Science in Society

Bryn Mawr College

Emergent Systems Working Group

March 26, 2003 and April 2, 2003
Rob Wozniak
A Developmental Psychologist Among the Emergenauts; Or, a Few Preliminary Reflections Made upon Observations Recorded during the Course of a Six-Month Voyage of Discovery Aboard the H.M.S. Emergence

Speaker's Notes

Additions, revisions, extensions are encouraged in the Forum and/or at
Participants 26 March
Participants 02 April


One Very General Question

“Are there general ‘laws of emergence’?   Or is the nature of emergence system or system class dependent?”


A Number of More Specific Questions


Emergence is closely related to self-organization.  Although self-organization has been variously defined, most definitions involve some variant of the following claim:  In self-organizing systems, global order (i.e., complex aggregate structure/behavior) results (emerges) from the local behaviors of simple agents following simple rules specifying conditions under which those agents act (interact) in such a way that the results of the agents’ actions are fed back as input to the operation of the rule system at some future time step.

Q1.  Emergence (of global order from local interactions) would appear to be criterial for self-organization so defined.  But is self-organization so defined criterial for emergence? 

Q2.  Must the rules of self-organizing systems be simple?  How simple?   How much less complex than aggregate behavior (of brains, cities, families, economies) does the rule system defining the behavior of individuals have to be?

Self-organization appears to depend on some minimum number of agents, many (but not necessarily all) of whom are operating in parallel (i.e., following the same rules under the same conditions).  As Flake (1998) puts it: “Complex systems with emergent properties are often highly parallel collections of similar units.  Ant colonies owe much of their sophistication to the fact that they consist of many ants...A parallel system is inherently more efficient...Parallel systems that are redundant have fault tolerance...some ants die...similar ants can substitute...and subtle variation among the units of a parallel system allows for multiple problem solutions to be attempted simultaneously” (p. 4).

Q3.  Are there limitations to massive parallelism with increases in rule system complexity, as for example, in biological systems.  While cells, for example, carry a complete copy of the genome, gene expression is a complex function of a given cell’s local environment.  Even ants, whose behavioral rule system may be less complicated than the genome, presumably act on only a subset of those rules as a function of their local environment.   Cells and ants, in other words, are functionally differentiated in ways that seem to violate the principle of massive parallelism; or are they?

Q4.  Could it be that the general rule in complex biological systems is something like “provide each agent with a full lexicon of rules but allow the subset of active rules to be determined by local information and to change over time as local conditions change?”  Are simple rule systems (e.g., Game of Life) just limiting conditions on this complexity or is this a principled distinction?

Randomness, Complexity/Criticality, Chaos

Resnick (1994) cites the following claim: “the study of self-organizing systems is, in some ways, the ‘related opposite’ of the study of chaos: in self-organizing systems, orderly patterns emerge out of lower-order randomness; in chaotic systems, unpredictable behavior emerges out of lower-level deterministic rules” (p. 14).  Holland (1998), on the other hand, argues that complex systems are neither random nor chaotic, i.e., they are characterized by “recognizable [and recurring] features and patterns” (p. 4).  And for Bak (1996), complex systems are to be distinguished from both equilibrium systems and chaotic systems in which there is uniformity of behavior (either very ordered or very disordered) throughout the system.  Crystals and gases and orbiting planets,” he suggests, “are not complex, but landscapes are” (p. 5).   Complexity, for Bak, is defined in terms of “large variability” indexed by scale-free phenomena in time and space (e.g., “avalanches of all sizes”, fractal structures) and that complexity so defined is an emergent characteristic of open systems that have self-organized to a state of “criticality.”

Q5.  What exactly does it mean for a system to be complex? 

Q6.  What is the relationship between randomness, complexity, and chaos?  Between complexity and criticality?

Q7.  In what sense, if at all, does randomness underlie emergence in self-organizing systems (in termites there is an element of randomness, but Langton’s ant and boids seem to be completely deterministic)

Q8.  Isn’t aggregate behavior in a complex, self-organizing system just as “unpredictable” from knowledge of local rules as it is in chaos?

Q9.  Is all complexity a function of perturbations in systems that have self-organized to criticality?

Q10.  Are emergence and complexity just two sides of the same coin?

