergy concept is much larger still than hitherto assumed. What
(Parunak, 2006) noted about human institutions, that the more difficult issue is to find
examples where stigmergy does not apply, extends to complex systems in general, and in
particular to systems that exhibit some form of cognition, cooperation, or organization
that is the result of evolution. When properly defined, the mechanism of stigmergy
appears to be nearly ubiquitous, and able to illuminate a variety of conceptual problems
in a non-trivial manner.
The matter of definition, however, is crucial to a proper understanding and
application. Definitions in the literature tend to be vague, restricted in scope, and
mutually incoherent (Dipple, Raymond, & Docherty, n.d.; Shell & Mataric, 2003).
Misunderstandings have arisen particularly because of a confusion between the general
notion of stigmergy and its specific instantiation in ant algorithms, i.e. the reinforcement
to appear in T. Lewis & L. Marsh (Eds.), Human Stigmergy: Theoretical Developments
and New Applications. Springer.
4
with pheromones of frequently traveled paths by virtual “ants”. The depositing of
pheromone traces is an example of what we will call quantitative, marker-based
stigmergy (Parunak, 2006). Stigmergy in the most general sense does not require either
markers or quantities. Another, even more common misunderstanding is that stigmergy
only concerns groups or swarms consisting of many agents. As we will show, stigmergy
is just as important for understanding the behavior of a single individual.
The next section of this paper will clarify the meaning of stigmergy, propose an
unambiguous definition, and summarize its benefits in explaining spontaneous forms of
coordination. We will then go into greater depth concerning the different components and
aspects of the mechanism. This will allow us to situate and classify the apparently very
different forms of stigmergy, while remaining focused on their common core.
Perhaps a last question to conclude this introductory section: if stigmergy is so
fundamental, ubiquitous and explanatorily powerful, then why has it taken so long for it
to be recognized? The more obvious answer is that the study of termites that gave rise to
this conception is a very specific discipline with no evident applications to other sciences.
Moreover, the defining publication (Grassé, 1959), appearing in French in a specialized
journal, obviously only reached a limited audience. Its reach appears to have widened
significantly only after Deneubourg, a researcher active in both French and English, and
the domains of both social insects and self-organizing systems, started applying the
concept outside of its original context.
But why did not someone else come up with this simple and elegant notion? A
more fundamental answer is that stigmergic interaction is by definition indirect, while our
mind is biased to look for direct causes of the phenomena we observe. If we note that
agents act in a coordinated way, our natural inclination is to seek the cause of one agent’s
behavior directly in another agent’s behavior, assuming that there is an immediate
communication from the one to other. Failing to find this link, we assume that the agents
are driven by the same cause, such as a shared instinct, plan, or leader that controls their
behavior. We do not spontaneously consider the option that one agent may drive another
agent’s behavior only via the indirect route of an unintentional trace left in a passive
environment.
Finally, we tend to assume that intelligent organization must be produced by an
intelligent agent, as illustrated by Paley’s well-known watchmaker argument (Dawkins,
1996). Darwin’s theory of natural selection provides a mechanism that can generate
complex organization without presupposing intelligence. However, its counter-intuitive
nature may be illustrated by the fact that, in spite of massive empirical evidence, it is still
being challenged by the “intelligent design” school (Behe, 2009). Another proposed
mechanism to generate coordinated activity, self-organization, is much more recent, and
is still far from being generally accepted and, even less, generally understood. I wish to
suggest here that stigmergy is another type of mechanism for generating complex
organization and intelligent behavior, which is related to both natural selection and self-
organization, but which has some distinct features of its own that may resolve some
outstanding problems with these previously proposed explanations.
to appear in T. Lewis & L. Marsh (Eds.), Human Stigmergy: Theoretical Developments
and New Applications. Springer.
5
The meaning of stigmergy
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) defined stigmergy as
“the stimulation of workers by the very performances they have achieved” (from the
original English abstract).
However, in a more recent review paper, (Parunak, 2006) proposes a different
reading of the Greek etymology that is at least as compelling: if we interpret stigma as
“mark” or “sign” and ergon as “action”, then stigmergy is “the notion that an agent’s
actions leave signs in the environment, signs that it and other agents sense and that
determine their subsequent actions”. Summarizing, in Grassé’s interpretation the product
of work (ergon) functions as a stimulus (stigma) for action; in Parunak’s interpretation,
action (ergon) leaves a mark (stigma). While this double interpretation may seem to add
to the confusion, it actually provides an elegant illustration of the bidirectional nature of
stigmergy. The process described by both Grassé and Parunak is a feedback loop, where
an action produces a mark which in turn incites an action, which produces another mark,
and so on (see Fig. 1). In other words, actions stimulate their own continued execution
via the intermediary of the marks they make—where a mark is a perceivable effect, trace
or product of an action.
This brings me to my own definition:
stigmergy is an indirect, mediated mechanism of coordination between actions, in
which the trace of an action left on a medium stimulates the performance of a
subsequent action.
to appear in T. Lewis & L. Marsh (Eds.), Human Stigmergy: Theoretical Developments
and New Applications. Springer.
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Fig. 1: the stigmergic feedback loop
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: as we will see, the mechanism applies perfectly well to the coordination of
actions performed by a single, unspecified agent, in which case there is no need to
identify different agents. Moreover, further extensions of the stigmergy concept can even
do away with the notion of agent altogether, and consider the coordination of “agentless”
actions that are merely events or physical processes—such as chemical reactions. This
views fits in with the ontology of action (Heylighen, 2011; Turchin, 1993), which sees
action as the primitive element from which all other concepts are derived. The concept of
agent remains useful, though, in cases where we wish to distinguish different agents able
to perform different actions.
As causal processes, actions have an antecedent or cause, and a consequent or
effect. In simple agent-based models used in artificial intelligence the antecedent is
usually called condition, and the consequent simply action. The condition specifies the
state of the world in which the action occurs, while the action specifies the subsequent
transformation of that state. The causal relation is represented as a “production rule” or
production, which consists of the simple relation:
condition
→
action
It is to be read as:
IF condition holds, THEN perform action
to appear in T. Lewis & L. Marsh (Eds.), Human Stigmergy: Theoretical Developments
and New Applications. Springer.
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For example, a thermostat will obey the production rule: IF the temperature is below the
goal temperature, THEN switch on the heating (Heylighen & Joslyn, 2003). While this
reading seems to imply an elementary cognitive process of sensation or perception, to
ascertain whether the condition holds, the notation is equally applicable to agentless,
physical processes. For example, consider the following chemical reaction:
NaOH + HCl → NaCl + H2O
The first part represents the necessary condition for the reaction to occur: an NaOH
molecule and an HCl molecule must be simultaneously present. The second part of the
reaction represents the product or result of the reaction: the formation of an NaCl
molecule together with an H2O molecule. More generally, we can write such reactions in
the following form (where the “+” operators represents a conjunction of the conditions or
resources necessary for the process to take place):
a + b + … → x + y + …
Chemical Organization Theory (Dittrich & Fenizio, 2007) is a formal framework
that shows how collections of such simple reactions can become coordinated by acting on
a shared medium, the “reaction vessel”, where they produce an evolving trace expressed
by the concentrations of the different “molecules” (a, b, …). This coordinated pattern of
activity defines an “organization”: a self-sustaining, dynamic network of interacting
“molecules”. While the inspiration for this model comes from chemistry, it is equally
applicable to other kinds of abstract actions in which the agent is ignored—such as
political and economic interactions (Dittrich & Winter, 2005, 2008)
According to our definition, the action part of a rule produces a change in the state
of the world. This means that it creates a new condition, which may activate another
condition → action rule, and thus a new action. For example, the thermostat, by switching
on the heating, will eventually produce the new condition “temperature high enough”,
which in turn will trigger the new action “switch heating off” (Heylighen & Joslyn,
2003). The NaCL molecule may react with another molecule in the solution and thus
produce yet another compound. This triggering of an action by a previous action via the
intermediary of its result is precisely what Grassé defined as stigmergy. Yet, the way we
arrived at this notion is so simple and general that it merely requires a minimal
assumption of causality. In the next sections, we will need to explain how such a simple
mechanism can produce such rich and unexpected phenomena.
First, we should note that the causal relation does not need to be fully
deterministic: in general, the condition is neither necessary nor sufficient for the action to
occur. According to Grassé’s definition of stigmergy, the condition merely stimulates the
performance of the action. This means that the presence of the condition makes the
performance of the action more probable. Formally:
to appear in T. Lewis & L. Marsh (Eds.), Human Stigmergy: Theoretical Developments
and New Applications. Springer.
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P(action | condition) > P(action),
where P(A) is the general probability of A occurring, and P(A|B) the conditional
probability of A occurring given that B is the case.
Note that in some cases, a condition may on the contrary inhibit an action, i.e.
make it less likely. For example, the presence of a red light makes it less likely that
someone would cross the street. In that case, we may still keep to the definition of
“stimulation” above, simply by considering the opposite or negation of that condition as
the stimulus: e.g. the disappearance of a red light makes it more likely that someone
would cross the street.
We must now introduce another core component of stigmergic activity, the
medium. The medium is that part of the world that undergoes changes through the
actions, and whose states are sensed as conditions for further actions. The medium is a
non-trivial entity, since many aspects of the world are either not affected by actions, or
not perceivable as conditions for new actions. For example, while I can clearly see the
clouds in the sky, no matter how hard I try, I cannot change their position. Vice-versa, I
have the power to throw a rock in the sea, but I cannot see where that rock will end up. In
either case, there is no basis for a stigmergic chain of actions triggering further actions.