Levels of Organization (Hierarchical Structure)

Employing the example of a standing wave produced by a boulder in a flowing stream, Holland claims that emergence “usually involves patterns of interaction that persist despite a continual turnover in the constituents of the patterns” (p. 7) and that “persistent patterns at one level of observation can become building blocks for persistent patterns at still more complex levels...At each level of observation the persistent combinations of the previous level constrain what emerges at the next level” (pp. 7-8).  Ants, though they may be following simple rules, are themselves complex organisms whose rule following is presumably a pattern emerging out of local interactions among populations of neurons, etc.  Indeed, systems of any level of complexity at all would seem to be composed of sub-systems that are themselves composed of subsystems, etc. etc.  Yet much of the discourse about emergence seems to be two-leveled, focusing on agents as units whose interactions yield complexity at the next-higher aggregate level.  Indeed, even Bak seems to fall prey to this tendency.  In describing that canonical example of self-organized criticality, the sand pile, he argues that as the pile begins to self-organize, “there is no global communication within the pile...just many individual grains of sand...[whose] addition...[transforms] the system from a state in which the individual grains follow their own local dynamics to a critical state where the emergent dynamics are global” (p. 51).

Q11.  How do we take the existence of multiple (not just two) levels of organization into account in conceptualizing/modeling emergence?

Q12.  Does emergence usually involve patterns of interaction that persist despite turnover in the constituents of the patterns?

Q13.  Aren’t small changes (local dynamics) in Bak’s sand pile locally catastrophic?   Is it reasonable to talk about local criticality for components of the sand pile? 

Q14.  Could local catastrophes (occurring in subsystems with their own states of self-organized criticality) constitute the self-organizing process that brings the sand pile as a whole to global criticality, at which point the size of landslides is limited only by the size of a grain of sand at one end and the total pile at the other (i.e., is scale-free)?


Almost everyone who comments on emergence argues that it is a case of the whole being “more than the sum of its parts” or as Paul put it earlier in the year (and I’m paraphrasing), properties of elements allow more than one outcome when elements interact, hence the behavior of the whole cannot in principle be understood solely in terms of properties of the elements.  Or again as Bak put it in discussing his sand-pile, once criticality has been reached, “the avalanches form a dynamic of their own, which can be understood only from a holistic description of the properties of the entire pile rather than from a reductionist description of individual grains...”  Emergent phenomena, in other words, cannot be understood in terms of agents operating in isolation; one must take into account both the agents and interactions among agents.

This appears to introduce a non-reductive element into the “science of complexity”.  Some like Holland, who describes a checkersplaying program as “fully reducible to the rules (instructions) that define it, so nothing remains hidden; yet the behaviors generated are not easily anticipated from an inspection of those rules” (p. 5) attempt to save reductionism by redefining it in terms of the transparency of the laws governing the system; but this seems to miss the point. It isn’t just the rules, it’s the rules and the interactions among rules (as well quite possibly as constraints placed on the rules by specifics of architecture and by the environment within which the system operates, see below) that lead to unanticipated behavior. 

Q15.  Do the rules governing agent behavior in a complex system interact in a principled fashion, i.e., can interactions among rules be described by meta-rules or are all such interactions in principle idiographic (in which case the “science” of emergent phenomena may be little different from any other purely historical enterprise)? 

Q16.  Once phenomena have emerged at a higher level of analysis than that of individual agents, won’t theoretical concepts and terms (e.g., “flock,” “neighborhood,” “temperature”) be required to describe the higher-level that do not have meaningfully exact counterparts (e.g., a group of birds, a group of residents, mean kinetic energy of molecules) at the lower level.  Another way of saying this is to ask whether theoretical meaning in higher-level terms and concepts depending on interactional phenomena at the higher-level won’t always, de facto, introduce a non-reductive element into a science of complexity.


Last week, Mark nicely described one sense of the term “unpredictable” when he suggested (and this is an approximate quotation) that “emergence involves aggregate phenomena that can not be intuited from the rules obeyed by individuals.”  This too is a common refrain in the literature.  As Bak says of the indicators of criticality “Zipf's law as well as the other three phenomena [the power law, 1/f noise, fractals] are emergent in the sense that they are not obvious consequences of the underlying dynamical rules." (p. 26).

Q17.  Is the unpredictability of emergent phenomena merely in the “eye of the beholder”?  Who is to say that a more powerful intellect than ours might not, in fact, be able to intuit the nature of aggregate phenomena from an inspection of local rules? 