On the other hand, I can both perceive and affect the arrangement of sand on a beach, and
this allows me to build an intricate sand castle via a coordinated sequence of condition →
action pairs. Neither the sea nor the sky is a stigmergic medium, but the beach is.
Note that most authors (e.g. Parunak, 2006) use the term “environment” for what I
call “medium”. This term is much less accurate, though. First, as noted, the environment
is not in general both perceivable and controllable. Second, the environment normally
denotes everything outside the system or agent under consideration. However, stigmergy
can also make use of an internal medium. For example, different physiological processes
in the body communicate via the release of hormones in the bloodstream (medium). This
communication is indirect: e.g. the liver does not directly send a message to the brain;
both merely “read” the hormonal messages deposited in the blood that irrigates both.
More generally, many aspects of the agent's own state, such as the agent's position, speed
and orientation, belong to the medium, since they are controllable and perceivable by self
and others. In the example of the chemical reactions, the medium is the reaction vessel
containing the solution in which the molecules are present.
Finally, if we conceive the environment as that part of the world that interacts
with an agent, then different agents live in different environments or “Umwelts”: not all
phenomena perceivable or controllable by one agent are similarly perceivable and
controllable by another agent. When we consider stigmergic coordination between
different agents, we need to define the medium as that part of the world that is
controllable and perceivable by all of them. This is necessary to ensure that the different
agents can interact via the medium. The role of the medium is to allow interaction or
communication between different actions, and thus, indirectly, between the agents that
to appear in T. Lewis & L. Marsh (Eds.), Human Stigmergy: Theoretical Developments
and New Applications. Springer.
9
perform the actions. It is this mediating function that underlies the true power of
stigmergy (Heylighen, 2006).
A final component of a stigmergic system is the mark or trace, i.e. the perceivable
change made in the medium by an action, which may trigger a subsequent action. I prefer
the term “trace” because it can denote an unplanned or even undesired side effect of the
action, unlike a “mark” which is normally made intentionally. As we will see, some
forms of stigmergy rely on intentionally made signs or signals (“markers”), but in the
most general situation, this is not the case. The trace is a consequence of the action, and
as such, it carries information about the action that produced it. We might see the trace as
a message deposited in the medium through which the pattern of activity communicates
with itself, or maintains a continuously updated “memory” of its achievements. From the
point of view of an individual agent, on the other hand, the trace is a challenge: a
situation that incites action, in order to remedy a perceived problem or shortcoming, or to
exploit an opportunity for advancement (Heylighen, 2012a).
Goal-directed action
Let us assume that actions are performed by agents with a minimal form of intentionality,
i.e. agents whose actions are appropriate to the conditions that trigger them, in the sense
that they help the agent to move toward its (implicit or explicit) goals. This is an
application of what Dennett (1989) called the “intentional stance”.
This assumption is less strong than it may seem, since natural agents (such as
living organisms) have the implicit goal of fitness (i.e. survival and reproduction) built
into them by natural selection, while artificial agents (such as thermostats or robots) have
their goals specified by their designers. Even natural, non-living objects, such as stones or
molecules, can be seen as goal-directed, in the sense that their dynamics can always be
modeled as trying to optimize some function of their state (Heylighen, 2011; Mesarović
& Takahara, 1975) (e.g. potential energy).
This assumption allows us to add a “virtual” component to the stigmergic
mechanism, i.e. a component that in a sense only exists for the observer: the tasks that the
stigmergic system is to perform. Since a stigmergic system does not plan, it generally
does not have any awareness or representation of the tasks, jobs or duties that it still has
to carry out. But for the outside observer, it may be helpful to use the term “tasks” as
shorthand for the actions that are to be performed. A task can be defined as an action that:
1) is required to achieve the agents' goals;
2) is not yet performed;
3) can be performed on the present medium once the right conditions arise.
This minimal intentionality means that actions are not random or blind, like the
mutations that underlie biological evolution, but generally produce some improvement in
the agent's situation, i.e. movement closer to the goal. Reaching a far-away goal,
however, requires more than a minimal intelligence: this will typically necessitate a
complex, coordinated scheme of actions, performed according to a specific order or logic.
to appear in T. Lewis & L. Marsh (Eds.), Human Stigmergy: Theoretical Developments
and New Applications. Springer.
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The difficulties involved in problem solving, planning, and project management may
remind us that there is no simple or obvious way to go from elementary actions to
complex activity schemes. This brings us to the problem of coordination (Crowston,
1997), which stigmergy appears to solve.
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 with function (Gershenson & Heylighen,
2005). The function is the achievement of the intended effect. A “structure” consists of
distinct elements (the actions or agents) that are connected in such a way as to form a
coherent whole. This brings us to focus on the connections that integrate the actions into
a synergetic, goal-directed whole.
According to coordination theory (Crowston, 1997), we can distinguish the
following fundamental dependencies or connections between actions or processes:
1) one action can be prerequisite for the next action: the product or output of the first
is a necessary condition or input for the second. This determines the sequential
organization of the process, or workflow, where activity moves step-by-step
through a sequence of tasks (what needs to be done next?).
2) two actions can require the same condition (input) and/or contribute to the same
effect or goal (output), i.e. they are performed in parallel. This determines the
allocation of resources (who receives what?) and the division of labor between
agents (who is to do what?).
Effective coordination means that the right actions are performed by the right agents at
the right time and place. Let us consider the building of a house as an activity that
requires coordination between its different tasks. The task of laying electricity obviously
can only be performed once the windows and roof are installed. Roofing is therefore
prerequisite for laying electricity, and the electricians will have to wait until the roofers
are finished. Plastering the interior walls, on the other hand, can only be done after the
electrical cables and outlets have been dug into the walls. This implies the sequence:
roofing → laying electricity → plastering. On the other hand, plumbing and laying
electricity can be performed simultaneously or in parallel, since they both require roofing
and are prerequisite for plastering, but are otherwise independent of each other. The
to appear in T. Lewis & L. Marsh (Eds.), Human Stigmergy: Theoretical Developments
and New Applications. Springer.
11
dependencies or connections between these different processes can be represented in the
following “workflow” diagram (Fig. 2).
ro ofi ng p la st er ing
laying
electricity
plumbing
pa in tin g
parallel
sequential
Fig. 2: parallel and sequential connections between tasks
This diagram represents only a small part of the complex of activities that is
necessary to construct a building. Construction work and other complex activities are
normally planned in detail beforehand, using tools such as project schedules and GANTT
charts, to specify the dependencies between the different tasks. This planning is necessary
to make sure that the work is efficiently performed, by avoiding situations such as the
plasterers turning up when the plumbing is still going on so that they cannot start their
work. The plan will normally specify the beginning and end of all the actions as well as
the agents that are to perform them, and possibly the places or resources that the agents
need to access. If everybody keeps to this plan, the plasterers will show up on the exact
time and place that the plumbers are supposed to have finished their work.
The problem with planning, of course, is that there will always be unforeseen
contingencies, such as the plumbers needing an extra day to finish their work, or, on the
contrary, finishing two days early. In both cases, the work is performed less efficiently
than it could be, either because the plasterers need to go home because the plumbing is
not ready yet, or stay home waiting for the work to finish when they could already have
started. Contingencies disturbing carefully laid-out plans can have even worse results, as
illustrated by the following joke:
A pensioner watches two city workers busy in the municipal park. The one digs a
series of deep holes at regular intervals. The other one then shovels the mounds of
earth carefully back into each hole, and flattens the soil. The pensioner asks him:
“Isn't that a waste of effort what you are doing?”, to which the worker replies:
“No, we always work this way, and it is very efficient. It is just that the third guy
who plants the trees did not show up today.”
One way to deal with such contingencies is to let the agents communicate about their
work. For example, the plumbers finishing early or late could call the plasterers to warn
to appear in T. Lewis & L. Marsh (Eds.), Human Stigmergy: Theoretical Developments
and New Applications. Springer.
12
them about the different finishing date. However, this assumes that agents know all other
agents that depend on their work, and have a general notion of what these dependencies
are so that they can improvise or reschedule their activity in the light of the new
information. With complex activities, this is tricky and can easily lead to
misunderstandings or confusions that make things worse. An alternative is that all agents
report to a supervisor, who keeps track of the plan, reschedules if need be, and warns
everyone involved of the changes. However, such central controller becomes a bottleneck
that is even more sensitive to disturbances, creating the risk that the whole plan falls apart
because the supervisor is not available to pass on reschedules.
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. On the other
hand, the municipal worker would fill a hole only on the condition that it contains a tree.
While this approach may seem natural for termites, who are anyway all
wandering around their nest building site, you might wonder whether it would not be
inefficient to demand that specialized workers visit the site every day while they are not
yet needed. However, this can be easily tackled with modern technology, by providing a
website on which the state of the work is registered in real time. In this way, the plumbers
can see immediately whether they are needed, without losing time traveling to the site.
The website plays the role of a medium providing special markers to guide the execution
of the work—similar to the pheromones used by ants.
This is in essence how a community of programmers residing in different parts of
the world collaboratively develop a complex suite of open-source software: they
regularly check their shared website for new modules, updates, requests for features, or
postings of bugs. They address these challenges by writing additional code or suggesting
solutions, posting these results in turn on the website for others to see and to elaborate
further (Bolici et al., 2009; Heylighen, 2007; Heylighen, Kostov, & Kiemen, 2013). Such
open source development has proven to be at least as effective as the traditional planned
software development performed in large corporations (Weber, 2004), without requiring
any central supervision or other complicated arrangements (Raymond, 1999).
Perhaps the only disadvantage compared to a perfectly designed and executed
plan, is that the stigmergic approach does not guarantee an optimal use of the
“workforce”. While the roofers are working, the plumbers must either wait or perform
another task. If they are busy with another task, there is no guarantee that it will be
finished exactly when the roofers finish their job. This suboptimal use of workers can be
minimized by creating a pool of available workers (much) larger than needed for this
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particular job, so that together they can keep track of several jobs in parallel. Assuming
that the tasks do not all start at the same time, there would always be some workers
available for any job that opens up, without requiring workers to wait long times in
between jobs, or tasks to wait long for workers to execute them. This is the approach
underlying the job ticketing systems used in call centers (Heylighen & Vidal, 2008;
Orrick, Bauer, & McDuffie, 2000), but also the one used by ants and termites. It explains
why the best-known applications of stigmergy typically rely on “massive parallelism”,
i.e. many agents active simultaneously (Manderick & Moyson, 1988). In the case of
software development, there is no particular time at which a coding job has to be done, so
programmers can be flexible in deciding when to produce an improvement suggested by
the stigmergic repository of tasks and products.
With such a stigmergic organization, no conflicts between instructions and reality
arise, no needless delays occur and no effort is wasted—whatever the contingencies that
may disturb the plan. Moreover, this solution is perfectly robust, and independent of any
errors in communication or control. It also does not depend on the number of agents,
tasks, or dependencies between tasks. This allows it to scale up to tasks of indefinite
sizes. The only requirements are that the agents can recognize the right conditions to start
their work, and that they can all access the medium in which these conditions are
registered. In summary, stigmergy provides an extremely simple and reliable solution to a
problem that is potentially unlimited in complexity.
Compared to traditional methods of organization, stigmergy makes absolutely
minimal demands on the agents. In particular, in stigmergic collaboration there is no need
for:
• planning or anticipation: agents only need to know the present state of the
activity; the overall goal, next step or end result is irrelevant for their present
work. In Wikipedia, there is no plan specifying which information should be
added to the encyclopedia when.
• memory: agents do not need to remember their previous activity; no information
about the state of the work needs to be stored anywhere except in the medium.
• communication: no information needs to be transferred between the agents,
except via the work done in the medium; there is in particular no need for the
agents to negotiate about who does what.
• mutual awareness: each agent works independently; it does not even need to
know that others participate. For example, contributors to Wikipedia generally do
not know each other or communicate with each other.
• simultaneous presence: there is in general no need for the agents to be present at
the same time or at the same place; tasks are registered in the medium so that they
can be picked up by agents whenever and wherever they are available. That is
how worldwide communities can collaborate on a single software project.
• imposed sequence: actions are performed automatically in the right order, since
an action will not be started until the right condition is in place; the workflow
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emerges spontaneously, as the completion of one task triggers the initiation of the
next task(s)
• imposed division of labor: each agent will only perform the actions for which it
has the required competence, i.e. for which it possesses adequate condition-action
rules; normally, the more “confident” the agent is about the right action (i.e. the
stronger the connection between condition and action), the more it will be
stimulated by the condition, and the quicker it will be to start the job; in this way,
tasks are automatically assigned to the most competent agents (Heylighen &
Vidal, 2008)
• commitment: agents do no need to commit to a particular task (in contradiction
to what (Jennings, 1993) claims about multi-agent coordination); an agent decides
on the spot what work it should do, depending on opportunity and other
contingent conditions; an agent that quits or otherwise becomes unavailable is
automatically replaced by another one
• centralized control or supervision: errors or perturbations are automatically
corrected, as they merely create a new condition stimulating new actions to deal
with the challenge; the activity is self-organizing: global organization emerges
from local interactions, without any centralized control directing the activity. For
example, bugs in open-source software are spotted by users, and resolved by other
contributors.
Stigmergy as self-organization
This last point deserves a further 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 & Joslyn, 2003; Rosenblueth, Wiener, & Bigelow, 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 an appropriate
compensatory action. This control mode does not require any planning, anticipation
(feedforward), memory, or understanding of what caused the deviation. To efficiently
control the effect, it is sufficient that the agent is able to exert an influence in the
“opposite direction” of any deviation, independently of its underlying cause (Gershenson
& Heylighen, 2005; de Latil, 1956).
This mechanism is well understood for individual agents (Powers, 1973).
Stigmergy illustrates how it can be extended to several interacting agents. Imagine a
group of non-communicating agents (e.g. ants, or people who do not speak a common
language) pushing a large obstacle out of the way across an irregular terrain. Individually,
each agent will correct its course based on the perceived movement of the load: e.g. if it
shifts too much to the left, the agent will push more towards the right. It does not matter
whether the deviation was caused by a hole in the surface, a sudden gust of wind, or the
misdirected action of another agent. The overall movement will be determined by the
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sum of the actions performed by all the individuals. As long as the agents push in
generally the same direction, it is irrelevant who did what. The agents can work perfectly
independently—perhaps even without knowing that someone else is pushing too—while
still producing a coordinated movement.
A similar mechanism is probably involved in bodily coordination, where different
muscles, tendons and bones contribute to the overall movement of the body. This may be
illustrated by the subsumption architecture used for the control of the different body parts
of many-legged robots (Brooks, 1991), where each limb functions more or less
autonomously in helping the robot to move forward, while the only higher-order control
imposed is the general direction of movement.
The only assumption we need to add to individual error-controlled regulation, is
that the goals of the agents are not contradictory—i.e. that error decrease for one agent
does not equal error increase for another agent—because then the agents will be involved
in a tug-of-war of opposing counteractions that can only end when the stronger subdues
the weaker. Note that the goals do not need to be identical for coordination to occur:
imagine that one group of agents pushes the obstacle to the east, while another group
pushes to the north. The net effect is that the load will move northeast, satisfying both
groups. It is only when one group pushes eastward and another group westward that a
conflict arises, without possibility for a compromise. In this two-dimensional movement
example, the probability for conflict still seems large. However, the larger the number of
aspects, components or degrees of freedom of the problem situation, the more freedom
there is for agents to focus on different goals without getting in each others’ way.
This independence of goal setting is what underlies the automatic division of
labor: each agent spontaneously focuses on the task that it deems most important (and for
which it is in general most competent). Thus, a variety of agents together can potentially
tackle very complex problems that require the achievement, in sequence or in parallel, of
many different partial objectives. We may assume that agents have acquired their
condition-action rules (and thus their implicit goals) through natural selection of
instinctual behavior or differential reinforcement of learned behavior. This means that
their condition-action rules are generally appropriate to the local environment, including
the other agents with which they regularly interact. Rules that are frequently in conflict
with the rules of other agents or the constraints of the environment are likely to be
eliminated eventually (Heylighen, 2008a).
Therefore, it is plausible to assume that even very different agents, e.g. belonging
to different species in an ecosystem, follow rules that are potentially synergetic (Corning,
1995; Heylighen, 2013b). Stigmergy seems to be a prime mechanism through which this
synergy is realized, by coordinating initially independent actions into a harmonious
whole. Thus, the group of agents can achieve much more substantial results collectively
than they would if they would work alone. It is this emergence of global order out of
local actions that constitutes the hallmark of self-organization (Heylighen, 2001). It
implies in particular that organization arises spontaneously from local activity, without
planning, centralization or external control. Problems, contingencies or disturbances will
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be tackled by the same local action: since there is no plan, there can be no deviation from
the plan and therefore no true “error”; everything is contingent and subject to the same,
incessant activity of adaptation or improvement.
Affordances, disturbances and feedback
Stigmergy exhibits another fundamental “signature” of self-organization (Heylighen,
2001; Theraulaz & Bonabeau, 1999): positive feedback. Error-controlled regulation
typically assumes negative feedback: the reduction of deviations away from the goal.
However, goal-directed action can as well make use of positive feedback: the
amplification of movements towards the goal (Maruyama, 1963). In the traditional
cybernetic perspective, changes in the situation not controlled by the agent tend to be
interpreted as perturbations, since they move the system away from a previously achieved
goal state (Heylighen & Joslyn, 2003; Maturana & Varela, 1980). However, as long as no
final goal is reached—which is the default situation in long-term, on-going projects, such
as building, extending and maintaining a termite hill—such contingent events may as
well facilitate as hinder the further movement toward the goal. When they hinder, we will
call them disturbances; when they facilitate, we can call them affordances (Gibson,
1977). In the most general case, we may call them diversions, since they divert action
from its on-going course, whether in a positive, negative or neutral way (Heylighen,
2012a). Assuming that agents are implicitly goal-directed, we may infer that they will
counteract the disturbances and reinforce or build upon the affordances, i.e. exert a
negative, respectively positive, feedback to negative, respectively positive, diversions.
Similarly, their reaction to a neutral diversion will be neutral: neither amplifying it nor
suppressing it.
Let us illustrate these notions with the paradigmatic case of termites erecting a
pillar as part of their nest construction. A bit of mud that is accidentally dropped in a
particular place, either by a termite, the wind or a passing bird, constitutes a diversion. In
this case, the diversion constitutes an affordance, since it provides a foundation on which
a taller mud structure can be erected. Stigmergic stimulation will lead termites to add
mud to the emerging heap, rather than to the flat surfaces surrounding it. The taller the
heap grows, the stronger the stimulus it will exert on termites passing by, and therefore
the faster its further growth. This positive feedback loop results in an accelerated
exploitation of the opportunity, diverting effort away from less promising alternatives,
and thus efficiently allocating agents and resources to the most productive activities.