Q18.  Is unpredictability merely a practical (even if principled) limitation as implied in the following passage from Bak: “In hindsight one can trace the history of a...[catastrophic change] in narrative language, using the methods of history rather than those of physics...[but] to predict the event, one would have to measure everything everywhere with absolute accuracy, which is impossible.  Then one would have to perform an accurate computation based on this information, which is equally impossible” (p. 61).

Q19.  Would emergent phenomena cease to be emergent if the relationship between aggregate phenomena and local interactions were completely understood? 

A much stronger sense of the term “predictable,” that does not depend on the eye of the beholder, asserts that for a systemic outcome to be predictable, the system’s state or at least the probability of the system’s being in a given state at time n must be deducible in principle from some initial state at time 1 and the laws describing the behavior of the system’s components.  Demonstrating that prediction in this strong sense is impossible in principle would provide a strong sense of unpredictability, immune to future epistemic advances.

Q20.  Is the relationship between aggregate phenomena and local interactions theoretically incomprehensible (i.e., the strong form of unpredictability)?  Is this what is meant by a system’s being “provably computationally universal” (i.e., no analytic solution, no adequate closed-form mathematical formulation)?

Q21.  Does theoretical incomprehensibility define the class of systems for which phenomena are emergent (i.e., is this a defining principle related to complexity)?  And if not, is “unpredictability simply an eye-of-the-beholder phenomenon?”

Top-Down Control vs. Bottom-Up Self-Organization

Craig Reynold’s famous simulation of the motion of a flock of birds (“boids”) as a self-organizing system of autonomous agents (see Flake, pp. 270-275) assigns to those agents three simple, weighted rules: a) avoid (move away from boids that are to close to reduce the probability of mid-air collisions); copy (fly in the general direction that the flock is moving by averaging the other boids’ velocities and directions); and center (minimize exposure to the flock’s exterior by moving toward the perceived center of the flock).  The result is “coordinated” movement within and of the flock as a whole that is said to “emerge” from the behavior of individual agents following locally applied rules.

Q22.  Don’t the copy and center rules of “boids,” which imply that an individual boid-as-agent is given information about the behavior of the flock as a whole (at least the flock minus self) before its individual velocity vector and hence position at the next time step is calculated, violate the principle of higher-order complexity emerging out of purely local interactions? 

Q23.  Is there something about the type of emergent organization in boids (in which properties of the whole partly determine the behavior of individual agents) that distinguishes it in principle from that in instances such as termites and Langton’s ant?

Resnick, Johnson (2001) and others present the contrast between bottom-up self-organization and top-down authority imposed organization in what is largely an either/or fashion.  Yet in the most complex systems (cities, brains, economies) both principles appear to be operative in some sort of interactive process (e.g., the interplay of zoning decisions with the global phenomena arising out of local neighborhood interactions, the interaction between systemic inhibitory effects of frontal cortex and phenomena arising out of the local behavior of neurons in motor cortex, the relationship between decisions made by central banks and the effects of purchasing decisions made by individuals, etc.).

Q24.  Won’t models of complex systems need eventually to represent not only both top-down and bottom-up effects but the rules governing their interactions; or will these rules of interaction themselves emerge from the interplay of the separate (and lower-order) top-down and bottom up rule systems?


Earlier in the year, if I recall and understood him correctly, Paul discussed “context” as that which creates change.  It is, in other words, simple interactions among simple things occurring in a context (e.g., the size of the playing field in the game of life) that generates global order.  Context is, in effect, any relevant influential factor(s), each of which may follow its own rules of interaction, that lie outside the rules governing the simple elements on which we focus.  Note that this idea seems closely tied to levels of analysis in that aspects of context so-defined and the original simple elements may themselves serve as a local elements in a higher-order complex system.  Indeed, hierarchical emergent systems are those in which emergence generates patterns that themselves become the basis for further emergence (as in biological evolution from inorganic to organic single-cell to multi-cellular organisms, etc.).

Q25.  Where is the environment (context) in models or even in discussions of self-organizing systems?  Ant colonies aren’t operating in a vacuum, neither are populations of neurons or neighborhoods.  Can the tendency to ignore a system’s environment be traced to inability to conceive of systems within systems so that emergent properties at more than two levels are simultaneously being taken into account?