Suppose now that a fragment of the thus erected column breaks off. This
constitutes a negative diversion, i.e. a disturbance. In this case, the perception of the
missing mud will stimulate the termites to fill the hole with new mud, thus counteracting
the deviation from the ideal column shape. Finally, a neutral diversion may arise, such as
a breeze blowing some termites off-course, so that they end up near a different column
than the one they were heading to. While making the activity deviate from the original
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course, this event neither facilitates nor hinders the work. Therefore, it will be neither
counteracted nor reinforced.
A similar dynamics occurs in Internet communities centered on a particular
forum, website or page. More activity on a particular site tends to produce more
interesting traces, such as discussions, wiki pages, or comments, which attract more
people and therefore contributions, such as additions to the wiki or replies to proposals,
which in turn incite more activity. Vice versa, less activity reduces the level of interest
for the products of that activity, and thus the number of potential further contributions.
Thus, web communities and their activities are subject to a clear positive feedback, where
the initially most promising “projects” grow very quickly, while the less promising ones
dwindle, losing the competition with the others, and potentially disappearing altogether.
In this way, work is divided relatively efficiently across a wide variety of projects,
ensuring that the most promising ones quickly “take off” without dissipating too much
energy in less promising ones.
The combination of positive and negative feedbacks is typical for complex,
adaptive or self-organizing systems (Heylighen, 2001; J. H. Holland, 1996). It makes the
system very flexible, allowing it to act and grow energetically when given the
opportunity, while maintaining a stable and robust configuration in the face of
disturbances. It also produces differentiation, by amplifying minute differences or chance
fluctuations into robust macroscopic structures (Nicolis & Prigogine, 1977). Finally, it
makes the system intrinsically non-linear, which implies that for the outside observer its
evolution is both unpredictable and uncontrollable.
Parallel action and the wisdom of crowds
As noted, (stigmergic) coordination has two aspects: parallel and sequential. Agents or
rules working in parallel simply add their effects together. Because their actions are
simultaneous, there is no time to interact, i.e. for the one to causally affect the other.
Therefore, their total effect is simply the aggregate, superposition or sum of their
individual effects. Rules working in sequence, however, by definition interact, since the
result of the former affects the performance of the latter. This allows non-linearity, i.e. a
total effect different from the sum of the individual effects. This total may be larger—in
which case there is amplification or positive feedback—, or smaller—which means
suppression or negative feedback. As we saw, amplification is useful to exploit
affordances, suppression to control disturbances. The combination of parallel and
sequential—or linear and non-linear—aspects provides maximal opportunities for an
efficient exploration and exploitation of the situation.
Since the power of non-linearity in self-organization is well known, it is worth
paying special attention here to the less studied benefits of linear or parallel activity. We
can distinguish two cases of parallel action: 1) two or more actions are performed on the
same object or task, i.e. the same part or aspect of the medium; 2) actions are performed
on separate, independent parts of the medium. The first case may be exemplified by
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termites adding mud to the same pillar, or agents pushing the same load. The second case
can be found when two termites add mud to two different pillars, or when the one is busy
repairing the nest while the other is collecting food.
This latter case is perhaps most intuitive, since it underlies the mechanism of the
division of labor. The advantages of the division of labor are well known: it enables
specialization, so that each agent can focus on the task it has most expertise with, and
thus the task it can perform most efficiently. We already argued that stigmergy tends to
automatically allocate tasks to the most competent agents. To maximally benefit from the
division of labor, we moreover need to ensure a sufficient diversity in the competencies
of the agents (Martens, 2004): the more diverse their expertise, the more likely it is that at
least some agent(s) will be particularly competent for a certain task. As a result, a more
diverse group of agents will normally be more productive than an equally large, but more
homogeneous, group.
This general principle can be illustrated by a classic ecological experiment: if two
identical patches of land are seeded with plants that belong either to one or a few species,
or to several different species, the more diverse patch will produce more biomass than the
more homogeneous one (Cardinale et al., 2007; Naeem & Li, 1997). (The overall yield
increases with the logarithm of the number of species.) The reason appears to be that
plants of different species use the available nutrients in somewhat different ways, thus
together being able to exploit the resources more completely (“niche complementarity”),
while moreover helping each other through synergies (Hector et al., 1999). This is an
example of parallel stigmergy where synergetic interaction is mediated by the shared
environment (land).
The benefit of diversity is not limited to situations where agents work in different
places or perform different tasks. When diverse agents tackle the same problem in
parallel, their aggregate solution will in general be better than the one of any single agent
or agent type. This phenomenon has been referred to as the “wisdom of crowds”
(Surowiecki, 2005) or “collective intelligence”. It can be exemplified by the situation
where a crowd of people are asked to guess how many beans are contained in a particular
jar, or how heavy a particular ox weighs. In such cases, the average of all the guesses is
typically more accurate than any particular guess. The reason is the law of large numbers:
if we assume that guesses exhibit a random deviation from the correct answer, then these
random deviations tend to cancel each other out when a large number of them are
aggregated. Each individual deviation is caused by the limited experience or inaccurate
perception of that individual. But when perspectives are diverse, the shortcomings of the
ones tend to compensate for the shortcomings of the others, providing a more balanced,
and therefore accurate, global perception (Heylighen, 1999, 2013b).
In summary, the greater the variety of agents that work on a particular task or set of
tasks, the better we can expect their overall performance to be. Note that parallelism or
independent action makes this effect stronger (Surowiecki, 2005): if the agents work in
sequence, later ones may still compensate for the limited experience of earlier ones, but
because of positive feedback early choices are likely to be amplified. This can lead to the
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accelerated exploitation of a good solution, but also to the collective converging to a poor
solution—a phenomenon termed “groupthink” or “collective stupidity” (Heylighen,
2013b). The development of pheromone trails by ants, which happens partly in parallel,
partly in sequence, illustrates the precarious trade-off between the benefits of
parallel/linear approaches (more wide-ranging exploration) and those of sequential/non-
linear ones (more efficient exploitation) (Heylighen, 1999).
Varieties and aspects of stigmergy
Within the broad category of stigmergic mechanisms, we can distinguish many examples
and special cases. To bring some order to these phenomena, we will develop a
classification of the different varieties of stigmergy. We will do this by defining
fundamental dimensions or aspects, i.e. independent parameters along which stigmergic
systems can vary. The fact that these aspects are continuous (“more or less”) rather than
dichotomous (“present or absent”) may serve to remind us that the domain of stigmergic
mechanisms is essentially connected: however different its instances may appear, it is not
a collection of distinct classes, but a space of continuous variations on a single theme—
the stimulation of actions by their prior results.
Individual vs. collective stigmergy
Perhaps the most intuitive aspect along which stigmergic systems can vary is the number
of agents involved. In the limit, a single agent can coordinate its different actions via
stigmergic interaction with its environment.
An elegant example discussed by (Theraulaz & Bonabeau, 1999) is the solitary
wasp Paralastor sp. building its nest in the shape of a mud funnel. The nest emerges in
qualitatively different stages S1, S2, …, S5. These subsequently perceived conditions or
stimuli each trigger a fitting action or response: S1 → R1, S2 → R2, …R5. Each building
action Ri produces as a result a new condition Si+1 that triggers the next action Ri+1. The
wasp does not need to have a plan for building such a nest, or to remember what it
already did, since the present stage of the activity is directly visible in the work already
realized.
However, the underlying rule structure becomes apparent when the sequence is
disturbed so that stages are mixed up. For example, the wasp’s initial building activity is
triggered by the stimulus S1, a spherical hole. When at stage S5 (almost complete funnel)
the observer makes such a hole on top of the funnel, the wasp “forgets” that its work is
nearly finished, and starts anew from the first stage, building a second funnel on top of
the first one. This little experiment shows that the activity is truly stigmergic, and can
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only run its course when the medium (the mud) reacts as expected to the different actions
performed on it, thus registering the information needed to guide the subsequent actions.
As (Theraulaz & Bonabeau, 1999) suggest, it is likely that collaborative
stigmergy evolved from the simpler case of individual stigmergy. Imagine that a second
wasp encounters the partially finished nest of the first wasp. It too will be stimulated to
act by the perception of the present state of work. It does not matter that this state was
achieved by another individual: the wasp anyway has no memory of previous actions—its
own or someone else’s. Assume further that the resulting structure is big enough to house
the two wasps. In this case, the wasps will have collaboratively built a nest for both,
without need for any additional coordination between their genetically programmed
building instructions. Assume that the structure is modular, like the nests of social wasps,
so that an unlimited number of modules can be added. In that case, the number of wasps
that may start working together simply by joining the on-going activity on an existing
nest can grow without limit.
This example illustrates how the number of agents collaborating on a stigmergic
project is actually much less fundamental than it may seem. The essence of the activity is
always the same. Assuming that the agents have the same competencies, adding more
agents merely increases manpower and therefore the size of the problem that can be
tackled, the speed of advance, or the eventual magnitude of the achievement. Only when
the agents are diverse can an increase in their number produce a qualitative improvement
in the solution.
The only complication added is that agents may get in each other's way, in the
sense that similar individuals perceiving the same stimulus are likely to move to the same
place at the same time, thus obstructing each other's actions. This problem is easily
tackled by an additional rule, which is already implicit in individual work but likely to
become reinforced during collaborative work: keep a minimum distance from obstacles—
including other agents. This rule is a well-known ingredient in the many successful
simulations of collectively moving animals, such as flocks, schools or swarms (Okubo,
1986), allowing densely packed groups of agents to follow complex, synchronized
trajectories without ever bumping into each other. In combination with the basic
stimulation by the stimulus object, this leads to what may look like a carefully thought-
out strategy of coordinated movement. An example are group hunting strategies, as used
e.g. by lions or wolves (Parunak, 2006). Each wolf is attracted to move towards the prey
(basic stimulus). On the other hand, each wolf is stimulated to stay as far away as
possible from the other wolves. The result is an efficient encirclement of the prey, which
is attacked simultaneously from all sides with no opening left for escape.
Quantitative vs. qualitative stigmergy
Quantitative stigmergy (Theraulaz & Bonabeau, 1999) refers to perceived conditions that
differ in strength or degree, and where stronger traces typically elicit more forceful
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(intense, frequent, …) actions. This quantitative variation is perhaps best captured using
my definition of stimulation in terms of conditional probability: the stronger the trace, the
larger the probability of a certain action given that trace. Over an extended period, higher
probability implies more frequent actions by more numerous agents, and therefore more
intense overall activity. The two paradigmatic cases of stigmergy, termite nest-building
and ant trail-laying, follow this quantitative logic. The higher the emerging heap of mud
(stronger trace), the more an individual termite is attracted to it, and therefore the larger
the probability or frequency of mud being added. The stronger the scent of pheromone on
a trail, the less likely an ant is to deviate from that trail, and therefore the higher the
probability that it too will reinforce the trail with additional pheromone. These are typical
examples of the positive feedback that efficiently amplifies positive developments.
But quantitative stigmergy can also be exemplified by negative feedback, where a
stronger trace leads to less activity. A human example can be found in the market
mechanism. Extensive buying of a good (action) reduces the supply and thus increases
the price, which is a quantitative trace left by the collective buying and selling activity. A
higher price will normally reduce the probability that someone would buy additional
stock of that good (negative stimulation). Thus, a higher price reduces demand, which in
turn will reduce the price. This mechanism of self-organizing, distributed control
(Heylighen, 1997) implements the “invisible hand” of the market. It stabilizes prices and
efficiently allocates production capacity to the goods that are most in demand (Witt,
2006).
Qualitative stigmergy (Theraulaz & Bonabeau, 1999) refers to conditions and
actions that differ in kind rather than in degree. In this case, a different trace stimulates a
different type of action. An example can be found in the different stages of the building
of a funnel-shaped nest by the solitary wasp that we discussed, where each stage requires
a particular type of building action. A human example can be found in “wiki” websites
that are edited by their own readers. A paragraph that contains a semantic mistake (e.g. in
the definition of a word) will elicit a corrective action (e.g. writing a new definition).
Different types of errors, vagueness, or lack of information will stimulate different types
of additions and corrections.
In practice, there is no clear boundary between quantitative and qualitative cases
of stigmergy. All non-trivial activities require a choice from a range of potential actions.
Which of the different possibilities will be chosen is typically determined
probabilistically: in some conditions one type of action is more likely, in other conditions
another type of action. As the one condition becomes more similar to the other, the
probabilities become more similar too. In the middle, the two probabilities may become
equal, as in the situation of Buridan's ass, which had to choose between two equally
attractive options. More generally, we may assume that the probability is equal to
P (ai | c), where {ai | i = 1, …, n} is a discrete set of possible actions, while the condition
c ∈ C varies continuously over the space C of all states that the world can have. In this
model, the probability (and therefore frequency or intensity) of an action varies
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approximately continuously (quantitative variation), while the action itself is chosen from
a discrete range of options (qualitative variation).
Sematectonic vs. marker-based stigmergy
Grassé's original definition of stigmergy concerned stimulation by the performed work
itself: in his observation, termites are stimulated by the mud heaps they have already
built. E. O. Wilson (1975), in his monumental “Sociobiology”, called this stimulation
sematectonic. However, in many cases social insects appear to be stimulated by
pheromone traces, which are left expressly as a means of communication, not as a
contribution to the work itself. In fact, it turned out that termites are actually stimulated
by the pheromones mixed in with the mud by co-workers rather than by the mud itself
(which was to be expected given that termites are blind). The situation is even clearer
with ants laying trails. In principle, ants could be guided by the perceivable results of
their activity—the way humans and large animals are guided by the trails of flattened
vegetation and sand eroded by the movement of previously passing individuals.
However, the effect of an ant's movement on its surrounding is so small as to make it
practically undetectable. Therefore, ants appear to have evolved a special type of
chemical markers—pheromones—that make the traces of their activity much more
salient. This type of indirect stimulation, not by the work itself but by a specially evolved
“side-effect”, has been called marker-based stigmergy (Parunak, 2006).
The evolution of markers is an obvious method to make stigmergy more efficient,
by more reliably focusing the agents' attention on the most relevant aspects of the work
that needs to be done. However, it entails an additional cost and complication in that
individuals need to perform the task of manufacturing markers in addition to the work
itself. A human example can be found in the Wikipedia encyclopedia on the web.
Readers are stimulated to improve existing pages either directly, by reading the text and
noticing its shortcomings, or indirectly, by reading comments that summarize the tasks
that still need to be done—such as adding references, clarifying ambiguous sentences, or
checking facts (Heylighen, 2007). The direct method exemplifies sematectonic
stigmergy, the indirect one marker-based stigmergy. The “markers” in this case are the
various “to do” notes that attract the attention to the problems that still require work.
A marker can be seen as an abstract, conventional sign, intentionally representing
the work to be done instead of mechanically registering its effects. In Peirce's semiotic
taxonomy of signs (Atkin, 2010; Burks, 1949), a marker is a symbol, while a
sematectonic trace is an index. As such, a marker may seem to belong to a higher-order
semiotic or communicative category of phenomena—a “meta-level” compared to the
“object level” of the work itself. However, as in all phenomena produced by evolution,
there is an essential continuity between the more primitive and the more “advanced”
versions, as we can illustrate with a well-known example.
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Many animals mark their territory by leaving traces of urine all around it.
Obviously, excreting urine was not initially intended as a communicative signal, but
merely as a way to get rid of liquid waste products. But since urine is easily perceived
because of its smell, while its presence is causally connected to the presence of its
producer, animals quickly learned to interpret it as a sign (“index”) of the presence of
another animal in the vicinity. Such a signal constitutes possibly vital information, which
is useful, both for the receiver, who is warned of a potentially dangerous rival, and for the
emitter, who can use it to frighten away newcomers from his territory. Thus, both parties
are taught by evolution to communicate more reliably by means of this signal, turning it
into a conventional marker of territory. As a result, animals have learned to deposit a
little urine at regular intervals around their territory rather than simply emptying their
bladder in a random place when it is full. This marker now supports stigmergic
coordination between foraging activities, by clearly delimiting each individual's hunting
grounds, and thus minimizing the risks of encounters ending in conflict.
The effect is equivalent to the human institution of “property rights”—the formal
establishment of what belongs to whom, which economists consider essential for
dependable transactions (Martens, 2004). The simplest way to establish a property right is
to put a fence around the territory that you consider to be your property. Like the urine
trace this provides a clearly perceivable signal to others that they should not trespass
there, obviating the need for individual communication with each of those others.
In this case, we see how something (smell) that was merely a side effect of a
primary action (getting rid of waste products) turned into an intentional, communicative
signal, even though the primary function of waste disposal is still essential. In the case of
pheromones, this original function, whatever it may have been, seems to have been lost,
leaving only the communicative function. But in the most general case, both functions,
primary and communicative, are likely to play a part. The fence, for example, not only
warns people not to trespass, but keeps cattle from getting out. Another human example
is an artist making a sketch. The sketch functions both as a first step towards performing
the intended work (e.g. drawing someone’s portrait) and as a representation of what the
finished work may look like—which can be used to convince a sponsor who may be
interested to order the finished work. The first function is sematectonic, the second one
marker-based.
Transient vs. persistent traces
After discussing basic aspects of stigmergy that are recognized in the literature (e.g.
Parunak, 2006), I wish to suggest a new dimension of variation. Parunak, in his attempt at
classification, proposed the dynamics of the environment (what I call medium) as a
crucial factor in stigmergy. However, there exists an infinite variety of potential
dynamics of different degrees of complexity, thus making classification practically
impossible. Moreover, a non-trivial dynamics seems better captured by causal rules, and
as such by a system of (agentless) actions transforming the state of the world. For
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example, a collectively edited website, like Wikipedia, may have some in-built
procedures that automatically correct formatting errors, add links, or signal
incoherencies. The fact that these actions are performed by computer programs (e.g.
“bots”) does not fundamentally distinguish them from the actions of human contributors,
since they all undergo the same stigmergic coordination. We have conceptualized the
medium as the passive component of the stigmergic system, which undergoes shaping
and molding by the actions, but does not participate in the activity itself.
But even a passive medium is subjected to dissipation, erosion, or the increase of
entropy entailed by the second law of thermodynamics. That means that structures and
markers tend to decay spontaneously—unless they are actively maintained and
reconstructed. Examples are the evaporation of pheromones and the wearing down of
termite hills by rain, wind and gravity. This decay is not a priori negative. The traces left
in the medium function as instructions for further work. It is obvious that without
continuing updates this information will little by little become obsolete as the situation
changes. For example, pheromone trails that point to exhausted food sources have
become not just irrelevant, but misleading, since they incite ants to make useless
journeys. Happily, pheromone trails that are no longer reinforced—because ants
following them do not return with food—will gradually diffuse, and thus lose their
attractiveness relative to trails that continue to receive reinforcement.