As just indicated, ant colonies, brains, neighborhoods, etc. don’t exist in isolation from a broader environment.  Indeed, their “success” presumably depends directly on their ability to adapt to their respective environments.  Indeed, Johnson suggests that inasmuch as negative feedback is “a way of indirectly pushing a fluid, changeable system towards a goal,...[it is]...a way of transforming a complex system into a complex adaptive system” (p. 139). Yet just as context seems to be largely lacking in discussions of “internal” principles of self-organization, so too does the problem of adaptation seem to be primarily given lip-service.

Q26.  If negative feedback pushes a system towards a goal, how is the goal set?

Q27.  How much does self-organization depend on internal principles such as feedback loops between individual agents and how much on need to adapt to a more global environment?

Q28. In complex biological systems, from ant colonies to brains, where does evolutionary selection operate?  On the local rules in the individual ants or neurons, which are presumably determined by genes, or on emergent systemic behavior?


Q29.  What is the role of architecture (i.e., spatial/anatomical connections among agents) vs. the role of rule-governance (e.g., fire/don’t fire; pick-up/don’t pick up) in emergence? 

Q30.  In what ways do architectural constraints and/or external input add to complexity of the system or influence emergent outcomes?  

Q31.  Is architecture simply reducible to density of interconnection and therefore probability of establishing a local feedback loop or must architecture itself (e.g., the anatomical architecture of the brain) be described in terms of higher-level principles?

Q32.  Are cities more like brains or like ant-colonies.

Nature and Mechanisms of Change

Catastrophism/Nonlinear change.  Bak claims that “because of their composite nature, complex systems can exhibit catastrophic behavior, where one part of the system can affect many others by a domino effect” (p. 12).

Q33.  How does catastrophic change necessarily reflect the composite nature of complex systems?

Developmental vs. Hierarchical Emergence.

Q34.  Is it reasonable to distinguish between two different domains of emergence, one developmental—as in catastrophic change in which novelty emerges over time—and the other hierarchical—in which novelty is a property of higher-levels of organization (i.e., in which “change” per se seems less relevant)?

Historicity.   Holland makes a strong claim for the ahistoricity of complex systems.  “The state of the model,” he writes, “is given by the configuration, and future possibilities depend only on that state, not on how it was achieved” (p. 116).  This view seems diametrically opposed to that of Bak, who argues that it is impossible to determine whether a given current state of a system is critical without knowing its history over an extended period of time.   As he puts it, “The phrase ‘you cannot understand the present without understanding history’ takes on a deeper and more precise meaning.  The laws for earthquakes cannot be understood just by studying earthquakes occurring in a human lifetime, but must take into account geophysical processes that occurred over hundreds of millions of years and set the stage for the phenomena that we are observing” (pp. 31-32).

Q35.  Under what circumstances can present states be fully described in terms of present characteristics without reference to history; and when is history not only relevant but necessary?

Stigmergy (Collective Representations/Distributed Cognition).  Johnson argues that among other things, “cities...possess a kind of emergent intelligence: an ability to store and retrieve information” (p. 100).  This would seem somewhat analogous, albeit on a very different time scale, to the system of pheromone tracks laid down, reinforced, etc. by individuals in an ant colony.  In both cases, local behavior following local rules creates relatively enduring changes in the environment that store information about certain aspects of collective behavior and make it available for use by (i.e., feedback to) other agents.   Resnick, in describing StarLogo, points out that patches allow turtles to communicate indirectly.  By changing the environment, i.e., altering the state of a given patch, they are able to alter the behavior of other turtles and leave behind reminders for themselves.  “The idea, he suggests, of making use of objects in the environment, rather than creating new internal representations, is an example of what is sometimes called ‘distributed cognition’” (p. 34).

Q36.  Is stigmergy a necessary characteristic of self-organizing systems?  Are collective representations of this sort in effect themselves emergent characteristics of the system?

Q37.  Have I overdone it with the questions already?


Bak, P. (1999).  How Nature Works.  The Science of Self-Organized Criticality.  NY: Springer Verlag.

Flake, G. W. (1998).  The Computational Beauty of Nature. Computer Explorations of Fractals, Chaos, Complex Systems, and Adaptation.  Cambridge, MA: MIT Press.

Holland, J. (1998).  Emergence. From Chaos to Order.  Cambridge, MA: Perseus Books.

Johnson, S. ( 2001). Emergence,  The Connected Lives of Ants, Brains, Cities, and Software.  New York: Simon & Schuster.

Resnick, M. (1994).  Turtles, Termites, and Traffic Jams.  Explorations in Massively Parallel Microworlds.  Cambridge, MA: MIT Press.

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