This is the same phenomenon of selective “forgetting” that characterizes memory
in the brain: neural connections that are no longer reinforced will gradually lose their
strength relative to recently reinforced ones. The speed of this forgetting depends on the
learning parameter, as defined in neural networks (Heskes & Kappen, 1992). A large
value of the parameter means that new changes in connection strength are large relative
to the cumulative effect of previous ones, thus promoting the speedy establishment of
new memory traces—but also the quick obsolescence of older traces. A small value, on
the other hand, means that older learning episodes continue to exert a strong effect. A
similar parameter probably controls the external memory of ants as laid down in
pheromone trails: newly added pheromone should be strong enough to allow trails
towards newly found food sources to eventually become more attractive than previously
found ones; yet, it should not be so strong that some recent journeys by ants carrying
food from a new, unproven source can overpower the signals pointing to an older source
whose reliability is evidenced by hundreds of successful journeys (Heylighen, 1999).
Given that what counts is the relative attractiveness of different options for action,
the “learning” parameter, which determines the intensity of new contributions to the
trace, is in practice equivalent to a “forgetting” parameter, which determines the rate of
decay of the existing trace. The optimal value of this parameter will depend on the speed
with which information becomes obsolete. This will depend on the variability in the
environmental diversions and the measures that are taken to control them. For example,
the location of a particular pillar in a termite hill is unlikely to become obsolete quickly,
since the disturbances and affordances that it regulates, such as protection against sun,
cold and predators or the creation of a comfortable interior microclimate, generally do not
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change position. Abundant food sources for ants, on the other hand, tend to change
location every few days or hours.
Some diversions, such as the sudden appearance of a predator or prey animal, are
even more short-lived. In this case, a trace inciting the appropriate action should be as
quick to appear as to disappear. Typical stigmergic signals will be acoustic (e.g. the
warning cry uttered by a monkey that spots a snake—which is marker-based) or visual
(e.g. the visible movement of a wolf towards a deer—which is sematectonic). The reason
is that sound and light, because of their wave nature, spread and decay almost
immediately. An intermediate decay speed is typical for chemical traces in a liquid
environment, where concentrations of molecules may change within minutes. An
example of such kind of stigmergic coordination are the chemical signals broadcasted by
bacteria that encounter either an affordance, such as food, or a disturbance, such as a
concentration of toxins (Ben-Jacob, Becker, Shapira, & Levine, 2004). The first type of
diffusing signal will create a chemical gradient that incites bacteria of the same colony to
swim towards the food source, so that they too can profit from it. In the second case, the
gradient will incite them to move away from the danger threatening their congener.
These examples illustrate once again that no sharp distinction can be made
between persistent and transient traces used in stigmergy: these are merely the opposite
ends of a continuum. Yet, the distinction may be useful for conceptual clarification.
Persistent traces lead to what may be called asynchronous stigmergy: the different agents
or productions do not need to be present at the same time, since the trace remains to guide
them at any later time. Asynchronous communication (Cristian, 1996) can be illustrated
by media such as fax, email, or websites. Its advantage is that information remains
available, so that it can be processed at the most appropriate occasion, and can
accumulate and mature over the longer term. Transient traces lead to synchronous
stigmergy: the agents need to be simultaneously present for the coordination to succeed.
Synchronous communication may be exemplified by media such as telephone and
Internet “chat”. Its advantage is that interaction, and therefore feedback, is instantaneous,
so that disturbances and coordination errors can be corrected without delay.
Synchronous communication is rarely conceived as stigmergic, since it is
typically used for direct interaction, such as conversation or discussion. Yet, a warning
cry or a chemical signal exemplify indirect interaction: they are targeted at no one in
particular but merely “released” in the medium. Examples of stigmergy in synchronous
interaction are even clearer when the signal is sematectonic. For example, a bird spotting
a danger (condition) will start to fly (action), and by this example (transient trace) set off
the whole flock to fly away (subsequent action). Synchronous stigmergy may be best
exemplified by the collective movement in herds, flocks or swarms (Moussaid, Garnier,
Theraulaz, & Helbing, 2009; Okubo, 1986), where the agents are continually adjusting
their trajectory on the basis of real-time perceptions of the movements of other agents.
A human example would be the self-organization of traffic, where drivers
continuously react to the traffic conditions they perceive, by e.g. stopping, accelerating,
or changing lanes, thus affecting these very conditions and the subsequent actions of
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other drivers. Roads, lanes, road markings and traffic signs, on the other hand, function
like a persistent trace developed over decades in order to stimulate the drivers to move in
a coordinated manner. The continuity between the two is demonstrated by the fact that in
sufficiently dense traffic lanes tend to self-organize and acquire some form of stability,
even when they leave no permanent trace (Helbing, 2001; Moussaid et al., 2009).
Nevertheless, when the surface is soft enough to show signs of erosion, like in dirt roads,
traces persist after the traffic stops, thus maintaining a memory of the self-organized
traffic pattern. This persistent trace reduces the time necessary to rebuild a coordinated
movement pattern when the traffic starts up again. It seems likely that most roads have
emerged in this manner across historical time.
Broadcast vs. Narrowcast
Another basic component of the stigmergic taxonomy proposed by (Parunak, 2006) is the
topology of the medium (or “environment”). Here the same difficulties arise as with the
dynamics: the potential topologies are unlimited in number and complication, making
classification intrinsically hard. Again, I suggest replacing this multidimensional,
qualitative notion by a one-dimensional, quantitative aspect: the range or scope of the
stigmergic process. The scope represents the size of the “neighborhood” across which a
stigmergic signal is perceivable. The two poles of the scope continuum may be called
broadcast and narrowcast. Broadcasted traces can be perceived by all agents involved.
Narrowcasted traces are perceivable by only one or a few agents. This will obviously
depend on the topology of the medium: a large trace in an uninterrupted, flat plain will be
visible from afar; the same trace in a landscape cut through by rocks, valleys and trees
will only be visible in a small region. It will also depend on the degree of diffusion of the
trace: traces such as sounds or smells that propagate easily will have a wider scope than
traces that remain localized, such as shapes and inscriptions.
As yet, there does not seem to be much research to clarify the differences between
broadcast and narrowcast. Implicitly, most studies of stigmergy assume broadcast within
a given group of agents, such as an ant colony, or an open source community. But
obviously, these groups themselves are limited in scope, and therefore there is always a
degree of narrowcast.
The situation becomes more complex—but also more interesting—when different
actions or agents have a different scope, so that A's traces e.g. may reach B, C and D,
while D's traces reach B and E. In this case, the topology of the stigmergic medium
becomes equivalent to a network where different nodes (A, B, C…) each are connected to
(i.e. can deposit traces perceivable by) different other nodes. The implication is that the
network paradigm—which is increasingly popular for modeling various complex and
self-organizing systems such as neural networks, social networks, citation networks, etc.
(Heylighen, 2008b; Newman, 2003)—could be viewed as a special case of the stigmergic
paradigm, albeit a rather complicated one. The stigmergic paradigm remains more
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general than the network paradigm in the sense that the scope of a stigmergic interaction
can vary, while the “scope” of a network connection is fixed. For example, a more
intense trace (e.g. more concentrated pheromone) will typically spread over a somewhat
larger scope, and thus influence more agents.
This stigmergic perspective may actually clarify some problems in traditional
network models. For example, we know that in the brain connections are not fixed, since
neurons can grow axons to connect with remote other neurons. To guide this growth
pattern, some neurotransmitter-like signal molecules must be able to diffuse outside of
the existing neurons and synapses, implying a more “broadcast” form of stigmergic
communication. Similarly, social networks are everything but well defined and fixed in
their scope: people's actions will typically have repercussions well beyond their present
friends and acquaintances, potentially bringing them in contact with a much wider circle
of people. We will leave these issues for future work, and just note that a stigmergic
analysis may extend even to typical network models, such as connectionist theories of
learning and thinking in the brain (see also (Heylighen, 2012b)).
Extending the human mind
Now that we have surveyed the most general properties of stigmergy in human, animal
and physical systems, it is worth investigating some specific applications to human
behavior. Next to its general function of coordination, stigmergy supports cognition and
cooperation in particular.
Traditionally, cognition has been viewed as the processing of information inside
the brain. More recent approaches, however, note that both the information and the
processing often reside in the outside world (Clark, 1998; Dror & Harnad, 2008; Hollan,
Hutchins, & Kirsh, 2000)—or what we have called the medium. For example, documents
function as an external memory for storing knowledge and data, while calculations are
typically performed on a piece of paper or on a calculator. Without such supporting
media, most advanced reasoning—as performed e.g. in science and technology—would
be simply impossible. Thus, the human mind extends into the environment (Clark &
Chalmers, 1998), “outsourcing” some of its functions to external support systems. The
reason is that our memory and information processing capabilities have rather strict
limitations (Heylighen, 2013a; Heylighen & Vidal, 2008)—most famously the “magical
number 7 plus or minus 2” which denotes the maximum number of items we can hold in
short-term memory. Books and computers are relatively recent inventions. However, the
use of an external medium for supporting cognition is probably as old as cognition itself.
In fact, our mental capabilities can be seen as an interiorization of what were
initially stigmergic interactions with the environment. The perspective of situated and
embodied cognition (Aydede & Robbins, 2009; Steels & Brooks, 1995) focuses on the
interaction between the agent and its environment: the agent senses the state of the
environment via its sensory organs and reacts to it by producing an appropriate action via
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its muscles or effectors: it reacts in the same way to the returning feedback signal. Such a
reaction requires merely a condition-action rule, which, as we saw, is nothing more than a
causal process transforming an antecedent into a consequent. As such, condition-action
rules are readily implemented in the simplest systems, such as thermostats. Yet, when the
activity of these rules is coordinated by stigmergy, it becomes capable of complex, goal-
directed behavior, such as building a wasp's nest, or a spider's web.
A classic example of the “intelligence” exhibited by such simple rules can be
found in Braitenberg vehicles—rudimentary automata equipped with just two sensors
(left and right) for light intensity, two wheels for movement, and connections between
them that increase the speed of the wheel in proportion to the intensity of light perceived
by its corresponding sensor (Braitenberg, 1986; Gershenson, 2004). The effect of these
causal connections is that the vehicle follows a complex trajectory that avoids as much as
possible all light sources, while apparently seeking a place of darkness where it comes to
rest. The very efficient adaptive and goal-seeking behavior of a Braitenberg vehicle
results from the stigmergic coordination between the actions performed in sequence or in
parallel by its wheels when reacting to sensed changes in conditions, where the one
complements or corrects the results produced by the other (Heylighen, 2010).
Both the strength and weakness of such stigmergic organization is that it lacks
internal memory: information about the state of the process is stored purely in the
medium from where it is sensed by the agent. The advantage is that there is no need for
the registration, maintenance, and recollection of information in the brain. The
disadvantage is that if the medium is disturbed, the trace and with it the memory may be
erased. We saw an example of this problem with the nest-building wasp: when the
experimenter creates a misleading trace on the nearly finished nest, the wasp starts
building a new nest on top of the old one, thus uselessly duplicating its effort. It is likely
that our capability for internal information storage evolved at least in part to avoid this
problem: if the state of the activity can be registered and processed internally, complex
activities can be planned even when the external medium does not cooperate.
Thanks to this capability, humans are much smarter than insects. Nevertheless,
our brain is an energy-intensive, costly organ, whose storage capacities remain quite
limited. That is why we continue to use stigmergy to support our memory and reasoning.
Let us discuss a few examples. Whenever we have to do a complex job, such as repairing
a bicycle, preparing a dinner, or filling out our tax forms, we tend to keep both the objects
we work on, and the different tools and resources that support the work at hand, in such a
way that they are easy to perceive and to use.
For example, while taking apart the bicycle we arrange all the screws and pieces
in clear view, close to the screwdrivers or pincers we will need to put them back on, so
that we are unlikely to forget what must be added when and where. Each tool or piece is a
stimulus for performing a particular action. The perceived state of the bicycle is the
condition that determines which action is to be performed when. If before we start we had
to analyze, plan and memorize all the steps that need to be taken in dissembling,
repairing, and then reassembling the bicycle, it is unlikely that we would ever succeed in
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this task. The arrangement of the physical components in space here plays the role of the
activity’s trace, which constantly guides the stigmergic coordination of actions.
Ergonomic studies have shown that the spatial arrangement of a workplace is
crucial to the efficient performance of work (Hollan et al., 2000; Kirsh, 1995, 1996). One
obvious reason is that when tools are positioned near to where they are likely to be used,
there will be less need for physical movement. However, stigmergy reminds us that good
arrangement saves cognitive effort as well as physical effort, by connecting the right
reminders to the right circumstances. For example, one of the reasons why “Post it” notes
are so popular is that they make it easy to spatially connect a cognitive “call for action”
(challenge, stimulus, marker) with the physical resource needed to perform the action.
Sticking a “Please photocopy!” note on a document, e.g., makes it obvious for anyone
passing what needs to be passed through the copying machine.
The full power of individual stigmergy is seen with creative work—such as
drawing a picture, writing a text, or modeling a piece of clay. Here, the provisional
results of the work are fully embodied in the trace, be it a sketch, a draft document, or a
clay shape. This preliminary registry of the work performed calls out for more. It
challenges the user to add, to enhance or to correct. Each addition changes the trace, thus
attracting the attention to further imperfections, or suggesting further additions. It would
be extremely difficult, if not impossible, to achieve the same level of sophistication in a
design that would only exist inside the creator's brain, where all the planning would take
place without any external medium to store it, test it, and be challenged by it.
While painters or writers may have a general idea of the piece they want to create,
the actual details will only take shape when that idea is exteriorized in a medium that can
be scrutinized and manipulated, so that its structure step-by-step acquires the ideal shape
for the purpose. That makes it possible to take into account all the possibly unforeseen
properties and side effects of an initially still abstract idea. This principle is at the basis of
the method of stigmergic prototyping (De Couvreur, Detand, Dejonghe, & Goossens,
2012; Dejonghe, Detand, & De Couvreur, 2011), in which a conceived artefact is
immediately given a rudimentary physical shape that can be easily tested out and thus
adapted to the circumstances. In contrast, the traditional approach first tries to design a
detailed, abstract blueprint of the artefact, but then often has to conclude that its physical
implementation does not work as intended, forcing the designer to go “back to the
drawing board”.
The evolution of cooperation
As we have noted several times, stigmergy does not distinguish between individual and
collective activity: the trace left in the medium coordinates actions, while being
indifferent as to the specific agent or agents initiating these actions. The only additional
requirement for collective action is that the different agents should not work at cross-
purposes, so that the one’s actions negate or obstruct the other one’s. But even such a
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conflict tends to remain localized to a small part or aspect of the trace, while allowing the
rest of the trace to develop unhindered.
An example can be found in Wikipedia “edit wars” (Sumi, Yasseri, Rung, Kornai,
& Kertész, 2011), in which two contributors who disagree about a particular statement in
a Wikipedia article repeatedly undo each others’ corrections. This does not prevent other
contributors from elaborating the rest of the article (and the encyclopedia). Often, the
conflict tends to get resolved by a third party who proposes a compromise statement that
the conflicting parties no longer object to. Even without third party intervention, the
conflict is unlikely to continue, either because the antagonists themselves chance upon a
statement that is acceptable to both, or because one of them simply gives up repeating the
same ineffectual action, and decides to focus on some more productive task.
From this stigmergic perspective, the emergence of cooperation between selfish
individuals seems a much less daunting issue than from a traditional evolutionary or
economic perspective (Axelrod, 1997). Traditional models of the evolution of
cooperation pit one individual against another one in a Prisoners’ Dilemma type of
interaction, where it pays to “defect” (i.e. be uncooperative) in the short run, even though
everybody would be better off being cooperative in the long run. Another common
paradigm is the Tragedy of the Commons, in which selfish individuals (“free riders”)
exploit—and eventually exhaust—the common good that others try to maintain
cooperatively (Feeny, Berkes, McCay, & Acheson, 1990; Hardin, 1968). For example, a
person who consumes more than his fair share of a common resource, such as water,
grass, or land, will leave less of the resource for the people dividing up the resources
more evenly. In such cases, the cooperative arrangement tends to be undermined by
selfish agents appropriating more benefit from it than earnest cooperators, thus tempting
others away from cooperation.
In the stigmergic paradigm, the common good (e.g. Wikipedia, or a network of
trails and roads connecting common destinations) is gradually built up via the
cooperation implicit in stigmergically coordinated actions. Free riders may profit from
this common good without putting in any effort in return. However, the benefit derived
from a stigmergic trace does not in general reduce the value of that trace. For example, an
ant that follows a pheromone trace laid by others without adding pheromone of its own
does not by that action make the pheromone trace less useful to the other ants. Similarly,
a person who downloads a piece of open source software without contributing to the
development of that software does not impose any burden on the software developers.
Thus, in a situation of stigmergy, a free rider or “defector” does not weaken the
cooperators, in contrast to situations like the Prisoners’ dilemma or Tragedy of the
Commons.
In a sense, by not contributing the free riding agent merely weakens its own
position, because it passes by the opportunity to adapt the trace to its own preferences. As
we saw, the stigmergic trace is the aggregate of many independent actions, each of which
helps the agent that performed it to achieve its goals. The ant that finds food but does not
leave a pheromone trace on its way back to the nest not only does not help others to get to
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that food: it also does not help itself, because without the trace it is very unlikely to find
the same food source again. The trace is both an individual and a collective “mental map”
that indicates effective actions (Heylighen, 1999). Not leaving a trace makes your own
future work harder than it needs to be.
Let us analyze the dynamics of free riding in more depth on an example inspired
by what may be the simplest type of stigmergy, the creation of a trail across irregular
terrain through the flattening of grass, dirt and other obstacles. Here, an easy-to-travel
path emerges as a side effect of the regular movement of people or animals, while
requiring no special effort from these agents. A more demanding version of this task is
the establishment and maintenance of a path through dense vegetation, like in a forest. As
quickly growing bushes and trees extend their branches, they eventually obstruct the path.
A person following that path will have to either duck around these obstacles, or remove
them, e.g. by cutting the twigs that intrude upon the open space. The first option may
demand somewhat less effort, but that applies only to the short term, as the underbrush
will grow until it becomes impassable. Somebody who regularly uses the path will be
motivated to follow the second course of action, and remove any obstruction before it
becomes insurmountable.
This preference is independent of the number of hikers actually using the path.
Yet, the larger the number of people applying the strategy, the less work any one of them
needs to perform. Thus, their actions are cooperative, as they help each other achieve
their objectives. But such cooperation is purely stigmergic, because they travel
independently of each other, at different times, and thus do not communicate about their
common purpose. People who only use the path occasionally may not contribute to this
ongoing clearing activity, and thus “free ride” on the effort of others. But unless the
others do enough work, the ones who use the path regularly will eventually have to make
the effort for purely selfish purposes, because without that effort they will not be able to
use the path anymore.
This example resembles the Prisoners’ Dilemma or the Tragedy of the Commons
in that there is a temptation to defect by letting the others do the hard work, while
profiting from their results. The crucial difference, however, is that such a free riding
strategy will eventually hurt the defector more than the “cooperator”, because the
cooperating agent will continue to clear its own path independently of any others
(cooperators or defectors) using that path, while the defecting agent will eventually
encounter a path that has become impassable without clearing effort, forcing it to either
become a stigmergic cooperator, or give up on passing altogether. Thus, a defector will in
the long run collect less benefit than a cooperator. This makes the strategy of non-
cooperation self-defeating.
In the short run, the free rider may seem to have the benefit over the cooperator of
spending less energy establishing and maintaining the trace. However, the cooperator
collects other benefits. First, as we noted with the ant leaving pheromone or the hiker
breaking off branches, the cooperating agent helps itself by creating a trace. Second, the
stigmergic interaction will boost the benefits of that individual trace by stimulating others
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to expand on it. For example, an ant creating a trail to a new food source will incite others
to explore the neighborhood of that source, potentially discovering even better sources or
shorter trails. Similarly, the hiker who partially cleared a path will thus increase the
probability of others following that same path while performing further clearing
themselves. This is the positive feedback of actions eliciting more actions that makes
stigmergy so effective. The free rider simply misses out on this potential amplification of
its actions.
The full power of such synergetic interaction supported by stigmergy is seen in
complex, creative work environments, where different agents contribute different skills,
experiences and perspectives. Here, the work done by one individual is enhanced by the
work of others with complementary abilities in a way that the single individual never
could have achieved. Wikipedia and communities developing open source software
development are prime examples, having achieved results that could not even have been
reached via hierarchical, command-and-control strategies of coordination (Heylighen,
2007; Heylighen et al., 2013). Smaller scale examples are people posting photos, ideas,
artwork, or essays on their blog, Twitter feed, or Facebook page, and getting feedback
from friends, followers, or strangers, which help them to further develop their insights,
while inspiring these others to build further on their experiences. In such cases, the
benefits that accrue to the “cooperators” are direct, concrete, and stimulating enough to
motivate them to produce more of such “public traces” in their medium of choice
(Wikipedia, Facebook, …).
Thanks to the user-friendly electronic medium, the material and human cost of
publishing such traces is nearly zero. This combination of strong motivation, minimal
cost, and effective stigmergic coordination turns the medium into a powerful system for
mobilizing joint action (Heylighen et al., 2013). The result is a rapidly expanding
“collaborative commons” (Rifkin, 2014)—a virtual workspace for stigmergic (and more
traditional) cooperation that encompasses the planet. This world-wide stigmergic medium
is presently developing into the equivalent of a global brain able to efficiently tackle the
collective challenges of society (Heylighen, 2008a, 2014).
While the ICT applications of human stigmergy most stir the imagination because
of their virtually unlimited scale, we need to remember that the same mechanism has
been supporting collaboration across human and evolutionary history. A final example
may illustrate some of the more down-to-earth applications. People who garden like to
show off the fruits of their labor to visitors, guiding them along flower beds, vegetable
yards and fruit trees. Visitors with some knowledge of gardening will spontaneously
comment on what they see. The resulting exchange of knowledge is triggered by the
visible trace of the gardening work, in which visitors e.g. note that certain flowers in the
garden are doing better or worse than in their own garden, prompting them to either ask
or give advice on how to tend that particular variety. If the garden was communal, this
sharing of information would naturally extend into sharing of physical work on the
garden, with individual gardeners concentrating on the plants or tasks they feel most
to appear in T. Lewis & L. Marsh (Eds.), Human Stigmergy: Theoretical Developments
and New Applications. Springer.
33
competent about or that are most in need of work. Thus, they create a more beautiful
garden for all, while reducing the individual workload.
Most forms of human cooperation have this stigmergic dimension, where actions
are triggered by the observable results of other people’s actions rather than by direct
requests or commands. The traffic example may remind us that most people do not
require the directions from a policeman in order to cooperatively produce a smooth flow
of vehicles. But because the explicit request from a policeman, co-worker or boss to
perform a particular action requires conscious processing—if only to decide whether we
will honor the request or not—we tend to be much more aware of such direct
communication. Therefore, it tends to remain in our memory as a driver of our actions.
Our reactions to the implicit challenge left in an evolving piece of work, on the other
hand, tend to be subconscious and automatic. Therefore, we assume that we decide to
perform a further action purely on our own initiative, ignoring that we are actually being
driven by the stigmergic organization of the medium. But the coordinated activity that
ensues is a truly ubiquitous mode of human cooperation, albeit one that has hardly
received any attention until now.
Conclusion
Our theoretical analysis and survey of the mechanism of stigmergy has illustrated how
wide-ranging, concrete and fundamental its applications are. Virtually all evolved
processes that require coordination between actions 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 all agents that have access to the medium, thus allowing them to coordinate
their actions without need for agent-to-agent communication. It also allows individual
agents to perform complex sequences of actions without need for a memory or plan that
keeps track of which action needs to be performed when. It even allows the coordination
of “agentless” actions, as exemplified by chemical or physical reactions, and investigated
by Chemical Organization Theory (Dittrich & Fenizio, 2007), a very promising new
approach for modeling the emergence of self-sustaining systems.
Thus, stigmergy can be seen as a fundamental mechanism of self-organization: it
allows global, coordinated activity to emerge out of local, independent actions. Like self-
organization in general, stigmergy relies on feedback: action elicits action, via the
intermediary of the trace. This feedback is typically positive, in that actions intensify and
elaborate the trace, thus eliciting more intense and diverse further actions. The resulting
virtuous cycle explains in part why stigmergic organization is so surprisingly effective,
enabling the construction of complex structures—such as a termite hill, a network of
trails, or a global encyclopedia—in a very short time, even when starting from scratch.
When necessary, feedback can also be negative: errors, disturbances or “overshoots” that
make the trace deviate from its ideal shape will elicit actions that correct the deviation.
to appear in T. Lewis & L. Marsh (Eds.), Human Stigmergy: Theoretical Developments
and New Applications. Springer.
34
We have examined different variations on this theme by distinguishing basic
aspects or dimensions in which the process can vary. The number of agents involved
turns out to be less fundamental than is generally assumed. Increasing that number will
qualitatively enhance the result only if the agents are sufficiently diverse in the actions
they contribute, yet sufficiently aligned in their strategies so that they do not hinder each
other. Like the number of agents, the difference between qualitative and quantitative
stigmergy does not seem essential, given that the notion of “stimulation” entails a
quantitative aspect of intensity or probability, while the actions that are stimulated more
or less intensively differ qualitatively. The difference between sematectonic traces—the
concrete, observable results of work performed—and markers—traces left intentionally
in order to guide subsequent actions, but without contributing directly to the work—is
important but subtle. The use of markers allows a more fine-grained control of stigmergic
coordination, but demands an advanced level of collective evolution, in which certain
traces have acquired an unequivocal, conventional meaning among the agents that use
them. The transience of the trace is crucial in order to ensure that the list of “to do’s”
remains up to date: in a quickly changing environment, actions need to adapt in time to
new circumstances, which means that an outdated trace should decay before it would
elicit too much useless activity; in a more stable environment, on the other hand,
persistent traces enable the accumulation of a long and detailed memory. A final
dimension of variation, the broadcast-narrowcast continuum, is as yet insufficiently
investigated. Nevertheless, it hints at an essential continuity between stigmergic
mechanisms of self-organization (using a typically broadcasted trace) and the better-
known, local interaction mechanisms, where the result of an action only affects linked or
neighboring agents.
We have then examined two more typically human applications of stigmergy, the
support of cognition and cooperation, while emphasizing their evolution out of more
primitive mechanisms that can be traced back to the first living organisms. Cognition is
an application of individual stigmergy: the trace of activity in a medium functions like an
external memory that facilitates storage and processing of information, thus reducing the
burden on the brain. However, the fact that this mechanism supports some degree of
intelligent activity even without a brain suggests that our cognitive abilities may have
evolved by simply interiorizing some of this functionality that was initially provided by
an external medium.
Cooperation is an effect of collective stigmergy. Stigmergic cooperation arises
spontaneously, without need for any cooperative intent from the individuals. Since it is
beneficial to the agents involved, evolution is likely to strengthen the condition-action
rules that make them interact stigmergically, while weakening the rules that may lead to
conflict or obstruction. Stigmergy moreover bypasses a classic obstacle to the evolution
of cooperation: the “tragedy of the commons” where “free riders”—who profit from the
fruits of cooperation without contributing to it—do better than the cooperators, therefore
eventually outcompeting them, and thus destroying the cooperative arrangement. The free
rider problem is avoided because cooperators (1) do not lose any benefit, since the trace
to appear in T. Lewis & L. Marsh (Eds.), Human Stigmergy: Theoretical Developments
and New Applications. Springer.
35
typically does not deteriorate through free rider exploitation; (2) get the additional benefit
that the work they do not only helps themselves, but stimulates others to expand on it.
Therefore, the free rider benefit of avoiding effort in building the trace does not seem
large enough to allow them to outcompete the cooperators. At worst, free riders may
continue to live side-by-side with cooperators, each collecting some benefit, but with the
long-term progress accruing primarily to the cooperators.
In conclusion, the concept of stigmergy allows us to explain a broad variety of ill-
understood phenomena of spontaneous coordination, in which some kind of apparently
intelligent activity emerges out of simple processes. Because of its non-intuitive nature,
its power of explanation is as yet poorly recognized. I hope that the present paper will
inspire further researchers to pick up the thread, and examine stigmergic mechanisms in
an ever-wider range of human and non-human activities. This should not only clarify
deep theoretical issues, but suggest a variety of as yet unimagined practical applications.
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